text:
Military Respiratory Therapy
Respiratory Therapy Programs Montgomery Bill
Respiratory Therapy Careers through VA GI Bill
Respiratory Therapy Schools Post 911 GI Bill
Respiratory Therapy in Florida
How to Become a Respiratory Therapist in Florida
Respiratory Therapy Schools by State
Salary in Florida
Respiratory Therapist Salary in Florida - FL
Statewide, the average Florida respiratory therapist salary is $52,000 with the average rising with advanced degrees and certification. For example, a respiratory therapist who specializes in neonatal respiratory therapy can make as much as $64,000. On the opposite end of the spectrum, respiratory technicians may see salaries more in the range of $30,000 to $35,000 to start.
According to indeed.com, salaries for respiratory therapists in the major cities of Florida are as follows:
Boca Raton - $50,000
Cape Canaveral - $51,000
Cocoa Beach - $51,000
Daytona - $48,000
Ft. Lauderdale - $51,000
Gainesville - $52,000
Jacksonville - $9,000
Key West - $50,000
Miami - $52,000
Naples - $49,000
Orlando - $47,000
Pensacola - $45,000
Saint Augustine - $48,000
Tallahassee - $49,000
Tampa - $48,000
West Palm - $48,000
Pediatric or neonatal respiratory therapist
Geriatric respiratory therapist
Sleep disorder specialists
Florida Respiratory Therapy Associations
The Florida Society of Respiratory Care (www.fsrc.org) is the professional association that serves as an advocate for and a network of respiratory therapists in the state. This active organization provides members with updates on medical and legislative issues, opportunities for continuing education, employment information, and access to resources, and venues to connect with fellow respiratory therapists.
Another excellent resource for respiratory therapists and aspiring RTs is the American Association for Respiratory Care (www.aarc.org). This site is a bit more sophisticated than its Florida based counterpart and provides members access to international news as well as more in-depth analysis of public affairs and medical issues that will affect the respiratory therapy field as a whole. This site offers respiratory therapists a more global perspective on issues affecting their profession and their patients while the Florida association offers more practical knowledge for members.
Respiratory Therapy Schools
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National Charity League, Inc. South Coast Chapter is one of more than 216 Chapters that thrive across 25 states. With a National Board of Directors representing the organization's eight regions, South Coast Chapter, which is part of Region 5, continues to carry out NCL's mission. One of the nation's most distinctive and well respected mother-daughter organizations, NCL is committed to volunteerism and supporting philanthropies through hands on activities in local communities. The organization holds strong traditions of the past, which are honored through cultural, education and philanthropic awareness. NCL, Inc. was established in Los Angeles, California, in 1925, and was incorporated in 1958. Annually, NCL members from coast-to-coast volunteer more than one million hands-on hours in local communities.
In 1961, a small group of Los Alamitos area women gathered to form a mother-daughter service group. After learning of the aims of NCL, they were chartered as South Coast Chapter in National Charity League, the twelfth national chapter. Mrs. Voler Viles became the first president. In 1963, they opened a thrift shop in Hawaiian Gardens. It netted $4,446.67 which greatly aided philanthropy endeavors. By 1966, the organization had 50 Patronesses and 42 Ticktockers. In 1968, the thrift shop hosted the first fashion show at one of the monthly meetings. Models sold what they were wearing to NCL Patronesses.
Today, South Coast Chapter, with members from the Long Beach and West Orange County areas, is a vibrant group of women and their daughters in grades 7-12. Our Chapter has over 116 Patronesses, 128 Ticktockers, approximately 97 Sustaining Members and 31 Junior Members. Our membership resides in the Los Alamitos Unified and Long Beach Unified School Districts, though some attend private schools throughout Orange County. In addition to the philanthropies the Chapter supports with monetary donations and hands-on service, the Chapter maintains a Thrift Boutique, Miss Charity's Attic, located at 3978 E. Cerritos Avenue in Los Alamitos. Funds raised at the Thrift Boutique are used not only to support our philanthropies but to give scholarships to deserving local high school senior girls.
In addition to our Thrift Boutique, our Chapter raises money by hosting an annual fundraiser entitled Tournament Day in late fall. Each grade level also hosts various events throughout the year including the We Care Food Drive, Sewing Bees and mother-daughter events. One of the highlights of the year is the Tribute luncheon, held in June, honoring those who have earned awards for their volunteer service, as well as the senior mothers and daughters who have completed their six years in the Chapter.


Andover Central at Wellington, ppd.
Arkansas City at El Dorado, ppd.
Belle Plaine at Wichita Independent, ppd.
Bishop Miege at St. Thomas Aquinas, ppd.
Blue Valley North at Maize, ppd.
Blue Valley West at Goddard, ppd.
Chaparral at Garden Plain, ppd.
Circle at Prairie View, ppd.
Dexter at Elk Valley, ppd.
Dodge City vs. Wichita East, ppd.
Douglass at Conway Springs, ppd.
Holton at Royal Valley, ppd.
Hutchinson Central Christian at Sunrise, ppd.
Kapaun Mount Carmel at Heights, ppd.
KC Sumner at Lincoln Prep (Mo.), ppd.
Leavenworth at Olathe North, ppd.
Lenexa St. James at KC Schlagle, ppd.
McLouth at Jackson Heights, ppd.
Medicine Lodge vs. Wichita Trinity, ppd.
Newton at Valley Center, ppd.
Olathe Northwest at SM North, ppd.
Olathe South at SM West, ppd.
Oxford at South Haven, ppd.
SM East at Lawrence, ppd.
SM Northwest at Olathe East, ppd.
Wichita Northwest at Bishop Carroll, ppd.


IN stock in the gallery NOW!!
Heigh-ho, heigh-ho, it's off to work they go! Commemorate the classic scene that introduced us to these hardworking, delightful dwarves. Romero Britto reimagines Snow White's loyal friends in his signature style of vivid color and lively patterns.


Players shall determine age division by the age they are at the last scheduled tournament of the year.
9 Hole stroke play tournaments for 11-12 Age Divisions for both boys and girls. Cost for the 11-12 Division is $12 per event or $70 for the entire tour.
18 Hole stroke play tournaments for 13-14, 15+ Divisions for both boys and girls. Cost for the 13-14 and 15+ Divisions are $15 per event or $85 for the entire tour.
Tee Times, in most cases are predetermined as a shotgun start. Pairings will be posted as a reminder at least one day prior to the event on this website. Players are to report and check in at least one half hour prior to start time.
Appropriate golf attire must be worn - All shirts must have sleeves and no denim is allowed. Hats must be worn with bill forward. Inappropriate behavior by any junior, witnessed by our staff/volunteers, fellow competitors, or employees of the host facility will result in disqualification from the current event and the next event without refund. Cell phones, pagers, Ipods, range finders and any type of electronic entertainment devices are not allowed. The FMJGT has the right to refuse service.


text:
Q: how to place image in the middle of the container and two buttons on bottom I am new to html and css. My question is how do I place image and two buttons to be sure that they will be displayed together? Look at the image to understand what i mean. Thanks!!!!
Height alignment

A: for the image centering you can just use:

Then for the buttons you can use:

    <button id="button1">button left</button>
    <button id="button2">button right</button>

and then this css:
#button1 {
    display: inline-block;
    width:120px;
    height:120px;
}
#button2 {
    display: inline-block;
    width:160px;
    height:160px;
}

Which you then combine into this:

    #button1 {
    display: inline-block;
    width:120px;
    height:120px;
}
#button2 {
    display: inline-block;
    width:160px;
    height:160px;
}

      <button id="button1">button left</button>
      <button id="button2">button right</button>

in case you're confused as to what the
 tag does it is just a line break in order to make sure that the buttons don't get placed next to the image.

A: This is my solution. Try opening the snippet in full screen, and then resize the browser.
When the width of the screen is greater than 768px(u can change this value) the width of the container is 500px.
And when the width is less, then the container takes full width of the screen.
This is handled by
.container {
  width: 500px;
  margin: 0 auto;
}

@media(max-width:768px) {
  .container {
    width: 100%;
  }
}

As for the buttons, their combined width will be always equal to that of the image.
This is handled by
.btn-container {
  font-size: 0;/*used for removing whitespace from inline elements*/
}

.btn-container button {
  width: 50%;
  font-size: initial;
  padding: 15px;
}

* {
  box-sizing: border-box;
}

.container {
  width: 500px;
  margin: 0 auto;
}

@media(max-width:768px) { /* can be any number less than this depending on ur choice */
  .container {
    width: 100%;
  }
}

img {
  display: block;
  width: 100%;
  height: 200px;
}

.btn-container {
  font-size: 0;
}

.btn-container button {
  width: 50%;
  font-size: initial;
  padding: 15px;
}

/*Space between */

.btn-holder {
  width: 50%;
  display: inline-block;
}

.btn-holder button {
  width: 100%;
}

.b1 {
  padding-right: 5px;
}

.b2 {
  padding-left: 5px;
}

    <button>button 1 </button>
    <button>button 1 </button>

If u want space between buttons

      <button>button 1 </button>

      <button>button 1 </button>

redpajama_set_name: RedPajamaStackExchange


We usually dance at Cooper House located in Huntsville's Old Town area, at 405 Randolph Avenue SE on Monday evenings from 7:00 pm - 9:00 pm. It's best to check, though, since occasionally dances are canceled or moved.
Site courtesy of bwalls web design. Copyright 2015.


Harira means "silky" in Arabic, perfectly describing this typical Northwest African dish—a thick, filling soup-stew made with chickpeas, lentils, rice and vegetables, and scented with a bunch of spices that add a distinctly aromatic flavor. It's an easy one-pot meal that's comforting and endlessly versatile. You wouldn't go wrong by adding a handful of shredded, roasted chicken to it, serving it traditionally with hard-boiled eggs, or drizzling tangy yogurt over the top.
Heat the olive oil in a medium saucepan over medium-low heat. Add the onion, celery and carrots, and cook, stirring occasionally, until softened, about 5 minutes. Stir in the turmeric, cinnamon, ginger, cumin and black pepper. Cook, stirring frequently, until fragrant, about 1 minute.
Add the tomatoes with their juices, chickpeas, lentils, rice, stock and salt. Cover the saucepan with a lid, and bring to a boil over high heat. Reduce the heat to low and simmer, stirring occasionally, until soft and thickened, about 50 minutes. Turn the heat off, stir in the parsley, and serve.
No comments yet on Hip Hip Harira: Northwest African Soup-Stew.


Description: As an educator, you work to make sure your students are in a physically safe classroom environment, but what about socially and emotionally? It is extremely important for students to feel valued, that their social identity and cultures are accepted, and that they are welcomed members of the classroom. This Creating Safe Classroom Environments course, delivered through an accredited school, helps educators gain the knowledge for building positive, trustworthy, and challenging curriculum and environments that allow students to flourish. These practices help to empower students to take charge of their own learning and goals.


text:
\section{Introduction}

Widespread interest in the van der Waals and Casimir forces
(see recent monographs\cite{1,2,3,4,5,6} and
reviews\cite{7,8,9,10,11,12}) is from the key role they play
in many physical phenomena ranging from condensed
matter physics to gravitation and cosmology.
It is common knowledge that the van der Waals force is of
quantum nature and originates from fluctuations of the
electromagnetic field. Casimir\cite{13} was the first to
generalize the van der Waals force bewtween two macrobodies
to separations where the effects of relativistic retardation
become important. The corresponding generalization of the
van der Waals interaction between an atom and a cavity wall
was performed by Casimir and Polder.\cite{14}
Both the van der Waals and Casimir forces are known under
the generic name {\it dispersion forces}.
In fact, the attractive dispersion forces between two
macrobodies, between a polarizable particle and a macrobody
and between two particles become dominant when separation
distances shrink below a micrometer. That is why these forces
are of great importance in nanotechnology where they can
play the useful role of a driving force which actuates a
microelectromechanical device.\cite{15,16}
Conversely, dispersion forces may be harmful leading
to a stable state of stiction, i.e., adhesion of free parts
of a microdevice to neighboring substrates or
electrodes.\cite{17,18}

A large body of experimental and theoretical research is
devoted to the problem of how to control the magnitude
and sign of the Casimir force. In regard to the Casimir
force with an opposite sign (the so-called {\it Casimir
repulsion}), it was possible to qualitatively demonstrate
it\cite{12} only in the case of two material bodies
separated with a liquid layer, as predicted by the
Lifshitz theory.\cite{5,6,19}
Experiments on modifying the magnitude of the attractive
Casimir force are numerous and varied. They are based
on the idea that modification of the optical properties
of the test bodies should lead to changes in the
force in accordance with the Lifshitz theory.
The Casimir force takes the largest magnitude when both
test bodies are made of good metal, e.g., of Au, which
is characterized by high reflectivity over a wide
frequency region. It was demonstrated\cite{20,21,22}
that the Casimir force between an Au sphere and a Si
plate is smaller by 25\%--40\% than in the case of two
Au bodies. This was explained by the fact that the
dielectric permittivity of Si along the imaginary frequency
axis is much smaller than that of Au. For an indium tin oxide
(ITO, In${}_2$O${}_3$:Sn) film interacting with an Au sphere
the gradient of the Casimir force was measured\cite{23,24}
to be roughly 40\%--50\% smaller than between an Au sphere
and an Au plate. In one more experiment\cite{25} it was
shown that for an Au sphere interacting with a plate made
of AgInSbTe the gradient of the Casimir force decreases
in magnitude by approximately 20\% when the material of
the plate in the crystalline phase is replaced with an
amorphous one. For a semimetallic plate, the gradient of
the Casimir force was reported to be 25\%--35\% smaller
than for an Au plate.\cite{26}

Keeping in mind the applications to micromachines, it is
important to control both decreases and increases
in the force magnitude. For this purpose, the difference
in the Casimir force between a Si plate and an Au sphere
was measured\cite{27,28} in the presence and in the
absence of 514\,nm Ar laser light on the plate.
The respective increase in magnitude of the Casimir
force by a few percent was observed when the plate is
illuminated with laser pulses. This was explained by an increase
in the charge carrier density up to five orders of magnitude
under the influence of light
 and respective changes in the
dielectric permittivity of the plate.

Investigation of the Casimir force between different materials not
only led to important experimental results with potential
applications in nanotechnology, but also raised unexpected
theoretical problems touching on the foundations of quantum
statistical physics. Thus, for two metal test bodies (an
Au-coated sphere of 150\,$\mu$m radius above an Au-coated plate) the
measured gradient of the Casimir force at laboratory temperature
was found to be in agreement with the Lifshitz theory of
dispersion forces only if the relaxation properties of free
charge carriers (electrons) are disregarded.\cite{29,30}
If these relaxation properties were taken into account by means of
the Drude model, the Lifshitz theory was found to be excluded by
the experimental data at almost 100\% confidence level.
Recently it was claimed\cite{31} that an experiment using an
Au-coated spherical lens of 15.6\,cm curvature radius above an
Au-coated plate is in agreement with theory taking into account
the relaxation properties of free electrons. The results of this
experiment are in contradiction with the above mentioned
measurement using a small sphere\cite{29,30} and another
experiment using large spherical lens.\cite{32}
(See Refs.\cite{33,34} for detailed critical discussion.)

For an Au sphere interacting with a Si plate illuminated with
laser pulses the experimental data for the difference  in the
Casimir forces in the presence and in the absence of light
agree with the Lifshitz theory only if the charge carriers of
dielectric Si in the absence of light are disregarded.\cite{27,28}
When the charge carriers are taken into account, the Lifshitz
theory is excluded by the data at a 95\% confidence level.
Similar results were obtained from the measurement\cite{35}
of the thermal Casimir-Polder force between ${}^{87}$Rb atoms
belonging to the Bose-Einstein condensate and a SiO${}_2$ plate:
theory is in agreement with the data when dc conductivity
of the dielectric plate is disregarded,\cite{35}
but the same theory is excluded by the data at a 70\%
confidence level when dc conductivity is taken into
account.\cite{36}

In this paper, we present complete experimental
and theoretical results for
the Casimir force between an Au-coated sphere and ITO films
deposited on a quartz substrate. Measurements were performed
using a modified multimode atomic force microscope (AFM) in
high vacuum. The main difference of this experiment in
comparison with Refs.\cite{23,24} is that in two sets of
measurements the ITO sample was used as is, but
another two sets of
measurements were done after the sample was subjected to
 UV treatment. Unexpectedly, it was observed that the UV
treatment results in a significant decrease in the
magnitude of the Casimir force (from 21\% to 35\% at
different separations). This decrease is not associated with
respective modifications of the optical properties of plates
under the influence of UV treatment, as was confirmed by
means of ellipsometry measurements (preliminary results of
this work based on only one data set were published in
Ref.\cite{38}).

The experimental results are compared with calculations
using the Lifshitz theory and different models of the
dielectric properties of the test bodies. Note that ITO
at room temperature is a good conductor at quasistatic
frequencies, but is transparent to visible and near
infrared light. Keeping this in mind, it was
suggested\cite{39} to use this material in investigations
of the Casimir force. Computations are done for a
four-layer system (ITO on quartz interacting with Au
through a vacuum gap). The experimental results for an
untreated ITO sample are found to be in agreement with
the Lifshitz theory if charge carriers are taken into
account. For a UV-treated sample, the Lifshitz theory
taking into account the charge carriers is excluded
by the experimental data at a 95\% confidence level.
These data are found consistent with computations
disregarding the charge carriers in the ITO sample.
Based on this, the hypothesis is proposed that the
UV treatment resulted in the transition of the ITO
film to a dielectric state without noticeable
change of its dielectric permittivity at the
laboratory temperature.

The paper is organized as follows. In Sec.~II we
describe the experimental setup used and the procedures
of sample preparation and characterization.
Section~III contains details of the electrostatic
calibrations. This includes determination of the residual
potential difference, the deflection coefficient,
the separation on contact,
and the calibration constant.
In Sec.~IV the experimental results for the Casimir
force are presented. We consider both the individual
and mean measured forces and calculate the random,
systematic and total experimental errors for an
untreated and UV-treated samples at a 95\% confidence
level.
Section~V is devoted to the comparison between
experiment and theory. Here, special attention
is paid to the complex refractive indices and
dielectric permittivities along the imaginary
frequency axis used in the computations.
All computational results are obtained in the
framework of different approaches to the problem
of free charge carriers in the Lifshitz theory.
In Sec.~IV the reader will find our conclusions
and discussion.

\section{Experimental setup and sample characterization}

All measurements of the total force (electrostatic plus
Casimir) between an Au-coated polystyrene sphere and
an ITO film on a quartz plate were performed using
a modified multimode AFM in a high vacuum.
In this section we describe the most important details
of the experimental setup and procedures used for a
sample preparation and characterization.

\subsection{Schematic of the experimental setup}

The commercial AFM (``Veeco") used in our measurements
was modified to be free of volatile organics. It was placed in a
high vacuum chamber (see Fig.~1). Only oil-free mechanical and
turbo pumps shown in Fig.~1 were used to obtain the vacuum.
As a result, the experiments were done at a pressure of
$10^{-6}\,$Torr. To ensure a low vibration noise environment,
we used an optical table and a sand damper box to prevent
coupling of the low frequency noise from the mechanical and
turbo pumps (see Fig.~1).

After the first use\cite{40} of the AFM to measure the Casimir
force, it has been employed for this purpose in many
experiments.\cite{20,21,22,23,24,25,26,27,28,41,42,43,44,45}
The AFM system consists of a head, piezoelectric actuator,
an AFM controller and computer. The head includes a diode
laser which emits a collimated beam with a waist of tens
of micrometers at the focus,
an Au-coated cantilever with attached sphere
that bends in response to the sphere-plate force, and
photodetectors which measure the cantilever deflection
through a differential measurement of the laser beam intensity.
The plate is mounted on the top of the piezoelectric actuator
which allows movement of the plate towards the sphere for
a distance of $2\,\mu$m. To change the sphere-plate distance
and avoid piezo drift and creep, a continuous 0.05\,Hz
triangular voltage signal was applied to this actuator.
The application of the voltages to both the piezoelectric
actuator and the laser, and the electronic processing and
digitizing of the light collected by the photodetectors
is done by the AFM controller (see Fig.~1).
The computer is used for data acquisition.
The cantilever deflection was recorded for about every
0.2\,nm movement of the piezoelectric actuator.

More specifically, the scheme of the experiment is as follows.
A total force $F_{\rm tot}$ acting between a sphere and
a plate causes an elastic deflection $z$ of the cantilever
in accordance with Hooke's law
\begin{equation}
F_{\rm tot}=kz,
\label{eq1}
\end{equation}
\noindent
where $k$ is the spring constant. When the separation distance
between the sphere and the plate is changed with the movement
of the piezoelectric element, the cantilever deflection will
correspond to the different forces it experiences at
different separations. This deflection causes the deviation
of the laser beam reflected off the cantilever tip which is
measured with photodiodes A and B (see Fig.~1).
The respective deflection signal $S_{\rm def}$ at various
separation distances leads to a force-distance curve.
Note that the signal $S_{\rm def}$ recorded by the photodetector
is not in force units but has to be calibrated according to
Eq.~(\ref{eq1}) and
\begin{equation}
z=mS_{\rm def},
\label{eq2}
\end{equation}
\noindent
where $m$ is the cantilever deflection in nm per unit photodetector
signal (sometimes called the optical lever sensitivity).
Here $S_{\rm def}$ is measured in volts and $m$ in nm/V.

To stabilize the laser used for the detection of deflection of
the AFM cantilever, we employed a liquid nitrogen cooling system,
which maintained the temperature of the AFM at 2${}^{\circ}$C.
This is the temperature at which all measurements were performed
in this experiment.
We attached a copper braid to the surface of the AFM laser soarce.
The other side of the braid was attached to a liquid nitrogen
reservoir, which was also located inside the vacuum chamber.
During the experiments the reservoir could be refilled through
a liquid feed-through (see Fig.~1). The cooling system helped us
to improve the spot size and to reduce the laser noise and drift.
It also served as an additional cryo pump to obtain the high
vacuum.

\subsection{Sample preparation and characterization}

The test bodies in this experiment consisted of an Au-coated sphere
and quartz plate coated with an ITO film. Measurements of the
Casimir force were performed for a sphere interacting with an
untreated or, alternatively, an UV-treated ITO sample.
First, we briefly consider the preparation of the sphere which was
done similar to previous
experiments.\cite{20,21,22,27,28,40,41,44,45}

We used a polystyrene sphere which was glued with silver epoxy
($20\times 20\,\mu\mbox{m}^2$ spot) to the tip of a triangular
silicon nitride cantilever with a nominal spring constant of
order 0.01\,N/m. The cantilever-sphere system was then coated
with a 10\,nm Cr layer followed by 20\,nm Al layer and finally
with a $105\pm 1\,$nm Au layer. This was done in an oil free
thermal evaporator at a $10^{-7}\,$Torr vacuum.
To make sure that the Au surface is sufficiently smooth,
the coatings were performed at a very low deposition rate of
3.75\,\AA/min.
The radius of an Au-coated sphere was determined using a
scanning electron microscope to be $R=(101.2\pm 0.5)\,\mu$m.
This was done after the end of force measurements.

The ITO film used in our experiment was prepared by RF sputtering
(Thinfilm Inc.) on a 1\,cm square single crystal quartz plate of
1\,mm thickness. The film thickness and nominal resistivity were
measured to be $d=(74.6\pm 0.2)\,$nm and $42\,\Omega$/sq, respectively.
The surface of the ITO film was cleaned using the following
procedure. First, the ITO sample was immersed in acetone and
cleaned in an ultrasonic bath for 15\,min. Then it was rinsed
3 times in DI water. This ultrasonic cleaning procedure and water
rinsing was repeated next with methanol followed by ethanol.
After completing of the ultrasonic cleaning, the sample was dried
in a flow of pure nitrogen gas. Next, electrical
contacts to copper wires were made by soldering with an indium
wire. The ITO sample was now ready for force
measurements in the high vacuum chamber which are done as described
below.

After the force measurements were completed, the ITO sample was
UV treated. For this purpose it was placed in a special air
chamber containing a UV lamp. A pen-ray Mercury lamp with
a length of $9.0^{\prime\prime}$ and outside diameter of
$0.375^{\prime\prime}$ was used as
the UV source. This lamp emits a spectrum with the primary peak
at the wavelength 254\,nm (5.4\,mW/cm${}^2$ at 1.9\,cm
distance) and a secondary peak at 365\,nm (0.2\,mW/cm${}^2$ at 1.9\,cm
distance). During the UV treatment the sample was placed at 1\,cm
from the lamp for 12 hours. After finish of the UV treatment,
the sample was cleaned as described above, and then the force
measurements were again performed.

An important part of surface characterization is the measurement of
roughness profiles on both an ITO sample and an Au-coated sphere.
The roughness of the untreated and UV-treated
ITO samples and the Au-coated sphere was
investigated using the AFM.
For the ITO plate before and after the UV treatment the roughness was
found to be the same.
A typical three-dimensional scan of an
ITO plate is shown in Fig.~2(a). As can be seen in this figure,
the roughness is represented by stochastically distributed
distortions. For comparison purposes, the two-dimensional AFM
scan of the surface of an ITO sample is shown in Fig.~2(b).
Here, the lighter tone corresponds to the larger height above the
minimum roughness level. The analysis of the data of AFM scans allows
to determine the fraction of plate area $v_i^{\rm (ITO)}$ with
heights $h_i^{\rm (ITO)}$ where $i=1,\,2,\,\ldots,\,N_1$ and $N_1$
is some chosen number. These heights are measured from the
absolute minimum level on the test body $h_1^{\rm (ITO)}=0$.
The resulting distribution function for an ITO plate is shown
in Fig.~3(a). The zero roughness level on an ITO sample,
relative to which the mean value of the roughness is equal to
zero,\cite{6,10} takes the value $H_0^{\rm (ITO)}=9.54\,$nm
with $N_1=18$. The respective variance describing the stochastic
roughness on an ITO sample\cite{6,10} is given by
$\delta_{\rm ITO}=2.28\,$nm. The distribution function for the
roughness on an Au-coated sphere
[$v_i^{\rm (Au)}$ as a function of $h_i^{\rm (Au)}$]
is presented in Fig.~3(b).
Here, the corresponding zero roughness level and variance are
given by $H_0^{\rm (Au)}=11.51\,$nm and $\delta_{\rm Au}=3.17\,$nm,
respectively, with $N_2=25$.

The presence of roughness on the surface determines the minimum
separation distance that can be achieved when the test bodies
are approaching. In fact the minimum separation $z_0$ (the
so-called separation on contact) is the separation between the zero
levels of the roughness on contact of the two surfaces.
The actual absolute separation between the zero roughness levels
on the bottom of an Au sphere and the ITO plate with account of
Eq.~(\ref{eq2}) is given by
\begin{equation}
a=z_0+z_{\rm piezo}+mS_{\rm def},
\label{eq3}
\end{equation}
\noindent
where $z_{\rm piezo}$ is the distance moved by the plate owing to
the voltage applied to the piezoelectric actuator.
Figure~4 illustrates the meaning of the average separation on
contact $z_0$ and other parameters entering Eq.~(\ref{eq3}).
In Sec.~VB the roughness profiles will be used to calculate
the theoretical values of the Casimir force.

\section{Electrostatic calibrations}

Electrostatic calibrations in the measurements of the Casimir
force need extreme care. They allow determination with
sufficient precision of values of such vital parameters as
the residual potential difference $V_0$, the separation on
contact $z_0$, the spring constant $k$, and the cantilever
deflection coefficient $m$. During calibration process
it is necessary to make sure that all relevant electric forces
acting in the experimental configuration are included in the
theoretical model used, and all possible background forces
are negligibly small (see, for instance, a
discussion\cite{46,47,48,49} on the role of patch potentials which
may exist due to the grain structure of metal coatings, surface
contaminants etc.).

To make electrostatic measurements, the ITO plate was connected to
a voltage supply (33120A,``Agilent Inc.'') operating with $1\,\mu$V
resolution, while the sphere remained grounded. A 1\,k$\Omega$
resistor was connected in series with the voltage supply to
prevent surge currents and protect the sample surface during
sphere-plate contact.
The cantilever-sphere system was mounted on the AFM head which
was connected to the ground. To reduce the electrical noise,
care was taken to make Ohmic contacts and eliminate all Schottky
barriers to the ITO plate and Au sphere. To minimize electrical
ground loops, all the electrical ground connections were
unified to the AFM ground. Ten different voltages $V_i$
($i=1,\,2,\,\ldots,\,10$) were applied to the plate in each
round of measurements. For an untreated plate these voltages were
in the range from --260 to --110\,mV in the first set of
measurements and from --265 to --115\,mV in the second set of
measurements. For a UV-treated plate the applied voltages were from
--25 to 150\,mV and from --5 to 140\,mV in the first and second
set of measurements, respectively.

The total force between the sphere and the plate is given by the
sum of electric $F_{\rm el}$ and Casimir $F$ forces.
In accordance with Eqs.~(\ref{eq1}) and (\ref{eq2}) it can be
represented in the form
\begin{equation}
F_{\rm tot}(a,V_i)=F_{\rm el}(a,V_i)+F(a)=
\tilde{k}S_{\rm def}(a,V_i),
\label{eq4}
\end{equation}
\noindent
where $\tilde{k}=km$ is the calibration constant.
This force was measured as a function of separation.
As described in Sec.~IIA, to change the separation a continuous
triangular voltage was applied to the AFM piezoelectric actuator.
Note that this piezoelectric actuator was calibrated
interferometrically.\cite{50,51}
Starting at the maximum separation of $2\,\mu$m, the ITO plate was
moved towards the Au sphere and the corresponding cantilever
deflection was recorded at every 0.2\,nm until the plate
contacted the sphere.

After the contact of the sphere and the plate, the cantilever-sphere
system vibrated with a large amplitude. To allow time for this
vibration to damp out, a 5\,s delay was introduced after every cycle
of data acquisation. To reduce random error, the total force at
each of ten voltages applied to the untreated plate was measured ten
times as a function of separation. The same was repeated for the
UV-treated plate.

The electric force between a sphere and a plate made of conductors is
given by\cite{6,52}
\begin{equation}
F_{\rm el}(a,V_i)=X(a)(V_i-V_0)^2,
\label{eq5}
\end{equation}
\noindent
where
\begin{eqnarray}
&&
X(a)=2\pi\epsilon_0\sum_{n=1}^{\infty}
\frac{\coth\alpha-n\coth{n\alpha}}{\sinh{n\alpha}},
\nonumber \\
&&
\cosh\alpha=1+\frac{a}{R},
\label{eq6}
\end{eqnarray}
\noindent
$V_0$ is the residual potential difference which can be present
due to different work functions of the sphere and plate materials,
and $\epsilon_0$ is the permittivity of the vacuum.
In the wide range of separations the function $X(a)$ can be
presented in the polynomial form\cite{21}
\begin{equation}
X(a)=-2\pi\epsilon_0\sum_{i=-1}^{6}c_i
\left(\frac{a}{R}\right)^i
\label{eq7}
\end{equation}
\noindent
with an error of about 0.01\%. The coefficients $c_i$ in
Eq.~(\ref{eq7}) are given by
\begin{eqnarray}
&&
c_{-1}=0.5,\ \  c_0=-1.18260,\ \  c_1=22.2375,
\nonumber \\
&&
c_2=-571.366,\ \
c_3=9592.45, \ \  c_4=-90200.5,
\nonumber \\
&&
c_5=383084, \ \  c_6=-300357.
\label{eq8}
\end{eqnarray}

As can be seen in Eqs.~(\ref{eq4}) and (\ref{eq5}), the total
force $F_{\rm tot}$ is characterized by the parabolic dependence
of an applied voltage $V_i$. The same is true for the total
deflection signal
\begin{equation}
S_{\rm def}(a,V_i)=S(a)+\frac{X(a)}{\tilde{k}}
(V_i-V_0)^2,
\label{eq9}
\end{equation}
\noindent
where $S(a)=F(a)/\tilde{k}$ is the deflection due to the
Casimir force.

As an example, in Fig.~5 we present as squares the measured deflection
signal $S_{\rm def}$ plotted as a function of the applied voltage for
(a) the untreated and (b)  UV-treated sample at a fixed separation
$a=75\,$nm between the sphere and the plate.
Then a $\chi^2$ fitting procedure was used to draw parabolas
[the solid lines in Fig.~5(a,b)] and to determine their vertices
and the coefficients $\beta(a)=X(a)/\tilde{k}$.
 This procedure was repeated at each
separation distance with a step of 1\,nm
(though data were acquired about every 0.2\,nm of $z_{\rm piezo}$,
only interpolated values at 1\,nm step were analyzed).
The vertex of each parabola corresponds to $V_0$ at each respective
separation. When $V_i=V_0$, the electrostatic force is equal to zero.
The fitting procedure was also repeated at every separation $a$.
{}From the parabolas shown in Fig.~5(a,b) it was obtained
$V_0=-(195.9\pm 0.5)\,$mV and $V_0=(64.7\pm 0.4)\,$mV, respectively.
The values of $V_0$ at separations from 60 to 300\,nm are shown in
Fig.~6(a) for an untreated and in Fig.~7(a) for a UV-treated sample
in the first measurement set.

As can be seen in Figs.~6(a) and 7(a),  there are
anomalous dependences of $V_0$ on $a$,
i.e., $V_0$ is not constant as expected if the electric force
is described by the exact Eqs.~(\ref{eq5}) and (\ref{eq6}).
Such dependences were found in several experiments measuring the
Casimir force and widely discussed in the literature.\cite{46,47,48,49,55}
They are often interpreted as a manifectation of an additional electric
force due to the presence of electrostatic surface impurities and space
charge effects on the sphere or plate surfaces.
In our case, however, these seeming anomalies do not indicate the
presence of some extra electric force other than that given by
Eqs.~(\ref{eq5}) and (\ref{eq6}). The point is that the preceding
analysis did not take into consideration the finiteness of the data
acquisition rate and, more importantly, the mechanical drift of the
sphere-plate separation. As a result, systematic
deviations occurred in
the residual potential difference $V_0$ in Figs.~6(a) and 7(a).
These systematic deviations have been investigated,\cite{53,54} and the
respective corrections have been introduced in the data for $V_0$
as a function of $a$.
The corrected results for $V_0$ as a function of separation for an
untreated sample are shown in Fig.~6(b) and for a UV-treated sample
in Fig.~7(b). Specifically, at $a=75\,$nm [see Fig.~5(a,b)] the
corrected values of $V_0$ for an untreated and UV-treated samples are
$V_0=-(195.6\pm 0.5)\,$mV and $V_0=(64.4\pm 0.4)\,$mV, respectively.
As is seen in Figs.~6(b) and 7(b), after the proper corrections
for the mechanical drift of separation distances and the finitness
of the data acquisition rate are introduced, the residual potential
difference remains constant in the limits of random errors.
This excludes the presence of any perceptible electric force
due to dust and contaminants in
addition to the one given by Eqs.~(\ref{eq5}) and (\ref{eq6}).
{}From Figs.~6(b) and 7(b) the following mean values for the residual
potential difference were found:
$V_0=-(196.8\pm 1.5)\,$mV for the untreated sample and
$V_0=(65\pm 2)\,$mV for the UV-treated sample.

We now discuss the deflection coefficient $m$ which enters
Eq.~(\ref{eq3}) and, thus, is needed to determine both the absolute
and relative sphere-plate separations.   The
deflection signals obtained by the application of the different
voltages to the plate can be used to determine $m$.  Here larger
$(V-V_0)^2$ will lead to correspondingly larger deflections and thus
sphere-plate contact at smaller $z_{\rm piezo}$.
This rate of change of
contact point with $S_{\rm def}$ gives the value of $m$.
However, as before, care must be
taken to make a precise determination of the point of
sphere-plate contact and correct the contact point for mechanical
drift of the sphere-plate separation.
Both corrections are already discussed in detail.\cite{53,54}
Briefly, the first of them is necessary, as even at the maximum
acquisition rate, data points are widely separated near the point of
contact due to the large force gradient at short separations. Thus an
interpolation procedure has to be used to determine the exact contact
point.  With respect to the second correction,
the contact points with two different applied $V$ but same
$(V-V_0)^2$ must be the same as the corresponding cantilever
deflections are equal.
Because of this any observed  change in the contact point
for these two applied voltages is due to sphere-plate drift. The
drift rate is the time rate of change in the contact points
for these voltages. Both
corrections are needed to obtain the precise relative sphere-plate
separation. As we discussed above,
neglect of the drift correction leads to anomalous
distance dependence behavior for the residual potential $V_0$.
The corrected values of
$m=(104.4\pm 0.5)\,$nm/V
for the untreated sample and
$m=(103.5\pm 0.6)\,$nm/V
for the UV-treated sample were determined
for the first measurement set.

In accordance with Eqs.~(\ref{eq3}) and (\ref{eq7}), the parabola
coefficient $\beta(a)$ depends on both the cantilever calibration
constant $\tilde{k}$ and the average separation on contact $z_0$.
Thus, the obtained values of $\beta(a)$ at different separations
can be used to determine both $z_0$ and $\tilde{k}$ using the least
$\chi^2$-fitting to Eq.~(\ref{eq7}) as described previously.\cite{53,54}
For this purpose the coefficient $\beta(a)$ was first fitted from a
starting point of 60\,nm to an end point $a_{\rm end}=1000\,$nm, and the
values of $z_0$ and $\tilde{k}$ were determined. Then $a_{\rm end}$
was decreased to 900\,nm and the fitting procedure repeated leading
to the corresponding values of $z_0$ and $\tilde{k}$.
The repetition of this procedure (in smaller steps below
$a_{\rm end}=400\,$nm) results in Figs.~8(a) and 9(a) demonstrating
the dependence of $z_0$ on $a_{\rm end}$ for an untreated and UV-treated
samples, respectively, in the first set of
our measurements. Similar results
were obtained for $\tilde{k}$ as a function of $a_{\rm end}$.

As can be seen in Figs.~8(a) and 9(a), there is an anomalous
dependence of $z_0$ on $a_{\rm end}$ caused, as above, by mechanical
drift in the sphere-plate separation.
After the respective corrections were introduced,\cite{53,54}
the obtained dependence
of the separation on contact $z_0$ on $a_{\rm end}$ is shown in
Fig.~8(b) for the untreated sample and in Fig.~9(b) for the UV-treated
sample. It can be seen that in both cases the corrected values
$z_0$ remain constant within the limits of random errors
independently of the value of $a_{\rm end}$ chosen.
The obtained mean values of $z_0$ are
$z_0=(29.5\pm 0.4)\,$nm
for the untreated sample and
$z_0=(29.0\pm 0.6)\,$nm
for the UV-treated sample.
In Fig.~10(a,b) the corrected values of the calibration constant
$\tilde{k}$ as a function of $a_{\rm end}$ obtained in the first
measurement set are shown for an untreated and UV-treated samples,
respectively. The respective mean values are as follows:
$\tilde{k}=(1.45\pm 0.02)\,$nN/V and
$\tilde{k}=(1.43\pm 0.02)\,$nN/V.
As is seen in Fig.~10(a,b), the individual values of $\tilde{k}$
determined with different $a_{\rm end}$ are constant in the limits
of random errors.
This concludes the electrostatic calibration of our measurement
system. It is pertinent to note that the fitting used above was
made to only the well understood electric force in the sphere-plate
configuration. In so doing it was confirmed that there are no other
perceptible electric forces due to surface patches, contaminants,
surface defects, such as pits and bubbles, etc.

The same calibration procedure, as described above, was repeated
when performing the second set of our measurements.
For the untreated sample, the following values of the parameters
were found:
$V_0=-(196.8\pm 1.5)\,$mV,
$z_0=(29.6\pm 0.5)\,$nm,
$\tilde{k}=(1.51\pm 0.02)\,$nN/V, and
$m=(104.4\pm 0.5)\,$nm/V.
For the UV-treated sample it was obtained:
$V_0=(64.8\pm 2)\,$mV,
$z_0=(29.0\pm 0.6)\,$nm,
$\tilde{k}=(1.51\pm 0.02)\,$nN/V, and
$m=(104.2\pm 0.6)\,$nm/V.
The parameters presented in this section were used to convert
the cantilever deflection signals into the values of the total
force and to find the values of absolute separations.

Note that for all values of the above parameters  the errors are
indicated at a 95\% confidence level.

\section{Measurement results for the Casimir force and
their errors}

According to Eq.~(\ref{eq4}) the experimental results for the
Casimir force between an Au sphere and an ITO plate are given by
\begin{equation}
F(a)=\tilde{k}S_{\rm def}(a,V_i)-F_{\rm el}(a,V_i),
\label{eq10}
\end{equation}
\noindent
where the electric force $F_{\rm el}$ is expressed by
Eqs.~(\ref{eq5})--(\ref{eq7}).
At each separation $a$ the measurement of $S_{\rm def}$ with
ten applied voltages was performed. This was repeated 10 times.
Altogether, 100 values of the Casimir force at each separation
were obtained from Eq.~(\ref{eq10}) in each measurement set for
both untreated and UV-treated samples. Here, we present the main
features of these data and determine the experimental errors.

\subsection{Mean measured Casimir forces}

In Fig.~11 the mean measured Casimir forces obtained from one
hundred individual values are shown as functions of separation
with solid lines for (a) an untreated sample and (b) a
UV-treated sample over the separation region from 60 to 300\,nm
in the first measurement set. In the insets, the same solid lines
are reproduced over a more narrow separation region from 60 to 100\,nm.
As an illustration, Fig.~11 shows by dots all 100 individual values of
the Casimir force plotted at separation distances with a step of 5\,nm
(in the insets with a step of 1\,nm). Figure~11(a) indicates a
40\%--50\% decrease in the force magnitude in comparison with the
case of two Au bodies in agreement with previous work\cite{23,24}
where a similar result was obtained for the Casimir pressure.
For example at $a=80\,$nm the measured Casimir force is --144\,pN
in contrast to --269\,pN for Au test bodies.
As can be seen in Fig.~11(a,b), the magnitudes of the Casimir force
from a UV-treated plate are 21\% to 35\% smaller than from
an untreated plate.

Figure~12 characterizes the statistical properties of the experimental
data for an untreated (right) and UV-treated (left) samples by
presenting the histograms for the measured Casimir force at
separations (a) $a=60\,$nm, (b) $a=80\,$nm, and (c) $a=100\,$nm
in the first measurement set. The histograms are described by
Gaussian distributions (dashed lines) with the standard deviations
equal to
(a) $\sigma_{G}=4.6\,$pN (right), $\sigma_{G}=5.0\,$pN (left),
(b) $\sigma_{G}=5.4\,$pN (right), $\sigma_{G}=5.4\,$pN (left),
and
(c) $\sigma_{G}=4.9\,$pN (right), $\sigma_{G}=4.7\,$pN (left).
The values of the respective mean measured Casimir forces can be found
in columns 2 and 5 of Table~I.
{}From Fig.~12 it is observed that the Gaussian distributions related
to the untreated and UV-treated samples do not overlap lending great
confidence to the effect of a decrease of the magnitude of the
Casimir force under the influence of UV-treatment.

In Table~I we present the mean magnitudes of the measured Casimir
force at different separations (first column) ranging from 60 to
300\,nm with the respective total experimental errors determined below
in Sec.~IVB. Columns 2 and 3 contain the force magnitudes obtained
in the first and second measurement sets for the untreated sample,
respectively. In columns 5 and 6 the respective results obtained for
the UV-treated sample in the first and second measurement sets are
presented. As can be seen in Table~I, the measurement data obtained
in the first and second measurement sets are in a very good
agreement. All differences between them are much less than the total
experimental errors presented in columns 4 and 7
(see Sec.~IVB).

\subsection{Random, systematic and total experimental errors}

Here we present the main results of the error analysis.
The variance of the mean Casimir force calculated from 100 measurement
results over the separation interval from 60 to 300\,nm is shown as
dots in Figs.~13(a) and 13(b) for the untreated and UV-treated samples,
respectively. The respective mean values are separation independent:
$\sigma=0.55\,$pN and $\sigma=0.5\,$pN.
They are equal to the random errors in the measured Casimir force
determined at a 67\% confidence level. To determine the random error
at a $\beta=95$\% confidence level, one should multiply $\sigma$ by
the student coefficient $t_{1.95/2}(99)=2$. Thus, the random errors
at a 95\% confidence level are equal to
$\Delta^{\!r}F=1.1\,$pN and $\Delta^{\!r}F=1.0\,$pN, respectively.

According to Eq.~(\ref{eq10}), the systematic error in the measured
Casimir forces is a combination of the systematic errors in the total
measured force and subtracted electric force. The systematic error in
the total measured force, $\Delta^{\! s}F_{\rm tot}$, is determined
by the instrumental noise including the background noise level, and
the errors in calibration. In Figs.~14(a) and 14(b) the error
$\Delta^{\! s}F_{\rm tot}$ determined at a 95\% confidence level is
shown by the long-dashed lines as a function of separation for the
untreated and UV-treated samples, respectively. The error in
calculation of the electric force, which plays the role of a systematic
error with respect to the Casimir force obtained from Eq.~(\ref{eq10}),
is mostly determined by the errors in the measurement of separations.
The latter are largely contributed by the errors in $z_0$ presented
in Sec.~III.
As a result, for the first measurement set, the errors in absolute
separations determined at a 95\% confidence level are equal to
$\Delta a=0.4\,$nm and $\Delta a=0.6\,$nm for the untreated and
UV-treated samples, respectively.
Note that due to Eq.~(\ref{eq5}) the error in $F_{\rm el}$
is different at different applied voltages $V_i$. As an illustration,
Fig.~14(a,b) shows with short-dashed lines the mean
$\Delta^{\! s}F_{\rm el}$ averaged over 10 applied voltages for the
untreated and UV-treated samples, respectively. The respective solid
lines in Figs.~14(a) and 14(b) demonstrate the total systematic
errors $\Delta^{\! s}F$ in the Casimir force as a function of separation.
They were obtained by adding in quadrature the systematic errors of the
total and electric forces.
As is seen in Fig.~14(a,b), at moderate and large separations the
major contribution to the systematic error in the Casimir force is
given by the systematic error in the total force. Only at short
separations the error in the electric force contributes significantly
to the systematic error in the Casimir force.

To obtain the total experimental error one should combine the random
and systematic errors. In Fig.~15(a,b) the random errors are shown
with the dashed lines for the untreated and UV-treated samples, respectively.
The lower solid lines in the same figure represent the systematic errors
which are dominant over the random ones in this experiment, especially
at short separations. Keeping in mind that both the random and
systematic errors considered above are characterized by the normal
distribution, they should be added in quadrature.
The resulting absolute total experimental errors
$\Delta^{\!\rm tot}F$ determined at a 95\% confidence
level are shown by the upper solid lines for the untreated [Fig.~15(a)]
and UV-treated [Fig.~15(b)] samples. The values of the absolute total
experimental errors at different separations are presented in column~4
of Table~I (for an untreated sample) and in column~7 for a
UV-treated sample. The relative total experimental error in the measured
Casimir force at $a=60\,$nm is equal to 0.82\% and 1.2\% for the
untreated and UV-treated samples, respectively. With the increase of
separation to $a=100\,$nm the respective errors increase to 2.3\%
and 3.6\% and further increase to 13.4\% and 24.2\% when separation
increases to $a=200\,$nm. At $a=300\,$nm the
relative total experimental
errors in the measured Casimir force for the untreated and UV-treated
samples achieve 37.5\% and 50\%, respectively.
For the sake of definiteness, these numerical values are given for
the first measurement set. However, in both sets the total
experimental errors are the same.

\section{Comparison between experiment and theory}

We next discuss the comparison between the experimental data
for the Casimir force and the theoretical predictions of the
Lifshitz theory. We compute theoretical results using different
approaches to the thermal Casimir force proposed in the
literature.\cite{6,8,10}
In the framework of the proximity force approximation which is
clearly applicable\cite{57} for the parameters of this experiment
the Lifshitz formula for the Casimir force between an Au-coated
sphere and an ITO film deposited on a quartz plate takes the form
\begin{eqnarray}
F(a,T)&=&
k_BTR\sum_{l=0}^{\infty}{\vphantom{\sum}}^\prime\int_0^{\infty}
k_{\bot}dk_{\bot}
\nonumber \\
&\times&
\left\{\ln\left[1-
r_{\rm TM}^{(1)}(i\xi_l,k_{\bot})
r_{\rm TM}^{(2)}(i\xi_l,k_{\bot})\,e^{-2aq_l}\right]\right.
\nonumber \\
&&+\left.
\ln\left[1-
r_{\rm TE}^{(1)}(i\xi_l,k_{\bot})
r_{\rm TE}^{(2)}(i\xi_l,k_{\bot})\,e^{-2aq_l}\right]\right\}.
\label{eq11}
\end{eqnarray}
\noindent
Here, $k_B$ is the Boltzmann constant, $T=275\,$K,
$\xi_l=2\pi k_BTl/\hbar$ with $l=0,\,1,\,2,\,\ldots$ are
the Matsubara frequencies, the primed sum means that the term
with $l=0$ is divided by 2, $k_{\bot}$ is the projection of the
wave vector onto the plate, and $q_l^2=k_{\bot}^2+\xi_l^2/c^2$.
The reflection coefficients on an Au body modeled as a semispace
for the transverse magnetic (TM) and transverse electric (TE)
polarizations of the electromagnetic field are given by
\begin{eqnarray}
&&
r_{\rm TM}^{(1)}(i\xi_l,k_{\bot})=
\frac{\varepsilon_l^{(1)}q_l-k_l^{(1)}}{\varepsilon_l^{(1)}q_l+
k_l^{(1)}},
\nonumber \\
&&
r_{\rm TE}^{(1)}(i\xi_l,k_{\bot})=
\frac{q_l-k_l^{(1)}}{q_l+k_l^{(1)}},
\label{eq12}
\end{eqnarray}
\noindent
where ${k_l^{(1)}}^2=k_{\bot}^2+\varepsilon_l^{(1)}\xi_l^2/c^2$ and
$\varepsilon_l^{(1)}\equiv\varepsilon^{(1)}(i\xi_l)$ is the dielectric
permittivity of Au along the imaginary frequency axis.

The reflection coefficients of an ITO film deposited on quartz plate
can be presented in the form\cite{6,58}
\begin{equation}
r_{\rm TM}^{(2)}(i\xi_l,k_{\bot})=
\frac{r_{\rm TM}^{(0,-1)}+
r_{\rm TM}^{(-1,-2)}e^{-2k_l^{(-1)}d}}{1+
r_{\rm TM}^{(0,-1)}r_{\rm TM}^{(-1,-2)}e^{-2k_l^{(-1)}d}}
\label{eq13}
\end{equation}
\noindent
and the same expression with the index TM replaced for TE.
Here, $r_{\rm TM,TE}^{(n,n')}$ are
the reflection coefficients on an
ITO layer of thickness $d$ ($n=0,{\ }n'=-1$) and on a thick
quartz plate modeled as a semispace ($n=-1,{\ }n'=-2$)
 \begin{eqnarray}
&&
r_{\rm TM}^{(n,n')}(i\xi_l,k_{\bot})=
\frac{\varepsilon_l^{(n')}k_l^{(n)}-
\varepsilon_l^{(n)}k_l^{(n')}}{\varepsilon_l^{(n')}k_l^{(n)}+
\varepsilon_l^{(n)}k_l^{(n')}},
\nonumber \\
&&
r_{\rm TE}^{(n,n')}(i\xi_l,k_{\bot})=
\frac{k_l^{(n)}-k_l^{(n')}}{k_l^{(n)}+k_l^{(n')}}.
\label{eq14}
\end{eqnarray}
\noindent
The notations used are the following:
$\varepsilon_l^{(0)}=1$,
$\varepsilon_l^{(-1)}=\varepsilon^{(-1)}(i\xi_l)$ and
$\varepsilon_l^{(-2)}=\varepsilon^{(-2)}(i\xi_l)$ are
the dielectric permittivities of ITO and quartz, respectively,
and ${k_l^{(n)}}^2=k_{\bot}^2+\varepsilon_l^{(n)}\xi_l^2/c^2$.
To perform computations of the Casimir force using
Eqs.~(\ref{eq11})--(\ref{eq14}) one needs the dielectric
permittivities of Au, ITO and quartz over a wide range of
imaginary frequencies.

\subsection{Complex indices of refraction and dielectric
permittivities
along imaginary frequencies}

We describe the imaginary part of the dielectric permittivity of Au,
${\rm Im}\,\varepsilon^{(1)}(\omega)$, by means of the tabulated
optical data.\cite{59} In the region $\omega<0.125\,$eV, where the
optical data are missing, the extrapolation by means of the
imaginary part of the Drude model dielectric permittivity with
the plasma frequency $\omega_p=9.0\,$eV and relaxation parameter
$\gamma=0.035\,$eV has been used. The dielectric permittivity
of Au along the imaginary frequencies was obtained by means of
the Kramers-Kronig relations.\cite{6} Using the so-called
weighted Kramers-Kronig relations it was recently shown\cite{60}
that the extrapolation by means of the Drude model with
$\omega_p$ and $\gamma$ indicated above is in excellent agreement
with the optical data measured over a wide frequency region.

For the underlying quartz plate we used the averaged dielectric
permittivity obtained\cite{61} in the Ninham-Parsegian
approximation\cite{5}
\begin{equation}
\varepsilon^{(-2)}(i\xi_l)=1+
\frac{C_{\rm IR}}{1+\frac{\xi_l^2}{\omega_{\rm IR}^2}}+
\frac{C_{\rm UV}}{1+\frac{\xi_l^2}{\omega_{\rm UV}^2}}
\label{eq15}
\end{equation}
\noindent
with the parameters
$C_{\rm IR}=1.93$, $C_{\rm UV}=1.359$,
$\omega_{\rm IR}=0.1378\,$eV, and
$\omega_{\rm UV}=13.38\,$eV.

The dielectric permittivity of ITO strongly depends on a layer
composition, thickness, etc. The literature on the subject is
quite extensive.\cite{62,63,64,65,66,67,68,69}
Specifically, the parametrization of the dielectric permittivity
of ITO was suggested\cite{69} using the Tauc-Lorentz
model\cite{70} and the Drude model.
This parametrization was used\cite{23,24} for the comparison between
the experimental data and computational results in the framework
of the Lifshitz theory. It was found, however, that the computed
magnitudes of the gradient of the Casimir force are substantially
larger than the mean measured ones.

To characterize the dielectric properties of ITO films used in our
experiment, we employed the untreated and UV-treated samples
prepared in the same way and under the same conditions as those
used in measurements of the Casimir force. The imaginary parts
of the dielectric permittivity of ITO,
${\rm Im}\,\varepsilon^{(-1)}(\omega)$,
was determined by means of ellipsometry
(J.~A.~Woollam Co.\cite{71}) for both untreated and UV-treated
samples. In the frequency region from 0.04 to 0.73\,eV the
IR-VASE ellipsometer was used.
The region of frequencies from 0.73 to 8.27\,eV was covered
with the help of VUV-VASE ellipsometer.
The experimental data obtained from ellipsometric measurements were
analyzed taking into account that the ITO resistivity decreases with
depth. This results in
different profiles of the dielectric permittivity of ITO at
different depths and typically in the so-called {\it top} and
{\it bottom} ${\rm Im}\,\varepsilon^{(-1)}(\omega)$ differing
in the frequency range $\omega<0.4\,$eV.
In Figs.~16(a,b) and 16(c,d) the experimental data for
${\rm Im}\,\varepsilon^{(-1)}(\omega)$ as a function of $\omega$
are shown by the solid lines for an untreated and UV-treated
samples, respectively. In the frequency range shown in Fig.~16(a,c)
the top and bottom permittivities coincide.
 The top ${\rm Im}\,\varepsilon^{(-1)}(\omega)$, which was found to lead
to a good agreement with the measured Casimir forces
for the untreated sample, is shown in Fig.~16(b,d) by the solid lines
in the frequency region from 0.04 to 0.8\,eV on a logarithmic scale.
It was
extrapolated in the region of low frequencies $\omega<0.04\,$eV
by means of the imaginary part of the Drude dielectric
function with the parameters
$\omega_p=1.5\,$eV, $\gamma=0.128\,$eV and
$\omega_p=1.5\,$eV, $\gamma=0.132\,$eV
for an untreated and UV-treated samples, respectively
(the dashed lines).

Precise computations of the Casimir force at separations
$a\geq 60\,$nm require knowledge of dielectric properties up to
$\omega\approx 16\,$eV. Because of this, the measured data for
${\rm Im}\,\varepsilon^{(-1)}(\omega)$
in Fig.~16(a,c) shown by the solid lines were extrapolated to higher
frequencies by means of the imaginary part of an oscillator
function
\begin{equation}
{\rm Im}\,\varepsilon^{(-1)}(\omega)=
\frac{g_0\gamma_0\omega}{(\omega^2-\omega_0^2)^2+\gamma_0^2\omega^2}.
\label{eq16}
\end{equation}
\noindent
The reasonable smooth extrapolations are bounded between the
short-dashed lines in Fig.~16(a,c). For an untreated sample [Fig.~16(a)]
the upper short-dashed line is described by Eq.~(\ref{eq16}) with the
oscillator parameters
$g_0=240.54\,\mbox{eV}^2$, $\gamma_0=8.5\,$eV and $\omega_0=9.0\,$eV.
For the lower short-dashed line we get
$g_0=111.52\,\mbox{eV}^2$, $\gamma_0=4.0\,$eV and $\omega_0=8.0\,$eV.
For the UV-treated sample [Fig.~16(c)] the oscillator parameters are
$g_0=280.28\,\mbox{eV}^2$, $\gamma_0=9.2\,$eV and $\omega_0=9.8\,$eV and
$g_0=128.28\,\mbox{eV}^2$, $\gamma_0=4.5\,$eV and $\omega_0=8.8\,$eV
for the upper and lower short-dashed lines, respectively.
As can be seen in Fig.~16(a,b,c,d), there are only minor differences
in the imaginary parts of the dielectric permittivities for the untreated
and UV-treated samples (the additional small peak near
 3\,eV for the untreated sample and insignificant variations
in the oscillator structure).
Note that the imaginary part of the ITO dielectric permittivity
suggested earlier\cite{69} and used in computations of the
gradient of the Casimir force\cite{23,24} is shown by the
long-dashed line in Fig.~16(a). It differs significantly from the
dielectric permittivity of our untreated ITO sample.
At lower frequencies deviations between the two permittivities
increase due to the larger $\omega_p=1.94\,$eV used.\cite{69}

Using the measured imaginary parts of dielectric permittivity of
ITO in Fig.~16(a,b,c,d),
the dielectric permittivities along the imaginary frequency
axis were obtained by means of the Kramers-Kronig relation.
The obtained results for the untreated sample are shown in
Fig.~17(a) by the two solids lines corresponding to the two
short-dashed lines in Fig.~16(a). In the same figure, the two dashed
lines indicate the range of dielectric permittivities along
the imaginary frequency axis for the case when the contribution of
free charge carriers were disregarded. For the UV-treated sample
the respective results obtained from the measured data in
Fig.~16(c,d) by means of the Kramers-Kronig relation are shown
in Fig.~17(b) by the two dashed lines. For the case when the
charge carriers in the UV-treated sample are disregarded, the
range of dielectric permittivities is indicated by the two
solid lines. {}From the comparison of Fig.~17(a) with Fig.~17(b)
it follows that the UV-treatment does not lead to any significant
changes in dielectric permittivity of an ITO sample as
a function of imaginary frequency.

\subsection{Theoretical results using different approaches to
the description of charge carriers}

Using the dielectric permittivities discussed in Sec.~VA
we have calculated the Casimir force $F(a,T)$ from Eq.~(\ref{eq11})
acting between an Au-coated sphere and both untreated and
UV-treated ITO samples over the range of separations from 60 to 300\,nm.
Then the surface roughness of Au and ITO films was taken into account
by means of geometrical averaging.\cite{6,10}
Note that this approximate method leads to the same results as a more
fundamental calculation based on the scattering approach\cite{72}
at short separation distances where the roughness correction reaches
maximum values (2.2\% at $a=60\,$nm and less than 1\% and 0.5\% at
$a\geq 90\,$nm and $a\geq 116\,$nm, respectively).
At separations of about the correlation length of surface roughness the
scattering approach predicts larger roughness corrections than the
method of geometrical averaging. At such large separations, however,
the effect of roughness is negligibly small and can be
disregarded.\cite{6}
As a result, the theoretical Casimir force between the rough surfaces
of an Au sphere and ITO plate was computed according to the following
expression:
\begin{eqnarray}
&&
F^{\rm theor}(a,T)=\sum_{i=1}^{N_1}\sum_{k=1}^{N_2}
v_i^{\rm (ITO)}v_k^{\rm (Au)}
\nonumber \\
&&~~~~~~~~~~~~~~~~\times
F(a+H_0^{\rm (ITO)}+H_0^{\rm (Au)}-h_i^{(\rm ITO)}
-h_k^{(\rm Au)},T),
\label{eq17}
\end{eqnarray}
\noindent
where all notations were introduced in Sec.~IIB.

The computational results using Eq.~(\ref{eq17}) in comparison with
the experimental data are shown in Fig.~18(a,b).
The theoretical Casimir forces between an Au sphere and an untreated ITO
sample are shown by the two solid lines in Fig.~18(a) over the separation
region from $a=60$ to 300\,nm. In the inset the same lines over a more
narrow separation region from 60 to 100\,nm are presented.
Computations were performed by Eqs.~(\ref{eq11}) and (\ref{eq17})
with the dielectric permittivity of Au along the imaginary frequency
axis indicated in Sec.~VA and dielectric permittivity of an untreated
ITO shown by the two solid lines in Fig.~17(a). In so doing the charge
carriers of ITO were taken into account. The experimental data for
the Casimir force (the first measurement set) are shown as crosses.
The arms of the crosses indicate the total experimental errors in the
separation distances and forces determined at a 95\% confidence level
(see Sec.~IVB). As can be seen in Fig.~18(a), the experimental data
are in a very good agreement with the theory within the limits of
theoretical uncertainties shown by the band between the two solid lines.

In Fig.~18(b) the comparison between the theoretical results
(the band between the two solid lines) and the experimental data
(crosses) is presented for a UV-treated sample. Here, to achieve the
agreement between experiment and theory, the charge carriers in the
ITO sample were disregarded. This means that the dielectric permittivity
of the UV-treated ITO shown by the two solid lines in Fig.~17(b) has been
used in computations. The inset in Fig.~18(b) demonstrates the
agreement achieved over a narrower separation region from 60 to 100\,nm.
The use of the dielectric permittivity of an ITO film with
the contribution of charge carriers disregarded
may seem somewhat unjustified
because the electric properties of an untreated and a UV-treated ITO
samples are very close.
To analyze this problem in more detail, in Fig.~19(a) we present the
comparison between experiment and theory for an untreated (the lower
pair of solid lines) and a UV-treated (the upper pair of solid lines)
samples over a separation range from 60 to 200\,nm.
As above, the experimental data are shown as crosses.
The same dielectric permittivities as in Fig.~18(a,b) were used in
computations. {}From Fig.~19(a) it is observed that theoretical results
with included (the lower pair of solid lines) and disregarded
(the upper pair of solid lines) contribution of charge carriers
do not overlap and are in very good agreement with the measurement
data for respective ITO samples.

Furthermore, in Fig.~19(b) we plot as crosses the measured Casimir
forces between a sphere and a UV-treated sample. In the same figure,
the two dotted lines show the computational results by using the
seemingly most natural dielectric permittivity of a UV-treated sample
shown by the two dashed lines in Fig.~17(b), i.e., taking into account
the free charge carriers. As can be observed in Fig.~19(b), substitution
of actual dielectric properties of a UV-treated ITO film at room
temperature in the Lifshitz theory results in drastic contradiction
with the measured Casimir forces. Note that the use of the bottom
dielectric permittivity of an ITO film discussed above instead of
the top would lead to larger in magnitude Casimir forces, i.e.,
to further increasing disagreement between experiment and theory
(note that the difference between the bottom and top permittivities
is relevant only to the contribution of free charge carriers).

In order to appreciate why the Lifshitz theory with the dielectric
permittivity disregarding charge carriers leads to
agreement with the measurement data for the UV-treated sample,
we consider the phenomenological prescription\cite{6,10} formulated
earlier to account for the
results of several experiments\cite{27,28,29,30,35,36}
discussed in Sec.~I.
 According to this
prescription, for dielectrics and semiconductors of
dielectric type free charge carriers should be disregarded,
whereas for metals they should be taken into account by
means of the plasma model. An important point in support of this
prescription is that the inclusion of relaxation properties of
electrons for metals with perfect crystal lattices and dc
conductivity for dielectrics in the Lifshitz theory results
in violation of the Nernst heat theorem.\cite{6,10}
The phenomenological prescription\cite{6,10} gave rise
to controversial discussions in the literature and even to
attempts to modify the Lifshitz theory.\cite{6,10}
One interesting consequence of this prescription is the
possibility to obtain significantly different Casimir forces
from samples with nearly equal dielectric permittivities.
To do this, one should consider a patterned Si plate with
two sections of different doping concentrations which oscillates
in the horizontal direction below an Au sphere.\cite{37}
If doping concentrations are chosen only slightly below and
above the critical value, the halves of a Si plate will be
in dielectric and metallic states, respectively.
This would lead to significantly different Casimir forces
with almost equal dielectric permittivities along the
imaginary frequency axis.

At this point one can hypothesize that the UV treatment of the
plate results in the Mott-Anderson phase
transition of an ITO film to a dielectric
state without noticeable change of its optical properties at
room temperature.  This hypothesis is supported by the observation
that the UV treatment of ITO leads to a lower mobility of charge
carriers.\cite{73}
The hypothesis proposed could be verified in future by the
investigation of electrical properties of the UV-treated ITO films
at very low temperature. Specifically, if the UV  treatment
transforms the ITO film from metallic to dielectric state, the
electric conductivity (which is similar for an
untreated and UV-treated films at room temperature) should
vanish when the temperature vanishes.

In the above computations the low-frequency behavior of the
dielectric permittivities of both Au and an untreated ITO was
described by the Drude model. We emphasize that almost the same
computational results leading to the same measure of agreement
between experiment and theory are obtained when the free charge
carriers in Au are described by the plasma model with the plasma
frequency $\omega_p=9.0\,$eV. The same is correct for untreated
ITO, but in this case the charge carriers should be described by
the plasma model with the so-called {\it longitudinal}\,\cite{63}
$\omega_p=1.3\,$eV. The value of this parameter
is determined by the physical processes at high frequencies rather
than from the extrapolation of the optical data measured at low
frequencies to zero frequency.
Note that the use of the plasma model for the description of charge
carriers for the UV-treated sample leads to the same computational
results for the Casimir force as shown by the two dashed lines in
Fig.~19(b). Thus, the inclusion of charge carriers into the Lifshitz
theory for the UV-treated sample cannot be reconciled with the
experimental data for the Casimir force shown in Fig.~19(b) as
crosses.

In this section the comparison between experiment end theory was
made using the data from the first measurement set.
The experimental data from the second set (see Table I) were also
compared with the same theoretical approaches. The results obtained
are found indistinguishable from those presented in Figs.~18(a,b)
and 19(a,b). Because of this, we do not discuss them at
greater length.

\section{Conclusions and discussion}

In the foregoing we have described the experimental observation
of the effect of significant decrease in the magnitude of the
Casimir force between an Au sphere and an ITO plate after the
UV-treatment of the latter. The main and unexpected feature of the
observed phenomenon is that a decrease in force
from 21\% to 35\% depending
on separation distance between the sphere and the plate was achieved
with no significant change of the dielectric permittivity of
the ITO film under the UV-treatment.

Measurement of the Casimir force requires precision laboratory
techniques and extreme care in all preparation procedures and
analysis. We performed our measurements using a multimode
AFM in a high vacuum chamber. In Sec.~II we have described the
setup used and all stages of the sample preparation and characterization
including the procedure of UV-treatment.

Special attention was paid to electrostatic calibrations
which are described
in Sec.~III. In the last few years calibration of the Casimir
force measurement
setup has attracted considerable interest and even become
controversial.\cite{46,47,48,49,55}
It was claimed that anomalous dependences of the residual potential
difference and separation on contact on the separation distance
observed in several experiments cast doubts on the measurements of
the Casimir force performed to date. It was also suggested that
inasmuch electrostatic calibrations are based on a fitting procedure
there is no principal difference detween independent measurements
of the Casimir
force\cite{20,21,22,23,24,25,26,27,28,29,30,35,36,37,38,40,41,42,43,44,45}
and deriving the Casimir force by means of a fit from some much larger
measured force of hypothetical origin.\cite{31}
In this respect we would like to note that the calibration consists
in determination of the parameters of a setup using well
established physical laws (in our case of electrostatics) and involves
only well understood and precisely measured forces. Because of this,
the use of some fitting procedure in the process of calibration is not,
under any circumstances, to be regarded as an evidence in favor
of the statement that
the measurement of the Casimir force is not independent. In fact, the
calibration procedure is a part of any measurement. On the contrary,
the extraction of the Casimir force by means of the fitting procedure
from much larger force, of which the major contribution
is not measured and whose origin is not
clearly understood,\cite{31} indicates that this is not an independent
measurement.

Keeping in mind these complicated issues, in Sec.~III we have
analyzed in detail different systematic deviations arising in the calibration
process. These systematic
deviations are some biases in a measurement which
always make the measured value higher or lower than the true value.
We demonstrated that if such deviations are not taken into account and
properly addressed, this results in the anomalies described in the
literature. To the contrary, we have shown that if the systematic
deviations due to finiteness of the acquisition rate and drift of
sphere-plate separation
are measured and removed by means of introducing the
 respective corrections, one arrives at the situation with no anomalies
in accordance with the well established laws of electrostatics.

In Sec.~IV we have presented our measurement results and the analysis
of random, systematic and total experimental errors. Here the main
result of our paper is demonstrated, i.e., that the UV-treatment of an
ITO film results in significant decrease in the magnitude of the
Casimir force. The histograms presented confirm that the Gaussian
distributions of the Casimir force between an Au sphere and an
untreated and, alternatively, a UV-treated sample do not overlap giving
a strong confirmation of the effect observed. The values of the total
experimental errors determined at a 95\% confidence level bring the
final confirmation to the effect of a decrease in the magnitude of
the Casimir force under UV treatment of the ITO sample.

The comparison of the experimental results obtained with the Lifshitz
theory was performed in Sec.~V. While the experimental data for an
untreated sample are in a very good agreement with
conventional applications of the Lifshitz formula for metals
(i.e., with inclusion of free charge carrier contribution),
the comparison of the data with theory for the UV-treated sample
resulted in a puzzle. The measured data were found to be in a very
good agreement with computations if the contribution of free charge
carriers is disregarded. In contrast, the inclusion of the
contribution of free charge carriers to the dielectric permittivity
of the UV-treated ITO sample
resulted in complete disagreement between the data and the
computational results. This is really puzzling if we take into
consideration that the ellipsometry measurements performed for both
the untreated and  UV-treated ITO films did not reveal any
significant differences in the imaginary parts of their dielectric
permittivities. According to the hypothetical explanation of this
phenomenon proposed in Sec.~V, the UV treatment of the ITO film
resulted in its Mott-Anderson
phase transition from the metal to dielectric state
with no significant changes in optical and electrical properties
at room temperature. Further investigations are needed for the
confirmation or rejection of this hypothesis. Specifically, one
should investigate the physical properties of complicated physical
compounds including their interaction with zero-point and thermal
fluctuations of the electromagnetic field.

Whether the proposed theoretical explanation is correct or not,
the observed phenomenon of the decreased Casimir force after the
UV treatment of an ITO sample can find prospective applications in
nanotechnology. In comparison with the case of an Au sphere
interacting with an Au plate, the Casimir force between an Au
sphere and a UV-treated ITO plate is decreased up to 65\%.
This result is of much practical importance for problems of lubrication
and stiction in micro- and nanoelectromechanical systems where the
Casimir and van der Waals forces may lead to collapse of the moving
parts of devices to the fixed electrodes, i.e., to loss of
functionality in devices. Significant decrease in the magnitude
of the Casimir force should be helpful for the resolution of such
problems.

\section*{Acknowledgments}

This work was supported by the DARPA Grant under Contract
No.~S-000354 (equipment, A.B., R.C.-G., U.M.),  NSF Grant
No.~PHY0970161 (C.-C.C., G.L.K., V.M.M., U.M.) and DOE Grant
No.~DEF010204ER46131 (G.L.K., V.M.M., U.M.).
G.L.K.\ and V.M.M.\ were also supported by the DFG Grant
BO\ 1112/20-1.

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text:
Roman Empire Centuriation land subdivision
By: Daniel Tesfamikael|Published on: Aug 28, 2017|Categories: Blog| 0 comments
Home » Roman Empire Centuriation land subdivision
The Roman Empire Centuriation, engineering masterpiece
Roman Empire Centuriation, what it is and how was the utilization management? Well, the land is one of the most important "monuments" of the Roman period. Hence the division of the land into regular grids is recognizable in the countryside. And it bears witness to the first management scheme of the land over vast areas of the Po Plain, north of Italy.
The aerial views
The man draws a land that looks like a sort of chess board. Just looking at aerial photographs we perceive the scale. These views from above are also the only way we have to see lots of other buried signs. For sure in those areas that the environment and the hydrographic changes in the Medieval period affected.
The land subdivision
The division of the land into grids is the centuriation (delimited by the centuriae), and square blocks characterized it. Therefore, the modular grids provided a useful tool not just for the distribution of the fields. But also for the colonization, and for the assignment of the lands to the soldiers that will be retired. As well as for the defense of the territory with the creation of a dense network of man made waterways used for irrigation and drainage of the fields. This model of land management played a key role in the process of the Roman expansion. In fact, it characterized the agriculture lands of the conquered territories.
The Cardo Maximus and the Decumanus Maximus
First of all, the Roman Empire centuriation was laid down along the axes of the two main roads. The Cardo Maximus and the Decumanus Maximus. The centuria is the module of the land division. So called because it was made up of one hundred small pieces, each of which known as heredium. There was also a further subdivision of the heredium into the actus quadratus and the iugerum. A square centuria was twenty actus long (710 meters). Hence it is about fifty hectares. As a result, clear traces of centuria are in a lot of places of the Roman Empire. Also outside the peninsula of Italy, some examples are in the Rhone valley and North Africa.
Ager Centuriatus Roman Centuriation
The typical scheme of a Roman centuriation
The Romans adopted many systems to set up a stable structure for the agriculture lands, as well as in the urban areas. Hence the schemes and the varieties of the settings depended on the economic and legal reasons in relation to the different periods and places where they were made. The scheme of the Roman Empire centuriation adopted in the north of Italy is the classic and widespread "ager centuriatus".
From the Umbilicus
First of all, they found the center of the city ("Umbelicus"), and they traced two perpendicular axes from it. In the detail, the first from east to the west direction called Decumanus Maximus. As the second from south to the north direction called the Cardo Maximus. So delimited the town, these two main roads continued through the surrounding territory. Hence they passed the four gates built on the walls of the town itself. As follow, the land surveyor stood in the "Umbelicus" of the town. Hence facing the west, he called ultra (hereafter) the part of the territory he had in front. Citra (herebefore) the part he had behind him. Dextra what was on his right and finally Sinistra what was on his left.
Roman Centuria Heredia and Jugerum
The Centuria
After that, they traced the secondaries Cardo and Decumanus on both sides of the two main axes. Also called limites quintarii, they were at an interval of 100 actus (about 3,5 km). And they divided the territory into square surfaces called saltus. Furthermore, they added other parallel lines to the road network. Always on the secondaries Cardo and Decumanus already drew. Hence these new lines were at a distance of 20 actus (710,40 m). As a result, they divided the territory into square areas, called centuria. The Decumanus Maximus was normally 40 feet wide (11,84 m), and the Cardo Maximus 20 feet (5,92 m). Furthermore, the limites quintarii were 12 feet (3,55 m) and the remaining roads 8 feet (2,37 m).
The subdivision of the Centuria
It is just at the end of the work on the road network that the real plot of the land will start. Therefore, they divided each Centuria in parallel lines along the cardines and the decumani. On a distance to each other of 2 actus (71,04 m). These bordered the square sections called Heredia with an area of about 0,5 hectares. In conclusion, in the Centuria we could find 100 Heredia (Centuria = centum Heredia). There is also a subdivision of each "Heredium" in two part, following the south-north way. In conclusion, these lines delimited the smaller ground unit, the jugerum. From jugum, amount of soil that could be plowed in one day by a pair of oxen. Hence that is the primitive Roman field, with an area of 2523 square meters.
The scheme of the Roman Empire centuriation just described may appear too rigid and abstract. But it answered, in a nearly perfect way, to a series of eminent practical order needs. Both politic and strategic, as well as agriculture and social profiles. And also under the administrative and fiscal ones.
The Via Emilia, Decumanus Maximus
Now, a Decumanus Maximus is one of the most important roads in the North of Italy. As a result, the road is the Via Emilia, and the region is Emilia Romagna. In fact, this main road goes from the town of Rimini to Piacenza. Hence it describes a straight line that goes from East to West. And also, on the Via Emilia, the Romans founded some important art cities of the region. With Rimini, we have Forlì Cesena, Imola, and Bologna. As well as the towns of Modena, Reggio Emilia, and Parma. The town of Piacenza is the end of this Decumanus Maximus. For sure, even in this region the Roman Empire centuriation exists till our time.
The Roman Empire centuriation in the north-east of Padua
And now let's see an area that preserves the Roman Empire centuriation till our time. In the detail, we are in the Northeast of Italy, in the Veneto region. In particular, in the northeast of Padua, that now is one of the most important art cities of Italy. As a result, this town (Patavium) was already a Roman colony. Hence there was an intensive cultivation around this place. For this reason, the center of the city (Umbilicus Urbis) could not coincide with the surrounding land (Umbilicus Agri). As a result, they moved the Umbilicus out of the city. Most of all, in a position as more as possible barycentric to the area of the centuriation. Hence linked to it by the Cardo Maximus of the Centuria itself.
The inclined cardines and decumans
Therefore, the place falls into the village of St Giorgio delle Pertiche. Here we find two important Roman roads. The ancient Via Aurelia as a Cardo Maximus and the Via Desman, as the Decumanus Maximus. The Decumans are inclined, compared to the ideal east-west direction, about 14,5 °. To follow the slopes of the highest point of the terrain and favor the drainage of water. And also to ensure the durability and integrity of the works. As well as the cardines deviate from the same small amount by the ideal north-south direction. Which allows the cultivated soils to receive the best distribution of the light from the sun.
The water network
In addition to the road, they also regulated and developed the water network. Which it is indispensable both for the maintenance of the works already done. As well as for the normal agriculture practice.
The inner structure of the centuriations
In this landscape, the inner structure of the Centuria differs from the ideal one. Because they are not ten, but eight transverse bands. Which they have a width of 2,5 actus (88,80 m). The transverse lines that divide it into the four parts are generally made up of ditches. Most of the time, we find the willow trees along the ditches. And also, the headlands are on both sides. Looking the fields, other lines are in between the previous ones. In fact, they further subdivide the Centuria in a transverse way. They consist of a small ruts that serve also for the drainage of rainwater.
The south-north direction
The harder is the determination of the longitudinal bands. Because the south-north direction lines have undergone a much greater alteration over time than the transversal ones. However, the most trusted hypothesis is that they divided the Centuria into 20 longitudinal bands. The width of 1 actus (35,52 m), and then in 160 plots or fields. With a surface of 1,25 jugers (3154 sqm). The longitudinal lines that divide the Centuria into four equal parts are usually tree-lined ditches (alder, oak, plane-tree, poplar, maple, …). While the other lines that delimit the fields, always in the south-north direction, consist of ruts and rows of vines ("planted").
The convex slope
The fields have a characteristic transversal convex slope. Very useful for the cultivation of the territory under consideration. Made largely of sandy-lime and clayey soils of difficult drainage. In fact, it guarantees the availability of a real soil mattress. That, for a depth of 30-40 cm, can absorb atmospheric precipitation up to 50% of its volume. And it allows with its inclination the regular flow of the water.
Drawning of a centuria
East-West section of a centuria
Centuria south-north section
Decumanus transverse section
Cardo transverse section
Ditches east-west section
Section east-west ditches
Ditches south-north section
South-north ditches section
Centuria field longitudinal section
Field transverse section
Axonometric drawing of a portion of a roman empire centuriation
Assonometry of a portion of the Centuria (see photo)
The drawing gives an image of how the typical landscape of the Centuria appeared in the area of Padua, northeast of Italy. As a result, a regular succession of fields characterized it. Hence plantings, headlands, and tree-lined ditches bordered these fields.
The Roman Centuriation museum
An interesting museum of the Roman Centuriation has been set up at the civic center of Borgoricco, a building commissioned by the famous Italian architect of the twentieth century Aldo Rossi. It is located within a Roman Centuriation of which large part of the north-eastern territory of Padua is characterized. Since 2009 this rich testimony is accessible to the public thanks to the scientific director Dr. Silvia Cipriano and to the Borgoricco Municipality chief culture officer Mrs Vanna Agostini.
Most of the information and images that are in this post were found in the Italian book entitled "La Centuriazione Compiuta" by the engineer Loris Vedovato and the architect Marino Zancanella (Santa Maria di Sala Municipal Library – August 1981).
By Daniel Tesfamikael
I'm the content Manager of Sightseeing in Italy. In addition to the blog posts, I manage all the articles of the website. As well as all the social media giving tips and solutions for travelers that are going to visit Italy. This is a country full of charm, able to satisfy all kind of needs. just make your choice…
Renzo Sindoca
Roman Empire centuriation
Beatrice I d'Este
Saint Luke blessed Virgin
Biodiversity garden Padua
Marostica human chess game
Brenta Riviera
The Ghetto in Venice
Birth of Venice
Treviso red chicory route
Cittadella medieval town
Merano, South Tyrol

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Washington, PA Home for Sale!
Master on the First Floor! Check Out the 3D Tour. Just click the icon. 4 Bedroom Colonial in a beautiful area of Washington Township. Directly across the rd from the popular Eagle Nest Park. Just minutes away for all amenities but located in a very quit rural community. One ace level lot with above ground pool allows you so many possibilities. The addition of the first floor master suite make this home perfect many family situations. 3 large bedrooms upstairs with a Jack and Jill bathroom make up the second floor. New Central Air (2017) and oil heat make this home very economical. A very traditional layout with the extensions for the master and covered porch that used to house a hot tub and could again. Two large sheds will handle your storage needs. Although the original garage was converted to the master BR a new garage could easily be added if desired. Schedule your tour today.


Firefighters found a cannabis farm after being called to a flooded property.
Police were called to Smith Street by Lancashire Fire and Rescue yesterday (Monday) and removed 40 cannabis plants growing inside and dismantled the farm.
An investigation into cannabis cultivation is under way.
A Lancashire Police spokesman said: "Yesterday Lancashire Fire and Rescue Service made us aware they had attended a report of a flooded property on Smith Street, Nelson and discovered a cannabis farm inside the property.
"Officers from the local policing team and immediate response have dismantled the farm and removed the 40 plants growing inside to be destroyed.
"Investigations are ongoing into the cannabis cultivation."


In the minimalist shoe arena, it's tough to find rain boots. I've had my eye on Vivobarefoot's Waterloo rain boots for awhile but until recently they weren't available here in the US.
I ordered a pair last week and am happy to report that they have a lot going for them and will be my go-to footwear on rainy and/or muddy days. And while they aren't designed for warmth, I'm guessing that with some thick wool socks I might keep my feet warm enough to trek through the slushy snow we often have here in my part of the world.
Watch the video below to get all the scoop on the pros and cons of these rain boots.
UPDATE: I went down from a size 10.5 to a size 10 and still had room for my Correct Toes (although not as much) but with less heel slippage.


Every year the Pharma Market Research Conference continues to amaze me! All the sessions were diverse, innovative and of high caliber. The topics are "real" and gives us the opportunity to actually get back to our individual roles and implement what we've learnt from this conference! The networking sessions allow for us to interact with our client partners from the industry and to share best practices, so we can all learn from each other. Overall, a truly impressive conference and I look forward to coming back next year!
perspectives on issues from market research firms, and other manufacturers.
The Pharma Market Research Conference is a terrific opportunity to stay up to date on the latest tools and techniques of our craft. The multi-track system offers flexibility to attend seminars that best meet your needs. And re-connecting with colleagues I haven't seen in a while was another positive benefit.
I thought the Pharma Market Research conference was a great venue to tap into key trends occurring in our industry, learn of cutting-edge market research approaches and technologies to tackle business challenges, and engage with colleagues in our field. The program and exhibits were excellent.
Every year this conference improves upon the prior year and this one was no exception. Great speakers, timely presentations and networking with colleagues were highlights.
The conference was a wonderful and efficient way to deeply engage with market research professionals.
It was a great forum to discuss the best ways to tackle the key challenges that we face in our day to day work. The keynote speakers and panelists were well selected, and the audience participated enthusiastically. There was also plenty of time allocated to catch up with prior acquaintances and/or network with new ones. All in all, a very productive experience … I will definitely be back next year!
An opportunity to network, learn new things and get insights into an ever-changing world of Pharma Market Research.
This conference is different from other conferences because it provides an intimate setting for the attendees to share a broad range of topics and ideas, despite the fact that conference continues to grow due to its success. As a speaker for panel discussions, I was also impressed with how engaged the audiences were and the quality of the questions that were asked. I learned a lot from my peers in two days!
The topics of presentations and discussions were very relevant to our job today; overall, the conference exceeded my expectations!
I found the PMRC very valuable, the presentation and roundtable content was strong, it was very good for networking, and I thought the vendor fair component was informative but not overbearing.
This year was my first time at Pharma Market Research Conference and I could not have been more impressed by the diversity as well as quality of sessions and round tables. The platform provides an excellent opportunity to stay up to date on key trends and also network and exchange key ideas with other stakeholders. I certainly look forward to coming back next year.
and excellent content – rather go to this rather than travel for other market research conferences.
I attended the Pharma Market Research Conference expecting a lot based on last year's conference – but once again I was impressed with the diversity of important topics, the strong representation from industry, and the number of ideas and insights I walked away with that my team and I can immediately implement. We may be at a crossroads in the industry – but sharing our talents and insights in this forum is a sure way to move forward!
It's designed by us, it's about us and it's for us in the market research community, to network with each other to learn about new research agencies and what they're doing and to share best practices. So it's a great conference because it's a good mix of client side and agency side so that really maximizes your knowledge.
I've actually been part of the Pharma Market Research Conference for a number of years now and for me it's a real opportunity to both share as well as learn. As someone who's been in the market research industry for quite a while, I find that I always walk away with something new, I find that I walk away with a belief I had that gets challenged and it's a great way to learn about new techniques, to meet new vendors and to reconnect with colleagues who on a day to day basis work with other companies and I don't have an opportunity to see and exchange ideas with.
Just the networking is unbelievable, networking among suppliers, networking among other manufacturers, it's a great experience. Again, I like the setting, it's very casual, very laid back and condusive to making connections. It's one of my favorite ones, we tend to put more folks at this conference from Kantar Health compared to other conferences and that's because we find it very productive toward our business.
It's just a nice balance. It's a great way to meet with people, connect with people, ask them what they're doing. It's formal when it needs to be and informal as well, just kind of nice mix of people and events. I think the fact that there's a forum where you can ask questions at the end of often very interesting presentations, I love the things like Casino Night, the fact that we have breakout sessions. All of that works very well and I think's it's well balanced so there's not too much of anything.
The highlights for me are a couple of things. One, to really hear the latest in research from some of the partners who have come here. Secondly is to meet new clients and tell them about our new opportunities and how we can help them grow their business and third is really just the social aspect of networking. This is one of the better opportunities that we've had to do networking and it's always a favorite conference of ours to come to. I think it's equal parts of fun and work. I think you do have to some work here and meet new people, don't be bashful about meeting others. And I think it's a really good opportunity to learn new things. The presentations are always good and the clients are always excited and interested to learn about what we can offer them.
For me, I would love to have another person come from my company so more of us could go to sessions. That to me would be big because we didn't want to leave the booth unattended but the sessions, going through the list, none of them were just your run of the mill, like what I would expect from other conferences. And I love that everything was market research, no matter who I talked to they were kind of speaking the same language.
For us, it's just to get to know some of the people that we talk to almost everyday outside of the work setting and to put a personality to who we're talking to and working with all the time.