text:
# When do unit fractions sum to an integer?

Unit fractions are rational numbers in the form $$\frac{1}{n}$$, where $$n$$ is an integer. In elementary number theory one can prove that the harmonic sum $$H_n= 1+ \frac{1}{2}+...+\frac{1}{n}$$ is never an integer. For elementary proof of this fact see the post: Elementary proof that the sum 1+...+1/n is not an integer

Take one step further, József Kürschák, in 1918, proved that the sum of the reciprocals of consecutive natural numbers (whether starting from 1 or not) is never an integer.

Unfortunately, the result does not hold with a border generalization when we consider the sum of arbitrary subsets of unit fractions. Examples include $$1=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=\frac{1}{2}+ \frac{1}{3}+ \frac{1}{7}+ \frac{1}{43}+ \frac{1}{1806}.$$ Erdős–Graham problem concerns with the existence of such unit fractions.

The question I ask now is: Without calculating the sum one by one, are there any nontrivial, characteristic properties that determines whether the given subset of unit fractions sums to an integer? One step back, is there any class of interesting subsets of unit fractions where the sum of each subset in the class has a non-integer sum?

• It's not hard to see that if $P$ is a perfect number, then $\sum_{d|P, d\neq 1} \frac{1}{d} = 1$. – SAWblade Nov 27 '18 at 20:14
• For any given finite subset of unit fractions, one obvious criterion is simply to sum them! You undoubtedly want something less obvious, but it might help to describe what you want in a "criterion." – Barry Cipra Nov 27 '18 at 20:32


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# High Energy Physics Seminars 2004

Seminars 2003 page

Schuster Colloquia: 2.30-3.30pm, Bragg Lecture Theatre

Normal seminar coordinates: Wednesdays 2-3pm, Moseley Lecture Theatre

 Wednesday 4 Feb Prof Otto Nachtmann (Heidelberg) Theory

Towards a nonperturbative foundation of the dipole picture   (Abstract)

 Wednesday 11 Feb, 2.30pm Prof Ed Hinds (Imperial) SCHUSTER COLLOQUIUM

Quantum gases in microscopic traps   (Abstract)

 Thursday 12 Feb, 3pm, 2nd Floor Seminar Room Prof Ed Hinds (Imperial) Experiment

Electric dipole moments: a search for new physics  (ppt only)

 Tuesday 17 Feb, 2-3pm Dr Stefan Gieseke (Cambridge)Blackett Lecture Theatre Theory

The new MC generator Herwig++   (Abstract)

 Wednesday 18 Feb, 2.30pm Prof Anthony Leggett (Illinois) SCHUSTER COLLOQUIUM

Testing the limits of quantum mechanics: motivation, state of play, prospects   (Abstract)

 Wednesday 3 March Simon Dean (Manchester) Experiment

Once in a Lifetime: Investigating Z -> tau tau -> e mu at D0   (Abstract)

 Wednesday 10 March Dr Peter Richardson (Durham - IPPP) Phenomenology

Simulation of multi-jet and lepton final states   (Abstract)

 Wednesday 17 March, 2.30pm Prof R J Young (UMIST/VUM) SCHUSTER COLLOQUIUM

Racing cars, spiders and Nanotubes   (Abstract)

 Wednesday 24 March Dr B. Todd Huffman (Oxford) Experiment

Why B Physics is Interesting (with a CDF focus)   (Abstract)

 Thursday 22 April Jozef Dudek (Oxford) Niels Bohr Common Room Theory

Pentaquark Phenomenology - Further States, Decay Systematics and Dynamics   (Abstract)

 Wednesday 28 April, 2.30pm Prof Ray Bishop (UMIST) SCHUSTER COLLOQUIUM

Confronting the Quantum Many-Body Problem   (Abstract)

 Thursday 29 April Dr David Bugg (RAL) Niels Bohr Common Room Experiment

Four sorts of mesons   (Abstract)

 Wednesday 5 May Dr Thomas Teubner (Liverpool) Theory

Testing the Standard Model at highest precision: g-2 of the muon and alpha_QED(M_Z)   (Abstract)

 Wednesday 12 May Dr Georg Weiglein (Durham) Theory

Higgs Physics and Supersymmetry at Present and Future Colliders   (Abstract)

 Wednesday 19 May Dr Kenneth Long (Imperial College) Bragg Lecture Theatre Experiment

Neutrino factory: motivation, machine and MICE   (Abstract)

 Thursday 20 May Prof Tony Signal (Massey Univ, NZ) 2pm, Niels Bohr Common Room Theory

Symmetry Breaking in Quark Distributions of the Proton   (Abstract)

 My Project, PAW and I Grid Security and Accounting   (Abstract)   (Abstract) Wednesday 26 May Bragg Lecture Theatre Yaw Ming Chia Shiv Kaushal

 Particle Identification at BaBar: establishing what's what! Study of the Central Tracker at DØ Run II   (Abstract)   (Abstract) Wednesday 2 June Bragg Lecture Theatre Christina Edgar Yu-Hsiang Lin Will Plano

 Diffractive Processes at the LHC Common Mode Noise in the ATLAS SCT silicon detector   (Abstract)   (Abstract) Thursday 10 June Bragg Lecture Theatre Andrew Pilkington Muhammad Shahzad Hassan Chagani

## Abstracts

4 Feb. O Nachtmann:
We study real and virtual photon-photon scattering in a nonperturbative framework and classify different contributions to this process. We investigate the approximations and assumptions that are necessary to derive something like the dipole model of high energy scattering from a generally nonperturbative description. We find that the naive dipole model formula has to be supplemented by an extra term describing rescattering corrections of the quark and antiquark forming the colour dipole.

11 Feb. E Hinds:
Clouds of cold atoms, collected and refrigerated by laser light, can be cooled to the lowest temperatures in the universe. This has created the new field of atom optics where cold atoms are manipulated, much as photons are controlled in traditional optics using mirrors, lenses, and waveguides. I will show some of the first movies of atom clouds being manipulated. From the viewpoint of basic science these clouds are a fantastic new tool for studying the quantum physics of gases close to absolute zero.

It is now becoming possible to confine and manipulate atoms and Bose Einstein condensates in extremely small traps and single-mode matter wave guides that are only ~10-8m across. Atoms flowing in such microscopic traps and tubes could provide the basis for a new technology similar to electronics but based on the flow and interaction of neutral atoms rather than on electricity in wires. I will describe how atom "chips" are being realised and how these might lead to sensitive new devices including integrated atom interferometers and perhaps quantum information processors.

17 Feb. S Gieseke:
The Monte Carlo event generator Herwig++ 1.0 for e+e- Annihilation is presented. Herwig++ is a complete rewrite of the existing Fortran program HERWIG. I will explain the underlying formalism of the new parton shower and the improvements that have been made in comparison to HERWIG. We have tested the program against a wide range of LEP data. I present these results and give an overview over planned future developments.

18 Feb. A Leggett:
I present the motivation for experiments which attempt to generate, and verify the existence of quantum superpositions of two or more states which are by some reasonable criterion "macroscopically" distinct and show that various a priori objections to this program made in the literature are flawed. I review the extent to which such experiments currently exist in the areas of free-space molecular diffraction, magnetic biomolecules, quantum optics and Josephson devices, and sketch possible future lines of development of the program.

3 Mar. S Dean:
The sum of signed impact parameters in a two-track system is proposed as a tool for discriminating channels with lifetime in the final state. Z -> tau tau -> e mu is shown to be a realistic process for studying this effect and the current best method of signal selection is presented.

10 Mar. P Richardson:
Following a brief review of the approximations and models involved in Monte Carlo simulations I will discuss recent progress in the simulation of high multiplicity final states from both particle decays and QCD radiation. These are important in the simulation of processes such as top production at the Tevatron and the search for new physics at the LHC.

17 Mar. R Young:
The presentation will be concerned with the relationships between structure and properties of high-performance fibrous materials. Spectacular advances have been made in the field of fibre-reinforced composite materials to underpin the technology of the modern Formula 1 racing car. Such composites materials have unprecedented levels of stiffness and strength being as strong and stiff as steel but with only a fraction of the density.

Silk is a protein-based polymer fibre that is employed widely by arthropods (spiders and insects) and a particularly strong version of spider silk, the dragline only 2 microns in diameter, can support the entire weight of a spider.

Carbon nanotubes are a newly-discovered fibrous form of carbon that are responsible in part for the development of "nanotechnology". The interest in single-wall carbon nanotubes has increased steadily since their discovery in 1993, due to their exceptional electronic and mechanical properties. Their outstandingly high Young's modulus (about 1 TPa and similar to diamond) and their structure-dependent electronic properties make them ideal candidates for applications ranging from nanoscale sensors to satellite tethers.

24 Mar. BT Huffman:
B physics is being pursued in many places around the world. There are detailed results coming from both hadronic and leptonic colliders on the masses, branching ratios, lifetimes, and the presence of mixing and CP violation from a variety of decay modes. There are even discoveries of new hadronic bound states. But through all of these detailed measurements it is important to realise that the Bottom quark provides us with an important and unique window on realms of physics that are far-removed from the relatively low energies required for its production. In this talk I will emphasize those aspects of B physics that may well help us to limit and define what laws govern nature beyond the standard model along with the results of the CDF experiment that are setting some of those limits.

22 April, J Dudek:
I will discuss the growing phenomenology of pentaquarks with particular emphasis on experimental observations which can discriminate between models.

Quark-based models have been proposed in which the pentaquark contains one unit of orbital angular momentum. In such pictures the $\theta$ is partnered by a spin-3/2 baryon with a mass separation dictated by spin-orbit forces. I will outline a model in which we find a small splitting. The existence of such a partner state would pose questions for the Chiral Soliton Model.

In general it is difficult to distinguish between a non-exotic pentaquark and a conventional baryon resonance. I will demonstrate that the flavour structure of certain pentaquark models is such that there are selection rules for the decay of pentaquarks that would not apply for three-quark states.

Finally, I will briefly present a simple quark model in which, it seems, one can find a realisation of the pentaquark structure proposed by Jaffe & Wilczek.

28 April, R Bishop:
Examples of quantum many-body systems abound in Nature. Thus, it is clear that in fields like molecular, solid-state, and nuclear physics most of the fundamental objects of discourse are interacting many-body systems. But even in elementary particle physics one is usually dealing with more than one particle. For example, at some level of reality a nucleon comprises three quarks interacting via gluons and surrounded by a cloud of mesons, which are themselves made of quark-antiquark pairs. Even more fundamentally, even the “physical vacuum” of any quantum field theory is endowed with an enormously complex infinite many-body structure due to virtual excitations. A key central role in modern physics is thus occupied by quantum many-body theory, where we are especially interested in the possible existence of any universal techniques that are powerful enough to treat the full range of many-body and field-theoretic systems. One such method is the coupled cluster method. This has become one of the most pervasive, most powerful, and most successful of all fully microscopic formulations of quantum many- body theory. It has probably been applied to more systems in quantum field theory, quantum chemistry, nuclear, subnuclear, condensed matter and other areas of physics than any other competing method. It has yielded numerical results which are among the most accurate available for an incredibly wide range of both finite and extended systems on either a spatial continuum or a regular discrete lattice. In this talk I aim to give an overview of the method itself and some illustrative examples of its power and range of applicability.

29 April, D Bugg:
The overall status of light q-qbar mesons, glueballs, hybrids and the light scalars will be sketched.

Crystal Barrel data identify a simple and fairly complete spectrum of q-qbar mesons up to 2400 MeV. In addition there are six `extra' states. Four of them coincide well with Lattice QCD predictions for the four lightest glueballs. Two others are candidates for a pair of JPC = 2-+ hybrids.

The light scalars Sigma, Kappa, f0(980) and a0(980) appear to make a nonet of weakly bound states resembling the deuteron.

5 May, T Teubner:
The anomalous magnetic moment of the muon is discussed, paying particular attention to the evaluation of the hadronic contributions. Confronted with the latest measurement from BNL, the Standard Model prediction currently shows a 2.7 sigma deviation, allowing -- but at the same time constraining -- new physics. I also present a new result for alpha_QED(M_Z) which influences the indirect determination of the Higgs mass from fits of electroweak precision observables.

12 May, G Weiglein:
The present status of precision tests of the electroweak Standard Model (SM) is summarised and the resulting indirect constraints on the mass of the SM Higgs boson are discussed. In the Minimal Supersymmetric extension of the Standard Model (MSSM) the mass of the lightest Higgs boson is not a free parameter as in the SM, and a firm upper bound can be established. The phenomenology of Higgs physics in the MSSM at the next generation of colliders is discussed. The possible interplay between the LHC and a future Linear Collider in analysing the mechanism of electroweak symmetry breaking and the underlying structure of Supersymmetric models is investigated.

19 May, K Long:
The discovery of neutrino oscillations implies that neutrinos are massive and that the Standard Model is incomplete, making the neutrino sector the only window on physics beyond the Standard Model that is presently accessible. The worldwide consensus is that only a Neutrino Factory - an intense high-energy neutrino source derived from the decay of a stored muon beam - will be adequate for the requisite precision studies. The physics case for the Neutrino Factory will be reviewed briefly and the layout of the facility summarised. The critical components of the facility are the proton driver, the pion-production target and collection system, the ionisation cooling channel and the muon acceleration system. These components will be reviewed and the status and plans of the relevant R&D programmes described. A key component of the machine R&D is the demonstration of ionisation cooling using the Muon Ionisation Cooling Experiment (MICE). The status of MICE will be described in detail.

20 May, A Signal:
Symmetries play a key role in modern physics, especially in the understanding of the strong interaction. Over the past fifteen years deep inelastic experiments have observed the breaking of a number of quark model symmetries. The problem I shall address is whether these observations at can tell us anything new about the non-perturbative physics that governs the structure of the proton. I shall introduce the meson cloud model, which allows the calculation of a number of symmetry breaking effects within a single framework, and compare predictions of the model with recent experimental data.

26 May, Y M Chia:
In this talk I will talk on my journey in becoming a particle physicist and the interesting things that I have met. I will talk about one of them here. I will also mention briefly what I am doing now and the benefits of being a PAW fan.

26 May, S Kaushal:
A brief introduction to the Grid and a look at some of the Grid related work being done in Manchester. GridSite is introduced and the security aspects discussed in detail. Accounting and accounting issues are also introduced.

2 June, C Edgar:
Reliably identifying particles is crucial in any analysis. The idea behind "bitwords" and the particle identification selectors they describe at BaBar are introduced. The role of Monte Carlo truth lists is also discussed. As a case study, preliminary research into identifying pions for the tau->5pi analysis is described.

2 June, Y-S Lin:
The performance of the central tracker for advanced tracking studies at DØ is reported. This upgrade version is used by the new package, l1ft2b.

Comparison of different samples from Monte Carlo is made, l1ft2b is also optimized and tracking efficiency of 98% is found using various equations to simulate the real tracking algorithm. Finally, an investigation of how to smear the fake rate down to 2% is presented.

2 June, W Plano:
A look at the process of estimation, maximum likelihood, minimum variance and a possibility of improving the resolution of dE/dx measurements. I will present my latest data on the subject and hopefully show that the prognosis is not as bad as it seems.

10 June, A Pilkington:
Measuring diffractive Higgs production by tagging protons in roman pot type detectors results in very good mass resolution and a reduction in the relevant backgrounds. The diffractive mechanism will be presented, along with the current best estimates in some of the background processes.

10 June, M Shahzad:
Common Mode Noise (CMN) is of particular concern in the analysis of binary data obtained from analogue signals which is effected by coherent distortions. The ATLAS SCT silicon detector is an example of such a system. CMN can create artificial hit patterns. Therefore, it is vital for a digital system to have negligible CMN. However CMN can only be estimated on a statistical basis, analysing some sample events. Gaussian CMN is most difficult to detect.

10 June, H Chagani:
The discovery potential of the scalar top from photon collisions is investigated at the TESLA collider looking in detail at the decay ~t -> t ~X^{0}. Various techniques are employed in an attempt to reduce the main background of top quark pair production, which happens to be a golden channel process at TESLA. Unfortunately, the same cannot be said for stop pair production.
Notes:
For help with AV equipment: Joe Lee, ext 54038 (please give 2-3 days notice)

 Last modified: http://www.hep.man.ac.uk/seminars.html Email: jenny@hep.man.ac.uk

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# Math Help - Divergence reverse process

1. ## Divergence reverse process

can anyone plz tell me how to get F(vector field) when im given DIV F(div means divergence )

2. ## What makes you think it's possible?

$F=(-y,xy,z), divF=x+1$
$G=(x^2/2,y,-xy), divG=x+1$

3. well i think there will be some way ....

4. Well, you can always say: Let S be the set of all possible vector fields F such that div F=x+1. In that case, the two examples I just gave you would both be elements in S. But you seem to be asking your question with the assumption that there is a one-to-one correspondence between vector fields and their divergences. This is not the case.

5. To add further, since $\nabla \cdot \nabla \times {\bf F} = 0$ where ${\bf F}$ is an arbitrary vector field, then you can add $\nabla \times {\bf F}$ to your vector field and it will lead to the same diverence.


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North Carolina Math 3 EOC Chapter 1

### North Carolina Math 3 EOC Chapter 1 Sample

1 pt
3.

To solve the equation , the function was graphed. At what points does the graph of the function cross the x-axis?

1 pt
4.

The graph of the function is shown below. What is the solution to the equation ?

1 pt
6.

A polynomial function has a range of $y\ge 22$. Which of these must the function have?

1 pt
11.

What are the intervals of increase of the function graphed below?

1 pt
12.

The graph of the function was translated 2 units to the left and 12 units up. The graph of which of these functions was produced?


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0
VLSI Design : Question Paper Dec 2011 - Electronics & Telecomm. (Semester 6) | Mumbai University (MU)

## VLSI Design - Dec 2011

### Electronics & Telecomm. (Semester 6)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1(a) Consider a MOS structure with p-type semiconductor substrate doped to Na=1016/cm3,a
SIO2insulator with thickness of 500oand an oxide charge density of 1011/cm2,and a
polysilicon gate. Calculate the flat band voltage. Assume that ∅GC=-1.1V
(5 marks)
1(b) What is Subthreshold conduction? What are the factors controlling the subthreshold current in long channel and short channel MOSFET? (5 marks) 1(c) What is velocity Saturation? How does it effects the I-V characteristics of a Short channel MOSFET? (5 marks) 1(d) Depletion mode n-channel device are not complementary to enhancement mode n-channel transistor and cannot match up with a p-channel enhancement mode transistor as load in an inverter circuit. Explain (5 marks) 1(e) The boundaries of the valid input signal regions that define the Noise Margins In an inverter (VIH & V1L) are defined as the voltage points where the magnitude of the inverter voltage gain is equal to unity. Explain why? (5 marks) 2(a) Explain the complete fabrication process steps for a CMOS inverter using n-well process with the help of cross sectional diagrams for all important masking steps(10 marks) 2(b) Consider a silicon-gate PMOS transistor with the following parameters:
Substrate doping ND=1016/cm3,Gate doping ND=1020/cm3,QOX=4x1010qC/cm2,
tOX=0.10 μm
(i) Determine the threshold voltage VT0 under zero bias at room temperature. Note that ε=3.97εoand εsi=11.7ε.
(ii) Determine the type (p-type or n-type) and amount of the channel Implant (NI/cm2) required to change the threshold voltage from VT0 to - 1 V and + 3 V.
(10 marks)
3(a) In the inverter circuit what is meant by Zp.u and Zp.d ? Derive relation between zp.u and zp.d if an NMOS inverter is to be driver from another NMOS inverter.(10 marks) 3(b) An enhancement mode n-channel MOSFET has the following parameters. Threshold voltage VT = 0.8 v. channel length modulation coefficient λ=0.05/V, μnCOX=20μA/V2.
Find the drain current for the following cases.
(i) Vg=5V, VD=4V, VS=2V.
(ii) Vg=2.8V, VD=5V, VS=1V.
(10 marks)
4(a) A reference inverter has (W/L)n =1/1 and (W/L)p=3/1. Draw the schematic and the stick diagram of a two input NAND gate and calculate the (W/L) ratios of transistors based on reference inverter design. (10 marks) 4(b) Draw the mask layout of the circult designed in question 4(a) in n-substrate and p-well.(10 marks) 5(a) Compare constant field scaling with constant voltage scaling and state advantages and limitations in both the methods. Show analytically how delay time, power density and current density are affected in terms of scaling factors In both the type of scaling methods.(10 marks) 5(b) Implement the following Boolean function in CMOS logic.
$$Y=\bar{\left(D+E+A\right).(D+C)}$$Draw the optimized stick diagram of the logic gate using Euler path.
(10 marks)
6(a) Draw the p-well CMOS inverter and explain the latch up effect in it. Why latch up must be prevented and what are the remedies to avoid the latch up problem in the circuit? (10 marks) 6(b) Implement a 2:1 multiplexer circuit using CMOS transmission gates. Write a Verilog module for the circuit at switch level of abstraction. Write a test bench to check the functionality of the circuit. (10 marks)

### Write short notes on any three

7(a) Ion implantation.(7 marks) 7(b) MOS capacitance.(7 marks) 7(c) Design rules and their necessity.(7 marks) 7(d) Short channel effects.(7 marks)


text:
# Matt's arXiv selection: week ending 5 October 2007.

From: Matthew Davis <mdavis_at_physics.uq.edu.au>
Date: Mon, 29 Oct 2007 22:41:14 +1000 (EST)

The following message was sent to the matts_arxiv list by Matthew Davis <mdavis_at_physics.uq.edu.au>

Hello again,

Thankfully the teaching semester is now over and this should give me a chance to
get you back up to date. For this week (which was now three weeks ago!) there
were 25 new preprints and 14 replacements:

------------------------------------------------------------------------------
\\
arXiv:0709.4554
Date: Fri, 28 Sep 2007 09:00:07 GMT (28kb)

Title: Feshbach resonances in mixtures of ultracold $^6$Li and $^{87}$Rb gases
Authors: B. Deh, C. Marzok, C. Zimmermann and Ph. W. Courteille
Categories: cond-mat.other cond-mat.soft
\\
We report on the observation of several Feshbach resonances in collisions
between ultracold $^6$Li and $^{87}$Rb atoms in their respective hyperfine
ground states $|F,m_F>=|1/2,1/2>$ and $|1,1>$. The resonances show up as trap
losses for the $^6$Li cloud induced by inelastic Li-Rb-Rb three-body
collisions. The magnetic field values where they occur represent important
benchmarks for an accurate determination of the interspecies interaction
potentials. A broad Feshbach resonance located at 1066.92 G opens interesting
prospects for the creation of ultracold heteronuclear molecules. We furthermore
observe a strong enhancement of the narrow p-wave Feshbach resonance in
collisions of $^6$Li atoms at 158.55 G in the presence of a dense $^{87}$Rb
cloud. The effect of the $^{87}$Rb cloud is to introduce Li-Li-Rb three-body
collisions occurring at a higher rate than Li-Li-Li collisions.
\\ ( http://arxiv.org/abs/0709.4554 , 28kb)
------------------------------------------------------------------------------
\\
arXiv:0709.4596
Date: Fri, 28 Sep 2007 12:28:09 GMT (177kb)

Title: Ground state fidelity from tensor network representations
Authors: Huan-Qiang Zhou, Roman Orus and Guifre Vidal
Categories: cond-mat.stat-mech cond-mat.str-el
\\
For any $D$-dimensional quantum lattice system, the fidelity between two
ground state many-body wave functions is mapped onto the partition function of
a $D$-dimensional classical statistical vertex lattice model with the same
lattice geometry. The fidelity per lattice site, analogous to the free energy
per site, is well-defined in the thermodynamic limit and can be used to
characterize the phase diagram of the model. We explain how to compute the
fidelity per site in the context of tensor network algorithms, and demonstrate
the approach by analyzing the two-dimensional quantum Ising model with
transverse and parallel magnetic fields.
\\ ( http://arxiv.org/abs/0709.4596 , 177kb)
------------------------------------------------------------------------------
\\
arXiv:0709.4609
Date: Fri, 28 Sep 2007 13:20:37 GMT (38kb)

Title: Super-Tonks-Girardeau regime in trapped one-dimensional dipolar gases
Authors: G. E. Astrakharchik and Yu. E. Lozovik
Categories: cond-mat.other
\\
Possible signatures of a super-Tonks-Girardeau gas in bosonic systems of
trapped quasi-one-dimensional dipoles are discussed at zero temperature. We
provide estimation of the frequency of the lowest compressional mode and
compare it to analytical results derived using harmonic approach in the high
density regime. We construct an exact mapping of the ground-state wave function
of one-dimensional dipolar system of bosons, fermions and Bose-Fermi mixture
and conclude that local properties and energy are the same at zero temperature.
A question of to which extent the dipolar potential can be treated long- or
short- range is discussed.
\\ ( http://arxiv.org/abs/0709.4609 , 38kb)
------------------------------------------------------------------------------
\\
arXiv:0709.4620
Date: Fri, 28 Sep 2007 14:28:38 GMT (244kb)

Title: Mott transition in one dimension: Benchmarking dynamical cluster
approaches
Authors: Matthias Balzer, Werner Hanke and Michael Potthoff
Categories: cond-mat.str-el cond-mat.supr-con
\\
The variational cluster approach (VCA) is applied to the one-dimensional
Hubbard model at zero temperature using clusters (chains) of up to ten sites
with full diagonalization and the Lanczos method as cluster solver. Within the
framework of the self-energy-functional theory (SFT), different cluster
reference systems with and without bath degrees of freedom, in different
topologies and with different sets of variational parameters are considered.
Static and one-particle dynamical quantities are calculated for half-filling as
a function of U as well as for fixed U as a function of the chemical potential
to study the interaction- and filling-dependent metal-insulator (Mott)
transition. The recently developed Q-matrix technique is used to compute the
SFT grand potential. For benchmarking purposes we compare the VCA results with
exact results available from the Bethe ansatz, with essentially exact dynamical
DMRG data, with (cellular) dynamical mean-field theory and full diagonalization
of isolated Hubbard chains. Several issues are discussed including convergence
of the results with cluster size, the ability of cluster approaches to access
the critical regime of the Mott transition, efficiency in the optimization of
correlated-site vs. bath-site parameters and of multi-dimensional parameter
optimization. We also study the role of bath sites for the description of
excitation properties and as charge reservoirs for the description of filling
dependencies. The VCA turns out to be a computationally cheap method which is
competitive with established cluster approaches.
\\ ( http://arxiv.org/abs/0709.4620 , 244kb)
------------------------------------------------------------------------------
\\
arXiv:0709.4675
Date: Fri, 28 Sep 2007 19:13:10 GMT (46kb)

Title: Measurement of the ac Stark shift with a guided matter-wave
interferometer
Authors: B. Deissler, K. J. Hughes, J. H. T. Burke, and C. A. Sackett
Categories: physics.atom-ph
\\
We demonstrate the effectiveness of a guided-wave Bose-Einstein condensate
interferometer for practical measurements. Taking advantage of the large arm
separations obtainable in our interferometer, the energy levels of the 87Rb
atoms in one arm of the interferometer are shifted by a calibrated laser beam.
The resulting phase shifts are used to determine the ac polarizability at a
range of frequencies near and at the atomic resonance. The measured values are
in good agreement with theoretical expectations. However, we observe a
broadening of the transition near the resonance, an indication of collective
light scattering effects. This nonlinearity may prove useful for the production
and control of squeezed quantum states.
\\ ( http://arxiv.org/abs/0709.4675 , 46kb)
------------------------------------------------------------------------------
\\
arXiv:0709.4577 (*cross-listing*)
Date: Fri, 28 Sep 2007 11:15:48 GMT (103kb)

Title: Sub-Kelvin Cooling of a Macroscopic Oscillator and femto-Newton Force
Measurement
Authors: F. Mueller, S. Heugel and L. J. Wang
Categories: physics.ins-det physics.optics
\\
Measuring very small forces, particularly those of a gravitational nature,
has always been of great interest, as fundamental tests of our understanding of
the physical laws. Ultra-long period mechanical oscillators, typically used in
such measurements, will have kT/2 of thermal energy associated with each degree
of freedom, owing to the equal-partition of energy. Moreover, additional
seismic fluctuations in the low frequency band can raise this equivalent
temperature significantly to 10^5 K. Recently, various methods using
opto-mechanical forces have been reported to decrease this thermal energy for
MHz, micro-cantilever oscillators, effectively cooling them. Here we show the
direct, dynamical cooling of a gram-size, macroscopic oscillator to 300 mK in
equivalent temperature - noise reduction by a factor of 10^6. By precisely
measuring the torsional oscillator's position, we dynamically provide an
external 'viscous' damping force. Such an added, dissipative force is
essentially free of noise, resulting in rapid cooling of the oscillator.
Additionally, we observe the time-dependent cooling process, at various cooling
force parameters. This parameter dependence agrees well with a simple physical
model which we provide. We further show that the device is sensitive to forces
as small as <100 fN - a force only a few percent of that typically exerted by a
single biological molecule or that observed in a typical gravity experiment. We
also demonstrate the dynamic control of the oscillator's natural frequency,
over a span of nearly two decades. The method may find important applications
in precision measurements of very weak forces.
\\ ( http://arxiv.org/abs/0709.4577 , 103kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0023
Date: Fri, 28 Sep 2007 22:30:59 GMT (97kb)

Title: Pairing with Unconventional Symmetry around BCS-BEC Crossover: Fermionic
Atoms in 2D Optical Lattices to Correlated Electron Systems
Authors: Dusan Volcko and Khandker F. Quader
Categories: cond-mat.supr-con cond-mat.other
\\
We study superfluid properties of fermions on a 2D lattice using a
finite-range pairing interaction derivable from an extended Hubbard model. We
obtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ and
extended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentum
distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients,
$v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties that
are strikingly different for d- and $s^*$ symmetries in the crossover region.
Fermionic atoms in 2D optical lattices may provide a way to observe these
signatures. We discuss possible experimental ramifications of our results.
\\ ( http://arxiv.org/abs/0710.0023 , 97kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0023
Date: Fri, 28 Sep 2007 22:30:59 GMT (97kb)

Title: Pairing with Unconventional Symmetry around BCS-BEC Crossover: Fermionic
Atoms in 2D Optical Lattices to Correlated Electron Systems
Authors: Dusan Volcko and Khandker F. Quader
Categories: cond-mat.supr-con cond-mat.other
\\
We study superfluid properties of fermions on a 2D lattice using a
finite-range pairing interaction derivable from an extended Hubbard model. We
obtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ and
extended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentum
distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients,
$v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties that
are strikingly different for d- and $s^*$ symmetries in the crossover region.
Fermionic atoms in 2D optical lattices may provide a way to observe these
signatures. We discuss possible experimental ramifications of our results.
\\ ( http://arxiv.org/abs/0710.0023 , 97kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0045
Date: Sat, 29 Sep 2007 08:02:03 GMT (829kb)

Title: Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical
Lattices
Authors: R. V. Mishmash, L. D. Carr
Categories: cond-mat.mes-hall
\\
Inspired by experiments on Bose-Einstein condensates in optical lattices, we
study the quantum evolution of dark soliton mean-field initial conditions in
the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum
measures is utilized in our analysis, including von Neumann and generalized
quantum entropies, quantum depletion, and number fluctuations. We find that
quantum effects cause the soliton to fill in. Moreover, soliton-soliton
collisions become inelastic, in strong contrast to the predictions of
mean-field theory. These features show that the lifetime and collision
properties of dark solitons in optical lattices provide clear signals of
quantum effects.
\\ ( http://arxiv.org/abs/0710.0045 , 829kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0208
Date: Mon, 1 Oct 2007 06:21:07 GMT (256kb)

Title: Hanbury Brown and Twiss correlations in atoms scattered from colliding
condensates
Authors: Klaus Molmer, A. Perrin, V. Krachmalnicoff, V. Leung, D. Boiron, A.
Aspect, C.I. Westbrook
Categories: cond-mat.other
\\
Low energy elastic scattering between clouds of Bose condensed atoms leads to
the well known s-wave halo with atoms emerging in all directions from the
collision zone. In this paper we discuss the emergence of Hanbury Brown and
Twiss coincidences between atoms scattered in nearly parallel directions. We
develop a simple model that explains the observations in terms of an
interference involving two pairs of atoms each associated with the elementary s
wave scattering process.
\\ ( http://arxiv.org/abs/0710.0208 , 256kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0348
Date: Mon, 1 Oct 2007 18:00:27 GMT (57kb)

Title: Finite-temperature Bell test for quasiparticle entanglement in the Fermi
sea
Authors: W.-R. Hannes, M. Titov
Categories: cond-mat.mes-hall
\\
We demonstrate that the Bell test cannot be realized at finite temperatures
in the vast majority of electronic setups proposed previously for quantum
entanglement generation. This fundamental difficulty is shown to originate in a
finite probability of quasiparticle emission from Fermi-sea detectors. In order
to overcome the feedback problem we suggest a detection strategy, which takes
advantage of a resonant coupling and of an additional detector cooling. Unlike
other proposals the designed Bell test provides a possibility to determine the
critical temperature for entanglement production in the solid state.
\\ ( http://arxiv.org/abs/0710.0348 , 57kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0353
Date: Mon, 1 Oct 2007 19:58:22 GMT (25kb)

Title: Trap-Imbalanced Fermion Mixtures
Authors: M. Iskin and C. J. Williams
Categories: cond-mat.supr-con cond-mat.other
Comments: 4 pages and 3 figures
\\
We analyze the ground state phases of two-component ($\uparrow$ and
$\downarrow$) population- and mass-balanced ($N_\uparrow = N_\downarrow$ and
$m_\uparrow = m_\downarrow$) but trap-imbalanced ($\omega_\uparrow \ne \omega_\downarrow$) fermion mixtures as a function of interaction strength from
the weak attraction (BCS) to the strong attraction (BEC) limit. In the BCS
limit, we find that the unpolarized superfluid (UPS) fermions are surrounded by
unpolarized normal (UPN) fermions, and that they exist only away from the
central core of the trapping potentials where the normal fermions are partially
polarized. As the interactions increase towards unitarity, we find that the
central core first becomes a UPN, and then transitions to a UPS. Further
increasing the interactions, we find that the central UPS region expands, but
the inner superfluid and normal regions shrink towards the edges until the
entire mixture becomes a UPS in the BEC limit.
\\ ( http://arxiv.org/abs/0710.0353 , 25kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0110
Date: Sun, 30 Sep 2007 06:48:05 GMT (122kb)

Title: Storage of spin squeezing in a two-component Bose-Einstein condensate
Authors: Guang-Ri Jin and Sang Wook Kim
Categories: quant-ph
Comments: 10 pages, 5 figures. This version is slightly different from the one
published in Phys. Rev. Lett
\\
Efficient control of spin squeezing in a two-component Bose-Einstein
Condensate is studied by rapidly turning-off the external field at a time that
maximal spin squeezing appears. We show that strong reduction of spin
fluctuation can be maintained in a nearly fixed direction for a long time. We
explain the underlying physics unambiguously, and present analytical
expressions of the maximal-squeezing time.
\\ ( http://arxiv.org/abs/0710.0110 , 122kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0112
Date: Sun, 30 Sep 2007 07:24:28 GMT (63kb)

Title: Improvement of conversion efficiency of atom-molecule Bose-Einstein
condensate
Authors: Guang-Ri Jin and Sang Wook Kim
Categories: quant-ph
Comments: 4 pages, 4 figures. To be appeared in J. Korean Phys. Society (JKPS)
\\
We investigate the stimulated Raman adiabatic passage in two-color
photoassociation for a atom-molecule Bose-Einstein condensate. By applying two
time-varying Guassian laser pulses that fulfill generalized two-photon
resonance condition, we obtain highly efficient atom-molecule conversion. The
efficiency depends on the free-bound detuning and the delay time between the
two pulses. By adjusting the parameters optimally, we achieve 92% conversion
efficiency.
\\ ( http://arxiv.org/abs/0710.0112 , 63kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0278
Date: Mon, 1 Oct 2007 12:46:41 GMT (180kb)

Title: Demonstration of fractional statistics of anyons in the Kitaev
lattice-spin model
Authors: Chao-Yang Lu, Wei-Bo Gao, Otfried G\"uhne, Xiao-Qi Zhou, Zeng-Bing
Chen, Jian-Wei Pan
Categories: quant-ph
\\
In two dimensions, the laws of physics permit the existence of exotic
quasiparticles--anyons--that do not fit into the usual categories of fermions
and bosons, but obey a new form of fractional statistics. They have been
predicted to live as excitations in fractional quantum Hall systems. Quantum
states with anyonic excitations can also be artificially designed in model
systems that have highly nontrivial ground states with topological order. A
prominent example is the Kitaev lattice-spin models, which opened the avenue of
fault-tolerant topological quantum computing. Demonstration of the anyonic
fractional statistics is not only of fundamental interest, but also a
cornerstone of the emerging field of topological quantum computation. While
there is fast progress in the theoretical proposals, an unambiguous observation
of fractional statistics associated with anyon braiding still remained a real
experimental challenge. On the one hand, although some signatures have been
observed in the fractional quantum Hall systems, these experiments did not
resolve individual anyons. On the other hand, controlling cold atomic or
moleculargases in optical lattices to realize the spin models is still beyond
the current experimental capabilities. Here we report the demonstration of the
fractional statistics of anyons by simulation of the Kitaev lattice-spin model
on a six-photon graph state. Our method is to first create the ground state and
excited state of the model Hamiltonian, and then implement the braiding and
fusion operations by single-qubit rotations. Our experimental platform could
also be seen as a quantum simulator, with good controllability and purity,
which may be promising for future studies of quantum many-body physics.
\\ ( http://arxiv.org/abs/0710.0278 , 180kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0285
Date: Mon, 1 Oct 2007 18:59:42 GMT (483kb)

Title: Quantum-limited metrology with product states
Authors: Sergio Boixo, Animesh Datta, Steven T. Flammia, Anil Shaji, Emilio
Bagan, and Carlton M. Caves
Categories: quant-ph
\\
We study the performance of initial product states of n-body systems in
generalized quantum metrology protocols that involve estimating an unknown
coupling constant in a nonlinear k-body (k << n) Hamiltonian. We obtain the
theoretical lower bound on the uncertainty in the estimate of the parameter.
For arbitrary initial states, the lower bound scales as 1/n^k, and for initial
product states, it scales as 1/n^(k-1/2). We show that the latter scaling can
be achieved using simple, separable measurements. We analyze in detail the case
of a quadratic Hamiltonian (k = 2), implementable with Bose-Einstein
condensates. We formulate a simple model, based on the evolution of
angular-momentum coherent states, which explains the O(n^(-3/2)) scaling for k
= 2; the model shows that the entanglement generated by the quadratic
Hamiltonian does not play a role in the enhanced sensitivity scaling. We show
that phase decoherence does not affect the O(n^(-3/2)) sensitivity scaling for
initial product states.
\\ ( http://arxiv.org/abs/0710.0285 , 483kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0086
Date: Sat, 29 Sep 2007 19:04:24 GMT (273kb)

Title: An Optical Lattice Clock with Spin-polarized 87Sr Atoms
Authors: Xavier Baillard (SYRTE), Mathilde Fouch\'e (SYRTE), Rodolphe Le Targat
(SYRTE), Philip G. Westergaard (SYRTE), Arnaud Lecallier (SYRTE),
Fr\'ed\'eric Chapelet (SYRTE), Michel Abgrall (SYRTE), Giovanni D. Rovera
(SYRTE), Philippe Laurent (SYRTE), Peter Rosenbusch (SYRTE), S\'ebastien Bize
(SYRTE), Giorgio Santarelli (SYRTE), Andr\'e Clairon (SYRTE), Pierre Lemonde
(SYRTE), Gesine Grosche (PTB), Burghard Lipphardt (PTB), Harald Schnatz (PTB)
Categories: physics.atom-ph
Proxy: ccsd hal-00175653
\\
We present a new evaluation of an 87Sr optical lattice clock using spin
polarized atoms. The frequency of the 1S0-3P0 clock transition is found to be
429 228 004 229 873.6 Hz with a fractional accuracy of 2.6 10^{-15}, a value
that is comparable to the frequency difference between the various primary
standards throughout the world. This measurement is in excellent agreement with
a previous one of similar accuracy.
\\ ( http://arxiv.org/abs/0710.0086 , 273kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0522
Date: Tue, 2 Oct 2007 13:19:42 GMT (712kb)

Title: Localisation and Delocalisation of Ultracold Bosonic Atoms in Finite
Optical Lattices
Authors: Dirk-S\"oren L\"uhmann, Kai Bongs, Klaus Sengstock, Daniela Pfannkuche
Categories: cond-mat.other
\\
We study bosonic atoms in small optical lattices by exact diagonalisation and
observe a striking similarity to the superfluid to Mott insulator transition in
macroscopic systems. The momentum distribution, the formation of an energy gap
and the pair correlation function show only a weak size dependence. For
non-commensurate filling we reveal a mixture of localised and delocalised
particles, which is sensitive to lattice imperfections. Breaking the lattice
symmetry causes a Bose glass like behaviour. We discuss the nature of excited
states and orbital effects by using a multi-band diagonalisation technique.
\\ ( http://arxiv.org/abs/0710.0522 , 712kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0607
Date: Tue, 2 Oct 2007 19:28:14 GMT (660kb)

Title: Localized modes of binary mixtures of Bose-Einstein condensates in
nonlinear optical lattices
Authors: F. Kh. Abdullaev, A. Gammal, M. Salerno, Lauro Tomio
Categories: cond-mat.other
\\
The properties of the localized states of a two component Bose-Einstein
condensate confined in a nonlinear periodic potential [nonlinear optical
lattice] are investigated. We reveal the existence of new types of solitons and
study their stability by means of analytical and numerical approaches. The
symmetry properties of the localized states with respect to the NOL are also
investigated. We show that nonlinear optical lattices allow the existence of
bright soliton modes with equal symmetry in both components, bright localized
modes of mixed symmetry type, as well as, dark-bright bound states and bright
modes on periodic backgrounds. In spite of the quasi 1D nature of the problem,
the fundamental symmetric localized modes undergo a delocalizing transition
when the strength of the nonlinear optical lattice is varied. This transition
is associated with the existence of an unstable solution, which exhibits a
shrinking (decaying) behavior for slightly overcritical (undercritical)
variations in the number of atoms.
\\ ( http://arxiv.org/abs/0710.0607 , 660kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0396
Date: Mon, 1 Oct 2007 22:11:43 GMT (156kb)

Title: Higher-order splitting algorithms for solving the nonlinear
Schr\"odinger equation and their instabilities
Authors: Siu A. Chin
Categories: physics.comp-ph physics.atom-ph
Comments: 10 pages, 8 figures, submitted to Phys. Rev. E
\\
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for $\dt k_{max}^2{<\atop\sim}2 \pi$, where
$k_{max}=\pi/\Delta x$.
\\ ( http://arxiv.org/abs/0710.0396 , 156kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0692
Date: Wed, 3 Oct 2007 02:14:34 GMT (824kb)

Title: Entanglement renormalization in fermionic systems
Authors: G. Evenbly, G. Vidal
Categories: quant-ph
\\
We demonstrate, in the context of quadratic fermion lattice models in one and
two spatial dimensions, the potential of entanglement renormalization (ER) to
define a proper real-space renormalization group transformation. Our results
show, for the first time, the validity of the multi-scale entanglement
renormalization ansatz (MERA) to describe ground states in two dimensions, even
at a quantum critical point. They also unveil a connection between the
performance of ER and the logarithmic violations of the boundary law for
entanglement in systems with a one-dimensional Fermi surface. ER is recast in
the language of creation/annihilation operators and correlation matrices.
\\ ( http://arxiv.org/abs/0710.0692 , 824kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0766
Date: Wed, 3 Oct 2007 11:52:30 GMT (236kb,D)

Title: Atomic diffraction in counter-propagating Gaussian pulses of laser light
Authors: Tapio P. Simula, Atom Muradyan and Klaus Molmer
Categories: quant-ph
\\
We present an analysis of atomic diffraction due to the interaction of an
atomic beam with a pair of Gaussian light pulses. We derive a simple analytical
expression for the populations in different diffraction orders. The validity of
the obtained solution extends beyond the Raman-Nath regime, where the kinetic
energy associated with different diffraction peaks is neglected, into the
so-called channeling regime where accurate analytical expressions have not
previously been available for the diffraction. Comparison with experimental
results and exact numerical solutions demonstrate the validity of our
analytical formula.
\\ ( http://arxiv.org/abs/0710.0766 , 236kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0733
Date: Wed, 3 Oct 2007 08:31:06 GMT (15kb)

Title: Total control over ultracold interactions via electric and magnetic
fields
Authors: Bout Marcelis, Boudewijn Verhaar, and Servaas Kokkelmans
Categories: physics.atom-ph
\\
The scattering length is commonly used to characterize the strength of
ultracold atomic interactions, since it is the leading parameter in the
low-energy expansion of the scattering phase shift. Its value can be modified
via a magnetic field, by using a Feshbach resonance. However, the effective
range term, which is the second parameter in the phase shift expansion,
determines the width of the resonance and gives rise to important properties of
ultracold gases. Independent control over this parameter is not possible by
using a magnetic field only. We demonstrate that a combination of magnetic and
electric fields can be used to get independent control over both parameters,
which leads to full control over elastic ultracold interactions.
\\ ( http://arxiv.org/abs/0710.0733 , 15kb)
------------------------------------------------------------------------------
\\
arXiv:0710.0927
Date: Thu, 4 Oct 2007 06:46:57 GMT (165kb)

Title: Optical pumping via incoherent Raman transitions
Authors: A. D. Boozer, R. Miller, T. E. Northup, A. Boca, and H. J. Kimble
Categories: quant-ph
\\
A new optical pumping scheme is presented that uses incoherent Raman
transitions to prepare a trapped Cesium atom in a specific Zeeman state within
the 6S_{1/2}, F=3 hyperfine manifold. An important advantage of this scheme
over existing optical pumping schemes is that the atom can be prepared in any
of the F=3 Zeeman states. We demonstrate the scheme in the context of cavity
quantum electrodynamics, but the technique is equally applicable to a wide
variety of atomic systems with hyperfine ground-state structure.
\\ ( http://arxiv.org/abs/0710.0927 , 165kb)
------------------------------------------------------------------------------
\\
arXiv:0710.1081
Date: Thu, 4 Oct 2007 19:52:31 GMT (92kb)

Title: Confinement effects in a guided-wave interferometer with
millimeter-scale arm separation
Authors: J. H. T. Burke, B. Deissler, K. J. Hughes and C. A. Sackett
Categories: physics.atom-ph
\\
Guided-wave atom interferometers measure interference effects using atoms
held in a confining potential. In one common implementation, the confinement is
primarily two-dimensional, and the atoms move along the nearly free dimension
under the influence of an off-resonant standing wave laser beam. In this
configuration, residual confinement along the nominally free axis can introduce
a phase gradient to the atoms that limits the arm separation of the
interferometer. We experimentally investigate this effect in detail, and show
that it can be alleviated by having the atoms undergo a more symmetric motion
in the guide. This can be achieved by either using additional laser pulses or
by allowing the atoms to freely oscillate in the potential. Using these
techniques, we demonstrate interferometer measurement times up to 72 ms and arm
separations up to 0.42 mm with a well controlled phase, or times of 0.91 s and
separations of 1.7 mm with an uncontrolled phase.
\\ ( http://arxiv.org/abs/0710.1081 , 92kb)
------------------------------------------------------------------------------

The replacements:

------------------------------------------------------------------------------
\\
arXiv:0709.4123
replaced with revised version Fri, 28 Sep 2007 14:00:25 GMT (272kb)

Title: Statistics of the polariton condensate
Authors: Paolo Schwendimann and Antonio Quattropani
Categories: cond-mat.other cond-mat.supr-con
\\ ( http://arxiv.org/abs/0709.4123 , 272kb)
------------------------------------------------------------------------------
\\
arXiv:0705.1258
replaced with revised version Fri, 28 Sep 2007 19:39:39 GMT (137kb)

Title: A method of state-selective transfer of atoms between microtraps based
on the Franck-Condon Principle
Authors: A. B. Deb, G. Smirne, R. M. Godun, C. J. Foot
Categories: physics.atom-ph
Comments: 8 pages, 6 figures. Accepted for publication Journal of Physics B
(Atomic, molecular and optical physics)
\\ ( http://arxiv.org/abs/0705.1258 , 137kb)
------------------------------------------------------------------------------
\\
arXiv:cond-mat/0702505
replaced with revised version Fri, 28 Sep 2007 22:20:41 GMT (436kb)

Title: Fermi-Luttinger liquid: Spectral function of interacting one-dimensional
fermions
Authors: M. Khodas, M. Pustilnik, A. Kamenev, L.I. Glazman
Categories: cond-mat.mes-hall
\\ ( http://arxiv.org/abs/cond-mat/0702505 , 436kb)
------------------------------------------------------------------------------
\\
arXiv:0704.3047
replaced with revised version Mon, 1 Oct 2007 12:56:36 GMT (949kb)

Title: Observation of atom pairs in spontaneous four wave mixing of two
colliding Bose-Einstein Condensates
Authors: A. Perrin (LCFIO), H. Chang (LCFIO), V. Krachmalnicoff (LCFIO), M.
Schellekens (LCFIO), D. Boiron (LCFIO), A. Aspect (LCFIO), C. I. Westbrook
(LCFIO)
Categories: quant-ph
Proxy: ccsd hal-00142991
\\ ( http://arxiv.org/abs/0704.3047 , 949kb)
------------------------------------------------------------------------------
\\
arXiv:0704.0291 (*cross-listing*)
replaced with revised version Tue, 2 Oct 2007 01:38:13 GMT (324kb)

Title: Approaching the Heisenberg limit in an atom laser
Authors: M. Jeppesen, J. Dugu\'e, G. R. Dennis, M. T. Johnsson, C. Figl, N. P.
Robins and J. D. Close
Categories: physics.atom-ph cond-mat.other
\\ ( http://arxiv.org/abs/0704.0291 , 324kb)
------------------------------------------------------------------------------
\\
arXiv:quant-ph/0701167
replaced with revised version Tue, 2 Oct 2007 12:13:46 GMT (636kb)

Title: Cold Atom Physics Using Ultra-Thin Optical Fibers: Light-Induced Dipole
Forces and Surface Interactions
Authors: G. Sagu\'e, E. Vetsch, W. Alt, D. Meschede and A. Rauschenbeutel
Categories: quant-ph
Comments: 4 pages, 4 figures. Accepted for publication in PRL
\\ ( http://arxiv.org/abs/quant-ph/0701167 , 636kb)
------------------------------------------------------------------------------
\\
arXiv:physics/0701272
replaced with revised version Tue, 2 Oct 2007 17:44:06 GMT (578kb)

Title: Experimental single-impulse magnetic focusing of launched cold atoms
Authors: David A. Smith, Aidan S. Arnold, Matthew J. Pritchard and Ifan G.
Hughes
Categories: physics.atom-ph physics.optics
Comments: Substantially revised to incorporate referee suggestions. 10 pages, 5
figures
\\ ( http://arxiv.org/abs/physics/0701272 , 578kb)
------------------------------------------------------------------------------
\\
arXiv:0708.2257
replaced with revised version Wed, 3 Oct 2007 17:25:15 GMT (412kb)

Title: Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong
Coupling and Non-Markovian Regimes
Authors: Nick Cummings, B. L. Hu
Categories: quant-ph
Comments: 12 pages, 5 figures; minor changes in grammar, wording, and
formatting. One unnecessary figure removed. Figure number revised (no longer
counts subfigures separately)
\\ ( http://arxiv.org/abs/0708.2257 , 412kb)
------------------------------------------------------------------------------
\\
arXiv:0709.2132
replaced with revised version Wed, 3 Oct 2007 15:28:37 GMT (177kb)

Title: Dynamics of vortices in weakly interacting Bose-Einstein condensates
Authors: Alexander Klein, Dieter Jaksch, Yanzhi Zhang and Weizhu Bao
Categories: quant-ph
Comments: 8 pages, 7 figures, one reference updated, typos corrected
Journal-ref: Phys. Rev. A 76, 043602 (2007)
DOI: 10.1103/PhysRevA.76.043602
\\ ( http://arxiv.org/abs/0709.2132 , 177kb)
-----------------------------------------------------------------------------
\\
arXiv:0706.2855
replaced with revised version Thu, 4 Oct 2007 08:27:10 GMT (22kb)

Title: Crystalline phase of strongly interacting Fermi mixtures
Authors: D. S. Petrov, G. E. Astrakharchik, D. J. Papoular, C. Salomon, G. V.
Shlyapnikov
Categories: cond-mat.stat-mech
Comments: 4 pages, 1 color figure, published version
Report-no: NSF-KITP-07-132
Journal-ref: Phys. Rev. Lett. 99, 130407 (2007)
DOI: 10.1103/PhysRevLett.99.130407
\\ ( http://arxiv.org/abs/0706.2855 , 22kb)
------------------------------------------------------------------------------
\\
arXiv:cond-mat/0702569 (*cross-listing*)
Date: Sat, 24 Feb 2007 14:20:32 GMT (20kb)
Date (revised v2): Mon, 14 May 2007 09:39:55 GMT (20kb)
Date (revised v3): Thu, 2 Aug 2007 04:04:31 GMT (23kb)

Title: Quantum rearrangement and self-consistent BCS-BEC crossover
thermodynamics
Authors: Ji-sheng Chen, Chuan-ming Cheng, Jia-rong Li, Yan-ping Wang
Categories: cond-mat.stat-mech hep-ph nucl-th quant-ph
and references updated
Journal-ref: Phys. Rev. A 76, 033617 (2007)
DOI: 10.1103/PhysRevA.76.033617
\\
Based on previous works, analytical calculational procedures for dealing with
the strongly interacting fermions ground state are further developed through a
medium dependent potential in terms of the Bethe-Peierls contact interaction
model. The methods are exact in the unitary limit regime and they lead to the
self-consistent equations analogous to the Hartree ones. The single particle
energy spectrum rearrangement effects on the thermodynamics due to the
additional instantaneous correlation potential contribution to the system
physical chemical potential and pressure, i.e., equation of state, which
enforces the classical thermodynamic consistency. The Dyson-Schwinger equations
represent implicitly the various Bethe-Goldstone expansion ones. In a
thermodynamically self-consistent way, the universal dimensionless factor is
analytically calculated to be $\xi=\049$, which defines the ratio of the
unitary fermions energy density to that of the ideal non-interacting ones at
T=0.
\\ ( http://arxiv.org/abs/cond-mat/0702569 , 23kb)
------------------------------------------------------------------------------
\\
arXiv:quant-ph/0703199
replaced with revised version Thu, 4 Oct 2007 09:43:10 GMT (706kb)

Title: Bose-Einstein condensate coupled to a nanomechanical resonator on an
atom chip
Authors: Philipp Treutlein, David Hunger, Stephan Camerer, Theodor W. H\"ansch,
and Jakob Reichel
Categories: quant-ph
Comments: published version (5 pages, 3 figures)
Journal-ref: Phys. Rev. Lett. 99, 140403 (2007)
\\ ( http://arxiv.org/abs/quant-ph/0703199 , 706kb)
------------------------------------------------------------------------------
\\
arXiv:0708.0253
replaced with revised version Thu, 4 Oct 2007 00:42:59 GMT (114kb)

Bose-Einstein condensates
Authors: Chaohong Lee, Libin Fu, Yuri S. Kivshar
Categories: quant-ph
\\ ( http://arxiv.org/abs/0708.0253 , 114kb)
-----------------------------------------------------------------------------
\\
arXiv:0707.2015
replaced with revised version Thu, 4 Oct 2007 18:04:36 GMT (152kb)

Title: Trapping of ultracold polar molecules with a Thin Wire Electrostatic
Trap
Authors: J. Kleinert, C. Haimberger, P. J. Zabawa, and N. P. Bigelow
Categories: physics.atom-ph
DOI: 10.1103/PhysRevLett.99.143002
\\ ( http://arxiv.org/abs/0707.2015 , 152kb)
------------------------------------------------------------------------------

Till next time,
Matt.

--
=========================================================================
Dr M. J. Davis,               Senior Lecturer in Physics
School of Physical Sciences,  email: mdavis_at_physics.uq.edu.au
University of Queensland,     ph   : +61 7 334 69824
Brisbane, QLD 4072,           fax  : +61 7 336 51242
Australia.                    http://www.physics.uq.edu.au/people/mdavis/
=========================================================================
Matt's arXiv selection: weekly summary of cold-atom papers from arXiv.org
http://www.physics.uq.edu.au/people/mdavis/matts_arXiv/
=========================================================================
Legal stuff: Unless stated otherwise, this e-mail represents only the
views of the sender and not the views of the University of Queensland
=========================================================================

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text:
# Convolutional Embedding for Edit Distance

31 Jan 2020

Edit-distance-based string similarity search has many applications such as spell correction, data de-duplication, and sequence alignment. However, computing edit distance is known to have high complexity, which makes string similarity search challenging for large datasets... (read more)

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# Tasks in which recursion is either the fastest or only way to produce a result [duplicate]

I've just finished studying recursion at university. One thing that stood out for me however was that in both the lectures and in the practical we completed, all the tasks we were asked to do could be performed faster, and in less code, using iterative means.
This was something the lecturer confirmed.

Could somebody please give me some examples of situations when recursion is a better solution than iterative techniques? Additionally, are there any situations in which recursion is the only way to sole a problem?

-

## marked as duplicate by Juho, vonbrand, Luke Mathieson, AJed, KavehFeb 23 '13 at 7:30

@DaveClarke: You're a star Dave - should I delete this topic then? – Andrew Martin Feb 20 '13 at 20:37
If you think it overlaps too much, then yes. – Dave Clarke Feb 20 '13 at 21:11

There are no questions which can only be solved with recursion. This is because they can be solved with Turing machines, which don't use recursion.

The set of problems which can be solved with a TM are exactly the same as the ones which can be solved with recursion (or its formal model, the Lambda Calculus).

In particular, if you want to simulate recursion iteratively, the way to do this is to use a data structure called a stack (which simulates the call stack for functions).

As for algorithms that can be solved better using recursion, there are tons. I'm surprised that your recursive versions were longer, as recursion usually leads to less code. This is one of the reasons haskell is gaining popularity.

Consider the algorithm quicksort, for sorting lists. In rough pseudocode, it's as follows:

function quicksort(list)
if length(list) <= 1
return list
pivot = first element of list
lessList = []
equalList = []
greaterList = []
for each element in list:
if element < pivot, add to lessList
if element == pivot, add to equalList
if element > pivot, add to greater list
sortedLess = quicksort(lessList)
sortedGreater = quicksort(greaterList)
return sortedLess ++ equalList ++ sortedGreater

where ++ means concatenation.

The code isn't purely functional, but by dividing the list into different parts, and sorting each sublist recursively, we get a very short $O(n\log n)$ sort.

Recursion is also very useful for recursive data structures. Often times you'll have a traversal on trees, of the following form:

function traverseTree(tree)
if (tree is a single node)
do something to that node
else, for each child of tree:
traverseTree(child)

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Thanks for this. We used recursion for things like Fibonnaci and Triangle numbers, where iterative means were much faster. These are fascinating. – Andrew Martin Feb 20 '13 at 22:41
You'll come across some problems where recursion isn't any slower, because the only non-recursive way to solve them is basically to build your own function call stack. Also, in languages like Lisp or Prolog, which support tail recursion, certain types of recursion can be made as efficient as iterative methods (because a new stack frame doesn't need to be created). – jmite Feb 20 '13 at 22:43
Easier answer: Your CPU is purely sequential, yet C (and Java, and Scheme, even latest FORTRAN) allow recursion. – vonbrand Feb 20 '13 at 23:03
@AndrewMartin, as it turns out, computing Fibonacci numbers using the recurrence directly as written (two function calls) is terrible, but you don't have to do it that way. And as the answer says, there are many, many situations in which a recursive algorithm is simply the only understandable way to express a computation. – vonbrand Feb 20 '13 at 23:09
@AndrewMartin, recursion is an important tool in the programmer's arsenal. Not required every day, but indispensable when you need it. Get familiar with the idea of recursion. – vonbrand Feb 21 '13 at 3:25

Anything that can be implemented through recursion can be implemented through iteration, and vice versa. So there is no task which it is impossible to accomplish without recursion (assuming a programming language that has the usual iterative constructs).

The cost of transforming a recursive program into an equivalent interative one is up to polylogarithmic time in most settings, and close to constant time (depending on the size of the code, but not on the size of the data) in practice. This is because the gist of the transformation from a recursive program to an iterative program is to push a record on a global stack every time a function is called, and pop that record when the function returns. This doesn't make any significant change to running time, other than memory management for the additional stack. So where a recursive program exists, an equally fast equivalent iterative program exists (for reasonable values of “equally”).

For some recursive programs, a transformation to an iterative program can significantly increase the complexity in terms of code maintenance. All that stack management can amount to significant amounts of code, especially to ensure that you have captured the right data in stack records.

A typical example where recursion is natural and avoiding it is cumbersome is tree traversal. Consider a program that manipulates binary trees and must often traverse them. A recursive traversal goes like this:

def traverse(tree):
if tree.left_child != None: traverse(tree.left_child)
if tree.right_child != None: traverse(tree.right_child)

An iterative traversal requires explicit stack maintenance — and this is a simplified example which doesn't maintain local data as it traverses the tree:

def traverse(tree):
stack = new_empty_stack()
stack.push(tree)
while not stack.is_empty():
node = stack.pop()


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# Instrumentation for Colliding Beam Physics (INSTR-17)

from 27 February 2017 to 3 March 2017
Budker Institute of Nuclear Physics
Asia/Novosibirsk timezone
Home > Timetable > Session details > Contribution details

# Contribution Contributed Oral

Tracking and vertex detectors

# The MEGII detector

## Speakers

• Prof. Paolo Walter CATTANEO

## Content

An overview of the conceptual design and construction status of the detector for the MEGII experiment, the upgrade of MEG, is presented. MEGII is designed to search for the $mu^+ to e^+$ decay with a sensitivity an order of magnitude better than MEG down to $5times 10^{-14}$. To achieve this sensitivity a muon decay rate a factor of two higher is required. The detector resolution on all physical parameters is expected to improve of a factor of two. The detector has been substantially redesigned to cope with the highest muon decay rate expected. Some detector components have been upgraded (calorimetry, beam line, calibration), others redesigned completely (drift chamber, timing counter), others added (Radiative decay counter). All main detector components are presented emphasizing the improvements with MEG. An estimate of the expected final sensitivity is presented.

## Summary

An overview of the conceptual design and construction status of the detector for the MEGII experiment, the upgrade of MEG, is presented. The detector has been substantially redesigned to cope with the highest muon decay rate expected. All main detector components are presented emphasizing the improvements with MEG.


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## Franklin's Notes

### Real closed field

A real closed field is a field which is elementarily equivalent to $\mathbb{R}$ as a model of the theory of fields in first-order logic. Some examples of real closed fields are

• The algebraic numbers $\mathbb{A}$

• The computable numbers

• The definable real numbers

• Any model of the reals constructed from a nonstandard model of arithmetic

• The surreal numbers

• The Puiseux series with real coefficients


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# How can reducing dimensionality with PCA help subsequent classification, if it does not have access to PCA eigenvectors?

I have coded a PCA by hand and am trying to make sense of the transformation. As a simple example, lets suppose my dataset has 2 instances with three features each:

>Instance #1: 2 3 4
>Instance #2: 2 4 1

These three features are of course with respect to the traditional X, Y, Z axes.

Suppose during PCA I find two significantly large eigenvalues corresponding to two vectors ( 1 1 2) and (1 2 3). By multiplying these vectors with each of my instances, I would get the following new features in a smaller space;

>Instance #1: 13 20
>Instance #2: 8  13

For example, 13 is computed from (2*1) + (3*1) + (4*2).

Now, here is my problem. When feeding these new features into a classifier, they are just numbers -- the classifier is not aware of them being along some direction (i.e., the classifier does not see the eigenvectors, it only sees the new features, which are the projections of the data on these eigenvectors).

Typically when demonstrating the benefits of PCA, one is shown a plot in which each number is a magnitude along a given direction. In those plots, one is easily able to see the benefits of PCA as the direction information helps to show how the numbers are located in the space. But when inputting the data to a classifier, the classifier is not aware of these directions, we only feed in the array of principal components (not eigenvectors), so I get confused on how the classifier exploits the direction information that it never sees...

You can understand PCA's main purpose with a simple example. Consider that your two variables $X$ and $Y$ are perfectly correlated i.e. all data points lie on a line passing through the origin. By performing PCA, you rotate the data to the direction of maximum variance. This will result in a data that has one constant dimension: the new rotated data (in the coordinates of principal components) will be a horizontal straight line located at $x = 0$.


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Kinetics of the Carbonic Acid System

There are two types of carbonic acid:

 (1a) true carbonic acid: H2CO3 (1b) composite (apparent) carbonic acid: H2CO3*  =  CO2(aq) + H2CO3 1

Each of these two acids is characterized by its own equilibrium constant (for the first dissociation step):

carbonic acid reaction formula equilibrium constant
(2a) true H2CO3   = H+ + HCO3- Ktrue
(2b) composite (apparent) H2CO3* = H+ + HCO3- K1

The link between the reaction formula and the equilibrium constant is established by the law of mass action. It yields:

 (3a) Ktrue = {H+} {HCO3-} / {H2CO3} (3b) K1 = {H+} {HCO3-} / ({CO2(aq) · H2O} + {H2CO3})

The aim is to unveil the kinetics behind this thermodynamic approach. It enables us to calculate the equilibrium constants Ktrue and K1) exclusively from kinetic rates.

Reaction Kinetics

Three components, CO2(aq), H2CO3, and HCO3-, are involved in the carbonic acid formation:2

Here, the chemical kinetics is completely determined by six individual rates, k12 to k32. Translating this diagram into a set of differential equations yields:

 (4a) – d [ 1 ] / dt   =   (k12+k13) [ 1 ] – k21 [ 2 ] – k31 [ 3 ] (4b) – d [ 2 ] / dt   =   (k21+k23) [ 2 ] – k12 [ 1 ] – k32 [ 3 ] (4c) – d [ 3 ] / dt   =   (k31+k32) [ 3 ] – k13 [ 1 ] – k23 [ 2 ]
 with the abbreviations: [ 1 ]  =  H+ + HCO3 [ 2 ]  =  H2CO3 [ 3 ]  =  CO2(aq) + H2O

From experiments we know that the rates for the slow reaction (k13, k31) and for the fast reaction (k12, k21) differ considerably from each other (by more than 5 orders of magnitude):

 (5) k13, k31   ≪   k12, k21

This allows us to neglect k13 and k31 in 4a. From the equilibrium condition for 4a, i.e. d[1]/dt = 0, then follows:

 (6) – d [ 1 ] / dt  =  k12 [ 1 ] – k21 [ 2 ]  =  0 ⇒ k21 / k12 = [ 1 ] / [ 2 ]

In fact, the ratio of rates on the right-hand side defines the equilibrium constant for the true carbonic acid:

 (7) Ktrue  =  [ 1 ] / [ 2 ]  =  {H+} {HCO3-} / {H2CO3}

Entering this relation, in form of [ 1 ] = Ktrue [ 2 ], into 4c yields:

 (8) – d [ 3 ] / dt  =  (k31+k32) [ 3 ] – (k13 Ktrue + k23) [ 2 ]

Usually the quantities in the round brackets are lumped together in two new rates:

 (9a) ka  =  k13 Ktrue + k23 (9b) kb  =  k31 + k32

Again, assuming equilibrium, i.e. d[3]/dt = 0, a second equilibrium constant emerges:

 (10) K0  =  ka / kb  =  [ 3 ] / [ 2 ]  =  {CO2(aq) · H2O} / {H2CO3}

In this way, the above diagram (where three components are interrelated by 6 kinetic rates) reduces to a simpler diagram where the same components are related by no more than two equilibrium constants, K0 and Ktrue:

Composite Equilibrium Constant K1

Conventionally, the two species CO2(aq) and H2CO3 are treated together as if they were one substance (denoted by H2CO3*). Just this was done in 1b above. The corresponding equilibrium constant is given in 3b, i.e.

 (11) K1  =  {H+} {HCO3-} / ({CO2(aq) · H2O} + {H2CO3})

The main idea is now to express the carbonic acid problem (characterized by two equilibrium constants Ktrue and K0 in the scheme above) by a single equilibrium constant, namely K1. We obtain the desired relation in two steps:

First, we use 7 to replace {H+}{HCO3-} in the nominator of 11:

 (12) K1 = Ktrue {H+} {H2CO3} / ({CO2(aq) · H2O} + {H2CO3}) = Ktrue / ({CO2(aq) · H2O}/{H2CO3} + 1)

Second, we insert 10 and get the final result:

 (13) K1  =  Ktrue / ( K0 + 1 )

The composite acidity constant of carbonic acid is then given by:

 (13b) pKa  =  – log K1

The interrelation between the three equilibrium constants (K1, K0, Ktrue) can be portrayed as follows:

Kinetic and Thermodynamic Parameters

For the kinetic rates the following estimates are given (at standard conditions: 25, 1 atm):

 k12 = 5·1010 M-1 s-1 Pocker & Blomkquist3 k21 = 1·107 s-1 Pocker & Blomkquist3 ka = kH2CO3 ≈ 18 s-1 Stumm & Morgan4 kb = kCO2 ≈ 0.04 s-1 Stumm & Morgan4

[Note: For most rates a parameter range – rather than a definite value – is given in literature. For example, in Stumm & Morgan we find kH2CO3 = 10 … 20 s-1 and kCO2 = 0.025 … 0.04 s-1.]

The numerical values of the kinetic rates in the table reveal the clear separation (or broad gap) between fast reactions (k12, k21) and slow reactions (ka, kb). Since ka is an upper bound of k23 and kb is an upper bound of k32 the assumption in 5 is fully justified.

Based on these four kinetic parameters we are able to calculate the three equilibrium constants:5

 (14a) K0 = ka/kb = 450 ⇔ log K0 = 2.65 (14b) Ktrue = k21/k12 = 2.0·10-4 M ⇔ log Ktrue = -3.7 (14c) K1 = Ktrue / ( K0 + 1 ) = 4.4·10-7 M ⇔ log K1 = -6.35

In fact, these are the “official” values of Ktrue and K1 presented already here.

Notes and References

1. This is not a reaction formula for H2CO3*; it is only an abbreviation for H2CO3*

2. A PowerPoint presentation of this topic is here

3. Pocker, Y., D. Bjorkquist: Stopped-flow studies of carbon dioxide hydration and bicarbonate dehydration in H2O and D2O acid–base and metal ion catalysis. J. Am. Chem. Soc. 99, 6537–6543, 1977  2

4. W. Stumm and J.J. Morgan: Aquatic Chemistry, Chemical Equilibria and Rates in Natural Waters, 3rd ed. John Wiley & Sons, Inc., New York, 1996  2

5. Please note the different units for K0 on one hand and for Ktrue and K1 on the other hand.


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# Electromagnatism Definition and 56 Discussions

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions (commonly called forces) in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy, the weak force and electromagnetic force are unified as a single electroweak force.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. The electromagnetic attraction between atomic nuclei and their orbital electrons holds atoms together. Electromagnetic forces are responsible for the chemical bonds between atoms which create molecules, and intermolecular forces. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms. Electromagnetism is very widely used in modern technology, and electromagnetic theory is the basis of electric power engineering and electronics including digital technology.
There are numerous mathematical descriptions of the electromagnetic field. Most prominently, Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.
The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.

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text: Perimeter = a+b+2c. Welcome to The Calculating the Perimeter and Area of Trapezoids (Smaller Numbers) (A) Math Worksheet from the Measurement Worksheets Page at Math-Drills.com. What are the lengths of the bases in meters? Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = 36 cm. : After working out the answer of each of the next questions, click adjacent button of see the correct answer. perimeter of trapezoid = upper base + lower base + left side + right side. Lorsque toutes les informations sont disponibles, ce calcul est aisé.Dans le cas contraire, le calcul du périmètre nécessite plusieurs étapes intermédiaires afin de trouver les dimensions manquantes. Area and perimeter formula sheets these area and circuit sheets create a formula reference sheet that is a great base for students. It may be printed, downloaded or saved and used in your classroom, home school, or other educational … Example: If the length of parallel sides of a regular trapezium is 10 cm and 12 cm, and the length of non-parallel sides is equal to 5 cm each. 1. Then, find the sum of all of the sides. There are certain properties of trapezoids that identify them as trapezoids-The base angles and the diagonals of an isosceles trapezoid are equal. The formula for the perimeter of a trapezoid is base 1 + base 2 + side a + side b, as seen in the figure below: You need more measurements for a trapezoid, as it is a more complex form in which all sides can have a different length. Therefore, perimeter of a trapezoid is a sum of lengths of all 4 sides. Isosceles Trapezoid Perimeter. Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what is its Perimeter? Problem 2: A trapezoidal floor plan’s perimeter is measured to be 12 meters. . Perimeter. Welcome to The Calculating the Perimeter and Area of Trapezoids (Larger Numbers) (A) Math Worksheet from the Measurement Worksheets Page at Math-Drills.com. Study math with us and make sure that "Mathematics is easy!" Calculate the area of a trapezoid whose height is 5 cm and the bases are 14 cm and 10 cm. Code logic − The code will use 5 variables in as all sides of trapezium and one for the perpendicular distance between the two parallel side. Calculate the area and perimeter of a trapezoid. Order. Perimeter of a trapezoid is defined as the sum of the length of the bases and legs of the trapezoid is calculated using Perimeter=Side A+Side B+Side C+Side D.To calculate Perimeter of a trapezoid, you need Side A (a), Side B (b), Side C (c) and Side D (d).With our tool, you need to enter the respective value for Side A, Side B, Side C and Side D and hit the calculate button. Area = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides. Perimeter of a trapezoid. Therefore a trapezoid with sides $$AB, BC, CD \text{ and}\text { AD}$$ has a perimeter formula that can be written as $Perimeter = AB + BC + CD + AD$ Think Tank. To find the perimeter of this trapezoid, first find the length of the larger base. P = 32 cm. Perimeter of a Trapezoid Teaching Resources @ www.tutoringhour.com 1) Perimeter = 2) Perimeter = 3) Perimeter = 4) Perimeter = 5) Perimeter = 6) Perimeter = 7) Perimeter = 39 in 50 yd 17 ft 8) Perimeter = 24 yd 54 ft 53 in 9) Perimeter = 40 ft 26 in 32 yd Find the perimeter of each trapezoid. and an altitude of 4 m. Its two bases have a ratio of 4:5. We have moved all content for this concept to for better organization. About. The perimeter of a trapezoid is the sum of all its sides. And perimeter, which is the measure of the outer edge of a shape. 2. Before we step into practical C Program to find Area of a Trapezoid example, Let see the definitions and formulas behind the Median and Area of a Trapezoid. The perimeter of the trapezoid is 36. Practice Question: Calculate perimeter of trapezoid for the following problems: N.B. Sign in Log in Log out. Geometry Math. Let b 1 = 14 cm and b 2 = 10 cm. If you wanted to go into engineering then a depth understanding of the concept is necessary. Then find the perimeter. Since they have no relationship to each other, there is no formula for it. Example 2. This math worksheet was created on 2015-09-08 and has been viewed 20 times this week and 163 times this month. Library. Solution. A trapezoid is a four-sided polygon, or “quadrilateral”, that has at least one set of parallel sides.There are two types of sides in a trapezoid: legs and bases. Its sides together to your site: perimeter of trapezoid perimeter of trapezoid is frequently used in various computations., first find the perimeter of trapezoid = upper base + left side + right side computations! 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