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A computer retailer sells only TFT and LCD monitors. In the graph abov

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A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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26 Dec 2014, 08:37
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Tough and Tricky questions: Word Problems.

A computer retailer sells only TFT and LCD monitors. In the graph above, the x-axis represents the day of the week and the y-axis represents the number of monitors sold. On which day was the ratio of the number of LCD monitors sold to the total number of monitors sold the greatest?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday

Kudos for a correct solution.

Attachment:

2014-12-26_1936.png [ 7.5 KiB | Viewed 3521 times ]

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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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26 Dec 2014, 09:42
To calculate the share of LCD monitors in total monitor sales, we first need to determine the number of LCD sales. Note that the total number of display sales is directly shown in the graph, but the number of LCD display sales needs to be calculated as the difference of total monitors and TFT monitors.

We get the following values:
$$Mon: \frac{10}{18}, Tue: \frac{10}{22}, Wed: \frac{12}{24}, Thu: \frac{10}{26}, Fri: \frac{12}{26}$$.

Now we can compare the figures and see that all values, except of Wednesday's number are smaller than $$\frac{1}{2}$$. Answer C it is.
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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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26 Dec 2014, 17:42
Bunuel wrote:

Tough and Tricky questions: Word Problems.

A computer retailer sells only TFT and LCD monitors. In the graph above, the x-axis represents the day of the week and the y-axis represents the number of monitors sold. On which day was the ratio of the number of LCD monitors sold to the total number of monitors sold the greatest?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday

Kudos for a correct solution.

Attachment:
2014-12-26_1936.png

LCD sales on each day = Mon-8. Tue-10 Wed-12 Thu-10 Fri-12

Ratio: Monday - 8/18
Tuesday - 10/22
Wednesday - 12/24
Thursday - 10/26
Friday - 12/26

Simplifying that Wednesday has the greatest ratio of LCD sales out of total sales

Ans C
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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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27 Dec 2014, 00:50
Since we want the ratio of LCD/Total Tv to be highest we need balance maximizing the LCD TV sales and keeping the total TV sales low.

If you observe the graph keenly you will realize that Wednesday is the only day when LCD Sales are equal to 50% of total sales. All rest days the % is much lower. Hence the ratio will be highest for Wednesday. Answer is C.
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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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01 Jan 2015, 11:14
A computer monitor dealer sells only TFT and LCD monitors. Based on the graph in the attachment , where the X axis represents the day of the week and the Y axis represents the amount of monitors sold , on which day was the share of LCD monitor sales the greatest.

a)Monday
b)Tuesday
c)Wednesday
d)Thursday
e)Friday

Attachments

pic.docx [24.17 KiB]

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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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01 Jan 2015, 12:28
a-computer-retailer-sells-only-tft-and-lcd-monitors-in-the-graph-abov-190775.html
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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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02 Jan 2015, 02:33
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No calculations done. Refer diagram below:

Attachment:

2014-12-26_1936.png [ 22.07 KiB | Viewed 3064 times ]

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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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02 Jan 2015, 05:19
sunita123 wrote:
A computer monitor dealer sells only TFT and LCD monitors. Based on the graph in the attachment , where the X axis represents the day of the week and the Y axis represents the amount of monitors sold , on which day was the share of LCD monitor sales the greatest.

a)Monday
b)Tuesday
c)Wednesday
d)Thursday
e)Friday

PLEASE SEARCH BEFORE POSTING! Thank you.
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Re: A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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08 Jan 2015, 09:37
Bunuel wrote:

Tough and Tricky questions: Word Problems.

A computer retailer sells only TFT and LCD monitors. In the graph above, the x-axis represents the day of the week and the y-axis represents the number of monitors sold. On which day was the ratio of the number of LCD monitors sold to the total number of monitors sold the greatest?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday

Kudos for a correct solution.

Attachment:
2014-12-26_1936.png

OFFICIAL SOLUTION:

The number of LCD sales is the difference between total sales and TFT sales.

For each day of the week, we can determine the ratio of the number of LCD monitors sold to the total number of monitors sold:
Monday: (18 – 10)/18 = 4/9
Tuesday: (22 – 12)/22 = 5/11
Wednesday: (24 – 12)/24 = 1/2
Thursday: (26 – 16)/26 = 5/13
Friday: (26 – 14)/26 = 6/13.

The greatest fraction is 1/2, so the ratio on Wednesday is the largest.

The correct answer is choice (C).
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A computer retailer sells only TFT and LCD monitors. In the graph abov  [#permalink]

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18 Oct 2018, 04:56
For this question no calculation but just a conceptual understanding of fractions is necessary:

The question asks us to find the maximum ratio of $$\frac{LCD}{(LCD+TFT)}$$.
How do we maximise this fraction? By minimising the denominator, i.e. LCD+TFT, and maximising the numerator, i.e. LCD.
Hence, what we should be looking for in the graph, is a large difference between total sales and TFT (=LCD sales) and a low value for TFT sales. Wednesday fulfills our condition and is the answer.

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A computer retailer sells only TFT and LCD monitors. In the graph abov   [#permalink] 18 Oct 2018, 04:56
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Excitation functions have been measured for complex fragment emission from the compound nucleus {sup 98}Mo, produced by the reaction of {sup 86}Kr with {sup 12}C. Mass asymmetric fission barriers have been obtained by fitting the excitation functions with a transition state formalism. The extracted barriers are {approximately} 5.7 MeV higher, on average, than the calculations of the Rotating Finite Range Model (RFRM). These data clearly show an isospin dependence of the conditional barriers when compared with the extracted barriers from {sup 90}Mo and {sup 94}Mo. Eleven different liquid/liquid extractants were synthesized based upon the chelating moieties 3,2-HOPO and 3,4-HOPO; additionally, two liquid/liquid extractants based upon the 1,2-HOPO chelating moiety were obtained for extraction studies. The Pu(IV) extractions, quite surprisingly, yielded results that were very different from the Fe(III) extractions. The first trend remained the same: the 1,2-HOPOs were the best extractants, followed closely by the 3,2-HOPOs, followed by the 3,4-HOPOs; but in these Pu(IV) extractions the 3,4-HOPOs performed much better than in the Fe(III) extractions. 129 refs. digital.library.unt.edu/ark:/67531/metadc685938/
A 1 MEGAWATT POLYPHASE BOOST CONVERTER-MODULATOR FOR KLYSTRON PULSE APPLICATION
This paper describes electrical design criteria and first operational results a 140 kV, 1 MW average, 11 MW peak, zero-voltage-switching 20 kHz polyphase bridge, boost converter/modulator for klystron pulse application. The DC-DC converter derives the buss voltages from a standard 13.8 kV to 2300 Y substation cast-core transformer. Energy storage and filtering is provided by self-clearing metallized hazy polypropylene traction capacitors. Three ''H-Bridge'' Insulated Gate Bipolar Transistor (IGBT) switching networks are used to generate the polyphase 20 kHz transformer primary drive waveforms. The 20 kHz drive waveforms are chirped the appropriate duration to generate the desired klystron pulse width. PWM (pulse width modulation) of the individual 20 kHz pulses is utilized to provide regulated output waveforms with adaptive feedforward and feedback techniques. The boost transformer design utilizes amorphous nanocrystalline material that provides the required low core loss at design flux levels and switching frequencies. Resonant shunt-peaking is used on the transformer secondary to boost output voltage and resonate transformer leakage inductance. With the appropriate transformer leakage inductance and peaking capacitance, zero-voltage-switching of the IGBT's is attained, minimizing switching losses. A review of these design parameters and the first results of the performance characteristics will be presented. digital.library.unt.edu/ark:/67531/metadc720900/
A-01 metals in stormwater runoff evaluation
As a part of the A-01 investigation required by the NPDES permit, an investigation was performed to ascertain the concentrations of metals specifically copper (Cu), lead (Pb), and zinc (Zn) in stormwater being discharged through the outfall. This information would indicate whether all water being discharged would have to be treated or if only a portion of the discharged stormwater would have to be treated. A study was designed to accomplish this. The first goal was to determine if the metal concentrations increased, decreased, or remained the same as flow increased during a rain event. The second goal was to determine if the concentrations in the storm water were due to dissolved. The third goal was to obtain background data to ascertain if effluent credits could be gained due to naturally occurring metals.Samples from this study were analyzed and indicate that the copper and lead values increase as the flow increases while the zinc values remain essentially the same regardless of the flow rate. Analyses of samples for total metals, dissolved metals, TSS, and metals in solids was complicated because in all cases metals contamination was found in the filters themselves. Some conclusions can be derived if this problem is taken into account when analyzing the data. Copper concentrations in the total and dissolved fractions as well as the TSS concentrations followed the hydrograph at this outfall but the copper in solids concentration appeared to peak in the first flush and decline to nondetectable rapidly over the course of the storm event. Lead was present in the total analysis but not present in the dissolved fraction or the solids fraction of the samples. The data for zinc was interesting in that the dissolved fractions were higher than the total fraction in three out of four samples. This is probably due to the high zinc concentrations on the filters being transferred to the dissolved faction of the sample. (Abstract Truncated) digital.library.unt.edu/ark:/67531/metadc695366/
1 MeV electron irradiation of solid Xe nanoclusters in Al : an in-situ HRTEM study.
Thin film samples of a simple embedded nanocluster system consisting of solid Xe precipitates in Al have been subjected to 1 MeV electron irradiation in a high-voltage electron microscope. High-resolution images have been recorded on videotape in order to monitor the changes to the system resulting from the passage of electrons through the film. Inspection of the video recordings (in some cases frame-by-frame) reveals that complex, rapid processes occur under the electron beam. These include, movement of small clusters, coalescence of neighboring clusters, shape changes, the apparent melting and resolidification of the Xe, and the creation and annealing of extended defects within the Xe lattice. A tentative interpretation of some of the observations is presented in terms of the electron-induced displacement processes at the surface of the clusters. digital.library.unt.edu/ark:/67531/metadc738815/
1 mil gold bond wire study.
In microcircuit fabrication, the diameter and length of a bond wire have been shown to both affect the current versus fusing time ratio of a bond wire as well as the gap length of the fused wire. This study investigated the impact of current level on the time-to-open and gap length of 1 mil by 60 mil gold bond wires. During the experiments, constant current was provided for a control set of bond wires for 250ms, 410ms and until the wire fused; non-destructively pull-tested wires for 250ms; and notched wires. The key findings were that as the current increases, the gap length increases and 73% of the bond wires will fuse at 1.8A, and 100% of the wires fuse at 1.9A within 60ms. Due to the limited scope of experiments and limited data analyzed, further investigation is encouraged to confirm these observations. digital.library.unt.edu/ark:/67531/metadc827545/
1 nA beam position monitoring system
A system has been developed at Jefferson Lab for measuring transverse position of very low current beams delivered to the Experimental Hall B of the Continuous Electron Beam Accelerator Facility (CEBAF). At the heart of the system is a position sensitive cavity operating at 1497 MHz. The cavity utilizes a unique design which achieves a high sensitivity to beam position at a relatively low cavity Q. The cavity output RF signal is processed using a down-converter and a commercial lock-in amplifier operating at 100 kHz. The system interfaces with a VME based EPICS control system using the IEEE, 488 bus. The main features of the system are simple and robust design, and wide dynamic range capable of handling beam currents from 1 nA to 1000 nA with an expected resolution better than 100 {mu}m. This paper outlines the design of the system. digital.library.unt.edu/ark:/67531/metadc675723/
1 Outreach, Education and Domestic Market Enhancement 2 Export Promotion and Assistance
Geothermal Energy Association supports the US geothermal industry in its efforts to bring more clean geothermal energy on-line throughout the world. Activities designed to accomplish this goal include: (1) developing and maintaining data bases, web pages, (2) commissioning of special studies and reports, (3) preparing, printing and distributing brochures and newsletters, (4) developing exhibits and displays, and participating in trade shows, (5) designing, producing and disseminating audio-video materials, (6) monitoring and coordinating programs carried out by US DOE and other Federal agencies, (7) holding workshops to facilitate communication between researchers and industry and to encourage their recognition of emerging markets for geothermal technology, (8) attending conferences, making speeches and presentation, and otherwise interacting with environmental and other renewable energy organizations and coalitions, (9) hosting events in Washington, DC and other appropriate locations to educate Federal, State and local representatives, environmental groups, the news media, and other about the status and potential of geothermal energy, (10) conducting member services such as the preparation and distribution of a member newsletter related to operating and maintaining s useful and viable association, and (11) performing similar kinds of activities designed to inform others about geothermal energy. The activities of the export promotion aim to assist industry in accomplishing the goal of successfully penetrating and developing energy in country with existing geothermal resources and a desire to develop them. Activities including in export promotion are: (1)needs analysis and assessment involve monitoring the progress of developing markets and projects overseas and working with US industry to determine what future activities by GEA would be of greatest assistance, (2) outreach includes the preparation and dissemination of brochures and videos for foreign professionals, officials and decision-makers as well as presentations of information of the geothermal technology and the capabilities of the US geothermal industry, (3) Market conditioning involves first, evaluating the market and challenges for conducting business successfully in a country followed by appropriate training or technical assistance, (4) Market developing includes activities conducted to assist industry in developing the market for sales of services and technology, including direct and reverse trade missions, support for industry to participate in conferences overseas to sell goods and services, and other activities. digital.library.unt.edu/ark:/67531/metadc783392/
A 1- to 5-MW, RCS-based, short-pulse spallation neutron source
Two accelerator configurations, the linac/compressor ring scheme and the linac/RCS scheme, are commonly used to provide the proton beam power for a short-pulse spallation neutron source. In one configuration, a full-power linac provides the beam power and a compressor ring shortens the pulse length from 1-ms down to 1 {micro}s. In the other, rapid cycling synchrotrons (RCSs) provide the beam power and also shorten the pulse length. A feasibility study of a staged approach to a 5-MW proton source utilizing RCS technology, allowing intermediate operation at 1 MW, was performed at ANL and is presented in this paper. This study is complementary to a study in progress at ORNL based on a linac and an accumulator ring. The 1-MW facility consists of a 400-MeV injector linac that delivers 0.5-mA time-averaged current, a synchrotron that accelerates the beam to 2 GeV at a 30-Hz rate, and two neutron-generating target stations. In the second phase, the 2-GeV beam is accelerated to 10 GeV by a larger RCS, increasing the facility beam power to 5 MW. digital.library.unt.edu/ark:/67531/metadc680327/
1-watt composite-slab Er:YAG laser. Revision 1
A diode-side-pumped discrete-optic Er{sup 3+} :YAG laser employs pump-light coupling through a sapphire plate diffusion-bonded to the laser slab, removing heat directly at the pump face of the slab instead of requiring conduction through to its far side. This lowers the temperature in the gain region and gives reduced thermal lensing, which produces exceptional beam quality (M{sup 2} {approx} 1.3) at output powers {approx} 0.3 Watt. Powers above 1 Watt have been demonstrated with peak slope efficiencies {approx}20%. The novel architecture is also applicable to other side-pumped lasers. digital.library.unt.edu/ark:/67531/metadc696997/
2-1/2-D electromagnetic modeling of nodular defects in high-power multilayer optical coatings
Advances in the design and production of high damage threshold optical coatings for use in mirrors and polarizers have been driven by the design requirements of high-power laser systems such as the proposed 1.8-MJ National Ignition Facility (NIF) and the prototype 12- kJ Beamlet laser system. The present design of the NIF will include 192 polarizers and more than 1100 mirrors. Currently, the material system of choice for high-power multilayer optical coatings with high damage threshold applications near 1.06 {mu}m are e-beam deposited HfO{sub 2}/Si0{sub 2} coatings. However, the optical performance and laser damage thresholds of these coatings are limited by micron-scale defects and insufficient control over layer thickness. In this report, we will discuss the results of our 2-1/2-D finite-element time- domain (FDTD) EM modeling effort for rotationally-symmetric nodular defects in multilayer dielectric HR coatings. We have added a new diagnostic to the 2-1/2-D FDTD EM code, AMOS, that enables us to calculate the peak steady-state electric fields throughout a 2-D planar region containing a 2-D r-z cross-section of the axisymmetric nodular defect and surrounding multilayer dielectric stack. We have also generated a series of design curves to identify the range of loss tangents for Si0{sub 2} and HfO{sub 2} consistent with the experimentally determined power loss of the HR coatings. In addition, we have developed several methods to provide coupling between the EM results and the thermal-mechanical simulation effort. digital.library.unt.edu/ark:/67531/metadc684881/
(02.2) Scoping experiments; (02.3) long-term corrosion testing and properties evaluation of candidate waste package basket material
The work described in this activity plan addresses Information Need 2.7.3 of the Yucca Mountain Site Characterization Plan (l), which reads Determination that the design criteria in lOCFR60.130 through 60.133 and any appropriate additional design objectives pertaining to criticality control have been met. This work falls under section WBS 1.2.2.5 2 (Basket Materials) of WBS 1.2.2.5 (Waste Package Materials) in the Work Breakdown Structure of the Yucca Mountain Site Characterization Project. digital.library.unt.edu/ark:/67531/metadc666681/
The 2.3 {angstrom} crystal structure of cholera toxin B subunit pentamer: Choleragenoid
Cholera toxin, a heterohexameric AB{sub 5} enterotoxin released by Vibrio cholera, induces a profuse secretory diarrhea in susceptible hosts. Choleragenoid, the B subunit pentamer of cholera toxin, directs the enzymatic A subunit to its target by binding to GM{sub 1} gangliosides exposed on the luminal surface of intestinal epithelial cells. We have solved the crystal structure of choleragenoid at 2.3 {Angstrom} resolution by combining single isomorphous replacement with non-crystallographic symmetry averaging. The structure of the B subunits, and their pentameric arrangement, closely resembles that reported for the intact holotoxin (choleragen), the heat-labile enterotoxin from E. coli, and for a choleragenoid-GM{sub 1} pentasaccharide complex. In the absence of the A subunit the central cavity of the B pentamer is a highly solvated channel. The binding of the A subunit or the receptor pentasaccharide to choleragenoid has only a modest effect on the local stereochemistry and does not perceptibly alter the subunit interface. digital.library.unt.edu/ark:/67531/metadc671655/
There are five 2.5 MHz ferrite cavities (h = 28) in the Main Injector with an R/Q of 500 that are presently used for coalescing for the Tevatron. For use with the Fermilab Recycler, feedforward (FF) beam loading compensation (BLC) is required on these cavities because they will be required to operate at a net of 2 kV. Under current Recycler beam conditions, the beam-induced voltage is of this order. Recently a system using a digital bucket delay module operating at 53 MHz (h = 588) was used to produce a one-turn-delay feedforward signal. This signal was then combined with the low level RF signal to the 2.5 MHz cavities to cancel the beam induced voltage. During current operation they have shown consistently to operate with over a 20 dB reduction in beam loading. digital.library.unt.edu/ark:/67531/metadc734139/
The 2.6 Angstrom resolution structure of Rhodobacter capsulatus bacterioferritin with metal-free dinuclear site and heme iron in a crystallographic 'special position'
A 2.14 ms candidate optical pulsar in SN1987A: Ten years after
We have monitored Supernova 1987A in optical/near-infrared bands from a few weeks following its birth until the present time in order to search for a pulsar remnant. We have found an apparent pattern of emission near the frequency of 467.5 Hz - a 2.14 ms pulsar candidate, first detected in data taken on the remnant at the Las Campanas Observatory (LCO) 2.5-m Dupont telescope during 14-16 Feb. 1992 UT. We detected further signals near the 2.14 ms period on numerous occasions over the next four years in data taken with a variety of telescopes, data systems and detectors, at a number of ground- and space-based observatories. The sequence of detections of this signal from Feb. 92 through August `93, prior to its apparent subsequent fading, is highly improbable (< 10{sup -10} for any noise source). We also find evidence for modulation of the 2.14 ms period with a {approx}1,000 s period which, when taken with the high spindown of the source (2-3 x 10{sup -10} Hz/s), is consistent with precession and spindown via gravitational radiation of a neutron star with a non- axisymmetric oblateness of {approx}10{sup -6}, and an implied gravitational luminosity exceeding that of the Crab Nebula pulsar by an order of magnitude. digital.library.unt.edu/ark:/67531/metadc690450/
2-D and 3-D Elastic Modeling with Shared Seismic Models
Several elastic models, both 2-D and 3-D, are being built for use in calculating synthetic elastic seismic data. The models will be made available to the research community, along with the synthetic data that are being calculated from them. These shared models have been proposed or contributed by participants in a collaborative industry, national laboratory, and university research project. The purpose of the modeling is to provide synthetic data to better understand elastic wave propagation and the effects of structural and stratigraphic complexities. The 2-D models are easier to design and change and synthetic calculations can be run relatively quickly in them. It will be possible to alter their layer properties and calculate time-lapse data sets from them. Field data will be available to accompany many of the 2-D models. 3-D models are more realistic, but more difficult to design and change. They also require considerably more computing resources to calculate synthetic data from them. A new 3-D model is being designed, and will be used for computing synthetic elastic data. digital.library.unt.edu/ark:/67531/metadc742716/
2-D electric fields and drifts near the magnetic separatrix in divertor tokamaks
A 2-D calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses anomalous radial diffusion, including perpendicular ion momentum, and classical cross-field drifts transport. Parallel and perpendicular currents yield a self-consistent electrostatic potential on both sides of the magnetic separatrix. Outside the separatrix, the simulation extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms - from viscosity, charge-exchange and poloidal damping, inertia, and {triangledown}B - contribute to the determining the potential. The model rigorously enforces cancellation of gyro-viscous and magnetization terms from the transport equations. The results emphasize the importance of E x B particle flow under the X-point which depends on the sign of the toroidal magnetic field. Radial electric field (E{sub y}) profiles at the outer midplane are small with weak shear when high L-mode diffusion coefficients are used and are large with strong shear when smaller H-mode diffusion coefficients are used. The magnitude and shear of the electric field (E{sub y}) is larger both when the core toroidal rotation is co-moving with the inductive plasma current and when the ion {triangledown}B-drift is towards the single-null X-point. digital.library.unt.edu/ark:/67531/metadc667325/
2-D Finite Element Cable and Box IEMP Analysis
A 2-D finite element code has been developed for the solution of arbitrary geometry cable SGEMP and box IEMP problems. The quasi- static electric field equations with radiation- induced charge deposition and radiation-induced conductivity y are numerically solved on a triangular mesh. Multiple regions of different dielectric materials and multiple conductors are permitted. digital.library.unt.edu/ark:/67531/metadc669433/
2-D image segmentation using minimum spanning trees
This paper presents a new algorithm for partitioning a gray-level image into connected homogeneous regions. The novelty of this algorithm lies in the fact that by constructing a minimum spanning tree representation of a gray-level image, it reduces a region partitioning problem to a minimum spanning tree partitioning problem, and hence reduces the computational complexity of the region partitioning problem. The tree-partitioning algorithm, in essence, partitions a minimum spanning tree into subtrees, representing different homogeneous regions, by minimizing the sum of variations of gray levels over all subtrees under the constraints that each subtree should have at least a specified number of nodes, and two adjacent subtrees should have significantly different average gray-levels. Two (faster) heuristic implementations are also given for large-scale region partitioning problems. Test results have shown that the segmentation results are satisfactory and insensitive to noise. digital.library.unt.edu/ark:/67531/metadc628011/
2-D Imaging of Electron Temperature in Tokamak Plasmas
By taking advantage of recent developments in millimeter wave imaging technology, an Electron Cyclotron Emission Imaging (ECEI) instrument, capable of simultaneously measuring 128 channels of localized electron temperature over a 2-D map in the poloidal plane, has been developed for the TEXTOR tokamak. Data from the new instrument, detailing the MHD activity associated with a sawtooth crash, is presented. digital.library.unt.edu/ark:/67531/metadc786989/
2-D linear motion system. Innovative technology summary report
The US Department of Energy's (DOE's) nuclear facility decontamination and decommissioning (D and D) program requires buildings to be decontaminated, decommissioned, and surveyed for radiological contamination in an expeditious and cost-effective manner. Simultaneously, the health and safety of personnel involved in the D and D activities is of primary concern. D and D workers must perform duties high off the ground, requiring the use of manlifts or scaffolding, often, in radiologically or chemically contaminated areas or in areas with limited access. Survey and decontamination instruments that are used are sometimes heavy or awkward to use, particularly when the worker is operating from a manlift or scaffolding. Finding alternative methods of performing such work on manlifts or scaffolding is important. The 2-D Linear Motion System (2-D LMS), also known as the Wall Walker{trademark}, is designed to remotely position tools and instruments on walls for use in such activities as radiation surveys, decontamination, and painting. Traditional (baseline) methods for operating equipment for these tasks require workers to perform duties on elevated platforms, sometimes several meters above the ground surface and near potential sources of contamination. The Wall Walker 2-D LMS significantly improves health and safety conditions by facilitating remote operation of equipment. The Wall Walker 2-D LMS performed well in a demonstration of its precision, accuracy, maneuverability, payload capacity, and ease of use. Thus, this innovative technology is demonstrated to be a viable alternative to standard methods of performing work on large, high walls, especially those that have potential contamination concerns. The Wall Walker was used to perform a final release radiological survey on over 167 m{sup 2} of walls. In this application, surveying using a traditional (baseline) method that employs an aerial lift for manual access was 64% of the total cost of the improved technology. However, for areas over approximately 600 m{sup 2}, the Wall Walker would cost less than the baseline. Using the Wall Walker 2-D LMS, ALARA exposure and worker safety is improved, and there is potential for increased productivity. This innovative technology performed better than the baseline by providing real-time monitoring of the tool or instrument position. Also, the Wall Walker 2-D LMS can traverse any two-dimensional path at constant speeds of up to 18.3 linear meters per minute (60 linear feet per minute). The survey production rate for the innovative technology was about 0.6 m{sup 2}/min (6 ft{sup 2}/min); the baseline production rate was approximately 0.3 m{sup 2}/min (3 ft{sup 2}/min), using the same surveying instrument and maximum scanning rate. digital.library.unt.edu/ark:/67531/metadc682357/
A 2-D Pore-Network Model of the Drying of Single-Component Liquids in Porous Media
The drying of liquid-saturated porous media is typically approaching using macroscopic continuum models involving phenomenological coefficients. Insight on these coefficients can be obtained by a more fundamental study at the pore- and pore-network levels. In this report, a model based on pore-network representation of porous media that accounts for various process at the pore-scale is presented. These include mass transfer by advection and diffusion in the gas phase, viscous flow in liquid and gas phases and capillary effects at the gas-liquid menisci in the pore throats. digital.library.unt.edu/ark:/67531/metadc709400/
A 2-D Self-Consistent DSMC Model for Chemically Reacting Low Pressure Plasma Reactors
This paper will focus on the methodology of using a 2D plasma Direct Simulation Monte Carlo technique to simulate the species transport in an inductively coupled, low pressure, chemically reacting plasma system. The pressure in these systems is typically less than 20 mtorr with plasma densities of approximately 10{sup 17} {number_sign}/m{sup 3} and an ionization level of only 0.1%. This low ionization level tightly couples the neutral, ion, and electron chemistries and interactions in a system where the flow is subsonic. We present our strategy and compare simulation results to experimental data for Cl{sub 2} in a Gaseous Electronics Conference (GEC) reference cell modified with an inductive coil. digital.library.unt.edu/ark:/67531/metadc717421/
2-D Simulations of Drainage Winds and Diffusion Compared to Observations
A vertically integrated dynamical drainage flow model is developed from conservation equations for momentum and mass in a terrain-following coordinate system. Wind fields from the dynamical model drive a Monte Carlo transport and diffusion model. The model needs only topographic data, an Eulerian or Lagrangian time scale and a surface drag coefficient for input data, and can be started with a motionless atmosphere. Model wind and diffusion predictions are compared to observations from the rugged Geysers CA area. Model winds generally agree with observed surface winds, and in some cases may give better estimates of area-averaged flow than point observations. Tracer gas concentration contours agree qualitatively with observed contours, and point predictions of maximum concentrations were correctly predicted to within factors of 2 to 10. Standard statistical tests of model skill showed that the accuracy of the predictions varied significantly from canyon to canyon in the Geysers are a. Model wind predictions are also compared to observations from the Savannah River Plant of SC which has gently rolling terrain. The model correctly simulated the slower development of drainage winds and slower deepening of the drainage layer in the Savannah River Valley, relative to the Geysers CA simulations. The SC simulations and observations suggest that drainage winds are more frequent in the southeast United States than is generally recognized. They may be responsible for some of the errors in air pollution concentration predictions made by Gaussian models which assume homogeneous winds and turbulence. digital.library.unt.edu/ark:/67531/metadc715610/
2-Fold G.M. Coincidence Unit
Report containing a diagram of a coincidence unit, outlining resistor values and other technical specifications. digital.library.unt.edu/ark:/67531/metadc100860/
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# what is the capacitance and inductance of an ideal wire?

I am reading a magazine for acoustics, one article is about the choice of speaker wire. The article said the ideal speaker wire should has no resistance, capacitance and inductance. I understand that for the low resistance in ideal case but doubts on the capacitance and inductance. We are driving in the speaker with AC signal, says ideal sinusoidal wave, in the text, it is given that the voltage drop on the capacitor which is connected to the AC power should be

$$v_c = I_{max}X_C\sin\omega t$$

where $X_C=1/(\omega C)$. My understanding is for ideal wire, the voltage potential on a short section on the wire should be zero, so we should have $v_c=0$ so does it mean $C\to \infty$ when $\omega\neq 0$?

Similar reasoning but on inductance, we have $$v_L = -I_{max}X_L\sin\omega t$$ so for ideal wire, $X_L$ should be zero. Are those reasoning corret?

This would actually be easier to answer over at the EE stackexchange site since there is a handy schematic editor built in.

First, note that, by speaker wire, we're actually referring to a speaker cable; in this case, a pair of wires.

For each wire, we can assign a series resistance and inductance (per foot), i.e., the $R$ and $L$ of each wire is in series with the load.

Since we do not want a voltage drop from one end of the wire to the other - we want all of the source voltage to appear across the load - the ideal case is that the resistance and inductance is zero, i.e., there is zero voltage drop from one end of the wire to the other.

Now, since we have a pair of wires, we can also define a mutual capacitance (per foot) between the wires. This capacitance appears in parallel with the load. If the capacitance is non-zero, higher frequency currents will be somewhat shunted around the load. So, ideally, the cable capacitance is zero, i.e., there is zero current shunted around the load.

• To be technically accurate with a transmission lumped line model, there should also be differential (parallel) conductance between the two wires. – K7PEH Apr 13 '15 at 16:27

Capacitance approaches infinity when the distance between plates approaches 0. A wire can be thought of as an infinite line of capacitors that have no spacing between them, so the capacitance of each of these capacitors is infinity.

Additionally, the equation for reactance, X, in terms of capacitance C is 1/ωC. We can conclude from this that X approaches 0 as C approaches infinity.


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# Determination of percentage of Methanol in an Alcohol based hand sanitiser [closed]

Note: I am looking for advice on a chemical test - not a sermon.
I expect that this is entirely on topic in this forum, downvotes and sermon comment notwithstanding.

More than about 5% of Methanol in alcohol based hand sanitisers indicates that corners have been cut during manufacture and that the product should be avoided.

I'm looking for an easy test to determine the approximate percentage of Methanol in an Ethanol / Methanol hand sanitiser mix. Many hand sanitisers may contain small percentages of Methanol (typically in the 1% - 5% range) and this is acceptable. Anything over 5% I'd like to avoid. Much over 5% (say 10% +) I'd like to be very clearly distinguished. If actual approximate percentage can be indicated, so much the better.

Ideally I'd like a test with either low cost, simple to use, readily available non-hazardous reagents (one can hope) or failing that, something that can be prepackaged for easy use by the unskilled.

In web searches I found a range of tests for Methanol but most were not very quantitative and most were not intended to work in an ethanol-methanol mixture.

Some guy y'know said:

Using disinfectants outside of a heathcare environment is still nonsense in the year 2020. Using disinfectants of questionable provenience is simply hazardous. Don´t do it.

The use of hand sanitisers is well covered in recommendation documents from regulatory authorities in many administrations and by internationally relevant bodies. Sanitisers are sold under regulatory guidelines which if followed would guarantee their safety when used appropriately. In the US many out of specification brands are being sold which are indistinguishable from those which comply. Several of the largest US sellers have been selling out of spec product. There is no way to determine provenance based on labelling.

While the use of soap and water is often a good or even superior solution it is incorrect to suggest that the use of sanitisers in general applications is nonsense.

In this instance I am interested NOT in their efficacy or application but re their specific bonafides with respect to a crucial component which is known to be used in excessive and illegal amounts in some cases.

I'm an engineer. Sanitisers are sold by a wide range of manufacturers and repackagers. I read labels, note sources, note claimed contents and viscosities and residence times and more.

• Using disinfectants outside of a heathcare environment is still nonsense in the year 2020. Using disinfectants of questionable provenience is simply hazardous. Don´t do it. – Karl Aug 1 at 12:13
• There's no such test. Methanol is very similar to ethanol. Perhaps it could be selectively oxidised, but strong oxidisers aren't particularly safe or freely available. – Mithoron Aug 1 at 14:31
• You could conceivably use mass spec or NMR, but neither method is conveniently available outside of labs. But to be fair, methanol is perfectly fine, provided you're not inhaling large amounts, swimming in it, or drinking it. – Zhe 2 days ago
• @Zhe For information. Some santisers in the US have been found to have only Methanol or high percentages of Methanol. These are reported to all or mostly have been manufactured in Mexico but I imagine labels are unlikely to reflect this. Reports indicate that regular use over 2 days can start to cause vision effects and blindness. This is also reportedly reversible if use is then stopped. It would be very useful if such products could be reaily detected in advance. My interest covers not only NZ where I live but other countries who may be being taken advantage of in the present circumstances. – Russell McMahon 2 days ago
• @RussellMcMahon If you're talking the composition being primarily methanol, that is very different from having some fraction of methanol. I think the main point is that the analysis you're talking about is non-trivial... – Zhe 2 days ago

Russell, agree with your down voting frustration but it is a common problem of any public forum. The bad news is that "simple" distinguishing test do exist, but they generate more toxic products (including a carcinogen) in a so-called iodoform test. Good for school labs only. The problem is not in distinguishing methanol versus ethanol, the problem is the matrix (as analytical chemists call it), i.e., these alcohols are present in a complex mixture.

The only reliable test test to determine methanol in a complex mixture like a hand sanitizer is gas chromatography. You need to consult a professional certified service to ask them to analyze the sanitizer. There is no home-kit or simple test to differentiate the two in a mixture.

• DV has now been followed by question closure :-). I've been active on SE for 9+ years, I'm in 50+ stack exchange groups where I have more than the basic 101 points and another 30 with ~= 101 rep. I'm a moderator of an active SE site. I have a reasonable idea of how to ask good questions on SE. I find the reactions here 'interesting'. I'm aware that in some groups it seem obligatory to give newcomers a hard time (and do not know if this is the case here), but it's an interesting experience. | I'm astounded that anyone thinks they could not perceive a focused question in my original post. :-) – Russell McMahon 2 days ago
• Russell McMahon, I am one of the major opponents of this unnecessary down voting issue in chemistry. I guess, it gives some people a dopamine boost. Chemistry also receives low quality queries from students as well because chemistry teachers at many schools are not that great. Anyway, you should not care on the other hand, because faceless and nameless people down voting a decent question have zero importance outside the internet (equivalent to generating a storm in a tea cup). ResearchGate disabled down voting option altogether. – M. Farooq 2 days ago
• I disagree with this absolute negative response and I plan on testing the burning splint variation (testing actually for oxygen) with a methanol/glycerine mixture on leaves versus ethanol/glycerine. For CH3OH, expect less CO2 and more pure O2. It will be fun and further fascinating if this biological-based experiment (based on a ScienceDirect article) that is performed on three plants (one with ethanol, and two with different doses of methanol) can actually roughly estimate the CH3OH loading. – AJKOER 2 days ago
• @AJKOER Any practical results that you achieve would be of interest. – Russell McMahon yesterday
• Not sure if I can achieve practical results. One obstacle that I have already been confronted with (source: a younger member of my family), is that it is advisable to talk to the plants. Perhaps I should have listened to my esteem colleagues. – AJKOER yesterday

It is likely that without sophisticated equipment that one cannot accurately determine methanol concentration.

That being said, my speculation on a possible process, for possible use outside of the lab, could be based on this source outline of relevant chemistry, to quote:

Methanol influences the oxidizing capacity of the atmosphere through reaction with the hydroxyl radical (Jiménez et al., 2003), its main sink, leading to the formation of water vapour and either CH3O or CH2OH radicals, which both react with O2 to give HO2 and formaldehyde (H2CO) (Millet et al., 2006 ). The photo-oxidation of formaldehyde, a key intermediate in the oxidation of numerous volatile organic compounds , leads to the formation of HO2 radicals and carbon monoxide (CO). ...

As such, consider an experiment consisting of placing a test sample of the hand sanitizer in an expandable transparent plastic bag along with some B-12 mixed with 3% H2O2 (which was shortly before made alkaline by adding Na2CO3 until CO2 evolution ceased) in direct sunlight. Periodically shake.

My expectation: The B-12 is a photocatalyst that turns clear with sunlight exposure. Some hydroxyl radicals, along with CO and O2 are produced in the reaction from the breakdown of the H2O2 and importantly, the CH3OH (methanol) in direct sunlight in the presence of B-12. The alluded to HO2 radical above at pH>5 (from the added alkaline Na2CO3) is now in the form of gaseous superoxide ($$\ce{.O2-}$$).

Perform a parallel run employing ethanol mixed with an ethanol-based hand sanitizer. The chemistry on photolysis differs and is discussed here.

Comparatively, I would expect a faster reaction with methanol over ethanol (accelerated loss of the B-12 coloration) and more/faster gas creation. If I am wrong on the latter point, not material, as it is still likely quantitatively different.

You may be able to use the measured timing of the volume of gas along with the timing of coloration lose, to assess relative methanol presence.

Note: Unfortunately, there is more than alcohol added to hand sanitizer mix (like a moisturizer, perhaps glycerine) which may make the comparative analysis even harder.

[EDIT] Now, some may have suspected that my suggested photolysis experiment was a bit far afield from classical analytical chemistry. Wrong, this experiment is definitely more so, but even greener, likely easy to implement at home, and decidedly fun. Select two (or more) small nearly identical green plants, treat the leaves of one with a glycerine/methanol mix and with the other substitute ethanol. Place each plant in a container which has been fulfilled with a fixed amount CO2 gas, but still should have some remaining air (plants apparently need to breathe O2 at night, but during daylight, on net, produce much more oxygen from CO2) where the very top part of the plant should be exposed to air. Place the open mouth vessel with the plant in sunlight with a thin transparent plastic seal. The plant demonstrating a greater consumption of CO2 and corresponding formation of pure oxyen can be tested by placing a glowing splint into the vessel. Record the seconds and/or the splint's position in the vessel until the burning bright oxygen flame is reduced/extinguished. This may produce a relative metric to judge the relative presence of methanol given its apparent photocatalytic acceleration of a leaf's ability for oxygen formation in sunlight.

Here is a supporting Science Direct source, to quote:

The results revealed that photosynthesis was greatly improved by methanol, as indicated by higher photosynthetic rates and stomatal conductance. The enhancement effect of methanol on photosynthesis was maintained for 3–4 days. Different methanol concentration treatments also increased intercellular CO2 concentration and transpiration rates.

As the methanol treatment is effective for days, repetition of the oxygen generation/sunlight treatment, after replenishing the CO2 supply, may be viable. Also, for very low added amounts of CH3OH, conducting a four-day trial run is recommended as time, assuming a constant rate of photosynthesis, is a multiplicative factor.

Finally, as to whether this can actually work, in practice, and could quantify variations in the concentration of CH3OH, remains to be demonstrated, AND I PLAN TO TEST IT.

By the way, the inspiration of my original photolysis path was based on my acquaintance in the photolysis literature of the reputed abilities of methanol, so the latter photosynthesis reported results with CH3OH should not be too surprising to some.

• Sorry, this is complete non-sense. That is not how analytical chemistry works. – M. Farooq 2 days ago
• True, I added the (obvious) qualifier, outside of one's lab. However, I have tested the relative strength of H2O2 with NaOCl at home via O2 evolution on several occasions. My photolysis suggested experiment is based on my experience working with B-12 and shares a similar gas evolution comparative path. Conducting classical analytical chemistry experiments is a luxury for many, and I am opened minded to at least consider improvising, when necessary, outside of the lab. I also suspect M. Farooq has never performed any fun experiments with direct sunlight and home photocatalyst like ZnO or B-12. – AJKOER 2 days ago
• Ajkoer, I don't your age group, but 20 years ago, I have had all this fun which excites you now ;-). What boggles my mind, is how conveniently you drag in free radicals and bleach in almost all your answers. – M. Farooq 2 days ago
• Actually, HOCl (in a Fenton-type reaction) and H2O2 (Fenton-like or Fenton with iron) engaging with transition metals manages to show up in disease proliferation (in our lungs and elsewhere) all by themselves (no need to drag them in), or somewhat extensively in AOP (advanced oxidation processes) to remove pollutants even, at times, using light, or more enjoyably use NaOCl (or HOCl) in a bleach battery (electrochemistry). I regret to inform all that photolysis, as the source above notes, is apparently all about radical formation and subsequent interactions (especially with O2). – AJKOER 2 days ago
• M. Farooq, for my first suggested photolysis based approach, your comment was 'non-sense'. As I have now have gone even more 'green' (as in vegetation) with my suggested second embodiment, I eagerly await your new depiction. – AJKOER 2 days ago


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# This DIY Turntable Just Got Freaky Fresh

Photography turntables are made for both the precise and lazy. Whether you are concerned about the precision of consistent angles during a photo shoot or you simply do not want to stand there rotating a plate after every picture — yes, it does get old — a lazy susan style automatic photography turntable is the ticket. This automatic 360° design made over at circuito.io satisfies both of these needs in an understated package

The parts required to make this DIY weekend project are about as minimal as they get. An Arduino Uno controls it all with a rotary encoder for input and a character LCD to display settings. The turntable moves using a stepper motor and an EasyDriver. It even takes care of controlling the camera using an IR LED.

The biggest obstruction most likely to arise is creating the actual laser cut casing itself. The circuito team avoided this difficulty by using Pololu‘s online custom laser cutting service for the 4 necessary laser cut parts. After all of the components have been brought together, all that is left to do is Avengers assemble. They provide step by step instructions for this process in such a straightforward way that you could probably put this sucker together blindfolded.

We have seen some other inspired photography turntables on Hackaday before. [NotionSunday] created a true turntable hack based off of the eject mechanism of an old DVD-ROM drive. With the whole thing spinning on the head assembly of a VCR, this is the epitome of letting nothing go to waste. We also displayed another very similar Arduino Uno controlled turntable created 2 years ago by [Tiffany Tseng]. There is even a non-electronic version out there of a DIY 360° photography turntable that only uses a lazy susan and tape measure. All of these photography turntable hacks do the job wonderfully, but there was something that we liked about the clean feel of this one. All of the necessary code for this project has been provided over at GitHub. What is your favorite photography turntable?

# DIY Capacitive Rotational Encoder on the Cheap with FR4

Rotary encoders are critical to many applications, even at the hobbyist level. While considering his own rotary encoding needs for upcoming projects, it occurred to [Jan Mrázek] to try making his own DIY capacitive rotary encoder. If successful, such an encoder could be cheap and very fast; it could also in part be made directly on a PCB.

The encoder design [Jan] settled on was to make a simple adjustable plate capacitor using PCB elements with transparent tape as the dielectric material. This was used as the timing element for a 555 timer in astable mode. A 555 in this configuration therefore generates a square wave that changes in proportion to how much the plates in the simple capacitor overlap. Turn the plate, and the square wave’s period changes in response. Response time would be fast, and a 555 and some PCB space is certainly cheap materials-wise.

The first prototype gave positive results but had a lot of problems, including noise and possibly a sensitivity to temperature and humidity. The second attempt refined the design and had much better results, with an ESP32 reliably reading 140 discrete positions at a rate of 100 kHz. It seems that there is a tradeoff between resolution and speed; lowering the rate allows more positions to be reliably detected. There are still issues, but ultimately [Jan] feels that high-speed capacitive encoders requiring little more than some PCB real estate and some 555s are probably feasible.

This project is a reminder that FR4 (whether copper-clad, etched, or blank) shows up in clever applications: copper tape and blank FR4 can be used to quickly prototype RF filters, PocketNC built an entire small CNC tool around FR4, and our own [Voja] wrote a full guide on making beautiful enclosures from FR4.

# Printed Parts Make DIY Electric Longboard Possible

Appalled by expensive electric longboards, [Conor Patrick] still wanted one, and wanted it now. So — naturally — he converted an existing board into a sprightly electric version at a fraction of the cost.

[Patrick] is using a capable 380KV Propdrive motor, capable of pushing him up to 30mp/h! A waterproof 120A speed controller and 6000mAh, 22.2V LiPo battery slim enough to fit under the board give the motor the needed juice. He ended up buying the cheapest RF receiver and remote combo to control the board, but it fit the all-important “want electric long board now” criterion.

# Dual Direction Gaming/Dining Room Beam Lights

Sometimes, you just can’t find something you want, and that’s when you break out the tools and get dirty with a bit of DIY. Reddit user [JaredBanyard] wanted a nice beam light for the dining room/gaming room. He ended up building one that shone both downward, on the table, and upward, adding some light to the room.

Warm white LED strip lighting was chosen, and two aluminum channels were glued together to hold them. After wiring the four LED strips together a diffuser was placed over them and then they were wired up and turned on to check the amount of light. With two strips per channel, even with the diffuser, there was plenty.

Each pair of channels were set into the main housing, which is made from Sirari hardwood. Two long outside side pieces make for a great looking final product, and the end pieces are sandwiched between the two outside pieces. After a bit of sanding and an application of matte polyacrylic, transformers were screwed inside and then the channels were placed on top. The circuitry was wired to a Z-Wave dimmer to control the lights remotely.

[JaredBanyard]’s put together a bill of materials and there are plenty of pictures. It’s a great, unique, light for the room, which includes a Duchess gaming table from boardgametables.com. For more lighting articles, check out this 2017 Hackaday Prize entry article on modular rail lighting, or this article about adding intelligence to your lighting solution.

[via Reddit]

# 3D Printed Lamp Even Prints the Nuts and Bolts

The first print to come off a shiny new 3D printer is usually a toy widget of some sort that will forever sit at your desk without purpose. The alternative is a practical project that is custom and personal like this 3D Printed Articulating Lamp. [IgorF2] shares his design for this wall mounted device which was created using Fusion 360.

The complete design consists of eight parts which includes the arms, nuts, and bolts, as well as the wall mount, each of which can be printed individually. These come together to form a structure that can be attached to a wall or your work bench. Though [IgorF2] has provided arm pieces of length 100 mm, 140 mm and 200 mm, you can mix and match to create a much larger project. The files are available for download from Thingiverse for your making pleasure.

We think this can be a great basic structure for someone looking at custom wall mounted projects. The lamp mount can be easily supplemented by a Raspberry Pi and Camera holder if you feel like live streaming your bench. Alternatively, it may be customized to become a motion detecting lamp just for fun. We hope to see some good use come of it in the future.

# 3D Printing on the Subway; Or Anywhere Else!

3D-Printed wearable electronics are on the rise, however our own [Naomi Wu] flipped it around and made a wearable 3D printer which not only is portable but also manufactures on the move!

The project starts with a baby carrier that was locally purchased, and the extra fat was trimmed off leaving behind only the primary harness and square frame. This square frame is left intact to provide stability to the mounted printer as well as some level of comfort to the wearer. [Naomi] then drills a number of new holes in the delta printer in question, of which fortunately the top is made of plastic. Using swivel screws and long screws, the upper part connects with the harness. The receptacle clamp for the upper part is 3D-printed as well, and provides a modular rigid fixture for the machine.

The lower part also uses a 3D-printed triangular base that has a slot for the carrier frame which attaches with the bottom part of the delta using screws. The project is powered via two 3 Ah batteries that are kept in place behind the printer using custom clamps made with PLA. The whole project works on the move, as demonstrated by [Naomi] in the video below.

From dissecting the baby carrier to puncturing holes in a harness using a screwdriver heated by a blow torch, this project has a lot of DIY in it. For those looking for a more productive motorised wearable, check out Adding Haptic Feedback For The Disabled. Continue reading “3D Printing on the Subway; Or Anywhere Else!”

# Network Analysers: The Electrical Kind

Instrumentation has progressed by leaps and bounds in the last few years, however, the fundamental analysis techniques that are the foundation of modern-day equipment remain the same. A network analyzer is an instrument that allows us to characterize RF networks such as filters, mixers, antennas and even new materials for microwave electronics such as ceramic capacitors and resonators in the gigahertz range. In this write-up, I discuss network analyzers in brief and how the DIY movement has helped bring down the cost of such devices. I will also share some existing projects that may help you build your own along with some use cases where a network analyzer may be employed. Let’s dive right in.

# Network Analysis Fundamentals

As a conceptual model, think of light hitting a lens and most of it going through but part of it getting reflected back.

The same applies to an electrical/RF network where the RF energy that is launched into the device may be attenuated a bit, transmitted to an extent and some of it reflected back. This analysis gives us an attenuation coefficient and a reflection coefficient which explains the behavior of the device under test (DUT).

Of course, this may not be enough and we may also require information about the phase relationship between the signals. Such instruments are termed Vector Network Analysers and are helpful in measuring the scattering parameters or S-Parameters of a DUT.

The scattering matrix links the incident waves a1, a2 to the outgoing waves b1, b2 according to the following linear equation: $\begin{bmatrix} b_1 \\ b_2 \end{bmatrix} = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix} * \begin{bmatrix} a_1 \\ a_2 \end{bmatrix}$.

The equation shows that the S-parameters are expressed as the matrix S, where and denote the output and input port numbers of the DUT.

This completely characterizes a network for attenuation, reflection as well as insertion loss. S-Parameters are explained more in details in Electromagnetic Field Theory and Transmission Line Theory but suffice to say that these measurements will be used to deduce the properties of the DUT and generate a mathematical model for the same.

# General Architecture

As mentioned previously, a simple network analyzer would be a signal generator connected and a spectrum analyzer combined to work together. The signal generator would be configured to output a signal of a known frequency and the spectrum analyzer would be used to detect the signal at the other end. Then the frequency would be changed to another and the process repeats such that the system sweeps a range of frequencies and the output can be tabulated or plotted on a graph. In order to get reflected power, a microwave component such as a magic-T or directional couplers, however, all of this is usually inbuilt into modern-day VNAs.
Continue reading “Network Analysers: The Electrical Kind”


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# How to predict future position of an object(bullet sync)?

There is a multiplayer game and server sends to all clients a message when a shot happens, containing bullet position, bullet velocity and timestamp. By having timestamp, we can calculate the lag, let's say it's 100ms.

My game uses Box2D. How can I predict the real and current bullet position by having such data? I guess velocity might also change a little bit too.

## 1 Answer

current_position = starting_position + ((lag_delay + time_elapsed ) * velocity)

Where "time elapsed" is how long we've known about the bullet existence. Ostensibly this doesn't need to be stored, as when the bullet is created client-side, it is 0, and afterwards we update its position every frame update.

The lag delay is merely just an extra bit of deltaTime applied when the bullet is first spawned.

• I guess this only works for linear, straight line bullets. What about ones that are affected by gravity? – Gintas_ Dec 30 '15 at 15:42
• Calculate the gravity for the lag_time as well. Seriously, all the lag_time is is a once-off "do this much movement as the bullet spawns" calculation. – Draco18s Dec 30 '15 at 15:43
• can you provide an example please? – Gintas_ Dec 30 '15 at 15:45
• pastebin.com/vuCsZc3B – Draco18s Dec 30 '15 at 16:04


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# Pochhammer symbol

(Redirected from Falling factorial power)
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In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation (x)n, where n is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which interpretation is being used in any particular article. Pochhammer himself actually used (x)n with yet another meaning, namely to denote the binomial coefficient $\tbinom xn$.[1]

In this article the Pochhammer symbol (x)n is used to represent the falling factorial (sometimes called the "descending factorial",[2] "falling sequential product", "lower factorial"):

$(x)_{n}=x(x-1)(x-2)\cdots(x-n+1)$

In this article the symbol x(n) is used for the rising factorial (sometimes called the "Pochhammer function", "Pochhammer polynomial", "ascending factorial",[2] "rising sequential product" or "upper factorial"):

$x^{(n)}=x(x+1)(x+2)\cdots(x+n-1).$

These conventions are used in combinatorics.[3] However in the theory of special functions (in particular the hypergeometric function) the Pochhammer symbol (x)n is used to represent the rising factorial.[4] A useful list of formulas for manipulating the rising factorial in this last notation is given in (Slater 1966, Appendix I). Knuth uses the term factorial powers to comprise rising and falling factorials.[5]

When x is a non-negative integer, then (x)n gives the number of n-permutations of an x-element set, or equivalently the number of injective functions from a set of size n to a set of size x. However, for these meanings other notations like xPn and P(x,n) are commonly used. The Pochhammer symbol serves mostly for more algebraic uses, for instance when x is an indeterminate, in which case (x)n designates a particular polynomial of degree n in x.

## Properties

The rising and falling factorials can be used to express a binomial coefficient:

$\frac{x^{(n)}}{n!} = {x+n-1 \choose n} \quad\mbox{and}\quad \frac{(x)_n}{n!} = {x \choose n}.$

Thus many identities on binomial coefficients carry over to the falling and rising factorials.

A rising factorial can be expressed as a falling factorial that starts from the other end,

$x^{(n)} = {(x + n - 1)}_n ,$

or as a falling factorial with opposite argument,

$x^{(n)} = {(-1)}^n {(-x)}_{{n}} .$

The rising and falling factorials are well defined in any unital ring, and therefore x can be taken to be, for example, a complex number, including negative integers, or a polynomial with complex coefficients, or any complex-valued function.

The rising factorial can be extended to real values of n using the Gamma function provided x and x + n are complex numbers that are not negative integers:

$x^{(n)}=\frac{\Gamma(x+n)}{\Gamma(x)},$

and so can the falling factorial:

$(x)_n=\frac{\Gamma(x+1)}{\Gamma(x-n+1)}.$

If D denotes differentiation with respect to x, one has

$D^n(x^a) = (a)_n\,\, x^{a-n}.$

The Pochhammer symbol is also integral to the definition of the hypergeometric function: The hypergeometric function is defined for |z| < 1 by the power series

$\,_2F_1(a,b;c;z) = \sum_{n=0}^\infty {a^{(n)} b^{(n)}\over c^{(n)}} \, {z^n \over n!}$

provided that c does not equal 0, −1, −2, ... . Note, however, that the hypergeometric function literature uses the notation ${(a)}_{{n}}$ for rising factorials.

## Relation to umbral calculus

The falling factorial occurs in a formula which represents polynomials using the forward difference operator Δ and which is formally similar to Taylor's theorem of calculus. In this formula and in many other places, the falling factorial (x)k in the calculus of finite differences plays the role of xk in differential calculus. Note for instance the similarity of

$\Delta (x)_{k} = k\ (x)_{k-1},$

to

$D x^k = k\ x^{k-1},$

A similar result holds for the rising factorial.

The study of analogies of this type is known as umbral calculus. A general theory covering such relations, including the falling and rising factorial functions, is given by the theory of polynomial sequences of binomial type and Sheffer sequences. Rising and falling factorials are Sheffer sequences of binomial type:

$(a + b)^{(n)} = \sum_{{j=0}}^n {n \choose j} (a)^{(n-j)}(b)^{(j)}$
$(a + b)_n = \sum_{{j=0}}^n {n \choose j} (a)_{n-j}(b)_{j}$

where the coefficients are the same as the ones in the expansion of a power of a binomial (Chu–Vandermonde identity).

Similarly, the generating function of Pochhammer polynomials then amounts to the umbral exponential,

$\sum_{n=0}^\infty (x)_n ~\frac{t^n}{n!} = (1+t)^x ~,$

as Δ(1+t )x = t (1+t )x.

## Connection coefficients

Since the falling factorials are a basis for the polynomial ring, we can re-express the product of two of them as a linear combination of falling factorials:

$(x)_m (x)_n = \sum_{k=0}^m {m \choose k} {n \choose k} k!\, (x)_{m+n-k}.$

The coefficients of the (x)m+nk, called connection coefficients, have a combinatorial interpretation as the number of ways to identify (or glue together) k elements each from a set of size m and a set of size n.

## Alternate notations

An alternate notation for the rising factorial

$x^{\overline{m}}=\overbrace{x(x+1)\ldots(x+m-1)}^{m~\mathrm{factors}}\qquad\mbox{for integer }m\ge0,$

and for the falling factorial

$x^{\underline{m}}=\overbrace{x(x-1)\ldots(x-m+1)}^{m~\mathrm{factors}}\qquad\mbox{for integer }m\ge0;$

goes back to A. Capelli (1893) and L. Toscano (1939), respectively.[6] Graham, Knuth and Patashnik[7] propose to pronounce these expressions as "x to the m rising" and "x to the m falling", respectively.

Other notations for the falling factorial include P(xn), xPn, Px,n, or xPn. (See permutation and combination.)

An alternate notation for the rising factorial x(n) is the less common (x)+n. When the notation (x)+n is used for the rising factorial, the notation (x)n is typically used for the ordinary falling factorial to avoid confusion.[1]

## Generalizations

The Pochhammer symbol has a generalized version called the generalized Pochhammer symbol, used in multivariate analysis. There is also a q-analogue, the q-Pochhammer symbol.

A generalization of the falling factorial in which a function is evaluated on a descending arithmetic sequence of integers and the values are multiplied is:

$[f(x)]^{k/-h}=f(x)\cdot f(x-h)\cdot f(x-2h)\cdots f(x-(k-1)h),$

where h is the decrement and k is the number of factors. The corresponding generalization of the rising factorial is

$[f(x)]^{k/h}=f(x)\cdot f(x+h)\cdot f(x+2h)\cdots f(x+(k-1)h).$

This notation unifies the rising and falling factorials, which are [x]k/1 and [x]k/−1, respectively.

## Notes

1. ^ a b Knuth, Donald E. (1992), "Two notes on notation", American Mathematical Monthly 99 (5): 403–422, arXiv:math/9205211, doi:10.2307/2325085, JSTOR 2325085. The remark about the Pochhammer symbol is on page 414.
2. ^ a b Steffensen, J. F., Interpolation (2nd ed.), Dover Publications, p. 8, ISBN 0-486-45009-0 (A reprint of the 1950 edition by Chelsea Publishing Co.)
3. ^ Olver 1999, p. 101
4. ^ so is the case in Abramowitz and Stegun's "Handbook of Mathematical Functions", P. 256
5. ^ Knuth, The Art of Computer Programming, Vol. 1, 3rd ed., p. 50.
6. ^ According to Knuth, The Art of Computer Programming, Vol. 1, 3rd ed., p. 50.
7. ^ Ronald L. Graham, Donald E. Knuth and Oren Patashnik in their book Concrete Mathematics (1988), Addison-Wesley, Reading MA. ISBN 0-201-14236-8, pp. 47,48

## References

• Olver, Peter J. (1999), Classical Invariant Theory, Cambridge University Press, ISBN 0-521-55821-2, MR 1694364
• Slater, Lucy J. (1966), Generalized Hypergeometric Functions, Cambridge University Press, MR 0201688


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#### Self-assembly of photoresponsive dendritic molecules = 광반응성 덴드리틱 분자의 자기조립

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Molecular self-assembly through specific interactions has provided an important basis of the bottom-up based nanotechnology for generation of nanostructures. Utilization of dendritic architectures in self-assembly is highly attractive partly because of the interesting characteristics encoded in their molecular structures, such as the cone-shape architecture, a large number of functional groups on the surface, easily tunable focal point, etc.. Also, the macromolecular nature of well-defined architecture is expected to fill the gap between polymeric and small molecular properties. By intelligent design of the molecular structure, the resulting structures can be also responsive to other external stimuli such as photochemical, chemical, or mechanochemical. Among these stimuli, light can be regarded as an ideal candidate to control the state of self-assembled structures because it acts in non-contact and site-specific fashion. Also, it is possible to precisely control the irradiation conditions by choosing proper irradiation time, intensity, wavelength, and polarizing direction. A novel photoresponsive bis-dendritic organogelator, consisting of a benzamide dendron and a diacetylene dendron, was synthesized and the physical behavior was studied. The bis-dendritic molecule showed physical gelation through self-assembled fibrillar network in solvents such as chloroform. When a chloroform solution of the compound was cast on a Si wafer in a stream of moist air, well-defined honeycomb patterns with the spherical cavities with diameter of ca. $1 \mu m$ were obtained. To utilize top-down lithographic techniques on the self-assembled structure generated by the bottom-up approach (breath figure), specific regions of the honeycomb patterns were exposed to UV using a line-patterned mask to induce selective chemical crosslinking between the diacetylene groups. Subsequent developing in acetone showed patterned honeycomb lines obtained at pre-defined locations. Fabrication of ...
Kim, Sang-Youlresearcher김상율researcher
Description
한국과학기술원 : 화학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
418710/325007  / 020065046
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 화학과, 2010.2, [ ix, 85 p. ]

Keywords

self-assembly; dendritic molecule; photoresponse; organogelator; 유기젤분자; 자기조립; 덴드리틱 분자; 광반응성

URI
http://hdl.handle.net/10203/31745
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=418710&flag=dissertation
Appears in Collection
CH-Theses_Ph.D.(박사논문)
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