# Linear scaling density

For example, consider a Temperature Transmitter and we all know by using a simple formula we can calculate the equivalent temperature from the RTD sensor output resistance And in the case of a thermocouple, a complex algorithm is required for converting its output millivolt into equivalent temperature.

There are three common techniques used in the data acquisition world including linear scaling, mapped scaling and formula scaling. All three methods have their place and time for use and will be described in this article. There are three techniques for scaling that we are going to cover here in this article: linear, mapping and formula.

These three techniques overlap a little bit as we will explain, but they are the primary methods used in the world of data acquisition. In certain instances where formula-based scaling is not available, mapping can sometimes be used to predefine a table based on the formula needed and vice versa. It is also worth noting that when working with a sensor that has an analog output, the units specified for that sensor are not set in stone. The technique of linear scaling should remind you a few your days back in basic algebra.

As previously stated, linear scaling works best with linear voltage or current outputs in which the minimum and maximum outputs represent specific values along with the sensors range. These specifications tell us two things:. The factor m can be solved by using the slope formula. After the scale factor has been determined, we simply plug the value m back into the slope-intercept formula and use one of our points to calculate our offset.

Given that this arithmetical operation is valid, we have verified that our scale factor and offset are correct. These specifications again tell us two things:. We will go about this example, in the same manner, we did the last one by first finding the scale factor and then plugging in a few numbers to calculate the offset.

This example does not apply only to type K thermocouples, but any type of commonly used resistive temperature sensor or other related sensors. However, there are some instances in which we would need to create our own mapping table.

One of these instances would be when we are working with a data acquisition system that is not preconfigured for use with resistive temperature sensors. This is not a very common situation that we run into, but it is worth mentioning. The other instance would be when we have a non-linear function and formula-based scaling is not available or is a piecewise function.

A good example of this would be when we are using a level sensor to calculate tank volume in a non-linear tank. Typically when we want to know what the volume of a fluid in a tank is we measure the depth or level of the tank. By knowing this, we can calculate the volume of the fluid. If the tank had a flat bottom and was the same diameter along with its height then this calculation would be simple, and we could use linear scaling like above.

However, typically these tanks are rounded and the level of the fluid does not directly correlate to the volume of fluid.

In this situation, we must use mapped scaling and a little bit of math to attain our desired result. For our example we will use a horizontal cylinder tank with a diameter of 5 ft. Instead, we will do the calculations and show you the value mapping table. Also, for this example, we will be using the level Transmitter again, but this time a 0 to 10V DC output and 0 to 5 ft WC range. If this is the mapping table programmed into your data acquisition system then the volume will be calculated rather than simply measuring the depth.

Typically the more points in your table the more accurate the calculations will turn out to be.ONETEP therefore combines the advantages of the plane-wave approach controllable accuracy and variational convergence of the total energy with respect to the size of the basis with computational effort that scales linearly with the size of the system.

The optimized NGWFs then provide a minimal localized basis set, which can be considerably smaller in size, but of equal or higher accuracy, than the unoptimized basis sets used in most linear-scaling approaches.

It is available to academics at a reduced rate, and licenses can be obtained for non-academic usage from the developers or through Accelrys ' Materials Studio package.

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Skylaris; P. Haynes; A. Mostofi; M. Payne Bibcode : JChPh. Haynes; C. Skylaris; A. Psi-k Newsletter. Computational chemistry software. Canvas Chemicalize Discovery Studio. List of molecular graphics systems.

List of protein-ligand docking software. List of quantum chemistry and solid-state physics software. Categories : Computational chemistry software Density functional theory software. Hidden categories: Articles lacking reliable references from October All articles lacking reliable references. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Add links.We present an overview of the onetep program for linear-scaling density functional theory DFT calculations with large basis set plane-wave accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions NGWFsexpressed in terms of periodic sinc psinc functions.

During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples.

We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Abstract We present an overview of the onetep program for linear-scaling density functional theory DFT calculations with large basis set plane-wave accuracy on parallel computers.These metrics are regularly updated to reflect usage leading up to the last few days. Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.

The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric. Find more information on the Altmetric Attention Score and how the score is calculated. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

A, 25 View Author Information. Cite this: J. A, 25— Article Views Altmetric. Citations Cited By. This article is cited by publications. Journal of Chemical Theory and Computation16 1 The Journal of Physical Chemistry A32 Superposition of Atomic Potentials: Simple yet Efficient. Journal of Chemical Theory and Computation15 3 Libraries of Extremely Localized Molecular Orbitals. Construction and Preliminary Assessment of the New Databanks.

The Journal of Physical Chemistry A45 Ricard, Srinivasan S. Journal of Chemical Theory and Computation14 11 Snyder, Jr.

Parrish, and Todd J. The Journal of Physical Chemistry Letters8 11 Journal of Chemical Theory and Computation13 5 Journal of Chemical Theory and Computation13 2 Kulik, Jianyu Zhang, Judith P.

Klinman, and Todd J. The Case of Catechol O-Methyltransferase.Contact Today. Instruments should be ranged to measure not only expected values but all values the system can produce. During upsets, actual values often exceed 20mA values for instruments tightly ranged for normal process conditions. But nonlinear relationships complicate scale adjustments. Most methods of flow measurement are nonlinear. Some calculations are always handled inside the transmitter mag-meters, Coriolis, Vortex, etc so that the mA signal is linear to flow for those types of meters.

Regardless of the type of obstruction orifice plate, Venturi or Pitot tube, etcthe DP is proportional to the square of the flow. Therefore the system must scale flow from the square root of the DP. The square root for DP-based flow can be taken either in the transmitter or in the controller but not both! We prefer to configure the transmitter to take the square root because, on the low end, a very small change in DP results in a large change in flow.

This makes low flows extra sensitive to electrical noise on the mA signal if the square root is taken in the controller. If it is not feasible to take the square root in the transmitter, and you are writing your own square root scaling logic in a controller instead of checking a square root option in a standard function block, then follow these steps. First, normalize the signal towhere 0 is 4 mA, 1 is 20 mA, and 0.

Multiply the resulting square rooted signal still by the flow scale span to get flow rate in engineering units. Typically, a flow element such an orifice plate or Venturi tube will come with a flow data sheet with expected process conditions and a table of flow rates for various DPs.

Then in the controller, scale the input from zero at 4mA to that maximum flow at 20mA. If the square root is taken in either the transmitter or controller but not boththe system will correctly calculate flow through the range of the meter. Checking the zero and full span DP, calibrating 4mA and 20mA, and verifying that the controller displays the correct flow at 4mA and 20mA is necessary but insufficient to verify square root configuration.

You must also apply one or more of the mid-range DPs from the flow data sheet to the meter and verify that the controller displays the correct flow rate. Fluid density is irrelevant to that measurement and calculation. For the most accurate mass flow, if any of the nominal process conditions on the flow data sheet differs from actual conditions in a way that significantly affects density, the flow should be compensated.Historams are constructed by binning the data and counting the number of observations in each bin.

Using a binwidth of 0. Eruptions were sometimes classified as short or long ; these were coded as 2 and 4 minutes. It would matter if we wanted to estimate means and standard deviation of the durations of the long eruptions. It would be very useful to be able to change this parameter interactively. A histogram can be used to compare the data distribution to a theoretical model, such as a normal distribution. The Galton data frame in the UsingR package is one of several data sets used by Galton to study the heights of parents and their children.

Using the base graphics hist function we can compare the data distribution of parent heights to a normal distribution with mean and standard deviation corresponding to the data:. Create the histogram with a density scale using the computed varlable. The smoothness is controlled by a bandwidth parameter that is analogous to the histogram binwidth. Most density plots use a kernel density estimatebut there are other possible strategies; qualitatively the particular strategy rarely matters.

Using base graphics, a density plot of the geyser duration variable with default bandwidth:. The lattice densityplot function by default adds a jittered strip plot of the data to the bottom:. Density estimates are generally computed at a grid of points and interpolated. Defaults in R vary from 50 to points. Computational effort for a density estimate at a point is proportional to the number of observations.

Storage needed for an image is proportional to the number of point where the density is estimated. Both ggplot and lattice make it easy to show multiple densities for different subgroups in a single plot. In ggplot you can map the site variable to an aesthetic, such as color :. Often a more effective approach is to use the idea of small multiplescollections of charts designed to facilitate comparisons.

Lattice uses the term lattice plots or trellis plots. These plots are specified using the operator in a formula:. Both the lattice and ggplot versions show lower yields for than for for all sites except Morris. A recent paper suggests there may be no error. Being able to chose the bandwidth of a density plot, or the binwidth of a histogram interactively is useful for exploration. Histograms and Density Plots.

Feature to Look For Some things to keep an eye out for when looking at data on a numeric variable: skewness, multimodality gaps, outliers rounding, e. Histograms Histogram Basics Historams are constructed by binning the data and counting the number of observations in each bin.

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The objective is usually to visualize the shape of the distribution. The number of bins needs to be large enough to reveal interesting features; small enough not to be too noisy.

### Square Root Scaling for Differential Pressure (DP) Flow Meters

A very small bin width can be used to look for rounding or heaping. Common choices for the vertical scale are bin counts, or frequencies counts per unit, or densities The count scale is more intepretable for lay viewers. The density scale is more suited for comparison to mathematical density models. Constructing histograms with unequal bin widths is possible but rarely a good idea.

### Histograms and Density Plots

For many purposes this kind of heaping or rounding does not matter. Superimposing a Density A histogram can be used to compare the data distribution to a theoretical model, such as a normal distribution.

This requires using a density scale for the vertical axis. Scalability Histograms scale very well. The computational effort needed is linear in the number of observations.The code is designed to perform DFT calculations on very large systems containing tens of thousands, hundreds of thousands or even millions of atoms.

It can be run at different levels of precision, ranging from ab initio tight binding up to full DFT with plane wave accuracy. It is capable of operation on a range of platforms from workstations up to high performance computing centres.

These web pages contain information on the code, and its applications, as well as separate areas for developers. A recent comprehensive overview is available on arXiv. While it is a complete, robust code, we are designating this release as a pre-release, as there are some changes that will be made over the next few months to improve the user-friendliness of the code. At present, we are looking for early adopters to use the code, submit bug reports and suggestions improvement.

We particularly welcome new developers of the code. The present roadmap for the code can be seen on the GitHub issues page. If you are interested in more details about O N methods, you can find a comprehensive review which we wrote here external linkalso available on arXiv.

The source code is available on GitHub. The manual is on ReadTheDocs While it is a complete, robust code, we are designating this release as a pre-release, as there are some changes that will be made over the next few months to improve the user-friendliness of the code.