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Related Concept Videos

Sampling Theorem01:15

Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Sampling Distribution01:12

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
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Sampling Continuous Time Signal01:11

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Sample Size Calculation01:19

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
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Basis function sampling: a new paradigm for material property computation.

Jonathan K Whitmer1, Chi-cheng Chiu1, Abhijeet A Joshi2

  • 1Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA and Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.

Physical Review Letters
|November 22, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a novel, parameter-free method for free energy calculations, improving convergence in physical simulations. The approach is geometrically robust and ideal for measuring material properties like elastic constants.

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Area of Science:

  • Computational Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Flat histogram methods, including Wang-Landau sampling, are vital for free energy calculations in diverse physical systems.
  • A key limitation of these methods is the reliance on unknown, a priori parameters, hindering convergence to the target free energy surface.

Purpose of the Study:

  • To develop and implement a new, parameter-free simulation method for enhanced free energy calculations.
  • To address the convergence challenges faced by existing flat histogram techniques.
  • To create a geometrically robust method suitable for in silico material property measurements.

Main Methods:

  • Derivation and implementation of a novel method utilizing orthogonal functions.
  • The method is designed to be parameter-free and geometrically robust.
  • Application of the method to calculate Frank elastic constants for the Lebwohl-Lasher liquid crystal model.

Main Results:

  • The new method demonstrates high effectiveness in achieving convergence for free energy calculations.
  • The technique is parameter-free, eliminating the need for prior knowledge of simulation parameters.
  • The method offers arbitrary levels of description for the free energy, enhancing its versatility.

Conclusions:

  • The developed parameter-free, orthogonal function-based method significantly improves free energy calculation convergence.
  • This approach is well-suited for in silico measurements of elastic moduli and other material properties.
  • The successful calculation of Frank elastic constants validates the method's utility in condensed matter physics and materials science.