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Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Random Variables01:09

Random Variables

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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Sequence Networks of Rotating Machines

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Related Experiment Videos

Rotation algorithm: generation of Gaussian self-similar stochastic processes.

M Vahabi1, G R Jafari

  • 1School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
PubMed
Summary

This study presents a novel interpolation method to generate Gaussian self-similar stochastic processes like fractional Brownian motions (fBms) and fractional Gaussian noises (fGns). The technique allows for creating correlated or uncorrelated series from existing ones, offering flexibility in stochastic process generation.

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Area of Science:

  • Stochastic Processes
  • Time Series Analysis
  • Mathematical Physics

Background:

  • Gaussian self-similar stochastic processes, including fractional Brownian motions (fBms) and fractional Gaussian noises (fGns), are fundamental in modeling complex systems.
  • Existing methods for generating these processes can be limited in flexibility and control.

Purpose of the Study:

  • To introduce a simple and practical interpolation method for generating Gaussian self-similar stochastic processes.
  • To explore the application of this method to various combinations of fBms and fGns.
  • To demonstrate the capability of generating correlated and uncorrelated series.

Main Methods:

  • Interpolation between two known series of Gaussian self-similar stochastic processes.
  • Application of a rotation algorithm to different pairs of fBms and fGns.
  • Analysis of the method's sensitivity with respect to the Hurst exponent.

Main Results:

  • The method's sensitivity varies based on the Hurst exponent of the input series.
  • It is possible to generate correlated series from uncorrelated ones (e.g., Brownian motion and white Gaussian noise).
  • Conversely, uncorrelated series can be generated from correlated ones.

Conclusions:

  • The proposed interpolation method offers a versatile approach to generating fBms and fGns.
  • The technique provides control over the correlation properties of the generated stochastic processes.
  • The method's behavior differs for fGns (starting from larger scales) and fBms (starting from smaller scales).