Coefficients Of Diffusion Equation Research Articles

Application of the Method of Galerkin to Non Linear Problem Stochastic Heat Conduction One-Dimensional

The Galerkin method is applied in the non-linear stochastic diffusion problem. The uncertainty is present in the coefficients of diffusion equation. The uncertainty is modeled by random variables. The chaos polynomials is used to approximate the stochastic behavior of the problem. The approximate solutions obtained through Galerkin method are compared with Monte Carlo simulation in terms of the statistical moments of random variables generated by the random field solution.

Neurobiological models of two-choice decision making can be reduced to a one-dimensional nonlinear diffusion equation.

The response behaviors in many two-alternative choice tasks are well described by so-called sequential sampling models. In these models, the evidence for each one of the two alternatives accumulates over time until it reaches a threshold, at which point a response is made. At the neurophysiological level, single neuron data recorded while monkeys are engaged in two-alternative choice tasks are well described by winner-take-all network models in which the two choices are represented in the firing rates of separate populations of neurons. Here, we show that such nonlinear network models can generally be reduced to a one-dimensional nonlinear diffusion equation, which bears functional resemblance to standard sequential sampling models of behavior. This reduction gives the functional dependence of performance and reaction-times on external inputs in the original system, irrespective of the system details. What is more, the nonlinear diffusion equation can provide excellent fits to behavioral data from two-choice decision making tasks by varying these external inputs. This suggests that changes in behavior under various experimental conditions, e.g. changes in stimulus coherence or response deadline, are driven by internal modulation of afferent inputs to putative decision making circuits in the brain. For certain model systems one can analytically derive the nonlinear diffusion equation, thereby mapping the original system parameters onto the diffusion equation coefficients. Here, we illustrate this with three model systems including coupled rate equations and a network of spiking neurons.

Diffusion equation coefficients for gas-phase energy transfer

Collisional energy transfer in gas-phase systems is generally modelled using a master equation, which requires a detailed model for the collisional energy transition density. The master equation can be approximated by a diffusion equation which is easier to treat numerically and only requires the specification of drift and diffusion coefficients. Published methods for calculating these coefficients suffer from numerical inaccuracy at high energies. The high energy limits for the drift and diffusion coefficients are derived for the exponential down model and the approach to this limit is examined. At moderately high energies (such as energies above the reaction threshold) the coefficients depend only weakly on the energy. The method is applied to the methyl radical association reaction.

Evaluation of the GFDL GCM climate variability: 2. Stochastic modeling and latitude‐temporal fields

This paper statistically analyzes and compares the variability of the observed and simulated (by the Geophysical Fluid Dynamic Laboratory general circulation model) northern hemisphere monthly surface air temperature latitude‐temporal fields. The objects used for the analysis are as follows: multivariate autoregressive and linear regression model parameters, the diffusion equation coefficients, and two‐dimensional spatial‐temporal spectral and correlation characteristics. The estimates reveal a significant latitudinal trend of all second moments. A comparative study of the estimates demonstrates a significant distinction between the character of the meridional circulations of the observed and simulated systems. The methodology and results presented make it clear that the variability validation problems can be formalized by applying standard statistical techniques of multivariate modeling and multidimensional spectral and correlation analysis to the data averaged spatially and temporally.

Observed versus Simulated Second-Moment Climate Statistics in GCM Verification

Abstract The observed and simulated (by the Hamburg GCM) Northern Hemisphere monthly surface air temperatures, averaged within different latitude bands, are statistically analyzed and compared. The objects used for the analysis are the two-dimensional spatial–temporal spectral and correlation characteristics, the multivariate autoregressive and linear regression model parameters, and the diffusion equation coefficients. A qualitative comparison shows that, generally, the shapes of the corresponding spectra and correlation functions are quite similar but that their numerical values and some features differ markedly, especially for the tropical regions. The spectra reveal a few randomly distributed maxima (along the frequency axis), the periods of which were not identical for both types of data. A comparative study of the estimates of the diffusion equation coefficients shows a significant distinction between the character of the meridional circulations of the observed and simulated systems. The approach de...