Search results for "Planck"
showing 10 items of 159 documents
On the generalization of the Boltzmann equation
1974
Starting from the Liouville equation and making use of projection operator techniques we obtain a compact equation for the rate of change of then-particle momentum distribution function to any order in the density. This equation is exact in the thermodynamic limit. The terms up to second order in the density are studied and expressions are given for the errors committed when one makes the usual hypothesis to derive generalized Boltzmann equations. Finally the Choh-Uhlenbeck operator is obtained under additional assumptions.
CMOS-compatible field effect nanoscale gas-sensor: Operation and annealing models
2008
Complete modelling of electrically controlled nanoscale gas sensors with Poisson, Wolkenstein, Fokker-Planck and continuity is presented. Based on a plausible Drift explanation we developed suitable models for sensitivity control and operational modes. An onset for CMOS-complying annealing procedures is given.
Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise
2008
In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …
Adaptive Gaussian particle method for the solution of the Fokker-Planck equation
2012
The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE). A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the SODE. The decomposition as well as the propagation is subject to possibly large numeric errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error…
Fokker–Planck equation with respect to heat measures on loop groups
2011
Abstract The Dirichlet form on the loop group L e ( G ) with respect to the heat measure defines a Laplacian Δ DM on L e ( G ) . In this note, we will use Wasserstein distance variational method to solve the associated heat equation for a given data of finite entropy.
CO2-recycling to the deep convecting mantle
2006
Institut fur Geowissenschaften, Johann Wolfgang Goethe-Universitat Frankfurt, 60054 Frankfurt, Germany (f.brenker@ em.uni-frankfurt.de) Max Planck Institute for Chemistry, Mainz, Germany (cvollmer@mpch-mainz.mpg.de) Ghent University, Department of Analytical Chemistry, Belgium (Laszlo.Vincze@UGent.be) University of Antwerp, Department of Chemistry, Belgium (bart.vekemans@ua.ac.be; koen.janssens@ua.ac.be) Institute of Experimental Physics, University of Debrecen, Hungary (szaloki@tigris.klte.hu) Institut fur Geowissenschaften, Johannes Gutenberg-Universitat, Mainz, Germany (nasdala@uni-mainz.de) KM Diamond Exploration Ltd., Vancouver, Canada (felixvkaminsky@cs.com)
Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
2011
AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.
Path integral solution handled by Fast Gauss Transform
2009
Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…
Approximate solution of the Fokker-Planck-Kolmogorov equation
2002
The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions i…
Ionic Transport through Chemically Functionalized Hydrogen Peroxide-Sensitive Asymmetric Nanopores
2015
We describe the fabrication of a chemical-sensitive nanofluidic device based on asymmetric nanopores whose transport characteristics can be modulated upon exposure to hydrogen peroxide (H2O2). We show experimentally and theoretically that the current-voltage curves provide a suitable method to monitor the H2O2-mediated change in pore surface characteristics from the electronic readouts. We demonstrate also that the single pore characteristics can be scaled to the case of a multipore membrane whose electric outputs can be readily controlled. Because H2O2 is an agent significant for medical diagnostics, the results should be useful for sensing nanofluidic devices.