Finally, relations to a class of self-propelled interacting particle systems with roosting force are presented and further applications of the geometric Langevin equations are given. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. We light up the geometry occuring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The first version of the geometric Langevin equation has already been detected before by Lelièvre, Rousset and Stoltz with a different derivation. VOLUME 87, NUMBER 26 PHYSICAL REVIEW LETTERS 24DECEMBER 2001 Self-Consistent Mode-Coupling Theory for Self-Diffusion in Quantum Liquids David R. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The various corrected forms of the real-valued CLE, the linear-noiseĪpproximation and a commonly used two moment-closure approximation.In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. Is also shown to provide a more accurate approximation of the chemical masterĮquation of simple biochemical circuits involving bimolecular reactions than Spectra and first passage times, hence admitting a physical interpretation. Quantities for the mean concentrations, the moments of intrinsic noise, power Although the molecule numbersĪre generally complex, we show that the "complex CLE" predicts real-valued The domain of the CLE to complex space, break down is eliminated, and the CLE'sĪccuracy for unimolecular systems is restored. Predictions for the mean concentrations and variance of fluctuations whichĭisagree with those of the chemical master equation. Particular, for unimolecular systems, these correction methods lead to CLE ![]() ![]() These methods introduce undesirable artefacts in the CLE's predictions. Various methods ofĬorrecting the CLE have been proposed which avoid its break down. Systems it is intrinsic to all representations of the CLE. Show that this issue is not a numerical integration problem, rather in many The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular. Negative quantities whenever the molecule numbers become sufficiently small. The CLE's main disadvantage is itsīreak down in finite time due to the problem of evaluating square roots of The stochastic dynamics of chemical systems. Then nonlinearities are introduced such that the semi-linear reaction Kramers equation describes particles which move and interact on the same time-scale. Download a PDF of the paper titled The complex chemical Langevin equation, by David Schnoerr and 2 other authors Download PDF Abstract: The chemical Langevin equation (CLE) is a popular simulation method to probe For the Kramers equation, moments are computed, the infinite system of moment equations is closed at several levels, and telegraph and diffusion equations are derived as approximations.
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