Brownian motion of free particles on curved surfaces
@article{CastaedaPriego2012BrownianMO, title={Brownian motion of free particles on curved surfaces}, author={Ram{\'o}n Casta{\~n}eda-Priego and Pavel Castro-Villarreal and Sendic Estrada-Jim'enez and Jos'e Miguel M'endez-Alcaraz}, journal={arXiv: Statistical Mechanics}, year={2012} }
Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion equation on curved manifolds [J. Stat. Mech. (2010) P08006]. Therefore, we use the latter in order to analytically investigate the whole diffusive dynamics in compact geometries, namely, the circle and the sphere. Our findings are corroborated by means of Brownian…
5 Citations
Observables for Brownian motion on manifolds
- Mathematics
- 2012
We study the geometrical influence on the Brownian motion over curved manifolds. We focus on the following intriguing question: what observables are appropriated to measure Brownian motion in curved…
Stochastic heat diffusion modelling with random walks on the non-uniformly gridded circle
- Mathematics2014 American Control Conference
- 2014
The Markov chain is characterized for a given grid in order to build a framework for the numerical approximation of the solution to the heat equation on Riemannian manifolds, which approximates the Laplace-Beltrami operator which is used on such manifolds.
Stochastic Heat Diffusion Modelling and the Discrete Laplace-Beltrami Operator on Non-Uniformly Gridded Closed Curves
- Mathematics
- 2015
: This paper presents a technique to approximate heat di ff usion on Riemannian manifolds. Specifically, the authors provide a framework to approximate the solution to the heat equation by using the…
Generally covariant state-dependent diffusion
- Physics
- 2013
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of…
Mixing-demixing transition and void formation in quasi-2D binary mixtures on a sphere.
- MathematicsThe Journal of chemical physics
- 2022
Motivated by observations of the heterogeneous domain structure on the surface of cells and vesicles and by domain formation due to the adsorption of complex molecules onto composite membranes, we…
References
SHOWING 1-10 OF 26 REFERENCES
A comprehensive introduction to differential geometry
- Mathematics
- 1975
Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introduction…
Quantum Field Theory and Critical Phenomena
- Physics
- 2002
Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for…
Phys
- Rev. E 60, 302
- 1999
Mech
- 282 373
- 1995
A: Math
- Gen. 31, 7005-7009
- 1998
Phys
- 106, 1880
- 1997