Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field

Open Communications in Nonlinear Mathematical Physics ◽

10.46298/ocnmp.7535 ◽

2021 ◽

Vol Volume 1 ◽

Author(s):

Giuseppe Gaeta

Keyword(s):

Force Field ◽

External Force ◽

Isotropic Case ◽

Uhlenbeck Process ◽

External Force Field ◽

Ornstein Uhlenbeck Process

We classify simple symmetries for an Ornstein-Uhlenbeck process, describing a particle in an external force field $f(x)$. It turns out that for sufficiently regular (in a sense to be defined) forces there are nontrivial symmetries only if $f(x)$ is at most linear. We fully discuss the isotropic case, while for the non-isotropic we only deal with a generic situation (defined in detail in the text).

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Bismuthene from sonoelectrochemistry as a superior anode for potassium-ion batteries

Journal of Materials Chemistry A ◽

10.1039/c9ta11000c ◽

2020 ◽

Vol 8 (1) ◽

pp. 453-460 ◽

Cited By ~ 18

Author(s):

Chao Shen ◽

Tianle Cheng ◽

Chunyan Liu ◽

Lu Huang ◽

Mengyang Cao ◽

...

Keyword(s):

Force Field ◽

External Force ◽

Potassium Ion ◽

Cycle Life ◽

High Rate ◽

Rate Performance ◽

Electrochemical Exfoliation ◽

Long Cycle Life ◽

External Force Field ◽

High Rate Performance

An external force field-assisted electrochemical exfoliation method was adopted to produce few-layered bismuthene nanosheets (FBNs). These FBNs exhibited a high rate performance and ultra-long cycle life for KIBs anode.

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Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

The European Physical Journal B ◽

10.1140/epjb/e2006-00116-y ◽

2006 ◽

Vol 50 (1-2) ◽

pp. 345-349 ◽

Cited By ~ 1

Author(s):

I. Kourakis ◽

A. P. Grecos

Keyword(s):

Force Field ◽

External Force ◽

Test Particle ◽

First Principles ◽

Particle Dynamics ◽

Field Modelling ◽

Mechanical Description ◽

Classical Test ◽

External Force Field ◽

Statistical Mechanical

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Deformation Behavior of Crystalline Polymer under External Force Field Investigated by X-ray and Neutron Scattering Techniques

KOBUNSHI RONBUNSHU ◽

10.1295/koron.66.527 ◽

2009 ◽

Vol 66 (12) ◽

pp. 527-535

Author(s):

Yoshinobu NOZUE ◽

Takashi SAKURAI ◽

Tatsuya KASAHARA ◽

Noboru YAMAGUCHI

Keyword(s):

Force Field ◽

Neutron Scattering ◽

External Force ◽

Deformation Behavior ◽

Crystalline Polymer ◽

X Ray ◽

External Force Field

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Limit motion of an Ornstein–Uhlenbeck particle on the equilibrium manifold of a force field

Journal of Applied Probability ◽

10.1017/s0021900200101627 ◽

1997 ◽

Vol 34 (04) ◽

pp. 924-938

Author(s):

Antonella Calzolari ◽

Federico Marchetti

Keyword(s):

Force Field ◽

Gradient Force ◽

Asymptotically Stable ◽

Natural Conditions ◽

Uhlenbeck Process ◽

Limit Process ◽

Damping Coefficients ◽

Ornstein Uhlenbeck Process ◽

Limit Motion ◽

Force Intensity

In this paper we consider a position–velocity Ornstein-Uhlenbeck process in an external gradient force field pushing it toward a smoothly imbedded submanifold of . The force is chosen so that is asymptotically stable for the associated deterministic flow. We examine the asymptotic behavior of the system when the force intensity diverges together with the diffusion and the damping coefficients, with appropriate speed. We prove that, under some natural conditions on the initial data, the sequence of position processes is relatively compact, any limit process is constrained on , and satisfies an explicit stochastic differential equation which, for compact , has a unique solution.

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