Distribution functions for the Brownian motion of particles in a periodic potential driven by an external force

1979 ◽  
Vol 34 (3) ◽  
pp. 313-322 ◽  
Author(s):  
H. D. Vollmer ◽  
H. Risken
Keyword(s):  
Brownian Motion ◽  
External Force ◽  
Periodic Potential ◽  
Distribution Functions

scholarly journals On the time spent above a level by Brownian motion with negative drift

1986 ◽  
Vol 18 (04) ◽  
pp. 1017-1018 ◽  
Author(s):  
J.-P. Imhof
Keyword(s):  
Brownian Motion ◽  
Limit Theorems ◽  
Distribution Functions ◽  
Probability Densities ◽  
Negative Drift

Limit theorems of Berman involve the total time spent by Brownian motion with negative drift above a fixed or exponentially distributed negative level. We give explicitly the probability densities and distribution functions, obtained via an equivalence of laws.

scholarly journals Enhancement of Brownian motion for a chain of particles in a periodic potential

2018 ◽  
Vol 97 (2) ◽  
Author(s):  
Tommy Dessup ◽  
Christophe Coste ◽  
Michel Saint Jean
Keyword(s):  
Brownian Motion ◽  
Periodic Potential ◽  
A Chain

Enhanced Diffusion in a Model of Molecular Motors with Potential Switching

2019 ◽  
Vol 18 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Ryota Shinagawa ◽  
Kazuo Sasaki
Keyword(s):  
Diffusion Coefficient ◽  
External Force ◽  
Molecular Motors ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Molecular Motor ◽  
Free Diffusion ◽  
Enhanced Diffusion ◽  
Additional Peak ◽  
Diffusion Enhancement

Diffusion enhancement is a phenomenon in which the diffusion coefficient of a system is increased by an external force and it becomes larger than that of the force-free diffusion in thermal equilibrium. It is known that this phenomenon occurs for a Brownian particle in a periodic potential under a constant external force. Recently, it was found that diffusion enhancement also occurred in a biological molecular motor, whose moving part could move itself by switching the potentials generated by the other parts. It was shown that the diffusion coefficient exhibited peaks as a function of a constant external force. Here, we report the occurrence of an additional peak and investigate the condition governing its appearance.

FRACTIONAL BROWNIAN MOTION WITH STOCHASTIC VARIANCE: MODELING ABSOLUTE RETURNS IN STOCK MARKETS

2008 ◽  
Vol 19 (08) ◽  
pp. 1221-1242 ◽  
Author(s):  
H. E. ROMAN ◽  
M. PORTO
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Markets ◽  
Distribution Functions ◽  
Conditional Heteroskedasticity ◽  
Arch Models ◽  
Variance Modeling ◽  
Probability Distribution Functions ◽  
Second Moments ◽  
Long Time

We discuss a model for simulating a long-time memory in time series characterized in addition by a stochastic variance. The model is based on a combination of fractional Brownian motion (FBM) concepts, for dealing with the long-time memory, with an autoregressive scheme with conditional heteroskedasticity (ARCH), responsible for the stochastic variance of the series, and is denoted as FBMARCH. Unlike well-known fractionally integrated autoregressive models, FBMARCH admits finite second moments. The resulting probability distribution functions have power-law tails with exponents similar to ARCH models. This idea is applied to the description of long-time autocorrelations of absolute returns ubiquitously observed in stock markets.

Hydrodynamic diffusion in active microrheology of non-colloidal suspensions: the role of interparticle forces

2015 ◽  
Vol 785 ◽  
pp. 189-218 ◽  
Author(s):  
N. J. Hoh ◽  
R. N. Zia
Keyword(s):  
Brownian Motion ◽  
External Force ◽  
Hydrodynamic Limit ◽  
Thermal Fluctuations ◽  
Longitudinal Force ◽  
Experimental Measurements ◽  
Interparticle Forces ◽  
Pair Density ◽  
Far From Equilibrium

Hydrodynamic diffusion in the absence of Brownian motion is studied via active microrheology in the ‘pure-hydrodynamic’ limit, with a view towards elucidating the transition from colloidal microrheology to the non-colloidal limit, falling-ball rheometry. The phenomenon of non-Brownian force-induced diffusion in falling-ball rheometry is strictly hydrodynamic in nature; in contrast, analogous force-induced diffusion in colloids is deeply connected to the presence of a diffusive boundary layer even when Brownian motion is very weak compared with the external force driving the ‘probe’ particle. To connect these two limits, we derive an expression for the force-induced diffusion in active microrheology of hydrodynamically interacting particles via the Smoluchowski equation, where thermal fluctuations play no role. While it is well known that the microstructure is spherically symmetric about the probe in this limit, fluctuations in the microstructure need not be – and indeed lead to a diffusive spread of the probe trajectory. The force-induced diffusion is anisotropic, with components along and transverse to the line of external force. The latter is identically zero owing to the fore–aft symmetry of pair trajectories in Stokes flow. In a naïve first approach, the vanishing relative hydrodynamic mobility at contact between the probe and an interacting bath particle was assumed to eliminate all physical contribution from interparticle forces, whereby advection alone drove structural evolution in pair density and microstructural fluctuations. With such an approach, longitudinal force-induced diffusion vanishes in the absence of Brownian motion, a result that contradicts well-known experimental measurements of such diffusion in falling-ball rheometry. To resolve this contradiction, the probe–bath-particle interaction at contact was carefully modelled via an excluded annulus. We find that interparticle forces play a crucial role in encounters between particles in the hydrodynamic limit – as they must, to balance the advective flux. Accounting for this force results in a longitudinal force-induced diffusion $D_{\Vert }=1.26aU_{S}{\it\phi}$, where $a$ is the probe size, $U_{S}$ is the Stokes velocity and ${\it\phi}$ is the volume fraction of bath particles, in excellent qualitative and quantitative agreement with experimental measurements in, and theoretical predictions for, macroscopic falling-ball rheometry. This new model thus provides a continuous connection between micro- and macroscale rheology, as well as providing important insight into the role of interparticle forces for diffusion and rheology even in the limit of pure hydrodynamics: interparticle forces give rise to non-Newtonian rheology in strongly forced suspensions. A connection is made between the flow-induced diffusivity and the intrinsic hydrodynamic microviscosity which recovers a precise balance between fluctuation and dissipation in far from equilibrium suspensions; that is, diffusion and drag arise from a common microstructural origin even far from equilibrium.

scholarly journals Brownian local times

1995 ◽  
Vol 8 (3) ◽  
pp. 209-232 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Brownian Motion ◽  
Brownian Bridge ◽  
Distribution Functions ◽  
Local Times ◽  
Explicit Formulas ◽  
Brownian Excursion ◽  
Reflecting Brownian Motion ◽  
Brownian Meander

In this paper explicit formulas are given for the distribution functions and the moments of the local times of the Brownian motion, the reflecting Brownian motion, the Brownian meander, the Brownian bridge, the reflecting Brownian bridge and the Brownian excursion.

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