scholarly journals Thermodynamic laws and equipartition theorem in relativistic Brownian motion

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
T. Koide ◽  
T. Kodama
Keyword(s):  
Brownian Motion ◽  
Equipartition Theorem

Highly Resolved Brownian Motion in Space and in Time

2019 ◽  
Vol 51 (1) ◽  
pp. 403-428 ◽  
Author(s):  
Jianyong Mo ◽  
Mark G. Raizen
Keyword(s):  
Brownian Motion ◽  
Solid Wall ◽  
Experimental Studies ◽  
Supercooled Liquid ◽  
Fluid Interfaces ◽  
Short Timescale ◽  
Brownian Particles ◽  
Equipartition Theorem ◽  
Energy Equipartition ◽  
Long Timescales

Since the discovery of Brownian motion in bulk fluids by Robert Brown in 1827 , Brownian motion at long timescales has been extensively studied both theoretically and experimentally for over a century. The theory for short-timescale Brownian motion was also well established in the last century, while experimental studies were not accessible until this decade. This article reviews experimental progress on short-timescale Brownian motion and related applications. The ability to measure instantaneous velocity enables new fundamental tests of statistical mechanics of Brownian particles, such as the Maxwell–Boltzmann velocity distribution and the energy equipartition theorem. In addition, Brownian particles can be used as probes to study boundary effects imposed by a solid wall, wettability at solid–fluid interfaces, and viscoelasticity. We propose future studies of fluid compressibility and nonequilibrium physics using short-duration pulsed lasers. Lastly, we also propose that an optically trapped particle can serve as a new testing ground for nucleation in a supersaturated vapor or a supercooled liquid.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Model demonstration of brownian motion

1971 ◽  
Vol 105 (12) ◽  
pp. 736-736
Author(s):  
V.I. Arabadzhi
Keyword(s):  
Brownian Motion
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