相关论文: Brownian Motion after Einstein: Some new applicati…

We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional…

We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where…

We consider different types of processes obtained by composing Brownian motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $% C(t)$ in different manners. We study also multidimensional iterated processes in…

Brownian motion in confinement and at interfaces is a canonical situation, encountered from fundamental biophysics to nanoscale engineering. Using the Lorenz-Mie framework, we optically record the thermally-induced tridimensional…

We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search…

Depuis le tout d\'ebut du XX${}^\text{e}$ si\`ecle, l'\'etude des processus stochastiques est un domaine tr\`es actif de la recherche en math\'ematiques. Parmi ces processus, le mouvement brownien --- dont l'\'etude math\'ematique a \'et\'e…

The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of…

We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian…

The aim of this paper is to remember and review several exceptional investigations on the theory of the Brownian motion. Although in these works the first correct hydrodynamic theories of the translational and rotational Brownian motion…

We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force…

We investigated three models of Brownian motors which convert rotational diffusion into directed translational motion by switching on and off a potential. In the first model a spatially asymmetric potential generates directed translational…

A particle that is immersed in a uniform temperature bath performs Brownian diffusion, as discussed by Einstein. But Sinai has realized that in a "random environment" the diffusion is suppressed. Follow-up works have pointed out that in the…

We establish an effective Markov theory for the rotational Brownian motion of hot nanobeads and nanorods. Compact analytical expressions for the effective temperature and friction are derived from the fluctuating hydrodynamic equations of…

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random…

Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family…

Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for…

A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also…

Biophotonic techniques are growing in rapid rhythms enabling the monitoring of subcellular structures and non-invasive theranostic interventions in cancer and autoimmune diseases. The integration of Biophotonics with nanotechnology and…

The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture…