Related papers: Brownian Motion - Past and Present
An "anorthodox" explanation of the recently discovered (1998) "acceleration" of the Universe is proposed.
The construction of the paths of all possible Brownian motions (in the sense of Knight) on a half line or a finite interval is reviewed.
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…
Einsteinian physics represents a distinct paradigm shift compared to Newtonian physics. There is worldwide interest in introducing Einsteinian physics concepts early in school curriculum and trials have demonstrated that this is feasible.…
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of…
In this paper we consider the iterated Brownian motion $ ^{\mu_1}_{\mu_2}\!I(t) = B_1^{\mu_1} ( | B_{2}^{\mu_2} (t)|) $ where $B_j^{\mu_j} , j=1,2$ are two independent Brownian motions with drift $\mu_j$. Here we study the last zero…
Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If \tau is the first…
We extend to the vector-valued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion. We also consider a Brownian motion as a Besov space valued random variable. It…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\'enyi entropy, the parameter of which being related in a…
We consider the problem of strong existence and uniqueness of a Brownian motion forced to stay in the quadrant by an electrostatic repulsion from the sides that works obliquely. The results are reminiscent of the study of a Brownian motion…
The migration of living cells obeys usually the Einstein law of Brownian motion. While the latter is due to the thermal motion of surrounding matter, the cells locomotion is generally associated to their vitality. In the present paper the…
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is…
In this paper we revisit the Brownian motion on the basis of {the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo in 1966. The importance of our approach is to…
I discuss Albert Einstein's 1916 General Theory of Relativity. I show that in Einstein's 1916 review paper, "the Foundation of the General Theory of Relativity", he derived his November 25, 1915 field equations with an additional term on…
We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
In this paper, we prove that a fuzzy set--valued Brownian motion $B_t$, as defined in [1], can be handle by an $R^d$--valued Wiener process $b_t$, in the sense that $B_t =\indicator{b_t}$; i.e. it is actually the indicator function of a…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…