Related papers: Brownian Motion for the School-Going Child
Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum…
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…
It is known that a full description of Brownian motion in the entire course of time should incorporate both kinetic and hydrodynamic effects, but a formula accounts for both effects has been established only in three dimension and only for…
The "Brownian map" is a fundamental object in mathematics, in some sense a 2-dimensional analogue of Brownian motion. Here we briefly explain this object and a bit of its history.
An elementary account of special relativity for school-children.
We study the problem of when a Brownian motion in the unit ball has a positive probability of avoiding a countable collection of spherical obstacles. We give a necessary and sufficient integral condition for such a collection to be…
Brownian motion has served as a pilot of studies in diffusion and other transport phenomena for over a century. The foundation of Brownian motion, laid by Einstein, has generally been accepted to be far from being complete since the late…
To stimulate the intellectual curiosity of elementary school students, we conducted a workshop in distance education aimed at exploring the microscopic world inside a cell. In this workshop, elementary school students motivated to learn…
In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…
Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are…
The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces [1]. Brownian motion, the motion of a small particle (pollen)…
A family of reflected Brownian motions is used to construct Dyson's process of non-colliding Brownian motions. A number of explicit formulae are given, including one for the distribution of a family of coalescing Brownian motions.
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.…
This chapter sets the stage for the rest of the book by exploring the role of intuition as a tool to deepen understanding in Einsteinian physics. Drawing on examples from the history of general relativity, we argue that the development of…
Interest in Brownian motion was shared by different communities: this phenomenon was first observed by the botanist Robert Brown in 1827, then theorised by physicists in the 1900s, and eventually modelled by mathematicians from the 1920s,…
Brownian motion provides a bedrock for the understanding of soft condensed matter and, therefore, of the physical description of the microscopic biological world. Inspired by this domain, and combining softness with hydrodynamic energy…
In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and…
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…
The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by…
This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…