相关论文: Einstein's Brownian motion model for chemotactic s…
We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce the…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years discoveries of many…
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…
Recent studies suggest that non-cooperative behavior such as cannibalism may also be a driving mechanism of collective motion. Motivated by these novel results we introduce a simple model of Brownian particles interacting by pursuit and…
The Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless real scalar field in Einstein's universe is studied. By assuming the small displacement condition, the dispersion in the momentum and position of a…
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely…
Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical constraints. These observations raise a fundamental question:…
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…
By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
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…
Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance…
Einstein's kinetic theory of the Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has…
This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further…
We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensionnal model of active particles. We…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a…