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Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a (3+1) slicing of spacetime, a Langevin equation for the dynamical conjugate momentum and a Fokker-Planck equation for…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
The dynamics of one and two identical spheres rolling in a nearly-levitating upflow of air obey the Langevin Equation and the Fluctuation-Dissipation Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631 (2005)]. To probe…
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for spectra of temporal fluctuations. Such non-local connections…
We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest $0^{+}$ and $1^{+}$-resonances in…
We examine long-time properties of the ideal dynamics of three--dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
In order to understand the origin of one-body dissipation in nuclei, we analyze the behavior of a gas of classical particles moving in a two-dimensional cavity with nuclear dimensions. This "nuclear" billiard has multipole-deformed walls…
These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation…
We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided into a grid of cells…
Large entropy fluctuations in a nonequilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2-freedom model with the so-called Gauss time-reversible thermostat. The local fluctuations (on a…
The statistical distribution for the case of an adiabatically isolated body was obtained in the framework of covariant quantum theory and Wick's rotation in the complex time plane. The covariant formulation of the mechanics of an isolated…