Related papers: A fresh look at the adhesion approximation
In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically.…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
Jeans instability of finite massive bodies at hydrostatic equilibrium is studied. Differential equation governing the evolution of infinitesimal disturbances is derived. We take into account radial inhomogeneity of mass density and other…
Composite likelihood usually ignores dependencies among response components, while variational approximation to likelihood ignores dependencies among parameter components. We derive a Gaussian variational approximation to the composite…
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
We explore two aspects of geometric approximation via a coupling approach to Stein's method. Firstly, we refine precision and increase scope for applications by convoluting the approximating geometric distribution with a simple translation…
A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
The gravitational instability of expanding shells is discussed. Linear and nonlinear terms are included in an analytical solution in the static and homogeneous medium. We discuss the interaction of modes and give the time needed for…
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…