Related papers: Time Invariant Scaling in Discrete Fragmentation M…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which…

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. Using a procedure inspired by the similar, but continuous case of jet fragmentation in QCD, this discretized process may be analyzed…

We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…

We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…

We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…

A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…

Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical…

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…

We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…

We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…

In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…

Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…

Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…

We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…

A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…

Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a…

We study the evolution of the universe which contains a multiple number of non-relativistic scalar fields decaying into both radiation and pressureless matter. We present a powerful analytic formalism to calculate the matter and radiation…

The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss…