相关论文: Stable distribution in fragmentation processes

A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of…

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the…

We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…

To predict allowable time-step size for the fully discretized nonlinear differential equations, a stability theory is developed using exact determination of an infinite perturbation series. Mathematical induction is used to determine the…

We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…

We consider two models (A and B) which can describe both two dimensional fragmentation and stochastic fractals. Model A exhibits multifractality on a unique support when describing a fragmentation process and on one of infinitely many…

This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…

We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect…

Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

Everyday thousands of meteoroids enter the Earth's atmosphere. The vast majority burn up harmlessly during the descent, but the larger objects survive, occasionally experiencing intense fragmentation events, and reach the ground. These…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…