相关论文: Stable distribution in fragmentation processes

In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $\Sigma$ and a stochastic memoryless map $\Psi$. After that, we extend the result to the class of large…

Motivated by the occurrence of "shattering" mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete--continuous fragmentation models.…

This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…

We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…

We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…

We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x>x_0 where x_0 is an atomic cut-off. Subsequently the fragmentation process continues for each of those daughter pieces whose sizes…

The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed…

We present a method to find the best temporal partition at any time-scale and rank the relevance of partitions found at different time-scales. This method is based on random walkers coevolving with the network and as such constitutes a…

Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional settings. However, they require a strict control of the…

We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…

This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…

We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

The segregation of plasmids in a bacterial population is investigated. Hereby, a dynamical model is formulated in terms of a size-structured population using a hyperbolic partial differential equation incorporating non-local terms (the…

We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…

We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\alpha$,…