Related papers: Rate-independent evolution of sets
Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
Visco-Energetic solutions of rate-independent systems are obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation is reinforced by a viscous correction, typically a quadratic perturbation of…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes,…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
In regimes where inertia is negligible, the temporal evolution is governed by overdamped dynamics. This limit is particularly relevant in soft-matter contexts, such as polymers, colloidal suspensions, and processes occurring at the cellular…
In this thesis we study properties of open quantum dissipative evolutions of spin systems on lattices described by Lindblad generators, in a particular regime that we denote rapid mixing. We consider dissipative evolutions with a unique…
We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and…
We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule.…
Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time,…
Using finite difference method, time evolution of a typical metal molecule metal system is studied by introducing a new method to solve general related Volterra integro differential equation (IDE). Discretization in time domain is applied…
In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…