Related papers: A dynamic model for viscoelasticity in domains wit…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by…
In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviours have previously been investigated typically using purely elastic substrates. For a…
We consider a well-known quasi-static model for the shape of a liquid droplet. The solution can be described in terms of time-evolving domains in $\mathbb{R}^n$. We give an example to show that convexity of the domain can be instantaneously…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…
This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies adopted by crawlers to achieve locomotion,…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient…
In this article we review existing literature on dynamic copulas and then propose an n-copula which varies in time and space. Our approach makes use of stochastic differential equations, and gives rise to a dynamic copula which is able to…
We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model…
A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stress recently reported in [1] is presented. The predictions of the model are in…
This paper discusses the time-dependence of the threshold function in the perfect plasticity model. In physical terms, it is natural that the threshold function depends on some unknown variable. Therefore, it is meaningful to discuss the…
In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…