Related papers: A Damage-Driven Model for Duchenne Muscular Dystro…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor $\epsilon$ are the fundamental variables. The evolution equations are based on a free energy that reduces to…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
This paper is concerned with the asymptotic analysis of a sequence of variational models of brittle damage in the context of linearized elasticity in the two-dimensional discrete setting. We consider a discrete version of Francfort and…
We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on…
Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The…
Muscular Dystrophy is a group of genetic disorders that progressively affect the strength and functioning of muscles, thereby affecting millions of people worldwide. The lifetime nature of MD requires continuous follow-up care due to its…
We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results…
Estimating intervention effects in dynamical systems is crucial for outcome optimization. In medicine, such interventions arise in physiological regulation (e.g., cardiovascular system under fluid administration) and pharmacokinetics, among…
This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…
Replication through cell division is one of the most fundamental processes of life and a major driver of dynamics in systems ranging from bacterial colonies to embryogenesis, tissues and tumors. While regulation often plays a role in…
Diffusion models have made breakthroughs in 3D generation tasks. Current 3D diffusion models focus on reconstructing target shape from images or a set of partial observations. While excelling in global context understanding, they struggle…
Multi-fingered hands are emerging as powerful platforms for performing fine manipulation tasks, including tool use. However, environmental perturbations or execution errors can impede task performance, motivating the use of recovery…
Simulation on directed graphs is an important method for understanding the dynamics in the systems where connectivity graphs contain cycles. Discrete Stochastic Heterogeneous Simulator (DiSH) is one of the simulation tools with wide…
Damage spreading for 2D Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions…
We study extended infection fronts advancing over a spatially uniform susceptible population by solving numerically a diffusive Kermack McKendrick SIR model with a dichotomous spatially random transmission rate, in two dimensions. We find a…
Accurately modeling the spatiotemporal evolution of tumor morphology from baseline imaging is a pre-requisite for developing digital twin frameworks that can simulate disease progression and treatment response. Most existing approaches…
The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction diffusion equations is built up on a mesoscopic…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
We study the genesis and the selective propagation of complex crack networks induced by thermal shock or drying of brittle materials. We use a quasi-static gradient damage model to perform large scale numerical simulations showing that the…