相关论文: The candy wrapper problem -- a temporal multiscale…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
Lipid membranes form the barrier between the inside and outside of cells and many of their subcompartments. As such, they bind to a wide variety of nano- and micrometer sized objects and, in the presence of strong adhesive forces, strongly…
We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an…
Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…
Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient…
The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integro-differential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters.…
Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
Background and Objective: The role of red blood cell dynamics is emphasised in certain cardiovascular diseases, and thus needs to be closely studied. A multiphase model of blood flow allows the resolution of locally varying density of red…
We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, and are also more…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
Biomarker measurements obtained by blood sampling are often used as a non-invasive means of monitoring tumour progression in cancer patients. Diseases evolve dynamically over time, and studying longitudinal observations of specific…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…
Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types.…
In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance, in the case of a bone tumor in a femur) initial colony. In…