Related papers: Fronts under arrest II: analytical foundations
When bacteria are grown on a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. The pedestrian dynamics are driven by aversion and cohesion, i.e. the tendency…
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that…
The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
In this work, we investigate the shape evolution of rotated, embedded, initially cylindrical grains (with [001] cylinder axis) in Ni under an applied synthetic driving force via molecular dynamics simulations and a continuum,…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
Most organisms grow in space, whether they are viruses spreading within a host tissue or invasive species colonizing a new continent. Evolution typically selects for higher expansion rates during spatial growth, but it has been suggested…
Foundation models (FMs) are changing the way medical images are analyzed by learning from large collections of unlabeled data. Instead of relying on manually annotated examples, FMs are pre-trained to learn general-purpose visual features…
This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that…
In this thesis I present most of the results obtained during my PhD, where I worked on different subjects regarding jamming in systems of frictionless spheres. In particular, I focused on microscopic properties of jammed packings, such as…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved…
Foundation models have shown great promise in various fields of study. A potential application of such models is in computer network traffic analysis, where these models can grasp the complexities of network traffic dynamics and adapt to…