Related papers: Boundedness in a nonlinear chemotaxis-consumption …
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…
We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),& x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega, t>0,\\ z_t=\Delta z-z+u,…
We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive…
It has been suggested recently that growth and division of a protocell could be modeled by a chemically active droplet with simple chemical reactions driven by an external fuel supply. This model is called the continuum model. Indeed it's…
We use colloidal suspensions encapsulated in emulsion droplets to model confined glass-forming liquids with tunable boundary mobility. We show dynamics in these idealized systems are governed by physical interactions with the boundary.…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
Biological sensory systems generally operate out of equilibrium, which often leads to their improved performance. Here, we study the sensitivity of ligand concentration for a general receptor model, which is generally in the non-equilibrium…
The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on…
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between two infinite membranes. Like previous works, we are…
Diffusive motion of regulatory enzymes on biopolymers with eventual capture at a reaction site is a common feature in cell biology. Using a lattice gas model we study the impact of diffusion and capture for a microtubule polymerase and a…
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When…
A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at…
Conditional density matrix represents a quantum state of subsystem in different schemes of quantum communication. Here we discuss some properties of conditional density matrix and its place in general scheme of quantum mechanics.
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
We derive the nonequilibrium conductance matrix for open stationary Chemical Reaction Networks (CRNs) described by a deterministic mass action kinetic equation. As an illustration, we determine the nonequilibrium conductance matrix of a CRN…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…