Related papers: Self-regulated biological transportation structure…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
We present an efficient and robust numerical model for simulation of electrokinetic phenomena in porous networks over a wide range of applications including energy conversion, desalination, and lab-on-a-chip systems. Coupling between fluid…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By…
Following up on a previous work we examine a model of transportation network in some source-sink flow paradigm subjected to growth and resource allocation. The model is inspired from plants, and we add rules and factors that are analogous…
In this paper we consider a 2D nonlinear and nonlocal model describing the dynamics of the dislocation densities. We prove the local well-posedness of strong solution to this system in the suitable functional framework, and we show the…
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…
It was hypothesized that the structures of biological transport networks are the result of either energy consumption or adaptation dynamics. Although approaches based on these hypotheses can produce optimal network and form loop structures,…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Cells control the size and organization of biomolecular condensates formed by liquid-liquid phase separation (LLPS), but multiple mechanisms likely contribute to this control and remain to be fully elucidated. Here we propose a…
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
We consider degenerate diffusion equations of the form $\partial_tp_t = \Delta f(p_t)$ on a bounded domain and subject to no-flux boundary conditions, for a class of nonlinearities $f$ that includes the porous medium equation. We derive for…
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…