Related papers: A model of morphogen transport II
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen…
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
We construct infinitely many incompressible Sobolev vector fields $u \in C_t W^{1,\tilde p}_x$ on the periodic domain $\mathbb{T}^d$ for which uniqueness of solutions to the transport equation fails in the class of densities $\rho \in C_t…
We prove existence and uniqueness of solutions for a system of PDEs which describes the growth of a sandpile in a silos with flat bottom under the action of a vertical, measure source. The tools we use are a discrete approximation of the…
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
The transmission of light through an ensemble of two-level emitters in a one-dimensional geometry is commonly described by one of two emblematic models of quantum electrodynamics (QED): the driven-dissipative Dicke model or the…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
We study longitudinal electric and thermoelectric transport coefficients of Dirac fermions on a simple lattice model where tuning of a single parameter enables us to change the type of Dirac cones from type-I to type-II. We pay particular…