相关论文: On the first bifurcation point for a free boundary…
The early stages of clot formation in blood vessels involve platelets adhesion-aggregation. Although these mechanisms have been extensively studied, gaps in their understanding still persist. We have performed detailed in-vitro experiments…
Alzheimer's disease is not the outcome of a single cause but the convergence of many. This review reframes dementia as a systemic failure, where amyloid plaques and tau tangles are not root causes but late-stage byproducts of the underlying…
This paper concerns a free boundary problem modeling tumor growth with angiogenesis and two time delays. The two delays represent the time taken for cells to undergo mitosis and modify the rate of cell loss because of apoptosis,…
Occlusive thrombosis in arteries causes heart attacks and strokes. The rapid growth of thrombus at elevated shear rates (~10,000 1/s) relies on shear-induced platelet aggregation (SIPA) thought to come about from the entanglement of von…
We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new…
This paper investigates the existence of periodic solutions in blood flow propagating through vessels with free boundary conditions via the bifurcation theory. It is rigorously proved that a local $C^1$-curve of small-amplitude periodic…
Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient…
In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a 1-D finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinct…
In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we…
The geometry of blood vessels strongly affects hemostasis and thrombosis through red blood cell (RBC) dynamics and platelet margination. Growing platelet aggregates, in turn, reshape the local vessel wall topography, leading to a strongly…
Multiple Sclerosis (MS) is a disorder that usually appears in adults in their thirties. It has a prevalence that ranges between 2 and 150 per 100 000. Epidemiological studies of MS have provided hints on possible causes for the disease…
A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields…
We consider the free boundary problem for a liquid drop of nearly spherical shape with capillarity, and we study the existence of nontrivial (i.e., non spherical) rotating traveling profiles bifurcating from the spherical shape, where the…
We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution…
The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in a porous pellet. A method has been proposed for the development…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Stroke is one of two main causes of death worldwide. Many individuals suffer from ischemic stroke every year. Only in US more over 700,000 individuals meet ischemic stroke due to blood clot blocking an artery to the brain every year. The…
We investigate bubble dynamics in a holographic superfluid undergoing a first-order phase transition with spontaneous $U(1)$ symmetry breaking. Near the nucleation threshold, the system exhibits universal critical behavior governed by a…
In the current manuscript, a first two-patch model with Allee effect and nonlinear dispersal is presented. We study both the ODE case and the PDE case here. In the ODE model, the stability of the equilibrium points and the existence of…