Related papers: On the first bifurcation point for a free boundary…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
Disturbances in calcium homeostasis in a cardiac myocyte can lead to calcium-overload conditions and abnormal calcium releases, which occur primarily in the following two phases of the action potential (AP): (a) triggered or late calcium…
This study investigates an SEIS PDE model with a free boundary, which captures the dynamics of epidemic transmission, including diseases like COVID-19. This parabolic PDE system is analyzed in a rotationally symmetric domain, and the…
The structure of the boundary layer region between the disc and a comparatively slowly rotating star is studied using a causal prescription for viscosity. The vertically integrated viscous stress relaxes towards its equilibrium value on a…
Blood clotting is an important physiological process to suppress bleeding upon injury, but when it occurs inadvertently, it can cause thrombosis, which can lead to life threatening conditions. Hence, understanding the microscopic…
In bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the…
Driven by diverse applications, several recent models impose randomly switching boundary conditions on either a PDE or SDE. The purpose of this paper is to provide tools for calculating statistics of these models and to establish a…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation…
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model…
The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half plane, in which reaction-diusion phenomena take place, exchanges mass with a line having a large diusion of its…
We investigate planar piecewise-smooth vector fields with a discontinuity line, focusing on the bifurcation of crossing limit cycles that arise when one of the vector fields is translated along the discontinuity set. We establish…
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freely-moving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is…
We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct…
Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…
In systems displaying a bulk first-order transition the order parameter may vanish continuously at a free surface, a phenomenon which is called surface-induced disorder. In the presence of surface-induced disorder the correlation lengths,…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…
Cerebrovascular diseases such as brain aneurysms are a primary cause of adult disability. The flow dynamics in brain arteries, both during periods of rest and increased activity, are known to be a major factor in the risk of aneurysm…
Understanding the mechanism of nucleation of the stable phase inside the metastable parent phase during a first order phase transition has been a subject of outstanding interest in natural science. The problem becomes even more challenging…