Related papers: A fractal graph model of capillary type systems
Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems, but need…
Suppose a graph-directed iterated function system consists of maps f_e with upper estimates of the form d(f_e(x),f_e(y)) <= r_e d(x,y). Then the fractal dimension of the attractor K_v of the IFS is bounded above by the dimension associated…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open…
Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are…
Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains…
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz…
In this paper, an anisotropic volume-preserving mean curvature type flow for star-shaped anisotropic $\omega_0$-capillary hypersurfaces in the half-space is studied, and the long-time existence and smooth convergence to a capillary Wulff…
Consider a routing problem consisting of a demand graph H and a supply graph G. If the pair obeys the cut condition, then the flow-cut gap for this instance is the minimum value C such that there is a feasible multiflow for H if each edge…
Objects moving in fluids experience patterns of stress on their surfaces determined by the geometry of nearby boundaries. Flows at low Reynolds number, as occur in microscopic vessels such as capillaries in biological tissues, have…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the…
Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump…
A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved,…
A mesoscopic or coarse-grained approach is presented to study thermo-capillary induced flows. An order parameter representation of a two-phase binary fluid is used in which the interfacial region separating the phases naturally occupies a…
In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called…
Intracardiac flow patterns are shaped by the coupled motion of the cardiac chambers and heart valves and provide important information about cardiac function. However, clinical flow imaging remains limited by exam times, noise, resolution,…
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded…
We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the…
Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is shown that the resulting systems are thermodynamically…