Related papers: A Model of Blood Flow in a Circulation Network
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
Transport networks are crucial for the functioning of natural and technological systems. We study a mathematical model of vascular network adaptation, where the network structure dynamically adjusts to changes in blood flow and pressure.…
We build an evolutionary scenario that explains how some crucial physiological constraints in the arterial network of mammals - i.e. hematocrit, vessels diameters and arterial pressure drops - could have been selected by evolution. We…
Several advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, based on a…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters.…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
In this paper we study the initial boundary value problem for the system $\Delta v= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathbf{q}|}\right)\nabla u\right)=-\nabla…
We consider a model of axisymmetric flows for a free boundary vortex embedded in a statically stable fluid at rest. We identify the boundary of the vortex by solving a variational problem. Then, we reduce the analysis of the dynamics of the…
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…
A basic model of a dynamical distribution network is considered, 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 prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
Our aim is to study the Total Variation Flow in Metric Graphs. First, we define the functions of bounded variation in Metric Graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness…
Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on…
We discuss the characteristics of the patterns of the vascular networks in a mathematical model for angiogenesis. Based on recent in vitro experiments, this mathematical model assumes that the elongation and bifurcation of blood vessels…
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
The relationship between blood flow and neuronal activity is widely recognized, with blood flow frequently serving as a surrogate for neuronal activity in fMRI studies. At the microscopic level, neuronal activity has been shown to influence…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…