Related papers: Flow Solutions of Transport Equations
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin 1/2.
We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the…
An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow,…
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well…
The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
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…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particles trajectories, we derive the corresponding governing equations for the concentration of the mobile and…
In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable…
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the…
In this paper we concern ourselves with an incompressible, viscous, isotropic, and periodic micropolar fluid. We find that in the absence of forcing and microtorquing there exists an infinite family of well-behaved solutions, which we call…
We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with $BV$ vector-fields that have divergence in $L^\infty$ (or in $L^1$) and that are nearly incompressible (see the text for…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable…
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established…
We study dynamic traffic assignment with side-constraints. We first give a counter-example to a key result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical edge-delay…
We construct a ring of flows where we can decompose autonomous nonlinear dynamical systems into smaller parts, then solve each part and finally put everything together to obtain the exact solution of these systems.