Related papers: Balance Laws and Transport Theorems for Flows with…
We consider an initial and boundary value problem invoked from the mathematical model for moisture transport in porous materials. Because of the difficulty appearing in the boundary condition, we have changed it and obtain the nonlinear…
We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. This is the situation encountered, for example, when analyzing the dynamics of sufficiently small particles immersed in a turbulent fluid and…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
We give a stochastic generalization of transport theorem on smooth manifold. Furthermore, we deduce a system of continuity equation and present some application on torus.
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
Polymer transport is investigated for two paradigmatic laminar flows having open and closed streamlines, respectively. For both types of flows we find transport depletion owing to the action of the polymers elastic degree of freedom. For…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
We present a generalized hydrodynamic stability theory for interacting particles in polydisperse particle-laden flows. The addition of dispersed particulate matter to a clean flow can either stabilize or destabilize the flow, depending on…
A generalized continuum framework for the theory of solute transport in fluids is proposed and systematically developed. This framework rests on the introduction of a generic force balance for the solute, a balance distinct from the…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and non-equilibrium thermodynamics. The governing equations of irreversible…
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…
We present the state-of-the-art theoretical modeling, molecular simulation, and coarse-graining strategies for the transport of gases and liquids in nanoporous materials (pore size 1-100 nm). Special emphasis is placed on the transport of…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…