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Despite the increasing use of the Particle Finite Element Method (PFEM) in fluid flow simulation and the outstanding success of the Generalized-alpha time integration method, very little discussion has been devoted to their combined…

First version: del Barco et al. submitted recently a comment [arXiv:0812.4070] on our latest Phys. Rev. Lett. [Phys. Rev. Lett. 101, 237204 (2008)], claiming three basic mistakes. We show here that their claims are unjustified and based on…

We revisit the molecular arguments underpinning the Eulerian model for compressible and diffusive flows, and conclude that a heat diffusive term appears to be missing in the original model. By studying a pure heat transfer problem, we…

Developing a quantitative understanding of wave plasma processes in the lower ionosphere requires a reasonably accurate theoretical description of the underlying physical processes. For such highly collisional plasma environment as the…

We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We…

Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

The possibility that the type of discontinuous flow changes as the conditions gradually (continuously) change is investigated in connection with the problems arising when the results of numerical simulations of magnetic reconnection in…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

The recent paper cited above claims that a molecular simulation of one specific model of supercooled water establishes a stable interface separating two metastable liquid phases, which would imply the existence of metastable two-liquid…

We investigate the question, "how does time flow?" and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to…

We investigate the charge transport properties of a relativistic drifting plasma using the kinetic theory within the relaxation time approximation. The collective drift induced by electromagnetic fields is described in terms of a suitably…

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For active dispersion process in…

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…

Considering the natural ventilation, the thermal behavior of buildings can be described by a linear time varying model. In this paper, we describe an implementation of model reduction of linear time varying systems. We show the consequences…

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity…

We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…

In this paper, we consider an age-structured jump model that arises as a description of continuous time random walks with infinite mean waiting time between jumps. We prove that under a suitable rescaling, this equation converges in the…

Here we comment on the paper by Arthur D. Yaghjian, Phys. Rev. E 78, 046606 (2008) (arXiv:0805.0142). The author provides an equation of motion for a point charged particle in a certain regime of system parameters (on the other hand,…

The main purpose of this paper is mathematical analysis on time-periodic flows of electrons and holes in semiconductors. The flows appear in a situation that alternating-current voltages are applied to devices. In this paper, we study the…