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$\text{CO}_{2}$ flooding is central to carbon utilization technologies, yet conventional waterflooding models fail to capture the complex interactions between CO$_2$ and formation fluids. In this study, one- and two-dimensional nuclear…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
An oxidation process is simulated for a bundle of metal tubes in a cross-flow. A fluid flow is governed by the incompressible Navier-Stokes equations. To describe the transport of oxygen, the corresponding convection-diffusion equation is…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…
The effects of outflow on the behavior of a viscous gaseous disc around a compact object in an advection-dominated state are examined in this paper. We suppose that the flow is steady, axisymmetric, and rotating. Also, we focus on the model…
Turbulent convection is ubiquitous in fluid systems. In particular, multi-physical convection problems involve mass, heat, and particle transfer. When the particles are charged and driven by a high-voltage electric field, both buoyancy and…
A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based…
Nuclear fusion could offer clean, abundant energy. However, managing the immense power exhausted from the core fusion plasma towards the divertor remains a major challenge. This is compounded in emerging compact reactor designs which…
Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
A proposed setting for thermonuclear (Type Ia) supernovae is a white dwarf that has gained mass from a companion to the point of carbon ignition in the core. In the early stages of carbon burning, called the simmering phase, energy released…
In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…
In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode…
Idealized convection-permitting simulations of radiative-convective equilibrium (RCE) have become a popular tool for understanding the physical processes leading to horizontal variability of tropical water vapor and rainfall. However, the…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
We investigate the nonequilibrium dynamics of a laser-pumped two-dimensional spinless Holstein model within a semiclassical framework, focusing on the melting and recovery of long-range charge-density-wave order. Accurately describing this…