An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic.

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached . However, epidemiological data from Europe suggest that this approach is .

A Model for Reinfections and the Transition of Epidemics.

Reinfections of infected individuals during a viral epidemic contribute to the continuation of the infection for longer periods of time. In an epidemic, contagion starts with an infection wave, initially growing exponentially fast until it reaches a maximum number of infections, following which it wanes towards an equilibrium state of zero infections, assuming that no new variants have emerged. If reinfections are allowed, multiple such infection waves might occur, and the asymptotic equilibrium state is one in which infection rates are not negligible.

A comprehensive spatial-temporal infection model.

Motivated by analogies between the spread of infections and of chemical processes, we develop a model that accounts for infection and transport where infected populations correspond to chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates, and for the important parameter , that include areal density and its spatial distribution.

Drying in porous media with gravity-stabilized fronts: experimental results.

In a recent paper [Yiotis et al., Phys. Rev.

Analytical solutions of drying in porous media for gravity-stabilized fronts.

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction.

Pore-network study of the mechanisms of foam generation in porous media.

Understanding the role of pore-level mechanisms is essential to the mechanistic modeling and simulation of foam processes in porous media. Three different pore-level events can lead to foam formation: snapoff, leave behind, and lamella division. The initial state of the porous medium (fully saturated with liquid or already partially drained), as surfactant is introduced, also affects the different foam-generation mechanisms.

Pore-network study of the characteristic periods in the drying of porous materials.

We study the periods that develop in the drying of capillary porous media, particularly the constant rate (CRP) and the falling rate (FRP) periods. Drying is simulated with a 3-D pore-network model that accounts for the effect of capillarity and buoyancy at the liquid-gas interface and for diffusion through the porous material and through a boundary layer over the external surface of the material. We focus on the stabilizing or destabilizing effects of gravity on the shape of the drying curve and the relative extent of the various drying periods.

Pattern formation in reverse filtration combustion.

Using a pore-network simulator we study pattern formation in reverse filtration combustion in porous media. The two-dimensional pore network includes all relevant pore-level mechanisms, including heat transfer through the pore space and the solid matrix, fluid and mass transfer through the pore space, and reaction kinetics of a solid fuel embedded in the pores. Both adiabatic and nonadiabatic cases are considered, the latter modeled with the inclusion of heat losses from the pore network to the ambient.

Mixing and reaction fronts in laminar flows.

Autocatalytic reaction fronts between unreacted and reacted mixtures in the absence of fluid flow propagate as solitary waves. In the presence of imposed flow, the interplay between diffusion and advection enhances the mixing, leading to Taylor hydrodynamic dispersion. We present asymptotic theories in the two limits of small and large Thiele modulus (slow and fast reaction kinetics, respectively) that incorporate flow, diffusion, and reaction.

Crossing the elliptic region in a hyperbolic system with change-of-type behavior arisingin flow between two parallel plates.

Change-of-type behavior from hyperbolic to elliptic is common to quasilinear hyperbolic systems. This issue is addressed here for the particular case of miscible flow of three fluids between two parallel plates. Change of type occurs at the leading edge of the displacement front and reflects the failing of the equilibrium assumption, necessary for the quasilinear hyperbolic formalism, at the front.

The critical gas saturation in a porous medium in the presence of gravity.

The critical gas saturation, S(gc), denotes the volume fraction of the gas phase at the onset of bulk gas flow during the depressurization of a supersaturated liquid in a porous medium. In the absence of gradients due to viscous or gravity forces, S(gc) is controlled by nucleation, capillary forces, and the rate of decline of the supersaturation. In this paper we address one important additional effect, that of buoyancy.

Effect of liquid films on the isothermal drying of porous media.

We study the effects of liquid films on the isothermal drying of porous media. They are important for the transport of liquid to an evaporation interface, far from the receding liquid clusters. Through a transformation, the drying problem is mapped to the Laplace equation around the percolation liquid clusters.

Nonlocal Kardar-Parisi-Zhang equation to model interface growth.

The dynamics of the growth of interfaces in the presence of noise and when the normal velocity is constant, in the weakly nonlinear limit, are described by the Kardar-Parisi-Zhang (KPZ) equation. In many applications, however, the growth is controlled by nonlocal transport, which is not contained in the original KPZ equation. For these problems we are proposing an extension of the KPZ model, where the nonlocal contribution is expressed through a Hilbert transform and can act to either stabilize or destabilize the interface.

Identification of the permeability field of a porous medium from the injection of a passive tracer.

We propose a method for the direct inversion of the permeability field of a porous medium from the analysis of the displacement of a passive tracer. By monitoring the displacement front at successive time intervals (for example, using a tomographic method), the permeability can be directly obtained from the solution of a nonlinear boundary-value problem. Well posedness requires knowledge of the pressure profile or the permeability at no-flow boundaries.