The classical theory of transport processes is based on the Boltzmann transport equation. The equation can be derived simply by defining a distribution function and inspecting its time derivative. From this equation, many important results can be derived. In addition to some of the textbook results from the Boltzmann transport equation, it is still being used in many contemporary research proje...

advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

Numerous theories have been presented over the years for quantifying bedload transport in streams and rivers. These derived using physical processes, statistical methods, semiempirical empirical methods rely on a variety of hydraulic, boundary, bed material properties. Most these equations represent instantaneous related to temporal hydraulic conditions are not well-suited estimate long-term av...

Inpainting, the technique of modifying an image in an undetectable form, is as ancient as art itself. The goalsand applications of inpainting are numerous, from the restoration of damaged paintings and photographs to the deletionof selected objects. In this talk, we will introduce a novel algorithm for digital inpainting of still images that attempts2 to replicate the basic techniqu...

The aim of the present research was to investigate the feasibility of a probability density function (PDF) methodology combined with a large eddy simulation (LES) for turbulent reactive mixing in industrial geometries. In order to incorporate the PDF transport equation into a LES context, a filtered version was employed, denoted as filtered density function (FDF) equation. Using FDF/LES, the yi...

We consider the theory of erosion and investigate connections to the theory of optimal transport. The mathematical theory of erosion is based on two coupled nonlinear partial differential equations. The first one describing the water flow can be considered to be an averaged NavierStokes equation, and the second one describing the sediment flow is a very degenerate nonlinear parabolic equation. ...

A three-dimensional numerical model is developed for the simulation of water flow and chemical transport through variably saturated porous media. The nonlinear flow equation is solved using the Galerkin finite element technique with the Picard iteration scheme and a continuous velocity field is obtained by separate application of the Galerkin technique to the flux equation. A two-site adsorptio...

Reactive systems in a thermochemical conversion domain are modelled considering N-specie, 1-energy and 2-mass conservation equations assuming negligible pressure gradient resulting N+3 non-linear coupled PDE system with dependency on thermodynamic transport properties. Typically, simplistic temperature-dependent polynomials chosen for estimating thermal conductivity specific heat, however, the ...

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