Related papers: Diffusion in multi-dimensional solids using Forman…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
The fabric of porous and fractured media contains solid regions (grains) and voids. The space conducting fluids is a system of connected voids with variable geometries. Relative to the grain sizes, the voids can be voluminous with three…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…
A recent solution of the inelastic Boltzmann equation that applies for strong dissipation and takes into account non-equipartition of energy is used to derive an explicit expression for the thermal diffusion factor. This parameter provides…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
Turbulent thermals emerge in a wide variety of geophysical and industrial flows, such as atmospheric cumulus convection and pollutant dispersal in oceans and lakes. When a buoyant fluid mass rises, or sinks, heat and mass transfers occur by…
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…
A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…