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By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the…
Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing…
We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…
The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability of a…
There are well-established connections between combinatorial optimization, optimal transport theory and Hydrodynamics, through the linear assignment problem in combinatorics, the Monge-Kantorovich problem in optimal transport theory and the…
The hydrophobic effect is the dominant force which drives a protein towards its native state, but its physics has not been thoroughly understood yet. We introduce an exactly solvable model of the solvation of non-polar molecules in water,…
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we treat conservation of momentum as a tensor equation and…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and tested extensively in…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
Relativistic fluid dynamics finds application in astrophysics, cosmology and the physics of high-energy heavy-ion collisions. In this thesis, we present our work on the formulation of relativistic dissipative fluid dynamics within the…
We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. The problem is…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…
Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…
We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary…