Related papers: Mathematical Model of a pH-gradient Creation at Is…
The mathematical model describing the stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed and investigated. The model is a part of a more general…
The mathematical model describing the non-stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed and investigated. The model is part of a more general…
The mathematical model describing the non-stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed. The model is a part of a more general model of the…
A mathematical model describing a steady pH-gradient in the solution of ampholytes in water has been studied with the use of analytical, asymptotic, and numerical methods. We show that at the large values of an electric current a…
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3]. The main…
This work focuses on the mathematical analysis of the Cauchy problem associated with a two-dimensional equation describing the dynamics of a thin fluid film flowing down an inclined flat plate under the influence of gravity and an electric…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable…
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation…
This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects such as Bose-Einstein condensates (BECs). In this regime,…
We present a model of groundwater dynamics under stationary flow and governed by Darcy's Law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of an homogeneous and…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
In this paper we develop an artificial initial boundary value problem for the high-order heat equation in a bounded domain $\Omega$. It is found an unique classical solution of this problem in an explicit form and shown that the solution of…
We present a hydrodynamical code based on the Smooth Particle Hydrodynamics technique implemented in an AP3M code aimed at solving the hydrodynamical and gravitational equations in a cosmological frame. We analyze the ability of the code to…
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that…
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…
In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first variation of a hydrophobic attraction domain functional. The…