Related papers: An Analysis of the Evolution Equations for a Gener…
Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic…
We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted…
This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems.…
We study the system of equations which describes barotropic (isentropic) flows of viscous compressible multi-fluids (mixtures of fluids). We study the relations between pressure, densities, concentrations, viscosities and other parameters…
We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…
This paper is concerned with the diffusion of a fluid through a viscoelastic solid undergoing large deformations. Using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the…
We prove the existence of unique regular solutions of steady-state buoyancy-driven flows of viscous incompressible heat-conducting fluids in 3D open channels under mixed boundary conditions. The model takes into account the phenomena of the…
In this work we consider a mathematical model of the water treatment process and determine the effective characteristics of this model. At the microscopic length scale we describe our model in terms of a lattice random walk in a…
We first established the dynamic equations to describe the noisy circling motion of a single particle and the corresponding probability conservation equation in both two dimensions and three dimensions, and then developed the evolution…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
Interactions between microorganisms and their complex flowing environments are essential in many biological systems. We develop a model for microswimmer dynamics in non-Newtonian Poiseuille flows. We predict that swimmers in…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…
The purpose of the present work is two folded: (1) we propose a new mechanism for the origin of bulk viscosity in cosmological context, and then, (2) we address the thermodynamic implications of viscous cosmology based on the thermodynamics…
This paper deals with a generalized length-preserving flow for convex curves in the plane. It is shown that the flow exists globally and deforms convex curves into circles as time tends to infinity.
The diffusion of active microscopic organisms in complex environments plays an important role in a wide range of biological phenomena from cell colony growth to single organism transport. Here, we investigate theoretically and…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…