相关论文: Bifurcation analysis in a frustrated nematic cell

We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…

We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus…

In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…

We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…

We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…

The uniqueness of equilibrium for a compressible, hyperelastic body subject to dead-load boundary conditions is considered. It is shown, for both the displacement and mixed problems, that there cannot be two solutions of the equilibrium…

In this paper, we prove the stability of half-degree point defect profiles in $\mathbb{R}^2$ for the nematic liquid crystal within Landau-de Gennes model.

Using computer simulations of an atomistic glass-forming liquid, we investigate the fluctuations of the overlap between a fluid configuration and a quenched reference system. We find that large fluctuations of the overlap develop as…

A novel flow instability emerging during a rheometric flow of a phase change material sheared in the vicinity of the solid-fluid transition is reported. Right above the onset of the flow induced crystallisation, the presence of the crystals…

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…

We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…

The classical problem of two uniformly charged infinite planes in electrochemical equilibrium with an infinite monovalent salt reservoir is solved exactly at the mean-field nonlinear Poisson-Boltzmann (PB) level, including an explicit…

We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields.…

We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…

We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…

In this work, we are motivated by a recent variant of the nonlinear Schrodinger (NLS) equation describing cold, dilute atomic condensates with quantum fluctuation effects. Our goal is to develop robust numerical methods capable of…

Mathematical models for physiological processes aid qualitative understanding of the impact of various parameters on the underlying process. We analyse two such models for human physiological processes: the Mackey-Glass and the Lasota…

Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…