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We consider a diffuse interface model describing a ternary system constituted by a conductive diblock copolymer and a homopolymer acting as solvent. The resulting dynamics is modeled by two Cahn--Hilliard--Oono equations for the copolymer…
In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in a…
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
Catalyst particles or complexes suspended in liquid films can trigger chemical reactions leading to inhomogeneous concentrations of reactants and products in the film. We demonstrate that the sensitivity of the liquid film's gas-liquid…
We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are…
We present a series of experimental investigations on binary mixtures of Bose-Einstein condensates. Our focus lies on the regime where the interaction parameters place the system at the threshold of miscibility. We demonstrate that the…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including…
We use the variational method to obtain approximate analytical expressions for the stationary pulselike solutions in birefringent fibers when differences in both phase velocities and group velocities between the two components and rapidly…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and…
A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better…
This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…
We present a computational study of static and dynamic linear polarizabilities in solution. We use different theoretical approaches to describe solvent effects, ranging from quantum mechanics/molecular mechanics (QM/MM) to quantum embedding…
Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived from the proper hydrodynamic balance…
This paper explores the analytical approach for obtaining the multiple solutions of three-wave interacting system in (1+1) dimensions. We present a novel approach by expressing the wave solutions in terms of Jacobi elliptic functions and…
We consider a model describing the steady flow of compressible heat-conducting chemically-reacting multi-component mixture. We show the existence of strong solutions under the additional assumption that the mixture is sufficiently dense. We…