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Mixtures of lipids and cholesterol are commonly used as model systems for studying the formation of liquid-ordered ($L_o$) domains in heterogeneous biological membranes. The simplest model system exhibiting coexistence between $L_o$ domains…
Triply periodic continuous morphologies arising a result of the microphase separation in block copolymer melts have so far never been observed self-assembled in systems of particles with spherically symmetric interaction. We report a…
Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase…
We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the…
We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a…
Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of…
Fibers of bent-core liquid crystals present an internal structure of a rolled smectic layer and can be used as optical waveguides. We used a field-theoretical Monte Carlo simulation to analyze the internal configuration of such fibers as a…
We demonstrate theoretically an atomic liquid phase that supports topologically nontrivial electronic structure. A minimum two-orbital model of liquid topological insulator in two dimensions is constructed within the framework of…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
Discotic colloids give rise to a paradigmatic family of liquid crystals with sound applications in Materials Science. In this paper, Monte Carlo simulations are employed to characterize the low-temperature liquid crystal phase diagram and…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the…
We study simple lattice systems to demonstrate the influence of interpenetrating bond networks on phase behavior. We promote interpenetration by using a Hamiltonian with a weakly repulsive interaction with nearest neighbors and an…
We study the different phases and the phase transitions in a system of $Y$-shaped particles, examples of which include Immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume…
Nano- to micro-sized particles with differently charged surface areas exhibit complex interaction patterns, characterized by both opposite-charge attraction and like-charge repulsion. While several successful models have been proposed in…
The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical…
We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low…
Biased diffusion of two species with conserved dynamics on a 2xL periodic lattice is studied via Monte Carlo simulations. In contrast to its simple one-dimensional version on a ring, this quasi one-dimensional model surprisingly exhibits…
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description.…