Mitja Slavinec

Impact of Nanoparticles on Nematic Ordering in Square Wells

Nematic liquid crystalline structures within square wells are studied numerically using both Lebwohl-Lasher lattice semimicroscopic and the Landau-de Gennes mesoscopic approach. At lateral boundary wall strong planar anchoring is enforced. The cell thickness h along the z Cartesian coordinate is assumed to be smaller than the characteristic square well size R. Using semimicroscopic modelling we restrict to effectively two-dimensional systems which we study in terms of the tensor nematic order parameter. We consider impact of appropriate nanoparticles (NPs) on nematic configuration for cases where R becomes comparable to the biaxial order parameter correlation length. In this case a star-like order reconstruction biaxial profile could be formed in absence of NPs. We demonstrate existence of a rich variety of different nematic structures, including topological defects, which are enabled by presence of appropriate NPs.

Nonstationary chimeras in a neuronal network

Chimeras are special states that are composed of coexisting spatial domains of coherent and incoherent dynamics, which typically emerge in identically coupled oscillators. In this paper, we study a network of nonlocally coupled Hindmarsh-Rose neurons that are subject to an alternating current. We show that chimera states emerge when the neurons are connected through electrical synapses. The considered model has two coexisting attractors, namely a limit cycle and a chaotic attractor, to which the dynamics converges in dependence on the initial conditions. While earlier research reported the existence of chimeras in Hindmarsh-Rose neuronal networks mainly through chemical synapses, here we show that an alternating current in an electrically coupled network can also evoke chimeras, whereby the spatial positions of coherent and incoherent domains vary with time. Remarkably, we also observe chimera states in locally coupled neurons through electrical synapses, which reduce the relaxation of nonlocallity in the coupling configuration. The existence of nonstationary chimeras is confirmed by means of a local order parameter.

Interval computing periodic orbits of maps using a piecewise approach

Abstract Interval arithmetic applied to simulation of dynamical systems has attracted a great deal of interest in recent years. Much of this research has been carried out in the calculation of fixed points or low-period windows for nonlinear discrete maps. This study proposes a novel interval computation based on a piecewise method to calculate periodic orbits for the logistic map. Using the cobweb plot, three rounding situations have been applied to a correct outward rounding, as required by interval arithmetic. The proposed method is compared with results in the literature and with the results obtained by means of the Matlab toolbox Intlab. The comparison is accomplished for nine case studies using the logistic map. Numerical results explicitly indicate that the proposed method produces intervals that are substantially narrower than those obtained with the traditional techniques.

Liquid Crystals as Phase Change Materials for Thermal Stabilization

Thermal stabilization exploiting phase change materials (PCMs) is studied theoretically and numerically. Using the heat source approach in numerical simulations, we focus on phase change temperature as a key factor in improving thermal stabilization. Our focus is to analyze possible mechanisms to tune the phase change temperature. We use thermotropic liquid crystals (LCs) as PCMs in a demonstrative system. Using the Landau-de Gennes mesoscopic approach, we show that an external electric field or appropriate nanoparticles (NPs) dispersed in LCs can be exploited to manipulate the phase change temperature.

Higher Mathematics in Physics

In physics all the laws and theorems connected with the physical quantities which vary in space and time, can be written with differential equations. These can be ordinary or partial, scalar or vector, but in several cases there is a system of a few or many coupled differential equations, depending on the dimension and complexity of the physical problem. While the differential equations are the local form of writing physical laws, the integral equations contain the whole space or time, or a definite space and time area. A typical example of writing equations in both forms is a set of Maxwell equations in electromagnetism or variational calculus connected with the minimization of the free energy. By setting and solving (analytically or numerically) these equation we can capture all the areas of physics, from mechanics and movement of point-like bodies, where the special physical branch called analytical mechanics introduces the concepts of generalized coordinates and impulses, Lagrangian and Hamiltonian, up to treatment of scalar and vector fields in electromagnetism and wave optics, quantum physics, thermodynamics, physics of fluids, probability theory etc.

Nematic Liquid Crystal Locking Menisci

We study meniscus driven locking of point defects of nematic liquid crystals confined within a cylindrical tube with free ends. Curvilinear coordinate system is introduced in order to focus on the phenomena of both (convex and concave) types of menisci. Franks description in terms of the nematic director field is used. The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.

Architecture of the virtual training system for buoyancy control

In this paper we present the structure of the simulator which would allow diving beginners to experience the effect of buoyancy control mechanisms before actually entering the water. We believe such training would be less stressful and safer for all participants, but it should also reduce the time in water needed to manage basic practical diving skills. Central design requirements for the system were: realistic modelling of diving physics, various options of man-machine interface and possibility of immersion. With future studies we plan to clarify to what extent the immersive VR interfaces are able to further improve the diving training experience.