Related papers: A model liquid crystal cell in an RC circuit
The internal dynamics of active gels, both in artificial (in-vitro) model systems and inside the cytoskeleton of living cells, has been extensively studied by experiments of recent years. These dynamics are probed using tracer particles…
Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric…
We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix…
We study dynamical optical response of a nematic liquid crystal cell that undergoes the splay-bend transition after applying the voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers integrated within a theoretical charge pump electrical circuit is considered. The…
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a…
We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order tensor. The model extends the previously developed director-based…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The dynamics of a liquid dielectric attracted by a vertical cylindrical capacitor is studied. Contrary to what might be expected from the standard calculation of the force exerted by the capacitor, the motion of the dielectric is different…
We develop a model for a driven cell- or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific…
We theoretically study a vibrating pair of parallel electrodes bridged by a (deformed) liquid droplet, which is a recently developed microfluidic device to harvest vibrational energy. The device can operate with various liquids, including…
We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation…
This letter presents a closed-form integral-equation formulation that models the director tilting in nematic liquid crystals. The proposed formulation is computationally efficient compared to numerical methods and provides a physical…
Lithium-ion batteries are used to store energy in electric vehicles. Physical models based on electro-chemistry accurately predict the cell dynamics, in particular the state of charge. However, these models are nonlinear partial…
A comprehensive approach for simulating lasing dynamics in a liquid crystal based laser is presented. The approach takes into account the transformation of the liquid crystal structure caused by applied voltage. In particular, it allows us…
This paper describes a simplified model of an electric circuit with a DC-DC converter and a PID-regulator as a system of integral differential equations with an identically singular matrix multiplying the higher derivative of the desired…
Nematic tactoids are spindle-shaped droplets of a nematic phase nucleated in the co-existing isotropic phase. According to equilibrium theory, their internal structure and shape are controlled by a balance between the elastic deformation of…
We introduce the "leaking elastic capacitor" (LEC) model, a nonconservative dynamical system that combines simple electrical and mechanical degrees of freedom. We show that an LEC connected to an external voltage source can be destabilized…