Related papers: A shape optimization problem for nematic and chole…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Anisotropic fluids appear in a diverse array of systems, from liquid-crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium's…
We consider the optimal control problem associated with a general version of the well known shallow lake model, and we prove the existence of an optimum in the class $L_{loc}^{1}\left(0,+\infty\right)$. Any direct proof seems to be missing…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for…
By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and internal structure under the influence of the osmotic compression caused by the presence of spherical particles that act as…
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…
In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is…
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…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
A model for the development of turbulent shear flows, created by non-uniform parallel flows in a confining channel, is used to identify the diffuser shape that maximises pressure recovery when the inflow is non-uniform. Wide diffuser angles…
We investigate a shape optimization problem of the Polya-Szego type and prove some results on symmetry and asymmetry of extremal domains.
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
Dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open…
If a static perturbation is applied to a liquid crystal, the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, one might ask: Does the director configuration change to minimize any…
The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…
The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
In this work we numerically study the switching dynamics of a 2D cholesteric emulsion droplet immersed in an isotropic fluid under an electric field, which is either uniform or rotating with constant speed. The overall dynamics depend…
We consider the strong and weak solutions to the Cauchy problem of the inhomogeneous incompressible nematic liquid crystal equations in two dimensions. We first establish the local existence and uniqueness of strong solutions by using the…