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We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…

Optimization and Control · Mathematics 2014-05-15 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle

Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…

Soft Condensed Matter · Physics 2017-08-23 Xingzhou Tang , Jonathan V. Selinger

We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the…

Soft Condensed Matter · Physics 2023-05-02 Daniel Castro , Hillel Aharoni

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Reza Behrou , Maroun Abi Ghanem , Brianna C. Macnider , Vimarsh Verma , Ryan Alvey , Jinho Hong , Ashley F. Emery , Hyunsun Alicia Kim , Nicholas Boechler

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…

Computer Vision and Pattern Recognition · Computer Science 2015-10-16 Konrad Simon , Ronen Basri

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here, we consider how such alignment can be achieved using a periodic square lattice of circular…

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field…

Optimization and Control · Mathematics 2015-04-27 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle , Kei Fong Lam

We study avenues to shape multistability and shape-morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium…

Soft Condensed Matter · Physics 2022-03-23 Andrei Zakharov , Daniel A. Beller

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

Fluidic Shaping is a novel method for fabrication of optical components based on the equilibrium state of liquid volumes in neutral buoyancy, subjected to geometrical constraints. The underlying physics of this method is described by a…

Fluid Dynamics · Physics 2026-02-17 Amos A. Hari , Moran Bercovici

We develop a Q-tensor model of nematic liquid crystals occupying a stationary surface which represents a fluidic material film in space. In addition to the evolution due to Landau--de\,Gennes energy the model includes a tangent viscous…

Fluid Dynamics · Physics 2023-10-06 Lucas Bouck , Ricardo H. Nochetto , Vladimir Yushutin

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a…

Soft Condensed Matter · Physics 2009-10-31 Joachim Stelzer , Ralf Bernhard

Manipulating the shape of a liquid droplet is essential for a wide range of applications in medicine and industry. However, existing methods are typically limited to generating simple shapes, such as ellipses, or rely on predefined…

Systems and Control · Electrical Eng. & Systems 2025-05-20 P. A. Diluka Harischandra , Quan Zhou

We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length…

Soft Condensed Matter · Physics 2021-09-22 Baoming Shi , Yucen Han , Lei Zhang

We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical…

Analysis of PDEs · Mathematics 2015-01-22 Gautam Iyer , Xiang Xu , Arghir Zarnescu

Long-range e.g. Coulomb-like interactions for (quantized) topological charges are observed experimentally in liquid crystals, bringing open question this article is exploring: how far can we take this resemblance with particle physics?…

Soft Condensed Matter · Physics 2025-11-14 Jarek Duda

A theoretical model of shape-anisometric particles embedded in a cubic lattice is formulated for binary mixtures combining rod-like, plate-like and spherical particles. The model aims at providing a tool for the prediction and…

Soft Condensed Matter · Physics 2011-05-31 Stavros Peroukidis , Alexandros G. Vanakaras , Demetri J. Photinos

A singular potential method in the Q tensor order parameter representation of a nematic liquid crystal is used to study the equilibrium configuration of a disclination dipole. Unlike the well studied isotropic limit (the so called one…

Soft Condensed Matter · Physics 2025-03-28 Lucas Myers , Carter Swift , Jonas Ronning , Luiza Angheluta , Jorge Vinals

The paper aims to reveal the relationship between the geometrical features and linear and nonlinear optical properties of InAs quantum dots (QDs). This problem is justified by the extreme variety offered by the recent advances in growth…

Mesoscale and Nanoscale Physics · Physics 2024-06-21 Grigor A. Mantashian

We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the…

Numerical Analysis · Mathematics 2022-10-05 Jingmin Xia , Patrick E. Farrell