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Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based…
When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a…
We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist…
Within the context of finite deformation elasticity theory the problem of deforming an open sector of a thick-walled circular cylindrical tube into a complete circular cylindrical tube is analyzed. The analysis provides a means of…
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
Precise manipulation of shape-morphing responsive materials is crucial for applications in soft robotics and adaptive structures. While notable precision has been achieved in thin two-dimensional sheets, an accurate volumetric…
This paper is devoted to the analysis of a numerical scheme based on the Finite Element Method for approximating the solution of Koiter's model for a linearly elastic elliptic membrane shell subjected to remaining confined in a prescribed…
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
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…
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This…
The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…