Related papers: Optimal control of plate shape with incompatible s…
In this paper, we present a 2D numerical model developed to simulate the dynamics of soft, deformable particles. To accommodate significant particle deformations, the particle surface is represented as a narrow shell composed of mass points…
Shape formation is one of the most thoroughly studied problems in programmable matter and swarm robotics. However, in many models, the class of shapes that can be formed is highly restricted due to the particles' limited memory. In the…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
The present paper treats the problem of finding the asymptotic bounds for the globally optimal locations of orthogonal stiffeners minimizing the compliance of a rectangular plate in elastostatic bending. The essence of the paper is the…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled…
In this work we consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts. Specifically, we model polymer self-assembly using Self-Consistent Field Theory and…
We consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type equation governing the evolution of the phase variable which takes into account the…
We present a phase-field model for simulating the solid-state dewetting of anisotropic crystalline films on non-planar substrates. This model exploits two order parameters to trace implicitly the crystal free surface and the substrate…
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…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
Graphene is well known to grow as flat sheets aligned with the growth substrate. Oriented graphene structures typically normal to the substrate have recently gained major attention. Most often, normal orientation is achieved in…
We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…
Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages…