Related papers: Optimal control of plate shape with incompatible s…

We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a positive weight. We give a variational principle for limit shapes…

We delineate a general theoretical framework to determine the substrate-regulated graphene morphology through energy minimization. We then apply such a framework to study the graphene morphology on a substrate with periodic surface grooves.…

In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance…

I pose the question of maximal Newtonian surface gravity on a homogeneous body of a given mass and volume but with variable shape. In other words, given an amount of malleable material of uniform density, how should one shape it in order…

Optimal embedding in the three-dimensional space of exponentially growing squeezed surfaces, like plants leaves, or 2D colonies of exponentially reproducing cells, is considered in the framework of conformal approach. It is shown that the…

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback…

We determine the shapes of pure cubic fields and show that they fall into two families based on whether the field is wildly or tamely ramified (of Type I or Type II in the sense of Dedekind). We show that the shapes of Type I fields are…

This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the…

Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many…

Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes…

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…

Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial…

Gridshells are defined as structures that have the shape and rigidity of a double curvature shell but consist of a grid instead of a continuous surface. This study concerns those obtained by elastic deformation of an initially flat two-way…

In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…

We investigate what determines the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional…

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…

We show the existence of a complete, strictly locally convex hypersurface within $\mathbb{H}^{n+1}$ that adheres to a curvature equation applicable to a broad range of curvature functions. This hypersurface possesses a prescribed asymptotic…

Controlling the shape of deformable linear objects using robots and constraints provided by environmental fixtures has diverse industrial applications. In order to establish robust contacts with these fixtures, accurate estimation of the…

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…