Related papers: A curvature-regularized variational problem with a…
We studied the curvature-driven roughening of a disk domain pattern with a variable interface window. The relaxation of interface is driven by negative surface tension . When a domain boundary propagates radially at a constant rate, we…
We consider an open, bounded, simply connected (Lipschitz) domain in $\mathbb{R}^d$, which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal…
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic composites. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip…
In the experiments on stress-induced phase transitions in SMA strips, several interesting instability phenomena have been observed, including a necking-type instability, a shear-type instability and an orientation instability. By using the…
We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…
We present a generic solution to the fundamental problem of how to connect two points in a plane by a smooth curve that goes through these points with a given slope. The smoothness of any curve depends both on its curvature and its length.…
A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating…
We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…