相关论文: Computing equilibrium states of cholesteric liquid…
We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is desired in applications where the…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…
Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…