Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations. In an earlier work, this strategy allowed us to develop a regularization method based on a thick interface model in one space variable. In the present paper, we significantly extend this framework and, in addition, encompass equations in several space variables. This new formulation includes the coupling of several distinct conservation laws and allows for a possible covering in space. Our main contributions are, on one hand, the design and analysis of a well-balanced finite volume method on general triangulations and, on the other hand, a proof of convergence of this method toward entropy solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a single conservation law without coupling). The core of our analysis is, first, the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and, second, a proof of convergence toward the entropy solution of the coupling problem.Comment: 37 page

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Proprioceptive Learning with Soft Polyhedral Networks

Proprioception is the "sixth sense" that detects limb postures with motor neurons. It requires a natural integration between the musculoskeletal systems and sensory receptors, which is challenging among modern robots that aim for lightweight, adaptive, and sensitive designs at a low cost. Here, we present the Soft Polyhedral Network with an embedded vision for physical interactions, capable of adaptive kinesthesia and viscoelastic proprioception by learning kinetic features. This design enables passive adaptations to omni-directional interactions, visually captured by a miniature high-speed motion tracking system embedded inside for proprioceptive learning. The results show that the soft network can infer real-time 6D forces and torques with accuracies of 0.25/0.24/0.35 N and 0.025/0.034/0.006 Nm in dynamic interactions. We also incorporate viscoelasticity in proprioception during static adaptation by adding a creep and relaxation modifier to refine the predicted results. The proposed soft network combines simplicity in design, omni-adaptation, and proprioceptive sensing with high accuracy, making it a versatile solution for robotics at a low cost with more than 1 million use cycles for tasks such as sensitive and competitive grasping, and touch-based geometry reconstruction. This study offers new insights into vision-based proprioception for soft robots in adaptive grasping, soft manipulation, and human-robot interaction.Comment: 20 pages, 10 figures, 2 tables, submitted to the International Journal of Robotics Research for revie

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Configurational and energy study of the (100) and (110) surfaces of the MgAl2O4 spinel by means of quantum-mechanical and empirical techniques

none3noneFrancesco Roberto Massaro;Marco Bruno;Fabrizio NestolaFrancesco Roberto, Massaro; Marco, Bruno; Nestola, Fabrizi

Multiple object tracking with context awareness

[no abstract