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Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

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The study of dynamically propagating rupture along interfaces is of prime importance in various fields and system sizes, including tribology (nm to m), engineering (mm to m) and geophysics (m to km) (Armstrong-Hélouvry et al., 1994; Ben-Zion, 2008; Vanossi ...

2022

Relation between Inner Structural Dynamics and Ion Dynamics of Laser-Heated Nanoparticles

Christoph Bostedt

When a nanoparticle is irradiated by an intense laser pulse, it turns into a nanoplasma, a transition that is accompanied by many interesting nonequilibrium dynamics. So far, most experiments on nanoplasmas use ion measurements, reflecting the outside dyna ...

AMER PHYSICAL SOC2021

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Crack front waves: A 3D dynamic response to a local perturbation of tensile and shear cracks

Jean-François Molinari, Fabian Barras, Damien Spielmann, Fatima-Ezzahra Fekak

Crack front waves are long-lived perturbations propagating along the crack front. They are triggered by heterogeneities on the crack plane, as for instance tough asperities, which disturb the crack front shape. Crack front waves are thought to leave a trac ...

PERGAMON-ELSEVIER SCIENCE LTD2020

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

Jan Sickmann Hesthaven, Deep Ray

MATHICSE2019

Primary invariants of Hurwitz Frobenius manifolds

Nicolas Gerson Orantin

Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and t ...

AMER MATHEMATICAL SOC2018

An overview of some recent results on the Euler system of isentropic gas dynamics

Elisabetta Chiodaroli

This overview is concerned with the well-posedness problem for the isentropic compressible Euler equations of gas dynamics. The results we present are in line with the programof investigatingthe efficiency of different selection criteria proposed in the li ...

Springer Heidelberg2016

An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws

Alfio Quarteroni

In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to ...

Springer Singapore Pte Ltd2016

Fluid-driven fracturing is used in a wide range of applications, including oil and gas extraction, geothermal energy recovery, and CO2 sequestration. In order to efficiently fracture the targeted rock formation, theoretical models provide estimates of the ...

2016

Analytical analysis of slow and fast pressure waves in a two-dimensional cellular solid with fluid-filled cells

Vladimir Dorodnitsyn, Bart Van Damme

Wave propagation in cellular and porous media is widely studied due to its abundance in nature and industrial applications. Biot's theory for open-cell media predicts the existence of two simultaneous pressure waves, distinguished by its velocity. A fast w ...

Acoustical Soc Amer Amer Inst Physics2016