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Statistical solutions of hyperbolic conservation laws I: Foundations
(2016)Research ReportReport -
Schemes with well-controlled dissipation-Hyperbolic systems in non-conservative form
(2015)Research reportsReport -
Schemes with Well controlled Dissipation (WCD) I
(2013)Research ReportWe consider the approximation of entropy solutions to nonlinear hyperbolic conservation laws, in the regime that small–scale effects drive the dynamics of shock waves in these solutions. We introduce and analyze a new class of numerical methods, referred to as the schemes with well-controled dissipation (WCD), which approximate entropy solutions with high–accuracy and can capture small scale dependent shock waves of arbitrary strength. ...Report -
Numerical solution of scalar conservation laws with random flux functions
(2012)Research ReportWe consider scalar hyperbolic conservation laws in several space dimensions, with a class of random (and parametric) flux functions. We propose a Karhunen–Loève expansion on the state space of the random flux. For random flux functions which are Lipschitz continuous with respect to the state variable, we prove the existence of a unique random entropy solution. Using a Karhunen–Loève spectral decomposition of the random flux into principal ...Report -
Tunneling time and weak measurement in strong field ionisation
(2015)Research ReportTunnelling delays is a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, ...Report -
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Well-balanced schemes for gravitationally stratified media
(2014)Research ReportWe present a well-balanced scheme for the Euler equations with gravitation. The scheme is capable of maintaining exactly (up to machine precision) a discrete hydrostatic equilibrium without any assumption on a thermodynamic variable such as specific entropy or temperature. The well-balanced scheme is based on a local hydrostatic pressure reconstruction. Moreover, it is computationally efficient and can be incorporated into any existing ...Report -
A machine learning framework for data driven acceleration of computations of differential equations
(2018)SAM Research ReportReport -
On the convergence of the spectral viscosity method for the incompressible Euler equations with rough initial data
(2019)SAM Research ReportReport