Concept

Équation différentielle de Bernoulli

Publications associées (25)

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Junming Duan

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Instanton theory of ground-state tunneling splittings with general paths

Christophe Louis Joseph Jean-Luc Vaillant, Mihael Erakovic

We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric p ...

2020

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

ODE parameter estimation through a runner's model application

The monitoring of sports' performance has become increasingly popular in the past years. For instance, high precision measurement of runners' speed, foot pace and heart beat are available among others. Usually, coaches are interested in summary statistics ...

2016

On the Asymptotic Validity of the Decoupling Assumption for Analyzing 802.11 MAC Protocol

Jean-Yves Le Boudec

Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. This decoupling assumption results from mean field convergence and is gen ...

Institute of Electrical and Electronics Engineers2012

Splitting Methods with Modified Potentials and Application to the Damped Wave Equation

Jonathan Rochat

In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient ...

2011

Active strain and activation models in cardiac electromechanics

Alfio Quarteroni, Ricardo Esteban Ruiz Baier, Simone Rossi

We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membra ...

2011

Optimal Control Theory with Applications in Economics

Thomas Alois Weber

This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of ...

MIT Press2011

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