Publications related to Burgers' equation

On the symmetries in the dynamics of wide two-layer neural networks

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023

LDP and CLT for SPDEs with transport noise

Lucio Galeati

In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...

SPRINGER2023

Blow-up, partial regularity and turbulence in incompressible fluid dynamics

Silja Noëmi Aline Haffter

Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...

EPFL2022

Experimental investigation of hydraulic fracture growth in an anisotropic rock with pre-existing discontinuities under different propagation regimes

Brice Tanguy Alphonse Lecampion, Seyyedmaalek Momeni, Guanyi Lu

Laboratory experiments have been carried out to investigate the growth of hydraulic fracture (HF) in an anisotropic rock with pre-existing discontinuities such as bedding planes and veins. The experiments are designed in light of scaling relationships that ...

2022

Ill-posedness of the quasilinear wave equation in the space 𝐻7/4(ln𝐻)−𝛽in ℝ2+1

Gaspard Ohlmann

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Numerical simulation of sediment dynamics with free surface flows

Arwa Mrad

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum ...

EPFL2021

Nonlinear evolution of the centrifugal instability using a semilinear model

François Gallaire, Eunok Yim

We study the nonlinear evolution of the axisymmetric centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semilinear approach. The model consists of two coupled equations: one for the linear evolution of the ...

Cambridge University Press2020

Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any ti ...

2020

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium

Thomas Frédéric Hilke

Metallic aluminium plays a key role in our modern economy. Primary metallic aluminium is produced by the transformation of aluminium oxide using the Hall-Héroult industrial process. This process, which requires enormous quantities of energy, consists in pe ...

EPFL2019

Adaptive WENO methods based on radial basis functions reconstruction

Jan Sickmann Hesthaven, Caterina Bigoni

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discon ...

Springer Verlag2017

Particle-size and -density segregation in granular free-surface flows

Christophe Ancey

When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this pape ...

Cambridge University Press2015

Equation of state of liquid mercury to 520 K and 7 GPa from acoustic velocity measurements

Livia Eleonora Bove Kado

Ultrafast acoustics measurements on liquid mercury have been performed at high pressure and temperature in a diamond anvil cell using picosecond acoustic interferometry. We extract the density of mercury from adiabatic sound velocities using a numerical it ...

American Institute of Physics2014

A microstructural approach to bed load transport: mean behaviour and fluctuations of particle transport rates

Christophe Ancey, Joris Heyman

This paper concerns a model of bed load transport, which describes the advection and dispersion of coarse particles carried by a turbulent water stream. The challenge is to develop a microstructural approach that, on the one hand, yields a parsimonious des ...

Cambridge University Press2014

A unified criterion for the centrifugal instabilities of vortices and swirling jets

François Gallaire

Swirling jets and vortices can both be unstable to the centrifugal instability but with a different wavenumber selection: the most unstable perturbations for swirling jets in inviscid fluids have an infinite azimuthal wavenumber, whereas, for vortices, the ...

Cambridge University Press2013

Computational Reduction for Parametrized PDEs: Strategies and Applications

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...

Springer Verlag2012

Generalized Flows Satisfying Spatial Boundary Conditions

Boris Buffoni

In a region D in R-2 or R-3, the classical Euler equation for the regular motion of an inviscid and incompressible fluid of constant density is given by partial derivative(t)v + (v . del(x))v = -del(xP), div(x)v = 0, where v(t, x) is the velocity of the pa ...

Birkhäuser-Verlag, Springer2012

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

Feride Tiglay

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

Charles Stuart, Hicham Georges Gebran

We consider second-order quasilinear elliptic systems on un-bounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions fo ...

2010

Drift stabilization of ballooning modes in an inward-Shifted LHD configuration

Wilfred Anthony Cooper, Jonathan Graves, Lucie Brocher

A drift-magnetohydrodynamic theory is applied to a background anisotropic pressure equilibrium state to generate a drift corrected ballooning mode equation. The ratio of the mode frequency to the hot particle drift frequency constitutes the critical expans ...

Wiley-VCH2010