Publications related to Concentration Compactness for critical wave maps

High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non flat bottom topography. To enable the construction of the ES schemes on moving mesh ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Hyperbolic representations of PU(1,n)

Gonzalo Emiliano Ruiz Stolowicz

The work is about the study of group representations in the group of isometries of a separable complex hyperbolic space. The main part is the classification of the representations of the group of isometries of a finite dimensional complex hyperbolic spa ...

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

On the scale dependence in the dynamics of frictional rupture: Constant fracture energy versus size-dependent breakdown work

Marie Estelle Solange Violay, Mathias Alexandre David Lebihain, François Xavier Thibault Passelègue, Fabian Barras, Federica Paglialunga

Potential energy stored during the inter-seismic period by tectonic loading around faults is released during earthquakes as radiated energy, frictional dissipation and fracture energy. The latter is of first importance since it is expected to control the n ...

2022

Semi-global controllability of a geometric wave equation

Joachim Krieger, Shengquan Xiang

We prove the semi-global controllability and stabilization of the

(1+1)-

dimensional wave maps equation with spatial domain 𝕊1 and target

𝕊k

. First we show that damping stabilizes the system when the energy is strictly below the threshold

2π

, where ha ...

2022

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

Tobias Johannes Schmid

For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...

AMER MATHEMATICAL SOC2022

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

MICROTOME PUBL2022

Invariance principles in the theory and computation of transport coefficients

Federico Grasselli

In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transpo ...

2021

Positive moments for scattering amplitudes

Riccardo Rattazzi, Francesco Riva, Brando Bellazzini, Marc Riembau Saperas

We find the complete set of conditions satisfied by the forward 2 -> 2 scattering amplitude in unitary and causal theories. These are based on an infinite set of energy dependent quantities (the arcs) which are dispersively expressed as moments of a positi ...

AMER PHYSICAL SOC2021

Concentration Compactness for critical wave maps

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High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

Hyperbolic representations of PU(1,n)

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

On the scale dependence in the dynamics of frictional rupture: Constant fracture energy versus size-dependent breakdown work

Semi-global controllability of a geometric wave equation

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Invariance principles in the theory and computation of transport coefficients

Positive moments for scattering amplitudes

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Hyperbolic representations of PU(1,n)

High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

Semi-global controllability of a geometric wave equation

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Invariance principles in the theory and computation of transport coefficients

Positive moments for scattering amplitudes

On the scale dependence in the dynamics of frictional rupture: Constant fracture energy versus size-dependent breakdown work