Quasilinear second order elliptic systems and topological degree

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are obse ...

Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2 pi. Because of their radiative coupling to the environment, all optical components are intrinsically non-Hermitian syste ...

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

We devise a generic and experimentally accessible recipe to prepare boundary states of topological or non topological quantum systems through an interplay between coherent Hamiltonian dynamics and local dissipation. Intuitively, our recipe harnesses the sp ...

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects, or local disorder and can even survive some random deformat ...

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

This thesis studies the origins and consequences of financial crises, and computational techniques to solve continuous-time economic models that explain such crises. The first chapter shows that financial recessions are typically characterised by a large ...

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 ...

Tokamak devices aim to magnetically confine a hydrogen plasma at sufficiently high pressure to achieve net energy production from nuclear fusion of light isotopes. Predictive modeling and optimization is crucial for reliable operation of tokamak reactors, ...

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

Quasilinear second order elliptic systems and topological degree

Chat with Graph Search

On a Finite-Size Neuronal Population Equation

The elliptical Ornstein-Uhlenbeck process

Crossing of the Branch Cut: The Topological Origin of a Universal 2 pi-Phase Retardation in Non-Hermitian Metasurfaces

Analysis-aware defeaturing of complex geometries with Neumann features

Dissipative boundary state preparation

Hilbert series, the Higgs mechanism, and HEFT

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Stochastic particle transport by deep-water irregular breaking waves

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Anomalous topological waves in strongly amorphous scattering networks

Fast global spectral methods for three-dimensional partial differential equations

Essays in macro-finance and deep learning

LDP and CLT for SPDEs with transport noise

Full-discharge simulation and optimization with the RAPTOR code, from present tokamaks to ITER and DEMO

Conservation of Forces and Total Work at the Interface Using the Internodes Method