Publications related to Einstein field equations

Mean-field transport equations and energy theorem for plasma edge turbulent transport

This paper establishes a mean-field equation set and an energy theorem to provide a theoretical basis in view of the development of self-consistent, physics-based turbulent transport models for mean-field transport codes. A rigorous averaging procedure ide ...

Cambridge University Press2024

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Carl Johan Peter Johansson

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Charles Stuart

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

2024

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

François Gallaire, Eunok Yim

We carry out a weakly nonlinear analysis of the centrifugal instability for a columnar vortex in a rotating fluid, and compare the results to those of the semi-linear model derived empirically by Yim et al. (J. Fluid Mech., vol. 897, 2020, A34). The asympt ...

Cambridge University Press2023

Columnlike free-interface flows: symmetry breaking and linear instability

Shahab Eghbali

This thesis is dedicated to the analysis of a subclass of interfacial flows, columnlike free-interface flows, from two view angles: (i) the symmetry breaking under geometry-induced or external forces, (ii) their stability against infinitesimal disturbances ...

EPFL2023

Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations

Michele Dolce

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size & epsilon;. Under the classical Miles-Howard stability condition on the Richardso ...

WILEY2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Siam Publications2023

Computation of the attenuation function of the lightning return-stroke current from electromagnetic fields measured in a short-duration time-window — Part II: Numerical implementation

Farhad Rachidi-Haeri, Marcos Rubinstein

In the present paper, we show, by means of numerical simulations, that electromagnetic field data obtained from the radiation of a return-stroke lightning discharge and measured over a short-duration time-window can be exploited to reconstruct the attenuat ...

Elsevier2023

A proof of the instability of AdS for the Einstein-massless Vlasov system

Georgios Moschidis

In recent years, the conjecture on the instability of Anti-de Sitter spacetime, put forward by Dafermos-Holzegel (Dynamic instability of solitons in 4 + 1 dimesnional gravity with negative cosmological constant, 2006. https://www.dpmms.cam.ac.uk/similar to ...

SPRINGER HEIDELBERG2022

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Ignacio Pagonabarraga Mora, Elena Sesé Sansa

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

AIP Publishing2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Scrutinizing thermally stimulated current transients originating from trapped charges in organic semiconductors: A drift-diffusion study

Frank Nüesch, Beat Ruhstaller

Thermally stimulated current (TSC) is a widely used technique to assess trap states and extract their density, energy, and capture rate using analytical expressions. In many cases, the latter are derived from physical models pertaining to inorganic semicon ...

AIP Publishing2022

Covariant formulation of relativistic mechanics

Miguel Alexandre Ribeiro Correia

Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The prin ...

American Physical Society2022

Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains

Rafael Vazquez Hernandez, Bernard Kapidani

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...

2022

MaxwellNet: Physics-driven deep neural network training based on Maxwell's equations

Demetri Psaltis, Joowon Lim

Maxwell's equations govern light propagation and its interaction with matter. Therefore, the solution of Maxwell's equations using computational electromagnetic simulations plays a critical role in understanding light-matter interaction and designing optic ...

AIP Publishing2022

Experimental investigation on the moment-rotation performance of pultruded FRP web-flange junctions

Thomas Keller

This paper aims to present an experimental investigation on the behavior of web-flange junctions (WFJs) rotational stiffness of pultruded fiber-reinforced polymer composites (FRP). Channels and I-sections were tested using a simple set-up, which was develo ...

ELSEVIER SCI LTD2021

Development of a novel two-phase flow solver for nuclear reactor analysis: algorithms, verification and implementation in OpenFOAM

Andreas Pautz, Carlo Fiorina, Stefan Radman

A porous medium-based representation of nuclear reactors and complex engineering systems more in general can significantly reduce simulation and modelling costs, while preserving a reasonable degree of accuracy via regime map-based correlations for modelli ...

2021

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

CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

Mrudhula Baskaran

We investigate experimentally and theoretically diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO2 dissolution from one side-wall. Since the negatively charged particles create an exclusion zone near th ...

ROYAL SOC CHEMISTRY2021

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021