Related papers: Analysis of ``Gauge Modes'' in Linearized Relativi…
In this paper we study the linear wave equation on an $n$-dimensional spatial domain. We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the…
We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit. We focus on a bounded region $M$ with a co-dimension…
We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models in spatial dimensions $d=2$ and 3. Doing so, we naturally uncover gauged models with dual higher-group symmetries and potential…
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…
Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been…
The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We expand the scope of the alternating direction method of multipliers (ADMM). Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain verifiable assumptions, converges to the set…
We study the resolution of discontinuous singularities in gas dynamics via multi-dimensional rarefaction waves. While the mechanism is well-understood in one spatial dimension, the rigorous construction in higher dimensions has remained a…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…
The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca,…
We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard…
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…