Related papers: Analysis of ``Gauge Modes'' in Linearized Relativi…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear equations of motion and presented a thorough analysis with no ambiguity…
Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are…
We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…
A Hamiltonian linearization of the rest-frame instant form of tetrad gravity (gr-qc/0302084), where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, in a completely fixed (non harmonic) 3-orthogonal Hamiltonian gauge is defined. For…
We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation,…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics…
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the…
Reference frames are crucial for describing local observers in general relativity. In quantum gravity, different proposals exist for how to treat reference frames. There are models with either classical or quantum reference frames.…
In a recent paper the first coauthor presented a new parabolic extension (PADM) of the standard 3+1 Arnowitt, Deser, Misner formulation of the equations of general relativity. By parabolizing first-order ADM in a certain way, the PADM…
We formulate the Lagrangian perturbation theory to solve the non-linear dynamics of self-gravitating fluid within the framework of the post-Newtonian approximation in general relativity, using the (3+1) formalism. Our formulation coincides…
We present several key advances to the Physics and Equality Constrained Artificial Neural Networks (PECANN) framework, substantially improving its capacity to solve challenging partial differential equations (PDEs). Our enhancements broaden…
For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also…
We consider a gravitational wave oscillating in an initially homogeneous, magnetized fluid. The fluid is perfectly conducting and isentropic, and the magnetic field is initially uniform. We find analytic solutions for the case in which the…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…