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We propose dualities of $\mathcal{N} = (0,2)$ supersymmetric boundary conditions for 3d $\mathcal{N} = 2$ gauge theories with orthogonal and symplectic gauge groups. We show that the boundary 't Hooft anomalies and half-indices perfectly…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…
The space-time of the Universe has been perturbed under a scalar field $\phi$ considering the minimum coupling between {\phi} and the background metric. The solutions of Einstein field equations have been obtained under perturbed geometry…
Novel applications of Numerical Relativity demand for more flexible algorithms and tools. In this paper, I develop and test a multigrid solver, based on the infrastructure provided by the Einstein Toolkit, for elliptic partial differential…
We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative…
In the context of warped conformal field theories (WCFT), the derivation of the warped Cardy formula relies on the zero mode spectrum being bounded from below. Generically, this is not true for holographic WCFTs in "canonical" ensemble,…
Dealing with boundary conditions in Smoothed Particle Hydrodynamics (SPH) poses significant difficulties, indeed being one of the SPHERIC Grand Challenges. In particular, wall boundary conditions have been pivotal in SPH model development…
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a…
This is the second and last paper of a series aimed at solving the local Cauchy problem for polarized $\mathbb U(1)$ symmetric solutions to the Einstein vacuum equations featuring the nonlinear interaction of three small amplitude impulsive…
In this paper we analyse semi-linear systems of partial differential equations which are motivated by the conformal formulation of the Einstein constraint equations coupled with realistic physical fields on asymptotically Euclidean (AE)…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a non linear boundary condition for these equations. Under appropriate assumptions, we prove…
We study interactions of electro-magnetic fields with the curvature tensor of the form $\lambda R_{\mu \nu \alpha \beta}F^{\mu \nu}F^{\alpha \beta}$. Such coupling terms though are invariant under general coordinate transformation and CPT,…
Gravitational wave (GW) constraints have recently been used to significantly restrict models of dark energy and modified gravity. New bounds arising from GW decay and GW-induced dark energy instabilities are particularly powerful in this…
The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…
The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.
The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…