Related papers: Realization of the D'B' boundary condition
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
A classical pseudodifferential operator $P$ on $R^n$ satisfies the $\mu$-transmission condition relative to a smooth open subset $\Omega $, when the symbol terms have a certain twisted parity on the normal to $\partial\Omega $. As shown…
$D$-brane boundary states for type II superstrings are constructed by enforcing the conditions that preserve half of the space-time supersymmetry. A light-cone coordinate frame is used where time is identified as one of the coordinates…
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this case posing the bifurcation problem with…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $\delta$, favoring a band insulator (BI), competes with the local repulsion…
We provide a simple method for writing the Dirac-Born-Infeld (DBI) equations of a Dp-brane in an arbitrary static background whose metric depends only on the holographic radial coordinate z. Using this method we revisit the Karch-O'Bannon's…
We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves.…
Correlated materials with open-shell d- and f-ions having degenerate band edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
We present a bosonic model, in which two bosons may form a bound pair with d-wave symmetry via the four-site ring exchange interaction. A d-wave pairing superfluid as well as a d-wave density wave (DDW) state, are proposed to be achievable…
We show that the Second Derivative (SD) technique of the absorption spectra of Rb atomic vapours confined in a nanocell with a thickness $\ell= \lambda/2=398$ nm allows to achieve close to Doppler-free spectroscopy. Narrow linewidth and…
The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…
We present an {\it exact} quantum theory for the bound states in the vicinity of an edge or a line of impurities in a $d_{x^2-y^2}$ superconductor. For a (110)-surface we show that a finite dispersion of the one dimensional band of bound…
In boundary element methods, the method of using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations…
In this work we made an analysis of the current status of velocity dependent (bound) field components in the framework of the standard electromagnetic theory. Preliminary discussions of the structure of the magnetic field due to an…
Dense lattices of photonic crystals can serve as artificial materials, with light propagation in these structures described by effective material parameters that surpass the capabilities of natural materials. In this study, we introduce a…
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are…