On Maltsev Digraphs

This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio

Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity

We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl tensor components on past null infinity are antipodally matched to those on future null infinity. The subalgebra of totally fluxless supertranslations near spatial infinity provides a natural isomorphism between the BMS-supertranslations on past and future null infinity. This proves that the flux of the supermomenta is conserved from past to future null infinity in a classical gravitational scattering process provided additional suitable conditions are satisfied at the timelike infinities.Comment: v2: corrected formula for epsilon in Eqs. A.4E and A.9 v1: (published version in JHEP) 49 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1808.0786

FDTD analysis of the tunneling and growing exponential in a pair of epsilon-negative and mu-negative slabs

Pairing together material slabs with opposite signs for the real parts of their constitutive parameters has been shown to lead to interesting and unconventional properties that are not otherwise observable for single slabs. One such case was demonstrated analytically for the conjugate (i.e., complementary) pairing of infinite planar slabs of epsilon-negative (ENG) and mu-negative (MNG) media [A. Alu, and N. Engheta, IEEE Trans. Antennas Prop., 51, 2558 (2003)]. There it was shown that when these two slabs are juxtaposed and excited by an incident plane wave, resonance, complete tunneling, total transparency and reconstruction of evanescent waves may occur in the steady-state regime under a monochromatic excitation, even though each of the two slabs by itself is essentially opaque to the incoming radiation. This may lead to virtual imagers with sub-wavelength resolution and other anomalous phenomena overcoming the physical limit of diffraction. Here we explore how a transient sinusoidal signal that starts at t = 0 interacts with such an ENG-MNG pair of finite size using an FDTD technique. Multiple reflections and transmissions at each interface are shown to build up to the eventual steady state response of the pair, and during this process one can observe how the growing exponential phenomenon may actually occur inside this bilayer.Comment: 14 pages, 9 figures, submitted to Phys Rev