5,418 research outputs found
Revisiting Rotational Perturbations and the Microwave Background
We consider general-relativistic rotational perturbations in homogeneous and
isotropic Friedman - Robertson - Walker (FRW) cosmologies. Taking linear
perturbations of FRW models, the general solution of the field equations
contains tensorial, vectorial and scalar functions. The vectorial terms are in
connection with rotations in the given model and due to the Sachs - Wolfe
effect they produce contributions to the temperature fluctuations of the cosmic
microwave background radiation (CMBR). In present paper we obtain the analytic
time dependence of these contributions in a spatially flat, FRW model with
pressureless ideal fluid, in the presence and the absence of a cosmological
constant. We find that the solution can be separated into an integrable and a
non-integrable part as is the situation in the case of scalar perturbations.
Analyzing the solutions and using the results of present observations we
estimate the order of magnitude of the angular velocity corresponding to the
rotation tensor at the time of decoupling and today.Comment: accepted for publication in Int. J. Mod. Phys.
Energy Contents of Gravitational Waves in Teleparallel Gravity
The conserved quantities, that are, gravitational energy-momentum and its
relevant quantities are investigated for cylindrical and spherical
gravitational waves in the framework of teleparallel equivalent of General
Relativity using the Hamiltonian approach. For both cylindrical and spherical
gravitational waves, we obtain definite energy and constant momentum. The
constant momentum shows consistency with the results available in General
Relativity and teleparallel gravity. The angular momentum for cylindrical and
spherical gravitational waves also turn out to be constant. Further, we
evaluate their gravitational energy-momentum fluxes and gravitational pressure.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.
On the Asymptotic Stability of De-Sitter Spacetime: a non-linear perturbative approach
We derive evolution and constraint equations for second order perturbations
of flat dust homogeneous and isotropic solutions to the Einstein field
equations using all scalar, vector and tensor perturbation modes. We show that
the perturbations decay asymptotically in time and that the solutions converge
to the De-Sitter solution. By induction, this result is valid for perturbations
of arbitrary order. This is in agreement with the cosmic no-hair conjecture of
Gibbons and Hawking.Comment: 11 pages, 2 figure
Distance-redshift from an optical metric that includes absorption
We show that it is possible to equate the intensity reduction of a light wave
caused by weak absorption with a geometrical reduction in intensity caused by a
"transverse" conformal transformation of the spacetime metric in which the wave
travels. We are consequently able to modify Gordon's optical metric to account
for electromagnetic properties of ponderable material whose properties include
both refraction and absorption. Unlike refraction alone however, including
absorption requires a modification of the optical metric that depends on the
eikonal of the wave itself. We derive the distance-redshift relation from the
modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes
whose cosmic fluid has associated refraction and absorption coefficients. We
then fit the current supernovae data and provide an alternate explanation
(other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure
Formal Verification of Neural Network Controlled Autonomous Systems
In this paper, we consider the problem of formally verifying the safety of an
autonomous robot equipped with a Neural Network (NN) controller that processes
LiDAR images to produce control actions. Given a workspace that is
characterized by a set of polytopic obstacles, our objective is to compute the
set of safe initial conditions such that a robot trajectory starting from these
initial conditions is guaranteed to avoid the obstacles. Our approach is to
construct a finite state abstraction of the system and use standard
reachability analysis over the finite state abstraction to compute the set of
the safe initial states. The first technical problem in computing the finite
state abstraction is to mathematically model the imaging function that maps the
robot position to the LiDAR image. To that end, we introduce the notion of
imaging-adapted sets as partitions of the workspace in which the imaging
function is guaranteed to be affine. We develop a polynomial-time algorithm to
partition the workspace into imaging-adapted sets along with computing the
corresponding affine imaging functions. Given this workspace partitioning, a
discrete-time linear dynamics of the robot, and a pre-trained NN controller
with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge
is to analyze the behavior of the neural network. To that end, we utilize a
Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible
segments of different ReLUs. SMC solvers then use a Boolean satisfiability
solver and a convex programming solver and decompose the problem into smaller
subproblems. To accelerate this process, we develop a pre-processing algorithm
that could rapidly prune the space feasible ReLU segments. Finally, we
demonstrate the efficiency of the proposed algorithms using numerical
simulations with increasing complexity of the neural network controller
Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field
The application of a magnetic field transverse to the easy axis, Ising
direction in the quasi-two-dimensional Kagome staircase magnet, Co3V2O8,
induces three quantum phase transitions at low temperatures, ultimately
producing a novel high field polarized state, with two distinct sublattices.
New time-of-flight neutron scattering techniques, accompanied by large angular
access, high magnetic field infrastructure allow the mapping of a sequence of
ferromagnetic and incommensurate phases and their accompanying spin
excitations. At least one of the transitions to incommensurate phases at \mu
0Hc1~6.25 T and \mu 0Hc2~7 T is discontinuous, while the final quantum critical
point at \mu 0Hc3~13 T is continuous.Comment: 5 pages manuscript, 3 pages supplemental materia
Symmetric and asymmetric excitations of a strong-leg quantum spin ladder
The zero-field excitation spectrum of the strong-leg spin ladder
(CHN)CuBr (DIMPY) is studied with a neutron time-of-flight
technique. The spectrum is decomposed into its symmetric and asymmetric parts
with respect to the rung momentum and compared with theoretical results
obtained by the density matrix renormalization group method. Additionally, the
calculated dynamical correlations are shown for a wide range of rung and leg
coupling ratios in order to point out the evolution of arising excitations, as
e.g. of the two-magnon bound state from the strong to the weak coupling limit
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