21,767 research outputs found
Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations
We linearize the Einstein equations when the metric is Bondi-Sachs, when the
background is Schwarzschild or Minkowski, and when there is a matter source in
the form of a thin shell whose density varies with time and angular position.
By performing an eigenfunction decomposition, we reduce the problem to a system
of linear ordinary differential equations which we are able to solve. The
solutions are relevant to the characteristic formulation of numerical
relativity: (a) as exact solutions against which computations of gravitational
radiation can be compared; and (b) in formulating boundary conditions on the
Schwarzschild horizon.Comment: Revised following referee comment
Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather
Geometric phases in dressed state quantum computation
Geometric phases arise naturally in a variety of quantum systems with
observable consequences. They also arise in quantum computations when dressed
states are used in gating operations. Here we show how they arise in these
gating operations and how one may take advantage of the dressed states
producing them. Specifically, we show that that for a given, but arbitrary
Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of
dressed states such that a given gate operation can be performed by the
Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a
geometric phase. We illustrate the new phase for several systems.Comment: 4 pages, 2 figure
High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
In this article, we present new results of high-order coupled cluster method
(CCM) calculations, based on a N\'eel model state with spins aligned in the
-direction, for both the ground- and excited-state properties of the
spin-half {\it XXZ} model on the linear chain, the square lattice, and the
simple cubic lattice. In particular, the high-order CCM formalism is extended
to treat the excited states of lattice quantum spin systems for the first time.
Completely new results for the excitation energy gap of the spin-half {\it XXZ}
model for these lattices are thus determined. These high-order calculations are
based on a localised approximation scheme called the LSUB scheme in which we
retain all -body correlations defined on all possible locales of
adjacent lattice sites (). The ``raw'' CCM LSUB results are seen to
provide very good results for the ground-state energy, sublattice
magnetisation, and the value of the lowest-lying excitation energy for each of
these systems. However, in order to obtain even better results, two types of
extrapolation scheme of the LSUB results to the limit (i.e.,
the exact solution in the thermodynamic limit) are presented. The extrapolated
results provide extremely accurate results for the ground- and excited-state
properties of these systems across a wide range of values of the anisotropy
parameter.Comment: 31 Pages, 5 Figure
Elasticity-driven Nanoscale Texturing in Complex Electronic Materials
Finescale probes of many complex electronic materials have revealed a
non-uniform nanoworld of sign-varying textures in strain, charge and
magnetization, forming meandering ribbons, stripe segments or droplets. We
introduce and simulate a Ginzburg-Landau model for a structural transition,
with strains coupling to charge and magnetization. Charge doping acts as a
local stress that deforms surrounding unit cells without generating defects.
This seemingly innocuous constraint of elastic `compatibility', in fact induces
crucial anisotropic long-range forces of unit-cell discrete symmetry, that
interweave opposite-sign competing strains to produce polaronic elasto-magnetic
textures in the composite variables. Simulations with random local doping below
the solid-solid transformation temperature reveal rich multiscale texturing
from induced elastic fields: nanoscale phase separation, mesoscale intrinsic
inhomogeneities, textural cross-coupling to external stress and magnetic field,
and temperature-dependent percolation. We describe how this composite textured
polaron concept can be valuable for doped manganites, cuprates and other
complex electronic materials.Comment: Preprin
The single leg squat: when to prescribe this exercise
The single leg squat (SLS) is an exercise that has been the subject of numerous research studies in recent years â primarily in the field of physiotherapy and sport rehabilitation, considering where the majority of literature has been published. The unilateral nature of the exercise has encouraged researchers and practitioners to identify what the key muscles are when performing this movement pattern and the factors that may be responsible for enhancing performance during this particular task
Exercise technique: the push press
The push press exercise has been used for years by coaches as one of many tools to enhance an athletesâ physical development. Recent research has further validated this exercise to augment power development. Thus, the aim of this paper is to outline the benefits this exercise has for strength and conditioning coaches
Cauchy boundaries in linearized gravitational theory
We investigate the numerical stability of Cauchy evolution of linearized
gravitational theory in a 3-dimensional bounded domain. Criteria of robust
stability are proposed, developed into a testbed and used to study various
evolution-boundary algorithms. We construct a standard explicit finite
difference code which solves the unconstrained linearized Einstein equations in
the 3+1 formulation and measure its stability properties under Dirichlet,
Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability
of a specific evolution-boundary algorithm under random constraint violating
initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte
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