3,794 research outputs found
Fast preparation of critical ground states using superluminal fronts
We propose a spatio-temporal quench protocol that allows for the fast
preparation of ground states of gapless models with Lorentz invariance.
Assuming the system initially resides in the ground state of a corresponding
massive model, we show that a superluminally-moving `front' that
quenches the mass, leaves behind it (in space) a state
to the ground state of the gapless model.
Importantly, our protocol takes time to produce
the ground state of a system of size ( spatial dimensions), while
a fully adiabatic protocol requires time
to produce a state with exponential accuracy in . The physics of the
dynamical problem can be understood in terms of relativistic rarefaction of
excitations generated by the mass front. We provide proof-of-concept by solving
the proposed quench exactly for a system of free bosons in arbitrary
dimensions, and for free fermions in . We discuss the role of
interactions and UV effects on the free-theory idealization, before numerically
illustrating the usefulness of the approach via simulations on the quantum
Heisenberg spin-chain.Comment: 4.25 + 10 pages, 3 + 2 figure
Cut Size Statistics of Graph Bisection Heuristics
We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin
Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Coupled problems with various combinations of multiple physics, scales, and
domains are found in numerous areas of science and engineering. A key challenge
in the formulation and implementation of corresponding coupled numerical models
is to facilitate the communication of information across physics, scale, and
domain interfaces, as well as between the iterations of solvers used for
response computations. In a probabilistic context, any information that is to
be communicated between subproblems or iterations should be characterized by an
appropriate probabilistic representation. Although the number of sources of
uncertainty can be expected to be large in most coupled problems, our
contention is that exchanged probabilistic information often resides in a
considerably lower dimensional space than the sources themselves. In this work,
we thus use a dimension-reduction technique for obtaining the representation of
the exchanged information. The main subject of this work is the investigation
of a measure-transformation technique that allows implementations to exploit
this dimension reduction to achieve computational gains. The effectiveness of
the proposed dimension-reduction and measure-transformation methodology is
demonstrated through a multiphysics problem relevant to nuclear engineering
A basing of the diffusion approximation derivation for the four-wave kinetic integral and properties of the approximation
International audienceA basing of the diffusion approximation derivation for the Hasselmann kinetic integral describing nonlinear interactions of gravity waves in deep water is discussed. It is shown that the diffusion approximation containing the second derivatives of a wave spectrum in a frequency and angle (or in wave vector components) is resulting from a step-by-step analytical integration of the sixfold Hasselmann integral without involving the quasi-locality hypothesis for nonlinear interactions among waves. A singularity analysis of the integrand expression gives evidence that the approximation mentioned above is the small scattering angle approximation, in fact, as it was shown for the first time by Hasselmann and Hasselmann (1981). But, in difference to their result, here it is shown that in the course of diffusion approximation derivation one may obtain the final result as a combination of terms with the first, second, and so on derivatives. Thus, the final kind of approximation can be limited by terms with the second derivatives only, as it was proposed in Zakharov and Pushkarev (1999). For this version of diffusion approximation, a numerical testing of the approximation properties was carried out. The testing results give a basis to use this approximation in a wave modelling practice
CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
CMB anisotropy measurements have brought the issue of global topology of the
universe from the realm of theoretical possibility to within the grasp of
observations. The global topology of the universe modifies the correlation
properties of cosmic fields. In particular, strong correlations are predicted
in CMB anisotropy patterns on the largest observable scales if the size of the
Universe is comparable to the distance to the CMB last scattering surface. We
describe in detail our completely general scheme using a regularized method of
images for calculating such correlation functions in models with nontrivial
topology, and apply it to the computationally challenging compact hyperbolic
spaces. Our procedure directly sums over images within a specified radius,
ideally many times the diameter of the space, effectively treats more distant
images in a continuous approximation, and uses Cesaro resummation to further
sharpen the results. At all levels of approximation the symmetries of the space
are preserved in the correlation function. This new technique eliminates the
need for the difficult task of spatial eigenmode decomposition on these spaces.
Although the eigenspectrum can be obtained by this method if desired, at a
given level of approximation the correlation functions are more accurately
determined. We use the 3-torus example to demonstrate that the method works
very well. We apply it to power spectrum as well as correlation function
evaluations in a number of compact hyperbolic (CH) spaces. Application to the
computation of CMB anisotropy correlations on CH spaces, and the observational
constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11,
199
Active cloaking of finite defects for flexural waves in elastic plates
We present a new method to create an active cloak for a rigid inclusion in a
thin plate, and analyse flexural waves within such a plate governed by the
Kirchhoff plate equation. We consider scattering of both a plane wave and a
cylindrical wave by a single clamped inclusion of circular shape. In order to
cloak the inclusion, we place control sources at small distances from the
scatterer and choose their intensities to eliminate propagating orders of the
scattered wave, thus reconstructing the respective incident wave. We then vary
the number and position of the control sources to obtain the most effective
configuration for cloaking the circular inclusion. Finally, we successfully
cloak an arbitrarily shaped scatterer in a thin plate by deriving a
semi-analytical, asymptotic algorithm.Comment: 19 pages, 14 figures, 1 tabl
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