428 research outputs found
Neutral and ionic dopants in helium clusters: interaction forces for the and
The potential energy surface (PES) describing the interactions between
and and an extensive
study of the energies and structures of a set of small clusters,
, have been presented by us in a previous series of
publications [1-3]. In the present work we want to extend the same analysis to
the case of the excited and of the
ionized Li moiety. We thus show here calculated
interaction potentials for the two title systems and the corresponding fitting
of the computed points. For both surfaces the MP4 method with cc-pV5Z basis
sets has been used to generate an extensive range of radial/angular coordinates
of the two dimensional PES's which describe rigid rotor molecular dopants
interacting with one He partner
Kikuchi ultrafast nanodiffraction in four-dimensional electron microscopy
Coherent atomic motions in materials can be revealed using time-resolved X-ray and electron Bragg diffraction. Because of the size
of the beam used, typically on the micron scale, the detection of
nanoscale propagating waves in extended structures hitherto has not
been reported. For elastic waves of complex motions, Bragg intensities
contain all polarizations and they are not straightforward to
disentangle. Here, we introduce Kikuchi diffraction dynamics, using
convergent-beam geometry in an ultrafast electron microscope, to
selectively probe propagating transverse elastic waves with nanoscale
resolution. It is shown that Kikuchi band shifts, which are sensitive
only to the tilting of atomic planes, reveal the resonance
oscillations, unit cell angular amplitudes, and the polarization
directions. For silicon, the observed wave packet temporal envelope (resonance frequency of 33 GHz), the out-of-phase temporal behavior of
Kikuchi's edges, and the magnitude of angular amplitude (0.3 mrad) and
polarization [011] elucidate the nature of the motion:
one that preserves the mass density (i.e., no compression or expansion)
but leads to sliding of planes in the antisymmetric shear eigenmode of
the elastic waveguide. As such, the method of Kikuchi diffraction
dynamics, which is unique to electron imaging, can be used to
characterize the atomic motions of propagating waves and their
interactions with interfaces, defects, and grain boundaries at the
nanoscale
The stability of Killing-Cauchy horizons in colliding plane wave space-times
It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes
occur in space-times representing the collision and subsequent interaction of
plane gravitational waves in a Minkowski background, are unstable with respect
to bounded perturbations of the initial waves, at least for the case in which
the initial waves have constant aligned polarizations.Comment: 8 pages. To appear in Gen. Rel. Gra
Bosonic Helium droplets with cationic impurities: onset of electrostriction and snowball effects from quantum calculations
Variational MonteCarlo and Diffusion MonteCarlo calculations have been
carried out for cations like Li, Na and K as dopants of small
helium clusters over a range of cluster sizes up to about 12 solvent atoms. The
interaction has been modelled through a sum-of-potential picture that
disregards higher order effects beyond atom-atom and atom-ion contributions.
The latter were obtained from highly correlated ab-initio calculations over a
broad range of interatomic distances.
This study focuses on two of the most striking features of the microsolvation
in a quantum solvent of a cationic dopant: electrostriction and snowball
effects. They are here discussed in detail and in relation with the nanoscopic
properties of the interaction forces at play within a fully quantum picture of
the clusters features
Practical sketching algorithms for low-rank matrix approximation
This paper describes a suite of algorithms for constructing low-rank
approximations of an input matrix from a random linear image of the matrix,
called a sketch. These methods can preserve structural properties of the input
matrix, such as positive-semidefiniteness, and they can produce approximations
with a user-specified rank. The algorithms are simple, accurate, numerically
stable, and provably correct. Moreover, each method is accompanied by an
informative error bound that allows users to select parameters a priori to
achieve a given approximation quality. These claims are supported by numerical
experiments with real and synthetic data
Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
Several important applications, such as streaming PCA and semidefinite
programming, involve a large-scale positive-semidefinite (psd) matrix that is
presented as a sequence of linear updates. Because of storage limitations, it
may only be possible to retain a sketch of the psd matrix. This paper develops
a new algorithm for fixed-rank psd approximation from a sketch. The approach
combines the Nystrom approximation with a novel mechanism for rank truncation.
Theoretical analysis establishes that the proposed method can achieve any
prescribed relative error in the Schatten 1-norm and that it exploits the
spectral decay of the input matrix. Computer experiments show that the proposed
method dominates alternative techniques for fixed-rank psd matrix approximation
across a wide range of examples
Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes
The mathematical formalism for linear quantum field theory on curved
spacetime depends in an essential way on the assumption of global
hyperbolicity. Physically, what lie at the foundation of any formalism for
quantization in curved spacetime are the canonical commutation relations,
imposed on the field operators evaluated at a global Cauchy surface. In the
algebraic formulation of linear quantum field theory, the canonical commutation
relations are restated in terms of a well-defined symplectic structure on the
space of smooth solutions, and the local field algebra is constructed as the
Weyl algebra associated to this symplectic vector space. When spacetime is not
globally hyperbolic, e.g. when it contains naked singularities or closed
timelike curves, a global Cauchy surface does not exist, and there is no
obvious way to formulate the canonical commutation relations, hence no obvious
way to construct the field algebra. In a paper submitted elsewhere, we report
on a generalization of the algebraic framework for quantum field theory to
arbitrary topological spaces which do not necessarily have a spacetime metric
defined on them at the outset. Taking this generalization as a starting point,
in this paper we give a prescription for constructing the field algebra of a
(massless or massive) Klein-Gordon field on an arbitrary background spacetime.
When spacetime is globally hyperbolic, the theory defined by our construction
coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4
The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations
AbstractA nonlocal boundary value problem for hyperbolic-parabolic equations in a Hilbert space H is considered. Difference schemes of second order of accuracy difference schemes for approximate solution of this problem are presented. Stability estimates for the solution of these difference schemes are established
A remark on kinks and time machines
We describe an elementary proof that a manifold with the topology of the
Politzer time machine does not admit a nonsingular, asymptotically flat Lorentz
metric.Comment: 4 page
The Effect of Sources on the Inner Horizon of Black Holes
Single pulse of null dust and colliding null dusts both transform a regular
horizon into a space-like singularity in the space of colliding waves. The
local isometry between such space-times and black holes extrapolates these
results to the realm of black holes. However, inclusion of particular scalar
fields instead of null dusts creates null singularities rather than space-like
ones on the inner horizons of black holes.Comment: Final version to appear in PR
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