4,907 research outputs found
Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
The distributions of inter-island gaps and captures zones for islands
nucleated on a one-dimensional substrate during submonolayer deposition are
considered using a novel retrospective view. This provides an alternative
perspective on why scaling occurs in this continuously evolving system.
Distributional fixed point equations for the gaps are derived both with and
without a mean field approximation for nearest neighbour gap size correlation.
Solutions to the equations show that correct consideration of fragmentation
bias justifies the mean field approach which can be extended to provide
closed-from equations for the capture zones. Our results compare favourably to
Monte Carlo data for both point and extended islands using a range of critical
island size . We also find satisfactory agreement with theoretical
models based on more traditional fragmentation theory approaches.Comment: 9 pages, 7 figures and 1 tabl
Uniqueness of static decompositions
We classify static manifolds which admit more than one static decomposition
whenever a condition on the curvature is fullfilled. For this, we take a
standard static vector field and analyze its associated one parameter family of
projections onto the base. We show that the base itself is a static manifold
and the warping function satisfies severe restrictions, leading us to our
classification results. Moreover, we show that certain condition on the
lightlike sectional curvature ensures the uniqueness of static decomposition
for Lorentzian manifolds.Comment: 14 page
Computation of molecular Hartree–Fock Wigner intracules
The computation of molecular Wigner intracules from Hartree–Fock wave functions using Gaussian basis functions is described. The Wigner intracule is a new type of intracule that contains information about both the relative position and momentum of the electrons. Two methods for evaluating the required integrals are presented. The first approach uses quadrature while the second requires summation of an infinite series.This research was partly supported by the Engineering
and Physical Sciences Research Council through a project
studentship (GR/R81121) to D.P.O. and an Advanced Research
Fellowship (GR/R77636) to N.A.B
Uniform and fast switching of window-size smectic A liquid crystal panels utilising the field gradient generated at the fringes of patterned electrodes
A method to enable smectic A (SmA) liquid crystal (LC) devices to switch uniformly and hence fast from the clear state to a scattered state is presented. It will allow the reduction of the switching time for a SmA LC panel of 1x1 m2 changing from a clear state to a fully scattered state by more than three orders to a few tens of milliseconds. Experimental results presented here reveal that SmA LC scattering initiates from the nucleated LC defects at the field gradient of the applied electric field usually along the edges of the panel electrode and grows laterally to spread over a panel, which takes a long time if the panel size is large. By patterning the electrodes in use, it is possible to create a large number of field gradient sites near the electrode discontinuities, resulting in a uniform and fast switching over the whole panel and the higher the pattern density the shorter the panel switching time. For the SmA LC panels used here, the ITO transparent electrodes are patterned by laser ablation and photolithography, respectively. It is shown that the defect nucleation time is much shorter than the growth time of the scattered region, hence it is possible to use the density of the field gradient sites to control the uniformity and switching time of a panel. Furthermore, the patterned SmA panels have a lower switching voltage than that of the non-patterned ones in general.The authors would like to thank the UK Engineering and Physical Sciences Research Council (EPSRC) for the support through the Platform Grant for Liquid Crystal Photonics (EP/F00897X/1) and Dr Anthony Davey for providing the organic SmA LC and Dow Corning Corp. for providing the siloxane-based SmA LC used in this study. The authors would also like to thank Dr Stuart Speakman for the helpful discussions.This is the final version of the article. It first appeared from Taylor & Francis via http://dx.doi.org/10.1080/02678292.2016.114201
Measures of gravitational entropy I. Self-similar spacetimes
We examine the possibility that the gravitational contribution to the entropy
of a system can be identified with some measure of the Weyl curvature. In this
paper we consider homothetically self-similar spacetimes. These are believed to
play an important role in describing the asymptotic properties of more general
models. By exploiting their symmetry properties we are able to impose
significant restrictions on measures of the Weyl curvature which could reflect
the gravitational entropy of a system. In particular, we are able to show, by
way of a more general relation, that the most widely used "dimensionless"
scalar is \textit{not} a candidate for this measure along homothetic
trajectories.Comment: revtex, minor clarifications, to appear in Physical Review
Integration of the Friedmann equation for universes of arbitrary complexity
An explicit and complete set of constants of the motion are constructed
algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models
consisting of an arbitrary number of non-interacting species. The inheritance
of constants of the motion from simpler models as more species are added is
stressed. It is then argued that all FLRW models admit what amounts to a unique
candidate for a gravitational epoch function (a dimensionless scalar invariant
derivable from the Riemann tensor without differentiation which is monotone
throughout the evolution of the universe). The same relations that lead to the
construction of constants of the motion allow an explicit evaluation of this
function. In the simplest of all models, the CDM model, it is shown
that the epoch function exists for all models with , but for
almost no models with .Comment: Final form to appear in Physical Review D1
3D Simulations of MHD Jet Propagation Through Uniform and Stratified External Environments
We present a set of high-resolution 3D MHD simulations of steady light,
supersonic jets, exploring the influence of jet Mach number and the ambient
medium on jet propagation and energy deposition over long distances. The
results are compared to simple self-similar scaling relations for the
morphological evolution of jet-driven structures and to previously published 2D
simulations. For this study we simulated the propagation of light jets with
internal Mach numbers 3 and 12 to lengths exceeding 100 initial jet radii in
both uniform and stratified atmospheres.
The propagating jets asymptotically deposit approximately half of their
energy flux as thermal energy in the ambient atmosphere, almost independent of
jet Mach number or the external density gradient. Nearly one-quarter of the jet
total energy flux goes directly into dissipative heating of the ICM, supporting
arguments for effective feedback from AGNs to cluster media. The remaining
energy resides primarily in the jet and cocoon structures. Despite having
different shock distributions and magnetic field features, global trends in
energy flow are similar among the different models.
As expected the jets advance more rapidly through stratified atmospheres than
uniform environments. The asymptotic head velocity in King-type atmospheres
shows little or no deceleration. This contrasts with jets in uniform media with
heads that are slowed as they propagate. This suggests that the energy
deposited by jets of a given length and power depends strongly on the structure
of the ambient medium. While our low-Mach jets are more easily disrupted, their
cocoons obey evolutionary scaling relations similar to the high-Mach jets.Comment: Accepted in ApJ, 32 pages, 18 figures, animations available from:
http://www.msi.umn.edu/Projects/twj/newsite/projects/radiojets/movies
Satellite observations of mesoscale eddy-induced Ekman pumping
Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 104–132, doi:10.1175/JPO-D-14-0032.1.Three mechanisms for self-induced Ekman pumping in the interiors of mesoscale ocean eddies are investigated. The first arises from the surface stress that occurs because of differences between surface wind and ocean velocities, resulting in Ekman upwelling and downwelling in the cores of anticyclones and cyclones, respectively. The second mechanism arises from the interaction of the surface stress with the surface current vorticity gradient, resulting in dipoles of Ekman upwelling and downwelling. The third mechanism arises from eddy-induced spatial variability of sea surface temperature (SST), which generates a curl of the stress and therefore Ekman pumping in regions of crosswind SST gradients. The spatial structures and relative magnitudes of the three contributions to eddy-induced Ekman pumping are investigated by collocating satellite-based measurements of SST, geostrophic velocity, and surface winds to the interiors of eddies identified from their sea surface height signatures. On average, eddy-induced Ekman pumping velocities approach O(10) cm day−1. SST-induced Ekman pumping is usually secondary to the two current-induced mechanisms for Ekman pumping. Notable exceptions are the midlatitude extensions of western boundary currents and the Antarctic Circumpolar Current, where SST gradients are strong and all three mechanisms for eddy-induced Ekman pumping are comparable in magnitude. Because the polarity of current-induced curl of the surface stress opposes that of the eddy, the associated Ekman pumping attenuates the eddies. The decay time scale of this attenuation is proportional to the vertical scale of the eddy and inversely proportional to the wind speed. For typical values of these parameters, the decay time scale is about 1.3 yr.This work was funded by NASA Grants NNX08AI80G, NNX08AR37G, NNX13AD78G, NNX10AE91G, NNX13AE47G, and NNX10AO98G.2015-07-0
The region with trapped surfaces in spherical symmetry, its core, and their boundaries
We consider the region in spacetime containing future-trapped
closed surfaces and its boundary \B, and derive some of their general
properties. We then concentrate on the case of spherical symmetry, but the
methods we use are general and applicable to other situations. We argue that
closed trapped surfaces have a non-local property, "clairvoyance", which is
inherited by \B. We prove that \B is not a marginally trapped tube in
general, and that it can have portions in regions whose whole past is flat. For
asymptotically flat black holes, we identify a general past barrier, well
inside the event horizon, to the location of \B under physically reasonable
conditions. We also define the core of the trapped region as that
part of which is indispensable to sustain closed trapped
surfaces. We prove that the unique spherically symmetric dynamical horizon is
the boundary of such a core, and we argue that this may serve to single it out.
To illustrate the results, some explicit examples are discussed, namely
Robertson-Walker geometries and the imploding Vaidya spacetime.Comment: 70 pages, 14 figures. Figure 6 has been replaced, and corrected.
Minor changes around Propositions 10.3 and 10.4, and some typos correcte
The Singularity Problem for Space-Times with Torsion
The problem of a rigorous theory of singularities in space-times with torsion
is addressed. We define geodesics as curves whose tangent vector moves by
parallel transport. This is different from what other authors have done,
because their definition of geodesics only involves the Christoffel connection,
though studying theories with torsion. We propose a preliminary definition of
singularities which is based on timelike or null geodesic incompleteness, even
though for theories with torsion the paths of particles are not geodesics. The
study of the geodesic equation for cosmological models with torsion shows that
the definition has a physical relevance. It can also be motivated, as done in
the literature, remarking that the causal structure of a space-time with
torsion does not get changed with respect to general relativity. We then prove
how to extend Hawking's singularity theorem without causality assumptions to
the space-time of the ECSK theory. This is achieved studying the generalized
Raychaudhuri equation in the ECSK theory, the conditions for the existence of
conjugate points and properties of maximal timelike geodesics. Hawking's
theorem can be generalized, provided the torsion tensor obeys some conditions.
Thus our result can also be interpreted as a no-singularity theorem if these
additional conditions are not satisfied. In other words, it turns out that the
occurrence of singularities in closed cosmological models based on the ECSK
theory is less generic than in general relativity. Our work is to be compared
with previous papers in the literature. There are some relevant differences,
because we rely on a different definition of geodesics, we keep the field
equations of the ECSK theory in their original form rather than casting them in
a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages
75-90, year 199
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