1,093 research outputs found
Pattern Formation and Dynamics in Rayleigh-B\'{e}nard Convection: Numerical Simulations of Experimentally Realistic Geometries
Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are
made, where possible, between theory and experiment by performing numerical
simulations of the Boussinesq equations for a variety of experimentally
realistic situations. Rectangular and cylindrical geometries of varying aspect
ratios for experimental boundary conditions, including fins and spatial ramps
in plate separation, are examined with particular attention paid to the role of
the mean flow. A small cylindrical convection layer bounded laterally either by
a rigid wall, fin, or a ramp is investigated and our results suggest that the
mean flow plays an important role in the observed wavenumber. Analytical
results are developed quantifying the mean flow sources, generated by amplitude
gradients, and its effect on the pattern wavenumber for a large-aspect-ratio
cylinder with a ramped boundary. Numerical results are found to agree well with
these analytical predictions. We gain further insight into the role of mean
flow in pattern dynamics by employing a novel method of quenching the mean flow
numerically. Simulations of a spiral defect chaos state where the mean flow is
suddenly quenched is found to remove the time dependence, increase the
wavenumber and make the pattern more angular in nature.Comment: 9 pages, 10 figure
O(\alpha_s) corrections to the decays of polarized W^+- and Z bosons into massive quark pairs
We present O(\alpha_s) results on the decays of polarized W^+- and Z bosons
into massive quark pairs. The NLO QCD corrections to the polarized decay
functions are given up to the second order in the quark mass expansion. We find
a surprisingly strong dependence of the NLO polarized decay functions on finite
quark mass effects even at the relatively large mass scale of the W^+- and Z
bosons. As a main application we consider the decay t -> b + W^+ involving the
helicity fractions \rho_{mm} of the W^+ boson followed by the polarized decay
W^+(\uparrow) -> q_1 qbar_2 for which we determine the O(\alpha_s) polar angle
decay distribution. We also discuss NLO polarization effects in the
production/decay process e^+e^- -> Z(\uparrow) -> q qbar.Comment: 25 pages, 2 figures and 1 tabl
Infrared behaviour of massless QED in space-time dimensions 2 < d < 4
We show that the logarithmic infrared divergences in electron self-energy and
vertex function of massless QED in 2+1 dimensions can be removed at all orders
of 1/N by an appropriate choice of a non-local gauge. Thus the infrared
behaviour given by the leading order in 1/N is not modified by higher order
corrections. Our analysis gives a computational scheme for the Amati-Testa
model, resulting in a non-trivial conformal invariant field theory for all
space-time dimensions 2 < d < 4.Comment: 12 pages, uses axodraw.sty; added comments at the end, and one
reference; to appear in Phys. Lett.
Theory for Metal Hydrides with Switchable Optical Properties
Recently it has been discovered that lanthanum, yttrium, and other metal
hydride films show dramatic changes in the optical properties at the
metal-insulator transition. Such changes on a high energy scale suggest the
electronic structure is best described by a local model based on negatively
charged hydrogen (H) ions. We develop a many-body theory for the strong
correlation in a H ion lattice. The metal hydride is described by a large
-limit of an Anderson lattice model. We use lanthanum hydride as a prototype
of these compounds, and find LaH is an insulator with a substantial gap
consistent with experiments. It may be viewed either as a Kondo insulator or a
band insulator due to strong electron correlation. A H vacancy state in LaH
is found to be highly localized due to the strong bonding between the electron
orbitals of hydrogen and metal atoms. Unlike the impurity states in the usual
semiconductors, there is only weak internal optical transitions within the
vacancy. The metal-insulator transition takes place in a band of these vacancy
states.Comment: 18 pages, 16 figures and 6 tables. Submitted to PR
Helicity Analysis of Semileptonic Hyperon Decays Including Lepton Mass Effects
Using the helicity method we derive complete formulas for the joint angular
decay distributions occurring in semileptonic hyperon decays including lepton
mass and polarization effects. Compared to the traditional covariant
calculation the helicity method allows one to organize the calculation of the
angular decay distributions in a very compact and efficient way. In the
helicity method the angular analysis is of cascade type, i.e. each decay in the
decay chain is analyzed in the respective rest system of that particle. Such an
approach is ideally suited as input for a Monte Carlo event generation program.
As a specific example we take the decay () followed by the nonleptonic decay for which we show a few examples of decay distributions which are
generated from a Monte Carlo program based on the formulas presented in this
paper. All the results of this paper are also applicable to the semileptonic
and nonleptonic decays of ground state charm and bottom baryons, and to the
decays of the top quark.Comment: Published version. 40 pages, 11 figures included in the text. Typos
corrected, comments added, references added and update
The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems
There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens
Combined CI+MBPT calculations of energy levels and transition amplitudes in Be, Mg, Ca, and Sr
Configuration interaction (CI) calculations in atoms with two valence
electrons, carried out in the V(N-2) Hartree-Fock potential of the core, are
corrected for core-valence interactions using many-body perturbation theory
(MBPT). Two variants of the mixed CI+MBPT theory are described and applied to
obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr
Mean flow and spiral defect chaos in Rayleigh-Benard convection
We describe a numerical procedure to construct a modified velocity field that
does not have any mean flow. Using this procedure, we present two results.
Firstly, we show that, in the absence of mean flow, spiral defect chaos
collapses to a stationary pattern comprising textures of stripes with angular
bends. The quenched patterns are characterized by mean wavenumbers that
approach those uniquely selected by focus-type singularities, which, in the
absence of mean flow, lie at the zig-zag instability boundary. The quenched
patterns also have larger correlation lengths and are comprised of rolls with
less curvature. Secondly, we describe how mean flow can contribute to the
commonly observed phenomenon of rolls terminating perpendicularly into lateral
walls. We show that, in the absence of mean flow, rolls begin to terminate into
lateral walls at an oblique angle. This obliqueness increases with Rayleigh
number.Comment: 14 pages, 19 figure
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.
Implementation and application of multiple potential natural vegetation models – a case study of Hungary
- …