64,499 research outputs found
Transverse modulational instability of partially incoherent soliton stripes
Based on the Wigner distribution approach, an analysis of the effect of
partial incoherence on the transverse instability of soliton structures in
nonlinear Kerr media is presented. It is explicitly shown, that for a
Lorentzian incoherence spectrum the partial incoherence gives rise to a damping
which counteracts, and tends to suppress, the transverse instability growth.
However, the general picture is more complicated and it is shown that the
effect of the partial incoherence depends crucially on the form of the
incoherence spectrum. In fact, for spectra with finite rms-width, the partial
incoherence may even increase both the growth rate and the range of unstable,
transverse wave numbers.Comment: 5 pages, submitted to Phys. Rev.
A case study of effective practice in mathematics teaching and learning informed by Valsinerâs zone theory
The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated âbest practiceâ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsinerâs zone theory. A finding of the study is that âsuccessfulâ practice is strongly tied to school context and the cultural practices that have been developed by school leaders and teachers to optimise student learning opportunities. We illustrate such an alignment of school culture and practice through a vignette based on a case of one âsuccessfulâ school
The Screen representation of spin networks. Images of 6j symbols and semiclassical features
This article presents and discusses in detail the results of extensive exact
calculations of the most basic ingredients of spin networks, the Racah
coefficients (or Wigner 6j symbols), exhibiting their salient features when
considered as a function of two variables - a natural choice due to their
origin as elements of a square orthogonal matrix - and illustrated by use of a
projection on a square "screen" introduced recently. On these screens, shown
are images which provide a systematic classification of features previously
introduced to represent the caustic and ridge curves (which delimit the
boundaries between oscillatory and evanescent behaviour according to the
asymptotic analysis of semiclassical approaches). Particular relevance is given
to the surprising role of the intriguing symmetries discovered long ago by
Regge and recently revisited; from their use, together with other newly
discovered properties and in conjunction with the traditional combinatorial
ones, a picture emerges of the amplitudes and phases of these discrete
wavefunctions, of interest in wide areas as building blocks of basic and
applied quantum mechanics.Comment: 16 pages, 13 figures, presented at ICCSA 2013 13th International
Conference on Computational Science and Applicatio
Diffraction of a shock wave by a compression corner; regular and single Mach reflection
The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions
Spread of Infectious Diseases with a Latent Period
Infectious diseases spread through human networks.
Susceptible-Infected-Removed (SIR) model is one of the epidemic models to
describe infection dynamics on a complex network connecting individuals. In the
metapopulation SIR model, each node represents a population (group) which has
many individuals. In this paper, we propose a modified metapopulation SIR model
in which a latent period is taken into account. We call it SIIR model. We
divide the infection period into two stages: an infected stage, which is the
same as the previous model, and a seriously ill stage, in which individuals are
infected and cannot move to the other populations. The two infectious stages in
our modified metapopulation SIR model produce a discontinuous final size
distribution. Individuals in the infected stage spread the disease like
individuals in the seriously ill stage and never recover directly, which makes
an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure
Non-Linear Canonical Transformations in Classical and Quantum Mechanics
-Mechanics is a consistent physical theory which describes both classical
and quantum mechanics simultaneously through the representation theory of the
Heisenberg group. In this paper we describe how non-linear canonical
transformations affect -mechanical observables and states. Using this we
show how canonical transformations change a quantum mechanical system. We seek
an operator on the set of -mechanical observables which corresponds to the
classical canonical transformation. In order to do this we derive a set of
integral equations which when solved will give us the coherent state expansion
of this operator. The motivation for these integral equations comes from the
work of Moshinsky and a variety of collaborators. We consider a number of
examples and discuss the use of these equations for non-bijective
transformations.Comment: The paper has been improved in light of a referee's report. The paper
will appear in the Journal of Mathematical Physics. 24 pages, no figure
Exact and asymptotic computations of elementary spin networks: classification of the quantum-classical boundaries
Increasing interest is being dedicated in the last few years to the issues of
exact computations and asymptotics of spin networks. The large-entries regimes
(semiclassical limits) occur in many areas of physics and chemistry, and in
particular in discretization algorithms of applied quantum mechanics. Here we
extend recent work on the basic building block of spin networks, namely the
Wigner 6j symbol or Racah coefficient, enlightening the insight gained by
exploiting its self-dual properties and studying it as a function of two
(discrete) variables. This arises from its original definition as an
(orthogonal) angular momentum recoupling matrix. Progress also derives from
recognizing its role in the foundation of the modern theory of classical
orthogonal polynomials, as extended to include discrete variables. Features of
the imaging of various regimes of these orthonormal matrices are made explicit
by computational advances -based on traditional and new recurrence relations-
which allow an interpretation of the observed behaviors in terms of an
underlying Hamiltonian formulation as well. This paper provides a contribution
to the understanding of the transition between two extreme modes of the 6j,
corresponding to the nearly classical and the fully quantum regimes, by
studying the boundary lines (caustics) in the plane of the two matrix labels.
This analysis marks the evolution of the turning points of relevance for the
semiclassical regimes and puts on stage an unexpected key role of the Regge
symmetries of the 6j.Comment: 15 pages, 11 figures. Talk presented at ICCSA 2012 (12th
International Conference on Computational Science and Applications, Salvador
de Bahia (Brazil) June 18-21, 2012
Size Gap for Zero Temperature Black Holes in Semiclassical Gravity
We show that a gap exists in the allowed sizes of all zero temperature static
spherically symmetric black holes in semiclassical gravity when only
conformally invariant fields are present. The result holds for both charged and
uncharged black holes. By size we mean the proper area of the event horizon.
The range of sizes that do not occur depends on the numbers and types of
quantized fields that are present. We also derive some general properties that
both zero and nonzero temperature black holes have in all classical and
semiclassical metric theories of gravity.Comment: 4 pages, ReVTeX, no figure
A new effective exchange rate index for the dollar and its implications for U.S. merchandise trade
An introduction to a new exchange-rate index to measure the foreign-exchange value of the dollar. The authors develop a model of U.S. merchandise trade, featuring the new index.Foreign exchange rates ; Dollar, American
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Strategies intended to resolve the problem of time in quantum gravity by
means of emergent or hidden timefunctions are considered in the arena of
relational particle toy models. In situations with `heavy' and `light' degrees
of freedom, two notions of emergent semiclassical WKB time emerge; these are
furthermore equivalent to two notions of emergent classical
`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,
in a geometric phase formalism, extended to include linear constraints, and
with particular care to make explicit those approximations and assumptions
used. I propose a new iterative scheme for this in the cosmologically-motivated
case with one heavy degree of freedom. I find that the usual semiclassical
quantum cosmology emergence of time comes hand in hand with the emergence of
other qualitatively significant terms, including back-reactions on the heavy
subsystem and second time derivatives. I illustrate my analysis by taking it
further for relational particle models with linearly-coupled harmonic
oscillator potentials. As these examples are exactly soluble by means outside
the semiclassical approach, they are additionally useful for testing the
justifiability of some of the approximations and assumptions habitually made in
the semiclassical approach to quantum cosmology. Finally, I contrast the
emergent semiclassical timefunction with its hidden dilational Euler time
counterpart.Comment: References Update
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