945 research outputs found
Indexed induction and coinduction, fibrationally.
This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)
Tailoring Single and Multiphoton Probabilities of a Single Photon On-Demand Source
As typically implemented, single photon sources cannot be made to produce
single photons with high probability, while simultaneously suppressing the
probability of yielding two or more photons. Because of this, single photon
sources cannot really produce single photons on demand. We describe a
multiplexed system that allows the probabilities of producing one and more
photons to be adjusted independently, enabling a much better approximation of a
source of single photons on demand.Comment: 4 pages, LaTex, 2 figures, twocolumn and RevTex Style for PR
Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field
Chiral liquid crystals often exhibit periodic modulations in the molecular
director; in particular, thin films of the smectic-C* phase show a chiral
striped texture. Here, we investigate whether similar chiral modulations can
occur in the induced molecular tilt of the smectic-A phase under an applied
electric field. Using both continuum elastic theory and lattice simulations, we
find that the state of uniform induced tilt can become unstable when the system
approaches the smectic-A--smectic-C* transition, or when a high electric field
is applied. Beyond that instability point, the system develops chiral stripes
in the tilt, which induce corresponding ripples in the smectic layers. The
modulation persists up to an upper critical electric field and then disappears.
Furthermore, even in the uniform state, the system shows chiral fluctuations,
including both incipient chiral stripes and localized chiral vortices. We
compare these predictions with observed chiral modulations and fluctuations in
smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and
epsf.st
Qualitative Properties of Magnetic Fields in Scalar Field Cosmology
We study the qualitative properties of the class of spatially homogeneous
Bianchi VI_o cosmological models containing a perfect fluid with a linear
equation of state, a scalar field with an exponential potential and a uniform
cosmic magnetic field, using dynamical systems techniques. We find that all
models evolve away from an expanding massless scalar field model in which the
matter and the magnetic field are negligible dynamically. We also find that for
a particular range of parameter values the models evolve towards the usual
power-law inflationary model (with no magnetic field) and, furthermore, we
conclude that inflation is not fundamentally affected by the presence of a
uniform primordial magnetic field. We investigate the physical properties of
the Bianchi I magnetic field models in some detail.Comment: 12 pages, 2 figures in REVTeX format. to appear in Phys. Rev.
Single Photons on Pseudo-Demand from Stored Parametric Down-Conversion
We describe the results of a parametric down-conversion experiment in which
the detection of one photon of a pair causes the other photon to be switched
into a storage loop. The stored photon can then be switched out of the loop at
a later time chosen by the user, providing a single photon for potential use in
a variety of quantum information processing applications. Although the stored
single photon is only available at periodic time intervals, those times can be
chosen to match the cycle time of a quantum computer by using pulsed
down-conversion. The potential use of the storage loop as a photonic quantum
memory device is also discussed.Comment: 8 pages, 7 Figs., RevTe
Theta angle versus CP violation in the leptonic sector
Assuming that the axion mechanism of solving the strong CP problem does not
exist and the vanishing of theta at tree level is achieved by some
model-building means, we study the naturalness of having large CP-violating
sources in the leptonic sector. We consider the radiative mechanisms which
transfer a possibly large CP-violating phase in the leptonic sector to the
theta parameter. It is found that large theta cannot be induced in the models
with one Higgs doublet as at least three loops are required in this case. In
the models with two or more Higgs doublets the dominant source of theta is the
phases in the scalar potential, induced by CP violation in leptonic sector.
Thus, in the MSSM framework the imaginary part of the trilinear soft-breaking
parameter A_l generates the corrections to the theta angle already at one loop.
These corrections are large, excluding the possibility of large phases, unless
the universality in the slepton sector is strongly violated.Comment: 5 pages, 2 figure
Spinor Field in Bianchi type-I Universe: regular solutions
Self-consistent solutions to the nonlinear spinor field equations in General
Relativity has been studied for the case of Bianchi type-I (B-I) space-time. It
has been shown that, for some special type of nonliearity the model provides
regular solution, but this singularity-free solutions are attained at the cost
of broken dominant energy condition in Hawking-Penrose theorem. It has also
been shown that the introduction of -term in the Lagrangian generates
oscillations of the B-I model, which is not the case in absence of
term. Moreover, for the linear spinor field, the term provides
oscillatory solutions, those are regular everywhere, without violating dominant
energy condition.
Key words: Nonlinear spinor field (NLSF), Bianch type -I model (B-I),
term
PACS 98.80.C CosmologyComment: RevTex, 21 page
Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
We have studied how 2- and 3- dimensional systems made up of particles
interacting with finite range, repulsive potentials jam (i.e., develop a yield
stress in a disordered state) at zero temperature and applied stress. For each
configuration, there is a unique jamming threshold, , at which
particles can no longer avoid each other and the bulk and shear moduli
simultaneously become non-zero. The distribution of values becomes
narrower as the system size increases, so that essentially all configurations
jam at the same in the thermodynamic limit. This packing fraction
corresponds to the previously measured value for random close-packing. In fact,
our results provide a well-defined meaning for "random close-packing" in terms
of the fraction of all phase space with inherent structures that jam. The
jamming threshold, Point J, occurring at zero temperature and applied stress
and at the random close-packing density, has properties reminiscent of an
ordinary critical point. As Point J is approached from higher packing
fractions, power-law scaling is found for many quantities. Moreover, near Point
J, certain quantities no longer self-average, suggesting the existence of a
length scale that diverges at J. However, Point J also differs from an ordinary
critical point: the scaling exponents do not depend on dimension but do depend
on the interparticle potential. Finally, as Point J is approached from high
packing fractions, the density of vibrational states develops a large excess of
low-frequency modes. All of these results suggest that Point J may control
behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure
New York: the animated city
The urban landscape of New York City is one that is familiar to many, but, through the medium of animation, this familiarity has been consistently challenged. Often metamorphic, and always meticulously constructed, animated imagery encourages reflective thinking. Focusing on the themes of construction, destruction, and interactivity, this article seeks to cast critical light upon the animated double life that New York City has lived through the following moving image texts: Disney’s Fantasia 2000 (1999), Patrick Jean’s computer-generated short Pixels (2009), and Rockstar Games’ open-world blockbuster Grand Theft Auto IV (2008)
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