1,463 research outputs found
Cosmological Imprint of an Energy Component with General Equation of State
We examine the possibility that a significant component of the energy density
of the universe has an equation-of-state different from that of matter,
radiation or cosmological constant (). An example is a cosmic scalar
field evolving in a potential, but our treatment is more general. Including
this component alters cosmic evolution in a way that fits current observations
well. Unlike , it evolves dynamically and develops fluctuations,
leaving a distinctive imprint on the microwave background anisotropy and mass
power spectrum.Comment: revised version, with added references, to appear in Phys. Rev. Lett.
(4 pages Latex, 2 postscript figures
Kasner and Mixmaster behavior in universes with equation of state w \ge 1
We consider cosmological models with a scalar field with equation of state
that contract towards a big crunch singularity, as in recent cyclic
and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to
anisotropy and curvature are suppressed, and the contraction is described by a
homogeneous and isotropic Friedmann equation if . We generalize the
results to theories where the scalar field couples to p-forms and show that
there exists a finite value of , depending on the p-forms, such that chaotic
oscillations are suppressed. We show that orbifold compactification also
contributes to suppressing chaotic behavior. In particular, chaos is avoided in
contracting heterotic M-theory models if at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde
Optical Absorption Characteristics of Silicon Nanowires for Photovoltaic Applications
Solar cells have generated a lot of interest as a potential source of clean
renewable energy for the future. However a big bottleneck in wide scale
deployment of these energy sources remain the low efficiency of these
conversion devices. Recently the use of nanostructures and the strategy of
quantum confinement have been as a general approach towards better charge
carrier generation and capture. In this article we have presented calculations
on the optical characteristics of nanowires made out of Silicon. Our
calculations show these nanowires form excellent optoelectronic materials and
may yield efficient photovoltaic devices
Formal Verification of Neural Network Controlled Autonomous Systems
In this paper, we consider the problem of formally verifying the safety of an
autonomous robot equipped with a Neural Network (NN) controller that processes
LiDAR images to produce control actions. Given a workspace that is
characterized by a set of polytopic obstacles, our objective is to compute the
set of safe initial conditions such that a robot trajectory starting from these
initial conditions is guaranteed to avoid the obstacles. Our approach is to
construct a finite state abstraction of the system and use standard
reachability analysis over the finite state abstraction to compute the set of
the safe initial states. The first technical problem in computing the finite
state abstraction is to mathematically model the imaging function that maps the
robot position to the LiDAR image. To that end, we introduce the notion of
imaging-adapted sets as partitions of the workspace in which the imaging
function is guaranteed to be affine. We develop a polynomial-time algorithm to
partition the workspace into imaging-adapted sets along with computing the
corresponding affine imaging functions. Given this workspace partitioning, a
discrete-time linear dynamics of the robot, and a pre-trained NN controller
with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge
is to analyze the behavior of the neural network. To that end, we utilize a
Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible
segments of different ReLUs. SMC solvers then use a Boolean satisfiability
solver and a convex programming solver and decompose the problem into smaller
subproblems. To accelerate this process, we develop a pre-processing algorithm
that could rapidly prune the space feasible ReLU segments. Finally, we
demonstrate the efficiency of the proposed algorithms using numerical
simulations with increasing complexity of the neural network controller
Quantum Cosmology for the General Bianchi Type II, VI(Class A) and VII(Class A) vacuum geometries
The canonical quantization of the most general minisuperspace actions --i.e.
with all six scale factor as well as the lapse function and the shift vector
present-- describing the vacuum type II, VI and VII geometries, is considered.
The reduction to the corresponding physical degrees of freedom is achieved
through the usage of the linear constraints as well as the quantum version of
the entire set of classical integrals of motion.Comment: 23 pages, LaTeX2e, No figure
Strong Brane Gravity and the Radion at Low Energies
For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for
strong gravity, in the low matter density regime, for slowly varying matter
sources. This is relevant for astrophysical or cosmological applications. The
warped compactification means the radion can not be written as a homogeneous
mode in the orbifold coordinate, and we introduce it by extending the
coordinate patch approach of the linear theory to the non-linear case. The
negative tension brane is taken to be in vacuum. For conformally invariant
matter on the positive tension brane, we solve the bulk geometry as a
derivative expansion, formally summing the `Kaluza-Klein' contributions to all
orders. For general matter we compute the Einstein equations to leading order,
finding a scalar-tensor theory with ,
and geometrically interpret the radion. We comment that this radion scalar may
become large in the context of strong gravity with low density matter.
Equations of state allowing to be negative, can exhibit behavior
where the matter decreases the distance between the 2 branes, which we
illustrate numerically for static star solutions using an incompressible fluid.
For increasing stellar density, the branes become close before the upper mass
limit, but after violation of the dominant energy condition. This raises the
interesting question of whether astrophysically reasonable matter, and initial
data, could cause branes to collide at low energy, such as in dynamical
collapse.Comment: 24 pages, 3 figure
A note on wavemap-tensor cosmologies
We examine theories of gravity which include finitely many coupled scalar
fields with arbitrary couplings to the curvature (wavemaps). We show that the
most general scalar-tensor -model action is conformally equivalent to
general relativity with a minimally coupled wavemap with a particular target
metric. Inflation on the source manifold is then shown to occur in a novel way
due to the combined effect of arbitrary curvature couplings and wavemap
self-interactions. A new interpretation of the conformal equivalence theorem
proved for such `wavemap-tensor' theories through brane-bulk dynamics is also
discussed.Comment: 8 pages, LaTeX, to appear in the Proceedings of the 2nd Hellenic
Cosmology Workshop, National Observatory of Athens, April 21-22, 2001,
(Kluwer 2001
Two dimensional QCD and abelian bosonization
A bosonized action, that reproduces the structure of the 't Hooft equation
for in the large- limit, up to regularization dependent terms, is
derived.Comment: paper revised, several signs and coefficients corrected. A comment on
regularization dependence and several references adde
Quintessence and cosmic acceleration
A cosmological model with perfect fluid and self-interacting quintessence
field is considered in the framework of the spatially flat
Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical
quantities depend on the volume scale factor of the Universe, the general
solution of the gravitational field equations can be expressed in an exact
parametric form. The quintessence field is a free parameter. With an
appropriate choice of the scalar field a class of exact solutions is obtained,
with an exponential type scalar field potential fixed via the gravitational
field equations. The general physical behavior of the model is consistent with
the recent cosmological scenario favored by supernova Type Ia observations,
indicating an accelerated expansion of the Universe.Comment: 6 pages, 3 figures, to appear in Int. J. Mod. Phys.
Matter density perturbations in interacting quintessence models
Models with dark energy decaying into dark matter have been proposed to solve
the coincidence problem in cosmology. We study the effect of such coupling in
the matter power spectrum. Due to the interaction, the growth of matter density
perturbations during the radiation dominated regime is slower compared to
non-interacting models with the same ratio of dark matter to dark energy today.
This effect introduces a damping on the power spectrum at small scales
proportional to the strength of the interaction and similar to the effect
generated by ultrarelativistic neutrinos. The interaction also shifts
matter--radiation equality to larger scales. We compare the matter power
spectrum of interacting quintessence models with the measurments of 2dFGRS. We
particularize our study to models that during radiation domination have a
constant dark matter to dark energy ratio.Comment: 11 pages, 4 figures, accepted for publication in Phys. Rev.
- …