2,148 research outputs found
Stretching the Inflaton Potential with Kinetic Energy
Inflation near a maximum of the potential is studied when non-local
derivative operators are included in the inflaton Lagrangian. Such terms can
impose additional sources of friction on the field. For an arbitrary spacetime
geometry, these effects can be quantified in terms of a local field theory with
a potential whose curvature around the turning point is strongly suppressed.
This implies that a prolonged phase of slow-roll inflation can be achieved with
potentials that are otherwise too steep to drive quasi-exponential expansion.
We illustrate this mechanism within the context of p-adic string theory.Comment: 4 page
Non-local dilaton coupling to dark matter: cosmic acceleration and pressure backreaction
A model of non-local dilaton interactions, motivated by string duality
symmetries, is applied to a scenario of "coupled quintessence" in which the
dilaton dark energy is non-locally coupled to the dark-matter sources. It is
shown that the non-local effects tend to generate a backreaction which -- for
strong enough coupling -- can automatically compensate the acceleration due to
the negative pressure of the dilaton potential, thus asymptotically restoring
the standard (dust-dominated) decelerated regime. This result is illustrated by
analytical computations and numerical examples.Comment: 11 pages, 1 figure ep
Interacting dark energy, holographic principle and coincidence problem
The interacting and holographic dark energy models involve two important
quantities. One is the characteristic size of the holographic bound and the
other is the coupling term of the interaction between dark energy and dark
matter. Rather than fixing either of them, we present a detailed study of
theoretical relationships among these quantities and cosmological parameters as
well as observational constraints in a very general formalism. In particular,
we argue that the ratio of dark matter to dark energy density depends on the
choice of these two quantities, thus providing a mechanism to change the
evolution history of the ratio from that in standard cosmology such that the
coincidence problem may be solved. We investigate this problem in detail and
construct explicit models to demonstrate that it may be alleviated provided
that the interacting term and the characteristic size of holographic bound are
appropriately specified. Furthermore, these models are well fitted with the
current observation at least in the low red-shift region.Comment: 20 pages, 3 figure
Effects of Random Link Removal on the Photonic Band Gaps of Honeycomb Networks
We explore the effects of random link removal on the photonic band gaps of
honeycomb networks. Missing or incomplete links are expected to be common in
practical realizations of this class of connected network structures due to
unavoidable flaws in the fabrication process. We focus on the collapse of the
photonic band gap due to the defects induced by the link removal. We show that
the photonic band gap is quite robust against this type of random decimation
and survives even when almost 58% of the network links are removed
Sever: A Robust Meta-Algorithm for Stochastic Optimization
In high dimensions, most machine learning methods are brittle to even a small
fraction of structured outliers. To address this, we introduce a new
meta-algorithm that can take in a base learner such as least squares or
stochastic gradient descent, and harden the learner to be resistant to
outliers. Our method, Sever, possesses strong theoretical guarantees yet is
also highly scalable -- beyond running the base learner itself, it only
requires computing the top singular vector of a certain matrix. We
apply Sever on a drug design dataset and a spam classification dataset, and
find that in both cases it has substantially greater robustness than several
baselines. On the spam dataset, with corruptions, we achieved
test error, compared to for the baselines, and error on
the uncorrupted dataset. Similarly, on the drug design dataset, with
corruptions, we achieved mean-squared error test error, compared to
- for the baselines, and error on the uncorrupted dataset.Comment: To appear in ICML 201
How Material Heterogeneity Creates Rough Fractures
Fractures are a critical process in how materials wear, weaken, and fail
whose unpredictable behavior can have dire consequences. While the behavior of
smooth cracks in ideal materials is well understood, it is assumed that for
real, heterogeneous systems, fracture propagation is complex, generating rough
fracture surfaces that are highly sensitive to specific details of the medium.
Here we show how fracture roughness and material heterogeneity are inextricably
connected via a simple framework. Studying hydraulic fractures in brittle
hydrogels that have been supplemented with microbeads or glycerol to create
controlled material heterogeneity, we show that the morphology of the crack
surface depends solely on one parameter: the probability to perturb the front
above a critical size to produce a step-like instability. This probability
scales linearly with the number density, and as heterogeneity size to the
power. The ensuing behavior is universal and is captured by the 1D ballistic
propagation and annihilation of steps along the singular fracture front
Complete Set of Homogeneous Isotropic Analytic Solutions in Scalar-Tensor Cosmology with Radiation and Curvature
We study a model of a scalar field minimally coupled to gravity, with a
specific potential energy for the scalar field, and include curvature and
radiation as two additional parameters. Our goal is to obtain analytically the
complete set of configurations of a homogeneous and isotropic universe as a
function of time. This leads to a geodesically complete description of the
universe, including the passage through the cosmological singularities, at the
classical level. We give all the solutions analytically without any
restrictions on the parameter space of the model or initial values of the
fields. We find that for generic solutions the universe goes through a singular
(zero-size) bounce by entering a period of antigravity at each big crunch and
exiting from it at the following big bang. This happens cyclically again and
again without violating the null energy condition. There is a special subset of
geodesically complete non-generic solutions which perform zero-size bounces
without ever entering the antigravity regime in all cycles. For these, initial
values of the fields are synchronized and quantized but the parameters of the
model are not restricted. There is also a subset of spatial curvature-induced
solutions that have finite-size bounces in the gravity regime and never enter
the antigravity phase. These exist only within a small continuous domain of
parameter space without fine tuning initial conditions. To obtain these
results, we identified 25 regions of a 6-parameter space in which the complete
set of analytic solutions are explicitly obtained.Comment: 38 pages, 29 figure
Penrose Quantum Antiferromagnet
The Penrose tiling is a perfectly ordered two dimensional structure with
fivefold symmetry and scale invariance under site decimation. Quantum spin
models on such a system can be expected to differ significantly from more
conventional structures as a result of its special symmetries. In one
dimension, for example, aperiodicity can result in distinctive quantum
entanglement properties. In this work, we study ground state properties of the
spin-1/2 Heisenberg antiferromagnet on the Penrose tiling, a model that could
also be pertinent for certain three dimensional antiferromagnetic
quasicrystals. We show, using spin wave theory and quantum Monte Carlo
simulation, that the local staggered magnetizations strongly depend on the
local coordination number z and are minimized on some sites of five-fold
symmetry. We present a simple explanation for this behavior in terms of
Heisenberg stars. Finally we show how best to represent this complex
inhomogeneous ground state, using the "perpendicular space" representation of
the tiling.Comment: 4 pages, 5 figure
Cosmological scaling solutions of minimally coupled scalar fields in three dimensions
We examine Friedmann-Robertson-Walker models in three spacetime dimensions.
The matter content of the models is composed of a perfect fluid, with a
-law equation of state, and a homogeneous scalar field minimally
coupled to gravity with a self-interacting potential whose energy density
red-shifts as , where a denotes the scale factor. Cosmological
solutions are presented for different range of values of and .
The potential required to agree with the above red-shift for the scalar field
energy density is also calculated.Comment: LaTeX2e, 11 pages, 4 figures. To be published in Classical and
Quantum Gravit
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