17,466 research outputs found
A Note On Stability of Steady Motion of a Rolling Disk
This note adds some critical remarks on the discussion presented in the
McDonald's paper ([1]) on stability of steady motion of the well known problem
of a disk rolling on a rough horizontal plane.Comment: 3 pages, 1 figur
Power-law solutions and accelerated expansion in scalar-tensor theories
We find exact power-law solutions for scalar-tensor theories and clarify the
conditions under which they can account for an accelerated expansion of the
Universe. These solutions have the property that the signs of both the Hubble
rate and the deceleration parameter in the Jordan frame may be different from
the signs of their Einstein-frame counterparts. For special parameter
combinations we identify these solutions with asymptotic attractors that have
been obtained in the literature through dynamical-system analysis. We establish
an effective general-relativistic description for which the geometrical
equivalent of dark energy is associated with a time dependent equation of
state. The present value of the latter is consistent with the observed
cosmological ``constant". We demonstrate that this type of power-law solutions
for accelerated expansion cannot be realized in f(R) theories.Comment: 22 pages, 1 figure, substantially rewritten, presentation improved.
Accepted for publication in Phys.Rev.
Cohomology for partial actions of Hopf algebras
In this work, the cohomology theory for partial actions of co-commutative
Hopf algebras over commutative algebras is formulated. This theory generalizes
the cohomology theory for Hopf algebras introduced by Sweedler and the
cohomology theory for partial group actions, introduced by Dokuchaev and
Khrypchenko. Some nontrivial examples, not coming from groups are constructed.
Given a partial action of a co-commutative Hopf algebra over a commutative
algebra , we prove that there exists a new Hopf algebra ,
over a commutative ring , upon which still acts partially and which
gives rise to the same cochain complex as the original algebra . We also
study the partially cleft extensions of commutative algebras by partial actions
of cocommutative Hopf algebras and prove that these partially cleft extensions
can be viewed as a cleft extensions by Hopf algebroids.Comment: 49 pages, a longer version, with some detailed proofs kept in the
appendi
Scalar Perturbations in a String Inspired Inflationary Scenario
We consider an inflationary model inspired in the low energy limit of string
theory. In this model, the scale factor grows exponentially with time. A
perturbation study is performed, and we show that there is a mode which
displays an exponential growth in the perturbation of the scalar field.Comment: 8 pages, latex fil
Using spherical wavelets to search for magnetically-induced alignment in the arrival directions of ultra-high energy cosmic rays
Due to the action of the intervening cosmic magnetic fields, ultra-high
energy cosmic rays (UHECRs) can be deflected in such a way as to create
clustered energy-ordered filamentary structures in the arrival direction of
these particles, the so-called multiplets. In this work we propose a new method
based on the spherical wavelet transform to identify multiplets in sky maps
containing arrival directions of UHECRs. The method is illustrated in
simulations with a multiplet embedded in isotropic backgrounds with different
numbers of events. The efficiency of the algorithm is assessed through the
calculation of Type I and II errors.Comment: 8 pages, 8 figures. Matches the published versio
Testing the Rastall's theory using matter power spectrum
The Rastall's theory is a modification of the General Relativity theory
leading to a different expression for the conservation law in the matter sector
compared with the usual one. It has been argued recently that such a theory may
have applications to the dark energy problem, since a pressureless fluid may
lead to an accelerated universe. In the present work we confront the Rastall's
theory with the power spectrum data. The results indicate a configuration that
essentially reduces the Rastall's theory to General Relativity, unless the
non-usual conservation law refers to a scalar field, situation where other
configurations are eventually possible.Comment: 14 pages, 6 figures in eps forma
Nematic droplets at fibres
The emergence of new techniques for the fabrication of nematic droplets with
nontrivial topology provides new routes for the assembly of responsive devices.
Here we perform a numerical study of spherical nematic droplets on fibres. We
analyse the equilibrium textures and find that, under certain conditions,the
nematic can avoid the nucleation of topological defects. We consider in detail
a homeotropic nematic droplet wrapped around a fibre with planar anchoring. We
investigate the effect of an electric field on the texture of this droplet such
type of system. In the presence of a DC field, the system undergoes a
Freederickzs-like transition above a given threshold . We also consider AC
fields, at high and low frequencies, and find that the textures are similar to
those observed for static fields, in contrast with recently reported
experiments.Comment: 8 pages, 5 figures, submitte
The effect of anchoring on nematic flow in channels
Understanding the flow of liquid crystals in microfluidic environments plays
an important role in many fields, including device design and microbiology. We
perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal
flowing under an applied pressure gradient in two-dimensional channels with
various anchoring boundary conditions at the substrate walls. We investigate
the relation between flow rate and pressure gradient and the corresponding
profile of the nematic director, and find significant departures from the
linear Poiseuille relation. We also identify a morphological transition in the
director profile and explain this in terms of an instability in the dynamical
equations. We examine the qualitative and quantitative effects of changing the
type and strength of the anchoring. Understanding such effects may provide a
useful means of quantifying the anchoring of a substrate by measuring its flow
properties
Chaos synchronization in long-range coupled map lattices
We investigate the synchronization phenomenon in coupled chaotic map lattices
where the couplings decay with distance following a power-law. Depending on the
lattice size, the coupling strength and the range of the interactions, complete
chaos synchronization may be attained. The synchronization domain in parameter
space can be analytically delimited by means of the condition of negativity of
the largest transversal Lyapunov exponent. Here we analyze in detail the role
of all the system parameters in the ability of the lattice to achieve complete
synchronization, testing analytical results with the outcomes of numerical
experiments.Comment: 5 pages, 5 figure
Position USBL/DVL Sensor-based Navigation Filter in the presence of Unknown Ocean Currents
This paper presents a novel approach to the design of globally asymptotically
stable (GAS) position filters for Autonomous Underwater Vehicles (AUVs) based
directly on the nonlinear sensor readings of an Ultra-short Baseline (USBL) and
a Doppler Velocity Log (DVL). Central to the proposed solution is the
derivation of a linear time-varying (LTV) system that fully captures the
dynamics of the nonlinear system, allowing for the use of powerful linear
system analysis and filtering design tools that yield GAS filter error
dynamics. Simulation results reveal that the proposed filter is able to achieve
the same level of performance of more traditional solutions, such as the
Extended Kalman Filter (EKF), while providing, at the same time, GAS
guarantees, which are absent for the EKF.Comment: Combined with 49th IEEE Conference on Decision and Control December
15-17, 2010 at the Hilton Atlanta Hotel in Atlanta, Georgia USA. 9 pages
complete with full proof
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