1,420 research outputs found
Null Energy Condition Violation and Classical Stability in the Bianchi I Metric
The stability of isotropic cosmological solutions in the Bianchi I model is
considered. We prove that the stability of isotropic solutions in the Bianchi I
metric for a positive Hubble parameter follows from their stability in the
Friedmann-Robertson-Walker metric. This result is applied to models inspired by
string field theory, which violate the null energy condition. Examples of
stable isotropic solutions are presented. We also consider the k-essence model
and analyse the stability of solutions of the form .Comment: 27 pages, references added, accepted for publication in Phys. Rev.
Stable Exact Solutions in Cosmological Models with Two Scalar Fields
The stability of isotropic cosmological solutions for two-field models in the
Bianchi I metric is considered. We prove that the sufficient conditions for the
Lyapunov stability in the Friedmann-Robertson-Walker metric provide the
stability with respect to anisotropic perturbations in the Bianchi I metric and
with respect to the cold dark matter energy density fluctuations. Sufficient
conditions for the Lyapunov stability of the isotropic fixed points of the
system of the Einstein equations have been found. We use the superpotential
method to construct stable kink-type solutions and obtain sufficient conditions
on the superpotential for the Lyapunov stability of the corresponding exact
solutions. We analyze the stability of isotropic kink-type solutions for string
field theory inspired cosmological models.Comment: 23 pages, v3:typos corrected, references adde
A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
In this paper, we consider input-output properties of linear systems
consisting of PDEs on a finite domain coupled with ODEs through the boundary
conditions of the PDE. This framework can be used to represent e.g. a lumped
mass fixed to a beam or a system with delay. This work generalizes the
sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a
recently developed concept of fundamental state and the associated
boundary-condition-free representation. The conditions of the generalized KYP
are tested using the PQRS positive matrix parameterization of operators
resulting in a finite-dimensional LMI, feasibility of which implies prima facie
provable passivity or L2-gain of the system. No discretization or approximation
is involved at any step and we use numerical examples to demonstrate that the
bounds obtained are not conservative in any significant sense and that
computational complexity is lower than existing methods involving
finite-dimensional projection of PDEs
Chaos in the BMN matrix model
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN)
matrix model. For this purpose, it is convenient to focus upon a reduced system
composed of two-coupled anharmonic oscillators by supposing an ansatz. We
examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single
Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two
cases, we show the existence of chaos by computing Poincar\'e sections and a
Lyapunov spectrum. The third case leads to an integrable system. As a result,
the BMN matrix model is not integrable in the sense of Liouville, though there
may be some integrable subsectors.Comment: 23 pages, 15 figures, v2: further clarifications and references adde
Analysis of scalar perturbations in cosmological models with a non-local scalar field
We develop the cosmological perturbations formalism in models with a single
non-local scalar field originating from the string field theory description of
the rolling tachyon dynamics. We construct the equation for the energy density
perturbations of the non-local scalar field in the presence of the arbitrary
potential and formulate the local system of equations for perturbations in the
linearized model when both simple and double roots of the characteristic
equation are present. We carry out the general analysis related to the
curvature and entropy perturbations and consider the most specific example of
perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added,
references added, accepted for publication in Class. Quant. Grav. arXiv admin
note: text overlap with arXiv:0903.517
A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions
The most general version of a renormalizable theory corresponding to a
dimensionless higher-derivative scalar field model in curved spacetime is
explored. The classical action of the theory contains independent
functions, which are the generalized coupling constants of the theory. We
calculate the one-loop beta functions and then consider the conditions for
finiteness. The set of exact solutions of power type is proven to consist of
precisely three conformal and three nonconformal solutions, given by remarkably
simple (albeit nontrivial) functions that we obtain explicitly. The finiteness
of the conformal theory indicates the absence of a conformal anomaly in the
finite sector. The stability of the finite solutions is investigated and the
possibility of renormalization group flows is discussed as well as several
physical applications.Comment: LaTeX, 18 pages, no figure
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