128,302 research outputs found
Selftuning and its footprints
We re-consider the self tuning idea in brane world models of finite volume.
We notice that in a large class of self tuning models, the four dimensional
physics is sensitive to the vacuum energy on the brane. In particular the
compactification volume changes each time the tension of the brane is modified:
consequently, observable constants, as the effective Planck mass or masses of
matter fields, change as well. We notice that the self tuning mechanism and the
stabilization mechanism of the size of the extra dimensions are generically in
apparent conflict. We focus on a self tuning model in six spacetime dimensions
to analyze how the above considerations are explicitely realized.Comment: 28 pages, JHEP style. v2: typos corrected and references added.
Published versio
Control Strategies for the Fokker-Planck Equation
Using a projection-based decoupling of the Fokker-Planck equation, control
strategies that allow to speed up the convergence to the stationary
distribution are investigated. By means of an operator theoretic framework for
a bilinear control system, two different feedback control laws are proposed.
Projected Riccati and Lyapunov equations are derived and properties of the
associated solutions are given. The well-posedness of the closed loop systems
is shown and local and global stabilization results, respectively, are
obtained. An essential tool in the construction of the controls is the choice
of appropriate control shape functions. Results for a two dimensional double
well potential illustrate the theoretical findings in a numerical setup
Volume Stabilization and Acceleration in Brane Gas Cosmology
We investigate toy cosmological models in (1+m+p)-dimensions with gas of
p-branes wrapping over p-compact dimensions. In addition to winding modes, we
consider the effects of momentum modes corresponding to small vibrations of
branes and find that the extra dimensions are dynamically stabilized while the
others expand. Adding matter, the compact volume may grow slowly depending on
the equation of state. We also obtain solutions with winding and momentum modes
where the observed space undergoes accelerated expansion.Comment: 20 pages, 3 figures, v2: comments and references added, to appear in
JCA
Looking Beyond Inflationary Cosmology
In spite of the phenomenological successes of the inflationary universe
scenario, the current realizations of inflation making use of scalar fields
lead to serious conceptual problems which are reviewed in this lecture. String
theory may provide an avenue towards addressing these problems. One particular
approach to combining string theory and cosmology is String Gas Cosmology. The
basic principles of this approach are summarized.Comment: invited talk at "Theory Canada 1" (Univ. of British Columbia,
Vancouver, Canada, June 2 - 4, 2005) (references updated
On the Transfer of Metric Fluctuations when Extra Dimensions Bounce or Stabilize
In this report, we study within the context of general relativity with one
extra dimension compactified either on a circle or an orbifold, how radion
fluctuations interact with metric fluctuations in the three non-compact
directions. The background is non-singular and can either describe an extra
dimension on its way to stabilization, or immediately before and after a series
of non-singular bounces. We find that the metric fluctuations transfer
undisturbed through the bounces or through the transients of the
pre-stabilization epoch. Our background is obtained by considering the effects
of a gas of massless string modes in the context of a consistent 'massless
background' (or low energy effective theory) limit of string theory. We discuss
applications to various approaches to early universe cosmology, including the
ekpyrotic/cyclic universe scenario and string gas cosmology.Comment: V2. Minor Clarifications V3. appendix and 2 figures added, typos
corrected, conclusions unchanged 12 pages, 6 figure
On Resilient Control of Nonlinear Systems under Denial-of-Service
We analyze and design a control strategy for nonlinear systems under
Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we
provide a characterization of the maximal percentage of time during which
feedback information can be lost without resulting in the instability of the
system. Motivated by the presence of a digital channel we consider event-based
controllers for which a minimal inter-sampling time is explicitly
characterized.Comment: 7 pages, 1 figur
- …