12,035 research outputs found
Coverage and Field Estimation on Bounded Domains by Diffusive Swarms
In this paper, we consider stochastic coverage of bounded domains by a
diffusing swarm of robots that take local measurements of an underlying scalar
field. We introduce three control methodologies with diffusion, advection, and
reaction as independent control inputs. We analyze the diffusion-based control
strategy using standard operator semigroup-theoretic arguments. We show that
the diffusion coefficient can be chosen to be dependent only on the robots'
local measurements to ensure that the swarm density converges to a function
proportional to the scalar field. The boundedness of the domain precludes the
need to impose assumptions on decaying properties of the scalar field at
infinity. Moreover, exponential convergence of the swarm density to the
equilibrium follows from properties of the spectrum of the semigroup generator.
In addition, we use the proposed coverage method to construct a
time-inhomogenous diffusion process and apply the observability of the heat
equation to reconstruct the scalar field over the entire domain from
observations of the robots' random motion over a small subset of the domain. We
verify our results through simulations of the coverage scenario on a 2D domain
and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision
and Control (CDC 2016
Brane Worlds, the Cosmological Constant and String Theory
We argue that traditional methods of compactification of string theory make
it very difficult to understand how the cosmological constant becomes zero.
String inspired models can give zero cosmological constant after fine tuning
but since string theory has no free parameters it is not clear that this is
allowed. Brane world scenarios on the other hand while they do not answer the
question as to why the cosmological constant is zero do actually allow a choice
of integration constants that permit flat four space solutions. In this paper
we discuss gauged supergravity realizations of such a world. To the extent that
this starting point can be considered a low energy effective action of string
theory (and there is some recent evidence supporting this) our model may be
considered a string theory realization of this scenario.Comment: 18 pages, 5 figures. Shorter version and a few new comments adde
Extra-dimensional cosmology with domain-wall branes
We show how to define a consistent braneworld cosmology in a model in which
the brane is constructed as a field-theoretic domain wall of finite thickness.
The Friedmann, Robertson-Walker metric is recovered in the region of the brane,
but, remarkably, with scale factor that depends on particle energy and on
particle species, constituting a breakdown of the weak equivalence principle on
sufficiently small scales. This unusual effect comes from the extended nature
of particles confined to a domain-wall brane, and the fact that they feel an
"average" of the bulk spacetime. We demonstrate how to recover the standard
results of brane cosmology in the infinitely-thin brane limit, and comment on
how our results have the potential to place bounds on parameters such as the
thickness of domain-wall braneworlds.Comment: 23 pages; v2 has additional references and reflects journal versio
Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models
We investigate the existence and properties of kink-like solitons in a class
of models with two interacting scalar fields. In particular, we focus on models
that display both double and single-kink solutions, treatable analytically
using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of
interest in applications that include Skyrmions and various
superstring-motivated theories. Exploring a region of parameter space where the
energy for very different spatially-bound configurations is degenerate, we show
that a newly-proposed momentum-space entropic measure called Configurational
Entropy (CE) can distinguish between such energy-degenerate spatial profiles.
This information-theoretic measure of spatial complexity provides a
complementary perspective to situations where strictly energy-based arguments
are inconclusive
Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model
Critical behaviour of a system, subjected to strongly anisotropic turbulent
mixing, is studied by means of the field theoretic renormalization group.
Specifically, relaxational stochastic dynamics of a non-conserved
multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a
random velocity field with prescribed statistics, is considered. The velocity
is taken Gaussian, white in time, with correlation function of the form
, where is
the component of the wave vector, perpendicular to the distinguished direction
("direction of the flow") --- the -dimensional generalization of the
ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.}
{\bf 131} 381] within the context of passive scalar advection. This model can
describe a rich class of physical situations. It is shown that, depending on
the values of parameters that define self-interaction of the order parameter
and the relation between the exponent and the space dimension , the
system exhibits various types of large-scale scaling behaviour, associated with
different infrared attractive fixed points of the renormalization-group
equations. In addition to known asymptotic regimes (critical dynamics of the
Potts model and passively advected field without self-interaction), existence
of a new, non-equilibrium and strongly anisotropic, type of critical behaviour
(universality class) is established, and the corresponding critical dimensions
are calculated to the leading order of the double expansion in and
(one-loop approximation). The scaling appears strongly
anisotropic in the sense that the critical dimensions related to the directions
parallel and perpendicular to the flow are essentially different.Comment: 21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial
text overlap with arXiv:cond-mat/060701
Stability of Scalar Fields in Warped Extra Dimensions
This work sets up a general theoretical framework to study stability of
models with a warped extra dimension where N scalar fields couple minimally to
gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk
scalars, and general domain-wall models. We derive the Schrodinger equation
governing the spin-0 spectrum of perturbations of such a system. This result is
specialized to potentials generated using fake supergravity, and we show that
models without branes are free of tachyonic modes. Turning to the existence of
zero modes, we prove a criterion which relates the number of normalizable zero
modes to the parities of the scalar fields. Constructions with definite parity
and only odd scalars are shown to be free of zero modes and are hence
perturbatively stable. We give two explicit examples of domain-wall models with
a soft wall, one which admits a zero mode and one which does not. The latter is
an example of a model that stabilizes a compact extra dimension using only bulk
scalars and does not require dynamical branes.Comment: 25 pages, 2 figures; v2: minor changes to text, references added,
matches published versio
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