99,444 research outputs found
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
We show that, near periodic orbits, a class of hybrid models can be reduced
to or approximated by smooth continuous-time dynamical systems. Specifically,
near an exponentially stable periodic orbit undergoing isolated transitions in
a hybrid dynamical system, nearby executions generically contract
superexponentially to a constant-dimensional subsystem. Under a non-degeneracy
condition on the rank deficiency of the associated Poincare map, the
contraction occurs in finite time regardless of the stability properties of the
orbit. Hybrid transitions may be removed from the resulting subsystem via a
topological quotient that admits a smooth structure to yield an equivalent
smooth dynamical system. We demonstrate reduction of a high-dimensional
underactuated mechanical model for terrestrial locomotion, assess structural
stability of deadbeat controllers for rhythmic locomotion and manipulation, and
derive a normal form for the stability basin of a hybrid oscillator. These
applications illustrate the utility of our theoretical results for synthesis
and analysis of feedback control laws for rhythmic hybrid behavior
Semilocal Defects
I analyze the interplay of gauge and global symmetries in the theory of
topological defects. In a two-dimensional model in which both gauge symmetries
and {\it exact} global symmetries are spontaneously broken, stable vortices may
fail to exist even though magnetic flux is topologically conserved. Following
Vachaspati and Ach\'ucarro, I formulate the condition that must be satisfied by
the pattern of symmetry breakdown for finite-energy configurations to exist in
which the conserved magnetic flux is spread out instead of confined to a
localized vortex. If this condition is met, vortices are always unstable at
sufficiently weak gauge coupling. I also describe the properties of defects in
models with an ``accidental'' symmetry that is partially broken by gauge boson
exchange. In some cases, the spontaneously broken accidental symmetry is not
restored inside the core of the defect. Then the structure of the defect can be
analyzed using an effective field theory; the details of the physics
responsible for the spontaneous symmetry breakdown need not be considered.
Examples include ``semilocal'' domain walls and vortices that are classically
unstable, but are stabilized by loop corrections, and ``semilocal'' magnetic
monopoles that have an unusual core structure. Finally, I examine the general
theory of the ``electroweak strings'' that were recently discussed by
Vachaspati. These arise only in models with gauge boson ``mixing,'' and can
always end on magnetic monopoles. Cosmological implications are briefly
discussed.Comment: 41 pages, CALT-68-178
A partition of unity approach to fluid mechanics and fluid-structure interaction
For problems involving large deformations of thin structures, simulating
fluid-structure interaction (FSI) remains challenging largely due to the need
to balance computational feasibility, efficiency, and solution accuracy.
Overlapping domain techniques have been introduced as a way to combine the
fluid-solid mesh conformity, seen in moving-mesh methods, without the need for
mesh smoothing or re-meshing, which is a core characteristic of fixed mesh
approaches. In this work, we introduce a novel overlapping domain method based
on a partition of unity approach. Unified function spaces are defined as a
weighted sum of fields given on two overlapping meshes. The method is shown to
achieve optimal convergence rates and to be stable for steady-state Stokes,
Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for
FSI in the case of a 2D mock aortic valve simulation. These initial results
point to the potential applicability of the method to a wide range of FSI
applications, enabling boundary layer refinement and large deformations without
the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur
Bounded Model Checking of State-Space Digital Systems: The Impact of Finite Word-Length Effects on the Implementation of Fixed-Point Digital Controllers Based on State-Space Modeling
The extensive use of digital controllers demands a growing effort to prevent
design errors that appear due to finite-word length (FWL) effects. However,
there is still a gap, regarding verification tools and methodologies to check
implementation aspects of control systems. Thus, the present paper describes an
approach, which employs bounded model checking (BMC) techniques, to verify
fixed-point digital controllers represented by state-space equations. The
experimental results demonstrate the sensitivity of such systems to FWL effects
and the effectiveness of the proposed approach to detect them. To the best of
my knowledge, this is the first contribution tackling formal verification
through BMC of fixed-point state-space digital controllers.Comment: International Symposium on the Foundations of Software Engineering
201
Gravitating discs around black holes
Fluid discs and tori around black holes are discussed within different
approaches and with the emphasis on the role of disc gravity. First reviewed
are the prospects of investigating the gravitational field of a black
hole--disc system by analytical solutions of stationary, axially symmetric
Einstein's equations. Then, more detailed considerations are focused to middle
and outer parts of extended disc-like configurations where relativistic effects
are small and the Newtonian description is adequate.
Within general relativity, only a static case has been analysed in detail.
Results are often very inspiring, however, simplifying assumptions must be
imposed: ad hoc profiles of the disc density are commonly assumed and the
effects of frame-dragging and completely lacking. Astrophysical discs (e.g.
accretion discs in active galactic nuclei) typically extend far beyond the
relativistic domain and are fairly diluted. However, self-gravity is still
essential for their structure and evolution, as well as for their radiation
emission and the impact on the environment around. For example, a nuclear star
cluster in a galactic centre may bear various imprints of mutual star--disc
interactions, which can be recognised in observational properties, such as the
relation between the central mass and stellar velocity dispersion.Comment: Accepted for publication in CQG; high-resolution figures will be
available from http://www.iop.org/EJ/journal/CQ
On Bouncing Brane-Worlds, S-branes and Branonium Cosmology
We present several higher-dimensional spacetimes for which observers living
on 3-branes experience an induced metric which bounces. The classes of examples
include boundary branes on generalised S-brane backgrounds and probe branes in
D-brane/anti D-brane systems. The bounces we consider normally would be
expected to require an energy density which violates the weak energy condition,
and for our co-dimension one examples this is attributable to bulk curvature
terms in the effective Friedmann equation. We examine the features of the
acceleration which provides the bounce, including in some cases the existence
of positive acceleration without event horizons, and we give a geometrical
interpretation for it. We discuss the stability of the solutions from the point
of view of both the brane and the bulk. Some of our examples appear to be
stable from the bulk point of view, suggesting the possible existence of stable
bouncing cosmologies within the brane-world framework.Comment: 35 pages, 7 figures, JHEP style. Title changed and references adde
Statistical properties of charged interfaces
We consider the equilibrium statistical properties of interfaces submitted to
competing interactions; a long-range repulsive Coulomb interaction inherent to
the charged interface and a short-range, anisotropic, attractive one due to
either elasticity or confinement. We focus on one-dimensional interfaces such
as strings. Model systems considered for applications are mainly aggregates of
solitons in polyacetylene and other charge density wave systems, domain lines
in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,
we find a shape instability which lead, via phase transitions, to tilted
phases. Depending on the regime, elastic or confinement, the order of the
zero-temperature transition changes. Thermal fluctuations lead to a pure
Coulomb roughening of the string, in addition to the usual one, and to the
presence of angular kinks. We suggest that such instabilities might explain the
tilting of stripes in cuprate oxides. The 3D problem of the charged wall is
also analyzed. The latter experiences instabilities towards various tilted
phases separated by a tricritical point in the elastic regime. In the
confinement regime, the increase of dimensionality favors either the melting of
the wall into a Wigner crystal of its constituent charges or a strongly
inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure
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