166 research outputs found
How to play a disc brake
We consider a gyroscopic system under the action of small dissipative and
non-conservative positional forces, which has its origin in the models of
rotating bodies of revolution being in frictional contact. The spectrum of the
unperturbed gyroscopic system forms a "spectral mesh" in the plane "frequency
-gyroscopic parameter" with double semi-simple purely imaginary eigenvalues at
zero value of the gyroscopic parameter. It is shown that dissipative forces
lead to the splitting of the semi-simple eigenvalue with the creation of the
so-called "bubble of instability" - a ring in the three-dimensional space of
the gyroscopic parameter and real and imaginary parts of eigenvalues, which
corresponds to complex eigenvalues. In case of full dissipation with a
positive-definite damping matrix the eigenvalues of the ring have negative real
parts making the bubble a latent source of instability because it can "emerge"
to the region of eigenvalues with positive real parts due to action of both
indefinite damping and non-conservative positional forces. In the paper, the
instability mechanism is analytically described with the use of the
perturbation theory of multiple eigenvalues. As an example stability of a
rotating circular string constrained by a stationary load system is studied in
detail. The theory developed seems to give a first clear explanation of the
mechanism of self-excited vibrations in the rotating structures in frictional
contact, that is responsible for such well-known phenomena of acoustics of
friction as the squealing disc brake and the singing wine glass.Comment: 25 pages, 9 figures, Presented at BIRS 07w5068 Workshop "Geometric
Mechanics: Continuous and discrete, finite and infinite dimensional", August
12-17, 2007, Banff, Canad
Manyfold Universe
We propose that our world is a brane folded many times inside the
sub-millimeter extra dimensions. The folding produces many connected parallel
branes or folds with identical microphysics - a Manyfold. Nearby matter on
other folds can be detected gravitationally as dark matter since the light it
emits takes a long time to reach us traveling around the fold. Hence dark
matter is microphysically identical to ordinary matter; it can dissipate and
clump possibly forming dark replicas of ordinary stars which are good MACHO
candidates. Its dissipation may lead to far more frequent occurrence of
gravitational collapse and consequently to a significant enhancement in
gravitational wave signals detectable by LIGO and LISA. Sterile neutrinos find
a natural home on the other folds. Since the folded brane is not a BPS state,
it gives a new geometric means for supersymmetry breaking in our world. It may
also offer novel approach for the resolution of the cosmological horizon
problem, although it still requires additional dynamics to solve the flatness
problem. Although there are constraints from BBN, structure formation, the
enormity of galactic halos and the absence of stars and globular clusters with
a discernible dark matter component, we show that the model is consistent with
current observational limits. It presents us with a new dark matter particle
and a new framework for the evolution of structure in our universe.Comment: 28 pages, latex, 2 .eps figure
How to Play a Disc Brake: A Dissipation-Induced Squeal
The eigenvalues of an elastic body of revolution, rotating about its axis of symmetry, form a ‘spectral mesh’. The nodes of the mesh in the plane ‘frequency’ versus ‘gyroscopic parameter’ correspond to the double eigenfrequencies. With the use of the perturbation theory of multiple eigenvalues, deformation of the spectral mesh caused by dissipative and nonconservative perturbations, originating from the frictional contact, is analytically described. The key role of indefinite damping and non-conservative positional forces in the development of the subcritical flutter instability is clarified. A clear mathematical description is given for the mechanism of excitation of particular modes of rotating structures in frictional contact, such as squealing disc brakes and singing wine glasses
Quantum Geometry and Gravity: Recent Advances
Over the last three years, a number of fundamental physical issues were
addressed in loop quantum gravity. These include: A statistical mechanical
derivation of the horizon entropy, encompassing astrophysically interesting
black holes as well as cosmological horizons; a natural resolution of the
big-bang singularity; the development of spin-foam models which provide
background independent path integral formulations of quantum gravity and
`finiteness proofs' of some of these models; and, the introduction of
semi-classical techniques to make contact between the background independent,
non-perturbative theory and the perturbative, low energy physics in Minkowski
space. These developments spring from a detailed quantum theory of geometry
that was systematically developed in the mid-nineties and have added a great
deal of optimism and intellectual excitement to the field.
The goal of this article is to communicate these advances in general physical
terms, accessible to researchers in all areas of gravitational physics
represented in this conference.Comment: 24 pages, 2 figures; report of the plenary talk at the 16th
International Conference on General Relativity and Gravitation, held at
Durban, S. Africa in July 200
Transporting Functions across Ornaments
Programming with dependent types is a blessing and a curse. It is a blessing
to be able to bake invariants into the definition of data-types: we can finally
write correct-by-construction software. However, this extreme accuracy is also
a curse: a data-type is the combination of a structuring medium together with a
special purpose logic. These domain-specific logics hamper any effort of code
reuse among similarly structured data.
In this paper, we exorcise our data-types by adapting the notion of ornament
to our universe of inductive families. We then show how code reuse can be
achieved by ornamenting functions. Using these functional ornament, we capture
the relationship between functions such as the addition of natural numbers and
the concatenation of lists. With this knowledge, we demonstrate how the
implementation of the former informs the implementation of the latter: the user
can ask the definition of addition to be lifted to lists and she will only be
asked the details necessary to carry on adding lists rather than numbers.
Our presentation is formalised in a type theory with a universe of data-types
and all our constructions have been implemented as generic programs, requiring
no extension to the type theory
Gravity and the Quantum
The goal of this article is to present a broad perspective on quantum gravity
for \emph{non-experts}. After a historical introduction, key physical problems
of quantum gravity are illustrated. While there are a number of interesting and
insightful approaches to address these issues, over the past two decades
sustained progress has primarily occurred in two programs: string theory and
loop quantum gravity. The first program is described in Horowitz's contribution
while my article will focus on the second. The emphasis is on underlying ideas,
conceptual issues and overall status of the program rather than mathematical
details and associated technical subtleties.Comment: A general review of quantum gravity addresed non-experts. To appear
in the special issue `Space-time Hundred Years Later' of NJP; J.Pullin and R.
Price (editors). Typos and an attribution corrected; a clarification added in
section 2.
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