119 research outputs found
Traffic Noise and the Hyperbolic Plane
We consider the problem of sound propagation in a wind. We note that the
rays, as in the absence of a wind, are given by Fermat's principle and show how
to map them to the trajectories of a charged particle moving in a magnetic
field on a curved space. For the specific case of sound propagating in a
stratified atmosphere with a small wind speed we show that the corresponding
particle moves in a constant magnetic field on the hyperbolic plane. In this
way we give a simple `straightedge and compass' method to estimate the
intensity of sound upwind and downwind. We construct Mach envelopes for moving
sources. Finally, we relate the problem to that of finding null geodesics in a
squashed anti-de Sitter spacetime and discuss the
symmetry of the problem from this point of view.Comment: Typos correcte
Symmetry Constraints and the Electronic Structures of a Quantum Dot with Thirteen Electrons
The symmetry constraints imposing on the quantum states of a dot with 13
electrons has been investigated. Based on this study, the favorable structures
(FSs) of each state has been identified. Numerical calculations have been
performed to inspect the role played by the FSs. It was found that, if a
first-state has a remarkably competitive FS, this FS would be pursued and the
state would be crystal-like and have a specific core-ring structure associated
with the FS. The magic numbers are found to be closely related to the FSs.Comment: 13 pages, 5 figure
Twistor geometry of a pair of second order ODEs
We discuss the twistor correspondence between path geometries in three
dimensions with vanishing Wilczynski invariants and anti-self-dual conformal
structures of signature . We show how to reconstruct a system of ODEs
with vanishing invariants for a given conformal structure, highlighting the
Ricci-flat case in particular. Using this framework, we give a new derivation
of the Wilczynski invariants for a system of ODEs whose solution space is
endowed with a conformal structure. We explain how to reconstruct the conformal
structure directly from the integral curves, and present new examples of
systems of ODEs with point symmetry algebra of dimension four and greater which
give rise to anti--self--dual structures with conformal symmetry algebra of the
same dimension. Some of these examples are analogues of plane wave
space--times in General Relativity. Finally we discuss a variational principle
for twistor curves arising from the Finsler structures with scalar flag
curvature.Comment: Final version to appear in the Communications in Mathematical
Physics. The procedure of recovering a system of torsion-fee ODEs from the
heavenly equation has been clarified. The proof of Prop 7.1 has been
expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda
Confronting Finsler space-time with experiment
Within all approaches to quantum gravity small violations of the Einstein
Equivalence Principle are expected. This includes violations of Lorentz
invariance. While usually violations of Lorentz invariance are introduced
through the coupling to additional tensor fields, here a Finslerian approach is
employed where violations of Lorentz invariance are incorporated as an integral
part of the space-time metrics. Within such a Finslerian framework a modified
dispersion relation is derived which is confronted with current high precision
experiments. As a result, Finsler type deviations from the Minkowskian metric
are excluded with an accuracy of 10^{-16}.Comment: To be published in General Relativity and Gravitatio
Gravitational deflection of light in Rindler-type potential as a possible resolution to the observations of Bullet Cluster 1E0657-558
The surface density -map and the convergence -map of Bullet
Cluster 1E0657-558 show that the center of baryonic matters separates from the
center of gravitational force, and the distribution of gravitational force do
not possess spherical symmetry. This hints that a modified gravity with
difference to Newtonian inverse-square law at large scale, and less symmetry is
worth investigating. In this paper, we study the dynamics in Randers-Finsler
spacetime. The Newtonian limit and gravitational deflection of light in a
Rindler-type potential is focused in particular. It is shown that the
convergence in Finsler spacetime could account for the observations of Bullet
Cluster.Comment: 11 page
Interior Regularity Estimates in High Conductivity Homogenization and Application
In this paper, uniform pointwise regularity estimates for the solutions of
conductivity equations are obtained in a unit conductivity medium reinforced by
a epsilon-periodic lattice of highly conducting thin rods. The estimates are
derived only at a distance epsilon^{1+tau} (for some tau>0) away from the
fibres. This distance constraint is rather sharp since the gradients of the
solutions are shown to be unbounded locally in L^p as soon as p>2. One key
ingredient is the derivation in dimension two of regularity estimates to the
solutions of the equations deduced from a Fourier series expansion with respect
to the fibres direction, and weighted by the high-contrast conductivity. The
dependence on powers of epsilon of these two-dimensional estimates is shown to
be sharp. The initial motivation for this work comes from imaging, and enhanced
resolution phenomena observed experimentally in the presence of
micro-structures. We use these regularity estimates to characterize the
signature of low volume fraction heterogeneities in the fibred reinforced
medium assuming that the heterogeneities stay at a distance epsilon^{1+tau}
away from the fibres
Decoherence and CPT Violation in a Stringy Model of Space-Time Foam
I discuss a model inspired from the string/brane framework, in which our
Universe is represented as a three brane, propagating in a bulk space time
punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the
bulk, the D-particles cross it, and from an effective observer on D3 the
situation looks like a ``space-time foam'' with the defects ``flashing'' on and
off (``D-particle foam''). The open strings, with their ends attached on the
brane, which represent matter in this scenario, can interact with the
D-particles on the D3-brane universe in a topologically non-trivial manner,
involving splitting and capture of the strings by the D0-brane defects. Such
processes are described by logarithmic conformal field theories on the
world-sheet. Physically, they result in effective decoherence of the string
matter on the D3 brane, and as a result, of CPT Violation, but of a type that
implies an ill-defined nature of the effective CPT operator. Due to electric
charge conservation, only electrically neutral (string) matter can exhibit such
interactions with the D-particle foam. This may have unique, experimentally
detectable, consequences for electrically-neutral entangled quantum matter
states on the brane world, in particular the modification of the pertinent EPR
Correlation of neutral mesons in a meson factory.Comment: 41 pages Latex, five eps figures incorporated. Uses special macro
Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories
Using Finsler brane solutions [see details and methods in: S. Vacaru, Class.
Quant. Grav. 28 (2011) 215001], we show that neutrinos may surpass the speed of
light in vacuum which can be explained by trapping effects from gravity
theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to
spacetimes in general and special relativity. In nonholonomic variables, the
bulk gravity is described by Finsler modifications depending on velocity/
momentum coordinates. Possible super-luminal phenomena are determined by the
width of locally anisotropic brane (spacetime) and induced by generating
functions and integration functions and constants in coefficients of metrics
and nonlinear connections. We conclude that Finsler brane gravity trapping
mechanism may explain neutrino super-luminal effects and almost preserve the
paradigm of Einstein relativity as the standard one for particle physics and
gravity.Comment: latex2e, 15 pages, v3, accepted to: Foundations of Physics 43 (2013
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