27,429 research outputs found
Quantum integrability of quadratic Killing tensors
Quantum integrability of classical integrable systems given by quadratic
Killing tensors on curved configuration spaces is investigated. It is proven
that, using a "minimal" quantization scheme, quantum integrability is insured
for a large class of classic examples.Comment: LaTeX 2e, no figure, 35 p., references added, minor modifications. To
appear in the J. Math. Phy
Stability of Solid State Reaction Fronts
We analyze the stability of a planar solid-solid interface at which a
chemical reaction occurs. Examples include oxidation, nitridation, or silicide
formation. Using a continuum model, including a general formula for the
stress-dependence of the reaction rate, we show that stress effects can render
a planar interface dynamically unstable with respect to perturbations of
intermediate wavelength
Geometry of Deformations of Relativistic Membranes
A kinematical description of infinitesimal deformations of the worldsheet
spanned in spacetime by a relativistic membrane is presented. This provides a
framework for obtaining both the classical equations of motion and the
equations describing infinitesimal deformations about solutions of these
equations when the action describing the dynamics of this membrane is
constructed using {\it any} local geometrical worldsheet scalars. As examples,
we consider a Nambu membrane, and an action quadratic in the extrinsic
curvature of the worldsheet.Comment: 20 pages, Plain Tex, sign errors corrected, many new references
added. To appear in Physical Review
Dual variables and a connection picture for the Euclidean Barrett-Crane model
The partition function of the SO(4)- or Spin(4)-symmetric Euclidean
Barrett-Crane model can be understood as a sum over all quantized geometries of
a given triangulation of a four-manifold. In the original formulation, the
variables of the model are balanced representations of SO(4) which describe the
quantized areas of the triangles. We present an exact duality transformation
for the full quantum theory and reformulate the model in terms of new variables
which can be understood as variables conjugate to the quantized areas. The new
variables are pairs of S^3-values associated to the tetrahedra. These
S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally
embedded in R^4), and the fact that there is a pair of variables for each
tetrahedron can be viewed as a consequence of an SO(4)-valued parallel
transport along the edges dual to the tetrahedra. We reconstruct the parallel
transport of which only the action of SO(4) on S^3 is physically relevant and
rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the
2-complex dual to the triangulation subject to suitable constraints whose form
we derive at the quantum level. Our reformulation of the Barrett-Crane model in
terms of continuous variables is suitable for the application of various
analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added,
TeX error correcte
The interaction between transpolar arcs and cusp spots
Transpolar arcs and cusp spots are both auroral phenomena which occur when
the interplanetary magnetic field is northward. Transpolar arcs are associated
with magnetic reconnection in the magnetotail, which closes magnetic flux and
results in a "wedge" of closed flux which remains trapped, embedded in the
magnetotail lobe. The cusp spot is an indicator of lobe reconnection at the
high-latitude magnetopause; in its simplest case, lobe reconnection
redistributes open flux without resulting in any net change in the open flux
content of the magnetosphere. We present observations of the two phenomena
interacting--i.e., a transpolar arc intersecting a cusp spot during part of its
lifetime. The significance of this observation is that lobe reconnection can
have the effect of opening closed magnetotail flux. We argue that such events
should not be rare
Asymptotic behavior of the Kleinberg model
We study Kleinberg navigation (the search of a target in a d-dimensional
lattice, where each site is connected to one other random site at distance r,
with probability proportional to r^{-a}) by means of an exact master equation
for the process. We show that the asymptotic scaling behavior for the delivery
time T to a target at distance L scales as (ln L)^2 when a=d, and otherwise as
L^x, with x=(d-a)/(d+1-a) for ad+1. These
values of x exceed the rigorous lower-bounds established by Kleinberg. We also
address the situation where there is a finite probability for the message to
get lost along its way and find short delivery times (conditioned upon arrival)
for a wide range of a's
Vorton Formation
In this paper we present the first analytic model for vorton formation. We
start by deriving the microscopic string equations of motion in Witten's
superconducting model, and show that in the relevant chiral limit these
coincide with the ones obtained from the supersonic elastic models of Carter
and Peter. We then numerically study a number of solutions of these equations
of motion and thereby suggest criteria for deciding whether a given
superconducting loop configuration can form a vorton. Finally, using a recently
developed model for the evolution of currents in superconducting strings we
conjecture, by comparison with these criteria, that string networks formed at
the GUT phase transition should produce no vortons. On the other hand, a
network formed at the electroweak scale can produce vortons accounting for up
to 6% of the critical density. Some consequences of our results are discussed.Comment: 41 pages; color figures 3-6 not included, but available from authors.
To appear in Phys. Rev.
Application of remote sensing to state and regional problems
There are no author-identified significant results in this report
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