421 research outputs found
Complete Embedded Self-Translating Surfaces under Mean Curvature Flow
We describe a construction of complete embedded self-translating surfaces
under mean curvature flow by desingularizing the intersection of a finite
family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte
Observation of Quantum Asymmetry in an Aharonov-Bohm Ring
We have investigated the Aharonov-Bohm effect in a one-dimensional
GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of
these systems are for the first time systematically studied as a function of
density. We observe phase-shifts of in the magnetoconductance
oscillations, and halving of the fundamental period, as the density is
varied. Theoretically we find agreement with the experiment, by introducing an
asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.
The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory
We compute the partition function of the conformal field theory on the
two-dimensional euclidean black hole background using path-integral techniques.
We show that the resulting spectrum is consistent with the algebraic
expectations for the SL(2,R)/U(1) coset conformal field theory construction. In
particular, we find confirmation for the bound on the spin of the discrete
representations and we determine the density of the continuous representations.
We point out the relevance of the partition function to all string theory
backgrounds that include an SL(2,R)/U(1) coset factor.Comment: 17 pages, references added and typos correcte
Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory
We show how to construct, starting from a quasi-Hopf algebra, or
quasi-quantum group, invariants of knots and links. In some cases, these
invariants give rise to invariants of the three-manifolds obtained by surgery
along these links. This happens for a finite-dimensional quasi-quantum group,
whose definition involves a finite group , and a 3-cocycle \om, which was
first studied by Dijkgraaf, Pasquier and Roche. We treat this example in more
detail, and argue that in this case the invariants agree with the partition
function of the topological field theory of Dijkgraaf and Witten depending on
the same data G, \,\om.Comment: 30 page
Multiwavelength Study on Solar and Interplanetary Origins of the Strongest Geomagnetic Storm of Solar Cycle 23
We study the solar sources of an intense geomagnetic storm of solar cycle 23
that occurred on 20 November 2003, based on ground- and space-based
multiwavelength observations. The coronal mass ejections (CMEs) responsible for
the above geomagnetic storm originated from the super-active region NOAA 10501.
We investigate the H-alpha observations of the flare events made with a 15 cm
solar tower telescope at ARIES, Nainital, India. The propagation
characteristics of the CMEs have been derived from the three-dimensional images
of the solar wind (i.e., density and speed) obtained from the interplanetary
scintillation data, supplemented with other ground- and space-based
measurements. The TRACE, SXI and H-alpha observations revealed two successive
ejections (of speeds ~350 and ~100 km/s), originating from the same filament
channel, which were associated with two high speed CMEs (~1223 and ~1660 km/s,
respectively). These two ejections generated propagating fast shock waves
(i.e., fast drifting type II radio bursts) in the corona. The interaction of
these CMEs along the Sun-Earth line has led to the severity of the storm.
According to our investigation, the interplanetary medium consisted of two
merging magnetic clouds (MCs) that preserved their identity during their
propagation. These magnetic clouds made the interplanetary magnetic field (IMF)
southward for a long time, which reconnected with the geomagnetic field,
resulting the super-storm (Dst_peak=-472 nT) on the Earth.Comment: 24 pages, 16 figures, Accepted for publication in Solar Physic
Critical behavior of collapsing surfaces
We consider the mean curvature evolution of rotationally symmetric surfaces.
Using numerical methods, we detect critical behavior at the threshold of
singularity formation resembling the one of gravitational collapse. In
particular, the mean curvature simulation of a one-parameter family of initial
data reveals the existence of a critical initial surface that develops a
degenerate neckpinch. The limiting flow of the Type II singularity is
accurately modeled by the rotationally symmetric translating soliton.Comment: 23 pages, 10 figure
Sigma models as perturbed conformal field theories
We show that two-dimensional sigma models are equivalent to certain perturbed
conformal field theories. When the fields in the sigma model take values in a
space G/H for a group G and a maximal subgroup H, the corresponding conformal
field theory is the limit of the coset model , and the
perturbation is related to the current of G. This correspondence allows us for
example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at
non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published
version
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
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