6,502 research outputs found
Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in and evolving by
a class of constrained surface diffusion flows. Our result, similar to earlier
results for the Willmore flow, gives both a positive lower bound on the time
for which a smooth solution exists, and a small upper bound on a power of the
total curvature during this time. By phrasing the theorem in terms of the
concentration of curvature in the initial surface, our result holds for very
general initial data and has applications to further development in asymptotic
analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1201.657
Randomly incomplete spectra and intermediate statistics
By randomly removing a fraction of levels from a given spectrum a model is
constructed that describes a crossover from this spectrum to a Poisson
spectrum. The formalism is applied to the transitions towards Poisson from
random matrix theory (RMT) spectra and picket fence spectra. It is shown that
the Fredholm determinant formalism of RMT extends naturally to describe
incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review
Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional \Phi^{4} field models
We show that the exact beta-function \beta(g) in the continuous 2D g\Phi^{4}
model possesses the Kramers-Wannier duality symmetry. The duality symmetry
transformation \tilde{g}=d(g) such that \beta(d(g))=d'(g)\beta(g) is
constructed and the approximate values of g^{*} computed from the duality
equation d(g^{*})=g^{*} are shown to agree with the available numerical
results. The calculation of the beta-function \beta(g) for the 2D scalar
g\Phi^{4} field theory based on the strong coupling expansion is developed and
the expansion of \beta(g) in powers of g^{-1} is obtained up to order g^{-8}.
The numerical values calculated for the renormalized coupling constant
g_{+}^{*} are in reasonable good agreement with the best modern estimates
recently obtained from the high-temperature series expansion and with those
known from the perturbative four-loop renormalization-group calculations. The
application of Cardy's theorem for calculating the renormalized isothermal
coupling constant g_{c} of the 2D Ising model and the related universal
critical amplitudes is also discussed.Comment: 16 pages, REVTeX, to be published in J.Phys.A:Math.Ge
An extreme ultraviolet spectrometer experiment for the Shuttle Get Away Special Program
An extreme ultraviolet (EUV) spectrometer experiment operated successfully during the STS-7 mission in an experiment to measure the global and diurnal variation of the EUV airglow. The spectrometer is an F 3.5 Wadsworth mount with mechanical collimator, a 75 x 75 mm grating, and a bare microchannel plate detector providing a spectral resolution of 7 X FWHM. Read-out of the signal is through discrete channels or resistive anode techniques. The experiment includes a microcomputer, 20 Mbit tape recorder, and a 28V, 40 Ahr silver-zinc battery. It is the first GAS payload to use an opening door. The spectrometer's 0.1 x 4.2 deg field of view is pointed vertically out of the shuttle bay. During the STS-7 flight data were acquired continuously for a period of 5 hours and 37 minutes, providing spectra of the 570 A to 850 A wavelength region of the airglow. Five diurnal cycles of the 584 A emission of neutral helium and the 834 A emission of ionized atomic oxygen were recorded. The experiment also recorded ion events and pressure pulses associated with thruster firings. The experiment is to fly again on Mission 41-F
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
Impurity spin relaxation in S=1/2 XX chains
Dynamic autocorrelations (\alpha=x,z) of an
isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin,
defined by a local change in the nearest-neighbor coupling, is either in the
bulk or at the boundary of the open-ended chain. The exact numerical
calculation of the correlations employs the Jordan-Wigner mapping from spin
operators to Fermi operators; effects of finite system size can be eliminated.
Two distinct temperature regimes are observed in the long-time asymptotic
behavior. At T=0 only power laws are present. At high T the x correlation
decays exponentially (except at short times) while the z correlation still
shows an asymptotic power law (different from the one at T=0) after an
intermediate exponential phase. The boundary impurity correlations follow power
laws at all T. The power laws for the z correlation and the boundary
correlations can be deduced from the impurity-induced changes in the properties
of the Jordan-Wigner fermion states.Comment: Final version to be published in Phys. Rev. B. Three references
added, extended discussion of relation to previous wor
Steady States of a Nonequilibrium Lattice Gas
We present a Monte Carlo study of a lattice gas driven out of equilibrium by
a local hopping bias. Sites can be empty or occupied by one of two types of
particles, which are distinguished by their response to the hopping bias. All
particles interact via excluded volume and a nearest-neighbor attractive force.
The main result is a phase diagram with three phases: a homogeneous phase, and
two distinct ordered phases. Continuous boundaries separate the homogeneous
phase from the ordered phases, and a first-order line separates the two ordered
phases. The three lines merge in a nonequilibrium bicritical point.Comment: 14 pages, 24 figure
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