946 research outputs found
The Entropy of a Binary Hidden Markov Process
The entropy of a binary symmetric Hidden Markov Process is calculated as an
expansion in the noise parameter epsilon. We map the problem onto a
one-dimensional Ising model in a large field of random signs and calculate the
expansion coefficients up to second order in epsilon. Using a conjecture we
extend the calculation to 11th order and discuss the convergence of the
resulting series
Reflection and Ducting of Gravity Waves Inside the Sun
Internal gravity waves excited by overshoot at the bottom of the convection
zone can be influenced by rotation and by the strong toroidal magnetic field
that is likely to be present in the solar tachocline. Using a simple Cartesian
model, we show how waves with a vertical component of propagation can be
reflected when traveling through a layer containing a horizontal magnetic field
with a strength that varies with depth. This interaction can prevent a portion
of the downward-traveling wave energy flux from reaching the deep solar
interior. If a highly reflecting magnetized layer is located some distance
below the convection zone base, a duct or wave guide can be set up, wherein
vertical propagation is restricted by successive reflections at the upper and
lower boundaries. The presence of both upward- and downward-traveling
disturbances inside the duct leads to the existence of a set of horizontally
propagating modes that have significantly enhanced amplitudes. We point out
that the helical structure of these waves makes them capable of generating an
alpha-effect, and briefly consider the possibility that propagation in a shear
of sufficient strength could lead to instability, the result of wave growth due
to over-reflection.Comment: 23 pages, 5 figures. Accepted for publication in Solar Physic
Dual Vortex Theory of Strongly Interacting Electrons: Non-Fermi Liquid to the (Hard) Core
As discovered in the quantum Hall effect, a very effective way for
strongly-repulsive electrons to minimize their potential energy is to aquire
non-zero relative angular momentum. We pursue this mechanism for interacting
two-dimensional electrons in zero magnetic field, by employing a representation
of the electrons as composite bosons interacting with a Chern-Simons gauge
field. This enables us to construct a dual description in which the fundamental
constituents are vortices in the auxiliary boson fields. The resulting
formalism embraces a cornucopia of possible phases. Remarkably,
superconductivity is a generic feature, while the Fermi liquid is not --
prompting us to conjecture that such a state may not be possible when the
interactions are sufficiently strong. Many aspects of our earlier discussions
of the nodal liquid and spin-charge separation find surprising incarnations in
this new framework.Comment: Modified dicussion of the hard-core model, correcting several
mistake
Field dependence of the vortex structure in chiral p-wave superconductors
To investigate the different vortex structure between two chiral pairing p_x
+(-) i p_y, we calculate the pair potential, the internal field, the local
density of states, and free energy in the vortex lattice state based on the
quasiclassical Eilenberger theory, and analyze the magnetic field dependence.
The induced opposite chiral component of the pair potential plays an important
role in the vortex structure. It also produces H^{1/2}-behavior of the
zero-energy density of states at higher field. These results are helpful when
we understand the vortex states in Sr2RuO4.Comment: 11 pages, 10 figures, to be published in Phys. Rev.
Detailed study of the ac susceptibility of Sr2RuO4 in oriented magnetic fields
We have investigated the ac susceptibility of the spin triplet superconductor
SrRuO as a function of magnetic field in various directions at
temperatures down to 60 mK. We have focused on the in-plane field configuration
(polar angle ), which is a prerequisite for inducing
multiple superconducting phases in SrRuO. We have found that the
previous attribution of a pronounced feature in the ac susceptibility to the
second superconducting transition itself is not in accord with recent
measurements of the thermal conductivity or of the specific heat. We propose
that the pronounced feature is a consequence of additional involvement of
vortex pinning originating from the second superconducting transition.Comment: Accepted for publication in Phys. Rev.
Melting and Dimensionality of the Vortex Lattice in Underdoped YBa2Cu3O6.60
Muon spin rotation measurements of the magnetic field distribution in the
vortex state of the oxygen deficient high-Tc superconductor YBa{2}Cu{3}O{6.60}
reveal a vortex-lattice melting transition at much lower temperature than that
in the fully oxygenated material. The transition is best described by a model
in which adjacent layers of ``pancake'' vortices decouple in the liquid phase.
Evidence is also found for a pinning-induced crossover from a solid 3D to
quasi-2D vortex lattice, similar to that observed in the highly anisotropic
superconductor Bi{2+x}Sr{2-x}CaCu{2}O{8+y}.Comment: 8 pages, 4 figures, 5 postscript file
Multi-layered Ruthenium-modified Bond Coats for Thermal Barrier Coatings
Diffusional approaches for fabrication of multi-layered Ru-modified bond coats for thermal
barrier coatings have been developed via low activity chemical vapor deposition and high activity
pack aluminization. Both processes yield bond coats comprising two distinct B2 layers, based on
NiAl and RuAl, however, the position of these layers relative to the bond coat surface is reversed
when switching processes. The structural evolution of each coating at various stages of the
fabrication process has been and subsequent cyclic oxidation is presented, and the relevant
interdiffusion and phase equilibria issues in are discussed. Evaluation of the oxidation behavior of
these Ru-modified bond coat structures reveals that each B2 interlayer arrangement leads to the
formation of α-Al 2 O 3 TGO at 1100°C, but the durability of the TGO is somewhat different and in
need of further improvement in both cases
Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects
We study muon-spin rotation (muSR) spectra in the mixed phase of highly
anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta
(BSCCO), by modeling the fluid and solid phases of pancake vortices using
liquid-state and density functional methods. The role of thermal fluctuations
in causing motional narrowing of muSR lineshapes is quantified in terms of a
first-principles theory of the flux-lattice melting transition. The effects of
random point pinning are investigated using a replica treatment of liquid state
correlations and a replicated density functional theory. Our results indicate
that motional narrowing in the pure system, although substantial, cannot
account for the remarkably small linewidths obtained experimentally at
relatively high fields and low temperatures. We find that satisfactory
agreement with the muSR data for BSCCO in this regime can be obtained through
the ansatz that this ``phase'' is characterized by frozen short-range
positional correlations reflecting the structure of the liquid just above the
melting transition. This proposal is consistent with recent suggestions of a
``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of
pinning disorder. Our results for the high-temperature liquid phase indicate
that measurable linewidths may be obtained in this phase as a consequence of
density inhomogeneities induced by the pinning disorder. The results presented
here comprise a unified, first-principles theoretical treatment of muSR spectra
in highly anisotropic layered superconductors in terms of a controlled set of
approximations.Comment: 50 pages Latex file, including 10 postscript figure
On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature
We consider the Glauber dynamics for the 2D Ising model in a box of side L,
at inverse temperature and random boundary conditions whose
distribution P either stochastically dominates the extremal plus phase (hence
the quotation marks in the title) or is stochastically dominated by the
extremal minus phase. A particular case is when P is concentrated on the
homogeneous configuration identically equal to + (equal to -). For
large enough we show that for any there exists
such that the corresponding mixing time satisfies
. In the non-random case
(or ), this implies that . The same bound holds when the boundary conditions are all
+ on three sides and all - on the remaining one. The result, although still
very far from the expected Lifshitz behaviour , considerably
improves upon the previous known estimates of the form . The techniques are based on induction over length
scales, combined with a judicious use of the so-called "censoring inequality"
of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to
its equilibrium measure.Comment: 39 pages, 8 figures; v2: typos corrected, two references added. To
appear on Comm. Math. Phy
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