1,625 research outputs found
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II
We continue the development, by reduction to a first order system for the
conormal gradient, of \textit{a priori} estimates and solvability for
boundary value problems of Dirichlet, regularity, Neumann type for divergence
form second order, complex, elliptic systems. We work here on the unit ball and
more generally its bi-Lipschitz images, assuming a Carleson condition as
introduced by Dahlberg which measures the discrepancy of the coefficients to
their boundary trace near the boundary. We sharpen our estimates by proving a
general result concerning \textit{a priori} almost everywhere non-tangential
convergence at the boundary. Also, compactness of the boundary yields more
solvability results using Fredholm theory. Comparison between classes of
solutions and uniqueness issues are discussed. As a consequence, we are able to
solve a long standing regularity problem for real equations, which may not be
true on the upper half-space, justifying \textit{a posteriori} a separate work
on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has
changed nam
Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
We establish the resolvent estimates for the Stokes operator in
Lipschitz domains in , for . The result, in particular, implies that the Stokes operator in a
three-dimensional Lipschitz domain generates a bounded analytic semigroup in
for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a
conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the
Stokes operator in Lipschitz domain
Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions
The nonnegative viscosity solutions to the infinite heat equation with
homogeneous Dirichlet boundary conditions are shown to converge as time
increases to infinity to a uniquely determined limit after a suitable time
rescaling. The proof relies on the half-relaxed limits technique as well as
interior positivity estimates and boundary estimates. The expansion of the
support is also studied
Quenched crystal field disorder and magnetic liquid ground states in Tb2Sn2-xTixO7
Solid-solutions of the "soft" quantum spin ice pyrochlore magnets Tb2B2O7
with B=Ti and Sn display a novel magnetic ground state in the presence of
strong B-site disorder, characterized by a low susceptibility and strong spin
fluctuations to temperatures below 0.1 K. These materials have been studied
using ac-susceptibility and muSR techniques to very low temperatures, and
time-of-flight inelastic neutron scattering techniques to 1.5 K. Remarkably,
neutron spectroscopy of the Tb3+ crystal field levels appropriate to at high
B-site mixing (0.5 < x < 1.5 in Tb2Sn2-xTixO7) reveal that the doublet ground
and first excited states present as continua in energy, while transitions to
singlet excited states at higher energies simply interpolate between those of
the end members of the solid solution. The resulting ground state suggests an
extreme version of a random-anisotropy magnet, with many local moments and
anisotropies, depending on the precise local configuration of the six B sites
neighboring each magnetic Tb3+ ion.Comment: 6 pages, 6 figure
Magnetothermodynamics of the Ising Antiferromagnet Dy2Ge2O7
We report systematic low temperature measurements of the DC magnetization, AC
susceptibility, and heat capacity of dysprosium pyrogermanate (Dy2Ge2O7) single
crystal and powder samples. Our results confirm that Dy2Ge2O7 is an anisotropic
antiferromagnet. The isothermal field dependent magnetization and the
integrated magnetic entropy both indicate that the Dy3+ ions behave as
Ising-like spins, analogous to those in the pyrochlore spin ice materials. Both
single-spin and collective spin relaxation phenomena appear to lead to spin
freezing in this material, again in analogy to observations in the spin ice
materials, suggesting that such phenomena may be generic to a broader class of
magnetic materials.Comment: Phys. Rev. B, in press (2008
Spin ice behavior in Dy2Sn2-xSbxO7+x/2 and Dy2NbScO7
We report the magnetic and thermal properties of Dy2Sn2-xSbxO7+x/2, x = 0,
0.25, and 0.5, and Dy2NbScO7. We find evidence for Ising-like single ion ground
states in the Dy2Sn2-xSbxO7+x/2 materials. These materials possess nearly the
same zero point entropy as the canonical spin ices Ho2Ti2O7 and Dy2Ti2O7,
strongly suggesting that they have spin ice states at low temperatures. We also
observe a somewhat reduced zero point entropy in Dy2NbScO7, which is possibly
associated with the higher level of cation disorder. The ice-like states in
these materials with cation disorder on the B-sites of the pyrochlore lattice
provide new evidence for the robust nature of spin ice behavior in the presence
of disorder
Is Thermal Instability Significant in Turbulent Galactic Gas?
We investigate numerically the role of thermal instability (TI) as a
generator of density structures in the interstellar medium (ISM), both by
itself and in the context of a globally turbulent medium. Simulations of the
instability alone show that the condenstion process which forms a dense phase
(``clouds'') is highly dynamical, and that the boundaries of the clouds are
accretion shocks, rather than static density discontinuities. The density
histograms (PDFs) of these runs exhibit either bimodal shapes or a single peak
at low densities plus a slope change at high densities. Final static situations
may be established, but the equilibrium is very fragile: small density
fluctuations in the warm phase require large variations in the density of the
cold phase, probably inducing shocks into the clouds. This result suggests that
such configurations are highly unlikely. Simulations including turbulent
forcing show that large- scale forcing is incapable of erasing the signature of
the TI in the density PDFs, but small-scale, stellar-like forcing causes
erasure of the signature of the instability. However, these simulations do not
reach stationary regimes, TI driving an ever-increasing star formation rate.
Simulations including magnetic fields, self-gravity and the Coriolis force show
no significant difference between the PDFs of stable and unstable cases, and
reach stationary regimes, suggesting that the combination of the stellar
forcing and the extra effective pressure provided by the magnetic field and the
Coriolis force overwhelm TI as a density-structure generator in the ISM. We
emphasize that a multi-modal temperature PDF is not necessarily an indication
of a multi-phase medium, which must contain clearly distinct thermal
equilibrium phases.Comment: 18 pages, 11 figures. Submitted to Ap
Indexed Left Atrial Adipose Tissue Area Is Associated With Severity of Atrial Fibrillation and Atrial Fibrillation Recurrence Among Patients Undergoing Catheter Ablation
Background: Epicardial adipose tissue (EAT) has been associated with adverse left atrial (LA) remodeling and atrial fibrillation (AF) outcomes, possibly because of paracrine signaling.
Objectives: We examined factors associated with a novel measure of EAT i.e., indexed LAEAT (iLAEAT) and its prognostic significance after catheter ablation (CA) of atrial fibrillation (AF).
Methods: We performed a retrospective analysis of 274 participants with AF referred for CA. LAEAT area was measured from a single pre-ablation CT image and indexed to body surface area (BSA) to calculate iLAEAT. Clinical, echocardiographic data and 1-year AF recurrence rates after CA were compared across tertiles of iLAEAT. We performed logistic regression analysis adjusting for factors associated with AF to examine relations between iLAEAT and AF recurrence.
Results: Mean age of participants was 61 +/- 10 years, 136 (49%) were women, mean BMI was 32 +/- 9 kg/m(2) and 85 (31%) had persistent AF. Mean iLAEAT was 0.82 +/- 0.53 cm(2)/m(2). Over 12-months, 109 (40%) had AF recurrence. Participants in the highest iLAEAT tertile were older, had higher CHA2DS2VASC scores, more likely to be male, have greater LA volume, and were more likely to have persistent (vs. paroxysmal) type AF than participants in the lowest iLAEAT tertile (p for all \u3c 0.05). In regression analyses, iLAEAT was associated with higher odds of AF recurrence (OR = 2.93; 95% CI 1.34-6.43).
Conclusions: iLAEAT can quantify LA adipose tissue burden using standard CT images. It is strongly associated with AF risk factors and outcomes, supporting the hypothesis that EAT plays a role in the pathophysiology of AF
Non-monotonic zero point entropy in diluted spin ice
Water ice and spin ice are important model systems in which theory can
directly account for zero point entropy associated with quenched
configurational disorder. Spin ice differs from water ice in the important
respect that its fundamental constituents, the spins of the magnetic ions, can
be removed through replacement with non-magnetic ions while keeping the lattice
structure intact. In order to investigate the interplay of frustrated
interactions and quenched disorder, we have performed systematic heat capacity
measurements on spin ice materials which have been thus diluted up to 90%.
Investigations of both Ho and Dy spin ices reveal that the zero point entropy
depends non-monotonically on dilution and approaches the value of Rln2 in the
limit of high dilution. The data are in good agreement with a generalization of
Pauling's theory for the entropy of ice.Comment: Accepted to be published in Phys. Rev. Let
Oscillatory Exchange Coupling and Positive Magnetoresistance in Epitaxial Oxide Heterostructures
Oscillations in the exchange coupling between ferromagnetic
layers with paramagnetic spacer layer
thickness has been observed in epitaxial heterostructures of the two oxides.
This behavior is explained within the RKKY model employing an {\it ab initio}
calculated band structure of , taking into account strong electron
scattering in the spacer. Antiferromagnetically coupled superlattices exhibit a
positive current-in-plane magnetoresistance.Comment: 4 pages (RevTeX), 5 figures (EPS
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