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 $L^2$ \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 $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ 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 $La_{2/3}Ba_{1/3}MnO_3$ layers with paramagnetic $LaNiO_3$ 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 $LaNiO_3$, 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