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

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

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

Controlling domain patterns far from equilibrium

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial profile stabilizes a propagating front at a fixed position or induces oscillations with frequency that scales like the square root of the field gradient. Nonmonotonic profiles produce a variety of patterns with controllable wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at http://t7.lanl.gov/People/Aric

A spinal organ of proprioception for integrated motor action feedback

Proprioception is essential for behavior and provides a sense of our body movements in physical space. Proprioceptor organs are thought to be only in the periphery. Whether the central nervous system can intrinsically sense its own movement remains unclear. Here we identify a segmental organ of proprioception in the adult zebrafish spinal cord, which is embedded by intraspinal mechanosensory neurons expressing Piezo2 channels. These cells are late-born, inhibitory, commissural neurons with unique molecular and physiological profiles reflecting a dual sensory and motor function. The central proprioceptive organ locally detects lateral body movements during locomotion and provides direct inhibitory feedback onto rhythm-generating interneurons responsible for the central motor program. This dynamically aligns central pattern generation with movement outcome for efficient locomotion. Our results demonstrate that a central proprioceptive organ monitors self-movement using hybrid neurons that merge sensory and motor entities into a unified network

Ferromagnetic Domain Distribution in Thin Films During Magnetization Reversal

We have shown that polarized neutron reflectometry can determine in a model-free way not only the mean magnetization of a ferromagnetic thin film at any point of a hysteresis cycle, but also the mean square dispersion of the magnetization vectors of its lateral domains. This technique is applied to elucidate the mechanism of the magnetization reversal of an exchange-biased Co/CoO bilayer. The reversal process above the blocking temperature is governed by uniaxial domain switching, while below the blocking temperature the reversal of magnetization for the trained sample takes place with substantial domain rotation

Patients’ quest for recognition and continuity in health care: time for a new research agenda?

User involvement is important in democratization of health care and is assumed to contribute to better and more relevant research. Despite increased requirements for user involvement in research, more studies are still needed. This study aimed at exploring what research agenda people with varied health problems consider as important, based on their own experience. The study had a phenomenological approach with a qualitative design. The sample consisted of 23 informants; nine had been critically ill and 14 were suffering from chronic muscle pain. Data were collected in five focus group interviews and one individual interview. A phenomenological approach was used in analyzing the data. Written consent was obtained from all the participants, and ethical considerations were taken throughout the entire research process. Despite various experiences among the participants, a quest to be taken seriously over time by healthcare professionals emerged as a strong meaning structure in both groups. Based on these experiences, continuity across lifetime changes turned out to be an important research topic for future research. User involvement should be appreciated in all parts of the research process. A crucial prerequisite is that the users get the opportunity to bring their own experiences into the process.acceptedVersio