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

Micromagnetic Domain Structures in Cylindrical Nickel Dots

The magnetic domain structures of cylindrical nickel dots (diameters from 40 nm to 1700 nm) with anisotropy parallel to the cylinder axis is predicted by the ratio of the dot diameter to the stripe period of unpatterned films with the same perpendicular anisotropy. The dominant domain structure for a given ratio increases in complexity as the ratio increases. We present evidence for the full micromagnetic domain structure for the simplest cases

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

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

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

Optical resonance imaging: An optical analog to MRI with sub-diffraction-limited capabilities

We propose here optical resonance imaging (ORI), a direct optical analog to magnetic resonance imaging (MRI). The proposed pulse sequence for ORI maps space to time and recovers an image from a heterodyne-detected third-order nonlinear photon echo measurement. As opposed to traditional photon echo measurements, the third pulse in the ORI pulse sequence has significant pulse-front tilt that acts as a temporal gradient. This gradient couples space to time by stimulating the emission of a photon echo signal from different lateral spatial locations of a sample at different times, providing a widefield ultrafast microscopy. We circumvent the diffraction limit of the optics by mapping the lateral spatial coordinate of the sample with the emission time of the signal, which can be measured to high precision using interferometric heterodyne detection. This technique is thus an optical analog of MRI, where magnetic-field gradients are used to localize the spin-echo emission to a point below the diffraction limit of the radio-frequency wave used. We calculate the expected ORI signal using 15 fs pulses and 87° of pulse-front tilt, collected using f/2 optics and find a two-point resolution 275 nm using 800 nm light that satisfies the Rayleigh criterion. We also derive a general equation for resolution in optical resonance imaging that indicates that there is a possibility of superresolution imaging using this technique. The photon echo sequence also enables spectroscopic determination of the input and output energy. The technique thus correlates the input energy with the final position and energy of the exciton

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

Bacterial cheating drives the population dynamics of cooperative antibiotic resistance plasmids

Inactivation of β‐lactam antibiotics by resistant bacteria is a ‘cooperative’ behavior that may allow sensitive bacteria to survive antibiotic treatment. However, the factors that determine the fraction of resistant cells in the bacterial population remain unclear, indicating a fundamental gap in our understanding of how antibiotic resistance evolves. Here, we experimentally track the spread of a plasmid that encodes a β‐lactamase enzyme through the bacterial population. We find that independent of the initial fraction of resistant cells, the population settles to an equilibrium fraction proportional to the antibiotic concentration divided by the cell density. A simple model explains this behavior, successfully predicting a data collapse over two orders of magnitude in antibiotic concentration. This model also successfully predicts that adding a commonly used β‐lactamase inhibitor will lead to the spread of resistance, highlighting the need to incorporate social dynamics into the study of antibiotic resistance.National Science Foundation (U.S.). Graduate Research Fellowship (Grant 0645960)Massachusetts Institute of Technology. Undergraduate Research Opportunities ProgramAmerican Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Mapping the ultrafast flow of harvested solar energy in living photosynthetic cells

Photosynthesis transfers energy efficiently through a series of antenna complexes to the reaction center where charge separation occurs. Energy transfer in vivo is primarily monitored by measuring fluorescence signals from the small fraction of excitations that fail to result in charge separation. Here, we use two-dimensional electronic spectroscopy to follow the entire energy transfer process in a thriving culture of the purple bacteria, Rhodobacter sphaeroides. By removing contributions from scattered light, we extract the dynamics of energy transfer through the dense network of antenna complexes and into the reaction center. Simulations demonstrate that these dynamics constrain the membrane organization into small pools of core antenna complexes that rapidly trap energy absorbed by surrounding peripheral antenna complexes. The rapid trapping and limited back transfer of these excitations lead to transfer efficiencies of 83% and a small functional light-harvesting unit

Exchange Field Induced Magnetoresistance in Colossal Magnetoresistance Manganites

The effect of an exchange field on electrical transport in thin films of metallic ferromagnetic manganites has been investigated. The exchange field was induced both by direct exchange coupling in a ferromagnet/antiferromagnet multilayer and by indirect exchange interaction in a ferromagnet/paramagnet superlattice. The electrical resistance of the manganite layers was found to be determined by the absolute value of the vector sum of the effective exchange field and the external magnetic field.Comment: 5 pages, 4 figure