Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments.Comment: To appear in Nonlinearit

Enhancement of the Binding Energy of Charged Excitons in Disordered Quantum Wires

Negatively and positively charged excitons are identified in the spatially-resolved photoluminescence spectra of quantum wires. We demonstrate that charged excitons are weakly localized in disordered quantum wires. As a consequence, the enhancement of the "binding energy" of a charged exciton is caused, for a significant part, by the recoil energy transferred to the remaining charged carrier during its radiative recombination. We discover that the Coulomb correlation energy is not the sole origin of the "binding energy", in contrast to charged excitons confined in quantum dots.Comment: 4 Fig

Local asymptotic normality for qubit states

We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations T_{n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian set-up is also optimal within the pointwise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.Comment: 16 pages, 3 figures, published versio

Why Did Belgium Pay Leopold’s Bonds?

The longitudinal-optical (LO)-phonon coupling is experimentally examined by the optical decay of various charged and neutral exciton species in single quantum dots, and the related Huang-Rhys parameters are extracted. A positive trion exhibits significantly weaker LO-phonon replicas in the photoluminescence spectrum than the neutral and negatively charged species. Model computations show that the strength of the replicas is determined by the Coulomb interactions between electrons and holes, which modify the localization of the envelope wave functions and the net charge distribution.Original Publication: Daniel Dufåker, Fredrik Karlsson, V Dimastrodonato, L O Mereni, Bo Sernelius, Per-Olof Holtz and E Pelucchi, Phonon replicas of charged and neutral exciton complexes in single quantum dots, 2010, PHYSICAL REVIEW B, (82), 20, 205421. http://dx.doi.org/10.1103/PhysRevB.82.205421 Copyright: American Physical Society http://www.aps.org/</p

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let

Coupled Numerical Analysis of Variations in the Capacity of Driven Energy Piles in Clay

Energy piles are an emerging alternative for the reduction of energy consumption to heat and cool buildings. Most of the research to date has focused on thermodynamic properties or axial and radial stress and strain of piles. This paper focuses on the effects of temperature fluctuation on the capacity of driven energy piles in clayey soils. Consolidation of clay surrounding driven piles affects the pile capacity (i.e., set up in clay). The heating and cooling periods of energy piles can create the excess pore-water pressure (EPWP, ue) or relax the existing one (e.g., due to pile driving or previous thermal loads) in clayey soils (due to the contraction and expansion of water) affecting the pile capacity. In the meantime, the thermal expansion and contraction of the pile also generate or relax the EPWP in the soil, which can be computed using the cavity-expansion theory. This paper studies the resulting changes in the pile capacity due to the daily and seasonal thermal cycles. The results show that thermal cycles in an energy pile can cause a decrease in the pile capacity leading to a delay in reaching the capacity after a complete clay set up

Growth Curve Models for the Analysis of Phenotype Arrays for a Systems Biology Overview of Yersinia pestis

The Phenotype MicroArray technology of Biolog, Inc. (Hayward, CA) measures the respiration of cells as a function of time in thousands of microwells simultaneously, and thus provides a high-throughput means of studying cellular phenotypes. The microwells contain compounds involved in a number of biochemical pathways, as well as chemicals that test the sensitivity of cells against antibiotics and stress. While the PM experimental workflow is completely automated, statistical methods to analyze and interpret the data are lagging behind. To take full advantage of the technology, it is essential to develop efficient analytical methods to quantify the information in the complex datasets resulting from PM experiments. We propose the use of statistical growth-curve models to rigorously quantify observed differences in PM experiments, in the context of the growth and metabolism of Yersinia pestis cells grown under different physiological conditions. The information from PM experiments complement genomic and proteomic results and can be used to identify gene function and in drug development. Successful coupling of phenomics results with genomics and proteomics will lead to an unprecedented ability to characterize bacterial function at a systems biology level