Microlocal Properties of Bisingular Operators

We study the microlocal properties of bisingular operators, a class of operators on the product of two compact manifolds. We define a wave front set for such operators, and analyse its properties. We compare our wave front set with the $SG$ wave front set, a global wave front set which shares with it formal similarities.Comment: 22 pages, 1 figure, 2 tables. Corrected typos, expanded section

Gas flow environment and heat transfer nonrotating 3D program

A complete set of benchmark quality data for the flow and heat transfer within a large rectangular turning duct is provided. These data are to be used to evaluate, and verify, three-dimensional internal viscous flow models and computational codes. The analytical contract objective is to select a computational code and define the capabilities of this code to predict the experimental results obtained. Details of the proper code operation will be defined and improvements to the code modeling capabilities will be formulated. Internal flow in a large rectangular cross-sectioned 90 deg. bend turning duct was studied. The duct construction was designed to allow detailed measurements to be made for the following three duct wall conditions: (1) an isothermal wall with isothermal flow; (2) an adiabatic wall with convective heat transfer by mixing between an unheated surrounding flow; and (3) an isothermal wall with heat transfer from a uniformly hot inlet flow

UREA/ammonium ion removal system for the orbiting frog otolith experiment

The feasibility of using free urease enzyme and ANGC-101 ion exchange resin to remove urea and ammonium ion for space system waste water applications was studied. Specifically examined is the prevention of urea and ammonia toxicity in a 30-day Orbiting Frog Otolith (OFO) flight experiment. It is shown that free urease enzyme used in conjunction with ANGC-101 ion-exchange resin and pH control can control urea and amonium ion concentration in unbuffered recirculating water. In addition, the resin does not adversely effect the bullfrogs by lowering the concentration of cations below critical minimum levels. Further investigations on bioburden control, frog waste excretion on an OFO diet, a trade-off analysis of methods of automating the urea/ammonium ion removal system and fabrication and test of a semiautomated breadboard were recommended as continuing efforts. Photographs of test equipment and test animals are shown

Spin-orbit coupling and spectral function of interacting electrons in carbon nanotubes

The electronic spin-orbit coupling in carbon nanotubes is strongly enhanced by the curvature of the tube surface and has important effects on the single-particle spectrum. Here, we include the full spin-orbit interaction in the formulation of the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes and study its consequences. The resulting theory is a four-channel Luttinger liquid, where spin and charge modes are mixed. We show that the analytic structure of the spectral function is strongly affected by this mixing, which can provide an experimental signature of the spin-orbit interaction.Comment: 4+epsilon pages, 1 figure; published versio

Theoretical analysis of influence of random alloy fluctuations on the opto-electronic properties of site-controlled (111)-oriented InGaAs/GaAs quantum dots

We use an $sp^3d^5s^*$ tight-binding model to investigate the electronic and optical properties of realistic site-controlled (111)-oriented InGaAs/GaAs quantum dots. Special attention is paid to the impact of random alloy fluctuations on key factors that determine the fine-structure splitting in these systems. Using a pure InAs/GaAs quantum dot as a reference system, we show that the combination of spin-orbit coupling and biaxial strain effects can lead to sizeable spin-splitting effects in these systems. Then, a realistic alloyed InGaAs/GaAs quantum dot with 25\% InAs content is studied. Our analysis reveals that the impact of random alloy fluctuations on the electronic and optical properties of (111)-oriented InGaAs/GaAs quantum dots reduces strongly as the lateral size of the dot increases and approaches realistic sizes. For instance the optical matrix element shows an almost vanishing anisotropy in the (111)-growth plane. Furthermore, conduction and valence band mixing effects in the system under consideration are strongly reduced compared to standard (100)-oriented InGaAs/GaAs systems. All these factors strongly indicate a reduced fine structure splitting in site-controlled (111)-oriented InGaAs/GaAs quantum dots. Thus, we conclude that quantum dots with realistic (50-80~nm) base length represent promising candidates for polarization entangled photon generation, consistent with recent experimental data

Perturbative test of single parameter scaling for 1D random media

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single parameter scaling holds to lowest order perturbation theory in the disorder strength. However, it is generically violated at higher order. This is explicitely exhibited for the Anderson model.Comment: minor corrections to previous version, to appear in Annales H. Poincar

RSB Decoupling Property of MAP Estimators

The large-system decoupling property of a MAP estimator is studied when it estimates the i.i.d. vector $\boldsymbol{x}$ from the observation $\boldsymbol{y}=\mathbf{A}\boldsymbol{x}+\boldsymbol{z}$ with $\mathbf{A}$ being chosen from a wide range of matrix ensembles, and the noise vector $\boldsymbol{z}$ being i.i.d. and Gaussian. Using the replica method, we show that the marginal joint distribution of any two corresponding input and output symbols converges to a deterministic distribution which describes the input-output distribution of a single user system followed by a MAP estimator. Under the $b$RSB assumption, the single user system is a scalar channel with additive noise where the noise term is given by the sum of an independent Gaussian random variable and $b$ correlated interference terms. As the $b$RSB assumption reduces to RS, the interference terms vanish which results in the formerly studied RS decoupling principle.Comment: 5 pages, presented in Information Theory Workshop 201

Ion-by-Ion DEM Determination: I. Method

We describe a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission line spectra. This technique involves fitting spectra using a number of components, each of which is the entire X-ray line emission spectrum for a single ion. It is applicable to high-resolution X-ray spectra of any collisionally ionized plasma and particularly useful for spectra in which the emission lines are broadened and blended such as those of the winds of hot stars. This method does not require that any explicit assumptions about the form of the DEM distribution be made and is easily automated.Comment: This paper was split in two. This version is part I. Part II may be found at astro-ph/050343

Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.