Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data

We consider the one-dimensional focusing nonlinear Schr\"odinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a B\"acklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski

Microscopic mechanisms of spin-dependent electric polarization in 3d oxides

We present a short critical overview of different microscopic models for nonrelativistic and relativistic magnetoelectric coupling including the so-called "spin current scenario", ab-initio calculations, and several recent microscopic approaches to a spin-dependent electric polarization in 3d oxides.Comment: 8 pages, 3 figure

Angle-resolved photoemission in doped charge-transfer Mott insulators

A theory of angle-resolved photoemission (ARPES) in doped cuprates and other charge-transfer Mott insulators is developed taking into account the realistic (LDA+U) band structure, (bi)polaron formation due to the strong electron-phonon interaction, and a random field potential. In most of these materials the first band to be doped is the oxygen band inside the Mott-Hubbard gap. We derive the coherent part of the ARPES spectra with the oxygen hole spectral function calculated in the non-crossing (ladder) approximation and with the exact spectral function of a one-dimensional hole in a random potential. Some unusual features of ARPES including the polarisation dependence and spectral shape in YBa2Cu3O7 and YBa2Cu4O8 are described without any Fermi-surface, large or small. The theory is compatible with the doping dependence of kinetic and thermodynamic properties of cuprates as well as with the d-wave symmetry of the superconducting order parameter.Comment: 8 pages (RevTeX), 10 figures, submitted to Phys. Rev.

Geophysical Exploration of Vesta

Dawn’s year-long stay at Vesta allows comprehensive mapping of the shape, topography, geology, mineralogy, elemental abundances, and gravity field using it’s three instruments and highprecision spacecraft navigation. In the current Low Altitude Mapping Orbit (LAMO), tracking data is being acquired to develop a gravity field expected to be accurate to degree and order ~20 [1, 2]. Multi-angle imaging in the Survey and High Altitude Mapping Orbit (HAMO) has provided adequate stereo coverage to develop a shape model accurate to ~10 m at 100 m horizontal spatial resolution. Accurate mass determination combined with the shape yields a more precise value of bulk density, albeit with some uncertainty resulting from the unmeasured seasonally-dark north polar region. The shape and gravity of Vesta can be used to infer the interior density structure and investigate the nature of the crust, informing models for Vesta’s formation and evolution

Masses of composite fermions carrying two and four flux quanta: Differences and similarities

This study provides a theoretical rationalization for the intriguing experimental observation regarding the equality of the normalized masses of composite fermions carrying two and four flux quanta, and also demonstrates that the mass of the latter type of composite fermion has a substantial filling factor dependence in the filling factor range $4/17 > \nu > 1/5$, in agreement with experiment, originating from the relatively strong inter-composite fermion interactions here.Comment: 5 pages, 2 figure

Cutaneous thermosensitivity differences among the face, hand and thigh appear not to exist for skin blood flow during normothermic states

Meeting abstrac

Cutaneous thermosensitivity differences among the face, hand and thigh appear not to exist for skin blood flow during normothermic states

Meeting abstrac

Neutrino Oscillations and Collider Test of the R-parity Violating Minimal Supergravity Model

We study the R-parity violating minimal supergravity models accounting for the observed neutrino masses and mixing, which can be tested in future collider experiments. The bi-large mixing can be explained by allowing five dominant tri-linear couplings $\lambda'_{1,2,3}$ and $\lambda_{1,2}$. The desired ratio of the atmospheric and solar neutrino mass-squared differences can be obtained in a very limited parameter space where the tree-level contribution is tuned to be suppressed. In this allowed region, we quantify the correlation between the three neutrino mixing angles and the tri-linear R-parity violating couplings. Qualitatively, the relations $| \lambda'_1 | < | \lambda'_2| \sim | \lambda'_3|$, and $|\lambda_1| \sim |\lambda_2|$ are required by the large atmospheric neutrino mixing angle $\theta_{23}$ and the small angle $\theta_{13}$, and the large solar neutrino mixing angle $\theta_{12}$, respectively. Such a prediction on the couplings can be tested in the next linear colliders by observing the branching ratios of the lightest supersymmetric particle (LSP). For the stau or the neutralino LSP, the ratio $|\lambda_1|^2: |\lambda_2|^2: |\lambda_1|^2 + |\lambda_2|^2$ can be measured by establishing $Br(e\nu): Br(\mu\nu) : Br(\tau\nu)$ or $Br(\nu e^\pm \tau^\mp ): Br(\nu\mu^\pm\tau^\mp) : Br(\nu\tau^\pm\tau^\mp)$, respectively. The information on the couplings $\lambda'_i$ can be drawn by measuring $Br(l_i t \bar{b}) \propto |\lambda'_i|^2$ if the neutralino LSP is heavier than the top quark.Comment: RevTex, 25 pages, 8 eps figure

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Determination of the parameters of semiconducting CdF2:In with Schottky barriers from radio-frequency measurements

Physical properties of semiconducting CdF_2 crystals doped with In are determined from measurements of the radio-frequency response of a sample with Schottky barriers at frequencies 10 - 10^6 Hz. The dc conductivity, the activation energy of the amphoteric impurity, and the total concentration of the active In ions in CdF_2 are found through an equivalent-circuit analysis of the frequency dependencies of the sample complex impedance at temperatures from 20 K to 300 K. Kinetic coefficients determining the thermally induced transitions between the deep and the shallow states of the In impurity and the barrier height between these states are obtained from the time-dependent radio-frequency response after illumination of the material. The results on the low-frequency conductivity in CdF_2:In are compared with submillimeter (10^{11} - 10^{12} Hz) measurements and with room-temperature infrared measurements of undoped CdF_2. The low-frequency impedance measurements of semiconductor samples with Schottky barriers are shown to be a good tool for investigation of the physical properties of semiconductors.Comment: 9 pages, 7 figure