Dilution Effects in Two-dimensional Quantum Orbital System

We study dilution effects in a Mott insulating state with quantum orbital degree of freedom, termed the two-dimensional orbital compass model. This is a quantum and two-dimensional version of the orbital model where the interactions along different bond directions cause frustration between different orbital configurations. A long-range correlation of a kind of orbital at each row or column, termed the directional order, is studied by means of the quantum Monte-Carlo method. It is shown that decrease of the ordering temperature due to dilution is much stronger than that in spin models. Quantum effect enhances the effective dimensionality in the system and makes the directional order robust against dilution. We discuss an essential mechanism of the dilute orbital systems.Comment: 5pages, 4 figure

Orbital order in classical models of transition-metal compounds

We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these models exhibit a long-range order which arises via an "order by disorder" mechanism. This strongly indicates that there is orbital ordering in the quantum version of these models, notwithstanding recent rigorous results on the absence of spin order in these systems.Comment: 7 pages, 1 eps fi

Colligative properties of solutions: II. Vanishing concentrations

We continue our study of colligative properties of solutions initiated in math-ph/0407034. We focus on the situations where, in a system of linear size $L$, the concentration and the chemical potential scale like $c=\xi/L$ and $h=b/L$, respectively. We find that there exists a critical value \xit such that no phase separation occurs for \xi\le\xit while, for \xi>\xit, the two phases of the solvent coexist for an interval of values of $b$. Moreover, phase separation begins abruptly in the sense that a macroscopic fraction of the system suddenly freezes (or melts) forming a crystal (or droplet) of the complementary phase when $b$ reaches a critical value. For certain values of system parameters, under ``frozen'' boundary conditions, phase separation also ends abruptly in the sense that the equilibrium droplet grows continuously with increasing $b$ and then suddenly jumps in size to subsume the entire system. Our findings indicate that the onset of freezing-point depression is in fact a surface phenomenon.Comment: 27 pages, 1 fig; see also math-ph/0407034 (both to appear in JSP

Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

Indirect Self-Modulation Instability Measurement Concept for the AWAKE Proton Beam

AWAKE, the Advanced Proton-Driven Plasma Wakefield Acceleration Experiment, is a proof-of-principle R&D experiment at CERN using a 400 GeV/c proton beam from the CERN SPS (longitudinal beam size sigma_z = 12 cm) which will be sent into a 10 m long plasma section with a nominal density of approx. 7x10^14 atoms/cm3 (plasma wavelength lambda_p = 1.2mm). In this paper we show that by measuring the time integrated transverse profile of the proton bunch at two locations downstream of the AWAKE plasma, information about the occurrence of the self-modulation instability (SMI) can be inferred. In particular we show that measuring defocused protons with an angle of 1 mrad corresponds to having electric fields in the order of GV/m and fully developed self-modulation of the proton bunch. Additionally, by measuring the defocused beam edge of the self-modulated bunch, information about the growth rate of the instability can be extracted. If hosing instability occurs, it could be detected by measuring a non-uniform defocused beam shape with changing radius. Using a 1 mm thick Chromox scintillation screen for imaging of the self-modulated proton bunch, an edge resolution of 0.6 mm and hence a SMI saturation point resolution of 1.2 m can be achieved.Comment: 4 pages, 4 figures, EAAC conference proceeding

Superconductivity and charge carrier localization in ultrathin La1.85Sr0.15CuO4/La2CuO4\mathbf{{La_{1.85}Sr_{0.15}CuO_4}/{La_2CuO_4}} bilayers

$\mathrm{La_{1.85}Sr_{0.15}CuO_4}$/$\mathrm{La_2CuO_4}$ (LSCO15/LCO) bilayers with a precisely controlled thickness of N unit cells (UCs) of the former and M UCs of the latter ([LSCO15\_N/LCO\_M]) were grown on (001)-oriented {\slao} (SLAO) substrates with pulsed laser deposition (PLD). X-ray diffraction and reciprocal space map (RSM) studies confirmed the epitaxial growth of the bilayers and showed that a [LSCO15\_2/LCO\_2] bilayer is fully strained, whereas a [LSCO15\_2/LCO\_7] bilayer is already partially relaxed. The \textit{in situ} monitoring of the growth with reflection high energy electron diffraction (RHEED) revealed that the gas environment during deposition has a surprisingly strong effect on the growth mode and thus on the amount of disorder in the first UC of LSCO15 (or the first two monolayers of LSCO15 containing one $\mathrm{CuO_2}$ plane each). For samples grown in pure $\mathrm{N_2O}$ gas (growth type-B), the first LSCO15 UC next to the SLAO substrate is strongly disordered. This disorder is strongly reduced if the growth is performed in a mixture of $\mathrm{N_2O}$ and $\mathrm{O_2}$ gas (growth type-A). Electric transport measurements confirmed that the first UC of LSCO15 next to the SLAO substrate is highly resistive and shows no sign of superconductivity for growth type-B, whereas it is superconducting for growth type-A. Furthermore, we found, rather surprisingly, that the conductivity of the LSCO15 UC next to the LCO capping layer strongly depends on the thickness of the latter. A LCO capping layer with 7~UCs leads to a strong localization of the charge carriers in the adjacent LSCO15 UC and suppresses superconductivity. The magneto-transport data suggest a similarity with the case of weakly hole doped LSCO single crystals that are in a so-called {"{cluster-spin-glass state}"

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

The topographical anatomy of the round window and related structures for the purpose of cochlear implant surgery

The treatment of total deafness using a cochlear implant has now become a routine medical procedure. The tendency to expand the audiological indications for cochlear stimulation and to preserve the remnants of hearing has brought new problems. The authors have studied the topographical anatomy of the internal structures of the ear in the area where cochleostomy is usually performed and an implant electrode inserted. Ten human temporal bones were obtained from cadavers and prepared in a formalin stain. After dissection of the bone in the area of round and oval windows, the following diameters were measured using a microscope with a scale: the transverse diameters of the cochlear and vestibular scalae at the level of the centre of the round window and 0.5 mm anteriorly to the round window, the distance between the windows and the distances from the end of the spiral lamina to the centre of the round window and to its anterior margin. The width of the cochlear scala at the level of the round window was 1.23 mm, and 0.5 mm anteriorly to the round window membrane it was 1.24 mm. The corresponding diameters for the vestibular scala are 1.34 and 1.27 mm. The distances from the end of the spiral lamina to the centre of the round window and to its anterior margin are 1.26 and 2.06 respectively. The authors noted that the two methods of electrode insertion show a difference of 2 mm in the length of the stimulated spiral lamina. The average total length of the unstimulated lamina is 2.06 and 4.06 in the two situations respectively

Colligative properties of solutions: I. Fixed concentrations

Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing point depression. The limit of infinitesimal concentrations is described in a subsequent paper.Comment: 28 pages, 1 fig; see also math-ph/0407035 (both to appear in JSP

Pulsed laser deposition growth of heteroepitaxial YBa2Cu3O7/La0.67Ca0.33MnO3 superlattices on NdGaO3 and Sr0.7La0.3Al0.65Ta0.35O3 substrates

Heteroepitaxial superlattices of [YBa2Cu3O7(n)/ La0.67Ca0.33MnO3(m)]x, where n and m are the number of YBCO and LCMO monolayers and x the number of bilayer repetitions, have been grown with pulsed laser deposition on NdGaO3 (110) and Sr0.7La0.3Al0.65Ta0.35O3 (LSAT) (001). These substrates are well lattice matched with YBCO and LCMO and, unlike the commonly used SrTiO3, they do not give rise to complex and uncontrolled strain effects due to structural transitions at low temperature. The growth dynamics and the structure have been studied in-situ with reflection high energy electron diffraction (RHEED) and ex-situ with scanning transmission electron microscopy (STEM), x-ray diffraction, and neutron reflectometry. The individual layers are found to be flat and continuous over long lateral distances with sharp and coherent interfaces and with a well-defined thickness of the individual layer. The only visible defects are antiphase boundaries in the YBCO layers that originate from perovskite unit cell height steps at the interfaces with the LCMO layers. We also find that the first YBCO monolayer at the interface with LCMO has an unusual growth dynamics and is lacking the CuO chain layer while the subsequent YBCO layers have the regular Y-123 structure. Accordingly, the CuO2 bilayers at both the LCMO/YBCO and the YBCO/LCMO interfaces are lacking one of their neighboring CuO chain layers and thus half of their hole doping reservoir. Nevertheless, from electric transport measurements on asuperlattice with n=2 we obtain evidence that the interfacial CuO2 bilayers remain conducting and even exhibit the onset of a superconducting transition at very low temperature. Finally, we show from dc magnetization and neutron reflectometry measurements that the LCMO layers are strongly ferromagnetic