Simulation of colloidal chain movements under a magnetic field

Short colloidal chains are simulated by the slithering-snake-algorithm on a simple cubic lattice. The dipole character of the colloidal particles leads to a long range dipole-dipole interaction. The solvent is simulated by the nearest neighbor Ising model. The aligning of the dipoles under a magnetic field gives rise to the chains to align on their part with the field direction.Comment: 3 pages for Int. J. Mod. Phys. C 16, issue

MULTIPLE STRUCTURAL BREAKS IN AUSTRALIA’S MACROECONOMIC DATA: AN APPLICATION OF THE LUMSDAINE AND PAPELL TEST

This paper employs all available annual time series data to endogenously determine the timing of structural breaks for 10 macroeconomic variables in the Australian economy. The ADF (Augmented Dickey and Fuller) test and the LP (Lumsdaine and Papell, 1997) test are used to examine the time series properties of the data. The ADF test results provide no evidence against the unit root null hypothesis in all ten macroeconomic variables. After accounting for the two most significant structural breaks in the data impacting on both the intercept and trend, the results from the LP test indicate that the null of at least one unit root is rejected for four of the variables under investigation at the 10 per cent level or better. We also found that the dates of structural breaks in most cases point to: (a) the oil/wages shock occurring in the 1973-1975 period, (b) the 1990-1991 recession; (c) the culmination of financial deregulation and innovation in the late 1980s; and (d) the 1997 Asian crisis.Unit roots Hypothesis, structural breaks, and Australian economy

Spectral tensor-train decomposition

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT decomposition and analyze its properties. We obtain results on the convergence of the decomposition, revealing links between the regularity of the function, the dimension of the input space, and the TT ranks. We also show that the regularity of the target function is preserved by the univariate functions (i.e., the "cores") comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting \textit{spectral tensor-train decomposition} combines the favorable dimension-scaling of the TT decomposition with the spectral convergence rate of polynomial approximations, yielding efficient and accurate surrogates for high-dimensional functions. To construct these decompositions, we use the sampling algorithm \texttt{TT-DMRG-cross} to obtain the TT decomposition of tensors resulting from suitable discretizations of the target function. We assess the performance of the method on a range of numerical examples: a modifed set of Genz functions with dimension up to $100$, and functions with mixed Fourier modes or with local features. We observe significant improvements in performance over an anisotropic adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online.Comment: 33 pages, 19 figure

Invertibility in groupoid C*-algebras

Given a second-countable, Hausdorff, \'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \lambda_x(a) is invertible for every x in the unit space of G, where \lambda_x refers to the "regular representation" of C*(G) on l_2(G_x). We also prove that, for every a in C*(G), there exists some x in G^{(0)} such that ||a|| = ||\lambda_x(a)||.Comment: 8 page

Robust procedure for creating and characterizing the atomic structure of scanning tunneling microscope tips

Scanning tunneling microscopes (STM) are used extensively for studying and manipulating matter at the atomic scale. In spite of the critical role of the STM tip, the control of the atomic-scale shape of STM tips remains a poorly solved problem. Here, we present a method for preparing tips {\it in-situ} and for ensuring the crystalline structure and reproducibly preparing tip structure up to the second atomic layer. We demonstrate a controlled evolution of such tips starting from undefined tip shapes.Comment: 12 pages preprint-style; 5 figure

A strongly inhomogeneous superfluid in an iron-based superconductor

Among the mysteries surrounding unconventional, strongly correlated superconductors is the possibility of spatial variations in their superfluid density. We use atomic-resolution Josephson scanning tunneling microscopy to reveal a strongly inhomogeneous superfluid in the iron-based superconductor FeTe0.55Se0.45. By simultaneously measuring the topographic and electronic properties, we find that this inhomogeneity in the superfluid density is not caused by structural disorder or strong inter-pocket scattering, and does not correlate with variations in Cooper pair-breaking gap. Instead, we see a clear spatial correlation between superfluid density and quasiparticle strength, putting the iron-based superconductors on equal footing with the cuprates and demonstrating that locally, the quasiparticles are sharpest when the superconductivity is strongest. When repeated at different temperatures, our technique could further help elucidate what local and global mechanisms limit the critical temperature in unconventional superconductors

The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters

To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70" and 0.25" with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular'' galaxy that is highly elongated by using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.Comment: 15 pages, 9 figures; accepted for publication in Astronomical Journa

Ion energy measurements on MAST using a midplane RFEA

Ion energy measurements have been made in the scrape off layer of the Mega Amp Spherical Tokamak (MAST) using a midplane retarding field energy analyser (RFEA) in H-mode plasmas during the inter-edge localised mode (ELM) period and during type I and type III ELMs. During the inter-ELM period at distances of 3 to 8 cm from the last closed flux surface (LCFS), ion temperatures of 20 to 70 eV have been measured giving an ion to electron temperature ratio of 2 to 7 with a mean of 4. During type III ELMs, an ion temperature of 50 eV has been measured 3 to 6 cm from the LCFS which decreases to 30 eV at distances 11 to 16 cm from the LCFS. During type I ELMs, an ion temperature of 40 eV has been measured at a distance of 10 to 15 cm from the LCFS.Comment: 15 pages, 5 figure

Electro-optic techniques for longitudinal electron bunch diagnostics

Electro-optic techniques are becoming increasingly important in ultrafast electron bunch longitudinal diagnostics and have been successfully implemented at various accelerator laboratories. The longitudinal bunch shape is directly obtained from a single-shot, non-intrusive measurement of the temporal electric field profile of the bunch. Further- more, the same electro-optic techniques can be used to measure the temporal profile of terahertz / far-infrared opti- cal pulses generated by a CTR screen, at a bending magnet (CSR), or by an FEL. This contribution summarizes the re- sults obtained at FELIX and FLASH