Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients

This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 Birkhäuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: ”Mathematical analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems” and partly by the Georgian Technical University grant in the case of the third author

Spectropolarimetric observations of Herbig Ae/Be Stars I: HiVIS spectropolarimetric calibration and reduction techniques

Using the HiVIS spectropolarimeter built for the Haleakala 3.7m AEOS telescope in Hawaii, we are collecting a large number of high precision spectropolarimetrc observations of stars. In order to precisely measure very small polarization changes, we have performed a number of polarization calibration techniques on the AEOS telescope and HiVIS spectrograph. We have extended our dedicated IDL reduction package and have performed some hardware upgrades to the instrument. We have also used the ESPaDOnS spectropolarimeter on CFHT to verify the HiVIS results with back-to-back observations of MWC 361 and HD163296. Comparision of this and other HiVIS data with stellar observations from the ISIS and WW spectropolarimeters in the literature further shows the usefulness of this instrument.Comment: 35 pages, 44 figures, Accepted by PAS

An experimental look at reasonable suspicion and police discretion

Purpose This study aims to demonstrate the need for further examination of legal judgments and the exercise of discretion in policing. Design/methodology/approach A factorial vignette survey with traffic stop scenarios based on US Court of Appeals decisions was administered to 396 police officers across six states. Officers were asked to indicate their assessment of the presence of reasonable suspicion and the likelihood that they would extend the stop for investigatory purposes. Findings Officers\u27 reasonable suspicion judgments are significantly influenced by the vignette facts and align with court ruling expectations. However, even in the presence of reasonable suspicion, responses indicate a limited use of officer discretion to extend the stop. Originality/value Analyses of officer decision-making often rely on large datasets with easy indicators of location, officer demographics and citizen demographics, but rarely consider the facts of individual cases. This study suggests more experimental research is needed to consider the impact of case facts on officer judgments and discretionary activity

Fluctuations in viscous fingering

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal finger width fluctuations that were not observed in previous experiments, which had lower aspect ratios and higher capillary numbers Ca. These fluctuations intermittently narrow the finger from its expected width. The magnitude of these fluctuations is described by a power law, Ca^{-0.64}, which holds for all aspect ratios studied up to the onset of tip instabilities. Further, for large aspect ratios, the mean finger width exhibits a maximum as Ca is decreased instead of the predicted monotonic increase.Comment: Revised introduction, smoothed transitions in paper body, and added a few additional minor results. (Figures unchanged.) 4 pages, 3 figures. Submitted to PRE Rapi

Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells

Viscous fingers in a channel with surface tension anisotropy are numerically studied. Scaling relations between the tip velocity v, the tip radius and the pressure gradient are investigated for two kinds of boundary conditions of pressure, when v is sufficiently large. The power-law relations for the anisotropic viscous fingers are compared with two-dimensional dendritic growth. The exponents of the power-law relations are theoretically evaluated.Comment: 5 pages, 4 figure

Structural and chemical embrittlement of grain boundaries by impurities: a general theory and first principles calculations for copper

First principles calculations of the Sigma 5 (310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However numerical results show a striking equivalence between the alkali metal Na and the semi metal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unravelled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the nett reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.Comment: 13 pages, 5 figures; Accepted in Phys. Rev.

NSTX Report on FES Joint Facilities Research Milestone 2010

Annual Target: Conduct experiments on major fusion facilities to improve understanding of the heat transport in the tokamak scrape-off layer (SOL) plasma, strengthening the basis for projecting divertor conditions in ITER. The divertor heat flux profiles and plasma characteristics in the tokamak scrape-off layer will be measured in multiple devices to investigate the underlying thermal transport processes. The unique characteristics of C-Mod, DIII-D, and NSTX will enable collection of data over a broad range of SOL and divertor parameters (e.g., collisionality ν*, beta β, parallel heat flux q||, and divertor geometry). Coordinated experiments using common analysis methods will generate a data set that will be compared with theory and simulation

Ground state properties of heavy alkali halides

We extend previous work on alkali halides by calculations for the heavy-atom species RbF, RbCl, LiBr, NaBr, KBr, RbBr, LiI, NaI, KI, and RbI. Relativistic effects are included by means of energy-consistent pseudopotentials, correlations are treated at the coupled-cluster level. A striking deficiency of the Hartree-Fock approach are lattice constants deviating by up to 7.5 % from experimental values which is reduced to a maximum error of 2.4 % by taking into account electron correlation. Besides, we provide ab-initio data for in-crystal polarizabilities and van der Waals coefficients.Comment: accepted by Phys. Rev.

A Spectral Method for Elliptic Equations: The Neumann Problem

Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $-\Delta u+\gamma u=f$ over $\Omega$ with a Neumann boundary condition. The problem is converted to an equivalent elliptic problem over the unit ball $B$, and then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials $u_{n}$ of degree $\leq n$ that is convergent to $u$. The transformation from $\Omega$ to $B$ requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For $u\in C^{\infty}(\overline{\Omega})$ and assuming $\partial\Omega$ is a $C^{\infty}$ boundary, the convergence of $\Vert u-u_{n}\Vert_{H^{1}}$ to zero is faster than any power of $1/n$. Numerical examples in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ show experimentally an exponential rate of convergence.Comment: 23 pages, 11 figure

Application of Dynamic System Identification to Timber Beams - part I

In this first part of a two-part paper, development of a method of dynamic system identification for timber beams is presented with an analytical verification of the method using a finite-element model. A method of global nondestructive evaluation for identifying local damage and decay in timber beams is investigated in this paper. Experimental modal analysis is used in conjunction with a previously developed damage localization algorithm. The damage localization algorithm utilizes changes in modal strain energy between the mode shapes of a calibrated model, representing the undamaged state of the beam of interest, and the experimentally obtained mode shapes for a timber beam. Analytical evaluations were performed to demonstrate and verify the use of this method of global nondestructive evaluation for the localization of damage or decay in timber beams. In a companion paper, experimental laboratory tests are presented that verify the use of dynamic system identification to locate damage within timber beams