Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

The 2004 Sumatra tsunami as recorded on the Atlantic coast of South America

The 2004 Sumatra tsunami propagated throughout the World Ocean and was clearly recorded by tide gauges on the Atlantic coast of South America. A total of 17 tsunami records were found and subsequently examined for this region. Tsunami wave heights and arrival times are generally consistent with numerical modeling results. Maximum wave heights of more than 1.2 m were observed on the coasts of Uruguay and southeastern Brazil. Marked differences in tsunami height from pairs of closely located tide gauge sites on the coast of Argentina illustrate the importance that local topographic resonance effects can have on the observed wave response. Findings reveal that, outside the Indian Ocean, the highest waves were recorded in the South Atlantic and not in the Pacific as has been previously suggested

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

Ghosts of the past and dreams of the future: the impact of temporal focus on responses to contextual ingroup devaluation.

addresses: University of Exeter, Exeter, UK. [email protected]: Journal Article; Research Support, Non-U.S. Gov'tCopyright © 2012 SAGE Publications. Author's draft version; post-print. Final version published by Sage available on Sage Journals Online http://online.sagepub.com/The authors investigated the impact of temporal focus on group members' responses to contextual ingroup devaluation. Four experimental studies demonstrated that following an induction of negative ingroup evaluation, participants primed with a past temporal focus reported behavioral intentions more consistent with this negative appraisal than participants primed with a future temporal focus. This effect was apparent only when a negative (but not a positive) evaluation was induced, and only among highly identified group members. Importantly, the interplay between temporal focus and group identification on relevant intentions was mediated by individual self-esteem, suggesting that focus on the future may be conducive to separating negative ingroup appraisals from individual self-evaluations. Taken together, the findings suggest that high identifiers' responses to ingroup evaluations may be predicated on their temporal focus: A focus on the past may lock such individuals within their group's history, whereas a vision of the future may open up opportunities for change

Penta-Hepta Defect Motion in Hexagonal Patterns

Structure and dynamics of penta-hepta defects in hexagonal patterns is studied in the framework of coupled amplitude equations for underlying plane waves. Analytical solution for phase field of moving PHD is found in the far field, which generalizes the static solution due to Pismen and Nepomnyashchy (1993). The mobility tensor of PHD is calculated using combined analytical and numerical approach. The results for the velocity of PHD climbing in slightly non-optimal hexagonal patterns are compared with numerical simulations of amplitude equations. Interaction of penta-hepta defects in optimal hexagonal patterns is also considered.Comment: 4 pages, Postscript (submitted to PRL

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

Near-source observations and modeling of the Kuril Islands tsunamis of 15 November 2006 and 13 January 2007

International audienceTwo major earthquakes near the Central Kuril Islands (Mw=8.3 on 15 November 2006 and Mw=8.1 on 13 January 2007) generated trans-oceanic tsunamis recorded over the entire Pacific Ocean. The strongest oscillations, exceeding several meters, occurred near the source region of the Kuril Islands. Tide gauge records for both tsunamis have been thoroughly examined and numerical models of the events have been constructed. The models of the 2006 and 2007 events include two important advancements in the simulation of seismically generated tsunamis: (a) the use of the finite failure source models by Ji (2006, 2007) which provide more detailed information than conventional models on spatial displacements in the source areas and which avoid uncertainties in source extent; and (b) the use of the three-dimensional Laplace equation to reconstruct the initial tsunami sea surface elevation (avoiding the usual shallow-water approximation). The close agreement of our simulated results with the observed tsunami waveforms at the open-ocean DART stations support the validity of this approach. Observational and model findings reveal that energy fluxes of the tsunami waves from the source areas were mainly directed southeastward toward the Hawaiian Islands, with relatively little energy propagation into the Sea of Okhotsk. A marked feature of both tsunamis was their high-frequency content, with typical wave periods ranging from 2?3 to 15?20 min. Despite certain similarities, the two tsunamis were essentially different and had opposite polarity: the leading wave of the November 2006 trans-oceanic tsunami was positive, while that for the January 2007 trans-oceanic tsunami was negative. Numerical modeling of both tsunamis indicates that, due to differences in their seismic source properties, the 2006 tsunami was more wide-spread but less focused than the 2007 tsunami

Proper orthogonal decomposition of solar photospheric motions

The spatio-temporal dynamics of the solar photosphere is studied by performing a Proper Orthogonal Decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low frequency oscillations, with frequencies in the range 20-130 microHz, dominate the most energetic POD modes (excluding solar rotation), and are characterized by spatial patterns with typical scales of about 3 Mm. Patterns with larger typical scales of 10 Mm, are associated to p-modes oscillations at frequencies of about 3000 microHz.Comment: 8 figures in jpg in press on PR

Manipulation and removal of defects in spontaneous optical patterns

Defects play an important role in a number of fields dealing with ordered structures. They are often described in terms of their topology, mutual interaction and their statistical characteristics. We demonstrate theoretically and experimentally the possibility of an active manipulation and removal of defects. We focus on the spontaneous formation of two-dimensional spatial structures in a nonlinear optical system, a liquid crystal light valve under single optical feedback. With increasing distance from threshold, the spontaneously formed hexagonal pattern becomes disordered and contains several defects. A scheme based on Fourier filtering allows us to remove defects and to restore spatial order. Starting without control, the controlled area is progressively expanded, such that defects are swept out of the active area.Comment: 4 pages, 4 figure