SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

CAUSAL APPROACH TO (2+1)-DIMENSIONAL QED

It is shown that the causal approach to (2 + 1)-dimensional quantum electrodynamics yields a well-defined perturbative theory. In particular, and in contrast to renormalized perturbative quantum field theory, it is free of any ambiguities and ascribes a nonzero value to the dynamically generated, nonperturbative photon mass. (C) 1994 Academic Press, Inc.

Virial coefficients from (2+1)-dimensional QED effective actions at finite temperature and density

From spinor and scalar (2 + 1)-dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These coefficients depend on a parameter theta related to the time-component of the gauge field, which plays an essential role for large gauge invariance. The variation of the parameter theta might lead to an interpolation between fermionic and bosonic virial coefficients, although these coefficients are singular for theta = pi/2.

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Two-matrix string model as constrained (2+1)-dimensional integrable system

We show that the 2-matrix string model corresponds to a coupled system of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific symmetry constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Backhand transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.

Search for Randall-Sundrum gravitons with 1 fb(-1) of data from p(p)over-bar collisions at root s=1.96 TeV

We search for decays of Kaluza-Klein excitations of the graviton in the Randall-Sundrum model of extra dimensions to e+e- and in 1 fb-1 of pp collisions at s=1.96 TeV collected by the D0 detector at the Fermilab Tevatron. We set 95% confidence level upper limits on the production cross section times branching fraction, which translate into lower limits on the mass of the lightest excitation between 300 and 900 GeV for values of the coupling k/M Pl between 0.01 and 0.1. © 2008 The American Physical Society.

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.

Semi-supervised dimensionality reduction based on partial least squares for visual analysis of high dimensional data

Dimensionality reduction is employed for visual data analysis as a way to obtaining reduced spaces for high dimensional data or to mapping data directly into 2D or 3D spaces. Although techniques have evolved to improve data segregation on reduced or visual spaces, they have limited capabilities for adjusting the results according to user's knowledge. In this paper, we propose a novel approach to handling both dimensionality reduction and visualization of high dimensional data, taking into account user's input. It employs Partial Least Squares (PLS), a statistical tool to perform retrieval of latent spaces focusing on the discriminability of the data. The method employs a training set for building a highly precise model that can then be applied to a much larger data set very effectively. The reduced data set can be exhibited using various existing visualization techniques. The training data is important to code user's knowledge into the loop. However, this work also devises a strategy for calculating PLS reduced spaces when no training data is available. The approach produces increasingly precise visual mappings as the user feeds back his or her knowledge and is capable of working with small and unbalanced training sets.

Three-dimensional portable document format: a simple way to present 3-dimensional data in an electronic publication

Three-dimensional (3D) models of teeth and soft and hard tissues are tessellated surfaces used for diagnosis, treatment planning, appliance fabrication, outcome evaluation, and research. In scientific publications or communications with colleagues, these 3D data are often reduced to 2-dimensional pictures or need special software for visualization. The portable document format (PDF) offers a simple way to interactively display 3D surface data without additional software other than a recent version of Adobe Reader (Adobe, San Jose, Calif). The purposes of this article were to give an example of how 3D data and their analyses can be interactively displayed in 3 dimensions in electronic publications, and to show how they can be exported from any software for diagnostic reports and communications among colleagues.

Lake surface water temperatures of European Alpine lakes (1989–2013) based on the Advanced Very High Resolution Radiometer (AVHRR) 1 km data set

Lake water temperature (LWT) is an important driver of lake ecosystems and it has been identified as an indicator of climate change. Consequently, the Global Climate Observing System (GCOS) lists LWT as an essential climate variable. Although for some European lakes long in situ time series of LWT do exist, many lakes are not observed or only on a non-regular basis making these observations insufficient for climate monitoring. Satellite data can provide the information needed. However, only few satellite sensors offer the possibility to analyse time series which cover 25 years or more. The Advanced Very High Resolution Radiometer (AVHRR) is among these and has been flown as a heritage instrument for almost 35 years. It will be carried on for at least ten more years, offering a unique opportunity for satellite-based climate studies. Herein we present a satellite-based lake surface water temperature (LSWT) data set for European water bodies in or near the Alps based on the extensive AVHRR 1 km data record (1989–2013) of the Remote Sensing Research Group at the University of Bern. It has been compiled out of AVHRR/2 (NOAA-07, -09, -11, -14) and AVHRR/3 (NOAA-16, -17, -18, -19 and MetOp-A) data. The high accuracy needed for climate related studies requires careful pre-processing and consideration of the atmospheric state. The LSWT retrieval is based on a simulation-based scheme making use of the Radiative Transfer for TOVS (RTTOV) Version 10 together with ERA-interim reanalysis data from the European Centre for Medium-range Weather Forecasts. The resulting LSWTs were extensively compared with in situ measurements from lakes with various sizes between 14 and 580 km2 and the resulting biases and RMSEs were found to be within the range of −0.5 to 0.6 K and 1.0 to 1.6 K, respectively. The upper limits of the reported errors could be rather attributed to uncertainties in the data comparison between in situ and satellite observations than inaccuracies of the satellite retrieval. An inter-comparison with the standard Moderate-resolution Imaging Spectroradiometer (MODIS) Land Surface Temperature product exhibits RMSEs and biases in the range of 0.6 to 0.9 and −0.5 to 0.2 K, respectively. The cross-platform consistency of the retrieval was found to be within ~ 0.3 K. For one lake, the satellite-derived trend was compared with the trend of in situ measurements and both were found to be similar. Thus, orbital drift is not causing artificial temperature trends in the data set. A comparison with LSWT derived through global sea surface temperature (SST) algorithms shows lower RMSEs and biases for the simulation-based approach. A running project will apply the developed method to retrieve LSWT for all of Europe to derive the climate signal of the last 30 years. The data are available at doi:10.1594/PANGAEA.831007.