Purely transmitting integrable defects

Some aspects of integrable field theories possessing purely transmitting defects are described. The main example is the sine-Gordon model and several striking features of a classical field theory containing one or more defects are pointed out. Similar features appearing in the associated quantum field theory are also reviewed briefly.Comment: 6 pages, to appear in Proceedings of the XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, June 200

Fast soliton scattering by delta impurities

We study the Gross-Pitaevskii equation (nonlinear Schroedinger equation) with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L^2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.Comment: 32 pages, 3 figure

Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions

We study a multigrid method for nonabelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This result is in accordance with theoretical arguments based on the analysis of the scale dependence of acceptance rates for nonlocal Metropolis updates. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint MS-TPI-94-

Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Methane emissions among individual dairy cows during milking quantified by eructation peaks or ratio with carbon dioxide

The aims of this study were to compare methods for examining measurements of CH4 and CO2 emissions of dairy cows during milking and to assess repeatability and variation of CH4 emissions among individual dairy cows. Measurements of CH4 and CO2 emissions from 36 cows were collected in 3 consecutive feeding periods. In the first period, cows were fed a commercial partial mixed ration (PMR) containing 69% forage. In the second and third periods, the same 36 cows were fed a high-forage PMR ration containing 75% forage, with either a high grass silage or high maize silage content. Emissions of CH4 during each milking were examined using 2 methods. First, peaks in CH4 concentration due to eructations during milking were quantified. Second, ratios of CH4 and CO2 average concentrations during milking were calculated. A linear mixed model was used to assess differences between PMR. Variation in CH4 emissions was observed among cows after adjusting for effects of lactation number, week of lactation, diet, individual cow, and feeding period, with coefficients of variation estimated from variance components ranging from 11 to 14% across diets and methods of quantifying emissions. No significant difference was detected between the 3 PMR in CH4 emissions estimated by either method. Emissions of CH4 calculated from eructation peaks or as CH4 to CO2 ratio were positively associated with forage dry matter intake. Ranking of cows according to CH4 emissions on different diets was correlated for both methods, although rank correlations and repeatability were greater for CH4 concentration from eructation peaks than for CH4-to-CO2 ratio. We conclude that quantifying enteric CH4 emissions either using eructation peaks in concentration or as CH4-to-CO2 ratio can provide highly repeatable phenotypes for ranking cows on CH4 output

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

Variation in enteric methane emissions among cows on commercial dairy farms

Methane (CH4) emissions by dairy cows vary with feed intake and diet composition. Even when fed on the same diet at the same intake, however, variation between cows in CH4 emissions can be substantial. The extent of variation in CH4 emissions among dairy cows on commercial farms is unknown, but developments in methodology now permit quantification of CH4 emissions by individual cows under commercial conditions. The aim of this research was to assess variation among cows in emissions of eructed CH4 during milking on commercial dairy farms. Enteric CH4 emissions from 1,964 individual cows across 21 farms were measured for at least 7 days per cow using CH4 analysers at robotic milking stations. Cows were predominantly of Holstein Friesian breed and remained on the same feeding systems during sampling. Effects of explanatory variables on average CH4 emissions per individual cow were assessed by fitting a linear mixed model. Significant effects were found for week of lactation, daily milk yield and farm. The effect of milk yield on CH4 emissions varied among farms. Considerable variation in CH4 emissions was observed among cows after adjusting for fixed and random effects, with the coefficient of variation ranging from 22 to 67% within farms. This study confirms that enteric CH4 emissions vary among cows on commercial farms, suggesting that there is considerable scope for selecting individual cows and management systems with reduced emissions

Search for the Proton Decay Mode proton to neutrino K+ in Soudan 2

We have searched for the proton decay mode proton to neutrino K+ using the one-kiloton Soudan 2 high resolution calorimeter. Contained events obtained from a 3.56 kiloton-year fiducial exposure through June 1997 are examined for occurrence of a visible K+ track which decays at rest into mu+ nu or pi+ pi0. We found one candidate event consistent with background, yielding a limit, tau/B > 4.3 10^{31} years at 90% CL with no background subtraction.Comment: 13 pages, Latex, 3 tables and 3 figures, Accepted by Physics Letters