On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum

We present our results for the on-shell Delta I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to 1/a = 1.31 GeV in the quenched approximation. The on-shell matrix elements are evaluated in two different frames: the center-of-mass frame and non-zero total-momentum frame. We employ the formula proposed by Lellouch and L\"uscher in the center-of-mass frame, and its extension for non-zero total momentum frame to extract the infinite volume, on-shell, center-of-mass frame decay amplitudes. We determine the decay amplitude at the physical pion mass and momentum from the chiral extrapolation and an interpolation of the relative momentum using the results calculated in the two frames. We have obtained Re(A_2) = 1.66(23)(^{+48}_{-03})(^{+53}_{-0}) x 10^{-8} GeV and Im(A_2) = -1.181(26)(^{+141}_{-014})(^{+44}_{-0}) x 10^{-12} GeV at the physical point, using the data at the relatively large pion mass, m_pi > 0.35 GeV. The first error is statistic, and the second and third are systematic. The second error is estimated with several fits of the chiral extrapolation including (quenched) chiral perturbation formula at next to leading order using only lighter pion masses. The third one is estimated with an analysis using the lattice dispersion relation. The result of Re(A_2) is reasonably consistent with experiment.Comment: 54 pages, 17 figures; added references, removed figure and corrected typ

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments

Nucleon structure with two flavors of dynamical domain-wall fermions

We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is about $(1.9{fm})^3$. The ratio of the isovector vector to axial charges, $g_A/g_V$, trends a bit lower than the experimental value as the quark mass is reduced toward the physical point. We calculate the momentum-transfer dependences of the isovector vector, axial, induced tensor and induced pseudoscalar form factors. The Goldberger-Treiman relation holds at low momentum transfer and yields a pion-nucleon coupling, $g_{\pi NN} = 15.5(1.4)$, where the quoted error is only statistical. We find that the flavor non-singlet quark momentum fraction $_{u-d}$ and quark helicity fraction $_{\Delta u-\Delta d}$ overshoot their experimental values after linear chiral extrapolation. We obtain the transversity, $_{\delta u-\delta d} = 0.93(6)$ in $\bar{\rm MS}$ at 2 GeV and a twist-3 polarized moment, $d_1$, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss the systematic errors in the calculation, with particular attention paid to finite-volume effects, excited-state contamination, and chiral extrapolations.Comment: 28 pages in two columns; 37 figures, 12 table

Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions

We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain wall fermions and the Iwasaki gauge action ($\beta = 2.13$). The inverse lattice spacing is $a^{-1} = 1.73$ GeV, and two spatial volumes of ((2.7{\rm fm})^3) and ((1.8 {\rm fm})^3) are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange mass is about 12 % heavier than the physical one. The structure function moments we present include fully non-perturbatively renormalized iso-vector quark momentum fraction, (_{u-d}), helicity fraction, (< x >_{\Delta u - \Delta d}), and transversity, (_{\delta u - \delta d}), as well as an unrenormalized twist-3 coefficient, (d_1). The ratio of the momentum to helicity fractions, (_{u-d}/_{\Delta u - \Delta d}), does not show dependence on the light quark mass and agrees well with the value obtained from experiment. Their respective absolute values, fully renormalized, show interesting trends toward their respective experimental values at the lightest quark mass. A prediction for the transversity, (0.7 _{\delta u -\delta d} < 1.1), in the (\bar{\rm MS}) scheme at 2 GeV is obtained. The twist-3 coefficient, (d_1), though yet to be renormalized, supports the perturbative Wandzura-Wilczek relation.Comment: 14 pages, 22 figures

Asymptotically optimal Bayesian sequential change detection and identification rules

Cataloged from PDF version of article.We study the joint problem of sequential change detection and multiple hypothesis testing. Suppose that the common distribution of a sequence of i.i.d. random variables changes suddenly at some unobservable time to one of finitely many distinct alternatives, and one needs to both detect and identify the change at the earliest possible time. We propose computationally efficient sequential decision rules that are asymptotically either Bayesoptimal or optimal in a Bayesian fixed-error-probability formulation, as the unit detection delay cost or the misdiagnosis and false alarm probabilities go to zero, respectively. Numerical examples are provided to verify the asymptotic optimality and the speed of convergence

Quantum Parton Shower with Kinematics

Parton showers which can efficiently incorporate quantum interference effects have been shown to be run efficiently on quantum computers. However, so far these quantum parton showers did not include the full kinematical information required to reconstruct an event, which in classical parton showers requires the use of a veto algorithm. In this work, we show that adding one extra assumption about the discretization of the evolution variable allows to construct a quantum veto algorithm, which reproduces the full quantum interference in the event, and allows to include kinematical effects. We finally show that for certain initial states the quantum interference effects generated in this veto algorithm are classically tractable, such that an efficient classical algorithm can be devised.Comment: 14 pages, 8 figure

Gravitational Wave Memory of Gamma-Ray Burst Jets

Gamma-Ray Bursts (GRBs) are now considered as relativistic jets. We analyze the gravitational waves from the acceleration stage of the GRB jets. We show that (i) the point mass approximation is not appropriate if the opening half-angle of the jet is larger than the inverse of the Lorentz factor of the jet, (ii) the gravitational waveform has many step function like jumps, and (iii) the practical DECIGO and BBO may detect such an event if the GRBs occur in Local group of galaxy. We found that the light curve of GRBs and the gravitational waveform are anti-correlated so that the detection of the gravitational wave is indispensable to determine the structure of GRB jets.Comment: Revtex4, 10 pages, 6 figures, Fig.2 and Fig.3 replaced, minor changes to text in Sec.I and Sec.V, typos corrected, some reference added, Version to be published in PR

Lattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture

Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns similar to those found in the experiment[Yamazaki and Mizuguchi, J. Phys. Soc. Jpn. \textbf{69} (2000) 2387]. Upon changing the initial granular density, resulting patterns undergo the percolation transition, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.Comment: 6 pages, 7 figure