Linear PDEs and numerical methods that preserve a multi-symplectic conservation law

Multisymplectic methods have recently been proposed as a generalization of symplectic ODE methods to the case of Hamiltonian PDEs. Their excellent long time behavior for a variety of Hamiltonian wave equations has been demonstrated in a number of numerical studies. A theoretical investigation and justification of multisymplectic methods is still largely missing. In this paper, we study linear multisymplectic PDEs and their discretization by means of numerical dispersion relations. It is found that multisymplectic methods in the sense of Bridges and Reich Phys. Lett. A, 284 (2001), pp. 184-193] and Reich J. Comput. Phys., 157 (2000), pp. 473-499], such as Gauss-Legendre Runge-Kutta methods, possess a number of desirable properties such as nonexistence of spurious roots and conservation of the sign of the group velocity. A certain CFL-type restriction on $\Delta t/\Delta x$ might be required for methods higher than second order in time. It is also demonstrated by means of the explicit midpoint method that multistep methods may exhibit spurious roots in the numerical dispersion relation for any value of $\Delta t/\Delta x$ despite being multisymplectic in the sense of discrete variational mechanics [J. E. Marsden, G. P. Patrick, and S. Shkoller, Commun. Math. Phys., 199 (1999), pp. 351-395]

Directional wind measurement derived from elastic backscatter lidar data in real time

The development of a capability to infer wind velocities simultaneously at a number of ranges along one direction in real time is described. The elastic backscatter lidar data used was obtained using the XM94 lidar, developed by Los Alamos National Laboratory for the US Army Chemical and Biological Detection Command. In some respects this problem is simpler than measuring wind velocities on meso-meteorological scales. Other requirements, particularly high temporal fidelity, have driven the development of faster software algorithms and suggested opportunities for the evolution of the hardware

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous H-alpha ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the center of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ~ 110 deg within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasiseparatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four H-alpha ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.Comment: 24 pages, 10 figures, Solar Physics (accepted

Large scale numerical investigation of excited states in poly(phenylene)

A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.Comment: RevTeX, 10 pages, 4 eps figures included using eps

The low-lying excitations of polydiacetylene

The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.Comment: LaTeX, 23 pages, 4 postscript tables and 8 postscript figure

Non-Critical Liouville String Escapes Constraints on Generic Models of Quantum Gravity

It has recently been pointed out that generic models of quantum gravity must contend with severe phenomenological constraints imposed by gravitational Cerenkov radiation, neutrino oscillations and the cosmic microwave background radiation. We show how the non-critical Liouville-string model of quantum gravity we have proposed escapes these constraints. It gives energetic particles subluminal velocities, obviating the danger of gravitational Cerenkov radiation. The effect on neutrino propagation is naturally flavour-independent, obviating any impact on oscillation phenomenology. Deviations from the expected black-body spectrum and the effects of time delays and stochastic fluctuations in the propagation of cosmic microwave background photons are negligible, as are their effects on observable spectral lines from high-redshift astrophysical objects.Comment: 15 pages LaTeX, 2 eps figures include

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function $Z(t)$ and diffusion coefficient $D$. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for $Z(t)$ and $D$ agree remarkably well with MD simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and cond-mat/0002058 combined Minor changes made to coincide with published versio

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Organizational and Leadership Implications for Transformational Development

Transformational development is a concept of change that originated in the Christian context but has now become generally used in the work of both secular and faith-based organizations. The growing use of the concept by organizations that are fundamentally different has naturally led to some confusion about what the concept means and what it takes to effectively implement it. In this article, we describe the key features of the concept and how they are important in determining the organizational requirements for its effective implementation. Drawing on a few cases, the paper highlights the centrality of faith in transformational development work

Azimuthal anisotropy at RHIC: the first and fourth harmonics

We report the first observations of the first harmonic (directed flow, v_1), and the fourth harmonic (v_4), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data tables are at http://www.star.bnl.gov/central/publications/pubDetail.php?id=3