During the past two decades data visualization has matured as an own sub-discipline in computer science. Its methods are successfully applied in almost all areas of science, engineering, and medicine, in order to depict and visually analyze data-both from experiment and simulation. The goal of data visualization is to achieve a better understanding of data by intuitive, perceptually efficient and interactively steerable depictions of the data. For this specific data analysis methods are combined with visualization techniques that utilize modern computer graphics. Quantum physics, however, so far remained largely omitted as application area, in particular due to the high dimensionality of the phenomena. However, the situation is not hopeless; on the contrary, there are many ways to visualize quantum mechanical phenomena. In this paper, this will be demonstrated by means of visualizations of simulation data from quantum chemistry and high-harmonic generation.

The High-End-Visualization Workshop is a tentatively annual meeting of active researchers in the field of scientific visualization with application domain scientists, in particular from high-performance computing. Historically it originated from a creative workshop involving members of the Numerical Relativity Group at the Max-Planck-Institute for Gravitational Physics in Potsdam, Germany, and researchers of the Department for Scientific Visualization at the Zuse-Institute Berlin, Germany, as well as astrophysicists from the Institute for Astrophysics at the University of Innsbruck, Austria. Since its original birth in 2004 the workshop has grown its own momentum.

Common myth suggests synchronicity and unidirectionality of nuclear and electronic fluxes. Accurate quantum dynamics simulations of the vibrating model system, aligned H2+, confirm this rule, but with exceptional opposite behaviours during short periods in the attosecond time domain. The ratio of electronic versus nuclear fluxes increases systematically, from small to large amplitude nuclear motions. Visualization of the electronic and nuclear densities and flux densities reveals that this is due to broader dispersion of electronic wavepackets compared to nuclear ones. The accurate results validate an efficient general method for quantum calculations of the fluxes in terms of densities, not flux densities.

The final evolution of a binary black-hole system gives rise t o a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for non-spinning binaries with unequal masses have pointed out that kick velocities ∼ 175 km/s can be reached for a mass ratio ≃ 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymme try is provided by the spins. Using two independent methods we show that the merger of such binaries yields veloc iti s as large as ∼ 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbit al angular momentum.

Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger, and ring-down stages of black hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.

The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.

Binary black-hole systems with spins aligned with the orbital angular momentum are of special interest, as studies indicate that this configuration is preferred in nature. If the spins of the two bodies differ, there can be a prominent beaming of the gravitational radiation during the late plunge, causing a recoil of the final merged black hole. We perform an accurate and systematic study of recoil velocities from a sequence of equal-mass black holes whose spins are aligned with the orbital angular momentum, and whose individual spins range from a = +0.584 to -0.584. In this way we extend and refine the results of a previous study and arrive at a consistent maximum recoil of 448 +- 5 km/s for anti-aligned models as well as to a phenomenological expression for the recoil velocity as a function of spin ratio. This relation highlights a nonlinear behavior, not predicted by the PN estimates, and can be readily employed in astrophysical studies on the evolution of binary black holes in massive galaxies. An essential result of our analysis is the identification of different stages in the waveform, including a transient due to lack of an initial linear momentum in the initial data. Furthermore we are able to identify a pair of terms which are largely responsible for the kick, indicating that an accurate computation can be obtained from modes up to l=3. Finally, we provide accurate measures of the radiated energy and angular momentum, finding these to increase linearly with the spin ratio, and derive simple expressions for the final spin and the radiated angular momentum which can be easily implemented in N-body simulations of compact stellar systems. Our code is calibrated with strict convergence tests and we verify the correctness of our measurements by using multiple independent methods whenever possible.

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of general relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late-inspiral stage on orbits with very low eccentricity and evolve for $\ensuremath{\sim}1200M$ through $\ensuremath{\sim}7$ orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass $\ensuremath{\sim}14\text{ }\text{ }\mathrm{cycle}$ before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to post-Newtonian (PN) calculations for the earlier parts of the inspiral provides a combined waveform with less than one cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform, which can now be simulated numerically. Contour plots of SNR as a function of $z$ and $M$ show that adLIGO can achieve $\mathrm{SNR}\ensuremath{\gtrsim}10$ for some intermediate mass binary black holes (IMBBHs) out to $z\ensuremath{\sim}1$, and that LISA can see massive binary black holes (MBBHs) in the range $3\ifmmode\times\else\texttimes\fi{}{10}^{4}\ensuremath{\lesssim}M/{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{10}^{7}$ at $\mathrm{SNR}g100$ out to the earliest epochs of structure formation at $zg15$.

We apply recently developed techniques for simulations of moving black holes to study dynamics and radiation generation in the last few orbits and merger of a binary black hole system. Our analysis produces a consistent picture from the gravitational wave forms and dynamical black hole trajectories for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of 1% among the simulations for the last orbit, merger and ringdown, resulting in a final black hole with spin parameter a/m = 0.69. Consequently, we are confident that this part of our waveform result accurately represents the predictions from Einstein’s General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass non-spinning black holes. We also find good agreement at a level of roughly 10% for the radiation generated in the preceding few orbits.

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of 1% among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein's General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass nonspinning black holes. The simulations result in a final black hole with spin parameter $a/m=0.69$. We also find good agreement at a level of roughly 10% for the radiation generated in the preceding few orbits.

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.

Recent developments in numerical relativity have made it possible to follow reliably the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5:1 mass ratio, which is expected based on analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86-116 kilometers per second, and the most reliable runs give kicks between 86 and 97 kilometers per second. This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts z greater than 10, halos with masses less than 10(exp 9) M(sub SUN) will have difficulty retaining coalesced black holes after major mergers.

Recent developments in numerical relativity have made it possible to reliably follow the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5:1 mass ratio, which is expected on the basis of analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86-116 km s(-1), and the most reliable runs give kicks between 86 and 97 km s(-1). This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts z greater than or similar to 10, halos with masses <= 10(9) M-circle dot will have difficulty retaining coalesced black holes after major mergers.