There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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The Cosmological simulation code GADGET-2

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Modified Gravity and Cosmology

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Black Holes, White Dwarfs, and Neutron Stars

Star Deaths and the Formation of Compact Objects. Cold Equation of State Below Neutron Drip. White Dwarfs. Cooling of White Dwarfs. General Relativity. The Equilibrium and Stability of Fluid Configurations. Rotation and Magnetic Fields. Cold Equation of State Above Neutron Drip. Neutron Star Models: Masses and Radii. Pulsars. Cooling of Neutron Stars. Black Holes. Compact X--Ray Sources. Accretion Onto Black Holes. Accretion Onto Neutron Stars and White Dwarfs. Gravitational Radiation. Supermassive Stars and Black Holes. Stellar Collapse and Supernova Explosions. Appendixes. References. Author Index. Subject Index.

Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects

Black holes, white dwarfs and neutron stars. The physics of compact objects.

Many numerical codes now under development to solve Einstein's equations of general relativity in $(3+1)$-dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions.'' The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability.

Numerical integration of Einstein’s field equations

We present a model for Cygnus X-1, involving an accretion disk around a black hole, which can explain the observed X-ray spectrum from 8 to 500 keV. In particular we construct a detailed model of the structure of an accretion disk whose inner region is considerably hotter and geometrically thicker than previous disk models. The inner region of the disk is optically thin to absorption, is gas-pressure dominated, and yields, from first principles, electron temperatures of 10/sup 9/ K and ion temperatures 3--300 times hotter. The spectrum above 8 keV is produced by inverse Compton scattering of soft X-ray photons in the two-temperature inner region of the disk. This spectrum is computed by numerical integration of the Kompane'ets equation, modified to account for escape of photons from a region of finite (order unity) electron scattering optical depth. (AIP)

Stuart L. Shapiro

Papers

Black Holes, White Dwarfs, and Neutron Stars

Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects

Black holes, white dwarfs and neutron stars. The physics of compact objects.

Numerical integration of Einstein’s field equations

A two-temperature accretion disk model for Cygnus X-1: structure and spectrum.