Diffusion and Mixing in Globular Clusters

Collisional relaxation describes the stochastic process with which a self-gravitating system near equilibrium evolves in phase-space due to the fluctuating gravitational field of the system. The characteristic timescale of this process is called the relaxation time. In this paper, we highlight the difference between two measures of the relaxation time in globular clusters: (1) the diffusion time with which the isolating integrals of motion (i.e., energy E and angular momentum magnitude L) of individual stars change stochastically and (2) the asymptotic timescale required for a family of orbits to mix in the cluster. More specifically, the former corresponds to the instantaneous rate of change of a star's E or L, while the latter corresponds to the timescale for the stars to statistically forget their initial conditions. We show that the diffusion timescales of E and L vary systematically around the commonly used half-mass relaxation time in different regions of the cluster by a factor of ∼10 and ∼100, respectively, for more than 20% of the stars. We define the mixedness of an orbital family at any given time as the correlation coefficient between its E or L probability distribution functions and those of the whole cluster. Using Monte Carlo simulations, we find that mixedness converges asymptotically exponentially with a decay timescale that is ∼10 times the half-mass relaxation time. © 2018. The American Astronomical Society. All rights reserved.

DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

The dynamical formation of stellar-mass black hole-black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M-tot roughly as proportional to M-tot beta, with beta greater than or similar to 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO's greater sensitivity to massive black hole binaries with M-tot less than or similar to 80 M-circle dot We find that for power-law BH mass functions dN/dM proportional to M-alpha with alpha <= 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about similar to 5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries

Detecting Triple Systems with Gravitational Wave Observations

The Laser Interferometer Gravitational Wave Observatory (LIGO) has recently discovered gravitational waves (GWs) emitted by merging black hole binaries. We examine whether future GW detections may identify triple companions of merging binaries. Such a triple companion causes variations in the GW signal due to: (1) the varying path length along the line of sight during the orbit around the center of mass; (2) relativistic beaming, Doppler, and gravitational redshift; (3) the variation of the light-travel time in the gravitational field of the triple companion; and (4) secular variations of the orbital elements. We find that the prospects for detecting a triple companion are the highest for low-mass compact object binaries which spend the longest time in the LIGO frequency band. In particular, for merging neutron star binaries, LIGO may detect a white dwarf or M-dwarf perturber at a signal-to-noise ratio of 8, if it is within 0.4 R⊙ distance from the binary and the system is within a distance of 100 Mpc. Stellar mass (supermassive) black hole perturbers may be detected at a factor 5 × (103×) larger separations. Such pertubers in orbit around a merging binary emit GWs at frequencies above 1 mHz detectable by the Laser Interferometer Space Antenna in coincidence

Finite Size Scaling of Domain Chaos

Numerical studies of the domain chaos state in a model of rotating Rayleigh-Benard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the predicted divergence near onset

Block time step storage scheme for astrophysical N-body simulations

Astrophysical research in recent decades has made significant progress thanks to the availability of various N-body simulation techniques. With the rapid development of high-performance computing technologies, modern simulations have been able to use the computing power of massively parallel clusters with more than 105 GPU cores. While unprecedented accuracy and dynamical scales have been achieved, the enormous amount of data being generated continuously poses great challenges for the subsequent procedures of data analysis and archiving. In this paper, we propose an adaptive storage scheme for simulation data, inspired by the block time step (BTS) integration scheme found in a number of direct N-body integrators available nowadays, as an urgent response to these challenges. The proposed scheme, namely, the BTS storage scheme, works by minimizing the data redundancy by assigning individual output frequencies to the data as required by the researcher. As demonstrated by benchmarks, the proposed scheme is applicable to a wide variety of simulations. Despite the main focus of developing a solution for direct N-body simulation data, the methodology is transferable for grid-based or tree-based simulations where hierarchical time stepping is used.FWN – Publicaties zonder aanstelling Universiteit Leide

Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday. Final versio

Whole-Genome Sequencing of Sake Yeast Saccharomyces cerevisiae Kyokai no. 7

The term ‘sake yeast’ is generally used to indicate the Saccharomyces cerevisiae strains that possess characteristics distinct from others including the laboratory strain S288C and are well suited for sake brewery. Here, we report the draft whole-genome shotgun sequence of a commonly used diploid sake yeast strain, Kyokai no. 7 (K7). The assembled sequence of K7 was nearly identical to that of the S288C, except for several subtelomeric polymorphisms and two large inversions in K7. A survey of heterozygous bases between the homologous chromosomes revealed the presence of mosaic-like uneven distribution of heterozygosity in K7. The distribution patterns appeared to have resulted from repeated losses of heterozygosity in the ancestral lineage of K7. Analysis of genes revealed the presence of both K7-acquired and K7-lost genes, in addition to numerous others with segmentations and terminal discrepancies in comparison with those of S288C. The distribution of Ty element also largely differed in the two strains. Interestingly, two regions in chromosomes I and VII of S288C have apparently been replaced by Ty elements in K7. Sequence comparisons suggest that these gene conversions were caused by cDNA-mediated recombination of Ty elements. The present study advances our understanding of the functional and evolutionary genomics of the sake yeast

Wetting theory for small droplets on textured solid surfaces

This work is supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2016M3D1A1900038). N.M.P. is supported by the European Research Council (ERC StG Ideas 2011 BIHSNAM n. 279985, ERC PoC 2015 SILKENE nr. 693670), by the European Commission under the Graphene Flagship (WP14 Polymer Composites, no. 696656). N.M.P. thanks Profs. Della Volpe and Siboni for useful comments on the paper