Relativistic Effects in Extreme Mass Ratio Gravitational Wave Bursts

Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for future space-borne gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). These events are characterized by long-period, nearly-radial orbits of compact objects around a central massive black hole. The gravitational radiation emitted during such events consists of a short burst, corresponding to periapse passage, followed by a longer, silent interval. In this paper we investigate the impact of including relativistic corrections to the description of the compact object's trajectory via a geodesic treatment, as well as including higher-order multipole corrections in the waveform calculation. The degree to which the relativistic corrections are important depends on the EMRB's orbital parameters. We find that relativistic EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately half of the events in our astrophysical model. The relativistic corrections tend to significantly change the waveform amplitude and phase relative to a Newtonian description, although some of this dephasing could be mimicked by parameter errors. The dephasing over several bursts could be of particular importance not only to gravitational wave detection, but also to parameter estimation, since it is highly correlated to the spin of the massive black hole. Consequently, we postulate that if a relativistic EMRB is detected, such dephasing might be used to probe the relativistic character of the massive black hole and obtain information about its spin.Comment: 13 pages, 8 figures, 2 tables. Replaced with version accepted for publication in the Ap.

Cutoff for the Ising model on the lattice

Introduced in 1963, Glauber dynamics is one of the most practiced and extensively studied methods for sampling the Ising model on lattices. It is well known that at high temperatures, the time it takes this chain to mix in $L^1$ on a system of size $n$ is $O(\log n)$. Whether in this regime there is cutoff, i.e. a sharp transition in the $L^1$-convergence to equilibrium, is a fundamental open problem: If so, as conjectured by Peres, it would imply that mixing occurs abruptly at $(c+o(1))\log n$ for some fixed $c>0$, thus providing a rigorous stopping rule for this MCMC sampler. However, obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple Markov chains. Already for the one-dimensional Ising model, showing cutoff is a longstanding open problem. We settle the above by establishing cutoff and its location at the high temperature regime of the Ising model on the lattice with periodic boundary conditions. Our results hold for any dimension and at any temperature where there is strong spatial mixing: For $\Z^2$ this carries all the way to the critical temperature. Specifically, for fixed $d\geq 1$, the continuous-time Glauber dynamics for the Ising model on $(\Z/n\Z)^d$ with periodic boundary conditions has cutoff at $(d/2\lambda_\infty)\log n$, where $\lambda_\infty$ is the spectral gap of the dynamics on the infinite-volume lattice. To our knowledge, this is the first time where cutoff is shown for a Markov chain where even understanding its stationary distribution is limited. The proof hinges on a new technique for translating $L^1$ to $L^2$ mixing which enables the application of log-Sobolev inequalities. The technique is general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure

Pathophysiological changes in inner hair cell ribbon synapses in the ageing mammalian cochlea

Mammalian cochlear inner hair cells (IHCs) are specialized sensory receptors able to provide dynamic coding of sound signals. This ability is largely conferred by their ribbon synapses, which tether a large number of vesicles at the IHC's presynaptic active zones, allowing high rates of sustained synaptic transmission onto the afferent fibres. How the physiological and morphological properties of ribbon synapses change with age remains largely unknown. Here, we have investigated the biophysical and morphological properties of IHC ribbon synapses in the ageing cochlea (9–12 kHz region) of four mouse strains commonly used in hearing research: early‐onset progressive hearing loss (C57BL/6J and C57BL/6NTac) and ‘good hearing’ strains (C57BL/6NTacCdh23+ and C3H/HeJ). We found that with age, both modiolar and pillar sides of the IHC exhibited a loss of ribbons, but there was an increased volume of those that remained. These morphological changes, which only occurred after 6 months of age, were correlated with the level of hearing loss in the different mouse strains, being most severe for C57BL/6NTac and C57BL/6J, less so for C57BL/6NTacCdh23+ and absent for C3H/HeJ strains. Despite the age‐related reduction in ribbon number in three of the four strains, the size and kinetics of Ca2+‐dependent exocytosis, as well as the replenishment of synaptic vesicles, in IHCs was not affected. The degree of vesicle release at the fewer, but larger, individual remaining ribbon synapses colocalized with the post‐synaptic afferent terminals is likely to increase, indicating the presence of a previously unknown degree of functional compensation in the ageing mouse cochlea

Evolution and instabilities of disks harboring super massive black holes

The bar formation is still an open problem in modern astrophysics. In this paper we present numerical simulation performed with the aim of analyzing the growth of the bar instability inside stellar-gaseous disks, where the star formation is triggered, and a central black hole is present. The aim of this paper is to point out the impact of such a central massive black hole on the growth of the bar. We use N-body-SPH simulations of the same isolated disk-to-halo mass systems harboring black holes with different initial masses and different energy feedback on the surrounding gas. We compare the results of these simulations with the one of the same disk without black hole in its center. We make the same comparison (disk with and without black hole) for a stellar disk in a fully cosmological scenario. A stellar bar, lasting 10 Gyrs, is present in all our simulations. The central black hole mass has in general a mild effect on the ellipticity of the bar but it is never able to destroy it. The black holes grow in different way according their initial mass and their feedback efficiency, the final values of the velocity dispersions and of the black hole masses are near to the phenomenological constraints.Comment: 10 pages, 8 figures, accepted for pubblication in "Astrophysics and Space Science

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

Timing interactions in social simulations: The voter model

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table

Cluster Approximation for the Contact Process

The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are not correlated. This assumption yields a first order phase transition from an active state to the adsorbing state. Despite the apparent failure of this approximation in describing the critical behavior, our approach provides an accurate description of the steady state properties for a significant range of desorption rates. Moreover, the resulting critical exponents are closer to the simulation values in comparison with site mean-field theory.Comment: 9 pages, Latex format, 2 postscript figure

Extreme mass ratio inspiral rates: dependence on the massive black hole mass

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.Comment: Accepted to CQG, special LISA issu

Ancient Maya Regional Settlement and Inter-Site Analysis: The 2013 West-Central Belize LiDAR Survey

During April and May 2013, a total of 1057 km2 of LiDAR was flown by NCALM for a consortium of archaeologists working in West-central Belize, making this the largest surveyed area within the Mayan lowlands. Encompassing the Belize Valley and the Vaca Plateau, West-central Belize is one of the most actively researched parts of the Maya lowlands; however, until this effort, no comprehensive survey connecting all settlement had been conducted. Archaeological projects have investigated at least 18 different sites within this region. Thus, a large body of archaeological research provides both the temporal and spatial parameters for the varied ancient Maya centers that once occupied this area; importantly, these data can be used to help interpret the collected LiDAR data. The goal of the 2013 LiDAR campaign was to gain information on the distribution of ancient Maya settlement and sites on the landscape and, particularly, to determine how the landscape was used between known centers. The data that were acquired through the 2013 LiDAR campaign have significance for interpreting both the composition and limits of ancient Maya political units. This paper presents the initial results of these new data and suggests a developmental model for ancient Maya polities