Dynamical Friction in Gravitational Atoms

Due to superradiant instabilities, clouds of ultralight bosons can spontaneously grow around rotating black holes, creating so-called "gravitational atoms". In this work, we study their dynamical effects on binary systems. We first focus on open orbits, showing that the presence of a cloud can increase the cross section for the dynamical capture of a compact object by more than an order of magnitude. We then consider closed orbits and demonstrate that the backreaction of the cloud's ionization on the orbital motion should be identified as dynamical friction. Finally, we study for the first time eccentric and inclined orbits. We find that, while ionization quickly circularizes the binary, it barely affects the inclination angle. These results enable a more realistic description of the dynamics of gravitational atoms in binaries and pave the way for dedicated searches with future gravitational wave detectors.Comment: 36 pages, 13 figure

Random redundant storage in disk arrays: Complexity of retrieval problems

Random redundant data storage strategies have proven to be a good choice for efficient data storage in multimedia servers. These strategies lead to a retrieval problem in which it is decided for each requested data block which disk to use for its retrieval. In this paper, we give a complexity classification of retrieval problems for random redundant storage

Superradiance: Axionic Couplings and Plasma Effects

Spinning black holes can transfer a significant fraction of their energy to ultralight bosonic fields via superradiance, condensing them in a co-rotating structure or "cloud". This mechanism turns black holes into powerful particle detectors for bosons with extremely feeble interactions. To explore its full potential, the couplings between such particles and the Maxwell field in the presence of plasma need to be understood. In this work, we study these couplings using numerical relativity. We first focus on the coupled axion-Maxwell system evolving on a black hole background. By taking into account the axionic coupling concurrently with the growth of the cloud, we observe for the first time that a new stage emerges: that of a stationary state where a constant flux of electromagnetic waves is fed by superradiance, for which we find accurate analytical estimates. Moreover, we show that the existence of electromagnetic instabilities in the presence of plasma is entirely controlled by the axionic coupling; even for dense plasmas, an instability is triggered for high enough couplings.Comment: 32 pages, 23 figure

Disks, spikes, and clouds: distinguishing environmental effects on BBH gravitational waveforms

Future gravitational wave interferometers such as LISA, Taiji, DECIGO, and TianQin, will enable precision studies of the environment surrounding black holes. In this paper, we study intermediate and extreme mass ratio binary black hole inspirals, and consider three possible environments surrounding the primary black hole: accretion disks, dark matter spikes, and clouds of ultra-light scalar fields, also known as gravitational atoms. We present a Bayesian analysis of the detectability and measurability of these three environments. Focusing for concreteness on the case of a detection with LISA, we show that the characteristic imprint they leave on the gravitational waveform would allow us to identify the environment that generated the signal, and to accurately reconstruct its model parameters.Comment: 8 pages, 4 figures, 2 tables plus appendice

On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the limitations of standard techniques and allow for the derivation of structural properties. We introduce this technique by application to a processor sharing queue with impatient customers that can retry if they renege. We are interested in structural properties of the value function of the system as a function of the arrival rate

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club

Orthogonal schedules in single round robin tournaments

A measure for the flexibility of a Home-Away Pattern set (HAP-set) is the width. The width of a HAP-set equals the size of the largest set of schedules compatible with the HAP-set, for which no match is scheduled in the same round in any two schedules. We prove lower and upper bounds on the width, and identify HAP-sets with largest possible width when the number of teams is a power of 2

Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure

Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components