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The population of binary black hole (BBH) mergers observed by the LIGO-Virgo-KAGRA (LVK) collaboration offers a window into the cosmic evolution of compact binaries and their formation. We employ the semi-analytic population-synthesis code…
Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of…
To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed…
The growing population of binary black holes (BBHs) observed by gravitational wave detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytic codes {\sc…
A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers -- hence the name, from the acronym…
Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity)…
We present a new pseudo-spectral code for the simulation of evolution systems that are second order in space. We test this code by evolving a non-linear scalar wave equation. These non-linear waves can be stably evolved using very simple…
We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…
In 1999, Lawrence and Zagier expressed the Witten-Reshetikhin-Turaev (WRT) invariant of the Poincar\'e homology sphere as the limiting value of the Eichler integral of a weight 3/2 modular form. Habiro's construction of the unified WRT…
We discuss the gravitational wave emission and the orbital evolution of a hierarchical triple system composed of an inner binary black hole (BBH) and an outer tertiary. Depending on the kick velocity at the merger, the merged BBH could…
The trans-Neptunian scattered disk exhibits unexpected dynamical structure, ranging from an extended dispersion of perihelion distance to a clustered distribution in orbital angles. Self-gravitational modulation of the scattered disk has…
The higher Bruhat orders $\mathcal{B}(n,k)$ were introduced by Manin-Schechtman to study discriminantal hyperplane arrangements and subsequently studied by Ziegler, who connected $\mathcal{B}(n,k)$ to oriented matroids. In this paper, we…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
The observed binary black hole (BBH) mergers indicate a large Galactic progenitor population continuously evolving from large orbital separations and low gravitational wave (GW) frequencies to the final merger phase. We investigate the…
The Volterra lattice is a well-known integrable family that is also a special class of replicator dynamics and whose members can be put in one-to-one correspondence with the directed cycle graphs. In this paper, we study a variation of the…
In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group $W$ afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced from linear…
The individual component spins of binary black holes (BBHs) are difficult to resolve using gravitational-wave observations but carry key signatures of the processes shaping their formation and evolution. Recent analyses have found…
The dynamical assembly of binary black holes (BBHs) in dense star clusters (SCs) is one of the most promising pathways for producing observable gravitational wave (GW) sources, however several other formation scenarios likely operate as…
Black holes (BH) are among the most unusual and exciting physical objects. Besides being simultaneously Relativistic and quantum mechanical objects, which allows the discovery and/or tests of new physics, BHs also present a lack of…
In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov…