We present a two-dimensional grid-based hydrodynamic simulation of a thin, viscous, locally isothermal corotating disk orbiting an equal-mass Newtonian binary point mass on a fixed circular orbit. We study the structure of the disk aftermultiple viscous times. The binarymaintains a central hole in the viscously relaxed diskwith radius equal to about twice the binary semimajor axis. Disk surface...

The number of domino tilings of the 2n× 2n square with a centered hole of size 2m×2m, a figure known as the holey square and denoted H(m, n), was conjectured by Edward Early to be 2n−m(2km,n + 1) . Although the conjecture has remained unsolved until now, specific cases were known, for example see [4]. In this paper, we answer the general conjecture in the affirmative, primarily via a theorem ab...

Quasi-static wedging of three-point contacts is investigated, wherein the concepts of virtual and redundant wedging due to a resultant force falling into a friction cone are proposed. We consider the fully-started case of a square peg and hole consisting of two point-surface contacts and one line-line contact. An analysis of the wedging diagram for this highly constrained configuration is carri...

Studies of one-and two-hole states in the 2D t-J model via series expansions Abstract We study one and two hole properties of the t-J model at half-filling on the square lattice using series expansion methods at T = 0. The dispersion curve for one hole excitations is calculated and found to be qualitatively similar to that obtained by other methods, but the bandwidth for small t/J is some 20% l...

Binary black hole systems with spins aligned with the orbital angular momentum are of special interest, as they may be the preferred end state of the inspiral of generic supermassive binary black hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins aligned with the orbital angular momentum but otherwise arb...

In the standard viewpoint, the temperature of a stationary black hole is proportional to its surface gravity. This is a semiclassical result and the quantum gravity effects are not taken into consideration. This research explores a unified expression for the black hole temperatures in the sense of a generalized uncertainty principle (GUP). Our argument is based on a heuristic analysis of a part...