Related papers: Closed Form Expressions for the Potentials and Acc…
We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\"odinger perturbation theory to show that, in…
We modify the recent analytic formula given by Allen and Casper for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate…
We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray…
A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model…
In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
A new method is developed which permits the reconstruction of the surface-density distribution in the galactic disk of finite radius from an arbitrary smooth distribution of the angular velocity via two simple quadratures. The existence of…
We establish a fine expansion for the geometric part of the Arthur-Selberg trace formula (as it was conjectured by Werner Hoffmann). For the general linear group, we deduce an expression for the contributions of regular by blocks unipotent…
There are many astrophysical scenarios where extreme mass ratio inspiral (EMRI) binaries can be surrounded by matter distribution. The distribution of mass can affect the dynamical properties (e.g. orbital frequency, average energy…
We construct a toric generalised K\"ahler structure on $\mathbb{C}P^2$ and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
The gravitational field of a massive, filamentary ring is considered. We provide an analytic expression for the gravitational potential and demonstrate that the exact gravitational potential and its gradient, thus the gravitational…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
Theoretical investigations are presented, and their results are discussed, of the laser acceleration of a single electron by a chirped pulse. Fields of the pulse are modeled by simple plane-wave oscillations and a $\cos^2$ envelope. The…
We present a theoretical and experimental analysis of circular-like orbits made by a marble rolling on a warped spandex fabric. We show that the mass of the fabric interior to the orbital path influences the motion of the marble in a…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
These notes were delivered as a series of NIMROD lectures at the Rutherford Appleton Laboratory by the author in February 1976 (RL-76-022). The purpose of these lectures was primarily two-fold: to discuss the classical theory of free point…
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
We derive a formula for the velocity distribution of an axially symmetric galaxy where the mass density is corrected using the mass formula from special relativity. We take some reasonable test mass densities and numerically compute the…
We study the possibility that galactic rotation curves can be explained by a gravitational potential that contains a linear term as well as a Newtonian one. This hypothesis, suggested by conformal gravity, does allow good fits to the…