Related papers: Closed Form Expressions for the Potentials and Acc…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both nonlinear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with…
We derive a simple, closed form expression for the potential of a thin exponential disk of stars interacting through gravitational potentials of the form $V(r)=-\beta /r+\gamma r/2$, the potential associated with fundamental sources in the…
A framework for premetric p-form electrodynamics is proposed. Independently of particular constitutive relations, the corresponding Maxwell equations are derived as a special case of stress theory in geometric continuum mechanics.…
Based on the generalized non-Markovian equations obtained earlier for a nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density [Markiv B.B., Omelyan I.P, Tokarchuk M.V., Condens. Matter Phys.,…
Context: The modelling of stationary galactic stellar populations can be performed using distribution functions. Aims: This paper aims to write explicit integrals of motion and distribution functions. Methods: We propose an analytic…
While the constant radial acceleration problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to a time parameter, has eluded…
We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…
Recent observations indicate that the universe's expansion has been accelerating of late. But recent theoretical work has highlighted the difficulty of squaring acceleration with the underlying assumptions of string theory, disfavoring most…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…
This letter derives closed-form expressions for the probability density function of the distance between two nodes located in heterogeneous concentric geometries, namely a disk or sphere and a surrounding annulus or spherical shell. Two…
Model of hard sphere system is important part of modern theories of liquids. Radial distribution function of hard sphere fluid represented in form of explicit analytical expression allows to obtain thermodynamic potentials in analytical…
Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears…
We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.
Recently we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each sub-unit…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
We generalize the treatment of the electronic spin degrees of freedom in density functional calculations to the case where the spin vector variables employed in the definition of the energy functional can vary in any direction in space. The…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…