相关论文: Representation of the gravitational potential of a…
We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…
Starting from an energy comprised of both a bulk term and a surface term, set in the space of special functions of bounded hessian, $SBH$, a relaxation problem in the context of second-order structured deformations was studied in…
We introduce a method to obtain the envelopes of eccentric orbits in axially symmetric potentials, $\Phi(R,z)$, endowed with $z$-symmetry of reflection. By making the transformation $z\rightarrow a+\sqrt{a^{2}+ z^{2}}$, with $a>0$, we…
We introduce a formalism to describe 2D-Potentials for 2D-matter (or charge) distributions with arbitrary elliptical symmetry including varying eccentricity and twisting of the iso-density curves. We use this approach to describe elliptical…
Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John's characterization of the unique ellipsoid of maximum volume contained in a convex body. The same idea applies to the…
A class of solutions of the gravitational field equations describing vacuum spacetimes outside rotating cylindrical sources is presented. A subclass of these solutions corresponds to the exterior gravitational fields of rotating cylindrical…
The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general…
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…
Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been…
We present a way to manipulate an electron trapped in a layered quantum dot based on near-threshold properties of one-body potentials. We show that potentials with a simple global parameter allows the manipulation of the wave function…
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…
Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even…
The explicit expression of ergotropy (a.k.a. available energy) of a classical system is known for the case when the system phase space density is continuous and with no plateaus. Here we provide the general expression of ergotropy that…
Based on density functional theory the influence of curvature on the depletion potential of a single big hard sphere immersed in a fluid of small hard spheres with packing fraction \eta_s either inside or outside of a hard spherical cavity…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
Relativistic dynamics of distributed mass and charge densities of the extended classical particle is discussed for arbitrary gravitational and electromagnetic fields. Vector geodesic relations for material space densities are consequences…
We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the…
The dynamics defined by a force field which is positively homogeneous of degree $-3$ can always be reduced, by simply constraining it. The dimension of the phase space is reduced by two dimensions, while it may only be reduced by one…
In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are…