Related papers: Spherical Potential Theory: Tools and Applications
We seek to compile a uniform set of basic capabilities and needs to maximize the yield of Solar System science with future Astrophysics assets while allowing those assets to achieve their Astrophysics priorities. Within considerations of…
Ellipsoids possess several beautiful properties associated with classical potential theory. Some of them are well known, and some have been forgotten. In this article we hope to bring a few of the "lost" pieces of classical mathematics back…
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…
The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of…
In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out.…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a…
In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of…
Accurate descriptions of reference systems are a central task in liquid-state theories for the study of more complex systems. Using scaled particle theory (SPT), we derive a fully analytical description of the thermodynamic properties of a…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\phi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the…
We discuss the physics potential of the solar neutrino experiments i) To explore the parameter space of neutrino mass and mixings; ii) To probe the physics of the Sun; iii) To explore nuclear physics of the neutrino-target interactions.…