In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly −1, a ratio that can be an independent test of the accuracy of a computed so...
Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial t...
Topological optimization uses two main optimization conditions aimed at achieving the maximum stiffness at minimum weight of the loaded object, while not exceeding the allowable stress. This process naturally creates complex structures with varying d...
Spiral galaxies are spinning, internally densified objects. The Virial Theorem explains galactic rotation curves via its linkage of the rotation rate to the gravitational self-potential (Ug) and the moment of inertia of oblate spheroids. We devise a...
Atmospheric climate science lacks the capacity to integrate thermodynamics with the gravitational potential of air in a classical quantum theory. To what extent can we identify Carnot’s ideal heat engine cycle in reversible isothermal and isent...
I propose a possible way to introduce the effect of temperature (defined through the virial theorem) into Einstein’s theory of general relativity. This requires the computation of a path integral on a ten-dimensional flat space in a four-dimens...
We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that resu...
Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, poi...
In the absence of work, the exchange of heat of a sample of matter corresponds to the change of its internal energy, given by the kinetic energy of random translational motion of all its constituent atoms or molecules relative to the center of mass o...
Several applications of quantum mechanics and information theory to chemical reactivity problems are presented with emphasis on equivalence of variational principles for the constrained minima of the system electronic energy and its kinetic energy co...
Over the past few decades, confined quantum systems have emerged to be a subject of considerable importance in physical, chemical and biological sciences. Under such stressed conditions, they display many fascinating and notable physical and chemical...
The total mass of a galaxy group, such as the Milky Way (MW) and the Andromeda Galaxy (M 31), is typically determined from the kinematics of satellites within their virial zones. Bahcall and Tremaine (1981) proposed the v2r estimator as an alternativ...
In this paper, we continue the study of the thermodynamics of fluid elements in isothermal turbulent self-gravitating systems, presented by molecular clouds. We build the model again on the hypothesis that, locally, the turbulent kinetic energy per f...
The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent m...
Based on noncommutative relations and the Dirac canonical dequantization scheme, I generalize the canonical Poisson bracket to a deformed Poisson bracket and develop a non-canonical formulation of the Poisson, Hamilton, and Lagrange equations in the...
In this paper, we theoretically investigate the stability of spin-wave solitons in Bose-Einstein condensates of repulsive magnons, confined by an inhomogeneous external magnetic field described by a Gaussian well. For this purpose, we use the quasi-o...
Gravity and electromagnetic interactions are the only fundamental physical interactions (outside the nuclear domain). In this work, we shall concentrate on Hamiltonians containing gravitational interaction, which according to general relativity must...
In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadroni...
We propose a reformulation of the mathematical formalism of many-electron quantum theory that rests entirely on the physical properties of the electronic system under investigation, rather than conventional mathematical assumption of Hermitian operat...
We apply Newtonian fractional-dimension gravity (NFDG), an alternative gravitational model, to some notable cases of galaxies with little or no dark matter. In the case of the ultra-diffuse galaxy AGC 114905, we show that NFDG methods can effectively...
Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years...
Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipatio...
Available inventories of baryonic mass in the universe are based largely on galactic data and empirical calculations made >20 years ago. Values falling below cosmological estimates underlie proposals that certain rarified gassy regions could have...
The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent “Quantal Newtonian” law (or differential virial theorem)....