Особенности применения теоремы вириала для магнитных систем с квазибессиловыми обмотками

The article shows that in a magnetic system with a thin-walled balanced winding close to a force-free one, a significant increase in the parameter θ=WM γ/M σМ , is possible, which, according to the virial theorem, characterizes the ratio of the energy of the magnetic system WM to the weight of equipment with a material density γ, where under the action of electromagnetic forces there appears a mechanical stress σМ. In a quasi-force-free magnetic system, the main part of the winding is in a state of local equilibrium, and only a relatively small part of the equipment is subject to stress. This part determines the weight of the entire system, and this weight can be minimized. The configurations of balanced thin-walled windings are developed, at the boundaries two boundary conditions are fulfilled simultaneously - the absence of the induction component normal to the boundary and the constancy of the product of induction and radius. The authors consider an example of a system consisting of a main part - a sequence of balanced "transverse" modules in the form of flat discs and end parts, consisting of a combination of "transverse" modules and "longitudinal" ones, having the form of rings elongated along the axis with balanced end parts. It is shown that in the system under consideration, the characteristic dimensionless parameter θ with an unlimited increase in the number of elements of the main part can reach a value of about 24, and when the number of these elements changes within 20 - 40, it changes from 6 to 9.

Erratum: Why is the ground state electron configuration for Lithium 1s(2)2s ?

For the variational calculation involving the 1s22s state, we inadvertently filed energy contributions into the wrong categories, with the result that the Virial Theorem appeared to be violated. The overall calculation of the energy was done correctly, and appropriate assignment of the different energy contributions now confirms that the Virial Theorem is obeyed. Obviously, our conclusions are unchanged.

CONSEQUENCES FROM THE ENERGY OF THE DIPOLE OR THE RATIONALE FOR THE IDEA OF NIKOLA TESLA

According to the virial theorem, a dipole has a small total energy at infinite negative potential energy and infinite positive kinetic energy, see [1] §10. Nikola Tesla was able to realize this energy in the car he built. The fundamental difficulties for creating a machine without an engine on gasoline energy have been overcome. But the experimental studies of Nikola Tesla were much ahead of the existing technologies, and according to my calculations, the breakdown voltage, for example, porcelain should be made orders of magnitude higher. Nikola Tesla could create a voltage of a billion volts, and according to modern data, the maximum voltage is a million volts. Moreover, it is necessary to use towers of great height to avoid breakdown. If we calculate the force created by the potential of the dipole and equate it with the force of attraction, then we will receive compensation for the gravitational field of the Earth.

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

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, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius’ virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law’s evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.

Towards B-Spline Atomic Structure Calculations

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 method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties

Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. In action mechanics, expressing the entropy of ideal gases as a capacity factor for sensible heat or enthalpy plus the configurational work to sustain the relative translational, rotational and vibrational action yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia and vibrational frequencies. Understanding how Clausius’ virial theorem balances the internal kinetic energy with field potential energy justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the evolutionary nature of the second law of thermodynamics. The ease of performing these operations is illustrated by three important chemical gas phase reactions, the reversible dissociation of the hydrogen molecules, lysis of water to hydrogen and oxygen and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work to overcome molecular interactions plus the configurational internal work of negative Gibbs energy as a function of volume or pressure may provide a practical guide for managing risk in industrial processes and climate change at the global scale.

Virial theorem in scalar tensor fourth order gravity

In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. $$f(R,\phi )+\omega (\phi )\,\phi _{;\alpha }\,\phi ^{;\alpha }$$ f ( R , ϕ ) + ω ( ϕ ) ϕ ; α ϕ ; α in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.

Analysis of Multipolar Linear Paul Traps for Ion–Atom Ultracold Collision Experiments

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 result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.