Entropic Balance Theory and Variational Field Lagrangian Formalism: Tornadogenesis

2014 ◽  
Vol 71 (6) ◽  
pp. 2104-2113 ◽  
Author(s):  
Yoshi K. Sasaki
Keyword(s):  
Lagrange Multiplier ◽  
Lagrangian Density ◽  
Classical Mechanics ◽  
Dipole Source ◽  
Balance Theory ◽  
Lagrangian Formalism ◽  
Classical Systems ◽  
Modern Physics ◽  
Variational Formalism ◽  
The Many

Abstract The entropic balance theory has been applied with outstanding results to explain many important aspects of tornadic phenomena. The theory was originally developed in variational (probabilistic) field Lagrangian formalism, or in short, variational formalism, with Lagrangian density and action appropriate for supercell-storm and tornadic phenomena. The variational formalism is broadly used in in modern physics, not only in classical mechanics, with Lagrangian density and action designed for each physical problem properly. The Clebsch transformation (equation) was derived in the classical variational formalism but has not been used because of the unobservable and nonmeteorological Lagrange multiplier. The entropic balance condition is thus developed from the Clebsch transformation, changing the unobservable nonmeteorological Lagrange multiplier to observable meteorological rotational flow velocity with entropy and making it applicable to tornadic phenomena. Theoretical details of the entropic balance are presented such as the entropic right-hand rule, entropic dipole, source and sink, overshooting mechanism of hydrometeors against westerlies and the existence of single and multiple vortices and their relation to tornadogenesis. These results are in reasonable agreement with the many observations and data analysis publications. The Clebsch transformation and entropic balance are the new balance conditions, different from the known other balance conditions such as hydrostatic, (quasi-)geostrophic, cyclostrophic, Boussinesq, and anelastic balance. The variations in calculus of variations and in the classical variational formalism are hypothetical. However, this article suggests that the hypothetical variations could be physical, relating to quantum variations and their interaction with the classical systems.

scholarly journals Lagrangian formulation of Newtonian cosmology

2014 ◽  
Vol 36 (3) ◽  
Author(s):  
H.S. Vieira ◽  
V.B. Bezerra
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Classical Mechanics ◽  
Lagrangian Formulation ◽  
Einstein Equations ◽  
Lagrangian Formalism ◽  
Newtonian Cosmology

In this paper, we use the Lagrangian formalism of classical mechanics and some assumptions to obtain cosmological differential equations analogous to Friedmann and Einstein equations, obtained from the theory of general relativity. This method can be used to a universe constituted of incoherent matter, that is, the cosmologic substratum is comprised of dust.

scholarly journals The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Models ◽  
Conservation Laws ◽  
Rarefied Gas ◽  
Classical Mechanics ◽  
Gauss Theorem ◽  
The Media ◽  
Velocity Circulation ◽  
The Times ◽  
The Many ◽  
Definition Of

There are many experimental facts that currently cannot be described theoretically. A possible reason is bad mathematical models and algorithms for calculation, despite the many works in this area of research. The aim of this work is to clarificate the mathematical models of describing for rarefied gas and continuous mechanics and to study the errors that arise when we describe a rarefied gas through distribution function. Writing physical values conservation laws via delta functions, the same classical definition of physical values are obtained as in classical mechanics. Usually the derivation of conservation laws is based using the Ostrogradsky-Gauss theorem for a fixed volume without moving. The theorem is a consequence of the application of the integration in parts at the spatial case. In reality, in mechanics and physics gas and liquid move and not only along a forward path, but also rotate. Discarding the out of integral term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, this term is difficult to introduce into the differential equation. Therefore, to account for all components of the motion, it is proposed to use an integral formulation. Next question is the role of the discreteness of the description of the medium in the kinetic theory and the interaction of the discreteness and "continuity" of the media. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics arises due to the fact that the distances between molecules in a rarefied gas are finite, the times between collisions are finite, but on definition under calculating derivatives on time and space we deal with infinitely small values. We investigate it

GEOMETRIC STRUCTURES IN PHYSICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260026 ◽  
Author(s):  
L. J. BOYA
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Gauge Theories ◽  
Classical Mechanics ◽  
The Past ◽  
Modern Physics

Geometry and Physics developed independently, until the past twentieth century, where physicists realized geometry is rather flexible and can adapt itself to the needs and characteristics of modern physics. Besides the use of Riemannian manifolds to describe General Relativity, classical mechanics encounters symplectic geometry, not to speak of the bundle connection ingredient of modern gauge theories; even Quantum Mechanics, after the initial Hilbert space period, is seeking nowadays to adapt itself better to a geometrical interpretation, by imperatives of the path integral description and also to incorporate more clearly the symplectic aspects of its classical antecedent.

Electromagnetic Analog of 3D Autonomous ODEs with Quadratic Nonlinearities

2014 ◽  
Vol 24 (05) ◽  
pp. 1450070
Author(s):  
A. E. Botha
Keyword(s):  
General Class ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Lagrangian Formalism ◽  
Resonance Imaging ◽  
First Order ◽  
Gradient Fields ◽  
Quadratic Nonlinearities ◽  
Confinement Fusion ◽  
Constant Gradient

It is shown that the general class of three-dimensional first-order ordinary differential equations with quadratic nonlinearities can be physically interpreted as the dynamics of a charged particle in an electromagnetic field, with a constant gradient B-field. The general class of equations is derived within the Lagrangian formalism of classical mechanics. As an application of this interpretation a new way of experimentally realizing the Lorenz chaotic attractors is proposed. The actual construction of such systems could be facilitated by existing magnetic resonance imaging technology, which already makes use of constant gradient fields, and may find applications in areas such as nuclear medicine and magnetic confinement fusion devices.

Time as an Expanding Labyrinth of Information

KronoScope ◽  
2010 ◽  
Vol 10 (1-2) ◽  
pp. 64-76 ◽  
Author(s):  
Paul Halpern
Keyword(s):  
General Relativity ◽  
Classical Mechanics ◽  
Information Space ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
Cosmological Expansion ◽  
Expansion Of The Universe ◽  
The Many ◽  
The Universe ◽  
Dense State

AbstractWe propose a model of time in physics that combines the determinism of classical mechanics, the irreversibility of thermodynamics, and the ever-bifurcating strands of the Many Worlds Interpretation of quantum mechanics, by means of an expanding, labyrinthine information space. We speculate that the growth of this space is linked to the cosmological expansion of the universe from its initial dense state by means of a generalization of general relativity to include the information space.

scholarly journals On The Shoulders of Giants Science Must Be Protected From Itself not Perceived and Not Realized Planetary Crime of the Century About Changing The Currently Dominant Paradigm The QuantumRelativistic Subconscious Building A General Theory of Physical Interactions by Solving Their Own Mechanical Models of Faraday and Maxwell

2020 ◽  
pp. 1-5
Author(s):  
Vladislav Cherepennikov ◽  
Keyword(s):  
General Theory ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Correct Solution ◽  
Successful Development ◽  
Modern Physics ◽  
Mechanical Models ◽  
Physical Interactions ◽  
Dominant Paradigm

The monograph presents the evidence of outstanding thinkers - enlighteners of humanity and “great representatives of classical mechanics” about the failure and necessity of “changing the currently dominant paradigm” of the quantum-relativistic subconscious by solving their own mechanical models of Faraday and Maxwell – “the only conceivable guiding thread for the further successful development of modern physics”. Academician V. F. Mitkevich. “A Mature theory in which physical facts are explained mechanically will be constructed by those who, by questioning nature itself, will be able to find the only correct solution to the questions posed by mathematical theory.” James Clark Maxwell

scholarly journals The “Chemical Mechanics” of the Periodic Table

2018 ◽  
Author(s):  
Arnout Ceulemans ◽  
Pieter Thyssen
Keyword(s):  
Periodic Table ◽  
Research Question ◽  
Short Note ◽  
Classical Mechanics ◽  
Central Force ◽  
Wave Mechanics ◽  
French Mathematician ◽  
The Many ◽  
Academy Of Sciences ◽  
Structure Of Matter

In 1969, the centennial of Mendeleev’s discovery of the periodic table was commemorated by an international conference devoted to the periodicity and symmetry of the elementary structure of matter. The conference was held in the Vatican and brought together a selected audience of first-rate atomic and nuclear scientists. In 1971, the proceedings were published in a joint publication [1] of the Academy of Sciences of Torino and the National Academy in Rome. Among the many interesting contributions, the American cosmologist John Archibald Wheeler described a mind-boggling journey from “Mendeleev’s atom to the collapsing star.” According to Wheeler [2], Mendeleev was convinced that the atom is not “deathlike inactivity” but a dynamic reality and Mendeleev expressed his hope that the discovery of an orderly pattern would “hasten the advent of a true chemical mechanics.” This hope has certainly been met by Schrödinger’s wave mechanics, which provides an accurate tool to simulate the properties of the elements. However, the overall structure and symmetry of the periodic table continues to defy understanding. The quest for an effective universal force law at the basis of the mechanics of multi-electron atoms forms the topic of this contribution. The search for central force laws should start with Bertrand’s theorem in classical mechanics. In 1873, the French mathematician Joseph Louis Bertrand presented to the Paris Academy a short note [3, 4] on central force laws that give rise to stable orbits. For a proper understanding of the research question which Bertrand was addressing, we start from an everyday experiment. A mass attached to a string can easily be swept around in a perfectly circular orbit by simply pulling on the string. The only requirement is that the force should be fixed and directed toward the center of the orbit. If we want the mass to go faster, we simply have to pull harder.

scholarly journals Quantum cosmology of a Hořava–Lifshitz model coupled to radiation

2019 ◽  
Vol 28 (10) ◽  
pp. 1950130
Author(s):  
G. Oliveira-Neto ◽  
L. G. Martins ◽  
G. A. Monerat ◽  
E. V. Corrêa Silva
Keyword(s):  
Detailed Balance ◽  
Gravitational Theory ◽  
Expected Value ◽  
Scale Factor ◽  
Many Worlds ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Variational Formalism ◽  
The Many ◽  
Parameter Values

In the present paper, we canonically quantize a homogeneous and isotropic Hořava–Lifshitz cosmological model, with constant positive spatial sections and coupled to radiation. We consider the projectable version of that gravitational theory without the detailed balance condition. We use the Arnowitt–Deser–Misner (ADM) formalism to write the gravitational Hamiltonian of the model and the Schutz variational formalism to write the perfect fluid Hamiltonian. We find the Wheeler–DeWitt equation for the model, which depends on several parameters. We study the case in which parameter values are chosen so that the solutions to the Wheeler–DeWitt equation are bounded. Initially, we solve it using the Many Worlds interpretation. Using wave packets computed with the solutions to the Wheeler–DeWitt equation, we obtain the scalar factor expected value [Formula: see text]. We show that this quantity oscillates between finite maximum and minimum values and never vanishes. Such result indicates that the model is free from singularities at the quantum level. We reinforce this indication by showing that by subtracting one standard deviation unit from the expected value [Formula: see text], the latter remains positive. Then, we use the DeBroglie–Bohm interpretation. Initially, we compute the Bohm’s trajectories for the scale factor and show that they never vanish. Then, we show that each trajectory agrees with the corresponding [Formula: see text]. Finally, we compute the quantum potential, which helps understanding why the scale factor never vanishes.

Multi-body dynamics and electromechanics: From a differential-geometric point of view

2005 ◽  
Vol 219 (2) ◽  
pp. 147-158
Author(s):  
P Maißer
Keyword(s):  
Differential Geometry ◽  
Laws Of Nature ◽  
Classical Mechanics ◽  
Point Of View ◽  
Theory Of Relativity ◽  
Geometric Point ◽  
Modern Physics ◽  
Intimate Relation ◽  
Linear Induction Machines ◽  
Multi Body

Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations. The mathematical-geometric considerations in mechanics serve as a prototype for other physical theories. Consequently, developments in modern physics in turn have a feedback to mechanics in terms of its representation. The laws of nature can be expressed as differential equations. The fact that these equations can be solved by average computers has led most engineers and many mathematical physicists to neglect geometrical aspects for solving and better understanding their problems. The intimate relation between geometry and analysis led to the differential geometry, which is a valuable tool for a better understanding in many physical disciplines like classical mechanics, electrodynamics, and nowadays in mechatronics. It has been the development of the theory of relativity that revealed the paramount importance of the differential geometry. Many problems in research and development can be studied by differential-geometric methods. Modern non-linear control theories, for instance, are entirely based on the differential geometry. This paper addresses some aspects in mathematical modelling of multi-body and electromechanical systems. The motivation for this research arises from applications of linear induction machines in modern transport technologies.

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