Explosion as a phase transition due to the change of the gradient symmetry of the distortion tensor.

Mapping Intimacies ◽

10.21203/rs.3.rs-216069/v1 ◽

2021 ◽

Author(s):

Alexander Braginsky

Keyword(s):

Phase Transition ◽

Elastic Medium ◽

Continuous Medium ◽

Equations Of State ◽

Fundamental Interaction ◽

Temperature Plasma ◽

Linear Defects ◽

Critical Stresses ◽

Distortion Tensor ◽

Conjugate Stress

Abstract It is shown that the destruction of a continuous elastic medium is a phase transition associated with a change in the gradient symmetry of the equations of state for the distortion tensor. The equations of state for the distortion tensor, as a compensating field of the minimal fundamental interaction, are derived from the action minimum. In a continuous elastic medium, the distortion tensor is proportional to the conjugate stress tensor. The continuous medium is destroyed at critical stresses or pressures. At the same time, the vortex tension of the distortion tensor penetrates into it and the elasticity disappears. As a result of this phase transition, linear defects and cracks are formed in solids state, and high-temperature plasma occurs in the gas and an explosion occurs. It is shown that the explosion and lightning are the same phase transition, which is caused by the occurrence of a critical vortex tension of the distortion tensor.

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The minimal interaction induced by the translation subgroup has a gap and possible relates to the strong fundamental interaction.

10.21203/rs.3.rs-216905/v1 ◽

2021 ◽

Author(s):

Alexander Braginsky

Keyword(s):

Continuous Medium ◽

Equations Of State ◽

Fundamental Interaction ◽

Phonon Interaction ◽

Symmetric State ◽

Electron Phonon Interaction ◽

Interaction Field ◽

Distortion Tensor ◽

First Time ◽

Translation Subgroup

Abstract The paper investigates the low-symmetric state of the compensating field of the distortion tensor and proves that there is a gap in this state. It is shown that the distortion tensor is the compensating field of the minimal interaction induced by the translation subgroup. On the example of electron pairing in a Cooper pair it was proved that the distortion tensor is responsible for the electron-phonon interaction. In this paper, for the first time, an exact wave solution for sound pressure in a continuous medium is obtained from the equations of state for the distortion tensor. It is shown that the sound is described as "massive" wave of the distortion tensor, the spectrum of which has the minimal frequency, which corresponds to a gap. The presence of a gap in the low-symmetric state gives grounds to believe that the distortion tensor, as a compensating interaction field, describes a strong fundamental interaction. As it is known, the description of the gap in the strong fundamental interaction is declared a Millennium problem by the Clay Mathematical Institute (CMI).

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The QCD Phase-Diagram Obtained from the NJL and the Extended-NJL Models for Quark and Hadron Phases

International Journal of Modern Physics Conference Series ◽

10.1142/s201019451760059x ◽

2017 ◽

Vol 45 ◽

pp. 1760059

Author(s):

Clebson A. Graeff ◽

Débora P. Menezes

Keyword(s):

Phase Transition ◽

Phase Diagram ◽

Equations Of State ◽

Original Formulation ◽

Qcd Phase Diagram ◽

Hadron Phase ◽

Vector Interaction ◽

Njl Model ◽

Quark Phase

We analyse the hadron/quark phase transition described by the Nambu-Jona-Lasinio (NJL) model [quark phase] and the extended Nambu-Jona-Lasinio model (eNJL) [hadron phase]. While the original formulation of the NJL model is not capable of describing hadronic properties due to its lack of confinement, it can be extended with a scalar-vector interaction so it exhibits this property, the so-called eNJL model. As part of this analysis, we obtain the equations of state within the SU(2) versions of both models for the hadron and the quark phases and determine the binodal surface.

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A New Lattice Boltzmann Model for Phase Transition Process

Volume 13: New Developments in Simulation Methods and Software for Engineering Applications; Safety Engineering, Risk Analysis and Reliability Methods; Transportation Systems ◽

10.1115/imece2009-10961 ◽

2009 ◽

Author(s):

Longjian Li ◽

Jianbang Zeng ◽

Quan Liao ◽

Wenzhi Cui

Keyword(s):

Phase Transition ◽

Lattice Boltzmann ◽

Equations Of State ◽

Density Ratio ◽

Transition Process ◽

Lattice Boltzmann Model ◽

New Model ◽

Phase Transition Process ◽

Simulation Results ◽

Boltzmann Model

A new lattice Boltzmann model, which is based on Shan-Chen (SC) model, is proposed to describe liquid-vapor phase transitions. The new model is validated through simulation of the one-component phase transition process. Compared with the simulation results of van der Waals fluid and the Maxwell equal-area construction, the results of new model are closer to the analytical solutions than those of SC model and Zhang model. Since the range of temperature and the maximum density ratio are increased, and the value of maximum spurious current is between those of SC and Zhang models, it is believed that this new model has better stability than SC and Zhang models. Therefore, the application scope of this new model is expanded. According to the principle of corresponding states in Engineering Thermodynamics, the simulations of water and ammonia phase transition process are implemented by using this new model with different equations of state. Compared to the experimental data of water and ammonia, the results show that the Peng-Robinson equation of state is more suitable to describe the water, ammonia and other substances phase transition process. Therefore, these simulation results have great significance for the real engineering applications.

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Prediction of 10-fold coordinated TiO2 and SiO2 structures at multimegabar pressures

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1500604112 ◽

2015 ◽

Vol 112 (22) ◽

pp. 6898-6901 ◽

Cited By ~ 32

Author(s):

Matthew J. Lyle ◽

Chris J. Pickard ◽

Richard J. Needs

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Electronic Properties ◽

First Principles ◽

Pressure Range ◽

Extrasolar Planets ◽

Equations Of State ◽

Space Group ◽

P Type ◽

Pressure Phase

We predict by first-principles methods a phase transition in TiO2 at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated structure with space group I4/mmm. This is the first report, to our knowledge, of the pressure-induced phase transition to the I4/mmm structure among all dioxide compounds. The I4/mmm structure was found to be up to 3.3% denser across all pressures investigated. Significant differences were found in the electronic properties of the two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implications of our findings were extended to SiO2, and an analogous Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, which are well-established models for the phase transitions in other AX2 compounds, including SiO2. As in TiO2, the transition to I4/mmm corresponds to the metallization of SiO2. This transformation is in the pressure range reached in the interiors of recently discovered extrasolar planets and calls for a reformulation of the equations of state used to model them.

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Phase Transitions

An Introduction to Statistical Mechanics and Thermodynamics ◽

10.1093/oso/9780198853237.003.0017 ◽

2019 ◽

pp. 205-222

Author(s):

Robert H. Swendsen

Keyword(s):

Phase Transition ◽

Free Energy ◽

Phase Transitions ◽

Helmholtz Free Energy ◽

Equations Of State ◽

Van Der Waals ◽

Ideal Gas ◽

Phase Rule ◽

Clapeyron Equation ◽

Maxwell Construction

Phase transitions are introduced using the van der Waals gas as an example. The equations of state are derived from the Helmholtz free energy of the ideal gas. The behavior of this model is analyzed, and an instability leads to a liquid-gas phase transition. The Maxwell construction for the pressure at which a phase transition occurs is derived. The effect of phase transition on the Gibbs free energy and Helmholtz free energy is shown. Latent heat is defined, and the Clausius–Clapeyron equation is derived. Gibbs' phase rule is derived and illustrated.

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Electrical properties, equations of state and phase transition in solid C 60 at high pressure

Chinese Physics ◽

10.1088/1009-1963/9/9/008 ◽

2000 ◽

Vol 9 (9) ◽

pp. 676-679 ◽

Cited By ~ 2

Author(s):

Bao Zhong-xing ◽

V H Schmidt ◽

N S Dalal ◽

C S Tu ◽

N J Pinto ◽

...

Keyword(s):

Phase Transition ◽

High Pressure ◽

Electrical Properties ◽

Equations Of State

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A general existence result for isothermal two-phase flows with phase transition

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891619500206 ◽

2019 ◽

Vol 16 (04) ◽

pp. 595-637

Author(s):

Maren Hantke ◽

Ferdinand Thein

Keyword(s):

Phase Transition ◽

Euler Equations ◽

Equations Of State ◽

Linear Equations ◽

Two Phase Flows ◽

Kinetic Relation ◽

Two Phase ◽

Uniqueness Results ◽

Wide Range ◽

Isothermal Euler Equations

Liquid–vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in [M. Hantke, W. Dreyer and G. Warnecke, Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition, Quart. Appl. Math. 71(3) (2013) 509–540]. This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of this work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and cavitation are discussed.

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