• Previous Article
    Bilinear equations in Hilbert space driven by paths of low regularity
  • DCDS-B Home
  • This Issue
  • Next Article
    Extremum estimates of the $ L^1 $-norm of weights for eigenvalue problems of vibrating string equations based on critical equations
doi: 10.3934/dcdsb.2020350

Topological phase transition III: Solar surface eruptions and sunspots

1. 

Department of Mathematics, Sichuan University, Chengdu, China

2. 

Department of Mathematics, Indiana University, Bloomington, IN 47405, USA

* Corresponding author: Shouhong Wang

Received  November 2019 Revised  October 2020 Published  November 2020

Fund Project: The authors are grateful for the referee's insightful comments. The work was supported in part by the US National Science Foundation (NSF), the Office of Naval Research (ONR), and by the Chinese National Science Foundation

This paper is aimed to provide a new theory for the formation of the solar surface eruptions and sunspots. The key ingredient of the study is the new anti-diffusive effect of heat, based on the recently developed statistical theory of heat by the authors [4]. The anti-diffusive effect of heat states that due to the higher rate of photon absorption and emission of the particles with higher energy levels, the photon flux will move toward to the higher temperature regions from the lower temperature regions. This anti-diffusive effect of heat leads to a modified law of heat transfer, which includes a reversed heat flux counteracting the heat diffusion. It is this anti-diffusive effect of heat and thereby the modified law of heat transfer that lead to the temperature blow-up and consequently the formation of sunspots, solar eruptions, and solar prominences. This anti-diffusive effect of heat may be utilized to design a plasma instrument, directly converting solar energy into thermal energy. This may likely offer a new form of fuel much more efficient than the photovoltaic devices.

Citation: Tian Ma, Shouhong Wang. Topological phase transition III: Solar surface eruptions and sunspots. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020350
References:
[1]

C. FoiasO. Manley and R. Temam, Attractors for the Bénard problem: Existence and physical bounds on their fractal dimension, Nonlinear Anal., 11 (1987), 939-967.  doi: 10.1016/0362-546X(87)90061-7.  Google Scholar

[2]

J. LinW. Soon and S. L. Baliunas, Theories of solar eruptions: A review, New Astronomy Reviews, 47 (2003), 53-84.   Google Scholar

[3] T. Ma, Theory and Methods of Partial Differential Equations (in Chinese), Beijing, Science Press, 2011.   Google Scholar
[4]

T. Ma and S. Wang, Statistical Theory of Heat, Hal preprint: hal-01578634, (2017). Google Scholar

[5]

——, Topological Phase Transitions I: Quantum Phase Transitions, Hal preprint: hal-01651908, (2017). Google Scholar

[6]

——, Topological Phase Transitions II: Spiral Structure of Galaxies, Hal preprint: hal-01671178, (2017). Google Scholar

[7]

A. A. Sokolov, Y. M. Loskutov and I. M. Ternov, Quantum Mechanics, Holt, Rinehart abd Winston, Inc., 1966. Google Scholar

show all references

References:
[1]

C. FoiasO. Manley and R. Temam, Attractors for the Bénard problem: Existence and physical bounds on their fractal dimension, Nonlinear Anal., 11 (1987), 939-967.  doi: 10.1016/0362-546X(87)90061-7.  Google Scholar

[2]

J. LinW. Soon and S. L. Baliunas, Theories of solar eruptions: A review, New Astronomy Reviews, 47 (2003), 53-84.   Google Scholar

[3] T. Ma, Theory and Methods of Partial Differential Equations (in Chinese), Beijing, Science Press, 2011.   Google Scholar
[4]

T. Ma and S. Wang, Statistical Theory of Heat, Hal preprint: hal-01578634, (2017). Google Scholar

[5]

——, Topological Phase Transitions I: Quantum Phase Transitions, Hal preprint: hal-01651908, (2017). Google Scholar

[6]

——, Topological Phase Transitions II: Spiral Structure of Galaxies, Hal preprint: hal-01671178, (2017). Google Scholar

[7]

A. A. Sokolov, Y. M. Loskutov and I. M. Ternov, Quantum Mechanics, Holt, Rinehart abd Winston, Inc., 1966. Google Scholar

[1]

Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020268

[2]

Peter Poláčik, Pavol Quittner. Entire and ancient solutions of a supercritical semilinear heat equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 413-438. doi: 10.3934/dcds.2020136

[3]

Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020264

[4]

Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in Cattaneo-Christov heat flux model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020344

[5]

Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216

[6]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020276

[7]

Wei Feng, Michael Freeze, Xin Lu. On competition models under allee effect: Asymptotic behavior and traveling waves. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5609-5626. doi: 10.3934/cpaa.2020256

[8]

Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217

[9]

Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020467

[10]

Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451

[11]

Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458

[12]

Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051

[13]

Chao Xing, Jiaojiao Pan, Hong Luo. Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020275

[14]

Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020073

[15]

Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070

[16]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017

[17]

Reza Lotfi, Zahra Yadegari, Seyed Hossein Hosseini, Amir Hossein Khameneh, Erfan Babaee Tirkolaee, Gerhard-Wilhelm Weber. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020158

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (9)
  • HTML views (20)
  • Cited by (0)

Other articles
by authors

[Back to Top]