# American Institute of Mathematical Sciences

January  2021, 26(1): 501-514. 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, 2021, 26 (1) : 501-514. doi: 10.3934/dcdsb.2020350
##### References:
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##### References:
 [1] C. Foias, O. 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. Lin, W. 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
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