
Previous Article
Rich dynamics of a simple delay hostpathogen model of celltocell infection for plant virus
 DCDSB Home
 This Issue

Next Article
On the role of pharmacometrics in mathematical models for cancer treatments
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 
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 antidiffusive effect of heat, based on the recently developed statistical theory of heat by the authors [
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), 939967. doi: 10.1016/0362546X(87)900617. Google Scholar 
[2] 
J. Lin, W. Soon and S. L. Baliunas, Theories of solar eruptions: A review, New Astronomy Reviews, 47 (2003), 5384. 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: hal01578634, (2017). Google Scholar 
[5] 
——, Topological Phase Transitions I: Quantum Phase Transitions, Hal preprint: hal01651908, (2017). Google Scholar 
[6] 
——, Topological Phase Transitions II: Spiral Structure of Galaxies, Hal preprint: hal01671178, (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. Foias, O. Manley and R. Temam, Attractors for the Bénard problem: Existence and physical bounds on their fractal dimension, Nonlinear Anal., 11 (1987), 939967. doi: 10.1016/0362546X(87)900617. Google Scholar 
[2] 
J. Lin, W. Soon and S. L. Baliunas, Theories of solar eruptions: A review, New Astronomy Reviews, 47 (2003), 5384. 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: hal01578634, (2017). Google Scholar 
[5] 
——, Topological Phase Transitions I: Quantum Phase Transitions, Hal preprint: hal01651908, (2017). Google Scholar 
[6] 
——, Topological Phase Transitions II: Spiral Structure of Galaxies, Hal preprint: hal01671178, (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] 
Manuel del Pino, Monica Musso, Juncheng Wei, Yifu Zhou. Type Ⅱ finite time blowup for the energy critical heat equation in $ \mathbb{R}^4 $. Discrete & Continuous Dynamical Systems  A, 2020, 40 (6) : 33273355. doi: 10.3934/dcds.2020052 
[2] 
Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete & Continuous Dynamical Systems  A, 2020, 40 (6) : 37373765. doi: 10.3934/dcds.2019230 
[3] 
ChuehHsin Chang, ChiunChuan Chen, ChihChiang Huang. Traveling wave solutions of a free boundary problem with latent heat effect. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021028 
[4] 
Luis Caffarelli, Fanghua Lin. Nonlocal heat flows preserving the L^{2} energy. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 4964. doi: 10.3934/dcds.2009.23.49 
[5] 
Bo Chen, Youde Wang. Global weak solutions for LandauLifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure & Applied Analysis, 2021, 20 (1) : 319338. doi: 10.3934/cpaa.2020268 
[6] 
Peter Poláčik, Pavol Quittner. Entire and ancient solutions of a supercritical semilinear heat equation. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 413438. doi: 10.3934/dcds.2020136 
[7] 
Juliana Fernandes, Liliane Maia. Blowup and bounded solutions for a semilinear parabolic problem in a saturable medium. Discrete & Continuous Dynamical Systems  A, 2021, 41 (3) : 12971318. doi: 10.3934/dcds.2020318 
[8] 
Takiko Sasaki. Convergence of a blowup curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems  S, 2021, 14 (3) : 11331143. doi: 10.3934/dcdss.2020388 
[9] 
Tetsuya Ishiwata, Young Chol Yang. Numerical and mathematical analysis of blowup problems for a stochastic differential equation. Discrete & Continuous Dynamical Systems  S, 2021, 14 (3) : 909918. doi: 10.3934/dcdss.2020391 
[10] 
Justin Holmer, Chang Liu. Blowup for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blowup profiles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 215242. doi: 10.3934/cpaa.2020264 
[11] 
Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in CattaneoChristov heat flux model. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020344 
[12] 
Giulia Luise, Giuseppe Savaré. Contraction and regularizing properties of heat flows in metric measure spaces. Discrete & Continuous Dynamical Systems  S, 2021, 14 (1) : 273297. doi: 10.3934/dcdss.2020327 
[13] 
DongHo Tsai, ChiaHsing Nien. On spacetime periodic solutions of the onedimensional heat equation. Discrete & Continuous Dynamical Systems  A, 2020, 40 (6) : 39974017. doi: 10.3934/dcds.2020037 
[14] 
Laure Cardoulis, Michel Cristofol, Morgan Morancey. A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020054 
[15] 
Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete & Continuous Dynamical Systems  S, 2021, 14 (2) : 745767. doi: 10.3934/dcdss.2020365 
[16] 
Youshan Tao, Michael Winkler. Critical mass for infinitetime blowup in a haptotaxis system with nonlinear zeroorder interaction. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 439454. doi: 10.3934/dcds.2020216 
[17] 
Alex H. Ardila, Mykael Cardoso. Blowup solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101119. doi: 10.3934/cpaa.2020259 
[18] 
Daniele Bartolucci, Changfeng Gui, Yeyao Hu, Aleks Jevnikar, Wen Yang. Mean field equations on tori: Existence and uniqueness of evenly symmetric blowup solutions. Discrete & Continuous Dynamical Systems  A, 2020, 40 (6) : 30933116. doi: 10.3934/dcds.2020039 
[19] 
Larissa Fardigola, Kateryna Khalina. Controllability problems for the heat equation on a halfaxis with a bounded control in the Neumann boundary condition. Mathematical Control & Related Fields, 2021, 11 (1) : 211236. doi: 10.3934/mcrf.2020034 
[20] 
Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2021, 17 (1) : 185204. doi: 10.3934/jimo.2019106 
2019 Impact Factor: 1.27
Tools
Article outline
[Back to Top]