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| Prof. Er Guokang’s paper has been published by the prestigious Annalen der Physik |
A paper by Prof. Er Guokang of the Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau (UM), on a new methodology for solving some reduced Fokker-Planck (FP) equations in high dimensions, was recently published by the prestigious Annalen der Physik (Annals of Physics, Berlin) which influenced the development of science, technology, and human society deeply and widely. Founded in 1790, Annalen der Physik is one of the world's oldest and most renowned physics journals, and has always been the home of innovative papers from the best and brightest minds in the field of physics, such as Albert Einstein, Max Planck, and many others.
Most of outstanding papers that founded the modern physics were first published in Annalen der Physik, such as Albert Einstein’s most renowned papers about mass-energy equivalence, special theory of relativity, light quanta, and Brown motion of molecules; Max Planck’s papers about quantum physics and Fokker-Planck equation; Erwin Schrödinger’s papers about quantum mechanics and Schrödinger equation; H. A. Lorentz’s paper about electro-magnetic force; L. E. Boltzmann’s papers about statistical mechanics and statistical thermodynamics; W. Heisenberg’s papers about uncertain principle of quantum theory; W. Röntgen’s papers about X-ray; L. Rayleigh’s paper about argon; H. Hertz’s paper about photoelectric effect, and so on. Many Nobel Prize winners in physics also published their original research results in Annalen der Physik.
A lot of problems in science and engineering are described with nonlinear stochastic dynamic systems and their relevant FP equations, but the problem of solving the FP equation in high dimensions has been a challenge for almost a century since the description on the Brown motion of molecules by Einstein in 1905 and the formulation of FP equation by Fokker and Planck thereafter. In Prof. Er Guokang’s paper on “Methodology for the solutions of some reduced Fokker-Planck equations in high dimensions”, a new methodology is formulated for solving the Fokker-Planck (FP) equations in high dimensions based on his idea that the state space of large nonlinear stochastic dynamic system is split into two subspaces. The FP equation relevant to the nonlinear stochastic dynamic system is then integrated over one of the subspaces. The FP equation for the joint probability density function of the state variables in another subspace is formulated with some techniques. Therefore, the FP equation in high-dimensional state space is reduced to some FP equations in low-dimensional state spaces, which are solvable with the exponential polynomial closure method which was also proposed by Prof. Er Guokang in 1998. Unlike the other methods that limit the number of system dimensions under four, the number of system dimensions is not limited with this method. The effectiveness of this method has been tested and proved with lots of numerical results. It provides an analytical tool for the investigation and application of large nonlinear stochastic dynamics systems arising from various areas of science and engineering.
Prof. Er is grateful for the great support for his research from UM’s Research and Development Administration Office.
