In this work, we study approximations of supercritical or suction vortices in tornadic flows and their contribution to tornadogenesis and tornado maintenance using self-avoiding walks on a cubic lattice. We extend the...In this work, we study approximations of supercritical or suction vortices in tornadic flows and their contribution to tornadogenesis and tornado maintenance using self-avoiding walks on a cubic lattice. We extend the previous work on turbulence by A. Chorin and collaborators to approximate the statistical equilibrium quantities of vortex filaments on a cubic lattice when both an energy and a statistical temperature are involved. Our results confirm that supercritical (smooth, “straight”) vortices have the highest average energy and correspond to negative temperatures in this model. The lowest-energy configurations are folded up and “balled up” to a great extent. The results support A. Chorin’s findings that, in the context of supercritical vortices in a tornadic flow, when such high-energy vortices stretch, they need to fold and transfer energy to the surrounding flow, contributing to tornado maintenance or leading to its genesis. The computations are performed using a Markov Chain Monte Carlo approach with a simple sampling algorithm using local transformations that allow the results to be reliable over a wide range of statistical temperatures, unlike the originally used pivot algorithm that only performs well near infinite temperatures. Efficient ways to compute entropy are discussed and show that a system with supercritical vortices will increase entropy by having these vortices fold and transfer their energy to the surrounding flow.展开更多
We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves signific...We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis Hastings method. The gained efficiency increases with spatial dimension （D）, from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L = 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ^＊ = 2/d and γ/υ^＊ = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.展开更多
The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov ch...The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov chain. Generally speaking, it is difficult togive an accurate analytical expression of the problem dealing with the SAW. It is wellknown that the SAW model is widely used in physics, chemistry and biology. For exam-展开更多
The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,includ...The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,including the exact enumeration and Monte Carlo method.These two basic quantities obeyed the relations deduced from the scaling law.The critical exponents and the lattice indexes were given by fitting the data of the computer experiments.It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall.The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW.However,as N→∞,the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model.That is quite different from the case of the NRW tail chain.展开更多
文摘In this work, we study approximations of supercritical or suction vortices in tornadic flows and their contribution to tornadogenesis and tornado maintenance using self-avoiding walks on a cubic lattice. We extend the previous work on turbulence by A. Chorin and collaborators to approximate the statistical equilibrium quantities of vortex filaments on a cubic lattice when both an energy and a statistical temperature are involved. Our results confirm that supercritical (smooth, “straight”) vortices have the highest average energy and correspond to negative temperatures in this model. The lowest-energy configurations are folded up and “balled up” to a great extent. The results support A. Chorin’s findings that, in the context of supercritical vortices in a tornadic flow, when such high-energy vortices stretch, they need to fold and transfer energy to the surrounding flow, contributing to tornado maintenance or leading to its genesis. The computations are performed using a Markov Chain Monte Carlo approach with a simple sampling algorithm using local transformations that allow the results to be reliable over a wide range of statistical temperatures, unlike the originally used pivot algorithm that only performs well near infinite temperatures. Efficient ways to compute entropy are discussed and show that a system with supercritical vortices will increase entropy by having these vortices fold and transfer their energy to the surrounding flow.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11275185 and 11625522, and the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China （No. Y5KF191CJ1）. Y. Deng acknowledges the Ministry of Education （of China） for the Fundamental Research Funds for the Central Universities under Grant No. 2340000034.
文摘We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk （SAW）, which violates the detailed balance condition and satisfies tile balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis Hastings method. The gained efficiency increases with spatial dimension （D）, from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L = 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ^＊ = 2/d and γ/υ^＊ = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.
基金Project supported by the National Natural Science Foundation of China.
文摘The self-avoiding walk (SAW) is an important model greatly different from the normalrandom walk in mathematics. Since a site that has been occupied once cannot be visitedagain by the walker, the SAW is not a Markov chain. Generally speaking, it is difficult togive an accurate analytical expression of the problem dealing with the SAW. It is wellknown that the SAW model is widely used in physics, chemistry and biology. For exam-
基金supported by the National Natural Science Foundation of China
文摘The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,including the exact enumeration and Monte Carlo method.These two basic quantities obeyed the relations deduced from the scaling law.The critical exponents and the lattice indexes were given by fitting the data of the computer experiments.It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall.The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW.However,as N→∞,the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model.That is quite different from the case of the NRW tail chain.
