Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scali...Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.展开更多
The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mech...The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional(2D)XY model,a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation.We study the 2D XY model with algebraically decaying interaction~1/r^(2+σ).Utilizing an advanced update strategy,we conduct LR Monte Carlo simulations of the model up to a linear size of L=8192.Our results demonstrate continuous phase transitions into a ferromagnetic phase forσ<2,which exhibit the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode.Furthermore,we fnd logarithmic scaling behaviors in the low-temperature phase atσ=2.The observed scaling behaviors in the low-temperature phase forσ≤2 agree with our theoretical analysis.Our fndings request further theoretical understanding and can be of practical application in cutting-edge experiments like Rydberg atom arrays.展开更多
This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -...This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -3D ) is presented in the Present paper,which is the most suitable one for the dual - structured - aquifer system. An example of Wenyinghu area is shown.By using the 2D-3D model, a satisfied result of the simulated area is achieved.展开更多
To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as ...To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.展开更多
Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the genera...Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.展开更多
A real-time mathematical model for two dimensional tidal flow and water quality is presented in this paper. The control-volume-based-finite-difference method and the 'power interpolation distribution' advocate...A real-time mathematical model for two dimensional tidal flow and water quality is presented in this paper. The control-volume-based-finite-difference method and the 'power interpolation distribution' advocated by Patankar [4] have been employed, and new boundary condition for tidal flow is recommended. The model is un- conditionally stable and convergent, and able to deal with irregular estuarine topography and movable boundary problems. Practical application of the model is illustrated by an example for the Swatou Bay. A fair agreement be- tween the values measured and computed demonstrates the validity of the model developed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12175316).
文摘Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.
基金supported by the National Natural Science Foundation of China(Grant Nos.12204173 and 12275263)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301900)supported by the Natural Science Foundation of Fujian Province 802 of China(Grant No.2023J02032)。
文摘The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional(2D)XY model,a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation.We study the 2D XY model with algebraically decaying interaction~1/r^(2+σ).Utilizing an advanced update strategy,we conduct LR Monte Carlo simulations of the model up to a linear size of L=8192.Our results demonstrate continuous phase transitions into a ferromagnetic phase forσ<2,which exhibit the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode.Furthermore,we fnd logarithmic scaling behaviors in the low-temperature phase atσ=2.The observed scaling behaviors in the low-temperature phase forσ≤2 agree with our theoretical analysis.Our fndings request further theoretical understanding and can be of practical application in cutting-edge experiments like Rydberg atom arrays.
文摘This paper points out that a successful numerical simulation is to construct a correct conceptional model which is very dose to the natural condition. A new model, two dimensional coupled three dimensional model (2D -3D ) is presented in the Present paper,which is the most suitable one for the dual - structured - aquifer system. An example of Wenyinghu area is shown.By using the 2D-3D model, a satisfied result of the simulated area is achieved.
文摘To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.
基金Supported by the National Natural Science Foundations of China(No.11271193)Humanities and Social Sciences Planning Foundation of Chinese Ministry of Education(11YJA910004)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(11KJB110005)Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)
文摘Recently, Kundu and Gupta （Metrika, 48：83 C 97, 1998） established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin （Annals of Statistics, 9：130 C 134, 1981） and Zheng （Acta Math. Appl. Sinica （in Chinese）, 10（2）： 247 C 253, 1987）. A simulation study shows that this approximation works very well.
文摘A real-time mathematical model for two dimensional tidal flow and water quality is presented in this paper. The control-volume-based-finite-difference method and the 'power interpolation distribution' advocated by Patankar [4] have been employed, and new boundary condition for tidal flow is recommended. The model is un- conditionally stable and convergent, and able to deal with irregular estuarine topography and movable boundary problems. Practical application of the model is illustrated by an example for the Swatou Bay. A fair agreement be- tween the values measured and computed demonstrates the validity of the model developed.
