We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of the total number N of particles a...We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of the total number N of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, especially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.展开更多
The four-probe technique is widely used in the characterization of electrical properties of solids and thin films. To investigate the influence of finite size probes with non-planar contact on the standard four-probe ...The four-probe technique is widely used in the characterization of electrical properties of solids and thin films. To investigate the influence of finite size probes with non-planar contact on the standard four-probe method, we have proposed an image method to simulate the potential distribution within the specimen. The numerical results show that for infinitely thick samples, the standard method can only provide accurate determination of resistivity (relative error below 1%) when the ratio of the average inter-electrode spacing to the diameter of the probe is greater than 3. We have also found that disregarding the probe size brings a less dominate error than that introduced by the approximate formula, when the sample's thickness is close to the inter-electrode spacing.展开更多
Long-span bridges are special structures that require advanced analysis techniques to examine their performance. This paper presents a procedure developed to model the Confederation Bridge using 3-D beam elements. The...Long-span bridges are special structures that require advanced analysis techniques to examine their performance. This paper presents a procedure developed to model the Confederation Bridge using 3-D beam elements. The model was validated using the data collected before the opening of the bridge to the public. The bridge was instrumented to conduct fullscale static and dynamic tests. The static tests were to measure the deflection of the bridge pier while the dynamic tests to measure the free vibrations of the pier due to a sudden release of the static load. Confederation Bridge is one of the longest reinforced concrete bridges in the world. It connects the province of Prince Edward Island and the province of New Brunswick in Canada. Due to its strategic location and vital role as a transportation link between these two provinces, it was designed using higher safety factors than those for typical highway bridges. After validating the present numerical model, a procedure was developed to evaluate the performance of similar bridges subjected to traffic and seismic loads. It is of interest to note that the foundation stiffness and the modulus of elasticity of the concrete have significant effects on the structural responses of the Confederation Bridge.展开更多
In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by ...In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L 〉 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.展开更多
We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product...We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|^(-(d-2+η))and a finite-size scaling function of the variables r/L and tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.展开更多
It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling f...It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.展开更多
For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior ...For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior can appear only when the number of agents in the model takes a finite value.Those changes of behavior can be related to the apparent phase transitions that appear in some physical models.We show examples in the Galam's model of opinion transmission and the Axelrod's model of culture formation stressing the role that the network of interactions has on the main results of both models.Finally,we present the phenomenon of system-size stochastic resonance by which a forcing signal(identified as an advertising agent)is optimally amplified by a population of the right(intermediate)size.Our work stresses the role that the system size has in the dynamics of social systems and the inappropriateness of taking the thermodynamic limit for these systems.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775032 and 10574028)
文摘We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of the total number N of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, especially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.
基金Project supported by the Innovation Project of the Shanghai Institute of Technical Physics,CAS(No.CXJJ-Q-DX-57)
文摘The four-probe technique is widely used in the characterization of electrical properties of solids and thin films. To investigate the influence of finite size probes with non-planar contact on the standard four-probe method, we have proposed an image method to simulate the potential distribution within the specimen. The numerical results show that for infinitely thick samples, the standard method can only provide accurate determination of resistivity (relative error below 1%) when the ratio of the average inter-electrode spacing to the diameter of the probe is greater than 3. We have also found that disregarding the probe size brings a less dominate error than that introduced by the approximate formula, when the sample's thickness is close to the inter-electrode spacing.
文摘Long-span bridges are special structures that require advanced analysis techniques to examine their performance. This paper presents a procedure developed to model the Confederation Bridge using 3-D beam elements. The model was validated using the data collected before the opening of the bridge to the public. The bridge was instrumented to conduct fullscale static and dynamic tests. The static tests were to measure the deflection of the bridge pier while the dynamic tests to measure the free vibrations of the pier due to a sudden release of the static load. Confederation Bridge is one of the longest reinforced concrete bridges in the world. It connects the province of Prince Edward Island and the province of New Brunswick in Canada. Due to its strategic location and vital role as a transportation link between these two provinces, it was designed using higher safety factors than those for typical highway bridges. After validating the present numerical model, a procedure was developed to evaluate the performance of similar bridges subjected to traffic and seismic loads. It is of interest to note that the foundation stiffness and the modulus of elasticity of the concrete have significant effects on the structural responses of the Confederation Bridge.
基金supported by the National Natural Science Foundation of China (Grant No. 10674177)the Youth Foundation of China University of Mining & Technology (Grant No. 2008A035)
文摘In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L 〉 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)received a postdoctoral fellowship funded by the KunmingUniversity of Science and Technology
文摘We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|^(-(d-2+η))and a finite-size scaling function of the variables r/L and tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.
基金Supported by National Natural Science Foundation of China(10835005,11221504,11005046)the MOE of China for Doctoral Site(20120144110001)
文摘It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.
基金support from MCyT(Spain)and FEDER(EU)through projects FIS2004-5073 and FIS2004-953.
文摘For some models of relevance in the social sciences we review some exam-ples in which system size plays an important role in the final outcome of the dynamics.We discuss the conditions under which changes of behavior can appear only when the number of agents in the model takes a finite value.Those changes of behavior can be related to the apparent phase transitions that appear in some physical models.We show examples in the Galam's model of opinion transmission and the Axelrod's model of culture formation stressing the role that the network of interactions has on the main results of both models.Finally,we present the phenomenon of system-size stochastic resonance by which a forcing signal(identified as an advertising agent)is optimally amplified by a population of the right(intermediate)size.Our work stresses the role that the system size has in the dynamics of social systems and the inappropriateness of taking the thermodynamic limit for these systems.
基金National Natural Science Foundation(10675060)Natural Science Fund for Colleges and Universities in Jiangsu Province(10KJB14002)Highly Educated Professional Fund for Nanjing Forestry University(B2010-14)