Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve coul...Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.展开更多
Precise zero-knowledge was introduced by Micali and Pass in STOC06. This notion captures the idea that the view of a verifier can be reconstructed in almost same time. Following the notion, they constructed some preci...Precise zero-knowledge was introduced by Micali and Pass in STOC06. This notion captures the idea that the view of a verifier can be reconstructed in almost same time. Following the notion, they constructed some precise zero-knowledge proofs and arguments, in which the communicated messages are polynomial bits. In this paper, we employ the new simulation technique introduced by them to provide a precise simulator for a modified Kilian＇s zero-knowledge arguments with poly-logarithmic efficiency （this modification addressed by Rosen）, and as a result we show this protocol is a precise zero-knowledge argument with poly-logaxithmic efficiency. We also present an alternative construction of the desired protocols.展开更多
The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Marda...The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in , unlike in the Stokes case （see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathgmatiques Pures et Appliqudes, 90（2）, 2008, 133-159]） where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 20573134, 10875011the Natural Science Foundation of Xuzhou Normal University under Grant No. 07PYL02
文摘Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.
基金the National Natural Science Foundation of China (No.60573031)New Century Excellent Talent Program of Education Ministry of China (No.NCET-05-0398)
文摘Precise zero-knowledge was introduced by Micali and Pass in STOC06. This notion captures the idea that the view of a verifier can be reconstructed in almost same time. Following the notion, they constructed some precise zero-knowledge proofs and arguments, in which the communicated messages are polynomial bits. In this paper, we employ the new simulation technique introduced by them to provide a precise simulator for a modified Kilian＇s zero-knowledge arguments with poly-logarithmic efficiency （this modification addressed by Rosen）, and as a result we show this protocol is a precise zero-knowledge argument with poly-logaxithmic efficiency. We also present an alternative construction of the desired protocols.
基金supported by the University of Rouen and the Fédération Normandie Mathématiques, respectively
文摘The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in , unlike in the Stokes case （see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathgmatiques Pures et Appliqudes, 90（2）, 2008, 133-159]） where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.
