In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of t...In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of the 0-condition was based on the numerical results of the mean square radius of gyration and end-to-end distance. It was found that at the 0 temperature Delta epsilon /kT equals -0.27. The exponents a in the Mark-Houwink equation with different interaction parameters are consistent with the results of experiments: under 0-condition, alpha= 0.5, and for a good solvent alpha =0.74-0.84, respectively.展开更多
This paper investigates consensus of flocks consisting of n autonomous agents in the plane, where each agent has the same constant moving speed v and updates its heading by the average value of the kn nearest agents f...This paper investigates consensus of flocks consisting of n autonomous agents in the plane, where each agent has the same constant moving speed v and updates its heading by the average value of the kn nearest agents from it, with vn and kn being two prescribed parameters depending on n. Such a topological interaction rule is referred to as k,-nearest-neighbors rule, which has been validated for a class of birds by biologists and verified to be robust with respect to disturbances. A theoretical analysis will be presented for this flocking model under a random framework with large population, but without imposing any a priori connectivity assumptions. We will show that the minimum number of k~ needed for consensus is of the order O（log n） in a certain sense. To be precise, there exist two constants C1 〉 C2 〉 0 such that, if k 〉 C1 logn, then the flocking mode] will achieve consensus for any initial headings with high probability, provided that the speed vn is suitably small. On the other hand, if k 〈 Ca ]ogn, then for large n, with probability 1, there exist some initial headings such that consensus cannot be achieved, regardless of the value of Vn.展开更多
We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformati...We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.展开更多
In this paper,we study the motion course of traffic flow on the slopes of a highway by applying a microscopic traffic model,which takes into account the next-nearest-neighbor interaction in an intelligent transportati...In this paper,we study the motion course of traffic flow on the slopes of a highway by applying a microscopic traffic model,which takes into account the next-nearest-neighbor interaction in an intelligent transportation system environment.Three common gradients of the highway,which are sag terrain,uphill terrain,and downhill terrain on a single-lane roadway,are selected to clarify the impact on the traffic flow by the next-nearest-neighbor interaction in relative velocity.We obtain the current-density relation for traffic flow on the sag,the uphill and the downhill under the next-nearest-neighbor interaction strategy.It is observed that the current saturates when the density is greater than a critical value and the current decreases when the density is greater than another critical value.When the density falls into the intermediate range between the two critical densities it is also found that the oscillatory jam,easily leads to traffic accidents,often appears in the downhill stage,and the next-nearest-neighbor interaction in relative velocity has a strong suppressing effect on this kind of dangerous congestion.A theoretical analysis is also presented to explain this important conclusion.展开更多
基金This work was supported by the National Natural Science Foundation of China (No. 29974019)
文摘In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Ae on a simple cubic lattice. Determination of the 0-condition was based on the numerical results of the mean square radius of gyration and end-to-end distance. It was found that at the 0 temperature Delta epsilon /kT equals -0.27. The exponents a in the Mark-Houwink equation with different interaction parameters are consistent with the results of experiments: under 0-condition, alpha= 0.5, and for a good solvent alpha =0.74-0.84, respectively.
文摘This paper investigates consensus of flocks consisting of n autonomous agents in the plane, where each agent has the same constant moving speed v and updates its heading by the average value of the kn nearest agents from it, with vn and kn being two prescribed parameters depending on n. Such a topological interaction rule is referred to as k,-nearest-neighbors rule, which has been validated for a class of birds by biologists and verified to be robust with respect to disturbances. A theoretical analysis will be presented for this flocking model under a random framework with large population, but without imposing any a priori connectivity assumptions. We will show that the minimum number of k~ needed for consensus is of the order O（log n） in a certain sense. To be precise, there exist two constants C1 〉 C2 〉 0 such that, if k 〉 C1 logn, then the flocking mode] will achieve consensus for any initial headings with high probability, provided that the speed vn is suitably small. On the other hand, if k 〈 Ca ]ogn, then for large n, with probability 1, there exist some initial headings such that consensus cannot be achieved, regardless of the value of Vn.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11671255 and 11701510)the Ministry of Economy and Competitiveness of Spain(Grant No.MTM2016-80276-P(AEI/FEDER,EU))the China Postdoctoral Science Foundation(Grant No.2017M621964)
文摘We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.
基金Supported by the Natural Science Foundation of China under Grant No.60904068,Natural Science Foundation of China under Grant No.10902076,Natural Science Foundation of China under Grant No.11072117,Natural Science Foundation of China under Grant No.61004113the Fundamental Research Funds for the Central Universities under Grant No.0800219198
文摘In this paper,we study the motion course of traffic flow on the slopes of a highway by applying a microscopic traffic model,which takes into account the next-nearest-neighbor interaction in an intelligent transportation system environment.Three common gradients of the highway,which are sag terrain,uphill terrain,and downhill terrain on a single-lane roadway,are selected to clarify the impact on the traffic flow by the next-nearest-neighbor interaction in relative velocity.We obtain the current-density relation for traffic flow on the sag,the uphill and the downhill under the next-nearest-neighbor interaction strategy.It is observed that the current saturates when the density is greater than a critical value and the current decreases when the density is greater than another critical value.When the density falls into the intermediate range between the two critical densities it is also found that the oscillatory jam,easily leads to traffic accidents,often appears in the downhill stage,and the next-nearest-neighbor interaction in relative velocity has a strong suppressing effect on this kind of dangerous congestion.A theoretical analysis is also presented to explain this important conclusion.
