Numerical Analysis of Laminar–Turbulent Transition by Methods of Chaotic Dynamics

Doklady Mathematics - This paper summarizes the results of studies of the laminar–turbulent transition in some fluid and gas dynamics problems obtained by applying numerical methods and...     

Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite Signs

This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of motion is presented and its Liouville integrability is shown. A bifurcation diagram is constructed, analysis of bifurcations of Liouville tori is carried out for the case of opposite-signed vortices, and the types of critical motions are identified.     

Research on the Evolution of Thinking Dynamics Attractor

ＲｅｓｅａｒｃｈｏｎｔｈｅＥｖｏｌｕｔｉｏｎｏｆＴｈｉｎｋｉｎｇＤｙｎａｍｉｃｓＡｔｔｒａｃｔｏｒＹａｎｇＱｉａｎ（杨谦）；ＺｈａｎｇＹｏｎｇｊｕｎ（张拥军）（ＳｏｕｔｈｗｅｓｔＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，６１００３１）Ｂａ...     

Ethnic Preferences,Social Distance Dynamics,and Residential Segregation: Theoretical Explorations Using Simulation Analysis∗

In this paper I consider theories of residential segregation that emphasize social distance and ethnic preference dynamics. I argue that these theories are more compelling than many critics have supposed, and I conclude that they deserve to be considered more carefully. I then use simulation methodology to assess the potential impact of social distance and ethnic preference dynamics on ethnic segregation under certain theoretically interesting conditions. Based on the results from the simulation analyses, I offer three conclusions: (1) status preferences and status dynamics have the capacity to produce high levels of status segregation but do not produce high levels of ethnic segregation under the specified simulation conditions; (2) ethnic preferences can, under certain theoretically interesting conditions specified in these simulations, produce high levels of ethnic segregation in the absence of housing discrimination; and (3) ethnic preferences and social distance dynamics can, when combined with status preferences, status dynamics, and demographic and urban-structural settings common in American cities, produce highly stable patterns of multi-group segregation and hyper-segregation (i.e., high levels of ethnic segregation on multiple dimensions) of minority populations. Based on these model-based theoretical explorations I speculate that the persistence of segregation in recent decades may have been overdetermined, that is, it may have been sustained by multiple sufficient causes including not only discrimination, but also social distance and preference dynamics. This raises the possibility that reductions in housing discrimination may not necessarily lead to large declines in ethnic segregation in the short run because social distance and preference dynamics may be able to sustain ethnic segregation at surprisingly high levels in the absence of housing discrimination.     

Dynamics of the Tippe Top—Properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm the oscillatory behavior of the inclination angle θ(t) for the symmetry axis of the Tippe Top, as predicted by the Main Equation for the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations.     

The Dynamics of Zeros of Finite-Gap Solutions of the Schrödinger Equation

We study a system of particles on a Riemann surface with a puncture. This system describes the behavior of zeros of finite-gap solutions of the Schrödinger equation corresponding to a degenerate hyperelliptic curve. We show that this system is Hamiltonian and integrable by constructing action-angle type coordinates.     

Convergence Types and Rates in Generic Karhunen-Loève Expansions with Applications to Sample Path Properties

Potential Analysis - We establish a Karhunen-Loève expansion for generic centered, second order stochastic processes, which does not rely on topological assumptions. We further investigate in...     

Effective Dynamics for N-Solitons of the Gross–Pitaevskii Equation

We consider several solitons moving in a slowly varying external field. We present results of numerical computations which indicate that the effective dynamics obtained by restricting the full Hamiltonian to the finite-dimensional manifold of N-solitons (constructed when no external field is present) provides a remarkably good approximation to the actual soliton dynamics. This is quantified as an error of size h ² where h is the parameter describing the slowly varying nature of the potential. This also indicates that previous mathematical results of Holmer and Zworski (Int. Math. Res. Not. 2008: Art. ID runn026, 2008) for one soliton are optimal. For potentials with unstable equilibria, the Ehrenfest time, log(1/h)/h, appears to be the natural limiting time for these effective dynamics. We also show that the results of Holmer et?al. (arXiv:0912.5122, 2009) for two mKdV solitons apply numerically to a larger number of interacting solitons. We illustrate the results by applying the method with the external potentials used in the Bose?CEinstein soliton train experiments of Strecker et?al. (Nature 417:150?C153, 2002).     

Dynamics of the Internet TCP–RED congestion control system

In this paper, the ideal case for the important congestion control algorithms, i.e., the TCP (transmission control protocol) algorithm and the RED (random early detection) algorithm, is analyzed, and the following results are found. First, mathematical analysis proves the existence of two equilibria of this dynamical system (of DDEs—delay differential equations), which has not been established in previous works. Second, reduction of the round-trip delay leads to the optimal design of the TCP–RED congestion control. Unfortunately, a drawback of TCP–RED is that package dropping and congestion are induced. The dynamics of the DDEs are considered for when congestion does not take place and the averaged queue length is between the minimum threshold and the maximum one. Stability and Hopf bifurcation of the DDEs are considered. We find that if the time delays are sufficiently large, Hopf bifurcation of the two equilibria will appear, and thus stationary motions with approximately constant rates of arrival, averaged queue length and oscillations with periodically varying forms will arise. Simulations illustrate the richness of the dynamics of the DDEs.     

Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage北大核心CSCD

在考虑成熟阶段具有密度制约的基础上,建立了一类具有卵-成熟阶段的同类相食模型.该文从两个方面讨论了模型的动力学性态：当种群不存在同类相食时,构造Lyapunov函数证明平衡点的全局渐近稳定性;当种群存在同类相食时,利用中心流形定理证明同类相食使模型产生鞍结点分支,通过构造Dulac函数说明在二维自治系统中不存在极限环,得到了平衡点的全局稳定性.最后,利用数值模拟验证了所得相应结果的正确性.     

A generalization of the Contou-Carrère symbol

Using techniques of Algebraic Geometry, the aim of this paper is to give a generalized definition of the Contou-Carrère symbol as a morphism of schemes. In fact, from formal schemes and Heisenberg groups, we provide a new definition of the Contou-Carrère symbol and a generalization of it associated with a separable extension . Moreover, a reciprocity law is proved and classical explicit reciprocity laws are recovered from it. This work is partially supported by the DGESYC research contract n. BFM2003-00078 and Castilla y León Regional Government contract SA064/01.     

Beppo Levi’s Analysis of the Paradoxes

This paper presents and comments the content of a note by Beppo Levi on logical paradoxes. Though the existence of this contribution is known, very little analysis of it is available in the literature. I put the emphasis on Levi’s usage of “elementation procedures” for solving the set-theoretical paradoxes, which is the most original part of Levi’s approach to the topic.     

Dynamics of Polynomial Automorphisms of C~N

ＤｙｎａｍｉｃｓｏｆＰｏｌｙｎｏｍｉａｌＡｕｔｏｍｏｒｐｈｉｓｍｓｏｆＣ~Ｎ￥ＺｈａｎｇＷｅｎｊｕｎ（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，Ｐ．Ｒ．Ｃｈｉａｎ，４７５００１）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓａｓｓｉｇｎｅｄｔｏｄｉｓ?..     

Karhunen-Loève expansions of <Emphasis Type="Italic">α</Emphasis>-Wiener bridges

We study Karhunen-Loève expansions of the process(X _t ^(α)) _t∈[0,T) given by the stochastic differential equation $ dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T) $ dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T) , with the initial condition X ₀^(α) = 0, where α > 0, T ∈ (0, ∞), and (B _t )t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X ^(α). As applications, we calculate the Laplace transform and the distribution function of the L ²[0, T]-norm square of X ^(α) studying also its asymptotic behavior (large and small deviation).     

Sensitivity Analysis to the Value of p of the ℓ p Distance Weber Problem

In this paper we analyze the sensitivity of the _p distance Weber problem to the value of p. We consider each power p to be in a range and not necessarily the same for each demand point. We find the set of possible optimal locations when p is in a given range. We also find the location that minimizes the expected cost, and find the Expected Value of Perfect Information. Computational results are presented.     

Recent Results on the Dynamics of Higher-dimensional Hénon Maps

We investigate different aspects of chaotic dynamics in Hénon maps of dimension higher than 2. First, we review recent results on the existence of homoclinic points in 2-d and 4-d such maps, by demonstrating how they can be located with great accuracy using the parametrization method. Then we turn our attention to perturbations of Hénon maps by an angle variable that are defined on the solid torus, and prove the existence of uniformly hyperbolic solenoid attractors for an open set of parameters.We thus argue that higher-dimensional Hénon maps exhibit a rich variety of chaotic behavior that deserves to be further studied in a systematic way.