Robust tori-like Lagrangian coherent structures

In general the term “Lagrangian coherent structure” (LCS) is used to make reference about structures whose properties are similar to a time-dependent analog of stable and unstable manifolds from a hyperbolic fixed point in Hamiltonian systems. Recently, the term LCS was used to describe a different type of structure, whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. A new kind of LCS was obtained. It consists of barriers, called robust tori that block the trajectories in certain regions of the phase space. We used the Double-Gyre Flow system as the model. In this system, the robust tori play the role of a skeleton for the dynamics and block, horizontally, vortices that come from different parts of the phase space.     

The emergence of coherent structures in coupled map lattices

We show how increasing spatial interaction leads to the merging of coherent structures from chaos in some systems of coupled map lattices. This phenomenon reflects the arising of new ground states in the corresponding model of statistical mechanics. If we further increase the coupling then, new ground states appear showing the coexistence of a large-scale coherent structure with a small-scale chaotic motion. This allows us to propose a generalization of the notion of spatial intermittency.     

Lagrangian coherent structures analysis of gas-liquid flow in a bubble column

The objective of this paper is to apply a new identifying method to investigating the gas-liquid two-phase flow behaviors in a bubble column with air injected into water.In the numerical simulations,the standard k-?turbulence model is employed to describe the turbulence phenomenon occurring in the continuous fluid.The Finite-Time Lyapunov Exponent(FTLE)and Lagrangian Coherent Structures(LCS)are applied to analyze the vortex structures in multiphase flow.Reasonable agreements are obtained between the numerical and experimental data.The numerical results show that the evolution of gas-liquid in the column includes initial and periodical developing stages.During the initial stage,the bubble hose is forming and extending along the vertical direction with the vortex structures formed symmetrically.During the periodical developing stage,the bubble hose starts to oscillate periodically,and the vortexes move along the bubble hose to the bottom of column alternately.Compared to the Euler-system-based identification criterion of a vortex,the FTLE field presents the boundary of a vortex without any threshold defined and the LCS represents the divergence extent of infinite neighboring particles.During the initial stage,the interfaces between the forward and backward flows are highlighted by the LCS.As for the periodical developing stage,the LCS curls near the vortex centers,providing a method of analyzing a flow field from a dynamical system perspective.     

非定常瞬态流动过程中的Lagrangian拟序结构与物质输运作用

从Lagrangian角度数值分析了圆柱瞬时起动过程中的非定常瞬态流动现象,如分离泡产生、破裂和涡脱落等及其产生的非定常效应,揭示了所列现象诱导的物质输运和迁移效应,首先采用双时间步长的特征线算子分裂算法数值模拟了圆柱起动过程中的瞬时流场,然后采用数值方法从流场中提取出Lagrangian拟序结构(LCSs),并根据非线性动力学理论研究了流动分离和旋涡演化过程中的物质输运作用,结果表明,圆柱瞬时起动后所产生的非定常阻力与相应瞬态现象中的物质输运有密切的关系:对称分离泡产生及其在流向方向的生长,能够使分离泡内压力升高且分布均匀,从而减小阻力;对称分离泡的失稳增强了分离泡与主流之间的物质输运作用,最终导致涡的脱落,并有利于推迟流动分离和减小分离区域,非定常流动中LCSs所描述的物质输运和迁移作用对流动控制的机理研究具有一定指导意义。     

Erratum and addendum to “A variational theory of hyperbolic Lagrangian coherent structures” [Physica D 240 (2011) 574-598]

This brief note corrects a minor error in the statement of the main result in Haller (2011) [1] on a variational approach to Lagrangian coherent structures. We also show that the corrected formulation leads to a substantial simplification of LCS criteria for two-dimensional flows.     

Fractal patterns on the onset of coherent structures in a coupled map lattice

We report the formation of Cantor set-like fractals during the development of coherent structures in a coupled map lattice (CML). The dependence of these structures on the size of the lattice as well as the first three dimensions of the associated fractal patterns are analyzed numerically.     

Hamiltonian and gradient structures in the Toda flows

In this paper we consider gradient structures in the dynamics and geometry of the asymmetri nonperiodic tridiagonal and full Toda flow equations. We compare and contrast a number of formulations of the nonperiodic Toda equations. In the case of the full Kostant (asymmetric) Toda flow we explain the role of noncommutative integrability in its qualitative behavior. We describe the relationship between the asymmetric Toda flows and the symmetric and indefinite Toda flows, and prove in particular that one may conjugate from the full Kostant Toda flows to the full symmetric Toda flows via a Poisson map.     

Identification of lagrangian coherent structures in the turbulent boundary layer

Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the ensemble-averaged inclination angle θ _R of typical LCS. θ _R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y ⁺=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y ⁺=100. The ensemble- averaged convection velocity U _c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal profile of the convection velocity U _c(y) accords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond. Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001)     

Compatibility of symplectic structures adapted to noncommutatively integrable systems

It is known that any integrable, possibly degenerate, Hamiltonian system is Hamiltonian relative to many different symplectic structures; under certain hypotheses, the ‘semi-local’ structure of these symplectic forms, written in local coordinates of action-angle type, is also known. The purpose of this paper is to characterize from the point of view of symplectic geometry the family of all these structures. The approach is based on the geometry of noncommutatively integrable systems and extends a recent treatment of the nondegenerate case by Bogoyavlenskij. Degenerate systems are comparatively richer in symplectic structures than nondegenerate ones and this has the counterpart that the bi-Hamiltonian property alone does not imply integrability. However, integrability is still guaranteed if a system is Hamiltonian with respect to three suitable symplectic structures. Moreover, some of the properties of recursion operators are retained.     

A resistance formula for coherent multi-barrier structures

Using the Landauer formula and the quantum S-matrix scattering theory, we derive a resistance formula for multi-barrier structure under phase coherent transmission condition. This formula shows that when the transport is coherent, the potential wells of the structure are just like conductors contributing to the overall resistance. And because the resistance formula is derived based on the scattering theory, the barrier resistance will change with the number of scattering centres (i.e. the number of barriers) in the structure.     

A very narrow spectral band

The power spectrum of the variablez in the Lorenz equations with =10,b=8/3, andr=200 appeared in previous work to contain a line superposed on a continuum. Analysis of an extended solution into consecutive segments with rather similar initial states, each segment spanning at least seven maxima ofz, shows that the apparent line is actually a narrow band. Solutions spanning at least 14000 maxima ofz would be needed to resolve the band by standard computation procedures. Multiplication of the right side of each equation by the same function can convert the band to a line, while leaving the points of the attractor unchanged. It is proposed that the spectrum of a completely coupled autonomous flow is, in a certain sense, unlikely to contain a superposition of lines and a continuum.     

Localized coherent structures of (2+1) dimensional generalizations of soliton systems

We briefly review the recent progress in obtaining (2+1) dimensional integrable generalizations of soliton equations in (1+1) dimensions. Then, we develop an algorithmic procedure to obtain interesting classes of solutions to these systems. In particular using a Painlevé singularity structure analysis approach, we investigate their integrability properties and obtain their appropriate Hirota bilinearized forms. We identify line solitons and from which we introduce the concept of ghost solitons, which are patently boundary effects characteristic of these (2+1) dimensional integrable systems. Generalizing these solutions, we obtain exponentially localized solutions, namely the dromions which are driven by the boundaries. We also point out the interesting possibility that while the physical field itself may not be localized, either the potential or composite fields may get localized. Finally, the possibility of generating an even wider class of localized solutions is hinted by using curved solitons.     

NMR probe of bulk electronic structures in H+ beam irradiated Bi2Te3 topological insulator

We report a nuclear magnetic resonance (NMR) study on H⁺ beam irradiated Bi₂Te₃ powdered single crystals. In this work, we demonstrate that the beam creates defects within its penetration range giving rise to delocalized charge carriers, thereby making further ¹²⁵Te NMR Knight shift and line broadening. Upon increasing temperature, the NMR line narrowing manifests the activated motions of thermally excited charge carriers in the irradiated sample. In contrast, it reveals that in the unirradiated sample the free-charge carriers at the Fermi level dominantly contribute to the Knight shift. Our results show that the orbital contribution to the Knight shift in the bulk state of Bi₂Te₃ becomes predominant in the system with the higher density of defects, as evidenced by modified electronic structures induced by the beam irradiation.     

Control methods for problems of mixing and coherence in chaotic maps and flows

We review a variety of control methods which are capable of enhancing the chaoticity and mixing properties of chaotic flows and also methods which work towards promoting the coherence properties of such flows. We discuss a parameter control method which can enhance the chaoticity and the rate of mixing of dissipative as well as conservative flows and outline methods which promote global mixing by the addition of noise and by preventing island formation. As the inverse side of this problem, we summarize methods which can create coherent structures in chaotic dynamical flows. We also discuss the utility of these methods from the point of view of applications as well as for understanding phenomena which occur in natural systems.     

Simulating the complex behavior of a leaky faucet

The complex behavior of leaky faucets is obtained by numerical simulation using a stochastic method introduced by Mannaet al. and the results are compared with experimental data. Typical return maps of thin faucets are reproduced.     

Nonlinear coherent states of the Fokas-Lagerstrom potential

In this paper, we introduce an algebraic approach to construct Fokas-Lagerstrom coherent states. To do so, we define deformed creation and annihilation operators associated to this system and investigate their algebra. We show that these operators satisfy the f-deformed Weyl-Heisenberg algebra. Then, we propose a theoretical scheme to generate the aforementioned coherent states. The present contribution shows that the Fokas-Lagerstrom nonlinear coherent states possess some non-classical features.     

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.     

Theoretical and experimental investigations of coherent phonon dynamics in sapphire crystal using femto- second time-resolved coherent anti-Stokes Raman scattering

We report on the theoretical and the experimental investigations of the coherent phonon dynamics in sapphire crystal using the femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) technique. The temporal chirped white-light continuum (WLC) is used for the Stokes pulse, therefore we can perform the selective excitation of the phonon modes without using a complicated laser system. The expected quantum beat phenomenon is clearly observed. The theoretical formulas consist very well with the experimental results. The dephasing times of the excited phonon modes, the wavenumber difference, and the phase shift between the simultaneously excited modes are obtained and discussed. This work opens up a way to study directly high-frequency coherent phonon dynamics in bulk crystals on a femtosecond time scale and is especially helpful for understanding the nature of coherent phonons.     

Perturbative evaluation of universal constants for a quartic map

We discuss a perturbative scheme for the determination of the bifurcation rate δ for a specific map, by extending Virendra Singh’s method of evaluating the scaling factor α. The method is applied to a quartic map and the values obtained, α = 1.690781026 and δ = 7.23682924 are in good agreement with the numerically computed values reported in the literature. The perturbative approach is found to be more efficient than other existing methods.