Staggered Quadrupolar Phase and Bicritical Point of Spin-1 Bond and Anisotropy Dilution Blume-Emery-Griffiths Model

Within the effective field theory (EFT), staggered quadrupolar phase and bicritical point of spin-1 bond and anisotropy dilution Blume-Emery-Griffiths model is studied on simple cubic lattice in the restricted range of biquadratic interaction and bilinear interaction ratio α≤-1. The phase diagrams present a line of staggered quadrupolar-paramagnetic (SQ-P) phase and a line of ferromagnetic-paramagnetic (F-P) phase, separated by a bicritical point (BCP). A large negative ratio and two different dilution factors magnify the range of the SQ phase and reduce range of ferromagnetic phase in T-α or T-D plane. These parameters can assist the reentrant behavior of the SQ-P line and suppress that of the F-P line. The influence of bond dilution on the BCP is dissimilar to that of anisotropy dilution. There is a degenerate pattern at ground state in T-D plane. Some results obtained by the pure BEG model is in qualitative agreement with the results of Monte Carlo simulations.     

Shear-thinning-induced chaos in taylor-couette flow

The effect of weak shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow, becomes lower as the shear-thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, a Hopf bifurcation emerges, which exists only for shear-thinning fluids.     

Bicritical behavior of period doublings in unidirectionally coupled maps

We study the scaling behavior of period doublings in two unidirectionally coupled one-dimensional maps near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. Note that the bicritical point corresponds to a border of chaos in both subsystems. For this bicritical case, the second response subsystem exhibits a type of non-Feigenbaum critical behavior, while the first drive subsystem is in the Feigenbaum critical state. Using two different methods, we make the renormalization-group analysis of the bicritical behavior and find the corresponding fixed point of the renormalization transformation with two relevant eigenvalues. The scaling factors obtained by the renormalization-group analysis agree well with those obtained by a direct numerical method.     

Chaotic capture of vortices by a moving body. I. The single point vortex case

The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the chaotic dynamics and is similar to that of other chaotic scattering phenomena. We show numerically that cases exist where the vortex can be captured around an elliptic point external to (and possibly far from) the body, and the existence of other very complicated motions are also demonstrated. Finally, generalizations of the problem of the vortex-body interaction are indicated, and some possible applications are postulated such as the interaction of line vortices with aircraft wings.     

Viscous Interaction Between a Vortex Tube and a Rotating Spherical Particle

The transient advection of a cylindrical vortex tube in a viscous incompressible flow field and its interaction with a rotating/spinning spherical particle has been investigated numerically at Reynolds numbers in the range of 20≤ Re≤200 for angular velocities of 0≤Ω≤0.5. The effects of vortex parameters such as size, circulation strength and initial position relative to the particle, on the temporal behavior of the lift and drag forces are studied. Vortex‐sphere interactions bring about major changes in the flow field particularly when coupled with particle rotation. It is observed that the forces acting on the particle are significantly influenced during the time that the vortex core is in the vicinity of the particle. The extent of these local changes are about ±30% in the drag coefficient and about ±200% in the lift coefficient as compared to flow over a rotating solid sphere with no vortex interaction. It is also found that a vortex with core radius between one and two particle diameters creates the strongest temporal variations in the lift and drag coefficients. Furthermore, maximum lift variations occur for the vortex‐particle head on collision, while a vortex with an offset distance of about one diameter from the principal flow axis generates the maximum drag variations.     

Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

Multicritical points in a system with random single-ion anisotropy

A system with two competing anisotropies, one of which is random, is considered. Phase diagram in the molecular field approximation with two bicritical points, and a region of metastability is constructed. The renormalization group analysis of the critical behaviour for such a system is carried out. Instead of one of the bicritical points a tetracritical point described by the decoupled fixed point is found.     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Phase glass is a Bose metal: a new conducting state in two dimensions

In the quantum rotor model with random exchange interactions having a nonzero mean, three phases, a (i) phase (Bose) glass, (ii) superfluid, and (iii) Mott insulator, meet at a bicritical point. We demonstrate that proximity to the bicritical point and the coupling between the energy landscape and the dissipative degrees of freedom of the phase glass lead to a metallic state at T = 0. Consequently, the phase glass is unique in that it represents a concrete example of a metallic state that is mediated by disorder, even in 2D. We propose that the experimentally observed metallic phase which intervenes between the insulator and the superconductor in a wide range of thin films is in actuality a phase glass.     

Nematic-smectic-A-smectic-C multicritical point: An alternative model

A new Landau-type phenomenological free-energy function to describe the nematic-smectic-A transition, smectic-A-smectic-C transition and nematic-smectic-C transition is proposed. The influence of pressure on the these phase transitions is discussed by varying the coupling between various order parameters. The phase diagram of the thermodynamic parameters is studied and a possible nematic-smectic-A-smectic-C bicritical point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a bicritical point is observed in the phase diagram. The obtained topology of the pressure-temperature phase diagram is consistent with experimental results.     

Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory

By Monte Carlo simulations on a 3D SO(5) rotator model it is shown that, in contrast to the epsilon expansions of the renormalization group, the bicritical point is stable to biquadratic perturbations of AF-SC (antiferromagnetism-superconductivity) repulsions, which are produced by quantum fluctuations originated from the Gutzwiller projection. Therefore, the present work completes the link from a physical projected SO(5) starting point to an asymptotic SO(5) symmetry point. The tetracritical point is stable for attractive AF-SC interactions. Critical exponents and ratios are evaluated by scaling analysis. Bicritical and tetracritical scaling functions are derived for the first time. Suggestions on experiments are given.     

The phase diagram of simple metamagnets as determined by the cluster variation method

In order to explore the global properties of a simple Ising metamagnet we computed the values of the coupling parameters for which the tricritical behavior is replaced by bicritical endpoints (Lifshitz point). The transition points are determined by means of the cluster variation method. The metamagnets studied have an antiferromagnetic coupling between the spins on two chosen sublattices and a ferromagnetic coupling between spins on the same sublattice. The following lattices and sublatices were considered: two-dimensional square, simple cubic and two different subdivisions of the fcc and bcc lattices each. The method used is based on the coincidence of two roots for the bicritical endpoints and of three roots for the tricritical point. In contrast to the molecular field and the pair approximation results, the presence or absence of the Lifshitz point depends on the lattice structure considered. We discuss the comparison of our results with the results from the renormalization theories.     

Stable periodic vortex shedding studied using computational fluid dynamics, laser sheet flow visualization, and MR imaging

Recirculating and detached flow patterns close to the carotid bifurcation are thought to play an important role in the development of carotid stenoses by promoting atherosclerosis. The aim of this study was to investigate a flow regime with strong transient characteristics, including vortex shedding and transport to develop methodologies appropriate to the analysis of carotid stenoses. The existence of a regular periodic vortex street behind a cylindrical flow obstruction was predicted and analysed in detail by Theodore van Karman in the early 20th century. This model was chosen in our study for both ease of phantom construction and of theoretical modelling using finite element computational fluid dynamics (CFD). The results of the theoretical calculations have been compared with two methods of flow visualization-laser sheet imaging and real-time echo planar magnitude MR imaging. Flow was investigated over a range of Reynold's number from 40 through 400 through which vortex shedding is predicted. Good overall agreement was obtained between the theoretical (16 mm-CFD) and experimental (16+/-2 mm-Laser, 17+/-2 mm-MRI) estimates of the Karman Vortex street wavelength for a Reynolds number of 200.     

How do singularities move in potential flow?

The equations of motion of point vortices embedded in incompressible flow go back to Kirchhoff. They are a paradigm of reduction of an infinite-dimensional dynamical system, namely the incompressible Euler equation, to a finite-dimensional system, and have been called a “classical applied mathematical playground”. The equation of motion for a point vortex can be viewed as the statement that the translational velocity of the point vortex is obtained by removing the leading-order singularity due to the point vortex when computing its velocity. The approaches used to obtain this result are reviewed, along with their history and limitations. A formulation that can be extended to study the motion of higher singularities (e.g. dipoles) is then presented. Extensions to more complex physical situations are also discussed.     

Multiparameter Critical Situations, Universality and Scaling in Two-Dimensional Period-Doubling Maps

We review critical situations, linked with period-doubling transition to chaos, which require using at least two-dimensional maps as models representing the universality classes. Each of them corresponds to a saddle solution of the two-dimensional generalization of Feigenbaum-Cvitanovi? equation and is characterized by a set of distinct universal constants analogous to Feigenbaum’s α and δ. One type of criticality designated H was discovered by several authors in 80-th in the context of period doubling in conservative dynamics, but occurs as well in dissipative dynamics, as a phenomenon of codimension 2. Second is bicritical behavior, which takes place in systems allowing decomposition onto two dissipative period-doubling subsystems, each of which is brought by parameter tuning onto a threshold of chaos. Types of criticality designated as FQ and C occur in non-invertible two-dimensional maps. We present and discuss a number of realistic systems manifesting those types of critical behavior and point out some relevant conditions of their potential observation in physical systems. In particular, we indicate a possibility for realization of the H type criticality without vanishing dissipation, but with its compensation in a self-oscillatory system. Next, we present a number of examples (coupled Hénon-like maps, coupled driven oscillators, coupled chaotic self-oscillators), which manifest bicritical behavior. For FQ-type we indicate possibility to arrange it in non-symmetric systems of coupled period-doubling subsystems, e.g. in Hénon-like maps and in Chua’s circuits. For C-type we present examples of its appearance in a driven Rössler oscillator at the period-doubling accumulation on the edge of syncronization tongue and in a model map with the Neimark–Sacker bifurcation     

Bicriticality in FexCo1-xTa2O6

X-ray and neutron-diffraction, dc magnetic susceptibility, magnetization, and specific-heat measurements are reported for FexCo(1-x)Ta2O6 mixed oxides. X-ray refinement indicates homogeneous samples for all the reported concentrations. The neutron-diffraction measurements reveal magnetic structures with double propagation vectors (+/-1/4,1/4,1/4) for CoTa2O6, and (1/2,0,1/2) and (0,1/2,1/2) for FeTa2O6. The latter remain unchanged in the Fe-rich samples, for 0.46< or =x<1.00, while the Co-rich samples show propagation vectors (+/-1/4,1/4,0) for 0.09< or =x<0.46. The temperature vs x phase diagram exhibits a bicritical point at about T=4.9 K and x=0.46. For this concentration, and at low temperatures, the system shows coexistence of both magnetic structures. This novel bicritical behavior is interpreted as induced by competition between the different magnetic and crystallographic structures.     

Acceleration and ejection of interacting ring vortices by radial flow

Exact solution of two-dimensional hydrodynamic equations for symmetrical configuration of four point vortices in the presence of radial flow is found. This solution describes the dynamics of a dipole toroidal vortex (consisting of two counter-rotating vortex rings) in such a flow. It is shown that in a convergent flow the ring vortices are compressed and ejected with acceleration along the symmetry axes of the system. Possible application to the problem of jets formation in active galaxy nuclei is considered.     

Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics

The combined experimental and numerical study finds a complex mechanism of Z(2) symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z(2) symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z(2)-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z(2) symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.     

涡发生器对高超声速轴对称进气道外部流动的影响

采用三维CFD黏性模拟考察涡发生器对高超声速轴对称进气道外部流动的影响.针对前缘钝化半径0.8 mm和3.2 mm的轴对称进气道外部流场,以涡发生器高度与当地位移边界层厚度比值为影响参数,考察流场结构与性能参数的影响规律.结果表明,涡发生器产生的干扰波系使得前缘激波向外偏移,下游近壁面流动与主流区出现明显的交换,下游流动出现明显的展向非均匀性.涡发生器对流动的影响沿流向逐渐减弱.在气流压缩性能方面,涡发生器下游压比、动压比沿流向开始增大,随后逐渐恢复到无涡发生器工况;Mach数、总压恢复系数开始降低,随后逐渐向无涡发生器工况趋近.涡发生器高度与当地位移边界层厚度的比值h可作为衡量其影响的重要参数.当h≤1.5时,进气道流场结构、性能参数的变化几乎可忽略,h≤3.0时进气道入口处性能参数几乎能够恢复到无涡发生器工况.