Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic （MHD） equations in induction- free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number （based on upstream mean velocity and channel height） for symmetry breaking bifurcation for a sudden expansion channel （1：4） is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately （non-magnetic case）. The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter （M）. It is expansion （1：4） is about 475 for the magnetic parameter M found that the critical value of Reynolds number for smooth = 2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.     

Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio

In this paper we analyse convective solutions of a two dimensional fluid layer in which viscosity depends exponentially on temperature. This problem takes in features of mantle convection, since large viscosity variations are to be expected in the Earth’s interior. These solutions are compared with solutions obtained at constant viscosity. Special attention is paid to the influence of the aspect ratio in the solutions presented. The analysis is assisted by bifurcation techniques such as branch continuation, which has proven to be a useful, systematic method for gaining insight into the possible stationary solutions satisfied by the basic equations. One feature presented by the fluid with non constant viscosity is the presence of pitchfork and saddle-node subcritical bifurcations and the presence of convective solutions below the linear critical threshold. The analysis also provides limits of existence of stationary solutions and draws the boundaries for time dependent convection.     

Bifurcation phenomena in a laser with saturable absorber I

We investigate the bifurcation diagram of a laser with saturable absorber in the low and medium intensity regimes. The linear stability of the stationary solutions corresponding to these regimes is studied. In the low intensity domain, a Hopf bifurcation point is determined from which a time-periodic solution emerges. This solution is contructed and its stability is analyzed in the vicinity of the bifurcation point. It is shown that this time-periodic solution is stable in a finite domain of the parameter space.     

单相三电平H桥逆变器分岔现象的研究

三电平逆变器相较于传统的两电平逆变器具有输出电压谐波畸变率小、开关管电压应力小等优点,因而在大功率场合受到了越来越多的关注. 本文针对一种复合式单相三电平逆变器,对其中的分岔和混沌现象进行了深入的研究,建立了电流闭环比例控制下的一阶离散模型,得到了不同时间段内的频闪映射模型. 以比例系数k,负载电阻R,负载电感L及输入电压E为变化参数,研究了三电平逆变器的分岔现象：通过分岔图和李雅普诺夫指数谱分析了慢变尺度下比例系数、负载电感、负载电阻和输入电压对系统动态性能的影响;通过折叠图直观地观测到了快变尺度下不同比例系数、负载电感所导致的分岔过程. 最后搭建了Matlab/Simulink仿真模型,得到了电流闭环比例控制时电流i的时域波形,仿真结果与理论分析相一致. 研究表明,正确选择单相三电平逆变器的电路参数对于其稳定运行具有重要意义. 关键词： 三电平逆变器 频闪映射 分岔 混沌     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Lattice electrons on a cylinder surface in the presence of rational magnetic flux and disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.     

Bifurcation phenomena in two-dimensional piecewise smooth discontinuous maps

In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border and has been successfully applied to explain nonsmooth bifurcation phenomena in physical systems. However, there exist a large number of switching dynamical systems that have been found to yield two-dimensional piecewise smooth maps that are discontinuous across the border. In this paper we present a systematic approach to the problem of analyzing the bifurcation phenomena in two-dimensional discontinuous maps, based on a piecewise linear approximation in the neighborhood of the border. We first motivate the analysis by considering the bifurcations occurring in a familiar physical system-the static VAR compensator used in electrical power systems-and then proceed to formulate the theory needed to explain the bifurcation behavior of such systems. We then integrate the observed bifurcation phenomenology of the compensator with the theory developed in this paper. This theory may be applied similarly to other systems that yield two-dimensional discontinuous maps.     

Stability analysis on the free surface phenomena of a magnetic fluid for general use

This paper presents an analysis for elucidating a variety of physical processes on the interface (free surface) of magnetic fluid. The present analysis is composed of the magnetic and the fluid analysis, both of which have no limitations concerning the interface elevation or its profile. The magnetic analysis provides rigorous interface magnetic field under arbitrary distributions of applied magnetic field. For the fluid analysis, the equation for interface motion includes all nonlinear effects. Physical quantities such as the interface magnetic field or the interface stresses, obtained first as the wavenumber components, facilitate confirming the relations with those by the conventional theoretical analyses. The nonlinear effect is formulated as the nonlinear mode coupling between the interface profile and the applied magnetic field. The stability of the horizontal interface profile is investigated by the dispersion relation, and summarized as the branch line. Furthermore, the balance among the spectral components of the interface stresses are shown, within the sufficient range of the wavenumber space.     

Electrokinetic phenomena in a kerosene-based magnetic fluid

We propose the methods for studying electrokinetic phenomena in magnetic colloidal systems (magnetic fluids), which make it possible to use the magnetic properties of particles of the disperse phase. Electrophoresis and the sedimentation potential in a kerosene-based magnetic fluid are studied. It is shown that only a small part (approximately one-thousandth) of all disperse particles in the magnetic fluid under investigation are charged, the sign of the particle charge being negative.     

Observations on period-doubling phenomena in a basic plasma experiment

Observations on period-doubling phenomena by exciting lower hybrid and ion cyclotron fluctuations in the presence of rf power in a plasma experiment are reported. The Feigenbaum number δ is calculated for the first two bifurcations and found to be 4.138. Nonlinear nature of the ion cyclotron oscillations gives rise to the interaction between modes that ultimately generate higher harmonics of the initial frequencies.     

压强梯度对托卡马克等离子体有理面上由磁场曲率驱动的漂移模的稳定效应

在流体模型内，我们导出了一个托卡马克等离子体内环形漂移模的色散关系，该色散关系包含了离子压强梯度、磁场梯度与曲率。一方面，磁场梯度与曲率驱动有理面上的不稳定性。另一方面，压强梯度使这些不稳定性稳定。通过解析和数值两种方法，我们获得了把不稳定性增长率压缩到零的临界压强梯度阈值。     

Parametric decay of a magnetic island structure

It is shown that a spatially periodic magnetic island structure can decay into a tearing mode and long-wavelength magnetohydrodynamic fluctuations. The tearing mode has a linger wavelength than that of the island structure, and the growth rate is proportional to $\text{?}{}^{\mathrm{<mtext>3</mtext><mtext>4</mtext>}}$, where ε is the ratio of the reconnection magnetic flux to the shear field flux in the original structure.     

Bifurcation phenomena in an impulsive model of non-basal testosterone regulation

Complex nonlinear dynamics in a recent mathematical model of non-basal testosterone regulation are investigated. In agreement with biological evidence, the pulsatile (non-basal) secretion of testosterone is modeled by frequency and amplitude modulated feedback. It is shown that, in addition to already known periodic motions with one and two pulses in the least period of a closed-loop system solution, cycles of higher periodicity and chaos are present in the model in hand. The broad range of exhibited dynamic behaviors makes the model highly promising in model-based signal processing of hormone data.     

Bifurcation phenomena of photodetached electron flux in parallel external fields

A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H$^- $ in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions. We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.     

New type of magnetic surface levels at a bicrystal boundary

The possibility of magnetic surface levels at a bicrystal boundary in anisotropic metals is pointed out. The existence of the electron orbit marked by geometrical factors is shown to lead to oscillations of static properties as a function of magnetic field and to geometrical resonance in an alternating electromagnetic field.     

High-frequency phenomena in organic conductors in a magnetic field

The propagation of electromagnetic waves in organic layered conductors with metallic conductance and a quasi-two-dimensional electron energy spectrum of arbitrary form is studied theoretically. The depth of penetration of the electromagnetic field into the conductor is found, and it is discovered to be sensitive to the polarization of the incident wave. This is done for an arbitrarily oriented (with respect to the layers) magnetic field so strong that the radius of curvature of the electron path is much smaller than the electron’s mean free path. It is established that studying these effects in experiments can reveal in detail the shape and dimensions of the Fermi surface and the relaxation properties of the conduction electrons. Zh. éksp. Teor. Fiz. 114, 676–686 (August 1998)