Temporal study of GRS 1915+105 with rms-flux relation: The importance of magnetic activities in the corona

The rms-flux relations for some observations of GRS 1915+105 are studied. The rms-flux relations of the light curves in only one state, state C or state A, can be described by the simple non-linear model provided Zhang; we thus interpret that such a linear relation reflects the relative importance of magnetic instability for X-ray emission in the corona of the system, compared to the thermal viscous instability for the X-ray emission in the accretion disk. The rms-flux relations for state B are very scattered, possibly because of the dominance of thermal viscous instability for the X-ray emission in the accretion disk. The complex rms-flux relations for the observations of transitions between two or three states are caused by the combination of the different rms-flux relations of these states. The underlying physical processes are the combination of magnetic topology in the corona and thermal viscous instability in the accretion disk.

     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

行波管放大器中辐射场的极限环振荡和混沌

以行波管放大器中辐射场的非线性不稳定阈值分析为基础，对辐射场从频率分叉到混沌的演化过程和不同区域这些非线性不稳定态的时间特性和频率特性进行了研究.在“软”非线性区域，辐射场表现为极限环振荡和频率分岔，频谱是离散的且相对于载波频率是不对称的.这种不稳定是阵发性的，适当的调节控制参量，可使器件工作在所需的定态或极限环振荡态上；在“硬”非线性区域，辐射场表现为非周期的随机振荡和频率混沌，频谱连续且频带很宽，场幅值较大的成分集中在接近于零频的低频范围里.这种不稳定是连续性的，不能通过调节参量来消除. 关键词： 行波管 辐射场 分岔 极限环 混沌     

Quantum properties near the instability boundary in optomechanical system

The properties of the system near the instability boundary are very sensitive to external disturbances, which is important for amplifying some physical effects or improving the sensing accuracy. In this paper, the quantum properties near the instability boundary in a simple optomechanical system have been studied by numerical simulation. Calculations show that the transitional region connecting the Gaussian states and the ring states when crossing the boundary is sometimes different from the region centered on the boundary line, but it is more essential. The change of the mechanical Wigner function in the transitional region directly reflects its bifurcation behavior in classical dynamics. Besides, quantum properties, such as mechanical second-order coherence function and optomechanical entanglement, can be used to judge the corresponding bifurcation types and estimate the parameter width and position of the transitional region. The non-Gaussian transitional states exhibit strong entanglement robustness, and the transitional region as a boundary ribbon can be expected to replace the original classical instability boundary line in future applications.     

Stability of nuclear rotational states

The stability of rotational states described by using a procedure of the Hartree-Fock-Bogoliubov method is discussed. The stability condition is obtained in a general form and some of its properties are examined with the aid of simplifying approximations. It is pointed out in conclusion that the Coriolis force might lead to the instability of rotational states for sufficiently large angular momenta. The instability of rotational states is caused by the instability of the pairing density, and also by that of the nuclear density distribution. In the former case it is shown that below the critical angular momentum, a first-order phase transition takes place and in some cases the rotational band breaks off. In the latter case, it might be considered that the assumption of an axially symmetric deformation is broken or large change of the equilibrium deformation is brought suddenly. Then discontinuous change of the rotational level might be seen at the unstable point.     

Enhancement of stability and accuracy of the moving particle semi-implicit method

As a Lagrangian gridless particle method, the MPS (Moving Particle Semi-implicit) method has been proven useful in a wide range of engineering applications. Up to now, most of MPS applications have been limited to problems with compressive stress states. This paper investigates the performance and stability of MPS method in simulation of more general hydrodynamic problems, including those characterized by tensile stresses or by changes in the stress states. It is shown that MPS-based simulations are prone to become destabilized in presence of attractive interparticle forces. This instability appears to be similar to the so-called tensile instability in SPH method. Two new modifications, namely, a modified Poisson Pressure Equation and a corrective matrix for pressure gradient model, are proposed to resolve this shortcoming. These two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of MPS method.     

On the response of an oscillatory medium to defect generation

We investigate the response of a system far from equilibrium close to an oscillatory instability to the induction of phase singularities. We base our investigation on a numerical treatment of the complex Ginzburg–Landau equation (CGLE) in two spatial dimensions, which is considered as an order-parameter equation for lasers and other nonlinear optical systems. Defects are randomly generated by a spatially modulated linear growth rate. In the amplitude-turbulent regime, no qualitative change of behaviour can be detected. Phase-turbulent patterns emerging due to the Benjamin–Feir instability are destroyed by the externally injected defects. One observes either states consisting of spiral structures of various sizes which resemble the vortex glass states of the unperturbed system or a travelling wave pattern containing moving topological defects. In parameter space, both states are separated by a well-defined phase boundary which is close to the line separating convectively from absolutely stable travelling waves. PACS 47.54.+r; 89.75.Kd; 42.65.Sf; 47.32.Cc; 47.27.Cn; 05.45.-a     

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.     

Particle lattice models and the dynamical instability of many-body systems

We consider the notion of dynamical instability of many-body systems wherein states, which are arbitrarily close initially, are not close at some other fixed time. In controlling the dynamics of interacting systems of identical Fermions moving on a lattice, we isolate a basic mechanism which causes instability.This work was supported in part by the National Science Foundation.     

Limiting stable states of high-Tc superconductors in the alternating current modes

The limiting current-carrying capacity of high-T _c superconductor and superconducting tape has been studied in the alternating current states. The features that are responsible for their stable formation have been investigated under the conduction-cooled conditions when the operating peak values of the electric field and the current may essentially exceed the corresponding critical values of superconductor. Besides, it has been proved that these peak values are higher than the values of the electric field and the current, which lead to the thermal runaway phenomenon when the current instability onset occurs in the operating modes with direct current. As a result, the stable extremely high heat generation exists in these operating states, which can be called as overloaded states. The limiting stable peak values of charged currents and stability conditions have been determined taking into account the flux creep states of superconductors. The analysis performed has revealed that there exist characteristic times defining the corresponding time windows in the stable development of overloaded states of the alternating current. In order to explain their existence, the basic thermo-electrodynamics mechanisms have been formulated, which have allowed to explain the high stable values of the temperature and the induced electric field before the onset of alternating current instability. In general, it has been shown that the high-T _c superconductors may stably operate in the overloaded alternating current states even under the not intensive cooling conditions at a very high level of heat generation, which is not considered in the existing theory of losses.     

Nucleation and collapse of the superconducting phase in type-I superconducting films

The phase transition between the intermediate and normal states in type-I superconducting films is investigated using magneto-optical imaging. Magnetic hysteresis with different transition fields for collapse and nucleation of superconducting domains is found. This is accompanied by topological hysteresis characterized by the collapse of circular domains and the appearance of lamellar domains. Magnetic hysteresis is shown to arise from supercooled and superheated states. Domain-shape instability resulting from long-range magnetic interaction accounts well for topological hysteresis.     

Limit cycles of the ballast resistor caused by intrinsic instabilities

Spatio-temporal patterns of the ballast resistor are investigated. It is well known that in a voltage-controlled ballast resistor an electrothermal instability leads to stable stationary states consisting of hot and cold domains. Such states may become oscillatory unstable, giving rise to the bifurcation of limit cycles. These limit cycles are not caused by the external circuit but by a recently proposed novel intrinsic mechanism. There are two types of oscillatory instabilities: bulk instabilities and boundary-induced instabilities. The bulk instabilities are caused by resistivities which are not monotonically increasing functions of the temperature. The boundary-induced instabilities occur in small systems with Neumann boundary conditions. To find the bulk instability, experiments with materials showing a metal-semiconductor transition or high-temperature superconductors are suggested. To understand these new phenomena, the equation of motion is reduced to ordinary differential equations where the instabilities can be discussed analytically.     

Modulational instability,quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.     

Fugacity and Density Expansion for Systems with Bound States

The fugacity expansion in different approximations for low densities and for systems with bound and scattering states is discussed. The meaning of a mixed expansion and the possibility to introduce a chemical picture for a system in which bound states dominate is proved. The possibility of a thermodynamical instability is shown.     

The stability of the simple cubic phase of phosphorus

The transition from the rhombohedral phase to the simple cubic phase of phosphorus under pressure is studied within the local density-functional formalism with use of the norm-conserving pseudopotential. The calculated transition pressure is 15.8GPa, which is in good agreement with the measured value, 10GPa. The bonding in the simple cubic phase is shown to be predominantly covalent. It is found that the instability of the simple cubic structure under low pressures is understood by a Peierls' instability, which is just the same as the case of arsenic. It is also shown that the mixing of atomic 3d-orbitals in the occupied states is important for stabilizing the simple cubic structure under high pressures.     

Switching of a spin valve with three magnetic layers

A spin valve with two pinned ferromagnetic layers sandwiching a free ferromagnetic layer with a thickness smaller than the spin diffusion length in the same layer and than the domain wall thickness is considered. The instability conditions are determined for various mutual orientations of the magnetization of the layers. The possibility of a considerable decrease in the instability threshold due to joint action of spin-polarized current and an external magnetic field is indicated. It is shown that in addition to collinear states, a nonequilibrium noncollinear state can exist, into which the system is switched after exceeding the instability threshold.     

Understanding the Yang-Mills ground state: The origin of colour confinement

The essential magnetic instability of the perturbative ground state of a non-abelian Yang-Mills theory recently discovered, is shown to lead to a family of degenerate states, the Savvidy states, where the Yang-Mills fields undergo an infinite (when the ultraviolet cut-off Λ→∞M) condensation process. These states build up the real Yang-Mills ground state, in which colour is confined and governed by the effective lagrangian of anisotropic chromodynamics (ACD), proposed by the present author a few years ago. This appears to solve the problem of confinement in QCD.     

Simple variational method for the closures of the Ornstein-Zernike equation: A study of liquid instability

In this paper a simple variational method is proposed for the solution of the integral equations for hard-core fluids. The variational method is applied to the equations of the mean-spherical approximation for systems consisting of square-well particles at very high densities. Using the static structure-factor singularity as a condition of absolute instability, no high density limit of metastable states is found, up to the density corresponding to the random dense packing.     

Current layers and filaments in a semiconductor model with an impact ionization induced instability

Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.     

Nature of the intrinsic relation between Bloch-band tunneling and modulational instability

In an example of Bose-Einstein condensates embedded in two-dimensional optical lattices, we show that in nonlinear periodic systems modulational instability and interband tunneling are intrinsically related phenomena. By direct numerical simulations we find that tunneling results in attenuation or enhancement of instability. On the other hand, instability results in asymmetric nonlinear tunneling. The effect strongly depends on the band gap structure and it is especially significant in the case of the resonant tunneling. The symmetry of the coherent structures emerging from the instability reflects the symmetry of both the stable and the unstable states between which the tunneling occurs. Our results provide evidence of the profound effect of the band structure on the superfluid-insulator transition.