Numerical simulations of pulsating detonations: II. Piston initiated detonations

Extremely long time, high-resolution one-dimensional numerical simulations are performed in order to investigate the evolution of pulsating detonations initiated and driven by a constant velocity piston, or equivalently by shock reflection from a stationary wall. The results are compared and contrasted to previous simulations where the calculations are initiated by placing a steady detonation on the numerical grid. The motion of the piston eventually produces a highly overdriven detonation propagating into the quiescent fuel. The detonation subsequently decays in a quasi-steady manner towards the steady state corresponding to the given piston speed. For cases where the steady state is one-dimensionally unstable, the shock pressure begins to oscillate with a growing amplitude once the detonation speed drops below a stability boundary. However, the overdrive is still being degraded by a rarefaction which overtakes the front, but on a time-scale which is very long compared with both the reaction time and the period of oscillation. As the overdrive decreases, the detonation becomes more unstable as it propagates and the nature (e.g. period and amplitude) of the oscillations change with time. If the steady detonation is very unstable then the oscillations evolve in time from limit cycle to period doubled oscillations and finally to irregular oscillations. The ultimate nature of the oscillations asymptotically approaches that of the saturated nonlinear behaviour as found from calculations initiated by the steady state. However, the nonlinear stability of the steady detonation investigated in previous calculations represents only the very late time (O(10⁵) characteristic reaction times) behaviour of the piston problem.     

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

The properties of a 2D quantum ring under rotating and external magnetic field effects are investigated. The Landau levels and their inertial effects on them are initially analyzed. Among the results obtained, it is emphasized that the rotation lifted the degeneracy of Landau levels. The second part deals with the electronic confinement in a 2D ring modeled by a hard wall potential. The eigenstates are described by Landau states as long as they are not too close to the ring edges. On the other hand, near the ring edges, the energies increase monotonically. These states are known as edge states. Edge states have a significant role in the physical properties of the ring. Thus, the Fermi energy and magnetization are analyzed. In the specific case of magnetization, two approaches are considered. In the first approach, an analytical result for magnetization is obtained but without considering rotation. Numerical results show the de Haas-Van Alphen (dHvA) oscillations. In the second approach, rotating effects are considered. In addition to the dHvA oscillations, the Aharonov–Bohm-type (AB) oscillations are verified, which are associated with the presence of edge states. The effects of rotation on the results are discussed and it is found that rotation is responsible for inducing AB oscillations.     

Perturbation-induced radiative decay of solitons

New results concerning emission of radiation (quasi-linear waves) from kinks described by various versions of a perturbed sine-Gordon equation are presented. Considered physical problems pertain to condensed matter physics and nonlinear optics. In perticular, intensities of Swihart wave emission from a fluxon in a long dc driven Josephson junction, and of spin wave emission from a domain wall in a weak ferromagnet driven by external constant magnetic field are calculated. A general estimate for an exponentially small intensity of emission from a kink oscillating near a bottom of an effective potential wall is obtained. A system of coupled double sine-Gordon equations describing a double DNA helix is briefly investigated. It is demonstrated that a collision of a bi-kink (a bound state of two 2Π-kinks belonging to different subsystems) with a 4Π-kink belonging to either subsystem may result in excitation of large-amplitude internal oscillations of both the colliding solitons, and the rate of radiative damping of those oscillations is found. At last, radiative effects accompanying motion of a stimulated-Raman-scattering soliton in a dissipative medium are studied.     

Diamagnetic domains and magnetostriction in beryllium

Magnetostriction was for the first time studied under the conditions of formation of diamagnetic domains (Condon domains). Transverse magnetostriction oscillations on a beryllium single crystalline plate oriented normally to magnetic field were measured in magnetic fields up to 7 T at temperatures down to 1.5 K. The relative amplitude of oscillations increased almost as the square of magnetic field and reached 10^?5. The signal had a sawtoothed shape corresponding to alternation of homogeneous and inhomogeneous (domain) states in the region of the existence of magnetic domains. The arising of domains was accompanied by singularities in the observed signals which is explained by an anomalous increase in the compressibility coefficient of the domain state: coefficient oscillations were more than 100 times larger than the value predicted by the standard theory. The observed relation between magnetization current and deformation led us to conclude that the compressibility of the metal was fully determined by conduction electrons. Magnetostriction then exactly compensated Fermi level oscillations. The position of the Fermi level therefore remained constant under magnetic field variations. In addition, the domain wall thickness had to increase as the plate grew thicker.     

Soliton of Bose–Einstein condensate in a trap with rapidly oscillating walls: II. Analysis of the soliton behavior upon a decrease in the wall oscillation frequency

This work is a continuation of our study [1], in which a two-scale analytical approach to the investigation of a soliton oscillon in a trap with rapidly oscillating walls has been developed. In terms of this approach, the solution to the equation of motion of the soliton center is sought as a series expansion in powers of a small parameter, which is a ratio of the intrinsic frequency of slow soliton oscillations to the frequency of fast trap wall oscillations. In [1], we have examined the case ε ? 1, in which, to describe the motion of the soliton, it is sufficient to restrict the consideration to the zero approximation of the sought solution. However, when the frequency of wall oscillations begins to decrease, while the parameter begins to increase, it is necessary to take into account corrections to the zero approximation. In this work, we have calculated corrections of the first and second orders in to this approximation. We have shown that, with an increase in, the role played by the corrections related to fast oscillations of the trap walls increases, which results in a complex shape of the envelope of oscillations of the soliton center. It follows from our calculations that, if the difference between the amplitudes of wall oscillations is not too large, the analytical solution of the equation of motion of the soliton center will coincide very well with the numerical solution. However, with an increase in this difference, as well as with a decrease in the wall oscillation frequency, the discrepancy between the numerical and analytical solutions generally begins to increase. Regimes of irregular oscillations of the soliton center arise. With a decrease in the frequency of wall oscillations, the instability boundary shows a tendency toward a smaller difference between the wall oscillation amplitudes. In general, this leads to enlargement of the range of irregular regimes. However, at the same time, stability windows can arise in this range in which the analytical and numerical solutions correlate rather well with each other. Our comparative analysis of the analytical and numerical solutions has allowed us not only to study their properties in detail, but also to draw conclusions on the limits of applicability of the analytical approach.     

Spectrum of flexural oscillations of a domain wall with drifting Bloch lines

It is observed that in single-crystalline yttrium iron garnet the amplitude of characteristic flexural oscillations of a 180° domain wall containing Bloch lines increases sharply when drift of the Bloch lines is excited. The resonance frequencies of these oscillations are virtually identical to those of flexural oscillations of a monopolar wall. It is shown experimentally that this phenomenon is most likely caused by a magnetic aftereffect. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 72–75 (10 January 1998)     

A bifurcation analysis of two coupled calcium oscillators

In many cell types, asynchronous or synchronous oscillations in the concentration of intracellular free calcium occur in adjacent cells that are coupled by gap junctions. Such oscillations are believed to underlie oscillatory intercellular calcium waves in some cell types, and thus it is important to understand how they occur and are modified by intercellular coupling. Using a previous model of intracellular calcium oscillations in pancreatic acinar cells, this article explores the effects of coupling two cells with a simple linear diffusion term. Depending on the concentration of a signal molecule, inositol (1,4,5)-trisphosphate, coupling two identical cells by diffusion can give rise to synchronized in-phase oscillations, as well as different-amplitude in-phase oscillations and same-amplitude antiphase oscillations. Coupling two nonidentical cells leads to more complex behaviors such as cascades of period doubling and multiply periodic solutions. This study is a first step towards understanding the role and significance of the diffusion of calcium through gap junctions in the coordination of oscillatory calcium waves in a variety of cell types. (c) 2001 American Institute of Physics.     

Finite,free torsional oscillations of hollow circular cylinders made of a mooney material

Finite, free torsional oscillations of hollow circular cylinders of arbitrary wall thickness and of arbitrary length are investigated. The material of the cylinder is assumed to be homogeneous, isotropic, elastic and incompressible. The governing differential equations of motion are obtained by the use of finite elasticity theory. While the exact solution of the problem requires a rather unrealistic body force distribution in the axial direction, it is shown that, in the solutions corresponding to long tubes and hollow disks, the error introduced by ignoring the body force distribution is negligibly small for large wavelengths.     

超燃火焰稳定凹腔自激振荡特性的数值研究

对超声速冷流条件下用于超燃冲压发动机的凹腔火焰稳定器的自激振荡特性进行研究.采用混合RANS/LES方法对非定常流场进行数值模拟,考虑了凹腔的长深比和后缘角度两个关键参数.混合RANS/LES方法很好的捕捉到流场非定常大尺度结构并揭示了凹腔自由剪切层的演化过程.对凹腔压力振荡历程进行幅频分析,所得到的频率和理论分析结果与文献计算结果符合的很好.结果表明,凹腔的长深比和后缘角度对凹腔自激振荡特性都有很大的影响.随着凹腔长深比的减小,振荡能量趋于集中到某些频率对应的振荡模式上.随着凹腔后缘倾角的减小,大部分频率对应的振荡很快的被削弱;相对于陡后缘凹腔,小角度后缘凹腔只有较高频率对应的振荡模式存在.     

Hamiltonian description of bubble dynamics

The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.     

Anomalous surface deceleration of a domain wall in an amorphous ferromagnet

On soft magnetic amorphous specimens, a rapid decrease in the surface amplitude of 180° domain wall oscillations relative to the bulk amplitude is observed with increasing frequency of the magnetizing field. The dynamics of the domain wall is studied by a magnetooptical method at the specimen surface and by the induction method in the bulk. The results of the experiment disagree with the theory, which takes into account the effect of eddy currents and predicts that, with increasing frequency, the surface amplitude of the domain wall oscillations should decrease slower than the bulk amplitude. The observed behavior of the domain wall is explained by its interaction with macroscopic defects at the specimen surface. This interaction gives rise to unsteady chaotic surface wall displacements, which lead to an increase by several orders of magnitude in the effective surface damping parameter in the Landau-Lifshits equation.     

弹性微管内气泡的非线性受迫振动

将弹性管壁视为膜弹性结构, 探索在外部声场作用下弹性微管内液柱-气泡-管壁构成耦合振动系统的非线性特征. 利用逐级近似法对系统非线性共振频率、基频和三倍频振动幅值响应、 分频激励共振机理等进行了理论分析. 基频和三倍频振动的幅-频响应数值结果表明: 气泡的轴向共振和管壁共振不能同时出现; 两垂直方向的振动均表现出幅值响应多值性, 进而可能引起系统的不稳定声响应; 三倍频振动在低频区的声响应强于高频区. 关键词： 弹性微管 受迫振动 非线性振动 气泡声响应     

Growth-induced instability in metabolic networks

Product-feedback inhibition is a ubiquitous regulatory scheme for maintaining homeostasis in living cells. Individual metabolic pathways with product-feedback inhibition are stable as long as one pathway step is rate limiting. However, pathways are often coupled both by the use of a common substrate and by stoichiometric utilization of their products for cell growth. We show that such a coupled network with product-feedback inhibition may exhibit limit-cycle oscillations which arise via a Hopf bifurcation. Our results highlight novel evolutionary constraints on the architecture of metabolism.     

Hysteresis, force oscillations, and nonequilibrium effects in the adhesion of spherical nanoparticles to atomically smooth surfaces

Equilibrium and nonequilibrium aspects of particle adsorption on the walls of fluid-filled nanochannels are examined via molecular dynamics simulations. The force on the particle and the free energy of the system are found to depend on the particle's history (hysteresis), in addition to its radial position and the wetting properties of the fluid, even when the particle moves quasistatically. The hysteresis is associated with changes in the fluid density in the gap between the particle and the wall, which persist over surprisingly long times. The force and free energy exhibit large oscillations with distance when the lattice of the structured nanoparticle is held in register with that of the tube wall, but not if the particle is allowed to rotate freely. Adsorbed particles are trapped in free-energy minima in equilibrium but can desorb if forced along the channel.     

Self-sustained oscillations in a plasma-wall system with strongly inhomogeneous diffusion of charged particles

A simple system with a hydrogen plasma confined by a magnetic field parallel to the bounding material wall is considered. The charged particles diffuse out of the plasma, recombine on the wall and return into the plasma volume as neutrals, which are ionized by electrons. It is demonstrated that macroscopic self-sustained oscillations are an intrinsic feature of such a system if the diffusion coefficient of charged particles is strongly inhomogeneous in the plasma.     

Nonlinear magnetoacoustic interactions in weak ferromagnets

The pinning and interaction of a single domain wall with normal magnetoelastic waves excited during its motion in a single-crystal yttrium orthoferrite plate, were discovered and investigated by a method based on the magneto-optical Faraday effect. The dependences of the bending wave amplitude and the spectra of shear waves, which can be excited by a moving domain wall, were calculated. The results obtained are interpreted with allowance for the interactions of excited oscillations in both the magnetic and elastic subsystems of the orthoferrite.     

Duration of transient oscillations in ring networks of unidirectionally coupled neurons

Properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network. The duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons. The distribution of the duration is approximated by a power-law function when the number of neurons is large. Further, transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases.     

Modeling of a self-excited pulse combustor and stability analysis

The major bottleneck for popularization and utilization of the conventional mechanical valve pulse combustors is the self-priming mode of gas supply. An aerodynamic valve (as against mechanical valve) self-excited pulse combustor of the Helmholtz-type with continuous supply of gas and air was designed and a mathematical model was established in this paper. The theoretical model employed well-stirred reactor model and a single step Arrhenius chemistry, and took those factors which might affect the combustion stability into account. The factors include the variation of the mass rate of the reactants affected by the pressure in the combustion chamber, the convective and radiation heat loss in the combustion chamber, and the heat transfer and wall friction in the tailpipe. The effect of wall temperature of combustion chamber, wall heat transfer coefficient, tailpipe length and friction coefficient on combustionstability were analyzed. The range of combustion oscillations can be predicted. It is theoretically and experimentally shown that combustion oscillations can be produced with a continuous supply of fuel and air without mechanical valves. The experimental data show qualitative agreement with predictions from the theoretical model. The theoretical model could be a tool for designing and optimizing the self-excited pulse combustor.     

Universal phase shift and nonexponential decay of driven single-spin oscillations

We study, both theoretically and experimentally, driven Rabi oscillations of a single electron spin coupled to a nuclear-spin bath. Because of the long correlation time of the bath, two unusual features are observed in the oscillations. The decay follows a power law, and the oscillations are shifted in phase by a universal value of approximately pi/4. These properties are well understood from a theoretical expression that we derive here in the static limit for the nuclear bath. This improved understanding of the coupled electron-nuclear system is important for future experiments using the electron spin as a qubit.