A note for the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions

In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional discrete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.

Cold Flow Experiments and Acoustic Investigation on Pressure Oscillation Induced by Flow Instability

Pressure oscillation in solid rocket motor is believed to be the results of the interaction between the flow instability and the acoustics of combustion chamber.Several reasonable and necessary hypothesizes are given to establish an equation to describe this coupling.A cold flow motor called CVS60D(corner vortex shedding 60°)was designed to study the flow-acoustic coupling based on theoretical analysis.Experimental investigations were carried out to determine the acoustics of CVS60D.Corner vortex shedding is generated at the backward facing step which is designed similar to the geometry of the motor with finocyl propellant after the burnout of its fins.A pintle was used to modify the velocity in the duct to change the frequency of vortex shedding.It is found that large amplitude pressure oscillation occurs when the pintle moves to a range of specific position,which indicates that the frequency of vortex shedding is close to one order of acoustic modes of combustion chamber.The amplitude of pressure oscillation changes as the pintle moves.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Review of relaxation oscillations in plasma processing discharges

Relaxation oscillations due to plasma instabilities at frequencies ranging from a few Hz to tens of kHz have been observed in various types of plasma processing discharges. Relaxation oscillations have been observed in electropositive capacitive discharges between a powered anode and a metallic chamber whose periphery is grounded through a slot with dielectric spacers. The oscillations of time-varying optical emission from the main discharge chamber show, for example, a high-frequency （- 40 kHz） relaxation oscillation at 13.33Pa, with an absorbed power being nearly the peripheral breakdown power, and a low-frequency （- 3 Hz） oscillation, with an even higher absorbed power. The high-frequency oscillation is found to ignite plasma in the slot, but usually not in the peripheral chamber. The kilohertz oscillations are modelled using an electromagnetic model of the slot impedance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations, and indicate a variety of behaviours dependent on the matching conditions. In low-pressure inductive discharges, oscillations appear in the transition between low-density capacitively driven and high-density inductively driven discharges when attaching gases such as SF6 and Ar/SF6 mixtures are used. Oscillations of charged particles, plasma potential, and light, at frequencies ranging from a few Hz to tens of kHz, are seen for gas pressures between 0.133 Pa and 13.33 Pa and discharge powers in a range of 75 1200 W. The region of instability increases as the plasma becomes more electronegative, and the frequency of plasma oscillation increases as the power, pressure, and gas flow rate increase. A volume-averaged （global） model of the kilohertz instability has been developed; the results obtained from the model agree well with the experimental observations.

Observation of low-frequency oscillation in argon helicon discharge

We present here a kind of low-frequency oscillation in argon helicon discharge with a half helical antenna.This time-dependent instability shows a global quasi-periodic oscillation of plasma density and electron temperature,with a typical frequency of a few tens of Hz which increases with external magnetic field as well as radiofrequency(RF)power.The relative oscillation amplitude decreases with magnetic field and RF power,but the rising time and pulse width do not change significantly under different discharge conditions.The oscillation can only be observed in some specific conditions of low magnetic fields and low RF power when the gas flows in from one end of the discharge area and out from another end.This global instability is suggested to be attributed to the pressure instability of neutral depletion,which is the result of compound action of gas depletion by heating expansion and gas replenishment from upstream.There are two kinds of oscillations,large and small amplitude oscillations,occurring in different discharge modes.This study could be a good verification of and complement to earlier experiments.This kind of spontaneous pulse phenomenon is also helpful in realizing a pulsing plasma source without a pulsed power supply.

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.

Dynamic instability of collective myosin Ⅱ motors

Some kinds of muscles can oscillate spontaneously,which is related to the dynamic instability of the collective motors.Based on the two-state ratchet model and with consideration of the motor stiffness,the dynamics of collective myosin Ⅱmotors are studied.It is shown that when the motor stiffness is small,the velocity of the collective motors decreases monotonically with load increasing.When the motor stiffness becomes large,dynamic instability appears in the forcevelocity relationship of the collective-motor transport.For a large enough motor stiffness,the zero-velocity point lies in the unstable range of the force-velocity curve,and the motor system becomes unstable before the motion is stopped,so spontaneous oscillations can be generated if the system is elastically coupled to its environment via a spring.The oscillation frequency is related to the motor stiffness,motor binding rate,spring stiffness,and the width of the ATP excitation interval.For a medium motor stiffness,the zero-velocity point lies outside the unstable range of the force-velocity curve,and the motion will be stopped before the instability occurs.

Prediction of Streamwise Flow-Induced Vibration of A Circular Cylinder in the First Instability Range

The streamwise flow-induced vibration of a circular cylinder with symmetric vortex shedding in the first instability range is investigated, and a wake oscillator model for the dynamic response prediction is proposed. An approach is applied to calibrate the empirical parameters in the present model; the numerical and experimental results are compared to validate the proposed model. It can be found that the present prediction model is accurate and sufficiently simple to be easily applied in practice.

Optical bistability of a composite system induced by a broadband squeezed vacuum

A composite system consisting of a degenerate optical parametric oscillator （DOPO） and N two-level atoms interacting with a broadband squeezed vacuum （SV） centred at frequency cas and an input monochromatic pumping field with a frequency ωp is analysed. The corresponding explicit analytical steady-state solutions in the central mode ωp = ωs are derived, and the result displays optical bistability （OB）. In addition, the influence of the broadband SV on the bistable behaviour is analysed in detail.

Controllable optical bistability in a three-mode optomechanical system with a membrane resonator

We study the optical bistability （OB） in a three-mode cavity optomechanical system, where an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission. By investigating the behavior of steady state solutions, we find that the left and right cavities will exhibit the bistable behavior simultaneously in this optomechanical system by adjusting the left and right coupling fields. In addition, one can control the OB threshold and the width of the OB curve via adjusting the coupling strength, the detuning, and the decay rate. Moreover, we further illustrate the OB appearing in the cavity by the effective potential as a function of the position.

Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics

We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.

Universality of Periodic Oscillation Induced in Side Branch of a T-Junction in Numerical Simulation

The flow instability through the side branch of a T-junction is analyzed in a numerical simulation. In a previous experimental study, the authors clarified the mechanism of fluid-induced vibration in the side branch of the T-junction in laminar steady flow through the trunk. However, in that approach there were restrictions with respect to extracting details of flow behavior such as the flow instability and the distribution of wall shear stress along the wall. Here the spatial growth of the velocity perturbation at the upstream boundary of the side branch is investigated. The simulation result indicates that a periodic velocity fluctuation introduced at the upstream boundary is amplified downstream, in good agreement with experimental result. The fluctuation in wall shear stress because of the flow instability shows local extrema in both the near and distal walls. From the numerical simulation, the downstream fluid oscillation under a typical condition has a Strouhal number of 1.05, which approximately agrees with the value obtained in experiments. Therefore, this periodic oscillation motion is a universal phenomenon in the side branch of a T-junction.

Wave Instability and Spatiotemporal Chaos in Reaction-Diffusion System with Oscillatory Dynamics

We investigate the Turing-like wave instability of the uniform oscillator in oscillatory mediums using theoretical and flumerical methods. A propagating wave pattern originated at the corner of the system emerges when the uniform oscillator becomes unstable via Thring-like wave instability. Bifurcations from periodically propagated wave patterns to quasi-periodically propagated wave patterns, then to spatiotemporal chaos occur, as the system size increases from the instability threshold of the uniform oscillator.

Induced ion-channel instability

In this paper, a new mechanism of electromagnetic instability, the induced ion-channel instability, is stud- ied. It is based on the transverse driven betatron oscillation of relativistic electron beam induced by an additional magnetic undulator with a period close to the betatron wavelength in an ion channel. As its amplitude is sensitive to the electron beam energy, the driven betatron oscillation may determine electron beam grouping in the ponderomotive potential by selecting the undulator strength and period, and it provides a new mechanism of electron bunching, re- sulting in electromagnetic instability. Under proper condition, a new free-electron laser based on this mechanism may be realized.

Two-phase flow instability in a parallel multichannel system

The two-phase flow instabilities observed in through parallel multichannel can be classified into three types,of which only one is intrinsic to parallel multichannel systems.The intrinsic instabilities observed in parallel multichannel system have been studied experimentally.The stable boundary of the flow in such a parallel-channel system are sought,and the nature of inlet flow oscillation in the unstable region has been examined experimentally under various conditions of inlet velocity,heat flux,liquid temperature,cross section of channel and entrance throttling.The results show that parallel multichannel system possess a characteristic oscillation that is quite independent of the magnitude and duration of the initial disturbance,and the stable boundary is influenced by the characteristic frequency of the system as well as by the exit quality when this is low,and upon raising the exit quality and reducing the characteristic frequency,the system increases its instability,and entrance throttling effectively contributes to stabilization of the system.

Flow instability of supercritical hydrocarbon fuel in a multi-channel cooling system

Thermally-induced flow instabilities are a critical issue in multi-channel regenerative cooling systems.In particular,the interactions between Density-Wave Oscillations(DWO)and Flow Maldistribution(FMD)can result in complex and disastrous instability phenomena.This study investigates the instability behaviors of hydrocarbon fluid in a four-channel system with a constant heat flux ratio using both frequency-and time-domain methods.As the heat flux increases,the in-tube flow sequentially destabilizes in each channel and converges to new equilibrium states,leading to the emergence of FMD phenomena.This also causes the system eigenvalue to change repeatedly from negative to positive rather than increasing monotonically.Additionally,the system eigenvalues are between those of the two most unstable channels,indicating that the stability behavior of the entire system is dictated by the most unstable channel.After FMD occurs,flow oscillations are activated in channels with weak stability,and the in-tube flow is observed to evolve into various flow patterns,including stable flow,self-sustained oscillation,oscillation divergence,quasiperiodic oscillation,and oscillation excursion.The novel instability mode of oscillation excursion involves a spontaneous transition of operating states.It oscillates from an equilibrium state and then stabilizes at a new operational state after oscillation-induced redistribution.However,the newfound stable state may also be only temporary,with the in-tube flow regressing to the initial state,resulting in quasi-periodic oscillation.

Influence of thermal inhibitor position and temperature on vortex-shedding-driven pressure oscillations

Vortex-acoustic coupling is one of the most important potential sources of combustion instability in solid rocket motors （SRMs）. Based on the Von Karman Institute for Fluid Dynamics （VKI） experimental motor, the influence of the thermal inhibitor position and temperature on vortex-shedding-driven pressure oscillations is numerically studied via the large eddy simulation （LES） method. The simulation results demonstrate that vortex shedding is a periodic process and its accurate frequency can be numerically obtained. Acoustic modes could be easily excited by vortex shedding. The vortex shedding frequency and second acoustic frequency dominate the pressure oscillation characteristics in the chamber. Thermal inhibitor position and gas temperature have little effect on vortex shedding frequency, but have great impact on pressure oscillation amplitude. Pressure amplitude is much higher when the thermal inhibitor locates at the acoustic velocity anti-nodes. The farther the thermal inhibitor is to the nozzle head, the more vortex energy would be dissipated by the turbulence. Therefore, the vortex shedding amplitude at the second acoustic velocity antinode near 3/4L （L is chamber length） is larger than those of others. Besides, the natural acoustic frequencies increase with the gas temperature. As the vortex shedding frequency departs from the natural acoustic frequency, the vortex-acoustic feedback loop is decoupled. Consequently, both the vortex shedding and acoustic amplitudes decrease rapidly.

On the Criteria of Instability for Electrochemical Systems

Both cyclic-voltammetry-based and impedance-based experimental criteria thathave been developed recently for the oscil-latory electrochemical systems are critically appraisedwith two typical categories of oscillators. Consistent conclusions can be drawn by the two criteriafor the category of oscillators that involve the coupling of charge transfer mainly with surfacesteps (e.g. ad- and desorption) such as in the electrooxidation of C_1 organic molecules. Whereas,impedance-based criterion is not applicable to the category of oscillators that involve the couplingof charge transfer mainly with mass transfer (e.g. diffusion and convection) such as in theFe(CN)_6^(3-) reduction accompanying periodic hydrogen evolution. The reason is that the negativeimpedance cannot include the feedback information of convection mass transfer induced by thehydrogen evolution. However, both positive and negative nonlinear feedbacks, i. e., thediffusion-limited depletion and convection-enhanced replenishment of the Fe(CN)_6^(3-) surfaceconcentration, that coexist between the bistability, i. e., Fe(CN)_6^(3-) reduction with and withouthydrogen evolution at lower and higher potential sides respectively, are all reflected in thecrossed cyclic voltammo-gram (CCV). It can be concluded that the voltammetry-based criterion (intime domain) is more intuitive, less time-consuming and has a wider range of applications than theimpedance-based one (in frequency domain).

CISK,EVAPORATION-WIND FEEDBACK MECHANISM AND 30—60 DAY OSCILLATIONS IN THE TROPICAL ATMOSPHERE

A baroclinic semi-geostrophic model with evaporation-wind feedback mechanism(EWFM) and CISK is established,two non-dimensional parameters a and η are introduced to represent EWFM and CISK,respectively.Analytic solutions of the model system are obtained,dynamics analyses and the model atmosphere calculations further confirm that EWFM and CISK are very important physical processes in leading to the low-frequency oscillations in the tropics.

Current oscillations during the electrochemical oxidation of sulfide in the presence of an external resistor

The electrochemical oxidation of sulfide on a polycrystalline platinum electrode was studied under potentiostatic condition when an external resistor is in series with the working electrode. Only two os- cillatory regions can be obtained in the absence of the external resistance, but four oscillatory regions, including two new current oscillations, were found in this system by controlling the external resistance. It is demonstrated that three oscillatory regimes, which arise on the positive branch of current-potential curve, can be classified as HN-NDR (Hidden N-shaped Negative Differential Resistance) oscillators. For the first oscillatory region, various transient complex phenomena, which result from the change of the electrode/electrolyte interface by accumulation of adsorbed element sulfur on the electrode, have been observed. The dynamic behavior of NDR (Negative Differential Resistance) oscillations, appearing along with negative branch of polarization curve, can transform from oscillations into bistability with a sufficient large external resistance in series. Two oscillatory regions in high-potential region classified as HN-NDR type oscillations are separated by a saddle-loop bifurcation. They displayed a sequence of bursting oscillations and irregular oscillations, respectively. The electrochemical oxidation of sulfide provides a model system for studying complex dynamics and possible application in sulfur removal.