Self-sustained Wave Research Articles

Structure and control of self-sustained target waves in excitable small-world networks

Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks. A dominant phase-advanced driving (DPAD) method, which is generally applicable for analyzing all oscillatory complex networks consisting of nonoscillatory nodes, is proposed to reveal the self-organized structures supporting this type of oscillations. The DPAD method explicitly explores the oscillation sources and wave propagation paths of the systems, which are otherwise deeply hidden in the complicated patterns of randomly distributed target groups. Based on the understanding of the self-organized structure, the oscillatory patterns can be controlled with an extremely high efficiency.

A ring-like heterogeneous medium-induced self-sustained target waves in excitable media

The formation of self-sustained target wave in a two-dimensional excitable medium into which a ring-like heterogeneous excitable medium is introduced is investigated. The numerical results show that the initial perturbation can produce a self-sustained target wave in an excitable medium when the excitabilities of two media and the size of the ring are appropriately chosen. The physical mechanism responsible for the formation of self-sustained target wave is analyzed.

Implementation of the thermonuclear process in D3He-9Be plasma on the basis of a Z pinch with an ultrafast laser ignition

A new concept of inertial-magnetic confinement fusion is proposed. This concept is based on a high-current Z pinch combined with a femtosecond laser. The fusion target is composed of a D3He fuel contained under a high pressure inside a sealed cylindrical capsule made from metallic 9Be. An electric discharge along the capsule preheats the target and transforms it into a state of compressed liner. A subsequent TW femtosecond-laser pulse focused on a target end face causes ultrafast cold ignition of a small portion of the D3He fuel. This laser impact generates energetic electrons and ions, which trigger a nuclear-physics mechanism of a catalytic heating of the fuel and also creates a detonation shock wave capable of propagating along the plasma filament. It is shown that the self-sustaining fusion burn wave can appear in the D3He-9Be plasma, in which case the bulk of the energy release is carried by nonradioactive ions, with the energy gain being in excess of 50. The possibility of probing the fusion process by means of gamma-ray spectroscopy is also discussed. The radiative-capture reactions 3He(d, γ), D(d, γ), and 3He(3He, γ) naturally accompanying the burning of the D3He fuel are shown to serve as a convenient diagnostic tool. A nuclear “marker” of D3He fusion on the basis of the detection of monochromatic gamma rays produced in the reaction 9Be(α, γn), which is induced in the liner beryllium shell by energetic fusion alpha particles, is also examined.

Numerical investigation of the compressible flow past an aerofoil

Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach numberM∞= 0.76 and a Reynolds numberRe= 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

Combining spiral and target wave detection to analyze excitable media dynamics

Excitable media dynamics is the lossless active transmission of waves of excitation over a field of coupled elements, such as electrical excitation in heart tissue or nerve fibers, cAMP signaling in the slime mold Dictyostelium discoideum or waves of chemical activity in the Belousov–Zhabotinsky reaction. All these systems follow essentially the same generic dynamics, including undamped wave transmission and the self-organized emergence of circular target and self-sustaining spiral waves. We combine spiral recognition, using the established phase singularity technique, and a novel three-dimensional fitting algorithm for noise-resistant target wave recognition to extract all important events responsible for the layout of the asymptotic large-scale pattern. Space–time plots of these combined events reveal signatures of events leading to spiral formation, illuminating the microscopic mechanisms at work. This strategy can be applied to arbitrary excitable media data from either models or experiments, giving insight into for example the microscopic causes for formation of pathological spiral waves in heart tissue, which could lead to novel techniques for diagnosis, risk evaluation and treatment.

Frontal polymerization with encapsulated initiator

Frontal Polymerization (FP) is a process that converts monomers into polymers by means of a propagating spatially localized reaction front. In the simplest case, a mixture of monomers and initiator is placed into a test tube and upon initiation of the reaction at one end of the tube, a self-sustained wave develops and propagates through the tube. Monomer/initiator systems can suffer from a limited pot life, meaning that over a period of time the systems will spontaneously polymerize before they can be used. One way to avoid the undesirable spontaneous polymerization is by microencapsulating the initiator. A mathematical model of nonadiabatic FP waves with encapsulated initiator is presented.

Deflagration-to-detonation transition in nitromethane mist/aluminum dust/air mixtures

Deflagration-to-detonation transitions (DDTs) in nitromethane mist/air mixture clouds, flaked aluminum dust/air mixture clouds, and nitromethane mist/flaked aluminum dust/air mixture clouds have been studied in an experimental tube of inner diameter 199 mm and length 29.6 m. The mist/dust/air multiphase mixtures were generated by injecting liquid/dust samples into the experimental tube. The droplet dimensions of the nitromethane mist cloud were analyzed, calculated, and measured. The multiphase fuel/air mixture clouds were ignited by means of an electric spark. The characteristics of different stages during the DDT process in the clouds of the various mixtures in the experimental tube have been studied and analyzed. A self-sustained quasi-detonation wave formed in the nitromethane mist/air mixture clouds, while a self-sustained detonation wave formed in the flaked aluminum dust/air mixture clouds and in the nitromethane mist/flaked aluminum dust/air mixture clouds. The detonation parameters of the clouds of the different mixtures have been studied and compared.

Combustion synthesis of TiN–Ti silicide and TiN–Si 3N 4 composites from Ti–Si 3N 4 powder compacts in Ar and N 2

Preparation of the TiN–Ti silicide and TiN–Si 3N 4 composites was conducted by solid-state and solid–gas combustion of the Ti–Si 3N 4 powder compacts in Ar and N 2, respectively. Effects of the sample stoichiometry on combustion characteristics and product compositions were studied. The dual roles played by Si 3N 4 in these two synthesis routes were investigated; that is, Si 3N 4 serves as a reactant in formation of the TiN–Ti silicide composite, but it is inert when producing the TiN–Si 3N 4 composite. For the samples with a molar ratio of Ti/Si 3N 4 between 4.0 and 9.0, the solid-state reaction with a self-sustaining combustion wave was achieved under Ar and final products were the composite materials of TiN with TiSi 2 and/or Ti 5Si 3. The increase of the Ti content in the reactant mixture facilitated formation of the Ti-rich silicide Ti 5Si 3, which enhanced the reaction exothermicity and led to an improvement in the phase conversion. As a result, the TiN–Ti 5Si 3 composites were obtained from the samples with Ti/Si 3N 4 = 7.75 and 9.0. On the other hand, the powder compact of Ti/Si 3N 4 = 3.0 was adopted to prepare the TiN–Si 3N 4 composite through solid–gas combustion under nitrogen of 0.45–1.82 MPa. It was found that the reaction of Ti with nitrogen was exothermic enough to sustain the combustion front in a self-propagating manner, during which Si 3N 4 acted as an inert diluent. The increase of nitrogen pressure contributed to a higher degree of nitridation. A nitrogen pressure as high as 1.48 MPa was required to achieve complete nitridation of Ti and to prevent Ti from reacting with Si 3N 4, thus resulting in formation of the TiN–Si 3N 4 composite free of impurities.

Fracture Waves Revisited

Self-sustaining fracture waves hypothesized by Galin and Cherepanov (1966) have been observed in shock-compressed glasses and in Prince Rupert’s drops, but their speed did not correspond to the predicted value. This controversy is addressed in the present note. We now assume that this speed is equal to the local velocity of sound in the particulate material just behind the wave front, and show that, then, it is in a reasonable agreement with test data. The specific heat spent on the self-sustaining fracture wave in soda lime glass is estimated to be 1 to 20 J/g for moderately high pressures.

Self-sustained nonlinear waves in traffic flow

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic ("inviscid") continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama, N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.

Investigation of Self-Sustaining Waves in Metastable Systems: Deflagration to Detonation Transition

Self-sustaining waves can propagate in metastable media; energy needed to support such waves is released by the wave itself. The examples are waves of combustion and waves of boiling in overheated liquids. As a rule, two regimes of propagation exist: subsonic and supersonic. The difference is based on the different mechanisms of medium activation. Processes of transition between those regimes were less studied up to now, in comparison with pure subsonic or supersonic modes. Knowing mechanisms of controlling detonation initiation is important to work out effective preventive measures, such as suppressing deflagration-to-detonation transition in the case of combustible mixture ignition, and mitigation of a detonation wave in case it is already developed. On the other hand, the advantages of burning fuel in a detonation regime in comparison with slow burning at constant pressure attract increasing attention to pulse detonation burning chambers and to their possible application to new generation engines. The deflagration-to-detonation transition can be a principal stage of the work cycle in a pulse detonation engine, and the knowledge of details ofthis process and means of control can significantly decrease the predetonation distance and optimize the device. This work contains a review of the results obtained in theoretical and experimental investigations of deflagration-to-detonation transition processes in gases. Influence of internal geometry and flow turbulization on the detonation onset is considered; the influence of temperature and fuel concentration in the unburned mixture is discussed. Transitional processes of overheated liquid boiling up are also analyzed.

Fast ignition by detonation in a hydrodynamic flow

A general concept of fast ignition by a hydrodynamic pulse is developed. The main statements of the concept are formulated having in mind the need to ignite the pre-compressed thermonuclear fuel of the inertial confinement fusion (ICF) target. Initially, combustion must be initiated inside the hydrodynamic flow during its action on the target. The conditions for propagating a self-sustaining thermonuclear-detonation wave from an igniter on the thermonuclear fuel of the ICF-target must be provided. For this, the deuterium–tritium (DT) igniter placed in the forward part of the hydrodynamic flow should not only be heated up to thermonuclear temperature, but also compressed to a density close to the density of the ICF-target fuel. It is shown that the detonation of the multilayer conical target (containing DT-ice and a heavy pusher) enables fast ignition of the ICF target fuel of 200–500 g/cm3 density at an implosion velocity of 300–500 km/s.

Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves

Driving a one-dimensional collisionless Maxwellian (Vlasov) plasma with a sufficiently strong longitudinal ponderomotive driver for a sufficiently long time results in a self-sustaining nonsinusoidal wave train with well-trapped electrons even for frequencies well below the plasma frequency, i.e., in the plasma wave spectral gap. Typical phase velocities of these waves are somewhat above the electron thermal velocity. This new nonlinear wave is being termed a kinetic electrostatic electron nonlinear (KEEN) wave. The drive duration must exceed the bounce period τB of the trapped electrons subject to the drive, as calculated from the drive force and the linear plasma response to the drive. For a given wavenumber a wide range of KEEN wave frequencies can be readily excited. The basic KEEN structure is essentially kinetic, with the trapped electron density variation being almost completely shielded by the free electrons, leaving just enough net charge to support the wave.

Radiation-induced cryocopolymerization of hydrogen cyanide and epichlorohydrin: Copolymerization traveling waves initiated by mechanical fracture at 77 K

Low-temperature (77–150 K) radiation-induced copolymerization of hydrogen cyanide (HCN) and epichlorohydrin (ECH) has been studied. Copolymers have been obtained in two modes of running the reaction, the thermally activated postpolymerization at slow heating of the preliminarily γ-irradiated system and the traveling wave of copolymerization initiated by local brittle fracture of solid samples at 77 K. The threshold values of parameters (a dose of preliminary irradiation, comonomer ratio in the initial mixture) necessary for the realization of the self-sustained wave mode of copolymerization have been determined. An increase in the HCN concentration in the initial comonomer mixture suppresses the copolymerization, and the yield of the copolymer decreases. Epichlorohydrin-soluble copolymers with the content of HCN units up to 5.7 mol % have been obtained as the result of the process.

Fabrication of MgSiN<sub>2</sub> Powders via Combustion Synthesis Process

The feasibility of synthesizing MgSiN2 powders through combustion synthesis process is demonstrated. A self-sustained combustion wave can be initiated with or without the addition of active diluent. The wave propagation resulted in a product with several secondary phases in addition to the main phase MgSiN2 when the combustion reaction was initiated without the addition of active diluent. As the active diluent was used in the reactant mixtures, the amounts of the secondary phases were decreased. The effect of active diluent addition on the phase composition and morphology of the final product was discussed. Furthermore, the use of MgSiN2 crystal seeds in the reactant mixtures was also investigated. It is found that the active diluent can facilitate the nitridation reaction. The experimental results showed that changing the experimental parameters such as the amount of active diluent and the MgSiN2 crystal seeds could optimize the fabrication of MgSiN2 powders through combustion synthesis process.

Bubble detonation as a self-sustained solitary wave with energy release

Previous experiments have shown that a bubble detonation wave is a resonant or self-sustained solitary wave in a bubble medium. Bubble detonation is modeled by a solitary wave with energy release in bubbles. The equation describing a solitary wave of small amplitude is shown to be an analog of nonlinear Boussinesq equation of the fourth order. A comparison of the solution obtained with averaged experimental pressure profiles shows that the analytical solution is suitable for describing bubble detonation waves with a finite pressure amplitude. In the model proposed, the time of action of solitary-wave compression on a separate bubble is several times the bubble oscillation period. This result agrees with experimental data and confirms the presence of a collective resonant effect in a bubble medium. Satisfactory agreement is obtained between experimental and theoretical data on the pressure profile and extent and velocity of bubble detonation waves.

On Self-Sustaining Fracture Waves

The breakage of a tiny tail on a head of solid glass just removed from a glass bath and treated by fluoric acid (a “Batavian tear") makes the tear explode into a cloud of dust with the sound like that of a shot. This explosion reminds that of TNT but TNT disintegrates into molecules of the order of 10−9 m while the glass particles of dust are of the order of 10−6 m and have the same chemical composition as the solid glass. Rock bursts in deep mines of South Africa and Russia represent another example of the sudden, explosive self-destruction. To explain this phenomenon the theory of self-sustaining fracture waves was suggested earlier by Galin and Cherepanov (1966). This theory was based on the analogy with detonation waves later criticized as insufficiently substantiated. The approach presented below is based only on the conservation laws and does not use any analogies. It proves that the self-sustaining fracture wave can propagate only in compressed structures at the speed of longitudinal elastic waves.

Layered superconductors as nonlinear waveguides for terahertz waves

We show that unusual nonlinear self-sustained waves, called nonlinear waveguide modes NWGMs, can propagate along thin slabs of layered superconductors. We show that these waves are stable in the main approximation for extremely anisotropic superconductors if the nonlinear wave amplitude is smaller than a critical value. These modes have no analogs among linear Josephson plasma waves and do not exist in thick samples. The magnetic field of the NWGM is distributed symmetrically with respect to the middle of the slab, decays far from the sample, and can change its sign inside. The impedance ratio of the tangential electric- and magnetic-field amplitudes for NWGMs can be of the order of unity, resulting in a nonmonotonic dispersion relation, k, strongly sensitive to the NWGM amplitudes. Thus, the “stopping light” phenomenon, now controlled by the magnetic-field amplitude, can be observed. Resonance excitations of the NWGMs should produce anomalies in the amplitude dependence of the reflectivity and transmissivity of the incident terahertz waves, which could be useful for terahertz devices.

The Nonlinear Dynamics of Time-Dependent Subcritical Baroclinic Currents

Abstract The nonlinear dynamics of baroclinically unstable waves in a time-dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time-dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear, a symmetry breaking is detected in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time-dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasigeostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded, the inviscid, linear problem is formally stable. However, calculations show that a small degree of nonlinearity is enough to destabilize the flow, leading to large amplitude vacillations and turbulence. When the most unstable wave is not the longest wave in the system, a cascade up scale to longer waves is observed. Indeed, this classically subcritical flow shows most of the qualitative character of a strongly supercritical flow. This result supports previous suggestions of the important role of background time dependence in maintaining the atmospheric and oceanic synoptic eddy field.

The effects of heat exchange and fluid production on the ignition of a porous solid

In this paper we study a system of nonlinear parabolic equations representing the evolution of small perturbations in a model describing the combustion of a porous solid. The novelty of this system rests on allowing the fluid and solid phases to assume different temperatures, as opposed to the well-studied single-temperature model in which heat is assumed to be exchanged at an infinitely rapid rate. Moreover, the underlying model incorporates fluid creation, as a result of reaction, and this property is inherited by the perturbation system. With respect to important physico-chemical parameters we look for global and blowing-up solutions, both with and without heat loss and fluid production. In this context, blowup can be identified with thermal runaway, from which ignition of the porous solid is inferred (a self-sustaining combustion wave is generated). We then proceed to study the existence and uniqueness of a particular class of steady states and examine their relationship to the corresponding class of time-dependent problems. This enables us to extend the global-existence results, and to indicate consistency between the time-independent and time-dependent analyses. In order to better understand the effects of distinct temperatures in each phase, a number of our results are then compared with those of a corresponding single-temperature model. We find that the results coincide in the appropriate limit of infinite heat-exchange rate. However, when the heat exchange is finite the blowup results can be altered substantially.