The stability of laminar explosion flames

The paper presents the results of a fundamental experimental and theoretical study of Darrieus–Landau, thermo-diffusive, instabilities in atmospheric explosions, and, on a smaller scale, in laboratory explosions in closed vessels. Pressure dependencies were sought to exploit the leading role of the Peclet number in the phenomena, so that similar Peclet numbers were achieved in both instances. However, in large atmospheric explosions large Peclet numbers were achieved by the size of the fireball, whereas in the closed vessel explosion it was achieved at a higher pressure by a much smaller flame, but because of the higher pressure, one endowed with a small laminar flame thickness. This study covers a much wider range of fuels and of pressures and the dependencies of the phenomena on both of these were carefully studied, although, for the atmospheric explosions, the data only covered propane and methane. The roles of both Markstein and Peclet numbers become clear and give rise to a more fundamental correlating parameter, a critical Karlovitz number, K_cl, for flame stability. This is based on the flame stretch rate, normalised by its multiplication by the chemical reaction time in a laminar flame. The experimentally measured dependencies of this key parameter on pressure and Markstein number are reported for the first time for so many different fuels. The critical Karlovitz number for flame stability decreases with increase in the strain rate Markstein number. As a result, it is possible to predict the extent of the unstable regime for laminar flames as a function of Ma_sr and pressure. Such data can be used to estimate the severity of large scale atmospheric explosions. As Ma_sr becomes highly negative, the regime of stability is markedly reduced.     

快速C60离子团在固体中的库仑爆炸过程Ⅰ——球壳层模型

研究了快速C₆₀离子团在固体中穿行时的库仑爆炸过程.假定离子团中离子之间位置矢量的取向是随机的,并且采用球壳模型描述C₆₀离子团的结构.借助于线性介电响应理论和等离子-极点近似介电函数,推导出C₆₀离子团自能的解析表达式.通过数值求解描述离子团半径变化的运动方程,可以发现自能中的“尾效应”可以降低C₆₀离子团的库仑爆炸速度,甚至可以稳定C₆₀离子团的结构. 关键词： 离子团 库仑爆炸 球壳模型     

Corrections to the Casimir–Polder potential arising from electric octupole coupling

ABSTRACT

Molecular QED theory is employed to derive a generalised formula for the dispersion potential between two molecules with mixed electric multipole polarisability tensors of arbitrary order at each centre. This expression is used to readily extract the pair energy shift between an electric dipole polarisable molecule and a mixed electric dipole–octupole polarisable one, and that between two mixed electric dipole–octupole polarisable species. This is done to see whether these interaction energies give rise to higher-order corrections to the Casimir–Polder potential, as was found in the previously calculated case of the dispersion energy shift between an electric dipole polarisable molecule and an electric octupole polarisable one. Interestingly, for orientationally averaged species, both of the computed interaction energies are independent of the octupole weight-3 term, are retarded, and may be interpreted as higher-order corrections in the fine structure constant to the leading dipole–dipole dispersion potential.     

Combustion effects in confined explosions

Results of shock-dispersed-fuel (SDF) explosion experiments are presented. The SDF charge consisted of a spherical 0.5-g PETN booster surrounded by 1 g of fuel, either flake aluminum (Al) powder or TNT. The charge was placed at the center of a sealed chamber. Three cylindrical chambers (volumes of 6.6, 20, and 40 l with L/D = 1) and three tunnels (L/D = 3.8, 4.65, and 12.5) were used to explore the influence of chamber volume and geometry on completeness of combustion. Detonation of the SDF charge created an expanding cloud of explosion product gases and hot fuel (Al or TNT). When this fuel mixed with air, it formed a turbulent combustion cloud that consumed the fuel and liberated additional energy (31 kJ/g for Al or 15 kJ/g for TNT) over and above detonation of the booster (6 kJ/g) that created the explosion. Static pressure gauges were the main diagnostic. Pressure and impulse histories for explosions in air were much greater than those recorded for explosions in nitrogen—thereby demonstrating that combustion has a dramatic effect on the chamber pressure. This effect increases as the confinement volume decreases and the excess air ratio approaches values between 2 and 3.5.     

Multipoint radiation induced ignition of dust explosions: turbulent clustering of particles and increased transparency

Understanding the causes and mechanisms of large explosions, especially dust explosions, is essential for minimising devastating hazards in many industrial processes. It is known that unconfined dust explosions begin as primary (turbulent) deflagrations followed by a devastating secondary explosion. The secondary explosion may propagate with a speed of up to 1000 m/s producing overpressures of over 8–10 atm, which is comparable with overpressures produced in detonation. Since detonation is the only established theory that allows rapid burning producing a high pressure that can be sustained in open areas, the generally accepted view was that the mechanism explaining the high rate of combustion in dust explosions is deflagration-to-detonation transition. In the present work we propose a theoretical substantiation of an alternative mechanism explaining the origin of the secondary explosion producing high speeds of combustion and high overpressures in unconfined dust explosions. We show that the clustering of dust particles in a turbulent flow ahead of the advancing flame front gives rise to a significant increase of the thermal radiation absorption length. This effect ensures that clusters of dust particles are exposed to and heated by radiation from hot combustion products of dust explosions for a sufficiently long time to become multi-point ignition kernels in a large volume ahead of the advancing flame. The ignition times of a fuel–air mixture caused by radiatively heated clusters of particles is considerably reduced compared with the ignition time caused by an isolated particle. Radiation-induced multipoint ignitions of a large volume of fuel–air ahead of the primary flame efficiently increase the total flame area, giving rise to the secondary explosion, which results in the high rates of combustion and overpressures required to account for the observed level of overpressures and damage in unconfined dust explosions, such as for example the 2005 Buncefield explosion and several vapour cloud explosions of severity similar to that of the Buncefield incident.     

Calculations of the EPR g-tensor using unrestricted two- and four-component relativistic approaches within the HF and DFT frameworks

ABSTRACT

Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework.     

A discrete model exhibiting successive bifurcations leading to the onset of turbulence

A simple discrete model which consists ofN limit-cycle oscillators interacting with a linear coupling is numerically investigated in order to study the sequence of oscillatory states leading to the onset of turbulence. The systems withN=2 and 3 are studied. The system ofN=2 does not exhibit a nonperiodic motion, whereas the system ofN=3 does exhibit a nonperiodic motion. It is shown that, as an external parameter changes, the system ofN=3 undergoes a sequence of bifurcations, exhibiting the singly periodic, doubly periodic and nonperiodic motions, successively. This is similar to the bifurcation scheme for the onset of turbulence proposed by Ruelle and Takens and experimentally shown by Gollub and Swinny in a rotating Couette flow. The successive bifurcations are investigated in details and new features are reported.     

Higher-Order Effects Induced Optical Solitons in Fiber

In this paper, we study the existence conditions of the soliton solutions induced by considering the higher-order effects such as the third-order dispersion (TOD), self-steepening (SS), and self-frequency shift arising from stimulated Raman scattering (SRS) simultaneously in optical soliton communication. Based on the Jacobian expansion method, we successfully obtain bright and dark solitons. The results shows that the resultant inclusion is in agreement with Mollenauer et al. [Physical Review Letters 45 (1980) 1095] when the SRS is not considered; while when the SRS is considered, the existence conditions of the higher-order effects induced bright and dark solitons are not only quite different from those of the group velocity dispersion (GVD)-induced and self-phase modulation (SPM)-induced solitons, but also different from those of the TOD- and SS-induced solitons discussed by Mollenauer et al. [Physical Review Letters 45 (1980) 1095].     

Triaxial octupole deformations and shell structure

Manifestations of pronounced shell effects are discovered when non-axial octupole deformations are added to a harmonic oscillator model. The degeneracies of the quantum spectra are in good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 525–530 (25 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Two-equation hybrid RANS–LES models: a novel way to treat k and ω at inlets and at embedded interfaces

A novel method for prescribing k and ω at inlets and RANS–LES interfaces in embedded LES is presented and evaluated. The method is based on the proposal by Hamba to use commutation terms at RANS–LES interfaces. Commutation terms are added to the k and ω equations in the region near the inlet (i.e. the RANS–LES interface). The proposed method can also be used when prescribing inlet values for k and ω in hybrid LES–RANS. The commutation terms are added in embedded LES at the LES side of the RANS–LES interface. The influence of the extent of the region where the commutation terms are added is investigated. It is found that it is most efficient to add commutation terms in only one cell layer adjacent to the interface; in this way, tuned constants are avoided. The commutation term in the ω equation is derived from transformation of the k and ? equations. When the commutation terms are used in only one cell layer, the commutation term in the k equation corresponds to a negative convection term. Hence, the commutation term can be omitted and a homogeneous Neumann inlet boundary condition can be used. The commutation term in the ω equation is retained. The novel method is evaluated for channel flow (Re_τ = 8000), boundary layer flow (Re_θ = 11, 000) and backward-facing step flow (Re_H = 28, 000). Hybrid LES–RANS is used for the first two flows and embedded LES for the backward-facing step flow.     

高空核爆炸下大气的X射线电离及演化过程数值模拟

利用数值模拟程序模拟了不同高度核爆炸下大气的X射线电离及演化过程.结果表明: X射线电离产生的电子数密度在射线到达后约100 ns时刻达到峰值, 峰值数密度随着到裸核区距离的增加而减小;电子具有较长的寿命, 电子寿命随着到裸核区距离的增加而增大; X射线电离空气产生正离子O⁺, O₂⁺, N₂⁺,爆高为120 km情况下 O⁺的峰值数密度与O₂⁺的相近,能维持约1 s. X射线对空气的电离影响范围在数十千米以内,在距裸核区较近的区域, 爆高为80 km时产生的电子峰值数密度比爆高为120 km时的电子峰值数密度高, 在距裸核区较远的区域则相反.     

标准映象的周期分岔及其向混沌的过渡

本文研究了标准映象的周期轨道在其余数R=1和R=0附近的行为,对于前者出现倍周期分岔序列,其分岔率δ及标度因子α和β与其它二维保面积映象的结果一致;对于后者发生同周期分岔,这与标准映象的奇对称性有关。文中还计算了混沌轨道的李雅普诺夫指数,发现在倍周期分岔序列的聚点k_∞附近,存在标度关系: λ=λ_∞+A(k—k_∞)+B(k—k_∞)^τ, 其中因子τ=0.32。这与理论推断的结果τ=(ln(2))/(l 关键词：     

EXACT SOLUTIONS OF THE MODIFIED GROSS–PITAEVSKII EQUATION IN "SMART" PERIODIC POTENTIALS IN THE PRESENCE OF EXTERNAL SOURCE

We report wide class of exact solutions of the modified Gross–Pitaevskii equation (GPE) in "smart" Jacobian elliptic potentials, in the presence of external source. Solitonlike solutions, singular solutions, and periodic solutions are found using a recently developed fractional transform in which all the amplitude parameters are nonzero. These results generalize those contained in (T. Paul, K. Richter and P. Schlagheck, Phys. Rev. Lett. 94 (2005) 020404.) for nonzero trapping potential.     

Influence of chemical kinetics on spontaneous waves and detonation initiation in highly reactive and low reactive mixtures

Understanding the mechanisms of explosions is important for minimising devastating hazards. Due to the complexity of real chemistry, a single-step reaction mechanism is usually used for theoretical and numerical studies. The purpose of this study is to look more deeply into the influence of chemistry on detonation initiated by a spontaneous wave. The results of high-resolution simulations performed for one-step models are compared with simulations for detailed chemical models for highly reactive and low reactive mixtures. The calculated induction times for H₂/air and for CH₄/air are validated against experimental measurements for a wide range of temperatures and pressures. It is found that the requirements in terms of temperature and size of the hot spots, which can produce a spontaneous wave capable to initiate detonation, are quantitatively and qualitatively different for one-step models compared to detailed chemical models. The time and locations when the exothermic reaction affects the coupling between the pressure wave and spontaneous wave are considerably different for a one-step and detailed models. The temperature gradients capable to produce detonation and the corresponding size of hot spots are much shallower and, correspondingly, larger than those predicted using one-step models. The impact of the detailed chemical model is particularly pronounced for the methane-air mixture. In this case, not only the hot spot size is much greater than that predicted by a one-step model, but even at the elevated pressure, the initiation of detonation by a temperature gradient is possible only if the temperature outside the gradient is rather high, so that can ignite a thermal explosion. The obtained results suggest that the one-step models do not reproduce correctly the transient and ignition processes, so that interpretation of the simulations performed using a one-step model for understanding mechanisms of flame acceleration, DDT and the origin of explosions must be considered with great caution.     

Universal behaviour in families of area-preserving maps

We have investigated numerically the behaviour, as a perturbation parameter is varied, of periodic orbits of some reversible area-preserving maps of the plane. Typically, an initially stable periodic orbit loses its stability at some parameter value and gives birth to a stable orbit of twice the period. An infinite sequence of such bifurcations is accomplished in a finite parameter range. This period-doubling sequence has a universal limiting behaviour: the intervals in parameter between successive bifurcations tend to a geometric progression with a ratio of $\text{1}\text{δ}\text{=}\text{1}\text{8.721097200}$…, and when examined in the proper coordinates, the pattern of periodic points reproduces itself, asymptotically, from one bifurcation to the next when the scale is expanded by α = ?4.018076704… in one direction, and by β = 16.363896879… in another. Indeed, the whole map, including its dependence on the parameter, reproduces itself on squaring and rescaling by the three factors α, β and δ above. In the limit we obtain a universal one-parameter, area-preserving map of the plane. The period-doubling sequence is found to be connected with the destruction of closed invariant curves, leading to irregular motion almost everywhere in a neighbourhood.     

An integrable coupled Alice–Bob modified Korteweg de-Vries system: Lax pairs,Bäcklund transformations,residual symmetries and exact solutions

ABSTRACT

A coupled Alice–Bob modified Korteweg de-Vries (mKdV) system is established from the mKdV equation in this paper, which is nonlocal and suitable to model two-place entangled events. The Lax integrability of the coupled Alice–Bob mKdV system is proved by demonstrating three types of Lax pairs. By means of the truncated Painlevé expansion, auto-Bäcklund transformation of the coupled Alice–Bob mKdV system and Bäcklund transformation between the coupled Alice–Bob mKdV system and the Schwarzian mKdV equation are demonstrated. Nonlocal residual symmetries of the coupled Alice–Bob mKdV system are researched. To obtain localized Lie point symmetries of residual symmetries, the coupled Alice–Bob mKdV system is extended to a system consisting six equations. Calculation on the prolonged system shows that it is invariant under the scaling transformations, space-time translations, phase translations and Galilean translations. One-parameter group transformation and one-parameter subgroup invariant solutions are obtained. The consistent Riccati expansion (CRE) solvability of the coupled Alice–Bob mKdV system is proved and some interaction structures between soliton–cnoidal waves are obtained by CRE. Moreover, Jacobi periodic wave solutions, solitary wave solutions and singular solutions are obtained by elliptic function expansion and exponential function expansion.     

快速C60离子团在固体中的库仑爆炸过程Ⅰ球壳层模型

研究了快速C60 离子团在固体中穿行时的库仑爆炸过程 .假定离子团中离子之间位置矢量的取向是随机的 ,并且采用球壳模型描述C60 离子团的结构 .借助于线性介电响应理论和等离子 极点近似介电函数 ,推导出C60 离子团自能的解析表达式 .通过数值求解描述离子团半径变化的运动方程 ,可以发现自能中的“尾效应”可以降低C60 离子团的库仑爆炸速度 ,甚至可以稳定C60 离子团的结构     

Double Hopf bifurcation induces coexistence of periodic oscillations in a diffusive Ginzburg–Landau model

We perform bifurcation analysis in a complex Ginzburg–Landau system with delayed feedback under the homogeneous Neumann boundary condition. We calculate the amplitude death region, and it turns out that the boundary of the amplitude death region consists of two Hopf bifurcation curves with wave number zero. The existence conditions for double Hopf bifurcations are established. Taking the feedback strength and time delay as bifurcation parameters, normal forms truncated to the third order at double Hopf singularity are derived, and the unfolding near the critical points is given. The bifurcation diagram near the double Hopf bifurcation is drawn in the two-parameter plane. The phenomena of amplitude death, the existence of stable bifurcating periodic solutions, and the coexistence of two stable periodic solutions with fast oscillation and slow oscillation respectively are simulated.     

Propagation features of head-on collision dust acoustic solitary waves in four-component quantum plasmas

ABSTRACT

In framework of the extended Poincaré–Lighthill–Kuo, the properties of dust acoustic (DA) solitary wave’s interaction are investigated in four-component quantum dusty plasma. Two Korteweg–de Vries equations describing the colliding DA solitary waves are derived by eliminating the secularities. By knowing the explicit form of the solitary wave solutions, the leading phase changes, trajectories and phase shifts are obtained, accordingly. The effects of various physical parameters such as the quantum mechanical parameters, the charge ratio between positive and negative dust particles, the mass ratio between negative and positive dust particles and the ratio of electron to ion temperatures are studied extensively. Our findings showed that these parameters play a significant role on the characteristics and basic features of DA solitary waves such as phase shifts in trajectories due to collision. The obtained results may be beneficial to understand well the collision of DA solitary waves that may occur in laboratory plasmas, space plasma as well as in plasma applications.