Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.     

Characterization of Growth Hillocks on the Surface of High-Pressure Synthetic Diamond

Diamond crystals,with dimensions of about 0.5-0.6mm,were synthesized in the presence of Fe-Ni and Fe-Ni-Si catalyst solvents under high-pressure-high-temperature(HPHT) conditions.The as-known dendritic pattern was clearly seen on the (111)or (100)planes of diamond single crystals grown using Fe-Ni as a catalyst solvent.However,the conventional dendritic pattern was not observed in diamonds grown in the presence of Fe-Ni-Si alloy catalyst.Trigonal-type,pyramid-type,polygonal-type and rectangular-type growth hillocks were clearly observed on the (111)and (100) surfaces of diamonds grown from the Fe-Ni-Si-C system,and the density of the hillocks is very high at some positions.Clear successive growth layers can also be found on the (111) planes of the high-pressure diamond single crystals grown in the presence of Fe-Ni-Si alloy catalyst.The growth hillocks distributed on the (111) and (100) planes of the diamonds generally occur on or near growth steps,and some of the hillocks terminate at certain solid inclusions and voids.Growth hillocks on the (111) and (100) surfaces directly indicate the spiral growth mechanismj under HPHT.A possible formation process for growth hillocks is proposed.     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

The reflection of the Lamb wave in a semi-infinite plate

The Lamb wave technique is used in the detection of internal defects inplates.The reflection of the Lamb wave at the free edge of the plate has been shownto be rather complicated.The reflected wave is usually composed of infinite numberof Lamb wave modes even in the case of incidence of one pure mode.The analysisof the reflection problem is complicated in nature as the orthogonality relations ofthe eigen modes of the Lamb wave concern both the stresses and displacements.Weadopt the principle of the least squares as a new approach to simplify the analysis,inwhich the eigen-modes are taken as the trial function.It seems to be simple and effective.In most cases a good enough result can be obtained on using an 8-bitmicrocomputer.Here the coefficients of the various reflected modes are calculated,some interesting phenomena on the mode conversion are indicated and the condi-tions on the pure mode reflection are given.     

Laser Generation of Surface Waves on Cylinder with a Slow Coating

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves.     

Detection of a longitudinal defect in a pipe based on guided circumferential waves techniques

Based on elasticity theory, the multi-modes and disperse characteristics of guided circumferential waves in a pipe were investigated theoretically and experimentally, the disperse curves of guided circumferential waves were gotten by numerical calculations. The relationships between the angle of beam transducer, frequency and guided circumferential modes were analyzed by our guided wave experiment system. Then single guided circumferential mode was excited in the pipe (O.D 88.8 mm, I.D 80.8 mm). An artificial longitudinal defect (25×1×0.7 mm) on the surface of the pipe was detected by use of the single guided circumferential wave. The results show that single guided circumferential mode can be excited in the pipe by choosing special frequency and special angle beam transducer, similar to the excitation of Lamb wave in a plate, and it can be used to find the longitudinal defect on a pipe surface.     

Recent advances on “ordered water monolayer that does not completely wet water” at room temperature

The molecular scales behavior of interfacial water at the solid/liquid interfaces is of a fundamental significance in a diverse set of technical and scientific contexts,ranging from the efficiency of oil mining to the activity of biological molecules.Recently,it has become recognized that,both the physical interactions and the surface morphology have significant impact on the behavior of interfacial water,including the water structures as well as the wetting properties of the surface.In this review,we summarize some of recent advances in the atom-level pictures of the interfacial water,which exhibits the ordered character on various solid surfaces at room or cryogenic temperature.Special focus has been devoted to the wetting phenomenon of"ordered water monolayer that does not completely wet water"and the underlying mechanism on model and some real solid surfaces at room temperature.The possible applications of this phenomenon are also discussed.     

Complex dynamical behaviors of compact solitary waves in the perturbed mKdV equation

In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary waves of the mKdV equation, namely, a compact solitary wave, to be a weak solution, which can be proved. It is shown that the compact solitary wave easily turns chaotic from the Melnikov theory. We focus on the sufficient conditions by keeping the system stable through selecting a suitable controller. Furthermore, we discuss the chaotic threshold for a perturbed system. Numerical simulations including chaotic thresholds, bifurcation diagrams, the maximum Lyapunov exponents, and phase portraits demonstrate that there exists a special frequency which has a great influence on our system; with the increase of the controller strength, chaos disappears in the perturbed system. But if the controller strength is sufficiently large, the solitary wave vibrates violently.     

Dendritic sidebranches of a binary system with enforced flow

In the present paper, the problem of sidebranches in the binary dendritic growth with enforced flow is studied. The positions of the first sidebranch and spacing of dendritic sidebranches are presented. For the neutral stable mode of dendritic growth, effects of various parameters on sidebranches are analysed. Our result shows that sidebranches are produced behind a critical point ξ'_C.     

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.     

各向异性表面张力对定向凝固中共晶生长形态稳定性的影响

研究各向异性表面张力对定向凝固中共晶生长形态稳定性的影响.应用多重变量展开法导出了共晶界面表达式和扰动振幅的变化率满足的色散关系.结果表明,共晶生长系统有两种整体不稳定性机理:由非震荡导致的"交换稳定性"机理和由震荡导致的"整体波动不稳定性"机理.震荡有四种典型模式,即:反对称-反对称(AA-),对称-反对称(SA-)、反对称-对称(AS-)和对称-对称(SS-)模式.稳定性分析表明:共晶界面形态稳定性取决于Peclet数ε的某一个临界值ε_*,当ε大于临界值ε_*时,共晶界面形态不稳定;当ε小于临界值ε_*时,共晶界面形态稳定.随着各向异性表面张力增大,对应于AA-,SA-和SS-模式的临界值ε_(aa*),ε_(sa*)和ε_(ss*)随之减小,表明各向异性表面张力减小这三种模式的稳定性区域;然而,随着各向异性表面张力增大,对应于AS-模式的临界值ε_(as*)随之增大,表明各向异性表面张力增大AS-模式的稳定性区域.     

Study of modulation instability in a temporally incoherent photorefractive ring resonator below the threshold with incoherent light

Modulation instability (MI) and evolution of pattern formation inside a passive non-linear photorefractive ring resonator having cavity-length longer than the coherence length of the light circulating in the resonating cavity has been theoretically analyzed. Dynamics of the system below the threshold conditions have also been analyzed, numerically using linear perturbation theory for the Kerr-type non-linearity. The process of modulation instability in a temporally incoherent cavity below the cavity threshold and the influence of various parameters such as the cavity-length, intensity feedback of the perturbed wave field, amplitude of the incoming beam and spatial frequency on the gain factor and the spatial spectral density have also been studied. For the perturbed wave field, it has been found that the growth rate of MI increases with increase in the intensity feedback as well as the spatial frequency. It has also been found that increasing the intensity feedback of the perturbed wave field, for a given value of the spatial frequency, the spatial spectral density of the perturbation at the output of the non-linear medium increases with the shifting peak positions to the higher spatial frequency side.     

Entanglement spectra of complex paired superfluids

We study the entanglement in various fully gapped complex paired states of fermions in two dimensions, focusing on the entanglement spectrum (ES), and using the Bardeen-Cooper-Schrieffer (BCS) form of the ground-state wave function on a cylinder. Certain forms of the pairing functions allow a simple and explicit exact solution for the ES. In the weak-pairing phase of ?-wave paired spinless fermions (? odd), the universal low-lying part of the ES consists of |?| chiral Majorana fermion modes [or 2|?| (? even) for spin-singlet states]. For |?|>1, the pseudoenergies of the modes are split in general, but for all ? there is a zero-pseudoenergy mode at a zero wave vector if the number of modes is odd. This ES agrees with the perturbed conformal field theory of the edge excitations. For more general BCS states, we show how the entanglement gap diverges as a model pairing function is approached.     

各向异性表面张力对深胞晶界面形态稳定性的影响

应用匹配渐近展开法和多变量展开法研究各向异性表面张力对定向凝固中深胞晶界面形态稳定性的影响, 通过寻找定向凝固系统的模式解获得了深胞晶界面形态满足的量子化条件. 结果表明, 与各向同性的定向凝固系统中深胞晶界面形态稳定性比较, 考虑各向异性表面张力的定向凝固中深胞晶生长界面形态也有两种整体不稳定性机制: 整体波动不稳定性和低频不稳定性. 随着各向异性表面张力的增加, 中性模式产生强振荡的枝晶结构的整体波动不稳定性的不稳定区域减小, 中性模式产生弱振荡的胞晶结构的低频不稳定性的不稳定区域增加.     

极端条件两相界面流与反应流机理、模型与算法研究进展

清华大学喷雾燃烧与推进实验室长期专注于极高速、强可压和高瞬变等极端条件下的两相流和反应流前沿科学问题,并致力于应用基础研究成果解决航空航天动力与推进系统的关键技术难题。综述了实验室近些年在极端条件下两相流动和含化学反应流动物理机理、数理模型与数值算法等方面的研究进展。首先,介绍了实验室发展的耦合高瞬变相变过程的强可压缩气液两相界面流的数理模型和高精度数值方法,以及针对激波受气液（曲）界面约束情况下,描述非定常激波透射/反射（如波角、波强等物理量关系）的激波动力学分析方法。其次,基于上述模型、算法与分析方法,实验室研究了激波液滴相互作用、高速液滴撞击壁面等一系列问题,解析了上述高瞬变过程中复杂波系与界面的时空演化过程。以被激波或壁面冲击的液滴内流体空化初生为例,揭示了曲界面汇聚膨胀波诱导流体空化的机理,推导了预测空化初生位置的理论公式。最后,介绍了面向发动机燃烧室内的强可压缩两相喷雾反应流动,实验室开发了基于Euler-Lagrange框架的高性能数值仿真软件TURFsim,并成功用于真实复杂几何结构的航空发动机燃烧室和超声速燃烧室的数值模拟。以典型的超声速混合层流动数值模拟为例,总结了斜激波增强混合层混合特性的规律及其物理机理,获得了极限条件火核生成及火焰的传播模式与机理,详细分析了液雾弥散与蒸发、小激波和局部爆震波的时空演化特性,提出使用"第三Damk?hler数Da_Ⅲ"定量表征燃烧模式,应用该无量纲参数成功进行了局部准等容燃烧过程的辨识与演化分析。上述研究结果对于航空航天发动机燃烧室复杂物理过程的理解及工程设计具有重要价值。      

未磁化等离子体介质切连科夫脉塞的线性理论

利用线性自洽场理论，讨论了电子在扰动场作用下的三维扰动．在此基础上，对常用的薄环形相对论电子环束在填充未磁化等离子体的介质筒慢波波导中激励的切连科夫辐射进行了详细的分析，导出了此电子环束与慢波系统中任意波导模互作用的色散方程和波增长率，并对其进行了详细的分析和讨论．分析表明切连科夫辐射是由其波导模与电子注模耦合所致．最后详细计算和分析了等离子体密度对色散特性和波增长率的影响 关键词：     

Mode Coupling in a Partially Filled Plasma Waveguide With a Dielectric Liner

The stimulated Raman scattering of a perturbed TM mode in a dielectric loaded partially filled plasma waveguide is considered. The radiation is the result of the scattering of pump electromagnetic wave, which is an EH waveguide mode, off of a space-charge wave. A nonlinear wave equation for a three-wave interaction is used to investigate the coupling of the space-charge and waveguide modes. Dispersion relations for electromagnetic modes are solved numerically to study the frequency characteristics of the interaction of the EH waveguide modes with the space-charge modes. Formulas for the growth rates of the backscattered wave near the electron cyclotron frequency are derived, and the effect of a dielectric liner on the growth rates is investigated. Numerical studies show that the presence of the dielectric liner has an effect on the phase-matching condition and leads to rather larger growth rates close to electron cyclotron resonance.      

Nonparaxial equation for linear and nonlinear optical propagation

The formalism of coupled-mode theory, specialized to the continuum of radiation modes, allows us to extend the standard parabolic wave equation to include nonparaxial terms and vectorial effects, and, in particular, to generalize the nonlinear Schr?dinger equation that describes propagation in the presence of an intensity-dependent refractive index.     

Ignition and transient dynamics of sub-limit premixed flames in microchannels

We examine, via two-dimensional numerical simulation of a model system, some unsteady transient ignition scenarios and sustained oscillatory combustion modes that can occur in a single-pass, conductive channel, premixed microburner. These issues are relevant to the problem of ignition, evolution to stable combustion and the operational modes of microcombustors. First, we describe an unsteady ignition sequence that may occur when a single-pass microburner with initially cold walls has its exit walls heated and maintained at a fixed temperature. In particular, we demonstrate that as the heat from the exit walls propagates down the microburner walls, a reaction wave is driven rapidly down the channel towards the inlet via a sequence of oscillatory ignition and quenching transients. This scenario has been observed experimentally during the ignition of a single-pass microburner. Secondly, we show how an initial axial wall temperature gradient can lead to a variety of sustained combustion modes within the channel, including stable stationary flames, regimes of periodic motion involving quenching and re-ignition, regimes of regular oscillatory combustion, and regimes consisting of a combination of re-ignition/quenching events and regular oscillatory motions, all of which have been observed experimentally.