Chaotic mixing induced transitions in reaction-diffusion systems

We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the rate of the chemical reaction. When the stirring is fast localized perturbations decay towards a spatially homogeneous state. When the stirring is slow (or fast reaction) localized perturbations propagate by advection in form of a filament with a roughly constant width and exponentially increasing length. The width of the filament depends on the stirring rate and reaction rate but is independent of the initial perturbation. We investigate this problem numerically in both closed and open flow systems and explain the results using a one-dimensional "mean-strain" model for the transverse profile of the filament that captures the interplay between the propagation of the reaction-diffusion front and the stretching due to chaotic advection. (c) 2002 American Institute of Physics.     

近海面大气折射对红外探测距离的影响

 基于几何光学和抛物线近似方法建立光线传播轨迹数学模型,计算最大探测距离（MIVR）,并分析蜃影出现的成因。通过数值分析及海上试验的对比验证,结果表明：在相同的风速条件下,MIVR会随海气温差的增大而减小;当海气温差不变时,随着风速的增大,MIVR逐渐减小;海气温差越大,MIVR的递减量越趋于平缓;MIVR与高度位置的对应关系几乎是一条标准的直线,且MIVR随着高度参数的减小而递减;通过与试验数据的对比,模型评估MIVR的准确率较高。     

Scaling of Huygens-front speedup in weakly random media

Front propagation described by Huygens' principle is a fundamental mechanism of spatial spreading of a property or an effect, occurring in optics, acoustics, ecology and combustion. If the local front speed varies randomly due to inhomogeneity or motion of the medium (as in turbulent premixed combustion), then the front wrinkles and its overall passage rate (turbulent burning velocity) increases. The calculation of this speedup is subtle because it involves the minimum-time propagation trajectory. Here we show mathematically that for a medium with weak isotropic random fluctuations, under mild conditions on its spatial structure, the speedup scales with the 4/3 power of the fluctuation amplitude. This result, which verifies a previous conjecture while clarifying its scope, is obtained by reducing the propagation problem to the inviscid Burgers equation with white-in-time forcing. Consequently, field-theoretic analyses of the Burgers equation have significant implications for fronts in random media, even beyond the weak-fluctuation limit.     

Diffusion and reaction-diffusion in fast cellular flows

Cellular structures, as the rolls generated by Rayleigh-Bénard instability, have always been an important topic in nonlinear science. The diffusion of a passive scalar in a given steady cellular flow becomes an interesting question in the limit of a large Péclet number, often realistic. The main result there is that the effective diffusion is somewhere in between the molecular diffusion and the "turbulent" diffusion. A new added twist to this is the reaction-diffusion case, where the front speed is the laminar propagation velocity (without flow) times the Péclet number to the power 1/4. I refine this last result and give the behavior of the prefactor in the Zel'dovich limit of a narrow reaction zone.     

自适应光学曲率波前传感器的衍射理论及其方案分析

曲率波前传感器是自适应光学中的一种很有前途的新型波前传感器。在对衍射理论和几何光学进行近似的基础上,研究了曲率波前传感器的理论分析方法,分析了曲率波前传感器的光学方案和信号获取方法。结果表明,从曲率传感器输出的信号经放大后可直接作为力或弯曲力矩施加到反射镜上,而不需要任何复杂的计算。变形镜可自动地向满足泊松方程的表面形状会聚。利用曲率传感器与双压电晶片反射镜的结合,有望获得一种低价、快速闭环控制的系统。     

Oscillatory thermal-diffusive instability of combustion waves in a model with chain-branching reaction and heat loss

In this paper we investigate the properties and the linear stability of premixed combustion waves in a non-adiabatic thermal-diffusive model with a two-step chain-branching reaction mechanism. Here we focus only on the emergence of the pulsating instabilities, and the stability analysis is carried out for Lewis numbers for fuel greater than one, and various values of Lewis number for radicals. We consider the problem in two spatial dimensions to allow perturbations of a multidimensional nature. It is demonstrated that the flame speed as a function of the parameters is a double-valued C-shaped function, i.e. for a given set of parameter values there are either two solutions, fast and slow solution branches, propagating with different speed, or the combustion wave does not exist. The extinction of combustion waves occurs at finite values of the parameters and non-zero flame speed. The flame structure demonstrates a slow recombination regime behaviour with negligible fuel leakage for the fast solution branch away from the extinction condition. For parameter values close to the extinction condition and on the slow solution branch, the fuel leakage is significant and a fast recombination regime is observed. It is demonstrated that two types of instabilities emerge in the model: the uniform planar and the travelling instability. The slow solution branch is always unstable due to the uniform perturbations. The fast solution branch is either stable or loses stability due to the travelling or uniform perturbations. The switching between the onset of various regimes of instability is due to the bifurcation of co-dimension two. In the adiabatic limit this bifurcation is found for Lewis number for fuel equal to one, whereas in the non-adiabatic case it moves towards values above unity. The properties of the travelling instability are studied in detail.     

White noise perturbation of the viscous shock fronts of the Burgers equation

We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock front plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, however, the front location is random and satisfies a central limit theorem with the variance proportional to the timet, ast goes to infinity. With probability arbitrarily close to one, the front width isO(1) for large time.     

基于模糊控制的自适应光学校正技术

自适应光学中普遍采用的比例-积分-微分(PID)控制严格依赖于变形镜的响应模型,响应模型的标定非常繁琐且性能容易随时间和温度而漂移.采用模糊控制摆脱了对变形镜响应模型的依赖,通过波面的快速重构,从波面中提取波面评价指标,将该评价指标及其微分作为模糊PID控制器的输入.选择模糊输入和输出论域的隶属度函数,设计出模糊规则库,通过模糊推理、解模糊等过程,对PID控制器的3个参数即比例kp、积分ki和微分kd进行模糊自整定,实现了自适应控制.采用高速数字信号处理器(DSP)设计了硬件验证测试平台,通过该平台的测试,证明该方法有效可行,在不需要变形镜响应矩阵的前提下,能够将光斑的衍射极限倍增因子β值从10—12校正到3—4,与传统的PID控制基本一致,但稳定性更好.因无需标定,故降低了变形镜的安装要求.     

High-field high-speed MAS resolution enhancement in 1H NMR spectroscopy of solids

Resolution in ¹H NMR spectra of solids can be significantly enhanced with fast magic-angle spinning and high magnetic fields. A variable field and spinning speed study up to 25 T and 40 kHz shows that the homogeneous line broadening is inversely proportional to the product of magnetic field strength and spinning speed. The combination of high field and fast speed yields a ¹H linewidth approaching the intrinsic limit determined by anisotropy of magnetic susceptibility. An analysis of the anisotropic magnetic susceptibility line broadening is presented.     

LD快轴准直柱透镜多参数加工公差分析理论

为了实现半导体激光器快轴准直柱透镜加工公差的快速、准确制定,在快轴光束准直理论分析的基础上,采用几何光学的方法建立了多参数加工公差理论模型。该模型以各个结构参数的极限偏差值作为公差初始值,以实际的加工精度作为边界条件,并根据具体的准直设计要求进行优化,实现各个参数公差的合理、快速分配。针对常见的TO-MOUNT型号中的一款快轴发散角为36°的半导体激光器设计了快轴准直柱透镜,利用该理论模型实现快轴准直柱透镜加工公差的快速制定,引入该公差后的ZEMAX仿真结果符合准直设计要求,且仿真的出射光束发散角与理论计算结果仅有1.1%的误差。     

Sound and light propagation in a weakly inhomogeneous atmosphere

Small-scale inhomogeneities caused by atmospheric turbulence have a considerable effect on sound and light propagation, producing the fluctuations of these wave fields. V A Krasilnikov [1, 2] performed experiments on phase and amplitude variations of a sound wave propagating through the atmosphere. Fluctuations of light-wave parameters occur, for example, in the well known phenomenon of star scintillation, apparently strongly connected with turbulent irregularities of the atmospheric temperature field [3, 4]‡.

Some calculations of phase (arrival angle) and amplitude fluctuations for a wave propagating through a turbulent medium are described by Krasilnikov [1, 3, 8]. All these and similar calculations are based on the geometrical optics (acoustics) approximation, which may be the reason for disagreement between calculation and experimental data in some cases. Thus, for example, amplitude fluctuations in the geometrical approximation turn out to be proportional to the distance of propagation through a turbulent medium to the power of 3/2. However, observations usually show much slower fluctuation growth.

This paper represents an attempt to consider the problem of amplitude and phase variations for a scalar wave field in terms of more general equations including some diffraction effects. Incidentally, the range of validity of geometrical optics theory becomes clear.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Front propagation in chaotic and noisy reaction-diffusion systems: a discrete-time map approach

We study the front propagation in reaction-diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as t ^1/2 in the pushed case and as t ^1/4 in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes. Received 17 July 2001     

Electromagnetic effects for the resonance-domain IR diffractive optics

Binary optics technology enables the manufacture of arrays of diffractive micro-optical elements which are used in many optoelectronic devices, e.g. the focal plane collection optics. The first-order diffraction grating efficiency decreases in the best part of the resonance-domain region of diffraction, i.e. when the grating period is close to the optical wavelength in the substrate material. A large fraction of the fast binary lens surface relief is built of staircase annular structures whose width is of wavelength scale. Therefore, the rigorous electromagnetic theory of gratings has been applied in this paper to calculate and analyze the diffraction effects for the resonance-domain longwave (8–12 μm) infrared (LWIR) binary optics. It is shown that electromagnetic effects limit the speed of the LWIR first-order diffractive lenses and the optical gain achievable with the diffractive lenses used as the focal plane collection optics in the IR detection systems.     

MLFMA用于三维电大复杂腔体电磁散射特性的快速计算

基于迭代物理光学法的多层快速多极子算法可高效、快速求解电大腔体的散射特性,给出混合算法的迭代公式.对工程上常见的弯曲较缓慢的S弯腔体,通过合适的分段结构化分组,避免两组之间存在的部分面元遮挡的情况,应用广义互易积分处理带有复杂终端的腔体.数值计算结果表明,所用方法准确并能极大地提高计算速度.     

Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: an in vitro study

The influence of cancellous bone microstructure on the ultrasonic wave propagation of fast and slow waves was experimentally investigated. Four spherical cancellous bone specimens extracted from two bovine femora were prepared for the estimation of acoustical and structural anisotropies of cancellous bone. In vitro measurements were performed using a PVDF transducer (excited by a single sinusoidal wave at 1 MHz) by rotating the spherical specimens. In addition, the mean intercept length (MIL) and bone volume fraction (BV/TV) were estimated by X-ray micro-computed tomography. Separation of the fast and slow waves was clearly observed in two specimens. The fast wave speed was strongly dependent on the wave propagation direction, with the maximum speed along the main trabecular direction. The fast wave speed increased with the MIL. The slow wave speed, however, was almost constant. The fast wave speeds were statistically higher, and their amplitudes were statistically lower in the case of wave separation than in that of wave overlap.     

Ultrasound assisted enzyme catalyzed transesterification of waste cooking oil with dimethyl carbonate

This work reports the production of biodiesel with waste cooking oil and dimethyl carbonate in solvent free system through transesterification by immobilized enzyme (Novozym 435) under the influence of ultrasound irradiation. The experiments were conducted in an ultrasonic water bath under three different conditions i.e. ultrasonic irradiation (UI) without stirring, UI coupled with stirring and only stirring to compare their overall effects on fatty acid methyl esters (FAME) conversion. As compared with the conventional stirring method, where FAME conversion was 38.69% at 4 h, the UI without stirring significantly enhanced the conversion of enzymatic transesterification to 57.68% for the same reaction time. However the reaction rate was further increased under the condition of ultrasonication coupled with stirring and resulted into higher conversion of 86.61% for the same reaction time. Effects of reaction parameters, such as temperature, ratio of DMC/oil, speed of agitation and enzyme loading on the conversion were investigated. Furthermore, repeated use of Novozym 435 showed gradual decline in both conversion as well as enzyme activity.