Chaotic mixing in a steady flow in a microchannel

We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.     

光子晶体光纤四波混频光谱中相位匹配特性的研究

与传统光纤不同,光子晶体光纤可以具有多个零色散波长,在四波混频光谱中,具有更丰富的相位匹配特性。目前很多文献报道了光子晶体光纤非线性光学特性的实验结果,但对其产生机理及光谱的变化规律缺乏详细的理论分析。为此对光纤中四波混频原理进行了分析,给出了高增益的相位匹配条件。利用多极法计算了光子晶体光纤的非线性系数及色散特性。对具有多个零色散波长光子晶体光纤的相位失配特性进行了分析,得到了相位匹配波长随泵浦波长及泵浦功率的变化规律。给出了相位匹配曲线,分析了不同色散曲线的相位匹配波长特点,两个零色散波长光子晶体光纤,在四波混频光谱中将激发出四个新的波长。实验得到了两个零色散波长光子晶体光纤的四波混频光谱,与理论分析一致,验证了相位匹配理论的可靠性。多个零色散波长光纤,能产生丰富的相位匹配曲线,会出现更多的四波混频波长,可以有效的控制光孤子及超短脉冲的四波混频及共振散射产生的光谱特性。为光子晶体光纤中基于四波混频的波长变换及超连续谱的研究提供了理论指导。     

混合弹性颗粒体系声衰减数值模拟

采用概率统计方法——蒙特卡罗方法,建立一种预测液固两相体系中混合弹性球形颗粒声衰减的理论模型。在单颗粒声散射和吸收的基础上,将连续超声波抽象离散化为大量独立的声子,追踪声散射过程,通过统计接收器探测声子数最终确定声衰减系数。采用数值方法对单一球形颗粒的液固两相体系中声衰减进行预测和比较,确定了该方法的可行性后将该方法推广到混合颗粒体系中,对玻璃微珠/铁粉构成的混合颗粒及多分散混合颗粒体系进行数值研究。结果表明:在体积浓度低于10%时,蒙特卡罗法预测得玻璃微珠或铁粉颗粒声衰减和ECAH,Lloyd和Berry,Waterman等建立的模型结果吻合。对于混合颗粒构成的两相体系,算例中,随着体积浓度增大到10%,声衰减系数随混合颗粒数目比的变化呈现出了非线性的变化,同时颗粒物性也会影响不同组分颗粒对声衰减的贡献,算例中铁粉颗粒比玻璃微珠对声衰减的影响更大。      

Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations

Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors’ orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.     

可压缩混合层流场光学效应分析与实验研究

利用量级分析和风洞实验研究了末制导光学外冷窗口典型流动(可压缩混合层流动)气动光学效应的规律性.理论分析主要针对视线误差(boresight error, BSE)与混合层流场特征参数之间的关系进行了讨论. 研究结果表明: 在可压缩混合层中影响时均BSE的特征参数主要有 对流马赫数、雷诺数、自由流与混合层界面剪切应力、自由流速度比和密度比等因素; 采用细光束穿越混合层流场的风洞试验结果主要证实了时均BSE与对流马赫数之间的关系. 关键词： 气动光学效应 可压缩混合层 对流马赫数     

Atmospheric CW-FM-LD-RR ladar for trace-constituent detection: a concept development

We formulate a general framework for simultaneous remote ranging and spectral selection of trace constituents by an appropriate use of frequency modulation combined with mixing and filtering. A theoretical model of a spectroscopic continuous-wave, frequency-modulated, laser-diode-based range-resolving (CW-FM-LD-RR) ladar is developed for the expected echo signal modulated by the nonlinear absorption. Relationships between the heterodyne echo-signal amplitudes and frequencies and trace-gas concentration for each range are analyzed. Features of the echo-signal inversion and its calibration are studied. It is analytically shown that, by suitable processing, the range-dependent concentration profile of the absorbing gas can be extracted.     

Comparison of RANS/CMC modeling of Flame D with conventional and with Presumed Mapping Function statistics

Numerical simulations of Sandia Flame D are presented using Reynolds-averaged formulations plus a two equation turbulence model for the flow and mixing fields and a first order Conditional Moment Closure for the flame model. The distributions of probability and Conditional Scalar Dissipation (CSD) in mixture fraction space are modeled first using a Beta PDF (Probability Distribution Function) plus a theoretical model for CSD and then using the consistent, Presumed Mapping Function-based formulation of Mortensen for both PDF and CSD, in both two and three stream mixing modes. It is shown that there is an improvement in predictions compared with experiment when using the consistent models.     

Anomalous pulse angle dependence of the single and double quantum echoes in a photoinduced spin-correlated coupled radical pair

In this work the response of a spin-correlated coupled radical pair to the sequence flash-t-P _ζ-τ-P _2ζ-T is investigated. For the theoretical analysis, the density operator formalism is used. Analytical expressions are derived for the electron spin single (SQ ESE) and double-quantum echoes (DQ ESE) as a function of pulse flip angle and singlet-triplet mixing angle. To illustrate the theoretical results, computer simulations are presented. In the limit of weak coupling, the “out-of-phase” SQ ESE is shown to be of a pure two-spin order having the maximal amplitude for the flip angle of 65.9°. The echo following the Hahn sequence vanishes in the same limit. This confirms the theoretical result already presented in the literature. However, the more general analysis shows that outside the weak coupling approximation the Hahn echo is of purely one-spin order, whereas the echo following the flash-t-P _ζ-τ-P _2ζ-t sequence has its maximal amplitude for the flip angle of 75° and the singlet-triplet mixing angle of 27°. The “in-phase” single- and double-quantum echoes are shown to vanish due to averaging out, within the electron spin resonance spectrometer deadtime, of contributions modulated with the sum and difference of the zero-quantum beat frequency and the frequency due to the spin-spin interaction within the pair. The calculated out-of-phase DQ ESE signal is inverted with respect to the out-of-phase SQ ESE and has only the half of its amplitude. The DQ ESE vanishes for the Hahn sequence. The echo has maximal amplitude in the weak-coupling limit for the flip angle of 65.9°. In contradiction to the analytical result previously published, the out-of-phase DQ ESE does not vanish for long τ and large zero-quantum-beat frequency.     

Theory of a “stimulated photorefractive backscattering and four-wave mixing” self-pumped phase conjugator

We give a theoretical analysis of a “stimulated photorefractive backscattering and four-wave mixing” (SPB-FWM) self-pumped phase conjugator (SPPC) in which the generation of the phase conjugate wave relies on both stimulated photorefractive backscattering (SPB) and four-wave mixing (FWM) processes. The two pumping beams in the FWM process are, respectively, the forward-propagating beam of which the generation is seeded by the fanning effect, and the backward-propagating beam that is generated by the SPB process. Assuming that the SPB interaction is seeded by the scattering centers in the crystal, we have calculated the threshold four-wave mixing coupling strength (γ₁l₁)_th as a function of the SPB two-wave mixing coupling strength (γ₂l₂) corresponding to the 2k grating and of the reflectivity R′ of the scattering centers. Above threshold, we have also calculated the phase-conjugate reflectivity with a numerical method. Our calculations show that the threshold as well as the reflectivity of a SPB-FWM SPPC strongly depend on γ₂l₂ and R′. It is also shown that a high phase-conjugate reflectivity can be easily realised in doped barium titanate crystals which are shown to have much larger γ₁ and γ₂ than an undoped one.     

Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice

There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet three conditions. First, the computed entropies must lie along the theoretical distribution of entropies as a function of total edge length, which Cushman showed was a parabolic function following from the fact that there is a normal distribution of permuted edge lengths, the entropy is the logarithm of the number of microstates in a macrostate, and the logarithm of a normal distribution is a parabolic function. Second, the entropy must increase over time through the period of the random mixing simulation, following the expectation that entropy increases in a closed system. Third, at full mixing, the entropy will fluctuate randomly around the maximum theoretical value, associated with a perfectly random arrangement of the lattice. I evaluated these criteria in a test condition involving a binary, two-class landscape using the Cushman method of directly applying the Boltzmann relation (s = klogW) to permuted landscape configurations and measuring the distribution of total edge length. The results show that the Cushman method directly applying the classical Boltzmann relation is fully consistent with these criteria and therefore fully thermodynamically consistent. I suggest that this method, which is a direct application of the classical and iconic formulation of Boltzmann, has advantages given its direct interpretability, theoretical elegance, and thermodynamic consistency.     

Pulse polarization entangled-photon generated by chaotic signals in a nonlinear micro-ring resonator for birefringence-based sensing applications

We propose a new concept of birefringence-based sensing using entangled-photon timing-walk-off compensation. Four-wave mixing within a micro-ring resonator is employed, which is introduced by the nonlinear Kerr effect. The two possible entangled photon pairs are randomly formed by using an external polarization control unit. Results obtained have shown that the entangled-photon walk-off state within the ring device can be compensated. This means that the changes in walk-off-state parameters can be measured in response to changes in the applied physical parameters. The experimentally determined relationship between temperature and the entangled-photon walk-off parameter is seen to be in good agreement with the theoretical predictions. The potential of using the proposed system for the development of birefringence-based sensing systems is discussed.     

Theoretical Description of the Third Order Parametric Wave Mixing in a Gas-Filled Capillary of Femto-Second Laser Pulse

The theoretical signal-pressure curves are calculated from approximate analytical solutions of the coupledequations describing the third order parametric wave mixing in a gas-filled capillary of femto-second laser pulses. Thecomparison with the corresponding experimental curves suggests that the following three factors exert important influ-ences on the degree of fitting between the theoretical and experimental results: the walk-off, the phase modulation, andthe third order harmonic of idler pulse.     

Mixing in a T-shaped micromixer at moderate Reynolds numbers

In the present work, the regimes of the flow and mixing of fluids in a T-shaped micromixer in the range of the Reynolds numbers from 1 to 1000 are investigated systematically with the aid of numerical modeling. The flow and mixing regimes are shown to alter substantially with increasing Reynolds numbers. Five different flow regimes have been identified in the total. The dependencies of the friction coefficient and mixing efficiency on the Reynolds number are obtained. A sharp increase in the mixing efficiency at a flow transition from the symmetric to asymmetric steady regime is shown. On the other hand, the mixing efficiency slightly drops in the laminar-turbulent transition region. A substantial influence of the slip presence on walls on flow structure in the channel and mixing efficiency has been revealed.     

Theoretical assessments of major physical processes involved in the depth resolution in sputter profiling

Two of the more important physical processes which militate against high depth resolution capabilities for ion-induced sputter sectioning associated with compositional analysis techniques are surface topography development and recoil atomic mixing. This review describes earlier, simplistic, theoretical modelling of such processes and describes new approaches based upon empirical evidence of the nature and magnitude of these processes. It is shown that, in general, the depth resolution of the sputtering technique will be a complex function of the depth probed and that both “broadenings” and “shifts” in depth evaluation are to be expected.     

Connecting electronic entropy to empirically accessible electronic properties in high temperature systems

A quantitative theoretical model connecting the thermopower and electronic entropy of molten systems is proposed, the validity of which is tested for semiconductors and metallic materials. The model accurately provides the entropy of mixing for molten semiconductors, as shown for the representative system Te–Tl. Predictions of the electronic entropy of fusion for compounds are in agreement with available data and offer a novel means to identify the correct electrical conductivity model when Hall measurements are not available. Electronic entropy for molten semiconductor and metallic systems is shown to reflect order in the molten and solid state. The model proves accurate at predicting the electronic state entropy contribution to the electronic entropy of mixing.     

在单零色散微结构光纤中一次抽运同时发生两组四波混频的实验观察

采用可以减小纤芯面积的小气孔设计方案巧妙设计并成功拉制了一根高非线性的单零色散微结构光纤.利用有限元法模拟并计算得到了该光纤的基模有效折射率、色散系数和非线性系数等基本属性随波长的变化关系,然后利用四波混频的有效相位失配方程模拟了其相位失配曲线.模拟表明,在该光纤中可以同时发生两组四波混频.在位于微结构光纤的正常色散区的0.800,0.810和0.820μm三个波长处,分别采用不同的功率抽运,在实验上都非常明显地观察到了分列于抽运波长两侧的四个增益波带的产生.经与相位失配曲线比较,发现它们满足相位匹配条件,从而证明了两组四波混频过程的同时发生.实验结果与理论预言符合得很好.发生在正常色散区的四波混频效应的产生可归结于负的四阶色散对相位匹配过程的贡献.本文研究可对微结构光纤的结构设计和基于四波混频的多波长转移技术的发展提供经验与借鉴,同时也对非常见波段激光器和宽带光源的开发具有参考意义.     

Phase-matched four-wave mixing of isolated waveguide modes of high-intensity femtosecond pulses in a hollow photonic-crystal fiber

Hollow-core photonic-crystal fibers with a special dispersion profile are shown to allow phase-matched nonlinear optical interactions of isolated air-guided modes of high-intensity femtosecond laser pulses confined in the hollow fiber core. We present theoretical and experimental studies of the four-wave mixing of fundamental and second-harmonic pulses of a Cr:forsterite laser with an initial pulse duration of about 50 fs and an intensity on the order of 10¹⁴ W/cm² in waveguide modes of a hollow photonic-crystal fiber with a core diameter of about 13μm.     

Theoretical Description of the Third Order Parametric Wave Mixing in a Gas-Filled Capillary of Femto-Second Laser Pulse

The theoretical signal-pressure curves are calculated from approximate analytical solutions of the coupled equations describing the third order parametric wave mixing in a gas-filled capillary of femto-second laser pulses, The comparison with the corresponding experimental curves suggests that the following three factors exert important influences on the degree of fitting between the theoretical and experimental results: the walk-off, the phase modulation, and the third order harmonic of idler pulse.     

可压缩混合层光学传输效应理论分析与实验研究

利用量级分析和风洞实验研究了可压缩混合层流动第二发展阶段气动光学效应的规律性.理论分析主要针对二维大尺度结构存在时视线误差(boresight error,BSE)与混合层流场及其特征参数之间的关系进行了讨论.研究结果表明:在混合层发展的第二阶段,时均BSE与对流马赫数呈现出复杂的非线性关系;同时还发现流场中的湍动能和混合层界面处的雷诺应力分布也是影响时均BSE的重要因素;采用细光束穿越混合层流场的风洞试验结果主要证实了时均BSE与对流马赫数之间的非线性关系.