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Experiments on divergent Richtmyer–Meshkov (RM) instability at a heavy gas layer are performed in a specially designed shock tube. A novel soap-film technique is extended to generate gas layers with controllable thicknesses and shapes. An unperturbed gas layer is first examined and its two interfaces are found to move uniformly at the early stage and be decelerated later. A general one-dimensional theory applicable to an arbitrary-thickness layer is established, which gives a good prediction of the layer motion in divergent geometry. Then, six kinds of perturbed SF$_6$ layers with various thicknesses and shapes surrounded by air are examined. At the early stage, the amplitude growths of the inner interface for various-thickness layers collapse quite well and also can be predicted by the Bell model for cylindrical RM instability at a single interface, which indicates a negligible interface coupling effect. Later, a rarefaction wave accelerates the inner interface, causing a dramatic rise in the growth rate. It is found that a thicker gas layer will result in a larger extent that the rarefaction wave can promote the instability growth. A modified Bell model accounting for both Rayleigh–Taylor (RT) instability and interface stretching caused by a rarefaction wave is established, which well reproduces the quick instability growth. At late stages, reverberating waves inside the layer are negligibly weak such that the inner interface growth is dominated by RM instability and RT stability. The major factors driving the outer interface development are a compression wave and interface coupling. A new interface coupling phenomenon existing uniquely in divergent geometry caused by the gradual thinning of the gas layer is observed and also modelled.
Circulating n-3 PUFA, which integrate endogenous and exogenous n-3 PUFA, can be better used to investigate the relationship between n-3 PUFA and disease. However, studies examining the associations between circulating n-3 PUFA and colorectal cancer (CRC) risk were limited, and the results remained inconclusive. This case–control study aimed to examine the association between serum n-3 PUFA and CRC risk in Chinese population. A total of 680 CRC cases and 680 sex- and age-matched (5-year interval) controls were included. Fatty acids were assayed by GC. OR and 95 % CI were calculated using multivariable logistic regression after adjustment for potential confounders. Higher level of serum α-linolenic acid (ALA), docosapentaenoic acid (DPA), DHA, long-chain n-3 PUFA and total n-3 PUFA were associated with lower odds of CRC. The adjusted OR and 95 % CI were 0·34 (0·24, 0·49, Pfor trend < 0·001) for ALA, 0·57 (0·40, 0·80, Pfor trend < 0·001) for DPA, 0·48 (0·34, 0·68, Pfor trend < 0·001) for DHA, 0·39 (0·27, 0·56, Pfor trend < 0·001) for long-chain n-3 PUFA and 0·31 (0·22, 0·45, Pfor trend < 0·001) for total n-3 PUFA comparing the highest with the lowest quartile. However, there was no statistically significant association between EPA and odds of CRC. Analysis stratified by sex showed that ALA, DHA, long-chain n-3 PUFA and total n-3 PUFA were inversely associated with odds of CRC in both sexes. This study indicated that serum ALA, DPA, DHA, long-chain n-3 PUFA and total n-3 PUFA were inversely associated with odds of having CRC in Chinese population.
We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ($k_p$ being the peak wavenumber in the shallow area of depth $h_2$), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role.
Boundary conditions at a liquid–solid interface are crucial to dynamics of a liquid film coated on a fibre. Here, a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid–solid slip on the Rayleigh–Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier–Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner et al. (Nat. Commun., vol. 6, issue 1, 2015, 7409).
Film-based holography employs the use of high-resolution films such as the use of photopolymers or photorefractive materials for recording. These materials, while having high resolution, have a couple of drawbacks. The film-based techniques are typically slow for real-time applications and difficult to allow direct access to the recorded hologram for manipulation and subsequent processing. With recent advances in high-resolution solid-state 2-D sensors and the availability of ever-increasing power of computers and digital data storage capabilities, holography coupled with electronic/digital devices has become an emerging technology with an increasing number of applications such as in metrology, nondestructive testing, and 3-D imaging. While electronic detection of holograms by a TV camera was first performed by Enloe et al. in 1966, hologram numerical reconstruction was initiated by Goodman and Lawrence. In digital holography, it has meant that holographic information of 3-D objects is captured by a CCD, and reconstruction of holograms is subsequently calculated numerically. Nowadays, digital holography means the following situations as well. Holographic recording is done by an electronic device, and the recorded hologram can be numerically reconstructed or sent to a display device (called a spatial light modulator) for optical reconstruction. Or, hologram construction is completely numerically simulated. The resulting hologram is sent subsequently to a display device for optical reconstruction. This aspect of digital holography is often known as computer-generated holography.
In photography, the intensity of a 3-D object is imaged and recorded in a 2-D recording medium such as a photographic film or a charge-coupled device (CCD) camera, which responds only to light intensity. Since there is no interference during recording, the phase information of the wave field is not preserved. The loss of the phase information of the light field from the object destroys the 3-D characteristics of the recorded scene, and therefore parallax and depth information of the 3-D object cannot be observed by viewing a photograph. Holography is a technique in which the amplitude and phase information of the light field of the object are recorded through interference. The phase is coded in the interference pattern. The recorded interference pattern is a hologram. It is reminiscent of Young’s interference experiment in which the position of the interference fringes depends on the phase difference between the two sources. Once the hologram of a 3-D object has been recorded, we can reconstruct the 3-D image of the object by simply illuminating the hologram or through digital reconstruction. We record the complex amplitude of the 3-D object in coherent holography, whereas in incoherent holography, we record the intensity distribution of the 3-D object. In this chapter, we discuss the principles of coherent holography.
To have some basic understanding of optical coherence, we discuss temporal coherence and spatial coherence quantitatively in the beginning of the Chapter. We then concentrate on spatial coherent image processing, followed by spatially incoherent image processing. While spatial coherent imaging systems lead to the concept of coherent point spread function and coherent transfer function, spatially incoherent imaging system introduces intensity point spread function and optical transfer function. Scanning image processing is also covered in the chapter, illustrating an important aspect in that a mask in front of the photodetector can change the coherence properties of the optical system. Finally, two-pupil synthesis of optical transfer functions is discussed, illustrating bipolar processing in incoherent imaging systems.
In modern optical processing and display applications, there are increased needs of a real-time device and such a device is called a spatial light modulator (SLM). Typical examples of SLMs are acousto-optics modulators (AOMs), electro-optic modulators (EOMs) and liquid crystal displays. In this chapter, we will concentrate on these types of modulators and discuss their uses, such as phase modulation and intensity modulation, in information processing.
We have introduced Gaussian optics and used a matrix formalism to describe light rays through optical systems in Chapter 1. Light rays are based on the particle nature of light. Since light has a dual nature, light is waves as well. In 1924, de Broglie formulated the de Broglie hypothesis, which relates wavelength and momentum. In this chapter, we explore the wave nature of light, which accounts for wave effects such as interference and diffraction.
The purpose of this chapter is twofold. We will first discuss basic aspect of signals and linear systems in the first part. As we will see in subsequent chapters that diffraction as well as optical imaging systems can be modelled as linear systems. In the second part, we introduce the basic properties of Fourier series, Fourier transform as well as the concept of convolution and correlation. Indeed, many modern optical imaging and processing systems can be modelled with the Fourier methods, and Fourier analysis is the main tool to analyze such optical systems. We shall study time signals in one dimension and signals in two dimensions will then be covered. Many of the concepts developed for one-dimensional (1-D) signals and systems apply to two-dimensional (2-D) systems. This chapter also serves to provide important and basic mathematical tools to be used in subsequent chapters.
This chapter contains Gaussian optics and employs a matrix formalism to describe optical image formation through light rays. In optics, a ray is an idealized model of light. However, in a subsequent chapter, we will also see a matrix formalism can also be used to describe, for example, a Gaussian laser beam under diffraction through the wave optics approach. The advantage of the matrix formalism is that any ray can be tracked during its propagation though the optical system by successive matrix multiplications, which can be easily programmed on a computer. This is a powerful technique and is widely used in the design of optical element. In this chapter, some of the important concepts in resolution, depth of focus, and depth of field are also considered based on the ray approach.
An easy-to-understand course book, based on the authentic lectures and detailed research, conducted by the authors themselves, on information optics, holography and MATLAB. This book is the first to highlight the incoherent optical system, provide up-to-date, novel digital holography techniques, and demonstrate MATLAB codes to accomplish tasks such as optical image processing and pattern recognition. This title is a comprehensive introduction to the basics of Fourier optics as well as optical image processing and digital holography. A step-by-step guide which details the vast majority of the derivations, without omitting essential steps, to facilitate a clear mathematical understanding. This book also features exercises at the end of each chapter, providing hands-on experience and consolidating understanding. An ideal companion for graduates and researchers involved in engineering and applied physics, as well as interested in the growing field of information optics.
High-molecular-weight glutenin subunits (HMW-GS) contribute to dough elasticity and bread baking quality in wheat. In this study, wheat varieties were classified based on their HMW-GS composition into three groups: 1Dx5 (5 + 10, Gaoyou 8901, Xinmai 28, Xinmai 19, Xinmai 26 and Jinbaoyin), 1Dx2 (2 + 12, Zhoumai 24, Xinmai 9 and Yumai) and 1Dx4 (4 + 12, Aikang 58). Sequence analysis showed that 1Dx-GY8901, 1Dx-XM28, 1Dx-XM19 and 1Dx-XM26 were similar to the 1Dx5 gene and clustered on the same branch, while 1Dx-AK58, 1Dx-ZM24, 1Dx-JBY, 1Dx-YM, 1Dx-XM9 and 1Dx-JBY were more similar to the 1Dx2 gene and clustered on the same branch with 1Dx.2.2. There was a mutation of Ser to Cys at position S2, for an extra Cys in the repeat regions of 1Dx-XM19, 1Dx-XM26, 1Dx-XM28 and 1Dx-GY8901. The wheat HMW-GS genes exhibited similar percentages of α-helix, extended strand, β-turn and random coil structure, with ranges of 13.33–13.59, 4.77–5.78, 7.08–9.18 and 72.3–73.94%, respectively. Sequence conservation and the composition of HMW-GS subunits were also analysed for a series of strong gluten wheat varieties, Xinmai 9 (1, 7 + 8, 2 + 12), Xinmai 19 (1, 7 + 9, 5 + 10), Xinmai 26 (1, 7 + 8, 5 + 10) and Xinmai 28 (1, 7 + 9, 5 + 10). The results of this work should facilitate future breeding efforts and provide the theoretical basis for wheat quality improvement.
According to Hamilton's rule, matrilineal-biased investment restrains men in matrilineal societies from maximising their inclusive fitness (the ‘matrilineal puzzle'). A recent hypothesis argues that when women breed communally and share household resources, a man should help his sisters' household, rather than his wife's household, as investment to the later but not the former would be diluted by other unrelated members (Wu et al., 2013). According to this hypothesis, a man is less likely to help on his wife's farm when there are more women reproducing in the wife's household, because on average he would be less related to his wife's household. We used a farm-work observational dataset, that we collected in the matrilineal Mosuo in southwest China, to test this hypothesis. As predicted, high levels of communal breeding by women in his wife's households do predict less effort spent by men on their wife's farm, and communal breeding in men's natal households do not affect whether men help on their natal farms. Thus, communal breeding by women dilutes the inclusive fitness benefits men receive from investment to their wife and children, and may drive the evolution of matrilineal-biased investment by men. These results can help solve the ‘matrilineal puzzle'.