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We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the basic energy $\|\sqrt{\rho_0}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2$ is small. In particular, the initial density may contain vacuum states and even have compact support. Moreover, the large time behavior of the solution is also obtained., Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:1507.06471, arXiv:1506.03884, Nonlinearity, 2017

This paper advances an alternative data-density method, which provides a more accurately and reliably identify on-line liquidus temperature (TL ) of molten aluminium electrolyte. An in-house computer program of data-density algorithm was developed for a complete investigates and analysis the relationship between data-density and temperature curve of molten aluminium electrolyte. Traditional step-cooling algorithm detects TL largely depending only on temperature curve geometry, such as inflection point is obvious or obscure and imperceptible. When there is not inflection point on temperature curve, in such case, traditional step-cooling algorithm is unable to firm clarify there exists TL or not, not mention to identify TL . Experiments and tests show that even slight or nearly no nuance of inflection point presented on the temperature curve, but there exists a little different data-density on the temperature curve, which can be captured and identified by data-density algorithm. Direct measurements in industrial cells by data-density algorithm is clearly outperforms conventional step-cooling first derivatives and step-cooling second derivatives methods for determining the TL of molten aluminium electrolyte.

One hundred and one years after J J Thomson was awarded the Nobel Prize for the discovery of the electron, the 2007 Nobel Prize for Physics was awarded to Professors Peter Grunberg and Albert Fert for the discovery of giant magnetoresistance (GMR) in which the spin as well as the charge of the electron is manipulated and exploited in nanoscale magnetic materials. The journey to GMR started with Lord Kelvin who 150 years ago in 1857 made the first observations of anisotropic magnetoresistance and includes Sir Neville Mott who in 1936 realized that electric current in metals could be considered as two independent spin channels. Modern technology also has a significant role to play in the award of this Nobel Prize: GMR is only manifest in nanoscale materials, and the development of nanotechnology growth techniques was a necessary pre-requisite; further, the considerable demands of the magnetic data storage industry to drive up the data density stored on a hard disk fuelled an enormous international research effort following the initial discovery with the result that more than 5 billion GMR read heads have been manufactured since 1997, ubiquitous in hard disks today. This technology drive continues to inspire exploration of the spin current in the field now known as spintronics, generating new ideas and applications. This review explores the science underpinning GMR and spintronics, the different routes to its discovery taken by Professors Grunberg and Fert, the new science, materials and applications that the discovery has triggered and the considerable potential for the future.

We present a novel-mastering concept of Two-dimensional structures using a single writing spot. We describe its implementation for the existing liquid immersion mastering set-up, from initial concept and feasibility analysis to mastered discs of up to 60 GB/layer data density.

We present the status of our efforts to demonstrate the feasibility of recording on a cover-layer protected dual-layer optical disc with a blue laser and NA=1.45 objective lens that is based on a solid immersion lens (SIL). We discuss the potential data density and some practical and theoretical considerations for the light path, the objective lens and the media. In particular, we show a lens design and results of prototype manufacturing for a NA=1.45 lens that focuses on the data layer of an optical disc through a sub-wavelength air gap and a 3 µm spin coated cover-layer that protects the data on the disc.

The storage capacity of a fluorescent bit-wise volumetric optical data storage system is limited by the inter-layer crosstalk and the maximum compensation range of spherical aberration induced by different layers inside the medium. Lens designs of far-field and near-field optical systems suitable for volumetric storage are presented. The maximum compensation range of each design is calculated. The storage densities of far-field and near-field confocal systems in terms of bits-in-2 are derived based on the maximum compensation ranges and appropriate data layer spacings that induce a -30 dB maximum level of inter-layer crosstalk. It is shown that an optimized near-field system is able to achieve 1.65 Tb-in-2 data density.

An experimental study was made of multichannel recording of one-dimensional high-density ( 5 × 107 bit/cm2) holograms. Characteristics of the process of recording of one-dimensional holograms in bulk photosensitive media were analyzed and the recorded data density was increased by a superposition of a hologram. The dependences of the recorded data density on the number of superpositions of holograms, on the thickness of the photosensitive layers, and on other parameters of the recording and reconstruction (readout) schemes were determined. The possibility of increasing the data capacity of holographic disks by interference copying and multiple superposition in thick-layer photosensitive materials was studied.

A study was made of a method for storing data by perforation of a thin film (Te or Ag on a Plexiglas substrate) by injection-laser radiation of wavelengths in the range 830–880 nm. Submicron (of area 0.5μ2 or more) holes were formed, so that the recorded data density corresponded to the level in audio disks.

Fourier holograms were recorded using a reference wave transmitted by a glass fiber. About 104 bits could be recorded and read out from a hologram of ~1 mm2 area and the signal/noise ratio in the reconstructed image was at least 10.

It is shown that conventional semiconductor lasers can be used for the retrieval of binary data from holograms in which the stored data density is ~104 bits/mm2.