A quantization property for blow up solutions of singular Liouville-type equations

Motivated by the study of self-dual vortices in gauge field theory (cf. (Vortices and Monopoles, Birkhauser, Boston, 1980; Solitons in Field Theory and Nonlinear Analysis, Monographs in Mathematics, Springer, New York, 2001)), we consider a “concentrating”solution-sequence u_k satisfying

     

Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source

In a conventional sinusoidal phase-modulating laser-diode (SPM-LD) interferometer, the wavelength of the LD is sinusoidally modulated by varying its injection current. However, the intensity modulation is associated with the wavelength modulation, which affects the measurement accuracy. We propose an SPM-LD interferometer insensitive to the intensity modulation of the light source, in which the influence of the intensity modulation is eliminated by choosing the appropriate sinusoidal phase modulation depth. Computer simulations and experiments are performed for real-time displacement measurement with the proposed SPM-LD interferometer. The measurement accuracy has been improved and the measurement repeatability is less than 1 nm. No additional components are required in our proposed method that leads to a simple system compared with the other previously proposed methods.     

Using diffractive optical element and Zygo interferometer to test large-aperture convex surface

A valid method for measuring the large-aperture convex surface by using a curved diffractive optical element (DOE) and a Zygo interferometer is demonstrated experimentally. In this method, the direct use of source and high-resolution CCD camera of Zygo interferometer represents a major advance in the areas of adjustment. The DOE, fabricated by combining laser direct writing and lithography, results in higher accuracy, efficiency and lower cost for testing aspheric compared with other types of DOE employed. We have fabricated one optical test system and measured a 110-mm-diameter convex surface of errors 44.3 nm rms and 311 nm P–V.     

Statistical models for spatial patterns of heavy particles in turbulence

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

Realisation of an effective dual-parameter sensor employing a single fibre Bragg grating structure

A novel technology for simultaneous and independent measurement of dual parameters is proposed and experimented. The length of a single fibre Bragg grating (FBG) is divided into two parts. The temperature variation and another measurand can be measured independently and simultaneously, and the thermal effect can be erased with great ease.     

Estimation of Symmetry-Constrained Gaussian Graphical Models: Application to Clustered Dense Networks

We propose a model selection algorithm for high-dimensional clustered data. Our algorithm combines a classical penalized likelihood method with a composite likelihood approach in the framework of colored graphical Gaussian models. Our method is designed to identify high-dimensional dense networks with a large number of edges but sparse edge classes. Its empirical performance is demonstrated through simulation studies and a network analysis of a gene expression dataset.     

On the use of the digital image correlation method for heterogeneous deformation measurement of porous solids

In this paper, several crucial issues arising from the application of the digital image correlation (DIC) method to the measurement of heterogeneous deformation of porous solids are discussed. To handle samples with complex geometry, the performance of the two commonly employed DIC methods, namely the subset-based DIC and the finite-element based DIC methods are first evaluated and compared. A combined DIC approach and an adaptive DIC approach suitable for samples with discontinuities/holes are then proposed. Aluminum plates with circular holes subject to compressive loading are employed to evaluate the accuracy of the proposed methods. It has been found that in addition to other factors such as the number of pixels and speckle size, the orientation of the camera lens also plays an important role on the measurement accuracy. A calibration method for the adjustment of camera orientation is proposed, which leads to a good agreement between the experimentally measured displacements and finite element simulation results. Another finding of the presented work is that for relatively stiff specimens, the deformation of the loading system itself must be considered in order to obtain an accurate displacement.     

人尿中多胺的离子交换富集和气相色谱测定

以离子交换法对尿样中的多胺进行预分离富集，确定了最佳的离子交换条件，同时比较了三种不同酰化剂的酰化效果，确定了最佳酰化条件，并用毛细管气相色谱法测定了尿中腐胺，尸胺，精脒，精胺的含量，结果表明癌症病人尿中多胺含量高于正常人。