An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

Perturbation theory for equilibrium properties of a binary mixture of hard discs

The radial distribution function (RDF) and thermodynamic properties of a two-dimensional hard-disc mixture are calculated by using the perturbation theory. Numerical results are given for theRDF, pressure and excess-free energy of the binary mixture of both additive and non-additive hard discs. It is found that the thermodynamic properties of the binary mixture of non-additive hard discs increase with Δ, the non-additive parameter.     

An experimental investigation into electromyography, constitutive relationship and morphology of crucian carp for biomechanical digital fish

Currently, the integrated biomechanical studies on fish locomotion come into focus, so it is urgent to provide reliable and systematic experimental results, and to establish a biomechanical digital fish database for some typical fish species. Accordingly, based on the control framework of Neural ControlActive Contraction of MusclePassive Deformation, the electromyography (EMG) signals, the mechanical properties and the constitutive relationship of skin, muscle, and body trunk, as well as morphological param...     

Nonlinear distribution function for a plasma obeying Vlasov-Maxwell system of equations

The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived, which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and trapped electrons in determining the stability, is also discussed.     

Effect of Polynomial Expressed Distribution Dust Particles for Unmagnetized Two-Ion-Temperature Dusty Plasma

Linear dispersion relation for linear wave and a Kadomtsev-Petviashvili (KP) equation for nonlinear wave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species. The numerical results of variationsof linear dispersion with respect to the different dust size distribution are given. Moreover, how the amplitude, width, and propagation velocity of solitary wave vary vs different dust size distribution is also studied numerically in this paper.     

New Ans(a)tze for Obtaining Exact Solutions of Nonlinear Schr(o)dinger-Type Equation

We propose two simple ans(a)tze that allow us to obtain different analytical solutions for two generalized versions of the nonlinear Schr(o)dinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schr(o)dinger equation which describe the femtosecond pulse propagation in monomode optical fiber.Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.     

A coupled cluster treatment of intramonomer electron correlation within symmetry-adapted perturbation theory: benchmark calculations and a comparison with a density-functional theory description

Symmetry-adapted perturbation theory (SAPT) with intramonomer electron correlation described by coupled cluster theory limited to single and double excitations was applied to 21 noncovalent complexes in their minimum geometries. The resulting benchmark contributions to the interaction energy were utilized to examine the accuracy of a more approximate variant of the SAPT method, where interacting molecules are described by density functional theory (DFT) with different functionals, like LDA, PBE, B3LYP, PBE0, M05, M05-2X, M06, and M06-2X (in all cases the asymptotic correction for the exchange-correlation functional has been utilized). Average errors for individual energy components of SAPT(DFT) are not larger than 10% for best functionals under study. Among the tested functionals PBE0, M05, and B3LYP should be especially recommended for the SAPT(DFT) approach. The M06 functional gives the largest errors with respect to SAPT(CCSD) and should not be used for describing intramonomer correlation in SAPT.     

Fabrication of broadband poly(vinylidene difluoride-trifluroethylene) line-focus ultrasonic transducers for surface acoustic wave measurements of anisotropy of a (1 0 0) silicon wafer

This paper investigates a new method for fabrication of broadband line-focus ultrasonic transducers by sol–gel spin-coating the poly(vinylidene difluoride-trifluroethylene) [P(VDF-TrFE)] copolymer film on a concave fine-polished beryllium copper backing. The ferroelectric hysteresis loops of the P(VDF-TrFE) films spin-coated from different molar ratios of VDF/TrFE, 77/23 and 55/45, were measured to select the better mixture. Owing to the better acoustic matching to water, compared with lead zirconate titanate (PZT), the fabricated transducers show relatively wide bandwidth of approximately 50 MHz with high central frequency of 60 MHz obtained at the focal plane when a fused-quartz acts as a reflecting target. Each one of the two finished transducers has a focal length of 5 mm and a full aperture angle of 90°. After applying the specially developed digital signal processing algorithm to the defocusing experiment data, which is called V(f,z) analysis method based on two-dimensional fast Fourier transform (2-D FFT), the operating frequency can extend from several MHz to over 90 MHz. Surface acoustic wave (SAW) velocities of a typical (1 0 0) silicon wafer was measured along various directions between [1 0 0] and [0 1 0] to represent the anisotropic features.     

Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state

Linear isotherm regularity is applied to generate an expression for the direct correlation function (DCF), based on the optimized random-phase approximation theory. We use the Lennard-Jones potential in the modelling of real fluids, in which its molecular parameters are state-dependent. Based on the perturbation theory, we assume that the core contribution of the DCF is related to the geometric effect via a linear form, which arises from the excluded volume, and the tail contribution is related to the long-range intermolecular interactions of the system via a non-linear form. We use this model to predict the behaviour of the structure factor, S(k), in a wide range of k values for the xenon and krypton liquids. Finally, we compare our results with the experimental and theoretical data available in literature. The model is also successful in the presentation of the Ornstein–Zernike behaviour of S(k) at the low-k region.     

高能工业CT用新型X射线源焦斑测量

 为了获得较高的空间分辩率，设计了一种新型小束斑驻波电子直线加速器，该加速器取消了加速腔中的鼻锥结构，而在耦合腔中设置鼻锥结构。用狭缝法代替小孔法测得X射线源的焦斑尺寸为1.4mm。讨论了射线源焦点对成像质量的影响，分析了在高能条件下小孔法不适合用于焦点测量的物理原因，用4种测量方法测量了该高能X射线源的参数，测得该系统的成像极限分辩率为2.5 lp/mm，最后对实验结果进行了分析。     

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear Schr(o)dinger Equation

By using the extended hyperbolic function method,we have studied a quintic discrete nonlinear Schr(o)dinger equation and obtained new exact localized solutions,including the discrete bright soliton solution,dark soliton solution,bright and dark soliton solution,alternating phase bright soliton solution,alternating phase dark soliton solution,and alternating phase bright and dark soliton solution,if a special relation is bound on the coefficients of the equation.     

高能工业CT用新型X射线源焦斑测量

为了获得较高的空间分辩率,设计了一种新型小束斑驻波电子直线加速器,该加速器取消了加速腔中的鼻锥结构,而在耦合腔中设置鼻锥结构。用狭缝法代替小孔法测得X射线源的焦斑尺寸为1.4mm。讨论了射线源焦点对成像质量的影响,分析了在高能条件下小孔法不适合用于焦点测量的物理原因,用4种测量方法测量了该高能X射线源的参数,测得该系统的成像极限分辩率为2.5 lp/mm,最后对实验结果进行了分析。     

Density functional theory study on antiferromagnetic interactions in a silver (I) complex of nitronyl nitroxide

A one-dimensional (1D) silver (I) complex of nitronyl nitroxide with fairly strong antiferromagnetic interaction, in which the metal ions are diamagnetic, is investigated by means of the ab initio crystal orbital method based on the density functional theory. The calculated values of the magnetic coupling constant (J) are close to the experimental measured J value in the periodic system. The magneto-structural correlation reveals that the existence of an antiferromagnetic coupling pathway along nitronyl nitroxide units via silver (I) ion in this system. The spin population distribution also shows the existence of spin delocalization along the ONCNO–Ag–ONCNO, which affords a rational interpretation for the antiferromagnetic interaction mechanism.     

Electrohydrodynamic flow analysis in a circular cylindrical conduit using Least Square Method

In this article, Electrohydrodynamic flow (EHD flow) in a circular cylindrical conduit is studied by a semi-exact and high efficient weighted residual method called Least Square Method (LSM). A principle of LSM is briefly introduced and later is employed to solve the described problem. Furthermore, the effects of the Hartmann electric number (Ha) and the strength of nonlinearity (α) on velocity profiles are discussed and presented graphically. Results are compared with numerical solution and obtained residuals are compared with those of HAM which previously were done by Mastroberardino in Ref. [3]. Outcomes reveal that LSM has an excellent agreement with numerical solution; also depicted residual functions showed that LSM is more acceptable than HAM especially for large values of Ha and α numbers, also it is simpler and needs fewer computations.     

Synthesis and fading of eighteenth‐century Prussian blue pigments: a combined study by spectroscopic and diffractive techniques using laboratory and synchrotron radiation sources

Prussian blue, a hydrated iron(III) hexacyanoferrate(II) complex, is a synthetic pigment discovered in Berlin in 1704. Because of both its highly intense color and its low cost, Prussian blue was widely used as a pigment in paintings until the 1970s. The early preparative methods were rapidly recognized as a contributory factor in the fading of the pigment, a fading already known by the mid‐eighteenth century. Herein two typical eighteenth‐century empirical recipes have been reproduced and the resulting pigment analyzed to better understand the reasons for this fading. X‐ray absorption and Mössbauer spectroscopy indicated that the early syntheses lead to Prussian blue together with variable amounts of an undesirable iron(III) product. Pair distribution functional analysis confirmed the presence of nanocrystalline ferrihydrite, Fe₁₀O₁₄(OH)₂, and also identified the presence of alumina hydrate, Al₁₀O₁₄(OH)₂, with a particle size of ～15 Å. Paint layers prepared from these pigments subjected to accelerated light exposure showed a tendency to turn green, a tendency that was often reported in eighteenth‐ and nineteenth‐century books. The presence of particles of hydrous iron(III) oxides was also observed in a genuine eighteenth‐century Prussian blue sample obtained from a polychrome sculpture.     

Power law distribution of seismic rates: theory and data analysis

We report an empirical determination of the probability density functions P_data(r) (and its cumulative version) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 ×5 km², 20 ×20 km² and 50 ×50 km² and time intervals and 1000 days. The data can be represented by asymptotic power law tails together with several cross-overs. These observations are explained by a simple stochastic branching process previously studied by many authors, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. We develop the full theory in terms of generating functions for describing the space-time organization of earthquake sequences and develop several approximations to solve the equations. The calibration of the theory to the empirical observations shows that it is essential to augment the ETAS model by taking account of the pre-existing frozen heterogeneity of spontaneous earthquake sources. This seems natural in view of the complex multi-scale nature of fault networks, on which earthquakes nucleate. Our extended theory is able to account for the empirical observation but some discrepancies, especially for the shorter time windows, point to limits of both our theoretical approach and of the ETAS model.     

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing different features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with general material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grading schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applications of such structures in engineering. Supported by the National Natural Science Foundation of China (Grant Nos. 10432030, 10125209, and 10572065) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions, Ministry of Education of China, and also supported by Qianjiang River Fellow Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University, Zhejiang, China     

Milling of Organic Solids in a Jet Mill. Part 2: Checking the Validity of the Predicted Rate of Breakage Function

The particle size distribution of fine chemicals in the solid state, like active pharmaceutical ingredients, is often a critical parameter. To achieve the desired particle size distribution, milling of such materials is usually the method of choice. Since these chemicals are often scarcely available, experimental optimization of milling is not possible. Therefore, a model to predict the milling conditions has been developed. The model estimates the rate of breakage function, and needs mechanical properties like hardness and yield strength as input to calculate the rate of breakage function. This paper attempts to check the validity of the model by a series of experiments. A comparison of the experimental results with the outcomes of the model using five different model compounds has been performed. It appears that the rate of breakage function can be estimated by: The model is able to rank the compounds by degree of fracture as an effect of milling. It was also possible to perform a quantitative prediction of the impact of milling pressure on the milling behavior. Finally, it appeared that the prediction of the large particles in the distribution was significantly better than small ones. Because the oversized material is usually the most critical parameter, the conclusion is that the model has acceptable practical applicability.     

Reflection models for soil and vegetation surfaces from multiple-viewing angle photopolarimetric measurements

The reflection properties of soil and vegetation surfaces have been investigated using airborne photopolarimetric data from the research scanning polarimeter (RSP). For both surface types, it was found that the ratios of total reflectances taken at two different wavelengths from visible and short-wave infrared channels are the same for different illumination and scattering geometries, and in general independent of the scattering angle. From an analysis of the angular and spectral dependencies of the intensity and polarization, we show that the modeled total and polarized reflectances can be expressed in the same form both for soil and vegetation surfaces, namely, as the product of geometrical scattering term depending only on illumination and viewing angles, and a term that varies solely with wavelength and scattering angle.