A novel design of a photonic crystal sensor with improved sensitivity

Biosensors, based on photonic crystal (PC), are emergent subject. The use of PCs in this area brought solutions to both miniaturization and integration challenges that have been facing research groups for long time. We are only recently, by engineering such defects, able to propagate light in complex structures containing molecules of different sizes and shapes. We propose a novel structure containing defects with various sizes. The PC is formed by a dielectric cylinders with permittivity 8.9 (alumina Al₂O₃) and a radius r = 0.2a (a is the square lattice constant), arranged in a square lattice. We use the finite difference time domain to investigate the sensitivity of the proposed sensor to water. The defect based sensing element is introduced in two directions 〈0 1〉 and 〈1 0〉. These simulations show a better sensitivity to water than other analytes. It appears in the transmission curves where the peak shifts to high frequency when the refractive index is changed.     

Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

A Continuous Sensitivity Equation (CSE) method is presented for shape parameters in turbulent wall-bounded flows modeled with the standard k–? turbulence model with wall functions. Differentiation of boundary conditions and their complex dependencies on shape parameters, including the two-velocity scale wall functions, is presented in details along with the appropriate methodology required for the CSE method. To ensure accuracy, grid convergence and to reduce computational time, an adaptive finite-element method driven by asymptotically exact error estimations is used. The adaptive process is controlled by error estimates on both flow and sensitivity solutions. Firstly, the proposed approach is applied on a problem with a closed-form solution, derived using the Method of the Manufactured Solution to perform Code Verification. Results from adaptive grid refinement studies show Verification of flow and sensitivity solvers, error estimators and the adaptive strategy. Secondly, we consider turbulent flows around a square cross-section cylinder in proximity of a solid wall. We examine the quality of the numerical solutions by performing Solution Verification and Validation. Then, Sensitivity Analysis of these turbulent flows is performed to investigate the ability of the method to deal with non-trivial geometrical changes. Sensitivity information is used to estimate uncertainties in the flow solution caused by uncertainties in the shape parameter and to perform fast evaluation of flows on nearby configurations.     

The influence of the micro-topology on the phononic band gaps in 2D porous phononic crystals

The phononic band structures of two-dimensional metal porous phononic crystals consisting of different lattices (the lattice structures transformed from square to triangle), and pores of various shapes (circle, square, and triangle) and sizes are studied numerically by using Finite Difference Time Domain (FDTD) scheme. It is found that for x-y mode waves, the absolute phononic band gaps (PBGs) rely more on the pore shapes. For triangular pores, the PBG is opening in the whole process of the lattice transformation, and for circular ones, the PBG is closed after a certain lattice structure. No PBG forms in the crystals with square pores. The PBG can be varied by adjusting the size of the pores. But a critical porosity exists for the opening of the PBG.     

Comparatively high in-field critical current in type-II superconductors from heterogeneous columnar pins: A molecular dynamics study

Theoretical work predicts that the strong dependence of T_c on pure shear strain within the a–b plane of optimally doped YBa₂Cu₃O_7?δ results in heterogenous columnar pins of vortex lines about dislocation lines and about nano-columns inclusions aligned in parallel to the c axis. The critical current of a rigid vortex lattice driven by the Lorentz force in the presence of such clusters of pin/antipin lines is computed using two-dimensional (2D) collective pinning theory and by numerical simulation of the corresponding 2D vortex dynamics. Both theory and computer calculation find that the antipin component of the heterogenous columnar pins contributes substantially to the net in-field critical current.     

Some general properties of the exact acoustic fields in horns and baffles

The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the “Webster” wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S～cosh², sinh², which, with their duals (III) the inverse catenoidal ducts S～sech², csch², have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S～sin² and inverse sinusoidal S～csc² ducts, that have no cut-off frequency, i.e., are acoustically “transparent”. It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by calculating, in elementary form, the exact acoustic fields in inverse catenoidal ducts, for all cases of (a) propagating waves above, (b) non-oscillating modes below and (c) transition fields at the cut-off frequency. The inverse catenoidal ducts consist of (A) the horn of cross-section S～sech², ressembling the “soliton” of non-linear water wave fame, and (B) the baffle of cross-section S～csch², which also matches two exponentially converging ducts, but has infinite, instead of finite, flare at the origin. The geometrical and acoustic properties of these ducts are illustrated by sets of six plots, in Figure 1(a) for the sech-horn and in Figure 1(b) for the csch-baffle; the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure, plotted as functions of position along the duct, for four frequencies ranging from the cut-off condition to the ray limit (or W.K.B.J. approximation).     

On the expansion of radiation intensity into (a/γ) power series in electrodynamics

An expression for the radiation intensity of a nonrelativistic system of charges integrated over all angles is obtained as a series of powers of small parameter (a/γ) up to the terms ～(a/γ)² inclusive. It differs by a new term ～(a/γ)². Besides other reasons, the inclusion of that new term restores the invariance relative to the small (～a) displacement of the coordinate system origin which was violated by an earlier expression.     

On the generalized Hermite-based lattice Boltzmann construction,lattice sets,weights, moments,distribution functions and high-order models

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Bofiz- mann （LB） construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function （EDF） are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly inatch some first hydrodynamic inoments thermally i） on-Cartesian lattice, ii） with thermal weights in the EDF, iii） whilst the highest possible hydrodynamic moments that are exactly reatched are obtained with the shortest on-Cartesian lattiee sets with some fixed real-valued temperatures, is also analyzed.     

Lattice constants of Langmuir-Blodgett films measured by atomic force microscopy

Langmuir-Blodgett (LB) films are examples of soft organic and related biological samples. Therefore it is essential to make sure that the mechanical scanning process does not disturb the specimen. We describe atomic force microscopy measurements of the lattice constants of Cd arachidate LB films. A lattice constant d_hk is revealed correctly by scanning parallel to the corresponding lattice line [hk]. Scanning in deviating directions enlarges the lattice spacing. The phenomena are explained with a simple model. Previous studies where such artefacts have not been reported are discussed.     

大小周期正方格子复合结构的光子带隙特性

把具有宽完全带隙的粗锐复合的周期常数为a的二维正方格子再与周期常数为a₂的大周期简单正方格子复合，发现大周期正方格子起缺陷作用.并发现当a₂<5a时,缺陷态明显地随入射角度变化.此变化随a₂的增大而减少.用FDTD方法计算了其透射和反射谱,结果表明缺陷峰透射率与a₂的大小成反比.另外还发现: 缺陷峰结构与大周期正方格子的圆柱直径的关系曲线与a₂关系不大.通过调节大周期正方格子的圆柱的直径，可获得单 关键词： 光子晶体 光子能隙 复式结构 缺陷态     

Structure and magnetic state of the films deposited by laser ablation of composite nickel and palladium targets

Transmission electron microscopy, electron diffraction, and vibrating-sample magnetometry are used to show that a metastable hcp structure can form in both nickel and Ni-Pd alloy films during alternating sputtering of the Ni and Pd components of composite targets. The hcp lattice parameters increase monotonically when the palladium content in a sputtered target increases in the range 0–75%. The ratio of the hcp lattice parameters c/a is close to the ideal ratio for the hcp lattice (1.63) within the limits of experimental error. In the as-deposited state, nickel and Ni-Pd alloy films with an hcp structure have no magnetic moment. Upon annealing, the films transform into a ferromagnetic state with an fcc structure. The concentration dependence of the lattice parameter of the fcc solid solution a ₀ is found to exhibit a positive deviation from Vegard’s law, which is characteristic of alloys with a concave liquidus line.     

Conductivity, magnetoresistance, and the Hall effect in granular Fe/SiO2 films

We have investigated the conductance, magnetoresistance, and Hall effect in granular Fe/SiO₂ films with size of the iron grains around 40 Å, whose volume fraction x lies in the range 0.3–0.7. The conduction activation regime has been established for x<0.6. On the insulator side of the transition we observed a giant negative magnetoresistance, falling off sharply as the metal volume fraction decreases. For x<0.4 we observed a large positive magnetoresistance of premagnetized samples, showing up in fields; ～100 Oe and characterized by large response times. The field dependence of the Hall effect in the dielectric samples, as in the metallic samples, correlates with their magnetization. We found that the Hall resistance is proportional to the square root of the longitudinal resistance, which cannot be explained by known models of the anomalous Hall effect.     

Relative partial photoionization cross-sections and photoelectron branching ratios of ethylene

Relative partial photoionization cross-sections and photoelectron branching ratios of the valence bands (~10–25 eV binding energy) of ethylene are reported over the photon energy ranges 18–100 eV and 21–100 eV, respectively. The four lowest ionization energy bands (1b⁻¹_1u, 1b⁻¹_1g, 3a⁻¹_g, and 1b⁻¹_2u) show monotonic cross-section decreases with photon energy from 33 eV, the 1b⁻¹_1u CC π band showing the least rapid decline. In contrast, the 2b⁻¹_3u and 2a⁻¹_g bands show almost constant cross-sections up to ~50 eV photon energy, followed by similar, although slower, monotonic decreases. This is attributed to the substantial carbon 2s character of the 2b_3u and 2a_g orbitais. The cross-section behaviour of all bands is interpreted with the aid of SCF-LCAO-MO calculations on the neutral molecule using the Gaussian-80 series of programs.     

Effect of sol–gel pH on XRD peak broadening,lattice strain,ferroelectric domain orientation,and optical bandgap of nanocrystalline Pb1.1(Zr0.52Ti0.48)O3

Nanocrystalline Pb_1.1(Zr_0.52Ti_0.48)O₃ (PZT) samples were prepared using a citrate–nitrate sol–gel process near the morphotropic phase boundary. The effect of pH on the lattice parameters (tetragonality and lattice constants), crystal structure [strain broadening, relative phase content, ferroelectric domain (FD) orientation and nanocrystallite size], microstructure (grain size and particle morphology) and optical bandgap was investigated. The samples were characterized using X-ray diffraction (XRD), the size strain plot (SSP) method, Fourier-transform infrared spectroscopy, and the classical Tauc relation. The particle morphology was investigated using field-emission scanning electron microscopy. The XRD results revealed a perovskite structure and coexisting tetragonal and rhombohedral phases for all PZT samples. Lattice strain and peak broadening were determined from SSP and XRD results. The behavior of these parameters was in agreement for all pH values. The optical bandgap for PZT was estimated from UV-vis absorption spectra. We found that for PZT the maximum relative tetragonal phase content, c/a ratio, and FD orientation along the a-axis occurred at pH 4.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

The boundary between the spin-glass and ferromagnetic states of the bond-random Ising model in the square lattice at T = 0

The bond-random (±J) Ising model in the square lattice is considered in the square cluster approximation. The boundary between the ferromagnetic and spin-glass states at T = 0 is obtained as the transition point from the asymmetric distribution of the effective fields to the symmetric distribution. The concentration of this transition, P_FG is obtained by solving the integral equation for the distribution function of the effective fields.     

Fractality of profit landscapes and validation of time series models for stock prices

We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (?q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form M ～ N ^a , but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.     

On the phase structure of five-dimensional SU(2) gauge theories with anisotropic couplings

The phase diagram of five-dimensional SU(2) gauge theories is explored using Monte Carlo simulations of the theory discretized on a Euclidean lattice using the Wilson plaquette action and periodic boundary conditions. We simulate anisotropic gauge couplings which correspond to different lattice spacings a₄ in four dimensions and a₅ along the extra dimension. In particular we study the case where a₅>a₄. We identify a line of first order phase transitions which separate the confined from the deconfined phase. We perform simulations in large volume at the bulk phase transition staying in the confined vacuum. The static potential measured in the hyperplanes orthogonal to the extra dimension hints at dimensional reduction. We also locate and analyze second order phase transitions related to breaking of the center along one direction.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

A Mössbauer study of the bipyramidal lattice site (2b) in BaFe12O19

The hyperfine fieldsH _f(T), center shifts δ(T) and relative recoilless fractionsf _a(T) at different lattice sites of barium ferrite were determined by Mössbauer spectroscopy of⁵⁷Fe over a temperature range from 12 to 723 K. For ferric iron in the crystalline site (2b), the recoilless fractionf _a(T) decreases most with increasing temperature in comparison with that of other sites, corresponding to a characteristic temperature {ie219-1}. These results indicate that the ferric iron in the site (2b) oscillates between two equivalent positions (4e) on either side of the symmetry plane normal to thec-axis.     

Pressure dependence of electronic structure and magnetic properties in Fe16N2

The electronic structures and magnetic properties of Fe₁₆N₂ system and their pressure dependence were investigated by using first-principles calculations based on the density functional theory. It has been found that the total magnetic moment in Fe₁₆N₂ system decreases monotonically as increasing pressure from 0 to 14.6 GPa. A phase transition from ferromagnetic (FM) to non-magnetic (NM) occurs with a volume collapse of around 0.008  at 14.6 GPa, The lattice constants a and c for magnetic results decrease monotonically as pressure increasing from 0 to 14.6 GPa, at 14.6 GPa, the lattice constant a decreases sharply, on the contrary, the lattice constant c increases abruptly. We think that the change of microscopic structure of Fe₁₆N₂ is responsible for the phase transition from FM to NM.