Modulation instability scenario in negative index materials

We present an investigation of the critical frequency windows permitting modulation instability in negative index materials. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective dispersive magnetic permeability in addition to the effective dielectric permittivity determining the propagation model for ultrashort pulses in negative index materials. We emphasize the influence of nonlinear dispersion terms, arising out of the combinatorial effect of the dispersive permeability with the nonlinear polarization, over the MI phenomena, the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near zero dispersion regime where higher order linear dispersive effects emerge. The results of linear stability analysis have been validated by direct numerical simulation of the governing equation using the split-step Fourier transform method. We show that second-order nonlinear dispersion opens up distinct MI windows with their appropriate conditions and unlike the first-order nonlinear dispersion term, the sign of it has got deep consequences in the modulation instability scenario.     

Effects of higher order nonlinearities on modulational instability in nonlinear oppositely directed coupler

We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic–quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spectral region which are symmetric to the zero point. Moreover, some spectra have a high cut-off frequency but a narrow spectral width, which is obviously beneficial to the generation of high-repetition-rate pulse trains.     

任意形状底扁壳的线性和非线性分析

本文提出了摄动差分法求解扁壳线性和非线性弯曲问题,由于采用了任意网格剖分,可处理复杂形状边界条件及多种荷载工况。数值算例表明,本文方法具有计算量少、计算精度高、适应性强等特点。     

Finite element criteria for some shells

Simple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static–geometric analogue.     

PROCEDURES FOR SOLVING SINGLE-PASS STRIP LAYOUT PROBLEMS

Strip layout is an important step in the planning of operations using blanking dies. Typically the strip layout problem has been resolved using methods which provide approximate solutions, since it is viewed as a class of general 2-D nesting problem which is NP-Hard. This implies that we need to investigate special cases of the strip layout problem that will permit polynomial running time algorithms, while having some practical application in processes of cutting shapes from sheet stock. In this paper we present an exact procedure with polynomial running time for die single-pass single-row layout problem. This problem tries to layout identical shapes on a strip that will go thorough a single row die only once, such as to maximize die number of parts to be yielded by the strip. The paper investigates this problem for two cases: the case for which die width of die strip is larger than any possible orientation of the part, and the case for which the width of die strip is restricted so mat not every orientation is feasible. We also consider the problem of cutting a sheet of metal into strips so as to maximize die sum of me parts yielded by each sheet.     

Elucidating the mechanism of cellular uptake and removal of protein-coated gold nanoparticles of different sizes and shapes

We investigated the mechanism by which transferrin-coated gold nanoparticles (Au NP) of different sizes and shapes entered mammalian cells. We determined that transferrin-coated Au NP entered the cells via clathrin-mediated endocytosis pathway. The NPs exocytosed out of the cells in a linear relationship to size. This was different than the relationship between uptake and size. Furthermore, we developed a mathematical equation to predict the relationship of size versus exocytosis for different cell lines. These studies will provide guidelines for developing NPs for imaging and drug delivery applications, which will require "controlling" NP accumulation rate. These studies will also have implications in determining nanotoxicity.     

New approach to determine the effects of polarization mode dispersion and chromatic dispersion on pulse and RF signals

We present a novel analytical expression relating the output state of polarization (SOP) and the polarization mode dispersion (PMD) vector, including polarization-dependent chromatic dispersion (PCD), in terms of the angle of precession of the output SOP around the PMD vector. We derive a number of new expressions incorporating for the first time this angle of precession. First, a general relation to study the effect of differential group delay, PCD, and chromatic dispersion on pulses of arbitrary shapes is given. From this general relation, we derive expressions for pulse broadening and power penalty for Gaussian pulses. Moreover, a new expression for PMD-induced power fading for single-sideband modulated radio frequency signals is also derived. Measured experimental results are presented to support the derived expressions.     

Spectral Fraunhofer regime: time-to-frequency conversion by the action of a single time lens on an optical pulse

We analyze a new regime in the interaction between an optical pulse and a time lens (spectral Fraunhofer regime), where the input pulse amplitude is mapped from the time domain into the frequency domain (time-to-frequency conversion). Here we derive in detail the conditions for achieving time-to-frequency conversion with a single time lens (i.e., for entering the spectral Fraunhofer regime) as well as the expressions governing this operation. Our theoretical findings are demonstrated both numerically and experimentally. A comparative study between the proposed single-time-lens configuration and the conventional dispersion + time-lens configuration for time-to-frequency conversion is also conducted. Time-to-frequency conversion with a single time lens can be used for applications similar to those previously proposed for the conventional time-to-frequency converters, e.g., high-resolution measurement of fast optical temporal waveforms. Moreover, our results also indicate that the spectral Fraunhofer regime provides additional capabilities for controlling and processing optical pulses.     

Oblique mid ocean ridge subduction modelling with the parallel fast multipole boundary element method

Geodynamic models describe the thermo-mechanical evolution of rheologically intricate structures spanning different length scales, yet many of their most relevant dynamic features can be studied in terms of low Reynolds number multiphase creep flow of isoviscous and isopycnic structures. We use the BEM-Earth code to study the interaction of the lithosphere and mantle within the solid earth system in this approximation. BEM-Earth overcomes the limitations of traditional FD/FEM for this problem by considering only the dynamics of Boundary Integral Elements at fluid interfaces, and employing a parallel multipole solver accelerated with a hashed octtree. As an application example, we self-consistently model the processes controlling the subduction of an oblique mid-ocean ridge in a global 3D spherical setting in a variety of cases, and find a critical angle characterising the transition between an extensional strain regime related to tectonic plate necking and a compressive regime related to Earth curvature effects.     

光滑有限元的声学研究：时域和频域分析

摘　要：在使用有限元进行声场的数值模拟中,存在着两个主要误差,一个是数值方法中常规的插值误差,另外一个是计算声学中所特有的耗散误差(dispersion error),后者则是影响声学模拟仿真置信度的最重要因素。产生耗散误差的本质原因是由于有限元的数值模型刚度“偏硬”造成的。为了控制耗散误差,最重要的是使数值模型更好的反映真实模型。本文采用了一种基于边光滑的有限元方法(ES-FEM)来对声场的时域和频域进行数值模拟研究。该方法只采用对复杂问题域适应性很强的三角形网格,通过引进基于边的广义梯度光滑技术,能够使得有限元系统得到适当的“软化”。关于时域和频域的算例表明了在使用同样网格的情况下,本方法在声学模拟中的精度都要比有限元模型的高。     

Line shapes of photon-gated persistent spectral hole burning in polarization spectroscopy

We introduce a method of polarization spectroscopy into photon-gated persistent spectral hole burning, which results in considerable improvement in the signal-to-background ratio. Fifty multiple spectral holes burnt into meso-phenyl-tetrabenzoporphyrinato-zinc/aromatic cyanide/poly(methyl methacrylate) were clearly detected by this measurement technique. We developed a simplified model to account for the hole shapes. Background birefringence combined with refractive dispersion is thought to play a key role in the generation of asymmetric line shapes.     

Dispersion and rheology of carbon nanotubes in polymers

We review two generic mechanisms of dispersion of carbon nanotubes in a low-viscosity solvent or high-viscosity polymer, focusing on the neat nanotubes not surface-functionalized in any way. We give estimates of the van der Waals energies involved in nanotube aggregates and examine two main techniques: ultrasonication and shear mixing. For ultrasonic dispersion methods, the local mechanical energy applied to individual tubes is high and bundle separation is assured in the cavitation regime. We analyze and estimate the tube scission during ultrasonic cavitation and predict the characteristic nanotube length L _lim below which scission does not occur. For shear-mixing, our analysis suggests that dispersion is possible in non-parallel bundled nanotube aggregates, in high-viscosity polymers, once a critical mixing time t* is reached. We then examine characteristic features of nanotube-polymer composite rheology and its aging/stability against re-aggregation. We show that at nanotube loading above overlap concentration the tubes form an elastic network in the matrix. Physical junctions of this network are strong and stable enough to provide a rubber-like elastic response with very slow relaxation.     

Magnetic collective excitations in the B phase of superfluid He-3

The dynamical susceptibility of the B phase of superfluid He-3 in the presence of dipolar coupling is calculated in the collisionless regime. Two poles of the susceptibility that correspond to the spin wave and the mode with energy gap (2/5)^1/2 2 are found. The result agrees with that of Tewordt and Einzel qualitatively and contradicts the recent work by Maki. The residue of the high-frequency mode becomes remarkable near the transition temperature. The dispersion relations of these modes atT=0 K and near the transition temperature are given in the most general form.     

Two-tone frequency-modulation spectroscopy for quantitative measurements of gaseous species: theoretical, numerical, and experimental investigation of line shapes

The capability of retrieving spectral information from line shapes recorded by two-tone frequency-modulation spectroscopy (TTFMS) is investigated. A TTFMS theory accounting for dispersion and nonlinear distortion of diode laser frequency modulation response is presented. The adequacy of the theory for a detailed modeling of line shapes recorded with high resolution is examined. An extensive error analysis of line parameters (i.e., width, intensity, and line center) retrieved by a nonlinear least-squares fitting procedure is made. Plots of residual errors with characteristic signatures that are due to incorrectly assigned modulation parameters and choice of line profile are presented. In least-squares fits to experimental oxygen data with a Voigt profile influence from collisional(Dicke) narrowing is clearly exhibited, and when we used a collisionally narrowed line profile deviations of the model were reduced to less than 0.2%. We demonstrate that accurate quantitative measurements by TTFMS over a wide range of concentrations, temperatures, and pressures are possible.     

Collective Excitations of a One-Dimensional Fermi Gas Under Harmonic Confinement

We study the spectrum of collective excitations of a spin-polarized Fermi gas confined in a one-dimensional harmonic trap at zero temperature. In the collisionless regime we evaluate exactly the dynamic structure factor, while in the collisional regime we solve analytically the linearized equations of hydrodynamics in the Thomas-Fermi approximation. We also verify the validity of the Thomas-Fermi theory by solving numerically a time-dependent nonlinear Schroedinger equation with a fifth-order interaction term. We find that in both the collisionless and the collisional regime the excitation frequencies of the Fermi gas are multiples of the trap frequency, analogously to the case of the one-dimensional homogeneous Fermi fluid where the velocities of zero and first sound coincide. Due to boson-fermion dynamical mapping our results for the spectrum apply as well to a one-dimensional Bose gas with hard-core point-like interactions (Tonks gas).     

Inhomogeneous effects in the quantum free electron laser

We include inhomogeneous effects in the quantum model of a free electron laser taking into account the initial energy spread of the electron beam. From a linear analysis, we obtain a generalized dispersion relation, from which the exponential gain can be explicitly calculated. We determine the maximum allowed initial energy spread in the quantum exponential regime and we discuss the limit of large energy spread.     

Simultaneous propagation of N dark solitons in optical fibres with higher order linear and nonlinear effects

We consider the simultaneous propagation of N fields in the normal dispersion regime of an optical fibre with higher order dispersion, stimulated Raman scattering and Kerr dispersion. The linear eigenvalue problem associated with the integrable form of the system equation is presented. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.     

Vibration maps of capacitive micromachined ultrasonic transducers by laser interferometry

A 1.8-mm × 1.8-mm capacitive micromachined ultrasonic transducer (CMUT) element is experimentally characterized by means of optical measurements. Optical displacement measurements provide information on the resonant behavior of the single membranes and also allow us to investigate the dispersion in the frequency spectrum of adjacent membranes. In addition, higher order mode shapes are observed, showing that either symmetrical or asymmetrical modes are excited in CMUT membranes. Laser interferometry vibration maps, combined with quantitative displacement measurements, provide information about the quality and repeatability of the fabrication process, which is a basic requirement for 2D array fabrication for ultrasound imaging     

Patterning titania with the conventional and modified micromolding in capillaries technique from sol–gel and dispersion solutions

Abstract

We report TiO₂ patterns obtained by a soft-lithographic technique called ‘micromolding in capillaries’ using sol–gel and dispersion solutions. A comparison between patterning with a sol–gel and dispersion solutions has been performed. The patterns obtained from sol–gel solutions showed good adhesion to the substrate and uniform shapes, but large shrinkage, whereas those obtained from dispersion solution had high solid content, but exhibited poor adhesion and non-uniform shapes. A fabrication method of a layer-by-layer structured pattern is also demonstrated. This type of pattern may find application in sensors, waveguides and other photonics elements. The occurrence of an undesirable residue layer, which hinders the fabrication of isolated patterns, is highlighted and a method of prevention is suggested.