Determination of particle size distribution in cements with admixtures by optical methods

In determining particle size in powders, a large number of methods are employed including sedimentation (e.g. sedimentation scale method, Andreason´s pipette method and others), chromatography, microscopy, electrozone testing, scatter methods and filtration methods among others, each one of these with their own particular characteristics and corresponding degrees of accuracy. In the study of cements, the most used of these methods are the filtration (and/or sifting method), and sedimentation, this last one based on Stoke´s Law which compares the rate of particle separation in a liquid

Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary π radians phase modulation and hybrid ternary modulation. Any deviation in the values of the amplitude and phase shift generates the appearance of a strong dc term. Experimental results confirm that the calculated configurations provide a FT with no dc term, thus showing the effectiveness of the proposal.This work was supported by the “Ministerio de Educación y Ciencia (Spain)” under projects FIS2005-05881-C02-01 and FIS2005-05881-C02-02, and by the “Generalitat Valenciana” under Project GV06/007

Higher accuracy approximate solution for oscillations of a mass attached to a stretched elastic wire by rational harmonic balance method

A second-order modified rational harmonic balance method is used for approximately solve the nonlinear differential equation that governs the oscillations of a system typified as a mass attached to a stretched elastic wire for which the restoring force for this oscillator has an irrational term with a parameter lambda that characterizes the system. A frequency-amplitude relation is constructed and this frequency is valid for the complete range of oscillation amplitudes A and parameter lambda, and excellent agreement of the approximate frequencies with the exact one is demonstrated and discussed. The discrepancy between the approximate frequency and the exact one never exceed 0.12%. This error corresponds to lambda = 1. while for lambda < 1 the relative error is much lower. For example, its value is lower than 0.017% for lambda = 0.5

Influence of Thickness on the Holographic Parameters of H-PDLC Materials

For photopolymers the compound concentrations and final thickness of the sample should be known in order to model hologram formation and introduce the reaction-diffusion kinetics of the monomer-polymer system. In principle the cell thickness can be controlled by bead spacers between the two pieces of ITO glass. In this paper we report a study of the influence of thickness on the holographic properties of this type of materials. To fit the physical and optical thickness of the samples we used the rigorous coupled wave analysis assuming an exponential decay in the refractive index modulation.The work was supported by the “Ministerio de Economía y Competitividad” of Spain under Projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the “Generalitat Valenciana” of Spain under Projects PROMETEO/2011/021 and ISIC/2012/013

Closed-Form Exact Solutions for the Unforced Quintic Nonlinear Oscillator

Closed-form exact solutions for the periodic motion of the one-dimensional, undamped, quintic oscillator are derived from the first integral of the nonlinear differential equation which governs the behaviour of this oscillator. Two parameters characterize this oscillator: one is the coefficient of the linear term and the other is the coefficient of the quintic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative values of these coefficients which provide periodic motions are considered. The set of possible combinations of signs of these coefficients provides four different cases but only three different pairs of period-solution. The periods are given in terms of the complete elliptic integral of the first kind and the solutions involve Jacobi elliptic function. Some particular cases obtained varying the parameters that characterize this oscillator are presented and discussed. The behaviour of the periods as a function of the initial amplitude is analysed and the exact solutions for several values of the parameters involved are plotted. An interesting feature is that oscillatory motions around the equilibrium point that is not at x = 0 are also considered.This work was supported by the “Generalitat Valenciana” of Spain, under Project PROMETEOII/2015/015 and by the Universidad de Alicante, Spain, under Project GITE-09006-UA

A novel rational harmonic balance approach for periodic solutions of conservative nonlinear oscillators

An analytical approximate procedure for a class of conservative single degree-of-freedom nonlinear oscillators with odd non-linearity is proposed. This technique is based on the generalized harmonic balance method in which analytical approximate solutions have rational forms. Unlike the classical harmonic balance techniques, in this new procedure the approximate solution and the restoring force are expanded in Fourier series prior to substituting them in the nonlinear differential equation. This approach gives us not only a truly periodic solution but also the frequency of the motion as a function of the amplitude of oscillation. Four nonlinear oscillators are presented to illustrate the usefulness and effectiveness of the proposed technique. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving a class of conservative nonlinear oscillatory systems

Exact and approximate solutions for the anti-symmetric quadratic truly nonlinear oscillator

The exact solution of the anti-symmetric quadratic truly nonlinear oscillator is derived from the first integral of the nonlinear differential equation which governs the behavior of this oscillator. This exact solution is expressed as a piecewise function including Jacobi elliptic cosine functions. The Fourier series expansion of the exact solution is also analyzed and its coefficients are computed numerically. We also show that these Fourier coefficients decrease rapidly and, consequently, using just a few of them provides an accurate analytical representation of the exact periodic solution. Some approximate solutions containing only two harmonics as well as a rational harmonic representation are obtained and compared with the exact solution.This work was supported by the “Generalitat Valenciana” of Spain (projects PROMETEO/2011/021 and ISIC/2012/013), and by the “Vicerrectorado de Tecnologías de la Información” of the University of Alicante, Spain (project GITE-09006-UA)

Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer

We focus on the novelty of three elements in holographic data storage systems (HDSS): the data pager, where we introduce a parallel-aligned liquid crystal on silicon (PA-LCoS) microdisplay; the recording material, where we consider the highly versatile PVA/AA photopolymer; and also in the architecture of the object arm, where a convergent correlator system is introduced. We show that PA-LCoS devices cannot implement pure hybrid-ternary modulated (HTM) data pages but a rather close approximation. Validation of the HDSS expressions for the convergent correlator and comparison with the widespread 4-f system is performed. Experimental results with PVA/AA material showing bit-error rates (BER) in the range of 10−3, further show its potential application for HDSS, and also demonstrate the validity of the testing platform and PA-LCoS calibration and optimization.Work supported by Ministerio de Trabajo y Competitividad of Spain (projects FIS2011- 29803-C02-01 and FIS2011-29803-C02-02), by Generalitat Valenciana of Spain (projects PROMETEOII/2015/015 and ISIC/2012/013), and by Univ. de Alicante (project GRE12-14

3D FDTD analysis of cross-talk in pixelated PA-LCos devices: impact of fill factor and size pixel on S2 and S3 parameters

In the last decades, new technology fabrication developments have permitted increased resolution and reduced pixel size of Liquid crystal on silicon (LCoS) microdisplays. However, the pixel size reduction triggers the microdisplay performance degradation due to different phenomena, such as the cross-talk between neighbouring pixels, fringing fields, out-of-plane reorientation of the liquid crystal director, and diffraction effects due to the pixelated grid pattern of the microdisplay. In this work, a full 3D simulation model has been applied to predict the liquid crystal director orientation as a function of space and external voltage. The scheme here considered provides the complete vectorial information of the electromagnetic field distribution produced by one single pixel illuminated by plane waves circularly polarised. This analysis is carried on for several pixel and gap sizes for different external voltages. This research focuses on S2 and S3 Stokes parameters and how their behaviour is affected due to the cross-talk phenomena previously presented.The work was supported by the “Generalitat Valenciana” (IDIFEDER/2021/014 cofunded by FEDER EU pro- gram, and project PROMETEO/2021/006, GRISOLIAP/2021/106), and by “Ministerio de Ciencia e Innovación” of Spain (projects PID2021-123124OB-I00; PID2019-106601RB-I00)

Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions

Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.This work was supported by the “Generalitat Valenciana” of Spain, under Project PROMETEO/2011/021, and by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain, under Project GITE-09006-UA