Search results for: nonlinear scattering

Authors: Stuart Bradley, Mathew Legg, Lilyan Panton

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Ultrasonic remote sensing is a useful tool for assessing the interior structure of complex targets. For these methods, significantly enhanced spatial resolution is obtained if the pulse is coded, for example using a linearly changing frequency during the pulse duration. Such pulses have a time-dependent spectral structure. Interpretation of the backscatter from targets is, therefore, complicated if the scattering is frequency-dependent. While analytic models are well established for steady sinusoidal excitations applied to simple shapes such as spheres, such models do not generally exist for temporally evolving excitations. Therefore, models are developed in the current paper for handling such signals so that the properties of the targets can be quantitatively evaluated while maintaining very high spatial resolution. Laboratory measurements on simple shapes are used to confirm the validity of the models.

Keywords: linear FM chirp, time-dependent acoustic scattering, ultrasonic remote sensing, ultrasonic scattering

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Authors: Minas Balyan

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In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Abdullah Eqal Al Mazrooei

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Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: S. S. Sathiesh

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The aim of this project is to study the radiation mechanism synchrotron and Inverse Compton scattering. Theoretically, we discussed spectral energy distribution for both. Programming is done for plotting the graph of Power-law spectrum for synchrotron Radiation using fortran90. The importance of power law spectrum was discussed and studied to infer its physical parameters from the model fitting. We also discussed how to infer the physical parameters from the theoretically drawn graph, we have seen how one can infer B (magnetic field of the source), γ min, γ max, spectral indices (p1, p2) while fitting the curve to the observed data.

Keywords: blazars/quasars, beaming, synchrotron radiation, Synchrotron Self Compton, inverse Compton scattering, mrk421

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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Authors: Bingjie Wang, Su-Yeon Kwon, Ik-Joong Kang

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A Surface-enhanced Raman Scattering (SERS) as the principle for enhancing Raman scattering by molecules adsorbed on rough metal surfaces or by nanostructures is used to detect the concentration change of γ-Aminobutyric Acid (GABA). As for the gold-chitosan nanoshell, it is made by using chitosan nanoparticles crosslinking with sodium tripolyphosphate(TPP) for the first step to form the chitosan nanoparticles, which would be covered with the gold sequentially. The size of the fabricated product was around 100nm. Based on the method that the sulfur end of the MPA linked to gold can form the very strong S–Au bond, and the carboxyl group, the other end of the MPA, can easily absorb the GABA. GABA is the mainly inhibitory neurotransmitter in the mammalian central nervous system in the human body. It plays such significant role in reducing neuronal excitability throughout the nervous system. When the system formed, it generated SERS, which made a clear difference in the intensity of Raman scattering within the range of GABA concentration. So it is obtained from the experiment that the calibration curve according to the GABA concentration relevant with the SERS scattering. In this study, DLS, SEM, FT-IR, UV, SERS were used to analyze the products to obtain the conclusion.

Keywords: chitosan-gold nanoshell, mercaptopropionic acid, γ-aminobutyric acid, surface-enhanced Raman scattering

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Authors: Dong Tang, Yongli Zhao

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The study of the microstructure of asphalt is of great importance for the analysis of its macroscopic properties. However, the peculiarities of the chemical composition of the asphalt itself and the limitations of existing direct imaging techniques have caused researchers to face many obstacles in studying the microstructure of asphalt. The advantage of small-angle X-ray scattering (SAXS) is that it allows quantitative determination of the internal structure of opaque materials and is suitable for analyzing the microstructure of materials. Therefore, the SAXS technique was used to study the evolution of microstructures on the nanoscale during asphalt aging. And the reasons for the change in scattering contrast during asphalt aging were also explained with the help of Fourier transform infrared spectroscopy (FTIR). SAXS experimental results show that the SAXS curves of asphalt are similar to the scattering curves of scattering objects with two-level structures. The Porod curve for asphalt shows that there is no obvious interface between the micelles and the surrounding mediums, and there is only a fluctuation of the hot electron density between the two. The Beaucage model fit SAXS patterns shows that the scattering coefficient P of the asphaltene clusters as well as the size of the micelles, gradually increase with the aging of the asphalt. Furthermore, aggregation exists between the micelles of asphalt and becomes more pronounced with increasing aging. During asphalt aging, the electron density difference between the micelles and the surrounding mediums gradually increases, leading to an increase in the scattering contrast of the asphalt. Under long-term aging conditions due to the gradual transition from maltenes to asphaltenes, the electron density difference between the micelles and the surrounding mediums decreases, resulting in a decrease in the scattering contrast of asphalt SAXS. Finally, this paper correlates the macroscopic properties of asphalt with microstructural parameters, and the results show that the high-temperature rutting resistance of asphalt is enhanced and the low-temperature cracking resistance decreases due to the aggregation of micelles and the generation of new micelles. These results are useful for understanding the relationship between changes in microstructure and changes in properties during asphalt aging and provide theoretical guidance for the regeneration of aged asphalt.

Keywords: asphalt, Beaucage model, microstructure, SAXS

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Authors: Boo-Sung Koh, Seung-Eock Kim

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In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection

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Authors: S. Wesebaum, S. Willeke

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Production companies are faced with an increasingly turbulent business environment, which demands very high production volumes- and delivery date flexibility. If a decoupling by storage stages is not possible (e.g. at a contract manufacturing company) or undesirable from a logistical point of view, load scattering effects the production processes. ‘Load’ characterizes timing and quantity incidence of production orders (e.g. in work content hours) to workstations in the production, which results in specific capacity requirements. Insufficient coordination between load (demand capacity) and capacity supply results in heavy load scattering, which can be described by deviations and uncertainties in the input behavior of a capacity unit. In order to respond to fluctuating loads, companies try to implement consistent and realizable input behavior using the capacity supply available. For example, a uniform and high level of equipment capacity utilization keeps production costs down. In contrast, strong load scattering at workstations leads to performance loss or disproportionately fluctuating WIP, whereby the logistics objectives are affected negatively. Options for reducing load scattering are e.g. shifting the start and end dates of orders, batch splitting and outsourcing of operations or shifting to other workstations. This leads to an adjustment of load to capacity supply, and thus to a reduction of load scattering. If the adaptation of load to capacity cannot be satisfied completely, possibly flexible capacity must be used to ensure that the performance of a workstation does not decrease for a given load. Where the use of flexible capacities normally raises costs, an adjustment of load to capacity supply reduces load scattering and, in consequence, costs. In the literature you mostly find qualitative statements for describing load scattering. Quantitative evaluation methods that describe load mathematically are rare. In this article the authors discuss existing approaches for calculating load scattering and their various disadvantages such as lack of opportunity for normalization. These approaches are the basis for the development of our mathematical quantification approach for describing load scattering that compensates the disadvantages of the current quantification approaches. After presenting our mathematical quantification approach, the method of batch splitting will be described. Batch splitting allows the adaptation of load to capacity to reduce load scattering. After describing the method, it will be explicitly analyzed in the context of the logistic curve theory by Nyhuis using the stretch factor α1 in order to evaluate the impact of the method of batch splitting on load scattering and on logistic curves. The conclusion of this article will be to show how the methods and approaches presented can help companies in a turbulent environment to quantify the occurring work load scattering accurately and apply an efficient method for adjusting work load to capacity supply. In this way, the achievements of the logistical objectives are increased without causing additional costs.

Keywords: batch splitting, production logistics, production planning and control, quantification, load scattering

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: G. Traini, V. Giacometti, R. Mirabelli, V. Patera, D. Pinci, A. Sarti, A. Sciubba, M. Marafini

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The MONDO (MOnitor for Neutron Dose in hadrOntherapy) project aims a precise characterisation of the secondary fast and ultrafast neutrons produced in particle therapy treatments. The detector is composed of a matrix of scintillating fibres (250 um) readout by CMOS Digital-SPAD based sensors. Recoil protons from n-p elastic scattering are detected and used to track neutrons. A prototype was tested with proton beams (Trento Proton Therapy Centre): efficiency, light yield, and track-reconstruction capability were studied. The results of a MonteCarlo FLUKA simulation used to evaluated double scattering efficiency and expected backgrounds will be presented.

Keywords: secondary neutrons, particle therapy, tracking, elastic scattering

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Authors: Francisco Velez, Juan David Gomez

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Dispersion effects on the Scattering for a semicircular canyon in a micropolar continuum are analyzed, by using a computational finite element scheme. The presence of microrotational waves and the dispersive SV waves affects the propagation of elastic waves. Here, a contrast with the classic model is presented, and the dependence with the micropolar parameters is studied.

Keywords: scattering, semicircular canyon, wave dispersion, micropolar medium, FEM modeling

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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Authors: A. Giniatoulline

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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: L. Bouzina, A. Bensafi, M. Duval, C. Mathis, M. Rawiso

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We study the stability and structural properties of mixtures of model nanoparticles and non-adsorbing polymers in the 'protein limit', where the size of polymers exceeds the particle size substantially. We have synthesized in institute (Charles Sadron Strasbourg) model nanoparticles by coating fullerene C60 molecules with low molecular weight polystyrene (PS) chains (6 PS chains with a degree of polymerization close to 25 and 50 are grafted on each fullerene C60 molecule. We will present a Small Angle Neutron scattering (SANS) study of Tetrahydrofuran (THF) solutions involving long polystyrene (PS) chains and fullerene (C60) nanoparticles. Long PS chains and C60 nanoparticles with different arm lengths were synthesized either hydrogenated or deuteriated. They were characterized through Size Exclusion Chromatography (SEC) and Quasielastic Light Scattering (QLS). In this way, the solubility of the C60 nanoparticles in the usual good solvents of PS was controlled. SANS experiments were performed by use of the contrast variation method in order to measure the partial scattering functions related to both components. They allow us to obtain information about the dispersion state of the C60 nanoparticles as well as the average conformation of the long PS chains. Specifically, they show that the addition of long polymer chains leads to the existence of an additional attractive interaction in between soft nanoparticles.

Keywords: fulleren nanoparticles, polymer, small angle neutron scattering, solubility

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Authors: C. Pislaru, A. Shebani

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This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the K-Means clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: system identification, nonlinear systems, neural networks, radial basis function, K-means clustering algorithm

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Authors: Mounir Bekaik, Messaoud Ramdani

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We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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Authors: Abdon Choque-Rivero

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The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Siriluk Ruangrungrote

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Analyses of available data from MFR-7 measurement were performed and discussed on the study of tropospheric aerosol and its consequence in Thailand. Since, ASSA (w) is one of the most important parameters for a determination of aerosol effect on radioactive forcing. Here the estimation of w was directly determined in terms of the ratio of aerosol scattering optical depth to aerosol extinction optical depth (ωscat/ωext) without any utilization of aerosol computer code models. This is of benefit for providing the elimination of uncertainty causing by the modeling assumptions and the estimation of actual aerosol input data. Diurnal w of 5 cloudless-days in winter and early summer at 5 distinct wavelengths of 415, 500, 615, 673 and 870 nm with the consideration of Rayleigh scattering and atmospheric column NO2 and Ozone contents were investigated, respectively. Besides, the tendency of spectral dependence of ω representing two seasons was observed. The characteristic of spectral results reveals that during wintertime the atmosphere of the inland rural vicinity for the period of measurement possibly dominated with a lesser amount of soil dust aerosols loading than one in early summer. Hence, the major aerosol loading particularly in summer was subject to a mixture of both soil dust and biomass burning aerosols.

Keywords: aerosol scattering optical depth, aerosol extinction optical depth, biomass burning aerosol, soil dust aerosol

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Authors: Karima Kimouche

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In this paper, we consider the asymptotic problems in spectral analysis of stationary causal random fields. We impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear random fields. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given.

Keywords: spatial nonlinear processes, spectral estimators, GMC condition, bootstrap method

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Authors: Aleksandr I. Korobov, Natalia V. Shirgina, Aleksey I. Kokshaiskiy, Vyacheslav M. Prokhorov

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The paper presents the results of an experimental study of the effect of reverse mechanical load-unloading on the mechanical, linear, and nonlinear elastic properties of n-AMg6/C60 nanocomposite. Samples for experimental studies of n-AMg6/C60 nanocomposite were obtained by grinding AMg6 polycrystalline alloy in a planetary mill with 0.3 wt % of C60 fullerite in an argon atmosphere. The resulting product consisted of 200-500-micron agglomerates of nanoparticles. X-ray coherent scattering (CSL) method has shown that the average nanoparticle size is 40-60 nm. The resulting preform was extruded at high temperature. Modifications of C60 fullerite interferes the process of recrystallization at grain boundaries. In the samples of n-AMg6/C60 nanocomposite, the load curve is measured: the dependence of the mechanical stress σ on the strain of the sample ε under its multi-cycle load-unloading process till its destruction. The hysteresis dependence σ = σ(ε) was observed, and insignificant residual strain ε < 0.005 were recorded. At σ≈500 MPa and ε≈0.025, the sample was destroyed. The destruction of the sample was fragile. Microhardness was measured before and after destruction of the sample. It was found that the loading-unloading process led to an increase in its microhardness. The effect of the reversible mechanical stress on the linear and nonlinear elastic properties of the n-AMg6/C60 nanocomposite was studied experimentally by ultrasonic method on the automated complex Ritec RAM-5000 SNAP SYSTEM. In the n-AMg6/C60 nanocomposite, the velocities of the longitudinal and shear bulk waves were measured with the pulse method, and all the second-order elasticity coefficients and their dependence on the magnitude of the reversible mechanical stress applied to the sample were calculated. Studies of nonlinear elastic properties of the n-AMg6/C60 nanocomposite at reversible load-unloading of the sample were carried out with the spectral method. At arbitrary values of the strain of the sample (up to its breakage), the dependence of the amplitude of the second longitudinal acoustic harmonic at a frequency of 2f = 10MHz on the amplitude of the first harmonic at a frequency f = 5MHz of the acoustic wave is measured. Based on the results of these measurements, the values of the nonlinear acoustic parameter in the n-AMg6/C60 nanocomposite sample at different mechanical stress were determined. The obtained results can be used in solid-state physics, materials science, for development of new techniques for nondestructive testing of structural materials using methods of nonlinear acoustic diagnostics. This study was supported by the Russian Science Foundation (project №14-22-00042).

Keywords: nanocomposite, generation of acoustic harmonics, nonlinear acoustic parameter, hysteresis

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Raina J. Olsen, Andrew K. Gillespie, John W. Taylor, Cristian I. Contescu, Peter Pfeifer, James R. Morris

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While adsorbent surfaces such as graphite are known to increase the melting temperature of solid H2, this effect is normally rather small, increasing to 20 Kelvin (K) relative to 14 K in the bulk. An as-yet unidentified phase transition has been observed in a system of H2 adsorbed in a porous, locally graphitic, Saran carbon with sub-nanometer sized pores at temperatures (74-101 K) and pressures ( > 76 bar) well above the critical point of bulk H2 using hydrogen adsorption and neutron scattering experiments. Adsorption data shows a discontinuous pressure jump in the kinetics at 76 bar after nearly an hour of equilibration time, which is identified as an exothermic phase transition. This discontinuity is observed in the 87 K isotherm, but not the 77 K isotherm. At higher pressures, the measured isotherms show greater excess adsorption at 87 K than 77 K. Inelastic neutron scattering measurements also show a striking phase transition, with the amount of high angle scattering (corresponding to large momentum transfer/ large effective mass) increasing by up to a factor of 5 in the novel phase. During the course of the neutron scattering experiment, three of these reversible spectral phase transitions were observed to occur in response to only changes in sample temperature. The novel phase was observed by neutron scattering only at high H2 pressure (123 bar and 187 bar) and temperatures between 74-101 K in the sample of interest, but not at low pressure (30 bar), or in a control activated carbon at 186 bar of H2 pressure. Based on several of the more unusual observations, such as the slow equilibration and the presence of both an upper and lower temperature bound, a reasonable hypothesis is that this phase forms only in the presence of a high concentration of ortho-H2 (nuclear spin S=1). The increase in adsorption with temperature, temperatures which cross the lower temperature bound observed by neutron scattering, indicates that this novel phase is denser. Structural characterization data on the adsorbent shows that it may support a commensurate solid phase denser than those known to exist on graphite at much lower temperatures. Whatever this phase is eventually proven to be, these results show that surfaces can have a more striking effect on hydrogen phases than previously thought.

Keywords: adsorbed phases, hydrogen, neutron scattering, nuclear spin

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Authors: A. Belmeguenai, K. Mansouri, R. Djemili

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This work present a new algorithm based on the nonlinear filter generator for speech encryption and decryption. The proposed algorithm consists on the use a linear feedback shift register (LFSR) whose polynomial is primitive and nonlinear Boolean function. The purpose of this system is to construct Keystream with good statistical properties, but also easily computable on a machine with limited capacity calculated. This proposed speech encryption scheme is very simple, highly efficient, and fast to implement the speech encryption and decryption. We conclude the paper by showing that this system can resist certain known attacks.

Keywords: nonlinear filter generator, stream ciphers, speech encryption, security analysis

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Authors: Nicolò Vaiana, Giorgio Serino

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The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis

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Authors: Peter Modregger, Özgül Öztürk

Abstract:

Glass fabric reinforced thermoplastic (GFRT) are composite materials, which combine low weight and resilient mechanical properties rendering them especially suitable for automobile construction. However, defects in the glass fabric as well as in the polymer matrix can occur during manufacturing, which may compromise component lifetime or even safety. One type of these defects is local fiber shifts, which can be difficult to detect. Recently, we have experimentally demonstrated the reliable detection of local fiber shifts by X-ray scattering based on the edge-illumination (EI) principle. EI constitutes a novel X-ray imaging technique that utilizes two slit masks, one in front of the sample and one in front of the detector, in order to simultaneously provide absorption, phase, and scattering contrast. The principle of contrast formation is as follows. The incident X-ray beam is split into smaller beamlets by the sample mask, resulting in small beamlets. These are distorted by the interaction with the sample, and the distortions are scaled up by the detector masks, rendering them visible to a pixelated detector. In the experiment, the sample mask is laterally scanned, resulting in Gaussian-like intensity distributions in each pixel. The area under the curves represents absorption, the peak offset refraction, and the width of the curve represents the scattering occurring in the sample. Here, scattering is caused by the numerous glass fiber/polymer matrix interfaces. In our recent publication, we have shown that the standard deviation of the absorption and scattering values over a selected field of view can be used to distinguish between intact samples and samples with local fiber shift defects. The quantification of defect detection performance was done by using p-values (p=0.002 for absorption and p=0.009 for scattering) and contrast-to-noise ratios (CNR=3.0 for absorption and CNR=2.1 for scattering) between the two groups of samples. This was further improved for the scattering contrast to p=0.0004 and CNR=4.2 by utilizing a harmonic decomposition analysis of the images. Thus, we concluded that local fiber shifts can be reliably detected by the X-ray scattering contrasts provided by EI. However, a potential application in, for example, production monitoring requires fast data acquisition times. For the results above, the scanning of the sample masks was performed over 50 individual steps, which resulted in long total scan times. In this paper, we will demonstrate that reliable detection of local fiber shift defects is also possible by using single images, which implies a speed up of total scan time by a factor of 50. Additional performance improvements will also be discussed, which opens the possibility for real-time acquisition. This contributes a vital step for the translation of EI to industrial applications for a wide variety of materials consisting of numerous interfaces on the micrometer scale.

Keywords: defects in composites, X-ray scattering, local fiber shifts, X-ray edge Illumination

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