Nonlinear Self Research Articles

Shear Horizontal Waves in a Nonlinear Elastic Layer overlying a Rigid Substratum

In this work, the propagation of shear horizontal (SH) waves in a homogeneous, isotropic and compressible nonlinear hyper-elastic layer having finite thickness is studied. The upper surface of the layer is assumed to be free from traction and the lower boundary is rigidly fixed. These waves are dispersive like the Love waves. The problem is examined by a perturbation method that balances the nonlinearity and dispersion in the analysis. A nonlinear Schrodinger equation is derived describing the nonlinear self modulation of the waves. Then, the effect of nonlinear properties of the material on the propagation characteristics and on the existence of solitary waves are discussed.

Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Abstract In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

Thermal diffusivity of 2,3-Pyridinediamine determination by thermal blooming

Abstract The nonlinear optical properties, optical limiting and self diffraction of 2,3-pyridinediamine in the solvent DMSO have been studied. The measurements were performed using a low power continuous wave (CW) from solid state laser (SDL) at 473 nm wavelength. The effect of the pH in 2,3-pyridinediamine solution on nonlinear optical properties, optical limiting and self diffraction pattern have been investigated. The results show the dependence of the nonlinear refractive index, nonlinear absorption coefficient, optical limiting threshold and number of diffraction rings on the pH values. This 2,3-pyridinediamine solution exhibit an interesting optical limiting performance with CW laser. Thermal blooming technique was applied to investigate the thermo-optical properties and the nonlinear refractive index. In this technique a pump beam was aligned collinearly. A localized change in the refractive index of the sample due to the thermal heating produced a thermal lens that was then detected by the study of the focusing and defocusing of the pump beam. With excellent nonlinear optical coefficient, the sample is expected to have potential applications in optical devices.

PAM–ASK optical logic gates in an optical fiber Sagnac interferometer

In this work we performed a numerical study of optical logic gates based on a Sagnac interferometer, operating with short optical pulses (10ps) in a PAM–ASK modulation scheme with binary amplitude modulation scheme. We examined the performance of a nonlinear Sagnac interferometer implementing two-input logical functions. We evaluated the effect resulting from an increment in the PAM coding parameter offset (ε), considering the anomalous group velocity dispersion (GVD) and nonlinear self phase modulation (SPM) in a lossless configuration. By analysing the transmitted output, we conclude it is possible to obtain logic gates OR for two different power-splitting ratios ρ of the coupler (ρ=0.1 and 0.2). After this step, we applied a dephasing control to the input pulses, aiming to achieve logic gates with ρ=0.3 and ρ=0.4 and to enhance the study of cases in which they had not been previously obtained. We obtained OR and AND logic gates with a phase variation study for ρ=0.1 and 0.2. For ρ=0.3 and 0.4, the variety and versatility of logic gates proved to be very broad where OR, AND and XOR gates were obtained.

Pole-placement self-tuning control of nonlinear Hammerstein system and its application to pH process control

By taking advantage of the separation characteristics of nonlinear gain and dynamic sector inside a Hammerstein model, a novel pole placement self tuning control scheme for nonlinear Hammerstein system was put forward based on the linear system pole placement self tuning control algorithm. And the nonlinear Hammerstein system pole placement self tuning control (NL-PP-STC) algorithm was presented in detail. The identification ability of its parameter estimation algorithm of NL-PP-STC was analyzed, which was always identifiable in closed loop. Two particular problems including the selection of poles and the on-line estimation of model parameters, which may be met in applications of NL-PP-STC to real process control, were discussed. The control simulation of a strong nonlinear pH neutralization process was carried out and good control performance was achieved.

Frequency locking in a nonlinear MEMS oscillator driven by harmonic force and time delay

Vibrations of a nonlinear self- and parametrically excited MEMS device driven by external excitation and time delay inputs are analysed in the paper. The model of MEMS resonator includes a nonlinear van der Pol function producing self-excitation, a periodically varied coefficient which represents Mathieu type of parametric excitation and furthermore, periodic force acting on the resonator. Analysis of frequency locking zones is presented with suggestions for a strategy of a closed loop control. Interactions between self- and parametric excitation lead to quasi-periodic oscillations but under specific conditions the motion becomes harmonic. The so called frequency locking, near the resonance zones is observed. This is caused by the second kind Hopf bifurcation (Neimark–Sacker bifurcation). The amplitudes of periodic oscillations are determined analytically by the multiple time scale method (MS) in the second order perturbation. The effect of external force has been observed by the internal loop occurring inside the frequency locking zone. The localisation of the zones and existence of the internal loop can be controlled by a selection of gains and time delay of displacement or velocity feedbacks.

Phase velocity effects of the wave interaction with exponentially sheared current

The nonlinear interaction between the unidirectional bichromatic wave-train and exponentially sheared current in water of an infinite depth is investigated. The model is based on the vorticity transport equation and the exact free surface conditions, without any assumptions for the existence of small physical parameters. Earlier works of the wave–current interaction were mainly restricted to either current acted on the monochromatic wave or irregular waves limited to irrotational current. Different from these previous works, no constraint is made in our model for amplitudes of the primary wave, and the current owns an exponential type profile along the vertical line. To ensure that the effect of vorticity on the phase velocity is consistent with earlier derivation, the case of a small amplitude wave traveling on the exponentially sheared current is examined firstly. Then the effect of nonlinearity on the phase velocity of primary waves in a bichromatic wave-train is considered. Accurate high-order approximations of the phase velocity are obtained under consideration of both the nonlinear wave self–self and mutual interactions. Finally, the combined effect of vorticity and nonlinearity on the phase velocity is investigated through the case of a bichromatic wave-train propagating on an exponentially sheared current. It is found that the characteristic current slope determines the effect of vorticity on the phase velocity caused by nonlinear wave self–self and mutual interactions, and the surface current strength may amplify/reduce this effect.

Experimental Demonstration of Electron Longitudinal-Phase-Space Linearization by Shaping the Photoinjector Laser Pulse

Control of the electron-beam longitudinal-phase-space distribution is of crucial importance in a number of accelerator applications, such as linac-driven free-electron lasers, colliders and energy recovery linacs. Some longitudinal-phase-space features produced by nonlinear electron beam self- fields, such as a quadratic energy chirp introduced by geometric longitudinal wakefields in radio-frequency (rf) accelerator structures, cannot be compensated by ordinary tuning of the linac rf phases nor corrected by a single high harmonic accelerating cavity. In this Letter we report an experimental demonstration of the removal of the quadratic energy chirp by properly shaping the electron beam current at the photoinjector. Specifically, a longitudinal ramp in the current distribution at the cathode linearizes the longitudinal wakefields in the downstream linac, resulting in a flat electron current and energy distribution. We present longitudinal-phase-space measurements in this novel configuration compared to those typically obtained without longitudinal current shaping at the FERMI linac.

High Contrast Optical “OR” Logic Gates Using a Photonic Crystal Fiber Modulated by PAM-ASK

In this work, we present a numerical study of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) in Photonic Fiber Crystals (PCFs) PCFs operating with two ultrashort fundamental soliton pulses of 100 fs, modulated by PAM-ASK with binary amplitude modulation to represent the logical level 1 and 0. The performance of a symmetric dual core NLDCPCF to execute two-input logical functions is examined. We evaluate the effect resulting from an increment in the PAM coding parameter offset (ε), considering the anomalous Group Velocity Dispersion (GVD), third-order dispersion (β3) and nonlinear effects Self Phase Modulation (SPM), Self-Steepening (SS), lntrapulse Raman Scattering (IRS) in a lossless configuration. Our results indicate that is possible to get logical operations for the cores 1 or 2 using a phase control to the input pulse in one of the fibers.

Pyrimidine Ring as Building Block for the Synthesis of Functionalized ?-Conjugated Materials

In the past two decades, π-conjugated organic compounds have attracted much attention due to their potential applications in various fields such as liquid crystals, light-emitting, and nonlinear optical materials and self assembling. Introduction of heteroaryl moieties into π-extended systems are particularly useful where electron transfer is necessary and is a way to modify and sometimes enhance properties of advanced “electro-optic”. In π-conjugated materials, azaheterocycles such as pyrimidine, which owing to its aromaticity, its strong electron-withdrawing character, its high dipolar interaction and its pH sensibility, presents the requested characteristics to be incorporated in organic materials in view of numerous and various applications. Such molecular architectures and their applications are reported in this review. Keywords: Pyrimidine, π-conjugated-materials, liquid crystals, non-linear optic, luminescence, charge transport, supramolecular assemblies

On the third harmonic generation in a medium with negative pump wave refraction

The propagation of the pump and its third harmonic pulses in a cubically nonlinear medium is considered theoretically, provided that the linear properties of the medium are characterized by a negative refractive index at the pump frequency and a positive refractive index at the harmonic frequency. For low-intensity interacting waves, the pump and third harmonic pulses propagate in opposite directions, but sufficiently intense pulses can produce a simulton—a solitary two-frequency wave that propagates in a certain direction as a single whole. The system of equations is investigated numerically for a model that, apart from the harmonic generation, includes the second-order group velocity dispersion and the nonlinear self- and cross-phase modulations of the interacting waves. The separation of the pump and harmonic pulses due to the difference in the directions of their group velocities and peculiarities of the Manley-Rowe relation for parametric processes in metamedia are discussed.

Generalized Brans-Dicke theories

In Brans-Dicke theory a non-linear self interaction of a scalar field ϕ allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict theallowed region of model parameters from the demandfor the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the ΛCDM model.

Origin of photo-induced transmitting oscillations in chalcogenide glasses

Light-induced oscillatory behaviors of transmission in chalcogenide glasses are investigated using a continuous wave tunable Ti-sapphire laser. It is shown that phase change, thermal fluctuation, nonlinear index change and periodic self focusing are not at the origin of light-induced oscillatory transmittance in chalcogenide glasses. Instead, results indicate that the interference of transmitting and reflecting light is at the origin of the oscillatory behaviors of transmitted light. Just like the principle of Fabry-Pérot interferometer, these interferences result in a periodic change in transmission as the related interferential beams get in and out of phase. However, this transmitting oscillatory behavior can be registered by the detector only when the change of optical path length difference initiated by photo-induced effects is slower enough compared with the corresponding response time of the detector. Several photo-structural effects contribute to that phenomenon including photo-expansion, photo-darkening, and permanent self focusing. It appears that fluctuations of the light source intensity induce a wide distribution of the oscillatory periods.

A performance study of an all-optical logic gate based in PAM-ASK

In this paper a numerical study of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) operating with two ultrashort fundamental soliton pulses of 2ps, modulated by PAM-ASK with binary amplitude modulation to represent the logical level 1 and 0, is presented. The performance of a symmetric dual core NLDC performing two-input logical functions is examined. Initially, we evaluate the effect resulting from an increment in the PAM coding parameter offset (ϵ), considering the anomalous Group Velocity Dispersion (GVD), nonlinear Self Phase Modulation (SPM) in a lossless configuration. We can conclude that is possible to get logical operations for the cores 1 or 2 since a phase control exists which is applied to the input pulse in fiber 1.

Analysis of an optical logic gate using a symmetric coupler operating with pulse position modulation (PPM)

In this paper we propose the operation of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) operating with a pulse position modulation (PPM). The performance of a symmetric NLDC realizing two-input AND/OR logical functions, which can be applied in transmission and processing of signals in all-optical form in TDM systems, is examined. This integrated symmetric NLDC logical gate operates with two ultrashort soliton light pulses (2ps), which are modulated in agreement with the technique of pulse position modulation (PPM). Initially, we evaluate the effect resulting of an increment in the PPM coding parameter offset (ε), for the temporal position of the output pulse, considering the anomalous group-velocity dispersion (GVD), nonlinear self phase modulation (SPM) and without loss propagation regime of input pulses, in the cores 1 and 2 of the NLDC. In this situation, we analyze the four possible situations for the two-input logical gate, modulating the 1 and 2 input pulses through temporal displacement and allowing a variation in the coding parameter offset. We can conclude that is possible to get AND/OR logical operations for the cores 1 or 2, without to insert PPM error, since a phase control (Δϕ) exists applied in agreement with the logical level of the input pulse in the core 1. Finally we define the truth table, considering the adequate phase difference and coding parameter offset for the stable operation of the AND/OR logical gate based in the symmetric NLDC.

A performance study of a logical gate using PPM optical pulse modulation for TDM systems

In this paper we propose the operation of an all-optical logical gate based in an acousto optical tunable filter (AOTF) operating with a pulse position modulation (PPM). The performance of an AOTF realizing two-input AND/OR logical functions, which can be applied in transmission and processing of signals in all-optical form in TDM systems, was examined. This novel integrated acousto optical logical gate operates with two ultrashort soliton light pulses (2ps), which are modulated in agreement with the technique of pulse position modulation (PPM). Initially, we evaluated the effect resulting of an increment in the acousto optical interaction length, for the temporal position of the output pulse, considering the anomalous group velocity dispersion (GVD), nonlinear self phase modulation (SPM) and without loss propagation regime of TE and TM input pulses not modulated. We have analyzed the four possible situations for the two-input logical gate, modulating the TE and TM input pulses through temporal displacement and allowing a variation in the coding parameter offset (ε). We can conclude that is possible to get AND/OR logical operations for the modes TM or TE, without to insert PPM error, since a phase control (Δϕ) exists (applied on the TM input pulse) in agreement with each situation in the truth table. Finally we defined the truth table, considering the adequate phase difference and coding parameter offset for the operation of the AND/OR logical gate based in the AOTF.

APPLICATION OF MULTIVARIABLE NONLINEAR ADAPTIVE GENERIC MODEL CONTROL TO A PACKED DISTILLATION COLUMN

Nonlinear adaptive generic model control and self-tuning PID control systems were applied to control the top and bottom product temperature of a packed distillation column separating methanol-water mixture. In the first control algorithm, an adaptive generic model control (AGMC) structure was proposed for dual temperature control of the system. In the second control algorithm, nonlinear self tuning PID (NLSTPID) control based on pole-placement technique was used to control the same system. For NLSTPID control purposes pseudo random binary sequence (PRBS) signal and recursive identification algorithm were used to estimate the relevant parameters of a polynomial NARMAX model. In this work, real-time application has been carried out. In both dynamic and control studies, perturbations in feed composition were utilized as the disturbance, and the reboiler heat duty and the reflux ratio were selected as the manipulated variables. The control performances have been obtained by using ISE and, in general, AGMC results were better than those of the STPID control algorithm.

Particle-in-cell method for numerical simulation of beam and plasma dynamics

The finite particle methods are widely applied for the numerical simulation of a continuous medium including continuum electrodynamics and simulation of charged particle beams. This method allows studying the detailed beam and plasma characteristics, the distribution function of particles, the nonlinear self and external fields. The so-called “particle-in-cell” method is the most effective for simulations in the physics of plasma and charged particle beams. Two examples illustrate the application of the particle-in-cell method in beam dynamics and plasma physics. The first is a program library for numerical simulation and optimization of multi-component ion beam transportation from ion sources where RFQ accelerators are presented. The latest version of the library was applied for simulations of transverse dynamics of an argon ion beam in the beam line from the 18 GHz ECR Ion Source to the linear RFQ accelerator of the RIKEN Beam Factory. A partial neutralization of ion beam charge due to secondary electrons was assumed to realize the real experimental conditions in the beam line and was used in simulation. The second is a summary of recent development of physical and mathematical basements and the first version of a computer code library aimed for the three-dimensional (3D) simulation of the ECR plasma and ion production in the ECR ion source.

Particle-in-cell method for numerical simulation of beam and plasma dynamics

The finite particle methods are Euler or Lagrange methods for mathematical description of a continuous medium. These methods are widely applied for the numerical simulation of a continuous medium including continuum electrodynamics and simulation of charged particle beams. The finite particle method allows studying the detailed beam and plasma characteristics, the distribution function of particles, the nonlinear self and external fields. The so-called ‘particle-in-cells’ method is a combination of both Euler and Lagrange methods, and it is most effective for simulations in the physics of plasma and charged particle beams. The basement and recent development of the particle-in-cells method are presented. Two examples illustrate the application of the particle-in-cells method in beam dynamics and plasma physics.

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Abstract. Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrödinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright-(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.