Pareto optimal design of layered bandgap materials with multiphase microstructures using evolutionary algorithms

An important characteristic of the periodic materials or structures is the existence of bandgap. This bandgap, which is dispersion-related, can be designed by controlling the materials layout within the periodic microstructures. In this paper, the topologies of periodic multiphase microstructures are optimized using a multiobjective genetic algorithm and two cases of studies are presented. The results show that 3-phase material can obtain quite better designs on the basis of fewer layers. This will be a reference for the design of phononic bandgap materials.     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

A fractional-order difference equation model of a third-order discrete phase-locked loop (FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.     

An efficient physical device-circuit simulator and its application to accurate design of millimeter wave oscillators

A rigorous one-dimensional physical device-circuit simulator is developed to accurately determine the transport properties and the electrical performance of semiconductor devices embedded into a passive circuit. The simulator is well suited to study the effects of device geometry, doping level, bias voltage, and mounting structure on the performance and to compare the accuracy and the computational efficiency of different physical models. The model is applied to determine the application limits of the drift-diffusion and hydrodynamic models when they are used to characterize the operation and to optimize the structure of cm- and mm-wave oscillators with two-terminal devices, and to produce a set of design curves which indicate the performance limits of different devices under various operating conditions.     

Single-mode fiber design proposal using evolutionary technique with ultra low bending-loss appropriate in FTTH application

A proposal for the new single mode optical fiber containing four cladding layer with ultra low bending loss is presented. The suggested design method is based on the Genetic Algorithm optimization technique. Compared to the work reported in [1], our designed structure exhibits very small bending loss over the wide communication band (1.3–1.65 μm). Simulation results show bending loss of 6.78e?14 dB/turn at 1.55 μm for single turn of 5 mm radius. The best value reported in [1] was 2e?3 dB/turn for the same wavelength and radius of curvature.     

Simple numerical control loop for stabilizing Nd:YAG and Nd:YLF single-mode oscillators

In order to get reliable and synchronisable smooth nanosecond range pulses, a high stability singlemode actively Q-switched laser oscillator has been developed which works with Nd:YAG or Nd:YLF. An electronic loop is used for longitudinal mode control. It is based on dual-mode beating detection and the design is mainly numerical. The system produces 10 pps jitter free pulses with ±2% amplitude stability and 100% singlemode spectral limitation. The method is equally suitable for producing repetitive dual-mode modulated pulses.     

Development and design of a phase-locked loop in the subterahertz and terahertz ranges for a harmonic of the signal of a centimeter-wave synthesizer

We describe a phase-locked loop of a backward-wave oscillator in the range 667–857 GHz for the 34th–45th harmonic of the reference signal of a centimeter-wave synthesizer. Multiplication of the reference-synthesizer frequency in the phase-locked loop is performed by using a subharmonic mixer based on semiconductor superlattices. The mixer, operated at room temperature, has a nonlinear electron conductance.     

A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements

Three methods of designing diffractive optical elements (DOE) are compared. The iterative Fourier transform algorithm (IFTA) is compared to an evolutionary strategy (ES) approach and a combination of both methods. It is shown that the combination of both methods produces a better solution than the iterative method and is faster than using the evolutionary strategy only.     

Trapped-ion quantum simulator: experimental application to nonlinear interferometers

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).     

Evaluation of irradiation-induced creep rate: application to the vacancy dislocation loop contribution

Irradiation (as in a nuclear reactor) drastically affects the defect structure and its time evolution in a material, and induces new creep mechanisms in it. We present a formalism to evaluate the contribution to creep owing to such mechanisms. Beginning with the phenomenological constitutive relation for the strain appropriate to a given mechanism, we put in simple statistical considerations to derive an expression for the corresponding creep rate. This formal expression is in terms of the defect production rate and a non-equilibrium probability distribution function involving the pertinent properties of the defect type concerned. A convenient approximation scheme for practical calculations is employed, that also makes contact with standard rate theory and provides a proper interpretation for the variables occurring there. As an illustration, we evaluate the contribution to irradiation-induced creep from the orientation-dependent shrinkage of vacancy dislocation loops in an applied stress field. The circumstances inducing transient and non-transient creep are clarified and a numerical estimate is given for the latter component.     

Strong coupling of nonlinear electronic and biological oscillators: reaching the "amplitude death" regime

Interaction between an electronic and a biological circuit has been investigated for a pair of electrically connected nonlinear oscillators, with a spontaneously oscillating olivary neuron as the single-cell biological element. By varying the coupling strength between the oscillators, we observe a range of behaviors predicted by model calculations, including a reversible low-energy dissipation "amplitude death" where the oscillations in the coupled system cease entirely.     

Mapping deformation method and its application to nonlinear equations

An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein－Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.     

New Lamé function and its application to nonlinear equations

In this Letter, a new kind of Lamé functions are given. Based on the new Lamé functions and Jacobi elliptic function, the perturbation method is applied to the nonlinear equations, and many multi-order solutions of novel forms are derived. In addition, it is shown that different Lamé functions can exist in the first order solutions of nonlinear system.     

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions.     

Elaboration of some signal processing algorithms in ultrasonic techniques: application to materials NDT

In ultrasonic techniques, information on defect characterization possibilities has required more evolved technique development than classical methods. To obtain a high probability of defect detection, these methods use signal-processing algorithms in order to enhance the signal-to-noise ratio. These methods are also used to discriminate between planar and volumetric defects. In this paper, some signal-processing algorithms are developed and implemented on a computer to allow their utilization in real-time processing of ultrasonics NDT results.     

EASY-GOING deconvolution: combining accurate simulation and evolutionary algorithms for fast deconvolution of solid-state quadrupolar NMR spectra

A fast and accurate fit program is presented for deconvolution of one-dimensional solid-state quadrupolar NMR spectra of powdered materials. Computational costs of the synthesis of theoretical spectra are reduced by the use of libraries containing simulated time/frequency domain data. These libraries are calculated once and with the use of second-party simulation software readily available in the NMR community, to ensure a maximum flexibility and accuracy with respect to experimental conditions. EASY-GOING deconvolution (EGdeconv) is equipped with evolutionary algorithms that provide robust many-parameter fitting and offers efficient parallellised computing. The program supports quantification of relative chemical site abundances and (dis)order in the solid-state by incorporation of (extended) Czjzek and order parameter models. To illustrate EGdeconv's current capabilities, we provide three case studies. Given the program's simple concept it allows a straightforward extension to include other NMR interactions. The program is available as is for 64-bit Linux operating systems.     

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.     

Analysis and design of nonlinear fiber Bragg gratings and their application for optical compression of reflected pulses

We demonstrate a novel split-step solution for analyzing nonlinear fiber Bragg gratings. The solution is used for designing nonlinear fiber Bragg gratings with a low reflectivity. The structure of the grating is designed according to the profiles of the incident and reflected pulses. We demonstrate our method for nonlinear compression of a pulse reflected from a fiber Bragg grating. The method allows us to obtain compressed pulses with a very low wing intensity.     

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.