Molecular structure dependence of acoustic nonlinearity parameter B/A for silicone oils

Exploring new acoustic parameters is essential to develop a noninvasive imaging technique for the surgery of silicone oil tamponades. In this study, the acoustic nonlinearity parameters B/A of varied silicone oil samples （e.g., linear or hyper-branched） are experimentally measured by using a modified thermodynamic method. The results show that： （i） when the concentration of the silicone oil with a molecular weight of 5 × 10^4 increases from 0.5 g/100 ml to 8 g/100 ml, the corresponding B/A value increases by about 18%, but the acoustic velocity only increases by about 0.1%; （ii） when the molecular weight of the hyper-branched silicone oil is enhanced from 2 × 10^5 to 1 × 10^6, the B/A value increases by about 22%, while the acoustic velocity is only raised by about 0.2%. This study suggests that the B/A parameter of the silicone oil is more sensitive to the change in its molecular structure than that of the acoustic velocity. Thus, the B/A parameter might be utilized as an effective index for the development and optimization of the noninvasive imaging of the surgery of silicone oil tamponades.

Self-heating tendency evaluation of sulfide ores based on nonlinear multi-parameters fusion

In order to reveal the nonlinear dynamics characteristics of unsteady self-heating process of sulfide ores, nine different kinds of sulfide ore samples from a pyrite mine in China were taken as experimental materials and their self-heating characteristics were measured in laboratory. Furthermore, the measured temperature was studied by integrating wavelet transform, nonlinear characteristic parameters extraction and fuzzy comprehensive evaluation. The results indicate that only the ore samples 1, 2, 6 and 9 have obvious self-heating phenomenon, and their self-heating initiative temperatures are 220 ℃, 239 ℃, 220 ℃ and 220 ℃, respectively, which means that they are difficult to produce self-heating under normal mining conditions. The correlation dimension of self-heating process is fraction and the maximum Lyapunov exponent is positive, which means that it is feasible to study the self-heating process based on chaotic dynamics theory. The nonlinearities of self-heating process of these four samples （ore samples 1, 2, 6 and 9） are 0.8227, 0.7521, 0.9401 and 0.8827 respectively and the order of the samples according to these results is： sample 6, sample 9, sample 1, sample 2, which is consistent with the measured results of self-heating characteristics. Therefore, the nonlinearity method can be used to evaluate the self-heating tendency of sulfide ores, and it is an effective verification of the reliability of measured results.

Simultaneous identification of unknown time delays and model parameters in uncertain dynamical systems with linear or nonlinear parameterization by autosynchronization

In this paper, we propose a general method to simultaneously identify both unknown time delays and unknown model parameters in delayed dynamical systems based on the autosynchronization technique. The design procedure is presented in detail by constructing a specific Lyapunov function and linearizing the model function with nonlinear parameterization. The obtained result can be directly extended to the identification problem of linearly parameterized dynamical systems. Two Wpical numerical examples confirming the effectiveness of the identification method are given.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

Numerical Analysis of the Nonlinear Parameterization of Waves in Currents over a Submerged Sill with a Non-Hydrostatic Model

An investigation of the effects of a uniform current strength direction(following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH,a non-hydrostatic numerical wave model.The nonlinear parameters(i.e.,asymmetry,skewness,and kurtosis) are calculated,and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured.In the shoaling area of the submerged sill,the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction.Whereas nonlinear parameters grow with the strengthening of the following currents over the crest,they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network （FBFN）. The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

A semi-analytical method to compute acoustic nonlinearity parameter of Cu,Ag and Au

In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.

Adaptive Fuzzy Neural Control of Dynamic System

Aim To build an adaptive fuzzy neural controller and simulate it. Methods\ Fuzzy logic and back propagation(BP) algorithm are combined to utilize their advantages while avoiding the disadvantages. Results and Conclusion\ Simulation results of the third order plant with disturbances and dead times show the validity of the presented controller. The presented controller can control cases that preceding controllers were unable to control.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton＇s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed- parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Low-frequency repetitive transcranial magnetic simulation prevents chronic epileptic seizure

Although low-frequency repetitive transcranial magnetic simulation can potentially treat epilepsy, its underlying mechanism remains unclear. This study investigated the influence of low-frequency re-petitive transcranial magnetic simulation on changes in several nonlinear dynamic electroenceph-alographic parameters in rats with chronic epilepsy and explored the mechanism underlying repeti-tive transcranial magnetic simulation-induced antiepileptic effects. An epilepsy model was estab-lished using lithium-pilocarpine intraperitoneal injection into adult Sprague-Dawley rats, which were then treated with repetitive transcranial magnetic simulation for 7 consecutive days. Nonlinear elec-electroencephalographic parameters were obtained from the rats at 7, 14, and 28 days post-stimulation. Results showed significantly lower mean correlation-dimension and Kolmogo-rov-entropy values for stimulated rats than for non-stimulated rats. At 28 days, the complexity and point-wise correlation dimensional values were lower in stimulated rats. Low-frequency repetitive transcranial magnetic simulation has suppressive effects on electrical activity in epileptic rats, thus explaining its effectiveness in treating epilepsy.

Nonlinear characteristics of induced spontaneous combustion process of sulfide ores

To investigate the relationship between nonlinear parameters and spontaneous combustion tendency of sulfide ores, nine different sulfide ore samples were taken from a pyrite mine in China, and induced spontaneous combustion experiment was carried out in the laboratory. Different stages of the induced spontaneous combustion process were studied by integrating wavelet technology and nonlinear dynamics theory. The results show that ignition points of all the ore samples are above 330 ℃, indicating that sulfide ores of the pyrite mine are difficult to combust spontaneously under normal mining conditions. Spontaneous combustion process includes three stages： incubation stage, development stage and approaching stage. The average temperature rising rate of the three stages are 1.0 ~C/min, 2.0 ~C/min and 4.2 ~C/min, respectively. During the spontaneous combustion process, mean values of approximate entropy and correlation dimension increase at first, and then decrease in the following stage. The mean value of the maximum Lyapunov exponent increases with the passage of reaction time. In a whole, correlation among the three nonlinear parameters firstly weakens, then enhances, and the best correlation period is at approaching stage. As ignition point increases, the maximum Lyapunov exponent of approaching stage decreases. Therefore, combustible tendency of sulfide ores could be qualitatively evaluated based on the maximum Lyapunov exponent of this stage.

Influences of tissue composition and structural features of biological media on the ultrasonic nonlinearity parameter

The Acoustic nonlinearity parameter is an important parameter in nonlinear acoustics. In this article, the nonlinearity parameter B / A of normal and eight kinds of pathological porcine liver tissues were measured by finite amplitude insert-substitution method. The mixture law for nonlinearity parameter is used to analyze and predict the volume fractions of the components in a given tissue. It was found that the nonlinearity parameter is sensitive to the pathological forms of biological tissues and the values of B / A depend on the tissue composition and structural features.

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs＇ collision factor theory

Based on Schaaff＇s collision factor theory （CFT） in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel＇s and Sehgal＇s laws for liquid binary mixtures.

Genetic programming-based chaotic time series modeling

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.

Study of the second harmonic sound field from a circular piston source and the influence in the nonlinearity parameter tomography

In the nonlinearity parameter B/A tomography using the second harmonic wav, it is very important to analyze the ultrasonic field of the transducer, especially the generation of the second harmonic wave in the nearfield. In this paper, the theoretical study and experimental measurements of the second harmoinc pressure field from a circular piston source are performed.And the effect on the nonlinearity parameter tomograaphy is discussed. The results will be used to decrease the error of reconstruction in nonlinearity parameter tomography and bring the ultrasoinc diagnosis a step forward

Ensemble Forecast for Tropical Cyclone Based on CNOP-P Method:A Case Study of WRF Model and Two Typhoons

In this paper,we set out to study the ensemble forecast for tropical cyclones.The case study is based on the Conditional Nonlinear Optimal Perturbation related to Parameter(CNOP-P)method and the WRF model to improve the prediction accuracy for track and intensity,and two different typhoons are selected as cases for analysis.We first select perturbed parameters in the YSU and WSM6 schemes,and then solve CNOP-Ps with simulated annealing algorithm for single parameters as well as the combination of multiple parameters.Finally,perturbations are imposed on default parameter values to generate the ensemble members.The whole proposed procedures are referred to as the PerturbedParameter Ensemble(PPE).We also conduct two experiments,which are control forecast and ensemble forecast,termed Ctrl and perturbed-physics ensemble(PPhyE)respectively,to demonstrate the performance for contrast.In the article,we compare the effects of three experiments on tropical cyclones in aspects of track and intensity,respectively.For track,the prediction errors of PPE are smaller.The ensemble mean of PPE filters the unpredictable situation and retains the reasonably predictable components of the ensemble members.As for intensity,ensemble mean values of the central minimum sea-level pressure and the central maximum wind speed are closer to CMA data during most of the simulation time.The predicted values of the PPE ensemble members included the intensity of CMA data when the typhoon made landfall.The PPE also shows uncertainty in the forecast.Moreover,we also analyze the track and intensity from physical variable fields of PPE.Experiment results show PPE outperforms the other two benchmarks in track and intensity prediction.