Nonlinearity in superconducting metamaterial structures, including spirally coupled lines

Extraction of battery parameters using a multi-objective genetic algorithm with a non-linear circuit model

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Summary form only given, as follows. E to H mode transition is a typical nonlinear problem in an inductive Plasma sources. The mode transition has been explained in terms of power balance. In this presentation, the nonlinear equivalent circuit modeling has been studied. The linear transformer modeling has been used for inductive plasma source. However, linear transformer model can not explain the mode transition. The nonlinear circuit model based on the assumption that induction field is coupled nonlinearly to the plasma. When nonlinear coupling effects included in the linear transformer model, this nonlinear harmonic oscillation problem can be expressed by Duffing equation. The advantage of Duffing equation is hysteresis as well mode transition can be explained.

There is substantial promise in the use of piezoelectric energy harvesting systems to power electronics and devices through the conversion of ambient vibrations into electrical energy. Accurately predicting the energy harvesting capability in these systems is of paramount importance as the harvesting structure and the associated circuit must be ‘tuned’ in concert to the signature of the ambient vibrations. Here, we develop a numerical simulation methodology for piezoelectric harvesting systems that allows for high-fidelity finite element models of the harvester electromechanics as well as realistic non-linear circuits models. Our approach synthesizes conventional harmonic finite element analysis and a harmonic balance approach that accounts efficiently for the non-linear circuit behavior, bypassing the need for computationally expensive time marching schemes. The proposed methodology solves, via an iterative residual reduction scheme, for the coupled electrical output and structural dynamics of the piezoelectric harvesting structure. The proposed method is well suited for integration into model-predictive design methods. By numerical examples we illustrate the capability of the proposed approach to predict previously unreported coupling phenomena between the non-linear circuit response and piezoelectric structural behavior. The increased accuracy in the circuit model and flexibility of this method over current models outweighs the increased numerical costs.

In the previous chapters, we discussed autoregressive linear mixed effects models. In this section, we discuss the relationships between the autoregressive linear mixed effects models and nonlinear mixed effects models, growth curves, and differential equations. The autoregressive model shows a profile approaching an asymptote, where the change is proportional to the distance remaining to the asymptote. Autoregressive models in discrete time correspond to monomolecular curves in continuous time. Autoregressive linear mixed effects models correspond to monomolecular curves with random effects in the baseline and asymptote, and special error terms. The autoregressive coefficient is a nonlinear parameter, but all random effects parameters in the model are linear. Therefore, autoregressive linear mixed effects models are nonlinear mixed effects models without nonlinear random effects and have a closed form of likelihood. When there are time-dependent covariates, autoregressive linear mixed effects models are represented by a differential equation and random effects. The monomolecular curve is one of the popular growth curves. We introduce other growth curves, such as the logistic curves and von Bertalanffy curves, and generalizations of growth curves. Re-parameterization is often performed in nonlinear models, and various representations of re-parameterization in monomolecular and other curves are provided herein.

Artiflcial neural networks (ANN) have gained attention as fast and ∞exible vehicles to microwave modeling and design. This paper reviews a recent advance of neural network modeling, i.e., state-space dynamic neural network (SSDNN) for transient behavioral modeling of high-speed nonlinear circuits. The SSDNN model can be directly trained from the input and output waveforms without relying on the circuit internal details. A training algorithm exploiting adjoint sensitivities is summarized for training the model in an e-cient manner. An example of the SSDNN technique for IC bufier modeling and its use with transmission line elements in high-speed interconnect design are included. DOI: 10.2529/PIERS060907175229 With the continuous increase of signal speed and frequency, signal integrity (SI) in VLSI pack- ages becomes more and more prominent. Fast and accurate representations of the nonlinear analog behaviors of driver/receiver bufiers are the key to the success of SI-based design of high-speed inter- connects with nonlinear terminations (1,2). As such, developing e-cient bufier models for transient applications has become an important topic (3{5). To ensure model reliability in circuit simula- tions, the model stability remains one of the most critical aspects of nonlinear transient modeling. In the neural network community, global asymptotical stability and global exponential stability have been studied for some special classes of dynamic networks, e.g., Hopfleld neural networks (6), recurrent neural networks (7), and discrete-time state-space neural networks (8). Recently stability for ANN-based analog microwave modeling has also been addressed (9). This paper summarizes a state-space dynamic neural network (SSDNN) technique for modeling nonlinear transient behaviors of IC drivers and receivers (5). We describe the detailed structure of SSDNN and how to train the model based on the transient waveforms from the original circuits. An example is provided to demonstrate the application of the SSDNN model in coupled transmission line environments. Let u 2 < M be transient input signals of a nonlinear circuit, e.g., input voltages and currents, and y 2 < K be transient output signals of a nonlinear circuit, e.g., output voltages and currents where M and K are the numbers of circuit inputs and outputs respectively. Based on combining state-space concept and continuous recurrent neural network method (10), the SSDNN nonlinear model is formulated as (5) ( _ x(t) = ix(t) + ?g ANN (u(t);x(t);w)

Study of non-linear dynamic behavior of open cracked functionally graded Timoshenko beam under forced excitation using harmonic balance method in conjunction with an iterative technique

This paper presents the calculated and the measured performance capability of a cage rotor induction machine used as a direct connected, crankshaft speed, combined starter-alternator for an automotive diesel engine in an experimental hybrid electric vehicle. The calculated results are based on a nonlinear equivalent circuit model of the machine which considers saturation in the stator and rotor magnetizing flux paths. The development details of this model are given as well as several sets of calculation results for the induction machine previously described. Finally, measured maximum performance results for the test machine are presented and compared with model based calculated results for the same operating conditions of speed, terminal voltage and current.

In this study, a single-degree-of-freedom structure with multiple nonlinear tuned mass dampers is investigated. A sinusoidal excitation is assumed to be applied to the structure. In order to obtain the results, a nonlinear mathematical model of the general system is obtained in the form of a set of nonlinear ordinary differential equations. Dry friction and cubic stiffness nonlinearities are considered for the nonlinear terms. To obtain steady-state frequency responses of the system, these nonlinear ordinary differential equations are transformed into a set of nonlinear algebraic equations by using Harmonic Balance Method. Fourier transformation is used in the calculation of the Fourier coefficients of the nonlinear forcing terms. Then, numerical solutions to the resulting nonlinear algebraic equations are obtained using Newton’s Method with Arc Length Continuation. The effect of the number of tuned mass dampers and their arrangement, i.e. in series or in parallel, on vibration reduction is observed by performing optimization on several cases and comparing them. In order to observe the separate and combined effects of the nonlinearities, and the number of tuned mass dampers used, several case studies are carried out using optimized case parameters with different combinations of the nonlinearities. The results of these case studies and the linear model are compared with each other to see the effect of the nonlinearities. Additionally, results of the system with optimum nonlinear tuned mass dampers are compared with that of the optimum linear tuned mass dampers and the effect of nonlinearities are discussed.

Intensity-dependent properties of semiconductors (SCs) are of great significance since they reveal a lot of information about materials’ nonlinear behavior. Field of nonlinear optics (NLO) has been revolutionized due to the invention of lasers. Lasers have made possible to discuss nonlinear effects in detail with great precision. Nonlinear optical properties, their basic theory and formulism, and nonlinear effects are explored in the chapter with concise details and attention. NLO is utilized to understand the nonlinear susceptibility and its dependence on field and frequency and its symmetry properties and effects. Maxwell equations are at the heart of NLO. The higher terms in the nonlinear susceptibility give rise to harmonics of higher order that are discussed in detail. Here, second harmonic generation (SHG) is discussed for biological visualization, and another nonlinear multiphoton imaging method that is called third harmonic generation (THG) is deliberated briefly. In non-centrosymmetric framework, the second-order nonlinearity is the most reduced order of nonlinear interaction. Third-order nonlinearities in SCs provide absorption coefficient and refractive index (RI) that depend upon intensity. On the basis of photon energies close or below to absorption edge, there are two types of nonlinearities called resonant and nonresonant optical nonlinearities. Some optical nonlinearities in SCs are also explained, such as optical nonlinearities due to photothermal effects. The electro-optic effect and intensity-dependent RI are elaborated in detail. Application of nonlinear effects and nonlinear optical SCs such as composites and polymers are studied. Application of nonlinear effects in photonic materials is reviewed. Nonlinear effects in bulk SCs such as aromatic derivatives benzil (Bz) and like meta-dinitrobenzene (m-DNB) have been briefly investigated.

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

When two or more signals of different frequencies pass through a nonlinear system, intermodulation distortion (IMD) occurs, resulting in the formation of spurious distortion signals. IMD is most commonly found in active circuits of a radio system, but it can also be found in passive wireless components such as lters, transmission lines, connectors, antennas, attenuators, and so on, especially when transmit power is quite high. Passive intermodulation (PIM) distortion is the name given to the IMD in the latter scenario. With the evolution of radio systems and the scarcity of radio spectrum, PIM interference is being recognized as a potential stumbling block to a radio network's maximum capacity. This article classifies the PIM sources in BS radio systems into two categories, internal and external sources. Internal sources are the radio's passive components such transmission lines, connections, antennas, and so on. External sources, on the other hand, are passive items that are located outside of the BS antenna but inside the RF signal path, such as metallic and rusted objects in the antenna near eld. The high power current flowing through such passive devices can cause nonlinear behavior, resulting in IMD for both types of sources. Also, a review of PIM mitigation techniques is presented in the article.

This paper describes the design of high gain amplifiers for space communications systems in the frequency range of 8–12 GHz using a PHEMT operated at the bias point where the maximum value of transconductance (Gm) occurs. The amplifiers design is based on the knowledge of the small signals equivalent circuit of a PHEMT F4×25 featured by a 0.25μm gate length. The amplifiers design processes involve synthesis of matching networks with Chebyshev response in passive and distribute elements using MDS and Libra programs. A negative feedback is used to achieve the stability condition and flat response of the gain amplifier. In order to predict I MD (intermodulation distortion), we use the “chen's” Non — Linear model modeling the drain current Ids(Vgs, Vds) and the first three associates derivaties. Finally, the performance of the amplifier was evaluating using “MDS” commercial simulation software. The achieved gain is 11.5 dB with an input and output VSWR of 1.9 in all the bandwidth.

Vehicle/structure interaction is extremely important in determining the structural performance of highway bridges. However, an accurate prediction of the generated vibrations and forces requires a high-fidelity nonlinear 3D model which is sufficiently representative of the actual vehicle and bridge structure. In spite of all the computational advancements, there are still many technical difficulties to obtain a converging solution from a coupled highly nonlinear and highly damped vehicle/structure models. This paper presents an iterative uncoupled approach to obtain an accurate estimation of the vehicle/structure interaction. The multi-axle vehicle is simulated using a nonlinear 3D multibody dynamics model. The bridge model also contains several nonlinear components to accurately model the bridge behavior. The vehicle/bridge interaction results are obtained through an iterative solution by exchanging the outputs of two uncoupled nonlinear models. A convergence criterion is selected to obtain a reliable solution after several of these iterations. Finally, a reduced-order model of the bridge is developed using a state-space model. The linear reduced-order model of the bridge is coupled with the nonlinear vehicle model to improve the solution time of the analysis. The results are in a very good agreement with the iterative uncoupled approach. © 2012 SPIE.

Using 0.3-μm AlGaAs/GaAs HEMT technology, we developed a 30-to-60-GHz monolithic frequency doubler which has a conversion loss of 5 dB and a fundamental signal suppression of 20 dB for a 0-dBm 30-GHz input signal. The doubler's performance is superior to those using similarly scaled AlGaAs/GaAs HEMT. For the design, we used a nonlinear circuit simulator based on the harmonic balance method, an empirical nonlinear HEMT model, and an electromagnetic field simulator. The calculated and measured results agreed well. We developed this in order to build a 60-GHz AlGaAs/GaAs HEMT-based single-chip monolithic transceiver.