Nonlinear Transmission Research Articles

GNSS Signal Distortion Estimation: A Comparative Analysis of L5 Signal from GPS II and GPS III

The nonlinear navigation payload transmission channel introduces errors at a system level, resulting in a distortion of the received signal and affecting differential positioning users. This work models the transmission channel of the navigation payload and uses the joint estimation algorithm to calculate the digital distortion and analog channel response of the transmission channel from the received signal. On the above basis, the algorithm and model are verified by GPS-L5 measured data, and the channel characteristics of GPS II and GPS III are deeply analyzed. The results show that the existing GPS IIF satellites have a digital distortion, which is negligible in GPS III satellites. Regarding the analog channel response, GPS III has better amplitude and group delay consistency than GPS II. Lastly, the ranging bias caused by the transmission channel of the navigation payload is provided to the user for reference, and GPS III is improved by approximately 0.02 m compared with GPS II. This study provides support for adjusting the satellite signal pre-distortion and enriches subsequent GNSS signal quality assessment work; it can also be used as a reference for differential positioning users.

Multi-wave, M-shaped rational and interaction solutions for fractional nonlinear electrical transmission line equation

In this paper, (2+1)− dimensional nonlinear fractional electrical transmission line equation (NLFETLE), which explains the wave variation in nonlinear systems, will be investigated. To convert our model into an ordinary differential equation (ODE) we adopt a conformable fractional (CF) operator. By combining exponential, polynomial, trigonometric, and hyperbolic functions, we will analyze multi-waves, periodic cross-kink, M-shaped rational and interaction solutions. We will also analyze degeneracies of hybrid waves through some graphical shapes.

Active-Type Continuously Variable Transmission System Based on a Twisted String Actuator

This letter presents an active-type twisted string actuator (TSA)-based continuously variable transmission (CVT). The proposed mechanism improves the advantage of the intrinsic CVT nature of TSA by compensating its nonlinear transmission ratio (TR) with the active and continuous conversion of the TR during contraction at a constant load as well as variable load. To change the TR, the proposed CVT adjusts the ratio of rotation between individual twists and overlap twists, which are two different types of string-twisting patterns. The performance of the TSA-based active CVT was experimentally assessed with the fabricated prototype and compared with a mathematical model. This adjustment in the rotation ratio between individual and overlap twists is realized using a planetary gear. By adjusting the rotating speed ratio between the sun and ring gear, the ratio of rotation between individual and overlap twists can be adjusted. Unlike the conventional TSA-based CVT, the proposed CVT can actively and continuously change the TR independent of the external load, even during operation. Consequently, it allows an increase in the operating range of the TSA while maintaining a high contraction speed.

Global COVID-19 Epidemic Prediction and Analysis Based on Improved Dynamic Transmission Rate Model with Neural Networks

The cross-regional spread of COVID-19 had a huge impact on the normal global social order. This paper aims to build an improved dynamic transmission rate model based on the conjugate gradient neural network predicting and analyzing the global COVID-19 epidemic. First, we conduct an exploratory analysis of the COVID-19 epidemic from Canada, Germany, France, the United States, South Korea, Iran, Spain, and Italy. Second, a two-parameter power function is used for the nonlinear fitting of the dynamic transmission rate on account of data-driven approaches. Third, we correct the residual error and construct an improved nonlinear dynamic transmission rate model utilizing the conjugate gradient neural network. Finally, the inflection points of the global COVID-19 epidemic and new outbreaks, as well as the corresponding existing cases are predicted under the optimal sliding window period. The experimental results show that the model presented in this paper has higher prediction accuracy and robustness than some other existing methods.

SOLITON WAVE GENERATION ON NONLINEAR TRANSMISSION LINES USING A PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM

In this article, analysis, designing, and generation of soliton waves are performed using nonlinear transmission lines (NLTLs). As a result of performing mathematical analysis processes, circuit parameters and values are determined. A particle swarm optimization (PSO) algorithm is used to determine the parameters and their values. The parameters obtained from the optimization are used to design a nonlinear transmission line. The circuit designed over the determined parameters is simulated with the LTspice program. Then, experiments of the created circuit design are carried out. The simulation data and the experimental implementation data are compared for the nonlinear transmission line circuit. Simulation and experiment results are found to be compatible.

Decoding the Bell-Shaped Calcium Spikes in Phosphorylation Cycles of Flagella

We investigate the messenger role of calcium ions implicated in the regulation of wave-like bending dynamics of flagella. The emphasis is on microtubules of flagellar axoneme serving as nonlinear transmission lines for bell-shaped spikes of calcium ions. The calcium sensitive proteins, such as calmodulin, exhibit activation dependence on the spike train frequency and amplitude. Here, we analyze a Ca2+ decoding module IDA-I1 whose activity is controlled by Ca2+ activated kinase. We find that trains of Ca2+ spikes are advantageous compared to a constant rise in Ca2+ concentration as being more efficient and much less prone to noisy fluctuations.

Collinear Nonlinear Mixed-Frequency Ultrasound with FEM and Experimental Method for Structural Health Prognosis

The principle about the nonlinear ultrasonic mixed frequency is introduced. A novel identification method for incipient structural health prognosis is proposed based on heterolateral co-linear mixed-frequency ultrasound to identify the micro-crack in mechanical structures. The modelling analysis methodology by the application of finite element analysis (FEM) is developed to simulate the nonlinear mixed-frequency ultrasonic wave transmission mechanism from the cracks with different depths and the excited frequency. The correlation models between the crack widths and the mixed-frequency nonlinear coefficients are established. An experimental method based on the nonlinear mixed-frequency ultrasonic theory is proposed to actuate the differential and sum-frequency characteristic mixed waves that interact with the defects of materials, which obtains the nonlinear coefficients to identify the depths of cracks in materials. The FEM model is verified to be effective at predicting the width of the cracks by comparing it with the testing data. The sizes of cracks have a positive correlation with the nonlinear coefficients of the mixed frequencies. A prognosis model for the mixed-frequency nonlinear coefficients is established to predict the crack depths of the specimen.

Optimal system, dynamical behaviors and exact solution of a nonlinear transmission line model by applying the Lie symmetry method

Optimal system, dynamical behaviors and exact solution of a nonlinear transmission line model by applying the Lie symmetry method

A novel frequency domain feature-based approach for diagnosis of failure faults in complex structures with interconnected joints

A wealth of complex structures with interconnected joints such as steel truss bridges and warehouses commonly exist in civil engineering, while they are easily subjected to joint faults like bolt loosening, breathing crack and chemical corrosion during their service, which would seriously affect structures’ safety, durability and reliability. Therefore, diagnosis of joint faults, especially at an early stage, would be essential and meaningful for complex structures. To overcome some limitations in existing diagnosis methods, a novel frequency domain feature-based approach for joint faults in complex structures is developed in this paper. In the new approach, complex structures are simplified as some simple and discrete unit substructures. Then, corresponding unit dynamic models are obtained for the dynamic analysis by considering effects of potential faults as additional nonlinear loads. Collecting vibration data of complex structures to be diagnosed only under different levels of harmonic excitations, which have different magnitudes but same frequency components, local frequency domain diagnosis features and indicators based on additional nonlinear loads and transmissibility functions are defined, and detailed procedures of the novel approach are shown accordingly. Finally, effectiveness and availability of the novel approach are verified through some experiments on a steel structure with bolted joints. Moreover, results of comparison study and effects of excitation frequency are discussed to show superiority of the proposed approach further.

Assessments of linear power flow and transmission loss approximations in coordinated capacity expansion problems

With rising shares of renewables and the need to properly assess trade-offs between transmission, storage and sectoral integration as balancing options, building a bridge between energy system models and detailed power flow studies becomes increasingly important, but is computationally challenging.Here, we compare approximations for two nonlinear phenomena, power flow and transmission losses, in linear capacity expansion problems that co-optimise investments in generation, storage and transmission infrastructure. We evaluate different flow representations discussing differences in investment decisions, nodal prices, the deviation of optimised flows and losses from simulated AC power flows, and the computational performance. By using the open European power system model PyPSA-Eur, we obtain detailed and reproducible results aiming at facilitating the selection of a suitable power flow model.Given the differences in complexity, the optimal choice depends on the application, the user’s available computational resources, and the level of spatial detail considered. Although the commonly used transport model can already identify key features of a cost-efficient system while being quick to solve, severe deficiencies under high loading conditions arise due to the lack of a physical grid representation. Moreover, disregarding transmission losses overestimates optimal grid expansion by 20%. Adding a convex relaxation of quadratic losses with three tangents to the linearised power flow and accounting for changing line impedances as the network is reinforced suffices to represent power flows and losses adequately in design studies. We show that the obtained investment and dispatch decisions are then sufficiently physical to be used in more detailed nonlinear simulations of AC power flow evaluating their technical feasibility.

Existence of solutions to a fully nonlinear free transmission problem

We study an equation governed by a discontinuous fully nonlinear operator. Such discontinuities are solution-dependent, which introduces a free boundary. Working under natural assumptions, we prove the existence of Lp-viscosity and strong solutions to the problem. The operator does not satisfy the usual structure conditions and to obtain the existence of solutions we resort to solving approximate problems, combined with a fixed-point argument. We believe our strategy can be applied to other classes of non-variational free boundary problems.

Fully nonlinear free transmission problems with nonhomogeneous degeneracies

We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.

Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules

A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions to Nonlinear Evolution Equation (NLEE) containing parameters of particular importance in biophysics and nanobiosciences. For this equation, we find trigonometric, hyperbolic, rational, and exponential function solutions, as well as soliton-like pulse solutions. A comparison with other approach indicates the legitimacy of the approach we devised as well as the fact that our method offers extra solutions. Finally, we plot 2D, 3D and contour visualizations of the exact results that we observed using our approach using appropriate parameter values with the help of software Mathematica 10.

Measurement of absorption cross sections of Co2+:MgAl2O4 crystals with transition of Co2+ ions along two orthogonal directions.

The nonlinear transmission curves of the Co2+:MgAl2O4 crystal at 1.5 µm are experimentally measured by the pump-probe technique. The measurement results demonstrate that the transition into the near-infrared absorption band is polarized not only along the C3 local symmetry axis, but also along the direction perpendicular to the C3 axis, arising from the distortion of oxygen tetrahedrons about the Co2+ ions along the four C3 local symmetry axes. The obtained saturation curves are analyzed using a theoretical model taking into account the transition of Co2+ ions along two orthogonal directions. The ground-state absorption cross sections for polarization parallel and perpendicular to the C3 axis are calculated to be 3.4×10-19cm2 and 2.6×10-20cm2, respectively. The excited-state absorption cross section for polarization parallel to the C3 axis is estimated to be4.2×10-20cm2.

Experimental investigation of supertransmission for an intrinsic localized mode in a cyclic nonlinear transmission line.

In this experimental study of the nonlinear loss mechanism between traveling localized excitation and the underlying extended normal mode spectrum for a 1D lattice, three types of cyclic, electric, nonlinear transmission lines (NLTLs) are used. They are nonlinear capacitive, inductive, and capacitive+inductive NLTLs. To maintain a robust, steady-state traveling intrinsic localized mode (ILM), a traveling wave driver is used. The ILM loses energy because of a resonance between it and the extended NLTL modes. A wake field excitation is detected directly from ILM velocity experiments by the decrease in ILM speed and by the observation of the wake. Its properties are quantified via a two-dimensional Fourier map in the frequency-wavenumber domain, determined from the measured spatial-time voltage pattern. Simulations support and extend these experimental findings. We find for the capacitive+inductive NLTL configuration, when the two nonlinear terms are theoretically balanced, the wake excitation is calculated to become very small, giving rise to supertransmission over an extended driving frequency range.

Memristor with BiVO4 nanoparticle as artificial synapse for neuroinspired computing

A memristor is very important for the development of an artificial neuromorphic system. However, the breakthrough of the limit of a work region for memristors remains challenging. Herein, a BiVO4 nanoparticle is proposed to be a high-performance artificial synapse for a neuromorphic system. A BiVO4-based artificial synapse exhibits superior bidirectional analog switching properties. Furthermore, the fundamental neurobiological synaptic functions in the BiVO4-based artificial synapse can be achieved, such as potentiation, a depression, nonlinear transmission, spike-time-dependent plasticity, pair-pulse facilitation, and the transition from short-term to long-term potentiation. Moreover, the movement of oxygen vacancies by an electric field is responsible for resistance switching. This work provides different insights into the design of an artificial synapse based on memristors.

Onset of Optical Instabilities in the Nonlinear Optical Transmission of Heliconical Cholesteric Liquid Crystals

We report the result of an accurate calculation of optical transmission of a light beam traveling along the helix direction of a heliconical cholesteric liquid crystal when the light intensity is affecting the director orientation by an effective optical torque. The study is based on the application of Ambartsumian’s layer addition modified method with the aim of taking into account the continuous modification of the wave field during propagation, which is quite strong when the light wavelength approaches the Bragg resonance. We show first, that the recently calculated red shift of the transmission gap is confirmed under the constant intensity approximation. Additionally, by taking into account the full modulation of the optical field occurring at wavelengths close to the Bragg resonance, a weak red shift is already observable at very low intensities, but quickly has the onset of instabilities in the optical transmission. We give the first account of this effect, which is dependent on the light intensity showing and that it corresponds to the onset of non-uniform distribution of the conical angle and pitch of the structure.

Chaotic Power Division Multiplexing for Secure Optical Multiple Access

This paper proposes a novel chaotic power division multiplexing (CPDM) for secure optical multiple access. The proposed CPDM can not only improve spectral efficiency and the user number by multiplexing spectrally overlaid OFDM signals at different power ratio, but also ensure the information security of the users by implementing chaotic encryption on the physical layer. The key space of the encryption scheme is up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${10^{98}}$</tex-math></inline-formula> , which can effectively resist the illegal acceptance. Furthermore, to meet future data traffic and multiple access demands, we first explore the beneficial combination of power dimension and mode dimension. A 30 Gb/s secure chaotic power division multiplexing and mode division multiplexing passive optical network (CPDM-MDM-PON) transmission over 5 km weakly coupled few-mode fiber (FMF) is experimental demonstrated. Experimental results show that, the proposed PON system has the appealing potential to attain high spectral efficiency and large traffic capacity and serve more users. The nonlinearity transmission impairments of single mode fiber and FMF are also investigated in this paper.

Solitary-wave dynamics in an [formula omitted]LC nonlinear transmission line with voltage bias

It was recently established that when an LC transmission line with a Schottky varactor is connected to a voltage terminal, a pulse is formed whose amplitude grows exponentially leading eventually to its instability after some finite propagation time. In the present study an R2LC nonlinear transmission line, consisting of a lumped circuit with unit cells composed of a linear inductance and a linear resistance in the primary branch, and a Schottky varactor shunted with a linear resistance in the secondary branch, all driven by a voltage terminal, is examined. Our objective is to investigate the effects of the competition between the two resistances, on the soliton amplification and propagation characteristics in general, along the nonlinear transmission line. The study is carried out in two steps: first, an analytical study is carried out within the framework of the reductive perturbation theory. This first step leads to a perturbed Korteweg–de Vries equation, in which the two resistances as well as the voltage terminal are regarded as perturbations. It is found that the electrical pulse amplitude is either exponentially amplified or exponentially depressed, depending on a specific relationship between the two resistances and the voltage terminal. Next the discrete line equations are directly solved numerically, assuming the analytically obtained pulse as input signal. This second analysis suggests a complex behaviour of the electrical pulse amplitude, in response to the influence of the two resistances. A particularly interesting behaviour observed in numerical simulations is the decay of a single-pulse soliton with propagation, and its burst into two-pulse and eventually multi-pulse soliton patterns after some finite propagation time. The proposed nonlinear transmission-line model can find widespread applications in complex transmission networks requiring high-power signals, as for instance in wideband and microwave digital signals, wireless, radar and sensor array processings.

State estimation for nonlinear state-space transmission models of tuberculosis.

Given the high prevalence of tuberculosis (TB) and the mortality rate associated with the disease, numerous models, such as the Gammaitoni and Nucci (GN) model, were developed to model the risk of transmission. These models typically rely on a quanta generation rate as a measurement of infectivity. Since the quanta generation rate cannot be measured directly, the unique contribution of this work is to develop state estimators to estimate the quanta generation rate from available measurements. To estimate the quanta generation rate, the GN model is adapted into an augmented single-room GN model and a simplified two-room GN model. Both models are shown to be observable, i.e., it is theoretically possible to estimate the quanta generation rate given available measurements. Kalman filters are used to estimate the quanta generation rate. First, a continuous-time extended Kalman filter is used for both adapted models using a simulation and measurement sampling rate of 60 s. Accurate quanta generate rate estimates are achieved in both cases. A more realistic scenario is also considered with a measurement sampling rate of one day. For these estimates, a hybrid extended Kalman filter (HEKF) is used. Accurate quanta generation rate estimates are achieved for the more realistic scenario. Future work could potentially use the HEKFs, the adapted models, and real-time measurements in a control system feedback loop to reduce the transmission of TB in confined spaces such ashospitals.