Nonlinear Self Research Articles

Highly dispersive optical solitons with generalized quadratic—cubic form of self—phase modulation by Sardar sub—equation scheme

AbstractThe highly dispersive optical solitons with generalized quadratic–cubic nonlinear self–phase modulation are the subject of this research. The governing model was reduced to an ordinary differential equation using the Sardar sub-equation method, which was then examined in two different ways. To provide a strong framework for the answers, the parameter limits were also listed.

Analysis of change of direction performance with dominant and non-dominant leg using linear and nonlinear approaches

ABSTRACT This study was aimed to analyse the lower limb kinematics during the change of direction (COD) performance with the dominant (DL) and non-dominant (NDL) leg using linear (traditional kinematics) and nonlinear (Self Organising Map-based cluster analysis) approaches. Three 5-0-5 COD performances with the DL and three with the NDL were performed by 23 (aged 21.6 ± 2.3 years) collegiate athletes. No significant difference was observed between the COD duration, and approach speed of DL and NDL. Significantly greater ankle abductions, knee and hip external rotations were identified in COD with DL, compared to NDL (p < .001, d > 0.8). Self Organising Maps portrayed a completely different coordination pattern profile during change of direction performance with the DL and NDL. The cluster analysis illustrated similar inter-individual coordination patterning when participants turned with their DL or NDL. No visible relationship was observed in the cluster analysis of the lower limb joint angles and angular velocities. Outcomes of this study portrayed that coordination patterning (combination of joint angles and the rate of change of angles) could portray the movement patterning differences in different tasks, while a sole investigation on the joint angles or angular velocities may not reveal the underlying mechanisms of movement patterning.

Power Tracking Control of Marine Boiler-Turbine System Based on Fractional Order Model Predictive Control Algorithm

The marine boiler-turbine system is the core part for the steam-powered ships with complicated dynamics. To improve the power tracking performance and fulfill the requirement of high utilization rate of fossil energy, the control performance of the system should be improved. In this paper, a nonlinear model predictive control method is proposed for the boiler-turbine system with fractional order cost functions. Firstly, a nonlinear model of the boiler-turbine system is introduced. Secondly, a nonlinear extended predictive self adaptive control(EPSAC) method is designed to the system. Then, integer order cost function is replaced with a fractional order cost function to improve the control performance, and also the configuration of the cost function is simplified. Finally, the superiority of the proposed method is proved accordring to the comparison experiments between the fractional order model predictive control and the traditional model predictive control.

Unified neutron star EOSs and neutron star structures in RMF models

In the framework of the Thomas-Fermi approximation, we systematically study the EOSs and microscopic structures of neutron star matter in a vast density range with n b ≈ 10−10-2 fm−3, where various covariant density functionals are adopted, i.e., those with nonlinear self couplings (NL3, PK1, TM1, GM1, MTVTC) and density-dependent couplings (DD-LZ1, DDME-X, PKDD, DD-ME2, DD2, TW99). It is found that the EOSs generally coincide with each other at n b ≲ 10−4 fm−3 and 0.1 fm−3 ≲ n b ≲ 0.3 fm−3, while in other density regions they are sensitive to the effective interactions between nucleons. By adopting functionals with a larger slope of symmetry energy L, the curvature parameter K sym and neutron drip density generally increases, while the droplet size, proton number of nucleus, core-crust transition density, and onset density of non-spherical nuclei, decrease. All functionals predict neutron stars with maximum masses exceeding the two-solar-mass limit, while those of DD2, DD-LZ1, DD-ME2, and DDME-X predict optimum neutron star radii according to the observational constraints. Nevertheless, the corresponding skewness coefficients J are much larger than expected, while only the functionals MTVTC and TW99 meet the start-of-art constraints on J. More accurate measurements on the radius of PSR J0740 + 6620 and the maximum mass of neutron stars are thus essential to identify the functional that satisfies all constraints from nuclear physics and astrophysical observations. Approximate linear correlations between neutron stars’ radii at M = 1.4M ⊙ and 2M ⊙, the slope L and curvature parameter K sym of symmetry energy are observed as well, which are mainly attributed to the curvature-slope correlations in the functionals adopted here. The results presented here are applicable for investigations of the structures and evolutions of compact stars in a unified manner.

Positive solutions of nonlinear matrix equations via fixed point results in relational metric spaces with w-distance

We consider the non-linear matrix equation (NME) of the form U = Q + ?ki =1A*i ?(U)Ai, where Q is an n?n Hermitian positive definite matrix,A1,A2,...,Am are n?n matrices, and ? is a non-linear self mapping of the set of all Hermitian matrices which are continuous in the trace norm. We discuss sufficient conditions ensuring the existence of a unique positive definite solution of the given NME. In order to do this, we introduce?w-contractive conditions involving modified simulation functions in relational metric spaces and derive fixed points results based on them, followed by two suitable examples. In order to demonstrate the obtained conditions, we consider three different sets of matrices. Three different types of examples (including randomly generated matrix and a complex matrix) are given, together with convergence and error analysis, as well as average CPU time analysis with different dimensions bar graphs, and visualization of solutions in surface plot.

Neural-Network-Based Nonlinear Self- Interference Cancelation Scheme for Mobile Stations With Dual-Connectivity

Dual-connectivity technology enables a base station to assign multiple carriers from various bands to a mobile station (MS), thus increasing its bandwidth and data rate. However, when the downlink frequency assigned to the MS is approximately twice its uplink frequency, the MS’s receiver will be seriously interfered by the nonlinear self-interference from its own transmitter. This paper addresses the problem of nonlinear self-interference cancelation for MSs operating in the dual-connectivity mode. Compared with conventional systems, this scenario faces some new challenges because of the wide variety of nonlinear interference components, including not only harmonics but also intermodulation products, and the more complicated interference channels, including both nonlinear and linear devices. In addition, the frequency, bandwidth and frequency-selective channel parameters of the interference are influenced by the uplink resource block allocation. To solve these problems, a two-part nonlinear self-interference canceler is proposed, where one part is designed as a neural network to capture the nonlinear characteristics, and the other part is designed as a linear filter to capture the linear characteristics. Furthermore, a low-complexity two-step training scheme is proposed to approximate the interference channel in the entire system bandwidth. Finally, a hardware prototype is implemented to verify the effectiveness of the proposed scheme. The experimental results show that the proposed scheme achieves more than 20 dB interference cancelation, and significantly outperforms the conventional polynomial-based and pure neural-network cancelation schemes.

Physical parameter space of bimetric theory and SN1a constraints

Bimetric theory describes a massless and a massive spin-2 field with fully non-linear (self-)interactions. It has a rich phenomenology and has been successfully tested with several data sets. However, the observational constraints have not been combined in a consistent framework, yet. We propose a parametrization of bimetric solutions in terms of the effective cosmological constant Λ and the mass mFP of the spin-2 field as well as its coupling strength to ordinary matter ᾱ. This simplifies choosing priors in statistical analysis and allows to directly constrain these parameters with observational data not only from local systems but also from cosmology. By identifying the physical vacuum of bimetric theory these parameters are uniquely determined. We work out the new parametrization for various submodels and present the implied consistency constraints on the physical parameter space. As an application we derive observational constraints from SN1a on the physical parameters. We find that a large portion of the physical parameter space is in perfect agreement with current supernova data including self-accelerating models with a heavy spin-2 field.

Modified Asano-Ohya-Khrennikov quantum-like model for decision-making process in a two-player game with nonlinear self- and cross-interaction terms of brain's amygdala and prefrontal-cortex.

In this report, we propose a modification on the Asano-Ohya-Khrennikov quantum-like decision-making process model of a two-player game by adding additional nonlinear terms to the related comparison step dynamical equation. The additions are in the form of a self-interaction and cross-interaction of the brain’s amygdala and prefrontal cortex. We show that the cross-interaction significantly determines the final decision of a player, whether it becomes a rational or an irrational choice. In contrast, the nonlinear self-interaction term provides a feedback mechanism that speeds up the corresponding decision-making process. We also suggest the form of expectation values of the overall reaction rate coefficients of those nonlinear terms by making an analogy with the original model formulation.

Electrodynamics in the 't Hooft gauge, a covariant operator approach

This article is devoted to describe the 't Hooft gauge electrodynamics by means of non-perturbative methods together with Heisenberg perturbation theory insights. The point is that this specific gauge choice introduces a non-linear photon field self interaction. So, this model is analyzed in a BRST framework in analogy to the non-Abelian cases. Finally, we show that the asymptotic transverse photon modes are the same as that of the linear gauge well known case while just the non-physical longitudinal sector get renormalized by such gauge self interaction. Then the physical gauge independence is explicitly verified.

A Comparative Study of Digital Self-interference Cancellation Techniques in In-Band Full-Duplex OFDM Systems

In-Band Full-Duplex is a powerful technique which theoretically doubles the spectral efficiency. It significantly contributes to the ever-increasing demand for high data rate and good connectivity of future communication systems. Self-Interference from the transceiver is the most challenging issue in In-Band Full-Duplex system implementation. In the presence of transmitter power amplifier non-linearity and phase noise in local oscillator, cancellation of the self-interference becomes more complex. In this paper, a detailed comparative study of two major Digital Self-Interference Cancellation techniques namely, Least Squares method based Dynamic Regression for Nonlinear Digital Self-Interference Cancellation and Least Mean Squares based Adaptive Nonlinear Digital Self Interference Cancellation is done. The study of the algorithms is done with Orthogonal Frequency Division Multiplexing that uses a bit-interleaved coded modulation system. The performance of the algorithms is studied in terms of bit error rate, convergence time and computation complexity in the presence of time varying fading channel with power amplifier non-linearity and phase noise.

Viability of bigravity cosmology

We revisit the question of viability of bigravity cosmology as a candidate for dark energy. In the context of the low energy limit model, where matter couples to a single metric, we study linear perturbations around homogeneous and isotropic backgrounds to derive the Poisson's equation for the Newtonian potential. Extending to second order perturbations, we identify the Vainshtein radius below which non-linear scalar self interactions conspire to reproduce GR on local scales. We combine all of these results to determine the parameter space that allows a late time de-Sitter attractor compatible with observations and a successful Vainsthein mechanism. We find that the requirement on having a successful Vainsthein mechanism is not compatible with the existence of cosmological solutions at early times.

Amplitude death criteria for coupled complex Ginzburg–Landau systems

Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, and thermoacoustic oscillators, to name a few applications. While studies have considered amplitude death on oscillator systems and in externally forced complex Ginzburg–Landau systems, a route to amplitude death has not been studied in autonomous continuum systems. We derive simple analytic conditions for the onset of amplitude death of one macroscopic wavefunction in a system of two coupled complex Ginzburg–Landau equations with general nonlinear self- and cross-interaction terms. Our results give a more general theoretical underpinning for recent amplitude death results reported in the literature, and suggest an approach for tuning parameters in such systems so that they either permit or prohibit amplitude death of a wavefunction (depending on the application). Numerical simulation of the coupled complex Ginzburg–Landau equations, for example, including cubic, cubic–quintic, and saturable nonlinearities, is used to illustrate the analytical results.

Manipulation of a ring-shaped beam via spatial self- and cross-phase modulation at lower intensity.

We report a tunable ring-shaped diffraction pattern via either nonlinear spatial self- or cross-phase modulation caused by the EIT-like effect in rubidium atomic vapor. During the propagation of an input Gaussian-profile beam, its output wavefront exhibits a ring-shaped diffraction pattern. Furthermore, the spot center can be tuned from dark to bright by varying individual experimental parameters, such as power, frequency detuning, the polarization state of the incident beams and atomic temperature, which makes the nonlinear phase shift evolve beyond 2π. In particular, the input intensity can be as low as 500 W m-2.

Experimental study of nonlinear characterization of hybrid SWCNTs/Ag-NPs fluids, using nonlinear diffraction technique

Based on nonlinear self- diffraction technique, the nonlinear optical properties of thin slice of matter can be obtained. Here, nonlinear characterization of nano-fluids consist of hybrid Single Wall Carbon Nanotubes and Silver Nanoparticles (SWCNTs/Ag-NPs) dispersed in acetone at volume fraction of 6x10-6, 9x10-6, 18x10-6 have been investigated experimentally. Therefore, CW DPSS laser at 473 nm focused into a quartz cuvette contains the previous nano-fluid was utilized. The number of diffraction ring patterns (N) has been counted using Charge - Coupled- Device (CCD) camera and Pc with a certain software, in order to find the maximum change of refractive index ( of fluids. Our result show that the fraction volume of 18x10-6 is more nonlinearity than others.

All-optical logic gates based on XPM effect under the PAM-ASK modulation in a symmetric dual NLDC

We investigate the possibility of achieving all-optical logical gates based in a symmetric double non-linear directional coupler (NLDC) working with pulses of 2 ps coded for the pulse amplitude modulation-amplitude shift keying (PAM-ASK), in a digital keying. The effects of group velocity dispersion, nonlinear self phase modulation and cross phase modulation (XPM) are taken into account in a lossless theoretical setup scheme. We analyze the amplitude and shape of the output pulses as a function of the modulation factor \((|\varepsilon |)\) to show that an OR gate can be readily realizable. Further, we also implement an optical sign phase shift in one of the NLDC input channels after the PAM-ASK modulator. We identify parameter regions on which the logical operations NAND, OR and XOR can be performed with the respective re-configurable scheme set by PAM-ASK modulation technique under the XPM effect.

Reduction of Nonlinear Optical Self Phase Modulation in Optical Fiber at 40 Gb/s

Reduction of Nonlinear Optical Self Phase Modulation in Optical Fiber at 40 Gb/s

Nonlinear self adjointness and exact solution of fokas.olver.rosenau.qiao (forq) equation

Abstract. Based on Lieis symmetry approach, conservation laws are constructed for Fokas-Olver-Rosenau-Qiao(FORQ) equation and exact solution is obtained. Nonlocal conservation theorem is used to carry out the analysis of conservation process. Nonlinear self adjointness concept is applied to FORQ equation, it is proved to be strict self adjoint. Characteristic equation and similarity variable help us fnd exact solution of FORQ equation. Compared with solutions found in previous papers, our solution is new and important, since it is not possible to fnd exact solution of FORQ equation quite easily

Design of an optimal state derivative feedback LQR controller and its application to an offshore steel jacket platform

This paper concerns with the optimal state derivative feedback LQR controller design for vibration control of an offshore steel jacket platform having active tuned mass damper against the wave induced disturbances. Considering that the state derivative signals such as acceleration and velocity are easier to measure rather than the state variables such as displacement, state derivative feedback control strategy is proposed to obtain practically applicable and easily realizable synthesis method. On the basis of convex optimization approach, state derivative feedback LQR controller design is formulated in Linear Matrix Inequalities (LMIs) form to get an optimal feasible solution set. Finally, an offshore steel jacket platform subject to nonlinear self excited wave force is used to illustrate the effectiveness of the proposed approach through simulations. The results show that proposed state derivative LQR controller is very effective in reducing vibration amplitudes of each floor of modeled offshore steel jacket platform and achieves compitable control performance to classical LQR controller design.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ``slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Role of spatial higher order derivatives in momentum space entanglement

We study the momentum space entanglement between different energy modes of interacting scalar fields propagating in general (D + 1)-dimensional flat space-time. As opposed to some of the recent works [1], we use Lorentz invariant normalized ground state to obtain the momentum space entanglement entropy. We show that the Lorenz invariant definition removes the spurious power-law behaviour obtained in the earlier works [1]. More specifically, we show that the cubic interacting scalar field in (1 + 1) dimensions leads to logarithmic divergence of the entanglement entropy and consistent with the results from real space entanglement calculations. We study the effects of the introduction of the Lorentz violating higher derivative terms in the presence of non-linear self inter- acting scalar field potential and show that the divergence structure of the entanglement entropy is improved in the presence of spatial higher derivative terms.