Nonlinear Source Research Articles

Via Impact on Passive Intermodulation Distortion in Planar Circuits

This work presents the passive intermodulation (PIM) induced by vias in microwave circuits. An analytical model combining the equivalent nonlinear source theory and the vector superposition principle is established to evaluate the PIM product of the vias array, which is influenced by the combination effect of the vias location, diameter, and number. The proposed model is verified and evaluated at 2.6 GHz. Good agreement between theory and experiment proves the logic and practicability of modeling. This work provides guidance for the low PIM optimization design of vias.

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

This study analyses an approach to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by an improper discretisation of the required source terms. The current work focuses on advection-diffusion models, in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used in heat and mass transfer problems or multiphase flows. The investigated scheme is applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. Further application of this work can be found in the method of manufactured solutions or in the immersed boundary method. This paper is dedicated to three aspects regarding proper inclusion of the source term in LBM schemes. Firstly, it identifies the differences observed between the ways in which source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the observed differences, and to identify their origin. Secondly, it analyses in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is valid for any source term discretization scheme. It is a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model and the Allen-Cahn equation. The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. The pitfalls of the commonly used acoustic and diffusive scalings are identified and discussed. Furthermore, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

Investigation of Oldroyd‐B fluid flow and heat transfer over a stretching sheet with nonlinear radiation and heat source

AbstractThe given investigation concerns the study of non‐Newtonian Oldroyd‐B fluid flow across a permeable surface along with nonlinear thermal radiation, chemical reactions, and heat sources. Equations modified are thus numerically evaluated by employing bvp4c‐technique. Obtained outcomes are exhibited graphically. Pictorial notations are used to investigate the consequences of necessary parameters of velocity, energy, and mass. Acquired outcomes provide promising agreement with already established consequences provided in the open literature. The obtained results guided that magnetic field parameter (), porosity parameter (), Deborah number reduce momentum boundary layer thickness, furthermore, growth in the relevant Deborah number improves the corresponding momentum boundary layer.

Model predictive temperature control of a closed-loop spray cooling system

A dynamic model of a closed-loop spray cooling system was proposed, and a model predictive temperature control algorithm was presented. The presented algorithm could quantitively estimate sudden changes in heat load, and then plan an optimized control path along which the temperature trajectory was numerically predicted to be the most stable. Then, the presented algorithm was integrated into a closed-loop spray cooling system, and its control performance was numerically studied. The results showed that, following a 20 W downward step change in heat load, the temperature was re-stabilized in 4 s, with its oscillation less than 0.14 K. Under identical conditions, the presented algorithm outperformed PID in terms of temperature stability, with its peak time shorter by 25–55%, settling time shorter by 38–51%, and average temperature offset smaller by 50–60%. This advantage was mainly because the presented algorithm compensated for hydraulic and thermal lags, two sources of control nonlinearity, by excessive regulation in advance. Unexpectedly, temperature overshoots of the presented algorithm and PID did not differ significantly, seemingly due to the algorithm-inherent estimation lag. From a system design perspective, the length of pump pipeline should be as short as possible, which proved to help reduce overshoot and settling time. Similarly, addition in heat load’s mass also helped reduce overshoot, but would result in an unfavorable long settling time, and vice versa. The simulation results were validated by experimental data, with error less than 10%.

Hilbert and Poincaré problems for semi-linear equations in rectifiable domains

The study of the boundary value problem with arbitrary measurable data originated in the dissertation of Luzin where he investigated the Dirichlet problem for harmonic functions in the unit disk. Recently, in \cite{R7}, we studied the Hilbert, Poincaré and Neumann boundary value problems with arbitrary measurable data for generalized analytic and generalized harmonic functions and provided applications to relevant problems in mathematical physics. The present paper is devoted to the study of the boundary value problem with arbitrary measurable boundary data in a domain with rectifiable boundary corresponding to semi-linear equation with suitable nonlinear source. We construct a completely continuous operator and generate nonclassical solutions to the Hilbert and Poincaré boundary value problems with arbitrary measurable data for Vekua type and Poisson equations, respectively. Based on that, we prove the existence of solutions of the Hilbert boundary value problem for the nonlinear Vekua type equation with arbitrary measurable data in a domain with rectifiable boundary. It is necessary to point out that our approach differs from the classical variational approach in PDE as it is based on the geometric interpretation of boundary values as angular (along non-tangential paths) limits. The latter makes it possible to also obtain a theorem on the boundary value problem for directional derivatives, and, in particular, of the Neumann problem with arbitrary measurable data for the Poisson equation with nonlinear sources in any Jordan domain with rectifiable boundary. As a result we arrive at applications to some problems of mathematical physics.

Defect Localization in Metal Plates Using Vibroacoustic Modulation

This paper reviews the state-of-the-art approaches in defect localization and specifies the remaining questions and challenges. Furthermore, this study presents a novel defect localization methodology using the nonlinear interaction of primary Lamb wave modes and vibroacoustic modulation (VAM), combined with damage imaging, to address the current shortcomings of defect localization. The study investigates this methodology experimentally with respect to defect interpretation, resolution, and applicability. Two Lamb waves with high and low frequencies, one being continuous and the other a tone burst, were excited using two different piezoelectric sensors. The amplitude of the measured signal at the first sideband frequency was evaluated with a short-time Fourier transform (STFT) and used for damage imaging via the delay and sum method. This study also includes a discussion on identifying the source of nonlinearity reflected in the first sideband. The experimental measurements prove that the localization of defect nonlinearity is possible with high accuracy, without the need for a baseline measurement, and with a minimum number of sensors. Sensitivity measurements with respect to the required length of the high-frequency tone burst and the sensor arrangement were also conducted.

Global well-posedness of wave equation with weak and strong damping terms p-Laplacian and logarithmic nonlinearity source term

We consider the following damped p-laplacian type wave equation with logarithmic nonlinearity utt−Δut−Δpu+ut=|u|q−2uln|u|,x∈Ω,t>0 in a bounded domain with homogeneous Dirichlet boundary condition. Firstly, we prove the local existence of weak solution by using contraction mapping principle. And in the framework of potential well, we show the global existence, energy decay and when the initial energy is subcritical, a sufficient condition for the solutions to blow up in finite time is derived, by combining the Nehari manifold with concavity argument. Then we parallelly extend the conclusions of global existence and energy decay for the subcritical case to the critical case by scaling technique. Besides, When the initial energy is supercritical, some new skills are invented to establish another finite time blow-up criterion for this problem.

Numerical simulation of modified nonlinear Schrodinger equation and turbulence generation

This article presents a numerical model to study wave turbulence in fluids. The model equation is derived by incorporating energy conservation (along with the usual fluid equations of a compressible flow), and the source of nonlinearity is the rise in temperature due to the acoustic wave's high amplitude. The nonlinear Schrödinger (NLS) and modified nonlinear Schrödinger (MNLS) equations have been derived and then solved numerically. A numerical simulation of the MNLS equation is used for investigating the turbulence generation and a semi-analytical method to understand the physics of localized structures of nonlinear waves. The numerical simulation is based on a pseudo-spectral approach to resolve spatial regimes, a finite difference method for temporal evolution. The results show a periodic pattern viz. Fermi–Pasta–Ulam (FPU) recurrence for NLS, while turbulence generation breaks down the FPU recurrence in MNLS. The turbulent power spectrum in the inertial sub-range approximately follows the Kolmogorov–Zakharov scaling (∼k−1.2).

Application of the disturb and observe algorithm together with a control system for the boost converter in photovoltaic applications

The boost-boost converter presents interesting characteristics for photovoltaic applications, due to the nature of the system where we can increase the voltage in an adequate and controlled way according to the load, in combination with an optimal control system we can obtain a better efficiency of an autonomous photovoltaic system, taking into consideration that a solar panel within its most significant properties to operate within the most efficient way needs natural conditions of irradiation and temperature that are closest to the SCT measurement standard, otherwise efficiency will be lost, Therefore, it is necessary to jointly implement a control system together with an algorithm that allows it to always be in maximum power conditions (MPP). According to the above, this article addresses the low voltage photovoltaic application of an isolated system, using a boost converter and a PI control system, together with an algorithm for obtaining the maximum power point, using two different photovoltaic systems, with the objective of showing that with an essential PI control we can obtain good efficiency of the two systems even with disturbances, as if a more robust control were implemented in photovoltaic applications, saving both operation cost and implementation time. The I-V (current-voltage) characteristics similar to a non-linear source of the photovoltaic module, require the inclusion of linearization of the photovoltaic module and with this to be able to design the control of the system, the proper functioning of the designed control has been tested through mathematical modeling and simulation.

Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code

In this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used for nonlinear problems. The semi-global algorithm is briefly presented, the C++ implementation is described and five sample simulations are shown. The accompanying C++ source code package is included. The high precision benchmark (long double and float128) shows the estimated calculation costs. The presented method turns out to be faster and more accurate than the global Chebyshev propagator. Program summaryProgram Title: SemiGlobalCppCPC Library link to program files:https://doi.org/10.17632/429rszyc65.1Developer's repository link:http://gitlab.com/cosurgi/SemiGlobalCppLicensing provisions: GNU General Public License 2Programming language: C++Nature of problem: The femto- and attosecond chemistry requires fast and high precision computation tools for quantum dynamics. Conventional software has problems with providing high precision calculation results (up to 33 significant digits), especially when the computation has to be as fast as possible.Solution method: This software fills in the gap by providing the semi-global algorithm [1–3] for arbitrary number of coupled electronic states for the time dependent Hamiltonian and nonlinear inhomogeneous source term. It is implemented in a way that allows computation with precision of 15, 18 or 33 significant digits, where the computation speed can be directly controlled by setting the required error tolerance. The semi-global algorithm [1–3] is implemented in C++ providing a 10× speed boost compared to original publication of semi-global algorithm implemented in Matlab/Octave [1–3].

Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems

A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general sources allows for quasi-best approximation with lowest-order finite element methods. This paper establishes the stability and a priori error control in the piecewise energy and weaker Sobolev norms under minimal hypotheses. Applications include the stream function vorticity formulation of the incompressible 2D Navier-Stokes equations and the von Kármán equations with Morley, discontinuous Galerkin, C^{0} interior penalty, and weakly over-penalized symmetric interior penalty schemes. The proposed new discretizations consider quasi-optimal smoothers for the source term and smoother-type modifications inside the nonlinear terms.

Long-time dynamics of a problem of strain gradient porous elastic theory with nonlinear damping and source terms

Of concern is a problem of strain gradient porous elastic theory with nonlinear damping terms, whose constitutive equations contain higher-order derivatives of the displacement in the basic postulates. The paper is based on the theory of ‘consistency’ due to Aouadi et al. [J. Therm. Stress. 43(2)(2020), 191–209] and Ieşan [American Institute of Physics, Conference Proceedings, 1329 (2011), 130–149], and contains four results. We firstly show that the system is global well posed by using maximal monotone operator. The second main result is the existence of global attractors which is proved by the method developed by Chueshov and Lasiecka [Long-time behavior of second order evolution equations with nonlinear damping. Mem. Amer. Math. Soc. vol. 195, no. 912, Providence, 2008; Von Karman evolution equations: well-posedness and long-time dynamics. Springer Monographs in Mathematics, Springer, New York, 2010]. By showing the system is gradient and asymptotically smooth, we establish the existence of global attractors with finite fractal dimension via a stabilizability inequality. Then we study the continuity of global attractors regarding the parameter in a residual dense set. The above results allow the damping terms with polynomial growth. Finally we discuss the exponential decay and global boundedness to the linear case of damping terms of the system. The assumption of equal-speed wave propagations is not needed for all of results obtained.

Comment on the paper “A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms, Mohamed Dilmi, Mourad Dilmi, Hamid Benseridi, Mathematical Methods in the Applied Sciences 2019, 42:6505‐6521”

Comment on the paper “A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms, Mohamed Dilmi, Mourad Dilmi, Hamid Benseridi, Mathematical Methods in the Applied Sciences 2019, 42:6505‐6521”

Effect of relativistic ponderomotive force on shock waves in a relativistic degenerate plasma

Abstract We investigate the effect of relativistic ponderomotive force on the propagation of shock waves in relativistic degenerate plasma, which is relevant to high-intensity laser-plasma experiments aimed at replicating extreme conditions on white dwarfs. We derive the KdV-Burger’s equation by incorporating the density modification induced by the ponderomotive force and hence demonstrate that this equation is a suitable model for shock waves affected by ponderomotive force. Unlike previous studies that use ponderomotive force as a source of nonlinearity to derive the nonlinear Schrödinger equation for envelope solitons, our study focuses on the effect of ponderomotive force on shocks produced by the intense laser. We show that the ponderomotive force can significantly modify the strength and shape of shock waves, providing insight into the underlying physics of shock waves in relativistic degenerate plasmas which may help to better understand experimental observations in this regime.

Entropy optimization of non-Newtonian hybrid nanofluid flow with non-linear radiation, exponential and thermal dependent heat source: Neuro-intelligent design

Entropy optimization of non-Newtonian hybrid nanofluid flow with non-linear radiation, exponential and thermal dependent heat source: Neuro-intelligent design

On the Fisher‐KPP model with nonlocal nonlinear sources

AbstractThe Cauchy problem considered in this paper is the following: where . When the coefficient remains positive, (1) is analogous to It is well known that when , the local solution of (2) blows up in finite time as long as the initial value is nontrivial. The main aim of this paper is to obtain sufficient conditions for global existence of solutions to (1) for and thus it forms a contrast to (2). The exponent produces an exact balance in the mass‐invariant scaling of diffusion and growth in (1). In particular, we prove that if , and where is the sharp constant of the inequality , then (1) admits a global classical solution. Moreover, the long time behavior of the solution is also discussed. In addition, we prove that when , the problem is solvable globally in time without any restriction on the initial data.

Exponential growth of solutions with L_p-norm of a nonlinear viscoelastic wave equation with strong damping and source and delay terms

" In this work, we are concerned with a problem for a viscoelastic wave equation with strong damping, nonlinear source and delay terms. We show the exponential growth of solutions with $L_{p}$-norm. i.e. $\displaystyle\lim_{t\rightarrow\infty}\Vert u\Vert_{p}^{p}\rightarrow\infty.$"

Design of a Nonlinear Model of a Pseudomorphic 0.15 μm рHEMT AlGaAs/InGaAs/GaAs Transistor

This paper studies the design of a nonlinear model of AlGaAs/InGaAs/GaAs рHEMT microwave-frequency range transistors with a gate length of 0.15 µm using parametric analysis methods. In the calculations, not only nonlinear current sources but also the dependences of the nonlinear gate-source and gate-drain capacitances on voltages are studied. It is shown that the proposed model makes it possible to describe the IV characteristics of the studied device adequately in the range of drain currents from 0 to 100 mA and the frequency range from 5 to 45 GHz. The error of the model does not exceed 3%.

Dynamics properties for a viscoelastic Kirchhoff-type equation with nonlinear boundary damping and source terms

This work is devoted to studying a viscoelastic Kirchhoff-type equation with nonlinear boundary damping-source interactions in a bounded domain. Under suitable assumptions on the kernel function g, density function, and M, the global existence and general decay rate of solution are established. Moreover, we prove the finite time blow-up result of solution with negative initial energy.

A nonconventional stability approach for a nonlinear Crank–Nicolson method solving degenerate Kawarada problems

Conventionally, the numerical stability of finite difference approximations of nonlinear Kawarada problems is shown only via frozen source terms, that is, ignoring potential jeopardization from quenching nonlinearities. The approach leaves an inadequacy behind even in the sense of localized stability analysis. This paper provides a much improved analysis of the numerical stability without freezing nonlinear source terms of the underlying equations. The strategy implemented can be extended for similar endeavors to higher dimensional cases. Simulation experiments are included.