Variable Coefficients Research Articles

Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic–quintic nonlinear Schrödinger equations with self-steepening

Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic–quintic nonlinear Schrödinger equations with self-steepening

Study on Nonlinear Behavior of Variable Thickness Plates

The analysis of variable-thickness plates is much more complicated than that of uniform-thickness plates because variable coefficients occur in the equations. In reality, this analysis is of great interest in various engineering disciplines, such as civil engineering, aerospace engineering, machine design, and so on. Although there is extensive literature on analyses of plates with constant thickness, a rather limited amount of technical literature is available on the solutions to problems dealing with plates with nonuniform thickness. The reason is that the analytical solutions meet insurmountable difficulties. Besides, the nonlinear analysis process also faces more difficulties than the linear analysis of structures. For these reasons, the nonlinear behavior of variable-thickness plates based on a finite element procedure is presented in this study. Although the topic is not special, it will help the engineer have a specific view of the nonlinear bending of the plate with variable thickness. This survey will be based on the change in geometrical parameters. Numerical solutions are then presented to verify the simplicity of this proposed procedure.

Effect of the mitochondrial membrane potential on the absorbance of the reduced form of cytochrome c oxidase

The effect of mitochondrial membrane potential (ΔΨm) on the absorbance of the reduced cytochrome c oxidase (COX) was evaluated in isolated rabbit heart mitochondria using integrating sphere optical spectroscopy. Maximal reduction of the mitochondrial cytochromes was achieved by either blowing nitrogen to remove oxygen, or by adding cyanide. Gradual depolarization of ΔΨm by adding increasing concentrations of uncoupler resulted in an increase of up to 50 % in the absorbance of cytochrome aa3 under nitrogen saturation, and of 25 % with cyanide. Cytochrome aa3 absorbance increases were also observed in the presence of cyanide with apyrase (20 %) or oligomycin (12 %). The bL heme absorbance also decreased as expected from ΔΨm depolarization. A ~ 1 nm red shift in the peak wavelength of cytochrome aa3 was observed under anoxic conditions as ΔΨm was depolarized. Importantly, cytochrome c and c1 absorbances remained constant at levels corresponding to full reduction under all experimental manipulations of ΔΨm, especially with cyanide. These data suggest that ΔΨm-dependent changes in the absorbance of reduced COX were due to a variable extinction coefficient of heme a and/or a3 as a function of ΔΨm. A similar increase in the reduced cytochrome aa3 absorbance without changes in cytochrome c and c1 was observed in the perfused rabbit heart when decreasing ΔΨm with uncoupler. Our results imply that COX absorbance in its fully reduced state does not simply reflect the oxygen tension but also the ΔΨm. This may prove useful in monitoring ΔΨm under anoxic or ischemic conditions in intact tissue.

Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics-informed augmentation

This paper presents a positivity-preserving discontinuous Galerkin (DG) scheme for the linear hyperbolic problem with variable coefficients on structured Cartesian domains. The standard DG spaces are augmented with either polynomial or non-polynomial basis functions. The primary purpose of these augmented basis functions is to ensure that the cell average from the unmodulated DG scheme remains positive. We explicitly obtain suitable basis functions by inspecting the method of characteristics on an auxiliary problem. A key result is proved which demonstrates that the unmodulated augmented DG scheme will retain a positive cell average, provided that the inflow, source term, and variable coefficients are positive. A simple scaling limiter can then be leveraged to produce a high-order conservative positivity-preserving DG scheme. Numerical experiments demonstrate the scheme is able to retain high-order accuracy as well as robustness for variable coefficients. To improve efficiency, an inexact augmented basis function can be obtained rather than a analytic non-polynomial solution to the auxiliary problem from the method of characteristics.

Spatial optical soliton cluster solutions in strongly nonlocal nonlinear media

A (2+1)-dimensional variable coefficient nonlinear Schrödinger equation (NLSE) is described under strongly nonlocal nonlinear media. The soliton cluster solutions are obtained by using the improved self-similar reduction and F-expansion method. The regulation of nonlinear coefficients on the dynamics of spatial optical solitons and the self-similar propagation characteristics of the optical soliton clusters are investigated. It is observed that dark solitons transmitted in nonlinear media show two different spatial distributions. It is also found that the peak intensity of the soliton cluster only fluctuates in a small range during the propagation process, but the soliton cluster after harmonic potential modulation has some loss during the propagation process. But the loss is not as dramatic as when bright solitons are modulated. A new kind of soliton cluster is formed after the modulation of dark solitons, which has great practical significance such as application in logic gates, all-optical devices.

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Purpose. Development of an approximate nonlinear model for the solution of the external ballistics problem with determination of the nonlinear system parameters and development of a methodology for calculating the aerodynamic characteristics of the cargo, located on the external suspension of unmanned aerial vehicle (UAV) in order to increase the efficiency of their delivery to the specified landing target by means of asymptotic approach with given parameters of the studied system and external load. Methodology. The development of an effective model was carried out using analytical and numerical research algorithms based on a nonlinear system of differential equations in a general form with time-varying coefficients. In order to obtain a solution to the nonlinear problem of external ballistics in a two-dimensional formulation, the assumption of a significant influence of the projection of the velocity function on the ordinate axis in relation to the component on the abscissa axis is introduced. The problem is reduced to the solution of a related system of differential equations with variable coefficients along the corresponding coordinates using the asymptotic approach for a small parameter of the coefficient of frontal aerodynamic resistance. Applied mathematical analysis and modeling have been used for the problem formulation considering studied environmental parameters. Findings. Analytical dependences of the nonlinear problem of ballistics and application of finite-element analysis (FEA) with respect to the cargo motion from the UAV in the presence of the initial speed and wind load in the plane of motion are proposed. It is shown that the obtained analytical solution is correlated with the direct numerical calculation of the basic differential equation with respect to the ordinate axis. Originality. A mathematical nonlinear model of the dynamic process is proposed, assuming the prevailing influence of the speed function along the ordinate axis compared to the function along the abscissa axis. To obtain an approximate analytical solution of the basic nonlinear system of differential equations with variable coefficients the asymptotic perturbation method is applied. The dependence for the axial displacement function is presented considering actual time-flight parameter. Practical value. The obtained analytical dependencies for estimating the time and distance reaching the target with the initial speed of movement and the presence of wind load can be used in applied problems of mathematical physics and engineering calculations of functional dependencies and control of the cargo delivery process and target reaching from an UAV. The obtained analytical results and the solution algorithm can be integrated into applied problems of mathematical physics and engineering calculations, particularly the development of ballistic system control algorithms.

Recent Progress of TGV Technology for High Performance Semiconductor Packaging

In recent semiconductor packaging, the adoption of through silicon via (TSV) technology has become crucial for the integration of 2.5 and 3D Si chips, and interposers. The TSV offers significant advantages including high interconnect density, shortened signal pathways, and improved electrical performance. However, challenges such as electrical loss, substrate warpage, and high manufacturing costs are associated with TSV implementation. In contrast, glass-based through-glass vias (TGVs) exhibit promising characteristics such as excellent insulation properties, cost-effectiveness, and variable coefficient of thermal expansion (CTE) values that mitigate warpage in stacked devices. Moreover, they facilitate miniaturization and support high-frequency applications. This paper provides an overview of recent advancements in glass substrate, TGV drilling techniques, functional layer depositions, and Cu-filling processes in semiconductor packaging evolution.

Exact Solutions for the Modified Burgers Equation with Additional Time-dependent Variable Coefficient

In this article, we investigated new travelling wave solutions for the modified Burgers equation with additional time-dependent variable coefficient via the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions. All solutions of this equation have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena. This method presents a wider applicability for handling nonlinear wave equations.

Pengaruh Inovasi Pada Aplikasi Access by KAI Terhadap Kualitas Pelayanan

Innovation in the Access by KAI application aims to provide better services to the public. However, this innovation encounters several issues such as limited technological access by the public, policy non-inclusivity, and lack of effectiveness in socialization efforts. Therefore, this study aims to investigate the impact of innovation in the Access by KAI application on service quality. Additionally, it aims to determine the effective contribution of innovation dimensions in the Access by KAI application to service quality. This research utilizes an associative method with a quantitative approach. Data was collected through observation and questionnaire results, while data analysis employed robust M-estimation regression. The results indicate that the quality of public service innovation is very high, and the quality of m-service is high. Furthermore, public service innovation obtains significant variable coefficient values at a significant level (α=0.05). This is indicated by the p-value of the public service innovation variable being 0.000<0.05, showing the influence of public service innovation on m-service quality in the Access by KAI application. The effective contribution of each dimension of public service innovation to m-service quality is as follows: relative advantage dimension 0.48%, compatibility dimension 29.03%, complexity dimension 14.22%, testability dimension 9.83%, and observability dimension 8.39%.

Dust magnetoacoustic waves in an inhomogeneous cylindrical four-component dusty plasma in the presence of polarization force

Abstract Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.

Low-complexity reconfigurable FIR lowpass equalizers for polynomial channel models

This paper introduces realizations of a reconfigurable finite-impulse-response (FIR) filter for simultaneous equalization and lowpass filtering. The main advantage of the proposed solutions is computational complexity reduction compared to existing solutions for a given performance, which leads to reduced hardware complexity. The proposed structures employ properties of both a variable bandwidth (VBW) filter and a variable equalizer (VE) with variable coefficients. The overall transfer function of the proposed reconfigurable lowpass equalizer (RLPE) is a weighted linear combination of fixed subfilters where the weights are directly determined by the bandwidth and one or several parameters of the channel needed to be equalized. The paper provides design procedures based on minimax optimization and introduces a fast design method for the filter with several variable parameters that can substantially decrease the design time. Filter order estimation expressions as well as complexity expressions are presented for all proposed realizations. Design examples include comparison of the RLPE structures and a common approach of using a regular FIR equalization filter requiring online redesign when the bandwidth or channel characteristics are changed. It is shown that the number of general multiplications can be reduced up to 91% using the proposed RLPE.

Analysis of High-Order Bright–Dark Rogue Waves in (2+1)-D Variable-Coefficient Zakharov Equation via Self-Similar and Darboux Transformations

This paper conducts an in-depth study on the self-similar transformation, Darboux transformation, and the excitation and propagation characteristics of high-order bright–dark rogue wave solutions in the (2+1)-dimensional variable-coefficient Zakharov equation. The Zakharov equation is instrumental for studying complex nonlinear interactions in these areas, with specific implications for energy transfer processes in plasma and nonlinear wave propagation systems. By analyzing bright–dark rogue wave solutions—phenomena that are critical in understanding high-energy events in optical and fluid environments—this research elucidates the intricate dynamics of energy concentration and dissipation. Using the self-similar transformation method, we map the (2+1)-dimensional equation to a more tractable (1+1)-dimensional nonlinear Schrödinger equation form. Through the Lax pair and Darboux transformation, we successfully construct high-order solutions that reveal how variable coefficients influence rogue wave features, such as shape, amplitude, and dynamics. Numerical simulations demonstrate the evolution of these rogue waves, offering novel perspectives for predicting and mitigating extreme wave events in engineering applications.This paper crucially advances the practical understanding and manipulation of nonlinear wave phenomena in variable environments, providing significant insights for applications in optical fibers, atmospheric physics, and marine engineering.

Novel FR4‐based low loss reconfigurable filter with four operating modes using movable transmission lines

AbstractIn the letter, a novel reconfigurable filter using movable transmission lines is proposed. The filter is based on substrate‐integrated‐suspended‐line structure with two inner layers, fabricated on low‐cost FR4 substrate. The suspension line and the cavity are completely covered by copper. The suspension line could be freely moved in the air cavity. In the novel structure, the coupled lines have a variable coupling coefficient. With the movements of two transmission lines, the filter has four operating modes and can be tuned, with low insertion loss of less than 0.45 dB, showing promising properties.

Periodic solitons of generalized coupled nonlinear Schrödinger equations with variable coefficients

Periodic solitons of generalized coupled nonlinear Schrödinger equations with variable coefficients

Axially Non-Uniform Properties Effected Electro-Elastic Fields in Bended Piezoelectric Semiconductor Beams

This paper studied the effects of axially non-uniform material and non-uniform doping on the electro-elastic fields in bent piezoelectric semiconductor beams. The mathematical model is established based on the phenomenological theory of piezoelectric semiconductor and Euler’s beam theory. To solve the governing equations with variable coefficients, the differential quadrature method is adopted. As two representative structures, the pure bending beam and cantilever beam are studied, respectively. From the calculated results, it can be found the varied material properties changed the effective stiffness, as a result, all the field quantities are altered. Meanwhile, the symmetry of all field quantities in a pure bending beam is broken. Considering different Gaussian doping parameters [Formula: see text] and [Formula: see text], it can be observed that the distribution rule of perturbation carrier density becomes complex. The increment of [Formula: see text] broadens the width of optimum range-producing carriers, however, the increment of [Formula: see text] describes the moving of the optimum range from left to right. Importantly, the introduction of non-uniform doping breaks the limitation of perturbation carrier density in a cantilever beam with uniform material properties, the maximum value of perturbation carrier density does not appear at the fixed end only. The obtained results could be the guidance in designing high-performance electric devices.

A principal-weighted penalized regression model and its application in economic modeling

This paper introduces a novel Principal-Weighted Penalized (PWP) regression model, designed for dimensionality reduction in large datasets without sacrificing essential information. This new model retains the favorable features of the principal component analysis (PCA) technique and penalized regression models. It weighs the variables in a large data set based on their contributions to principal components identified by PCA, enhancing its capacity to uncover crucial hidden variables. The PWP model also efficiently performs variable selection and estimates regression coefficients through regularization. An application of the proposed model on high-dimensional economic data is studied. The results of comparative studies in simulations and a real example in economic modeling demonstrate its superior fitting and predictive abilities. The resulting model excels in accuracy and interpretability, outperforming existing methods.

Hexagonal finite differences for the two-dimensional variable coefficient Poisson equation

For many years, finite differences in hexagonal grids have been developed to solve elliptic problems such as the Poisson and Helmholtz equations. However, these schemes are limited to constant coefficients, which reduces their usefulness in many applications. The main challenge is accurately approximating the diffusive term. This paper presents examples of both successful and unsuccessful attempts to obtain accurate finite differences based on a hexagonal stencil with equilateral triangles to approximate two-dimensional Poisson equations. Local truncation error analysis reveals that a second-order scheme can be achieved if the derivative of the diffusive coefficient is included. Finally, we provide numerical examples to verify the accuracy of the proposed methods.

Novel nonlinear quantum dust acoustic waves for modified variable coefficients Zakharove–Kusnetsov equation in dusty plasma

In this paper, the direct similarity reduction method is used to reduce the modified variable coefficient Zakharove–Kusnetsov equation (vcmZK), which represents the propagation of quantum dust acoustic waves (QDAWs) in an inhomogeneous magnetized dusty plasma field, into a nonlinear ordinary differential equation (NODE). Moreover, the Jacobi elliptic method is used to solve the NODE, where many novel double periodic, kink, and solitary wave solutions are obtained. Additionally, we have chosen to plot periodic, kink, and soliton QDAWs solutions according to some choices for the variable coefficients. According to the a chieved results, we can conclude that the choices of the functional forms of the variable coefficients can control the QDAWs propagation. Finally, the new discovered results may have many important applications in astrophysics, atmospheric science, nanotechnology, and industrial plasma physics.

On the limiting amplitude principle for the wave equation with variable coefficients

In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence form. Under suitable assumptions on the coefficients and on the source term, we establish the LAP for space dimensions 2 and 3. This result is extended to one space dimension with an appropriate modification. We also quantify the LAP and thus provide estimates for the convergence of the time-domain solution to the frequency-domain solution. Our proofs are based on time-decay results of solutions of some auxiliary problems.

A Lithium-Ion Battery Remaining Useful Life Prediction Model Based on CEEMDAN Data Preprocessing and HSSA-LSTM-TCN

Accurate prediction of the Remaining Useful Life (RUL) of lithium-ion batteries is crucial for reducing battery usage risks and ensuring the safe operation of systems. Addressing the impact of noise and capacity regeneration-induced nonlinear features on RUL prediction accuracy, this paper proposes a predictive model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) data preprocessing and IHSSA-LSTM-TCN. Firstly, CEEMDAN is used to decompose lithium-ion battery capacity data into high-frequency and low-frequency components. Subsequently, for the high-frequency component, a Temporal Convolutional Network (TCN) prediction model is employed. For the low-frequency component, an Improved Sparrow Search Algorithm (IHSSA) is utilized, which incorporates iterative chaotic mapping and a variable spiral coefficient to optimize the hyperparameters of Long Short-Term Memory (LSTM). The IHSSA-LSTM prediction model is obtained and used for prediction. Finally, the predicted values of the sub-models are combined to obtain the final RUL result. The proposed model is validated using the publicly available NASA dataset and CALCE dataset. The results demonstrate that this model outperforms other models, indicating good predictive performance and robustness.