Nonlinear Form Research Articles

Gyrotactic microorganisms swimming in magneto-Sutterby-nanofluid over a sliding cylinder set in a Darcy-Forchheimer porous space with Arrhenius kinetics

This current study aims to analyze the bioconvection effect of gyrotactic microorganisms in a Sutterby nanofluid flow across a slippery horizontal cylinder with the participation of Arrhenius kinetics. The model for bioconvection analysis includes factors such as Brownian motion, thermophoresis, magnetic field, gravitation, and chemical reaction. The Darcy-Forchheimer rule is applied to assess the porous space’s resistance. By employing the necessary similarity maps, the PDEs in their nonlinear form are converted into a system of coupled ODEs. The converted ODEs are numerically computed by employing the Runge–Kutta-Fehlberg technique in combination with the shooting strategy. The impacts of significant physical factors on transport characteristics and engineering parameters are depicted with the dint of Mathematica software in tables and figures. The study showed that enhancing the chemical reaction and activation energy factors significantly inflates the nanoparticles’ concentration. Moreover, it must be acknowledged that the moment profile rarefies with the Darcy number’s elevation, but higher Forchheimer number seems to have the opposite effect. The new findings of this study have potential implications in biotechnology and automobile industry.

Dynamical system analysis in teleparallel gravity with boundary term

In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, f(T, B)rightarrow -T+tilde{f}(T, B), and define the dynamical variables to form the autonomous dynamical system. The critical points are obtained in two well-motivated forms of f(T, B), one that involves the logarithmic form of the boundary term B, and the other one is the non-linear form of the boundary term. The position of critical points is shown in the different evolutionary phases of the Universe such as radiation, matter, and de-Sitter phase. The stability condition of each of the critical points of both the models is derived and the behavior of each point has been obtained mathematically and through the phase portrait. The evolution of standard density parameters such as radiation (Omega _{r}), matter (Omega _{m}), and dark energy (Omega _{DE}) are also analyzed. Further to connect with the present cosmological scenario, the behavior of deceleration and equation of state parameter both in the dark energy phase (omega _{DE}) and total (omega _{tot}) are shown from the initial condition of the dynamical variables. The accelerating behaviour has been obtained for both models.

Developing a thermodynamic model for the circulating air using an opaque system

AbstractThe paper focuses on energy modelling that involves a concatenated structure of a linear time‐invariant system. A block‐structured (BS) technique was adopted for a nonlinear system identification. Using the superimposition principle, the model mapped the thermodynamic state variables as an indirect function of time to the output function. The available energy and degradation of solar radiation are determined through a black box model. For testing and validation purposes, a solar collector with recirculating air was considered. The basic principle is to establish a relation between state variables and the performance parameters, without invoking the conventional thermodynamic relationship between them. The output of the model was compared with the validation data to ensure whether or not there was any affinity between them. The sigmoidal, wavenet, and polynomial forms of nonlinearity provided a good fit to the experimental dataset. The mean absolute percentage error encountered while estimating the collector efficiency was noticed to vary from −4.85 × 10−03% to 1.22 × 10−03%. Similarly, it falls in the domain of −4.73 × 10−04% to 7.78 × 10−02% for the second law efficiency. The maximum heat loss rate (BS model) obtained across the first and second passages of the solar air collector was 235.41 and 218.19 W at the air mass flow rate of 8.10 g/s, which is congruent to the validation dataset.

Resonant NLSE in the presence of spatio-temporal and intermodal dispersion is dominated by a myriad of nonlinearities

This article is dedicated to investigating a myriad of nonlinear forms of the resonant nonlinear Schrödinger equation, which is one of the essential examples of evolution equations, and providing some observations. The resonant nonlinear Schrödinger equation, in the presence of spatio-temporal and inter-modal dispersion, was addressed using the recently introduced Kudryashov’s method, and solution functions were obtained for eleven different nonlinear forms (Kerr, power, parabolic, dual-power, polynomial, triple-power, quadratic-cubic, generalized quadratic-cubic, anti-cubic, generalized anti-cubic, and parabolic law with non-local nonlinearity). The study will contribute to the literature not only by examining such a diverse set of nonlinear forms together but also by investigating the impact of the degree of nonlinearity and the coefficients of different nonlinearity terms on soliton behavior. Detailed examinations of all these points, the results obtained, observations, and necessary comments have been made in the relevant sections.

Exposure levels for carbon monoxide in nuclear submarine atmosphere

This work proposes exposure limits for carbon monoxide in the nuclear submarine environment. Linear and non-linear forms of the Coburn-Foster-Kane equation were used to evaluate carbon monoxide exposure for an environment with low oxygen content, different exposure times and crew physical activity levels. We evaluated the 90-day Continuous Exposure Guidance Level, 24-h and 1-h Emergency Exposure Guidance Levels and 10-day and 24-h Submarine Escape Action Levels. The results showed that the concentration of carbon monoxide in the environment must not exceed 9 ppm for the 90-day Continuous Exposure Guidance Level, 35 ppm for the 24-h Emergency Exposure Guidance Level, 90 ppm 1-h Emergency Exposure Guidance Level, 60 ppm for the 10-day Submarine Escape Action Level and 80 ppm for the 24-h Submarine Escape Action Level. Comparing these values with those established by the National Research Council for the United States Navy, the limits proposed by this work are verified to be lower, which may indicate a risk to the health of the crew. They also show the impact of the crew's level of physical activity on the formation of carboxyhemoglobin.

Bentonite-Clay/CNT-Based Nano Adsorbent for Textile Wastewater Treatment: Optimization of Process Parameters

Dyes are the most carcinogenic organic compounds that are discarded by most of the textile industries without any prior treatment, which is harmful for the environment. This study aims to develop a bentonite-clay/carbon-nanotube (CNT)-based adsorbent to treat textile wastewater for water sustainability. The preliminary and post-characterization of adsorbent involves scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and Brunauer–Emmett–Teller (BET) and energy-dispersive X-ray (EDX) analysis to determine the changes in surface morphology, functional group, and surface area of the adsorbent. Linear and nonlinear isotherms and kinetic studies were performed to explore the sorption mechanism. The results show that the nonlinear form of the Langmuir isotherm best fits adsorption with a qmax of 550 mg/g. The adsorption followed the nonlinear pseudo-first-order kinetics, favoring chemisorption with R2 ≈ 1 and X2 = 0.22. Maximum dye removal (89.9%) was achieved under the optimum conditions of pH 3, an adsorbent dose of 100 mg, and a contact time of 120 min, with an initial COD concentration of 1140 mgL−1. This study has demonstrated the successful application of a bentonite-clay/CNT-based adsorbent on textile wastewater treatment.

Discrete-Time Gompertz Model for Adana Breed Pigeons

The mathematical animal growth models in the literature are not in the form of linear models. These growth models in the literature are not in linear form. There are different numerical analysis methods for the estimation of the parameters found in these functions and specific software have been produced to estimate the unknown parameters in these mathematical models and to apply these methods. In these nonlinear mathematical growth models, there may be more than one parameter. For these and other reasons, the number of mathematical numerical operations in estimating parameters is quite high. In this study, the discrete time stochastic Gompertz model (DTSGM) was considered to determine the growth of Adana pigeons. A model is used in which the parameter in the model is estimated by an adaptive Kalman filter (AKF). The aim of this research is to reveal the validity of both the model and the estimation method for Adana breed domestic pigeons. Daily weight measurements of 28 Adana pigeons were considered and estimated using DTSGM and AKF methods in this framework. DTSGM in conjunction with AKF has been shown to provide a convenient analysis tool for modeling daily weight estimates of Adana pigeons.

Self-defocusing nonlinear coupled system with PT-symmetric super-Gaussian potential.

The stationary solutions of the coupled nonlinear Schrödinger equation with self-defocusing nonlinearity and super-Gaussian form of parity-time (PT) symmetric potential in an optical system have been analyzed. The stationary eigenmodes of the ground and excited states and the influence of the gain/loss coefficient on the eigenvalue spectra are discussed. The threshold condition of the PT-symmetric phase transition of the high and low-frequency modes has been studied. Also, the variation of the threshold values with the coupling constant and the effect of the nonlinearity on the eigenmodes are analyzed. The stability of the solution is verified using the linear-stability analysis. In addition, the power distribution of the fundamental solutions with the propagation, in the two channels of the system, is analyzed in the PT and broken PT regimes.

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. We show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

Pure-Cubic Optical Solitons and Stability Analysis with Kerr Law Nonlinearity

In this research paper, we investigate the effects of third-order dispersion and nonlinear dispersion terms on soliton behavior for pure-cubic solitons in the absence of chromatic dispersion. The research proceeds in several stages. First, we derive the nonlinear ordinary differential equation form by utilizing the complex wave transform. In the second stage, we employ a simplified version of the new extended auxiliary equation method to derive both bright and singular optical solitons. Subsequently, we examine the influence of model parameters on these bright and singular solitons in the third stage. To support our findings, we present solution functions accompanied by effective graphical simulations. We report observations regarding the effects of parameters in the relevant sections. The validity of our results is confirmed through their satisfaction of the model equation. Furthermore, we apply the Vakhitov-Kolokolov stability criterion to ensure the stability of the obtained bright soliton solution. Notably, the novelty of this paper lies in its application of a simplified version of the extended auxiliary equation approach to recover optical solitons. This study stands apart from previously published works that utilized various expansion approaches, yielding a distinct spectrum of results.

Thermally nonlinear analysis of propagating cracks under generalized thermal shock

In this paper, the thermally nonlinear response of stationary and moving cracks in isotropic media subjected to a hyperbolic thermal shock in the framework of the eXtended Finite Element Method (XFEM) is examined. For this purpose, the thermally nonlinear fully coupled Lord-Shulman (LS) model is considered as governing equations. In addition, two cases of material properties, temperature-dependent (TD) and temperature-independent (TID), are assumed. The geometry, including a predefined crack, is modeled using the XFEM for spatial discretization. For modeling the dynamic crack growth within the XFEM, the Maximum Tangential Stress (MTS) criterion is modified based on the stress field near the tip of a growing crack to calculate the dynamic crack growth angle. Besides, the nonlinear form of the Newmark integration scheme is implemented for the numerical integration in the time domain. Finally, a method based on one of the Barnet-Lothe tensors for isotropic materials is employed to extract the stress intensity factors (SIFs). In the provided examples, the effects of thermal nonlinearity, the temperature-dependency of material properties, and the LS relaxation time on the crack propagation path are explored.

Sulfation Effects of Chondroitin Sulfate to Bind a Chemokine in Aqueous Medium: Conformational Heterogeneity and Dynamics from Molecular Simulation.

The sulfation patterns and degree of sulfation of chondroitin sulfate (CS), an important class of glycosaminoglycans (GAG), and their interactions with chemokines are accountable for various diseases. To realize the underlying mechanism of such complex biological phenomena at a molecular level and their application in rational drug design, a study on conformations and dynamics of CSs is necessary. To explore this, in this study, we performed a series of atomistic molecular dynamics (MD) simulations with different sulfated variants of octadecasaccharide CS, like CS-C, CS-E, and CS-T, in their free forms and when bound to the protein chemokine CXCL8 dimer in an aqueous medium. The calculated binding free energy of CSs with the CXCL8 dimer is favorable, and the degree of sulfation favors the complexation process further with prominent hydrophobic and hydrogen-bonded interactions. We find that the recognition is associated with the configurational entropy loss of the CS molecules as calculated from the Gaussian mixture approach, which supports that the degree of sulfation regulates the process. Cluster analysis through the k-means algorithm and end-to-end distance measurement revealed that although the free CS molecules adopted linear conformations, the nonlinear conformations during binding with protein were noted. Adaptation of nonlinear forms in the bound forms is noteworthy for the less-sulfated CS-C and CS-E. Apart from favorable 4C1 conformations, the occasional appearance of skew-boat forms from the free-energy map of ring pucker for the GlcUA unit was observed, which remains unaffected by the sulfation. We find that during recognition, the average relaxation time of intra-CS and inter-CS-CXCL8 hydrogen bonds (HBs) is about a magnitude lesser than that of CS-water HBs, most prominent on the involvement of higher sulfated CS-T analogues. The translational motion of surrounded water molecules in CSs exhibited sublinear diffusion, and the degree of sublinearity increases around the heavily sulfated molecules due to the hindrance created by them as well as the presence of the chemokine and exhibited markedly slow heterogeneous diffusion.

Nonlinear vibrations of doubly curved micropanels reinforced by graphene nanoplates in length direction under non-uniform thermal loading

Structures made of composites are quite common in different industries entailing automotive, marine, and aircraft industries, thanks to their favorable lightweight and strength. This study investigated the nonlinear vibrations of the various shapes of size-dependent graphene nanoplatelets reinforced micropanels under non-uniform thermal loading. In diverse ways in the axial direction, the material characteristics of graphene nanoplates (GPLs) alter. Taylor’s series expansion terms in curvature coordinates are used to illustrate the displacement field. Nonlinear von Karman theory and Hamiltonian principle work together to derive the nonlinear form of the pertinent equations and boundary conditions. Strain gradient theory with consideration for inherent length scale characteristics is investigated to account for size effects. By discretizing the spatial domain equations, deriving Duffing-type equations, and using Kronecker and Hadamard products, the governing equations and numerous nonlinear boundary edges are resolved. Using the techniques and answers outlined above, the results section is produced. There are four sections for this research. The findings are cross-checked with those from other studies that have been published in the first section. The effects of geometric and physical factors are shown in Parts 2, 3, and 4 on the nonlinear to linear frequency curve, the nonlinear frequency curve, and the sensitivity of the nonlinear frequency-to-size effect (SNFSE).

The Luxembourg–Gorky effect for elastic shear horizontal guided waves — Analytical and numerical modelling

The Luxembourg–Gorky (L–G) effect for elastic shear horizontal guided waves is investigated. A new non-classical theoretical model of wave dissipation is proposed to explain the nonlinear modulation transfer. The nonlinear form of the Kelvin–Voigt model is used in these investigations. The analytical work is validated using numerical simulations based on the Local Interaction Simulation Approach (LISA), implemented for the nonlinear wavefield. The analytical and simulated results – that are in good agreement – not only explain the acoustic equivalent of the L–G effect but also demonstrate how the severity of damage and carrier frequencies of the excited waves influence the nonlinear modulation transfer behind this effect. The work presented is in good agreement with the analytical models that explain the original L–G effect for electromagnetic waves.

Zero-valent Ni/NiO core-shell nanosheets supported on graphene for highly efficient dye adsorption: Isotherm, kinetic and thermodynamic study

In this study, a novel zero-valent nickel/nickel oxide@graphene nanosheets (ZVNi-NiO@Gr) composite was successfully fabricated by a single-step method and used as nanoadsorbents for the removal of crystal violet dye (CV) from its contaminated aqueous solution. Morphological characterization of nZVNi-NiO shows unique morphology with two-dimensional core-shell nanosheets supported on graphene layers. The one-step simultaneous preparation of nZNi-NiO nanosheets on the graphene notably limits the effect of nZNi-NiO agglomeration and enhanced the adsorption sites on the surface. The adsorption performance of ZVNi-NiO@Gr was investigated in terms of pH, temperature, initial concentration of CV dye, and contact period. The results showed that the maximum adsorption capacity climbed from 1028 to 1230 mg/g with increasing temperature from 30° to 45°C, and CV dye adsorption was preferable in alkaline media at pH 10. The isothermal and kinetic analysis showed that the nonlinear form of the Freundlich isotherm model and pseudo-second-order kinetic model is more fitting for adsorption data. The results of the thermodynamic study indicated that the adsorption of CV dye was spontaneous, endothermic and physical. The unique structure of ZVNi-NiO@Gr and the synergistic effect made it promising adsorbent for removing cationic dyes from aqueous media, and it can be used practically to treat wastewater of textile industries.

Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates

In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. This study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or sech-like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of captivating behaviors in the matter-wave smooth positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate density profile of matter-wave smooth positons in BECs, providing valuable insights into their controllable behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects.

Exact Solutions of Nonlinear Second-Order Autonomous Ordinary Differential Equations: Application to Mechanical Systems

Many physical processes can be described via nonlinear second-order ordinary differential equations and so, exact solutions to these equations are of interest as, aside from their accuracy, they may reveal beforehand key properties of the system’s response. This work presents a method for computing exact solutions of second-order nonlinear autonomous undamped ordinary differential equations. The solutions are divided into nine cases, each depending on the initial conditions and the system’s first integral. The exact solutions are constructed via a suitable parametrization of the unknown function into a class of functions capable of representing its behavior. The solution is shown to exist and be well-defined in all cases for a general nonlinear form of the differential equation. Practical properties of the solution, such as its period, time to reach an extreme value or long-term behavior, are obtained without the need of computing the solution in advance. Illustrative examples considering different types of nonlinearity present in classical physical systems are used to further validate the obtained exact solutions.

Numerical study of the model described by the fourth order generalized nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinearity

Using the simplest equation method, exact solutions of the model described by the fourth order generalized nonlinear Schrödinger equation with cubic-quintic-septic-nonic form of nonlinearity are obtained. Some of the main properties of the analytical model are established, such as dispersion relation, conservation of energy and linear instability. The split-step Fourier method is used to derive a numerical scheme for solving the model. The reflection of the properties of the analytical model in the numerical scheme is confirmed. Numerical simulations of the exact solutions of the model are performed, and approximation errors are measured. A numerical experiment is carried out on the interaction of two bright solitary waves.

Optical solitons of a cubic-quartic nonlinear Schrödinger equation with parabolic law nonlinearity in optical metamaterials

This paper aims to reveal the effects of the fourth-order dispersion and parabolic law which comes from self-phase modulation on the soliton behavior of the cubic-quartic nonlinear Schrödinger equation (CQ-NLSE) by using the modified new Kudryashov method. First, applying the complex wave transformation, the nonlinear ordinary differential form (NODE) has been obtained. Then, the modified new Kudryashov method (mNKM) has been expressed and applied. In the next step, linear algebraic system has been gained and solved. Then analytical soliton solution of the CQ-NLSE has been derived and checked for accuracy so that it satisfies the main equation. For the obtained solution functions, bright and singular soliton solutions have been gained and their graphical presentations have been made. The effects of both the fourth-order dispersion parameter and the parabolic law nonlinearity on the soliton dynamics have been examined and the necessary comments have been made. To our best knowledge, no such study has been reported for the equation examined.

Observer normal form design for the nonlinear MIMO systems using coupled auxiliary dynamics

This paper presents a transformation of a class of nonlinear multiple-input and multiple-output (MIMO) dynamical systems into a class of extended nonlinear normal forms. The extended normal forms are compatible with the widely used high-gain observer, which enables the estimation of the system’s states. It is realized by using a series of transformations which are performed by means of the so-called dynamics extension method, which explicitly supplies a set of auxiliary dynamics and a change of coordinates. Many researchers have focused their efforts on transforming nonlinear dynamical systems into normal forms of nonlinear observers. However, few of proposed transformations have been specifically developed for MIMO systems using an extended dynamics transformation. The main objective of this work is to fill this gap and provide a class of nonlinear dynamical systems that support the extended dynamics method, which can lead to a better understanding of their structures. Additionally, the results are highlighted by studying a class of nonlinear systems that describe the Dengue fever infection status of both human and mosquito populations. Finally, the effectiveness of the proposed high-gain observer is verified through a numerical example.