Nonlinear Form Research Articles

The Impact of Climate Change on Food Insecurity in The Southern African Development Community

Despite the fact that the Southern African region is one of the most vulnerable to climate change, research on the impact of climate change on food insecurity in the SADC region as a whole is scarce. We make two major contributions to the literature. First, we examine how climate change affects a group of SADC countries. Second, in contrast to previous studies, we supplement an analysis of climate change on crop yield with an analysis of climate change on other food insecurity indicators such as food affordability, malnutrition, and a food insecurity measure. Relying on the system generalized method of moments (GMM) estimator, results show that precipitation has a statistically significant impact on all four indicators of food insecurity in both its linear and non-linear forms; precipitation has the greatest impact on food affordability, followed by its negative impact on malnutrition; and temperature -whether in its linear or nonlinear form- has no statistically significant influence on all four indicators of food insecurity. However, temperature change gains statistical significance in explaining movements in food security after controlling for the interaction of temperature and precipitation. The policy implications of these findings highlight the need to increase precipitation availability in the SADC region by designing sustainable irrigation programs while also implementing climate change mitigation initiatives alongside those designed to ensure food affordability and access to a healthy and decent meal, particularly for the poor.

A Globally Stable Adaptive Controller for the Human Shank Dynamics

Abstract In this paper, we propose a globally stable adaptive controller for the human shank motion tracking problem that appears in neuromuscular electrical stimulation systems. The control problem is complicated by the fact that the mathematical model of the human shank dynamics is nonlinear and the parameters enter in a nonlinear and nonseparable form. To solve the problem, we first derive a nonlinearly parameterized regressor equation (NLPRE) that is used with a new parameter estimator specifically tailored for this NLPRE. This estimator is then combined with a classical feedback linearizing controller to ensure the tracking objective is globally achieved. A further contribution of the paper is the proof that parameter convergence, and consequent global tracking, is guaranteed with an extremely weak interval excitation requirement. A simulation study comparing the proposed adaptive controller with existing ones in the literature shows comparable human shank tracking performance but with fewer parameter estimates and without requiring knowledge of bounds for the unknown parameters.

RAFA: Redundancies-assisted Algebraic Fault Analysis and its implementation on SPN block ciphers

Algebraic Fault Analysis (AFA) is a cryptanalysis for block ciphers proposed by Courtois et al., which incorporates algebraic cryptanalysis to overcome the complexity of manual analysis within the context of Differential Fault Analysis (DFA). The effectiveness of AFA on lightweight block ciphers has been demonstrated. However, the complexity of the algebraic systems prevents it from attacking heavyweight block ciphers efficiently. In this paper, we propose a novel cryptanalysis called Redundancies-assisted Algebraic Fault Analysis (RAFA) to facilitate the solution of algebraic systems in the setting of heavyweight block ciphers. The core idea of RAFA is to expedite SAT solvers by modifying the algebraic systems, which is accomplished via two methods. The first method introduces redundant constraints, which is proposed for the first time in the context of algebraic cryptanalysis. The second one is a sophisticated linearization of the nonlinear Algebraic Normal Form (ANF). It takes RAFA for about 9.68 hours to attack AES-128. To the best of our knowledge, this is the first work that uses a general SAT solver to attack AES with only a single injection of byte-fault. Moreover, RAFA can attack AES-128 in 50.92 and 27.54 minutes for nibble- and bit-based fault model, respectively. In comparison, the traditional DFA algorithm implemented by pure C takes 4 ~ 5 hours under all three fault models investigated in this work. Moreover, in order to show the generality of RAFA, we also apply it to other heavyweight block ciphers. The best results show that RAFA could recover the key of Serpent-256 and SPEEDY-r-192 in 20.7 and 1.5 hours using only three faults, respectively. In comparison, AFA could not break these two ciphers even when 30 bits and 50 bits of their keys are known, respectively. Furthermore, no DFA work on Serpent or SPEEDY is known using comparable fault models.

Autonomous reliable intelligent control design under condition monitoring mechanism: Applied to hypersonic flight vehicles

For the six-degree of freedom dynamics of hypersonic flight vehicle, an autonomous reliable intelligent controller using online estimation and condition monitoring is designed in this paper. Based on model transformation, the outer-loop trajectory tracking is converted to the inner-loop attitude tracking. According to the aerodynamic model of large flight envelope and the thrust model of combined engine, the original dynamics is transformed into a switched nonlinear form. For each subsystem, neural network and nonlinear observer are employed to deal with aerodynamic uncertainty and external disturbance, while modeling errors are built to design composite update laws. Considering that the statically unstable HFV is prone to large deviation due to mode switching and wind disturbance, the condition monitoring signal with finite-time robust design is introduced to adjust control surfaces. With the average dwell time on the switching signal, the stability of the whole switched system is proved using Lyapunov approach. Simulation studies are performed to show the effectiveness of the design.

Application of q-HATM over Fractional in Time Model for Advection-Dispersion Equation with Variable Migration Parameters

In this article, an extended and more generalized method of homotopy analysis method (HAM), known as q-homotopy analysis transform method (q-HATM) is employed to develop solutions for highly nonlinear form of various time-fractional advection-dispersion models (TFADE). The proposed methodology of q-HATM is a conjunction of two different strong methodologies, that are HAM and Laplace transform technique (LTT) which makes the scheme much more capable to develop the convergent series solutions for differential equations with high nonlinearity. In this work, two different examples are constructed for the nonlinear time-fractional form of dispersion models corresponding to distance dependent dispersion and velocity components and also for the time dependent decay rate system and solutions are constructed by using q-HATM in generalized form. The graphical comparison is made for different types of variable functions and also for the different fractional order indexes. Prominent impact of fractional derivative indexes is significantly observed over both the examples of dispersion models. Hence, proposed examples shows that the q-HATM is much convenient to handle the nonlinear systems of fractional models.

Synthesis of Graphene Nanoplatelet-Alginate Composite Beads and Removal of Methylene Blue from Aqueous Solutions

The discharge of various types of wastewater into natural streams leads to significant problems by increasing the toxicity of the wastewater. For this reason, methods and materials are being developed by researchers in line with effective, economic, and environmental principles. In this study, the removal of methylene blue, a toxic dyestuff, from aqueous solutions was investigated by synthesizing sodium alginate (SA) and graphene nanoplatelet-sodium alginate composite (SA-GNP) beads. The structural characteristics of the materials were analyzed using FTIR, TGA, optical microscope, and SEM methods. All parameters determining the efficiency of the methylene blue adsorption system were optimized in a batch system. The effects of various factors, such as adsorbent amount, contact time, adsorption temperature, dye concentration, solution pH, pHzpc values of SA and SA-GNP beads, presence of different ions, and beads swelling, on the adsorption process, were investigated. To investigate the mechanism of the adsorption system, the adsorption data were fitted to a non-linear form of the Langmuir, Freundlich, and Temkin equilibrium isotherm models, as well as the Pseudo-first-order (PFO), Pseudo-second-order (PSO), and Bangham kinetic models. High regression coefficients were achieved in the studied kinetic and isotherm models (0.86 ≤ R2 ≤ 0.99), and the experimental data were found to be compatible with the model parameters. Maximum adsorption capacities (qm) of 167.52 mg/g and 290.36 mg/g were obtained for the SA and SA-GNP adsorbents, respectively, at 308 K. The optimum temperature for both adsorption systems was found to be 308 K. The efficiency of methylene blue dyestuff removal was improved with graphene nanoplatelet-based adsorbents.

Numerical analysis of ferromagnetic Carreau fluid flow comprising viscos dissipation aspects

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger [Formula: see text] and [Formula: see text].

Computational modeling of wave propagation in plasma physics over the Gilson–Pickering equation

In this paper, the Gilson–Pickering equation is studied which enables a wave propagation in plasma physics and crystal lattice theory. Based on the auxiliary transformations, some sets of the nonlinear form of ODE along with some analytic solutions are derived. To study the characterizations of the new waves, the crystal lattice theory and plasma physics is studied by using the modified exponential Jacobi technique and generalized rational tan(ϕ/2)-expansion technique. Through the new approaches, some solitary solutions are proposed. Meanwhile, influence of the coefficients in that equation for the periodic and soliton is illustrated. The effect of the free variables on the solutions is investigated. The behavior of these solutions on qualitatively of different structural natures relying on physical parameters coefficients is analyzed. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applied in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and plenty other applied sciences. For more details about the physical dynamical representation of the presented solutions, are illustrated with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approaches can be applied to several equations arising from all nonlinear applied sciences.

4-Chlorophenol adsorption from water solutions by activated carbon functionalized with amine groups: response surface method and artificial neural networks

4-Chlorophenol pollution is a significant environmental concern. In this study, powdered activated carbon modified with amine groups is synthesized and investigated its efficiency in removing 4-chlorophenols from aqueous environments. Response surface methodology (RSM) and central composite design (CCD) were used to investigate the effect of different parameters, including pH, contact time, adsorbent dosage, and initial 4-chlorophenol concentration, on 4-chlorophenol removal efficiency. The RSM-CCD approach was implemented in R software to design and analyze the experiments. The statistical analysis of variance (ANOVA) was used to describe the roles of effecting parameters on response. Isotherm and kinetic studies were done with three Langmuir, Freundlich, and Temkin isotherm models and four pseudo-first-order, pseudo-second-order, Elovich, and intraparticle kinetic models in both linear and non-linear forms. The synthesized adsorbent was characterized using X-ray diffraction (XRD), Fourier transforms infrared spectroscopy (FTIR), and scanning electron microscopy (SEM) analyses. The results showed that the synthesized modified activated carbon had a maximum adsorption capacity of 316.1 mg/g and exhibited high efficiency in removing 4-chlorophenols. The optimal conditions for the highest removal efficiency were an adsorbent dosage of 0.55 g/L, contact time of 35 min, initial concentration of 4-chlorophenol of 110 mg/L, and pH of 3. The thermodynamic study indicated that the adsorption process was exothermic and spontaneous. The synthesized adsorbent also showed excellent reusability even after five successive cycles. These findings demonstrate the potential of modified activated carbon as an effective method for removing 4-chlorophenols from aqueous environments and contributing to developing sustainable and efficient water treatment technologies.

Novel Aspects of Cilia-Driven Flow of Viscoelastic Fluid through a Non-Darcy Medium under the Influence of an Induced Magnetic Field and Heat Transfer

The spontaneous movement of natural motile cilia in the form of metachronal waves is responsible for fluid transport. These cilia, in particular, play important roles in locomotion, feeding, liquid pumping, and cell delivery. On the other hand, artificial cilia can be useful in lab-on-a-chip devices for manipulation processes. In this study, a novel model for the ciliated tapered channel in Sutterby fluid flow under the impact of an induced magnetic field and heat transport is proposed. The Darcy–Brinkman–Forchheimer law for porous media with a viscous dissipation function is considered. With the help of lubrication theory, the simplified non-linear form of the leading equation with cilia-oriented boundary conditions is achieved. The analytical results of differential equations are based on the topological perturbation approach. The numerical simulation is performed to elaborate on the physical interpretations of emerging parameters through computer software.

Nonlinear Optimal Control for Six-Phase Induction Generator-Based Renewable Energy Systems

The article aims at optimizing six-phase induction generator-based renewable energy systems (6-phase IGs or dual star induction generators) through a novel nonlinear optimal control method. Six-phase induction generators appear to be advantageous compared to three-phase synchronous or asynchronous power generators, in terms of fault tolerance and improved power generation rates. The dynamic model of the six-phase induction generator is first written in a nonlinear and multivariable state-space form. It is proven that this model is differentially flat. The 6-phase IG is approximately linearized around a temporary operating point recomputed at each sampling interval to design the optimal controller. The linearization is based on first-order Taylor series expansion and the Jacobian matrices of the state-space model of the 6-phase IG. A stabilizing optimal (H-infinity) feedback controller is designed for the linearized state-space description of the six-phase IG. The feedback gains of the controller are computed by solving an algebraic Riccati equation at each iteration of the control method. Lyapunov analysis is used to demonstrate global stability for the control loop. The H-infinity Kalman Filter is also used as a robust state estimator, which allows for implementing sensorless control for 6-phase IG-based renewable energy systems. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by the state variables of the 6-phase IG, under moderate variations of the control inputs.

Cross-linked chitosan-epichlorohydrin/bentonite composite for reactive orange 16 dye removal: Experimental study and molecular dynamic simulation

Chitosan/bentonite beads (CsB) composites were prepared from chitosan (Cs) and bentonite (B) and cross-linked with epichlorohydrin for removal of reactive orange 16 (RO16) and methylene blue (MB). The adsorption results have shown that the (Cs20B80), 20 % wt of (Cs) and 80 % (B), was selected as the best adsorbent for (MB) and (RO16) dyes. SEM, EDX, FTIR, BET, and pHpzc were implemented to investigate the features of Cs, B, and Cs20B80 samples. The influence of contact time (0–72 h), initial RO16 concentration (15–300 mg/L), temperature (30, 40, and 50 °C), the quantity of adsorbent (1–4 g/L), ion strength (0.1–1 M), and solution pH (3–10) on RO16 adsorption onto Cs20B80 were explored. The pseudo-second-order and the Langmuir models fit adequately the adsorption kinetic results and the isotherms ones respectively. Also, the maximal monolayer capacities calculated using the non-linear form of the Langmuir isotherm are 55.27, 55.29, and 70.80 mg/g, at 30, 40 and 50 °C. Based to the statistical physics model, the RO16 could be retained on the surface of Cs20B80 through a non-parallel orientation. The RO16 adsorption process is endothermic and natural, as demonstrated by thermodynamic studies. After three regeneration cycles, the Cs20B80 composite has shown an adsorption capacity of around 20 % compared to the initial one. The adsorption energy of RO16 onto Cs, B, and Cs20B80 examined using the Monte Carlo simulation method (MC) ranged from −164.8 to −303.7 (kcal/mol), showing the potential of the three adsorbants for RO16 dye. Also, the process of adsorption of RO16 dye on the surface of Cs20B80 composite indicates several kinds of physical interactions, involving electrostatic interaction, hydrogen bonding, and π-π interactions, this finding was proved theoretically via molecular dynamic simulations.

A microstructure estimation Transformer inspired by sparse representation for diffusion MRI

Diffusion magnetic resonance imaging (dMRI) is an important tool in characterizing tissue microstructure based on biophysical models, which are typically multi-compartmental models with mathematically complex and highly non-linear forms. Resolving microstructures from these models with conventional optimization techniques is prone to estimation errors and requires dense sampling in the q-space with a long scan time. Deep learning based approaches have been proposed to overcome these limitations. Motivated by the superior performance of the Transformer in feature extraction than the convolutional structure, in this work, we present a learning-based framework based on Transformer, namely, a Microstructure Estimation Transformer with Sparse Coding (METSC) for dMRI-based microstructural parameter estimation. To take advantage of the Transformer while addressing its limitation in large training data requirement, we explicitly introduce an inductive bias-model bias into the Transformer using a sparse coding technique to facilitate the training process. Thus, the METSC is composed with three stages, an embedding stage, a sparse representation stage, and a mapping stage. The embedding stage is a Transformer-based structure that encodes the signal in a high-level space to ensure the core voxel of a patch is represented effectively. In the sparse representation stage, a dictionary is constructed by solving a sparse reconstruction problem that unfolds the Iterative Hard Thresholding (IHT) process. The mapping stage is essentially a decoder that computes the microstructural parameters from the output of the second stage, based on the weighted sum of normalized dictionary coefficients where the weights are also learned. We tested our framework on two dMRI models with downsampled q-space data, including the intravoxel incoherent motion (IVIM) model and the neurite orientation dispersion and density imaging (NODDI) model. The proposed method achieved up to 11.25 folds of acceleration while retaining high fitting accuracy for NODDI fitting, reducing the mean squared error (MSE) up to 70% compared with the previous q-space learning approach. METSC outperformed the other state-of-the-art learning-based methods, including the model-free and model-based methods. The network also showed robustness against noise and generalizability across different datasets. The superior performance of METSC indicates its potential to improve dMRI acquisition and model fitting in clinical applications.

МЕТОД РИТЦА В НЕЛИНЕЙНЫХ РАСЧЕТАХ ОДНОПРОЛЕТНЫХ ЖЕЛЕЗОБЕТОННЫХ БАЛОК.

The paper considers the calculations of single-span reinforced concrete bent beams, taking into account the nonlinear relationship between stresses and strains. Deflections of beams according to the Ritz method are given as a series of trigonometric functions with undetermined coefficients. Nonlinearity is taken into account by the "moment-curvature" dependence in the form of a cubic parabola. The functional of the total energy of the beam and the load acting on it has a non-linear form with respect to indefinite coefficients, which are found with the help of a computer mathematics package from the condition of the minimum of this functional. Two examples are given for a statically determinate reinforced concrete articulated beam under the action of a uniformly distributed load and a statically indefinite reinforced concrete beam under the action of a concentrated force. A comparison with an elastic solution is made. The coordinate functions of the Ritz method are given for single-span beams with other boundary conditions.

Nonlinear dynamics of a vertical pipe subjected to a two-phase, solid-liquid internal flow

In this paper, a numerical study is carried out on a simply supported pipe model which conveys a two-phase, solid-liquid flow. First, a system of nonlinear, partial differential equations of dimensionless, two-phase, solid-liquid flow pipeline is established. Then, the above mentioned partial differential equation system is discretized by the Galerkin method of finite order to obtain a system of ordinary differential equations. Finally, the natural frequency characteristics of the corresponding linear system are solved to approximate the stability range of the nonlinear system, the structural response characteristics of which are solved by the Newton-Raphson method. The dimensionless aspect ratio, the dimensionless liquid-phase volume, and the dimensionless gravity coefficient are chosen to analyze the impact on the critical velocity of buckling and structural nonlinear response characteristic in this research. The research results indicate that a change to the above parameters will cause the critical speed to change in a linear or non-linear form. Moreover, at subcritical speeds, the vibrations are damped; at critical speeds, steady-state vibrations with extremely small amplitudes with a single frequency are seen; and at supercritical speeds, the pipeline model will produce buckling in different directions according to initial values.

A novelty Multi-Step Associated with Laplace Transform Semi Analytic Technique for Solving Generalized Non-linear Differential Equations

In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms with few time. To investigate of this technique, selected examples to show the ability, validity, accurately and effectiveness.

Synergistic effects of binary surfactant mixtures in the adsorption of diclofenac sodium drug from aqueous solution by modified zeolite

In this paper, the surfactant-modified clinoptilolite zeolite (with two methods) were used to remove diclofenac sodium (DFS) as a widely used drug in an aqueous solution. Clinoptilolite was modified by using pure cationic surfactant (cetyltrimethylammonium chloride, CTAC) and the mixed surfactants of CTAC + Triton-X100 (TX100). In the new approach, the synergistic effects between CTAC and TX100 were determined by surface tension measurements in different mole fractions and the optimum ratio (y1 ≈ 0.8) was identified with the maximum synergism. According to the mole fraction of this composition, the surface of clinoptilolite was modified by mixed surfactants (MSMZ) for the adsorption of DFS and then results compared with modified zeolite with pure cationic surfactant (SMZ). The raw and modified (SMZ and MSMZ) zeolites were characterized by Fourier transform infrared spectroscopy (FT–IR), BET analysis, the scanning electron microscopy (SEM) images, Zeta potential and X-ray. The experimental data of adsorption in equilibrium conditions were also analyzed using different adsorption isotherm models (Langmuir, Freundlich, Hill, Khan, Sips, Redlich-Peterson and Toth) in non-linear forms, and finally, the best model consistent with experimental data is determined (SMZ:Sips and MSMZ:Toth). According to the best isotherm model, the amount of absorption capacity in MSMZ was obtained almost 57% higher than SMZ. In addition, the kinetic adsorption data were correlated with eight various models in order to selection the best model for these systems. The kinetic adsorption data were well described by fractal-like pseudo-first-order (FL-PFO) and IKL models for SMZ and MSMZ adsorbents, respectively. Eight error functions were used to estimate the best fitted isotherm and kinetic models.

Multiple utilities targeting in energy integration considering rigorous temperature-enthalpy relations

Energy integration is a strong concern in process synthesis. Most methods are applied with simplifying assumptions for better computational efficiency. Enthalpies are obtained considering constant heat capacities, which is coherent for some processes. However, for streams in near-critical or phase-changing conditions, enthalpy may vary in a strongly nonlinear form. This paper proposes an optimization approach using concepts from Pinch Analysis for utility and heat exchange area targeting considering process and utility stream heat capacity variations with temperature. Decision variables are heat recovery approach temperature (HRAT), final utility temperatures, and energy duties for each available utility. Three case studies were evaluated. Large differences in utility allocations were observed (e.g., in Example 1, for the rigorous cp case, no medium- or low-pressure steam is applied, while high-pressure steam heat duty is 2.32 times the value from the constant cp case). Processing times were reasonable for early design stages (around one minute).

Pure-cubic optical solitons to the Schrödinger equation with three forms of nonlinearities by Sardar subequation method

In this work, it is used three families of nonlinearities such as Kerr law, Power Law and Parabolic law over the High-order dispersive Nonlinear Schrödinger equation to inquire optical soliton solutions and diverse solutions by employing the Sardar Sub-equation method. Considering the constraint relation on some parameters of the NLSE, it is obtained bright and dark optical soliton solutions. However, under a certain condition on the method parameters, it is exposed singular soliton and trigonometric function solutions. More precisely, for ρ=a24b, a new form of the complex solutions are obtained. The obtained results are depicted in 2D and 3D to show out the peakon soliton in Figure 2 compared to Yıldırım et al. (2020); Zayed et al. (2020) and Rezazadeh et al. (2020). These results could probably give a new way for designing optical fibers devices to update the communication flux.

Fast Quantum State Discrimination with Nonlinear Positive Trace‐Preserving Channels

AbstractModels of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension . For every normalizable linear or nonlinear positive map ϕ on bounded linear operators X, there is an associated normalized PTP channel . Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator.