Linearized Research Articles

Bio-filtration of Organic Pollutants: Simulation and Mathematical Modelling of Toluene and n-propanol

AbstractVolatile organic compounds (VOCs) are chemical substances that evaporate quickly, releasing harmful fumes into the atmosphere. Among the various VOCs, toluene and n-propanol are particularly interesting due to their widespread occurrence and considerable industrial impact. This study uses a bio-reactor with microbial biofilm formation to present the bio-degradation of a composition of toluene (methylbenzol) and n-propanol (1-propanol). It predicts the coupled inhibition effect of n-propanol on the toluene removal efficiency. The bio-filtration process is modelled as a dynamical system using a set of deterministic nonlinear partial differential equations. The differential equation with its appropriate conditions describes the bio-filtration processes occurring in two distinct phases: the biofilm phase and the gaseous phase. The differential equation is solved using the Chebyshev pseudospectral method and the local linearization method to understand the physical dynamics of the mathematical model. The effectiveness of the spectral-based method was evaluated by comparing its accuracy to known results in the limiting cases of the current dynamical model. A parametric and partial rank correlation coefficient (PRCC) analysis of the dimensionless parameters is conducted. It was found that toluene removal is enhanced by the additional desorption rate constant, ζ2. Increasing the air-biofilm coefficient for n-propanol supports the removal of n-propanol but not that of toluene. The findings of this study contribute to improvements in bio-degradation modelling and enhance our understanding of volatile organic compounds.

Thermal and Computational Analysis of MHD Dissipative Flow of Eyring-Powell Fluid: Non-Similar Approach via Overlapping Grid-Based Spectral Collocation Scheme

The aim of the present study is to numerically investigate the non-similar flow and heat transfer in a dissipative Eyring-Powell fluid (EPF) over a stretching surface. A constant magnetic field is applied perpendicular to the stretched surface to explore the impact of the Lorentz force. Both viscous and magnetic dissipation are considered to comprehensively examine their effects on heat transfer. The problem in hand does not admit self-similar solutions as the non-Newtonian fluid parameter varies with the spatial variable along the stream-wise direction. Consequently, the set of nonlinear partial differential equations, modeling the flow problem is nondimensionalized primarily by employing a pseudo-similarity variable and stream-wise coordinate. The non-dimensional set of nonlinear partial differential equations is solved by a newly developed and efficient “overlapping multi-domain bivariate spectral local linearization method (OMD-BSLLM)”. The current study includes residual error analysis and convergence tests to demonstrate the accuracy of the numerical method applied to the current mathematical model. Graphs show fluid flow and heat transfer results for different flow parameters, while tables display skin friction and Nusselt number values. The results indicate that the non-Newtonian fluid parameter enhances both the velocity profile and temperature distribution. The fluid decelerates with increasing the dimensionless stream wise coordinate and Hartmann number. Viscous dissipation and dimensionless stream-wise coordinate enhances the temperature profile.

A local discontinuous Galerkin methods with local Lax-Friedrichs flux and modified central flux for one dimensional nonlinear convection-diffusion equation

In this paper, we study the local discontinuous Galerkin (LDG) method for one-dimensional nonlinear convection-diffusion equation. In the LDG scheme, local Lax-Friedrichs numerical flux is adopted for the convection term, and a modified central flux is proposed and applied to the nonlinear diffusion coefficient. The modified central flux overcomes the shortcomings of the traditional flux, and it is beneficial in proving the L2 stability of the LDG scheme. By virtue of the Gauss-Radau projections and the local linearization technique, the optimal error estimates are also obtained. Numerical experiments are presented to confirm the validity of the theoretical results.

Forecasting economic growth by combining local linear and standard approaches

Today, developing economies are of major importance for global macroeconomic development. However, the empirical analysis and especially the forecasting of macroeconomic time series remain difficult due to a lack of sufficient data, data frequency, high volatility, and non-linear developments. These difficulties require more sophisticated approaches to obtain reliable forecasts. Therefore, we propose an improved forecasting method especially for growth data based on a data-driven local linear trend estimation with an extended iterative plug-in algorithm for determining the bandwidth endogenously. This approach allows a smooth trend estimation that takes care of temporary changes in trend processes. Further, the naïve random walk model is extended for forecasting by including a local linear, time-varying drift. We apply this method to GDP development for six developing and two advanced economies and compare different forecast combinations. The combinations that include the local linear approach and the random walk with a local linear trend improve forecasting accuracy and reduce variance.

Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.

Spectral Heat Transfer Coefficient (SHTC) for Thermal Design Analysis - Part 2: Leveraging Diabatic Wall Conditioning for Nonlinear Regime

Abstract There are two main issues of interest in the context of Newton's law of cooling as applied to turbine aerothermal designs. First, in a linear aerothermal regime, how do we deal with a non-isothermal wall where the wall surface temperature is non-uniform? Secondly, what can we do if an aerothermal system becomes nonlinear, manifested by qualitatively large changes of the flow field affected by heat transfer? In Part 1, a new spectral heat transfer coefficient (SHTC) method has been introduced for blade thermal analysis subject to non-isothermal walls in a linear aerothermal regime. Part 2 is devoted to address the issue of nonlinearity when the temperature field actively interacts with the velocity field as in many practical aerothermal problems. It is noted that the conventional approach rests heavily on an adiabatic state, so much so that its working range becomes overly restrictive. To move away from the adiabatic state, we take advantage of smooth (‘differentiable’) heat flux-wall temperature relation afforded by strong solid diffusion. A local linearization can be utilized by decomposing a full thermal variable into a nonlinear base as the reference and a locally linear perturbation. This split enables us to directly compute a nonlinear base as well as to carry out a linearized scaling with the SHTC (HTC) on top of the selected nonlinear aerothermal base state. The results of several computational case studies clearly and consistently support the validity and effectiveness of the present approach and method implementation.

Non‐linear coordinated control of LPMG‐based direct drive wave energy conversion system with supplementary energy storage system based on feedback linearization

AbstractThe linear permanent magnet generator (LPMG)‐based direct drive wave energy conversion system (DDWECS) works under perpetual fluctuations of ocean waves. Short‐term energy storage, such as electrochemical energy storage, is usually adopted in a supplementary energy storage system (SESS) to buffer power fluctuations. Since the investigated DDWECS consists of various non‐linear components such as insulated gate bipolar transistors (IGBTs)‐based power electronic converters, the unremitting changes of system working conditions caused by ocean wave effects will degrade the dynamic performance with conventional linear controllers which are implemented via local linearization around a single working condition. This paper proposes the multiple feedback linearization based non‐linear coordinated control (MFLNCC) scheme for coordinating non‐linear plants in DDWECS with SESS such as the machine‐side converter (MSC), the grid‐side converter (GSC) and DC/DC converter in SESS. The enhanced dynamic performance of the proposed MFLNCC in DDWECS with SESS is validated under different scenarios.

Adaptive pseudospectral successive convex optimization for six-degree-of-freedom powered descent guidance

Guidance for six-degrees-of-freedom powered descent is more challenging due to its stronger nonlinearity compared to three-degrees-of-freedom. The standard convex programming algorithm has been difficult to effectively address this problem. To enhance the performance of successive convex programming in terms of both optimality and accuracy, an adaptive pseudospectral successive convex optimization algorithm is proposed in this paper. First, it transforms the nonlinear optimal control problem into a convex subproblem by integrating global pseudospectral discretization with local linearization. Second, a parameter-adaptive successive convexification algorithm is proposed, which adaptively adjusts the trust region size based on the update rate of the optimal trajectory. Last, the global error and local error are accurately calculated based on the pseudospectral method. To tackle the issue of excessively large local errors caused by nonlinearity, an adaptive grid method is proposed to refine the mesh grid. Simulation results demonstrate the efficacy of the proposed pseudospectral convex optimization method and adaptive mesh grid method in reducing local errors and improving solution accuracy. Furthermore, the proposed parameter-adaptive successive convex optimization algorithm exhibits adaptability and optimality across different initial conditions, while also improving solution accuracy.

Mapping soil organic carbon density via geographically weighted regression with smooth terms: A case study in Shanxi Province

Soil, as the largest organic carbon reservoir in terrestrial ecosystems, plays a crucial role in the global carbon cycle. Accurately predicting the spatial distribution of soil organic carbon density (SOCD) is highly important for estimating organic carbon stocks and guiding agricultural production. Due to the complex relationship between the spatial distribution of SOCD and environmental factors, its relationship with a specific region is not exclusively linear or nonlinear; both types of relationships may coexist simultaneously. In this study, a new model, geographically weighted regression with smooth terms (SGWR), was proposed. This model can simultaneously consider both global spatial nonlinear relationships and local spatial nonstationary relationships. It was utilized to predict SOCD in Shanxi Province and was compared to multiple linear regression (MLR), generalized additive models (GAM) and geographically weighted regression (GWR) in terms of spatial prediction performance. The results showed that SGWR was highly competitive in predicting the spatial distribution of SOCD in Shanxi Province. Of factors influencing SOCD in Shanxi Province, elevation and slope were considered local linear variables, while the normalized difference vegetation index (NDVI), gross primary productivity (GPP), annual precipitation (AP), and soil moisture (SM) were considered global nonlinear variables. Among these factors, the NDVI and GPP had the most significant impacts on the distribution of SOCD, while elevation and SM had the least significant impacts on it. The results imply that integrating global linear, local linear, and global nonlinear relationships concurrently, as implemented in SGWR, improves predictive accuracy compared to approaches that solely address either local or global linear relationships based on environmental variable changes in SGWR. The results of this study indicate that the SGWR model is potentially a competitive method for digital soil mapping.

Entropy optimization in multigrade motor oil based nanofluid: a spectral and sensitivity analysis with particle shape and dispersion effects

PurposeThis study aims to enhance heat transfer efficiency while minimizing friction factor and entropy generation in the flow of Nickel zinc ferrite (NiZnFe2O4) nanoparticles suspended in multigrade 20W-40 motor oil (as specified by the Society of Automotive Engineers). The investigation focuses on the effects of the melting process, nonspherical particle shapes, thermal dispersion and viscous dissipation on the nanofluid flow.Design/methodology/approachThe fundamental governing equations are transformed into a set of similarity equations using Lie group transformations. The resulting set of equations is numerically solved using the spectral local linearization method. Additionally, sensitivity analysis using response surface methodology (RSM) is conducted to evaluate the influence of key parameters on response function.FindingsHigher dispersion reduces entropy production. Needle-shaped particles significantly enhance heat transfer by 27.65% with melting and reduce entropy generation by 45.32%. Increasing the Darcy number results in a reduction of friction by 16.06%, lower entropy by 31.72% and an increase in heat transfer by 17.26%. The Nusselt number is highly sensitive to thermal dispersion across melting and varying volume fraction parameters.Originality/valueThis study addresses a significant research gap by exploring the combined effects of melting, particle shapes and thermal dispersion on nanofluid flow, which has not been thoroughly investigated before. The focus on practical applications such as fuel cells, material processing, biomedicine and various cooling systems underscores its relevance to sectors such as nuclear reactors, tumor treatments and manufacturing. The incorporation of RSM for friction factor analysis introduces a unique dimension to the research, offering novel insights into optimizing nanofluid performance under diverse conditions.

Response surface methodology-based new model to optimize heat transfer and shear stress for ferrites/motor oil hybrid nanofluid

PurposeThis study aims to optimize heat transfer efficiency and minimize friction factor and entropy generation in hybrid nanofluid flows through porous media. By incorporating factors such as melting effect, buoyancy, viscous dissipation and no-slip velocity on a stretchable surface, the aim is to enhance overall performance. Additionally, sensitivity analysis using response surface methodology is used to evaluate the influence of key parameters on response functions.Design/methodology/approachAfter deriving suitable Lie-group transformations, the modeled equations are solved numerically using the “spectral local linearization method.” This approach is validated through rigorous numerical comparisons and error estimations, demonstrating strong alignment with prior studies.FindingsThe findings reveal that higher Darcy numbers and melting parameters are associated with decreased entropy (35.86% and 35.93%, respectively) and shear stress, increased heat transmission (16.4% and 30.41%, respectively) in hybrid nanofluids. Moreover, response surface methodology uses key factors, concerning the Nusselt number and shear stress as response variables in a quadratic model. Notably, the model exhibits exceptional accuracy with $R^2$ values of 99.99% for the Nusselt number and 100.00% for skin friction. Additionally, optimization results demonstrate a notable sensitivity to the key parameters.Research limitations/implicationsLubrication is a vital method to minimize friction and wear in the automobile sector, contributing significantly to energy efficiency, environmental conservation and carbon reduction. The incorporation of nickel and manganese zinc ferrites into SAE 20 W-40 motor oil lubricants, as defined by the Society of Automotive Engineers, significantly improves their performance, particularly in terms of tribological attributes.Originality/valueThis work stands out for its focus on applications such as hybrid electromagnetic fuel cells and nano-magnetic material processing. While these applications are gaining interest, there is still a research gap regarding the effects of melting on heat transfer in a NiZnFe_2O_4-MnZnFe_2O_4/20W40 motor oil hybrid nanofluid over a stretchable surface, necessitating a thorough investigation that includes both numerical simulations and statistical analysis.

State Space Representation of Jiles-Atherton Hysteresis Model and Application for Closed-Loop Control.

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles-Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.

On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing

On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing

Strong Consistency of Incomplete Functional Percentile Regression

This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data.

From local utility to neural networks

We introduce and analyze two preference-based notions of local linearity in the spirit of Machina (1982). We show how the weaker among the two extends Machina’s local utility analysis, and that the stronger among the two characterizes continuous finite piecewise linear (CFPL) utility functions. We introduce a representation of the decision maker’s preference called the neural-network utility representation that is equivalent to the CFPL representation, in which the decision maker evaluates an alternative through a neural network.

Feasibility of using in situ UV/Vis spectrometer probe for measuring COD in WWTP based on UASB reactor

The aim of this work is to report the use of a UV/Vis spectrometer for real time, in situ monitoring of the chemical oxygen demand (COD) in a municipal wastewater treatment plant (WWTP) operating with upflow anaerobic sludge blanket (UASB) reactor, installed in south of Brazil. The spectrometer was used according to the factory calibration procedures: global, local offset and local linear. COD probe measurements were compared to laboratory analyses for the calibration procedures. Continuous operation led to increasing errors, which was related to grime deposition on the probe window and avoided with periodic cleaning. Performance of the probe measurements versus laboratory analyses was evaluated with coefficient of determination, root mean squared error (RMSE), relative RMSE, RMSE to standard deviation ratio (RSR) and Student’s t-test. It is concluded that the best calibration procedures is the local linear, for the influent and the effluent of UASB reactor. The probe consists of an improvement to real time and in situ monitoring of South America WWTPs.

Optimal attitude control for landing on asteroid with a flexible lander

The recently developed flexible lander offers a potential option for future asteroid landing missions due to its advantages in suppression of rebound and overturning. The strong nonlinear dynamics and control constraints of the flexible lander hinder the online implementation of optimal attitude feedback control. To generate the optimal attitude control rapidly, a constrained inhomogeneous approximating sequence of Riccati equations (CI-ASRE) method is proposed. The saturation function is firstly constructed to incorporate control magnitude constraints into dynamics so that the constraints can be analytically handled. Subsequently, to avoid singularity, a partial factorization strategy is proposed to convert the constrained dynamics into two parts, a pseudolinear term and an inhomogeneous term. This factorization enables the nonlinear problem to be expressed as the limit of a sequence of inhomogeneous linear quadratic problems while avoiding local linearization. At last, the analytical CI-ASRE is newly derived to iteratively solve these problems to rapidly obtain optimal feedback control. The computational simplicity and effectiveness of the CI-ASRE method overcome difficulties of optimal attitude control problems of the flexible lander associated with control constraints, strong nonlinearity, and online feedback control generation. The effectiveness of the proposed method for the flexible lander is verified using a landing scenario on asteroid 433 Eros.

BMB-LIME: LIME with modeling local nonlinearity and uncertainty in explainability

The majority of eXplainable Artificial Intelligence (XAI) methods assume the local linearity of the decision boundary, leading to significant errors when dealing with non-linear local decision boundaries. Moreover, explanation methods relying on perturbation samples yield only a constant value for feature contributions. This study aims to overcome these limitations by introducing a novel explanation method that accurately captures non-linear local classification boundaries or regression splines while also quantifying the uncertainty associated with each feature contribution. Expanding upon the state-of-the-art XAI method, Local Interpretable Model-agnostic Explanations (LIME), we propose a nonlinear local explainer called BMB-LIME (Bootstrap aggregating Multivariate adaptive regression splines Bayesian LIME). BMB-LIME is constructed using weighted multivariate adaptive regression splines (MARS) with bootstrap aggregating and models the uncertainty of feature contributions within a Bayesian framework. Through a series of experiments, we demonstrate the superior performance of the BMB-LIME local explainer over baseline methods in terms of local fidelity and stability. Its adjusted r-squared is statistically significant by at least 80.5 percent, and it consistently demonstrates over 89.1 percent consistency in feature contribution and Jaccard similarity across diverse real-world and simulated datasets. The proposed method not only enhances fidelity and stability but also improves the measurement of uncertainty in explanations, thereby significantly contributing to the trustworthiness and transparency of XAI.

A generating absorbing boundary condition for simulating wave interaction with maritime structures in current or at forward speed

The lack of suitable boundary conditions in practical surface wave simulations with maritime structures in current or at forward speed may cause energy in the computational domain to accumulate due to spurious wave reflection. The common way to prevent wave reflection is to use passive wave absorbers, such as damping zones or relaxation zones, which requires larger domains at the cost of computational effort. Our goal is to derive a local generating absorbing boundary condition (GABC) for long-crested irregular waves on top of a mean flow, using the flow to model the forward speed of a structure such as a ship. Earlier work has demonstrated that a local GABC for free surface waves has a performance similar to passive wave absorbers, but at a reduced computational effort. New in the present work is that we extend, verify and validate the GABC in the presence of a nonzero mean flow. The GABC is designed to be accurate for a range of wave components in irregular sea states, with the resulting reflection coefficients for each component lower than a chosen value, say 5%. Having used potential flow theory for its derivation means that the boundary should not be placed at the exact location where wave breaking is expected, such as very close to the structure in the domain, or in the surf zone in coastal modeling. For the application with ships in this article that does not pose a limitation. The performance is demonstrated for a range of dimensionless wave number between 0 and 6. Such a boundary condition is obtained through a rational approximation of the linear dispersion relation with a mean flow, in combination with vertical derivatives of the solution variables along the boundary. Local linearization means that the GABC incorrectly considers bound, nonlinear wave components to be freely propagating wave components. Bound components, however, tend to have smaller amplitudes and do not appear to affect performance for the considered cases. Results of simulations with regular and irregular waves, on top of flows with different magnitudes and directions, are found to agree with the theory. The main source of differences is the implementation of the second derivate in the GABC near the free surface. Simulations of a Wigley hull at forward speed in irregular waves are compared to an experiment that was conducted specifically for validating the ABC. The data of the experiment are available as open data through doi: 10.4121/21320604. The comparison between simulation and experiment demonstrates that the GABC with a mean flow can be applied not only for theoretical simulations with propagating waves, but also for more practical applications with a structure in the domain.

Irreversibility and spectral analysis for nanofluid with melting and higher order slip effects

This work is intended to examine the impacts of first and second-order velocity slips, viscous dissipation, and melting on mixed convective flow of nickel zinc ferrite + SAE 20W-40 motor oil based nanofluid along a stretching or shrinking sheet for the first time. The multigrade 20W-40 motor oil is categorized by Society of Automotive Engineers (SAE). An irreversibility analysis has also been performed using the second law of thermodynamics. The resulting non-dimensional flow-governing equations are modified into ODEs (Ordinary Differential Equations) and then the numerical estimates are provided by adopting the spectral local linearization method. Next, the efficiency of the above-mentioned spectral procedure is verified through the maximum error norms. Finally, the influence of important parameters included in this evaluation on the flow profiles and physical quantities is systematically represented. Based on the findings, the melting effect enhances the heat transference rate by 24.6% and reduces entropy by 38.4%. The use of higher-order velocity slips and viscous dissipation effects results in a lower friction factor. In the presence and absence of ferrite particles, the streamline visualization is clarified. This type of simulation is extremely useful for the readers in considering the rates of cooling or heating at electromagnetic interfaces, industrial devices, orthopedic joint replacements, aircraft turbines, bone plate surgeries, and so on.