Solution Of Model Research Articles

On the Mathematical Background of Sliding Mode-Based Friction Compensation of a Micro-Telemanipulation System

Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov’s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

The solution of super-scale DEA models based on preference character

The basic relationships and intrinsic laws in the data envelopment analysis (DEA) are the basis for designing fast solutions for big data DEA models. By delving into these relationships, it becomes feasible to address super-scale DEA problems more swiftly, aligning with the need for timeliness in real-world efficiency evaluations and reducing time costs. This paper leverages the intrinsic characteristics of DEA to formulate a DEA model scale reduction approach, offering reliable theoretical support for solving super- scale DEA problems. Initially, the partially ordered set theory to prove the relationship between the efficient decision making units (DMUs) of DEA and the maximal element of the partially ordered set. Building on this, a DEA model based on maximal element set (DEA-PS) is constructed based on the theory of partially ordered set theory, and the equivalence between DEA-PS model and the original DEA model is proved. Furthermore, it is proved that the dominant theorem exists in the solution of multiple classical DEA models, and a method of super-scale DEA models based on dominant theorem is given. The conclusions of this paper theoretically reveal the relationship between efficient DMUs and maximal elements, from this relationship, two key insights emerge: (1) Regardless of how huge the number of DMU is, the proposed method in this paper can realize the scale reduction of the DEA model quickly, (2) The algorithm has good compatibility with all current big data DEA model algorithms.

Fractional-order analysis of temperature- and rainfall-dependent mathematical model for malaria transmission dynamics

Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models.

Dynamic Solitary Wave Solutions Arising in Nonlinear Chains of Atoms Model

This article consists of several travelling wave soliton solutions for solving a complex nonlinear chains of atoms model with long-range interactions via the generalized auxiliary equation method. We have converted considered PDE into nonlinear ODE by utilizing the specific wave transformation. The solutions attained in the form of periodic, bright, singular, W and M types. The adapted method seems a very impressive and competent avenue to obtain the exact soliton solutions of several advanced distinct models. Moreover, to understand the physical nature of the newly attained solutions 2D, 3D and contour-type graphs are presented with distinct dimensions. Additionally, sensitivity and stability through a dynamical system and with the use of different initial conditions are successfully analyzed.

Computational Fuzzy Modelling Approach to Analyze Neuronal Calcium Dynamics With Intracellular Fluxes.

Mathematical neuroscience investigates how calcium distribution in nerve cells affects the neurological system. The interaction of numerous systems is necessary for the operation of several cellular processes in neuron cells, such as calcium, buffer, ER etc. The dynamics of interacting parameters give useful information on neural cell function. This work uses a mathematical model to analyze the dynamic interactions of buffer and ER inside neurons, considering their spatial properties. While buffers bind to calcium ions and lower their concentration, the endoplasmic reticulum (ER) serves as a reservoir, holding a significant number of free calcium ions. The uncertainty of initial values of calcium concentration poses challenges for researchers to develop calcium signaling models. In this article, we examined the exact solution and approximate solution of the mathematical model that was analyzed using the fuzzy undetermined coefficient approach. MATLAB is being used to perform the simulation. Endoplasmic reticulum and buffer have been found to have a substantial impact on calcium signaling. Fuzzy differential equation Provides a useful tool for evaluating complicated processes with imprecise values when ordinary differential equations perform not precisely. They allow for the examination of dynamic processes under fuzzy settings, which contributes to advances research.

Data-Driven Shelf Stocking: Robustness and Vertical-Location Effect

In this article, we study a shelf-stock allocation problem in a data-driven setting where the demand distribution is unknown. The retailer needs to decide which commodities to place on each level of the shelf (location decision), and determine the stock level for each selected commodity at the shelf (stock decision) that can be adjusted based on updated demand prediction, under constraints on allocation and capacity, so as to maximize total expected profit. Key issues of the problem include demand endogeneity on vertical-location effect and the demand ambiguity that may arise from the ever shorter life cycles of commodities and other complicated determinants. We address the problem in a rolling-horizon fashion and develop a two-phase data-driven robust optimization model leveraging a decision-dependent Wasserstein metric that incorporates time-series demand forecasts and captures vertical-location effect under demand ambiguity. We derive tractable solution schemes for the model, in which the phase-I model determines the optimal location decision by solving one instance of mixed-integer linear program, while the phase-II model admits an analytical solution for updating the optimal stock. Furthermore, we discuss the sensitivity implications on how the ambiguity aversion impacts the optimal stock, and prove the consistency of the model solution under regularity condition on the underlying demand process that well justifies the asymptotic performance of the proposed data-driven approach. Finally, we extend our model to incorporate substitution effect, and conduct sufficient numerical experiments with real-life data that demonstrate the performance of our model.

Three-Dimensional MT Conductive Anisotropic and Magnetic Modeling Using A − ϕ Potentials Employing a Mixed Nodal and Edge-Based Element Method

Magnetotelluric (MT) sounding is a geophysical technique widely utilized in mineral resource surveys, where conductivity and magnetic permeability serve as essential physical parameters for forward modeling and inversion. However, the effects of conductive anisotropy and non-zero magnetic susceptibility are usually ignored. In this study, we present a three-dimensional (3D) MT modeling algorithm using Coulomb-gauged electromagnetic potentials, incorporating a mixed nodal and edge-based finite element method capable of simulating MT responses for conductive anisotropic and magnetic anomalies. Subsequently, the algorithm’s accuracy was validated in two steps: first, it was compared with analytical solutions for a 1D magnetic model; then, a comparison was made with previously published numerical results for a 3D generalized conductive anisotropic model. The results of two tests show that the maximum relative error is below 0.5% for both models. Furthermore, representative models were computed to comprehensively analyze the responses of MT. The findings illustrate the relationship between anisotropic parameters and electric fields and emphasize the significance of considering the impact of magnetic susceptibility in magnetite-rich regions.

Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

AbstractThis study investigates the (3 + 1)-dimensional extended Kairat-II model using Lie-Bäcklund symmetry (LBS) and the improved modified extended tanh-function approach (IMETFA). The bifurcation and sensitivity analyses are conducted to understand the stability and chaotic behavior of the model. Through graphical visualizations of phase diagrams, Lyapunov exponents, power spectra, fractal dimension and recurrence plots, the complex dynamics and stability characteristics of the model are elucidated. Additionally, the research focuses on the derivation of dark soliton and various combo soliton solutions of the Kairat-II model. The derived soliton solutions are graphically displayed in 3D and 2D plots. The obtained results are new and have never been reported in the literature for the considered equation.

Tensions between sanctions and insolvency law: Searching for a model solution with a focus on the European Union and Poland

AbstractThis article explores the conflict between insolvency law and sanctions law, particularly in the context of European responses to Russia's invasion of Ukraine. Historically, conflicts between legal systems have shaped laws, and modern insolvency law continues this struggle by determining creditor priorities in cases where debtors cannot fully satisfy them. The article highlights how recent sanctions, which freeze assets to restrict the economic activities of sanctioned individuals and entities, complicate insolvency proceedings. The European Union, along with Poland, has imposed unprecedented sanctions on Russia, including bans on transactions, asset freezes, and trade restrictions. These sanctions, while aimed at political objectives, often push businesses into insolvency by preventing access to resources. Case studies such as GoSport in Poland, Amsterdam Trade Bank in the Netherlands, and Fortenova in Croatia demonstrate the complexities that arise when businesses linked to sanctioned entities become insolvent. Key issues include the legal treatment of frozen assets, creditor satisfaction, and the potential for sanctioned entities to benefit from bankruptcy proceedings. Poland has revised its sanctions law, introducing provisions for the appointment of independent managers to oversee sanctioned companies, ensuring continued operations without benefiting sanctioned owners. However, uncertainty remains over the management and distribution of frozen assets, with no clear framework in place. The article concludes that insolvency and sanctions law, though often in conflict, must be applied flexibly to address individual cases. A balanced approach is needed to protect creditors while adhering to the political and legal objectives of sanctions.

Spectral expansion methods for prediction uncertainty quantification in systems biology

Uncertainty is ubiquitous in biological systems. For example, since gene expression is intrinsically governed by noise, nature shows a fascinating degree of variability. If we want to use a model to predict the behaviour of such an intrinsically stochastic system, we have to cope with the fact that the model parameters are never exactly known, but vary according to some distribution. A key question is then to determine how the uncertainties in the parameters affect the model outcome. Knowing the latter uncertainties is crucial when a model is used for, e.g., experimental design, optimisation, or decision-making. To establish how parameter and model prediction uncertainties are related, Monte Carlo approaches could be used. Then, the model is evaluated for a huge number of parameters sets, drawn from the multivariate parameter distribution. However, when model solutions are computationally expensive this approach is intractable. To overcome this problem, so-called spectral expansion (SE) methods have been developed to quantify prediction uncertainty within a probabilistic framework. Such SE methods have a basis in, e.g., computational mathematics, engineering, physics, and fluid dynamics, and, to a lesser extent, systems biology. The computational costs of SE schemes mainly stem from the calculation of the expansion coefficients. Furthermore, SE effectively leads to a surrogate model which captures the dependence of the model on the uncertainty parameters, but is much simpler to execute compared to the original model. In this paper, we present an innovative scheme for the calculation of the expansion coefficients. It guarantees that the model has to be evaluated only a restricted number of times. Especially for models of high complexity this may be a huge computational advantage. By applying the scheme to a variety of examples we show its power, especially in challenging situations where solutions slowly converge due to high computational costs, bifurcations, and discontinuities.

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.

Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: application to T-models

We develop a method to compute the slow-roll expansion for the Hubble parameter in inflationary models in a flat Friedmann-Lemaître-Robertson-Walker spacetime that is applicable to a wide class of potentials including monomial, polynomial, or rational functions of the inflaton, as well as polynomial or rational functions of the exponential of the inflaton. The method, formulated within the Hamilton-Jacobi formalism, adapts the form of the slow-roll expansion to the analytic form of the inflationary potential, thus allowing a consistent order-by-order computation amenable to Padé summation. Using T-models as an example, we show that Padé summation extends the domain of validity of this adapted slow-roll expansion to the end of inflation. Likewise, Padé summation extends the domain of validity of kinetic-dominance asymptotic expansions of the Hubble parameter into the fast-roll regime, where they can be matched to the aforesaid Padé-summed slow-roll expansions. This matching in turn determines the relation between the expansions for the number N of e-folds and allows us to compute the total amount of inflation as a function of the initial data or, conversely, to select initial data that correspond to a fixed total amount of inflation. Using the slow-roll stage expansions, we also derive expansions for the corresponding spectral index ns accurate to order 1/N2, and tensor-to-scalar ratio r accurate to order 1/N3 for these T-models.

Exploring stacking fault energy with the axial Ising model: A renewed approach

In this work we revisit the axial Ising model for computing intrinsic stacking fault energies (γISF), which are important in alloy design. We find that the supercell approach, which directly compares the energies of fcc stacking with and without a fault, is a specific solution of the Ising model and is the most elegant and efficient among the solutions of the same order of accuracy. Contrary to the traditional belief that only the supercell approach can capture the effect of local chemistry, we demonstrate that local chemistry also influences γISF in the axial Ising model. We also propose a new formula γISF=5EABABC−5EABC, which is similarly efficient, simpler, and more accurate compared to the widely used γISF=EAB+2EABAC−3EABC. We tested the new formula on pure Ni, Ni-Co alloys, and Cr-Mn-Fe-Co-Ni high entropy alloys and found satisfactory results.

Coastline target detection based on UAV hyperspectral remote sensing images

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.

Designing a resilient supply chain network: A multi-objective data-driven distributionally robust optimization method

Uncertainty of supply chain disruption poses a significant challenge to decision-making in many real-life problems. In this paper, a new multi-objective data-driven distributionally robust optimization (MDDRO) model for the resilient supply chain network (RSCN) design problem under disruption scenario is developed, which includes minimizing the total cost, carbon emissions, and delivery time. In the context of supply chain disruption, it is important self-evidently that products can be supplied normally and the practical demand can be met. In handling the partial probability distribution information of the considered uncertain demand, this paper uses a data-driven Wasserstein-Moment ambiguity set (WMAS), which incorporate the Wasserstein metric and Moment information, and a robust counterpart to transform the developed model into a tractable approximation form. The finite-sample performance guarantee of the optimal solution of MDDRO model with Wasserstein-Moment ambiguous chance constraint is given. An accelerated Branch and cut algorithm (BCA) is constructed to solve the MDDRO model. Finally, through the investigation of a real-life case and sensitivity analysis of key parameters, some managerial insights are put forward.

Exact solution of a mathematical model for human muscular motion

An ordinary differential equation (ODE) which models human muscular movement is considered. A functional form of the model parameter is specified through the Lie symmetry approach, yielding a different expression from the one derived in the previous study (Kosugi et al., 2019). The Lie point symmetries corresponding to the model parameter are employed for derivation of exact solution.

Less is more: Optimisation of variable catalyst loading in CO[formula omitted] electroreduction

The electrochemical conversion of CO2 is a promising method of carbon-neutral chemical production. However, commercial realisation in aqueous electrolytes is challenging, due to competition with the hydrogen evolution reaction (HER), and the propensity for CO2 to participate in the carbonate equilibrium reactions. These two phenomena are linked through OH− ions, as both the by-product of the catalytic reactions and the culprit behind the parasitic carbonate reactions. By reducing the local catalyst loading where the CO2 concentration is low, the HER is decreased more than the reactions that are dependent on CO2 as a reactant. Therefore, it is possible to improve reaction selectivity and reactant utilisation while reducing the capital cost of catalyst. We demonstrate this theory through an analytical solution of a 1D flow electrolyser model. We extend this to a comprehensive model of a contemporary gas-diffusion electrode (GDE) setup. We find that the operation costs are dominated by the electrolyser power consumption and, to a lesser degree, the cost of CO2 and its recovery at the anode. We numerically obtain the catalyst loading profiles that maximise operating profit. The optimisation process reveals that profits are maximised for high gas flow rates, and consequently, low single pass conversions, where the CO2 concentration is as high as possible. However, when lower gas flow rates are used for practical reasons, variable catalyst loadings are shown to lead to significant operational improvements, especially in the production of higher C products that require a greater number of electrons transferred. The model is made freely available in MATLAB and its use is encouraged in determining the applicability of variable catalyst loading to future experimental setups.

A neurodynamic optimization approach to distributed nonconvex optimization based on an HP augmented Lagrangian function

This paper develops a neurodynamic model for distributed nonconvex-constrained optimization. In the distributed constrained optimization model, the objective function and inequality constraints do not need to be convex, and equality constraints do not need to be affine. A Hestenes–Powell augmented Lagrangian function for handling the nonconvexity is established, and a neurodynamic system is developed based on this. It is proved that it is stable at a local optimal solution of the optimization model. Two illustrative examples are provided to evaluate the enhanced stability and optimality of the developed neurodynamic systems.

A novel binary data classification algorithm based on the modified reaction-diffusion predator-prey system with Holling-II function.

In this study, we propose a modified reaction-diffusion prey-predator model with a Holling-II function for binary data classification. In the model, we use u and v to represent the densities of prey and predators, respectively. We modify the original equation by substituting the term v with f-v to obtain a stable and clear nonlinear decision surface. By employing a finite difference method for numerical solution of the original model, we conduct various experiments in two-dimensional and three-dimensional spaces to validate the feasibility of the classifier. Additionally, with consideration for wide real applications, we perform classification experiments on electroencephalogram signals, demonstrating the effectiveness and robustness of the classifier in binary data classification.

Deep operator network surrogate for phase-field modeling of metal grain growth during solidification

A deep operator network (DeepONet) has been constructed that generates accurate representations of phase-field model simulations for evolving two dimensional metal grain morphology growing from melt. These representations serve as lower resolution, computationally efficient stand-ins for quick parameter space exploration of solutions to the Allen–Cahn equations that dictate the phase-field model simulations. The experimental target for the phase-field model is a uranium casting system cooling a 434 g uranium charge from a maximum temperature of 1400 °C at an average rate of 30 °Cmin, traversing the crystallographic phases of the pure metal. Experimental parameters inform the phase-field model, whose higher resolution computational model solutions are used to train the DeepONet in a given parameter space with the aim of developing a faster, more efficient method for predicting the solidifying metal’s microstructure at different potential experimental values. The final DeepONet generates high accuracy, lower resolution predictions with cumulative relative approximation error over all timesteps of less than 0.5%, while ensuring solutions remain within physically feasible ranges. These relative error values are comparable with other state-of-the-art DeepONet models for microstructure evolution, while significantly reducing the amount of training data required. Training a convolutional neural network simultaneously with the DeepONet, enforcing realistic values at the complex metal grain boundaries, and mathematically encoding boundary conditions into the structure of the DeepONet improved prediction accuracy and computational efficiency over a standard DeepONet model.