Solution Of Model Research Articles

Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel

In this work, we analyse the fractional order West Nile Virus model involving the Atangana-Baleanu derivatives. Existence and uniqueness solutions were obtained by the fixed-point theorem. Another impressive aspect of the work is illustrated by simulations of different fractional orders by calculating the numerical solutions of the mathematical model.

An adaptive positive preserving numerical scheme based on splitting method for the solution of the CIR model

This paper aims to investigate an adaptive numerical method based on a splitting scheme for the Cox-Ingersoll-Ross (CIR) model. The main challenge associated with numerically simulating the CIR process lies in the fact that most existing numerical methods fail to uphold the positive nature of the solution. Within this article, we present an innovative adaptive splitting scheme. Due to the existence of a square root in the CIR model, the step size is adaptively selected to ensure that, at each step, the value under the square-root does not fall under a given positive level and it is bounded. Moreover, an alternate numerical method is employed if the chosen step size becomes excessively small or the solution derived from the splitting scheme turns negative. This alternative approach, characterized by convergence and positivity preservation, is called the “backstop method”.Furthermore, we prove the proposed adaptive splitting method ensures the positivity of solutions in the sense that it would be possible to find an interval such that for all stepsizes belong, the probability of using the backstop method can be small. Therefore, the proposed adaptive splitting scheme avoids using the backstop method with arbitrarily high probability. We prove the convergence of the scheme and analyze the convergence rate. Finally, we demonstrate the applicability of the scheme through some numerical simulations, thereby corroborating our theoretical findings.

Carbon emission reduction dynamic decision-making in the electricity supply chain with different carbon emission allowance principles

To address the impacts of typical principles for allocating initial carbon emission allowance, namely, the grandfathering and benchmarking principles on long-term emission reduction strategies, this paper presents four differential game models for an electricity supply chain consisting of a single electricity supplier and a single electricity retailer. The equilibrium solutions for different models are obtained and comparatively analyzed. The results show that the power supplier exhibits greater emission reduction efforts and, therefore, that the retailer has higher profits under the benchmarking principle than under the grandfathering principle. Moreover, under the two principles, the level of the power supplier’s emission reduction efforts is related to the decision-making modes of the electricity supply chain. Under specific conditions, the power supplier’s profit is also higher under the benchmarking principle than under the grandfathering principle. In addition, this study extends the models to investigate the constrained differential game models and obtains the game equilibrium solutions, which can be proved as saddle point equilibria.

Prediction of spatiotemporal dynamics using deep learning: Coupled neural networks of long short-terms memory, auto-encoder and physics-informed neural networks

Several classic reaction-diffusion models using partial differential equations (PDEs) have been established to elucidate the formation mechanism of vegetation patterns. However, predictive modeling of complex spatiotemporal dynamics using traditional numerical methods can be significantly challenging in many practical scenarios. Physics-Informed Neural Networks (PINNs) provide a new approach to predict the solution of PDEs. However, the generalization of PINNs is not satisfactory when pretrained PINNs is directly used in non-trained space (defined as explorations). This may be attributed to the lack of training in the time dimension. Therefore, a framework (LA-PINNs) is proposed to predict the evolutionary solution of the non-dimensional vegetation-sand model. The framework couples neural networks of Long-Short Terms Memory, Auto-Encoder and Physics-Informed Neural Networks. The predictions of LA-PINNs are much better than those of PINNs. Then we studied the effects of hyperparameters on the accuracy of predictions. Based on training in time dimension by LSTM module and pretraining for quick-training strategy, LA-PINNs can improve the accuracy of explorations.

Deep Ring-Block-Wise Network for Hyperspectral Image Classification.

Deep learning has achieved many successes in the field of the hyperspectral image (HSI) classification. Most of existing deep learning-based methods have no consideration of feature distribution, which may yield lowly separable and discriminative features. From the perspective of spatial geometry, one excellent feature distribution form requires to satisfy both properties, i.e., block and ring. The block means that in a feature space, the distance of intraclass samples is close and the one of interclass samples is far. The ring represents that all class samples are overall distributed in a ring topology. Accordingly, in this article, we propose a novel deep ring-block-wise network (DRN) for the HSI classification, which takes full consideration of feature distribution. To obtain the good distribution used for high classification performance, in this DRN, a ring-block perception (RBP) layer is built by integrating the self-representation and ring loss into a perception model. By such way, the exported features are imposed to follow the requirements of both block and ring, so as to be more separably and discriminatively distributed compared with traditional deep networks. Besides, we also design an optimization strategy with alternating update to obtain the solution of this RBP layer model. Extensive results on the Salinas, Pavia Centre, Indian Pines, and Houston datasets have demonstrated that the proposed DRN method achieves the better classification performance in contrast to the state-of-the-art approaches.

Convergence rates and central limit theorem for 3-D stochastic fractional Boussinesq equations with transport noise

This work investigates the 3-D stochastic modified fractional Boussinesq equations driven by transport noise on the torus. The existence of weak solutions is initially established through Galerkin approximation and compactness techniques. Subsequently, we demonstrate that the weak solutions of stochastic modified fractional Boussinesq equations converge to the unique solution of a deterministic Boussinesq model with fractional dissipation, subject to an appropriate noise scaling, along with providing the quantitative estimates with explicit convergent rates. Finally, the central limit theorem with an explicit convergence rate is established based on the aforementioned scaling limit. It is noteworthy that the scaling limit result of stochastic modified fractional Boussinesq equations to deterministic Boussinesq models with additional fractional dissipation implies that the transport noise regularizes the modified fractional Boussinesq equations, thus leading to “approximate weak uniqueness”.

One-dimensional N-layer thermal modelling as a basis for effective machine learning training data generation for nondestructive testing of composite parts.

The analytical solution of the one-dimensional N-layer thermal model (NLM) was successfully employed to generate training data for a machine learning (ML) based procedure for the nondestructive inspection of carbon fiber reinforced composite parts with infrared thermography (IRT). The main objective was to identify a reliable correlation between the experimental data of a pulsed IRT experiment and the NLM prediction, thereby enabling the use of simulated data for ML training. This paper focuses on the initial stages of this process, in more detail on the analytical modelling and experimental data preprocessing, such as normalization, correction of experimental shortcomings and feature selection for machine learning. For pulse phase thermography (PPT) simulated and experimentally derived phase data was compared directly in the frequency domain. Therefore, the features for training and validation of ML were defined from those phase spectra in frequency domain. The suitability of these features for automated and reliable defect depth and/or defect material detection was investigated in both simulated and measured IRT test data. As a basis for feature selection, we used referenced and normalized phase-frequency curves as a function of defect depth. A correlation was identified between the results of the experimental and the simulated feature sets, both qualitatively and quantitatively. To demonstrate the practical applicability of this method, two different, generic ML techniques, multilayer perceptron and random forest regression, were tested as examples. The investigation was performed on plates made of multidirectional carbon fiber reinforced polymer (CFRP) with artificial defects made from three different materials.

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.

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.

Computational insights into tumor invasion dynamics: A finite element approach

The finite element scheme is proposed and analyzed for the solution of an acid-mediated tumor invasion model. The reaction–diffusion equation shows the evolution in the tumor cell density, H+ ions concentration, and healthy tissue density over time. The coupled non-linear partial differential equations are discretized in time with the implicit Euler method and in space with standard Galerkin finite element. To solve the non-linear and coupled terms of the system a fixed point iteration scheme is presented. Moreover, a mass-lumped scheme is adopted to reduce the computation cost. The cut-off method is used to compute the bounded solutions of the PDEs. Finally, The effects of proliferation rate and healthy tissue degradation rate are investigated.

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.

An instrumentation guide to measuring thermal conductivity using frequency domain thermoreflectance (FDTR).

Frequency Domain Thermoreflectance (FDTR) is a versatile technique used to measure the thermal properties of thin films, multilayer stacks, and interfaces that govern the performance and thermal management in semiconductor microelectronics. Reliable thermal property measurements at these length scales (≈10nm to ≈10μm), where the physics of thermal transport and phonon scattering at interfaces both grow in complexity, are increasingly relevant as electronic components continue to shrink. While FDTR is a promising technique, FDTR instruments are generally home-built; they can be difficult to construct, align, and maintain, especially for the novice. Our goal here is to provide a practical resource beyond theory that increases the accessibility, replicability, and widespread adoption of FDTR instrumentation. We provide a detailed account of unpublished insights and institutional knowledge that are critical for obtaining accurate and repeatable measurements of thermal properties using FDTR. We discuss component selection and placement, alignment procedures, data collection parameters, common challenges, and our efforts to increase measurement automation. In FDTR, the unknown thermal properties are fit by minimizing the error between the phase lag at each frequency and the multilayer diffusive thermal model solution. For data fitting and uncertainty analysis, we compare common numerical integration methods, and we compare multiple approaches for fitting and uncertainty analysis, including Monte Carlo simulation, to demonstrate their reliability and relative speed. The instrument is validated with substrates of known thermal properties over a wide range of isotropic thermal conductivities, including Borofloat silica, quartz, sapphire, and silicon.

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.

A reinvestigation on combined dry and wet adhesive contact considering surface tension

The present study theoretically explores combined dry and wet adhesive contact between a rigid sphere and elastic semi-half substrate, in which dry contact is encircled by liquid bridge. We consider threefold effects of liquid bridge on contact behavior, namely Laplace pressure induced by the curved surface of liquid meniscus, surface tension at the triple-phase junction and alternation of adhesion energy between solid surfaces ascribed to liquid immersion. A clear novelty in this study is the investigation on the effect of surface tension at the vapor-liquid-solid junction on the adhesive contact response, in contrast to previous studies. The model solution predicts that the contact behavior and adhesive strength are strongly dependent on surface wettability (manifested by contact angle), liquid volume and the contact system's rapidity in achieving thermodynamic equilibrium. It is found that the transition of the pull-off force is evidently different from Maugis-Dugdale model in terms of a couple of interesting characteristics. Moreover, it is unveiled that the jump instabilities and hysteresis of force-separation curves are highly affected by surface wettability and liquid volume. These theoretical results can not only shed lights on the mechanism of liquid-mediated adhesion employed by animals and plants, but also provide us inspiration for development of biomimetic adhesive devices.

Bayesian material flow analysis for systems with multiple levels of disaggregation and high dimensional data

AbstractMaterial flow analysis (MFA) is used to quantify and understand the life cycles of materials from production to end of use, which enables environmental, social, and economic impacts and interventions. MFA is challenging as available data are often limited and uncertain, leading to an under‐determined system with an infinite number of possible stocks and flows values. Bayesian statistics is an effective way to address these challenges by principally incorporating domain knowledge, quantifying uncertainty in the data, and providing probabilities associated with model solutions. This paper presents a novel MFA methodology under the Bayesian framework. By relaxing the mass balance constraints, we improve the computational scalability and reliability of the posterior samples compared to existing Bayesian MFA methods. We propose a mass‐based, child and parent process framework to model systems with disaggregated processes and flows. We show posterior predictive checks can be used to identify inconsistencies in the data and aid noise and hyperparameter selection. The proposed approach is demonstrated in case studies, including a global aluminum cycle with significant disaggregation, under weakly informative priors and significant data gaps to investigate the feasibility of Bayesian MFA. We illustrate that just a weakly informative prior can greatly improve the performance of Bayesian methods, for both estimation accuracy and uncertainty quantification.

EXTRACTION AND CONCENTRATION OF RHENIUM FROM NITRATE-CONTAINING RHENIUM DESORBATE

Extraction technology plays a key role in the industrial production of rhenium, accounting for more than 70% of the world's production of this element. In aqueous and alkaline solutions, rhenium is present in the form of the anion ReO4 - , which necessitates the use of anion exchange extractants based on tertiary amines. Despite the widespread application and many years of research on rhenium extraction with amines, the obtained data remain contradictory. The extraction of rhenium from aqueous solutions by an amine extractant occurs through an anion exchange mechanism with the formation of the complex TAAHReO4. To increase the solubility of amine salts in the organic phase, high-molecular-weight aliphatic alcohols, such as decyl alcohol, are added, which act as modifiers of the organic phase without extracting rhenium themselves. The aim of this work is to investigate the extraction of rhenium with trialkylamine from a model solution that simulates the composition of nitrate desorbate obtained from the processing of uranium ores. Specifically, various factors affecting the extraction and reextraction of rhenium are studied to determine the optimal parameters of these processes. The study uses trialkylamine as the extractant and decyl alcohol as the modifying additive. The results of the study show that the optimal parameters for rhenium extraction are: an extractant concentration of TAA:DA:kerosene=40:5:55 (% by volume), an organic to aqueous phase ratio of V_org/aq = 1:5, an extraction time of 5 minutes, and a rhenium extraction rate of up to 75%. Similar results were obtained with an extractant concentration of TAA:DA:kerosene = 30:10:60 and an extraction time of 5 minutes, where the rhenium extraction rate was about 74%. The re-extraction of rhenium is most efficiently carried out using an ammonia solution with a concentration of 114 g/L NH3⋅H2O and a phase contact time of 10 minutes, with a re-extraction rate of 85.5%. Similar results were obtained with the addition of 174 g/L (NH4)2SO4, where the rhenium re-extraction rate was 82%.

Optimizing Higher Education for Entrepreneurship Digital economy and Innovation: A Novel Spatial Analysis Approach

The paper extensively examined the intricate components underpinning innovation ability, culminating in the construction of a linear spatial model delineating innovation and entrepreneurship prowess. This paper analyzed the components of the connotation of innovation ability, then constructs a linear spatial model of innovation and entrepreneurship ability, proposes a multi-objective function model of the utilization efficiency and allocation efficiency of education resources, and uses the grey correlation algorithm The experimental simulation and model solution are carried out. The simulation results show that, through the optimization, the utilization efficiency and allocation efficiency of the educational resources for innovation and entrepreneurship for all are increased by 18.72\% and 20.98\% respectively, and tend to be in equilibrium, which can achieve the optimization of educational resources allocation. Among all people, the correlation value with ideal entrepreneurship is 0.3177, achieving the most excellent innovation and entrepreneurship education.

Simultaneous assessment of NAD(P)H and flavins with multispectral fluorescence lifetime imaging microscopy at a single excitation wavelength of 750nm.

Autofluorescence characteristics of the reduced nicotinamide adenine dinucleotide and oxidized flavin cofactors are important for the evaluation of the metabolic status of the cells. The approaches that involve a detailed analysis of both spectral and time characteristics of the autofluorescence signals may provide additional insights into the biochemical processes in the cells and biological tissues and facilitate the transition of spectral fluorescence lifetime imaging into clinical applications. We present the experiments on multispectral fluorescence lifetime imaging with a detailed analysis of the fluorescence decays and spectral profiles of the reduced nicotinamide adenine dinucleotide and oxidized flavin under a single excitation wavelength aimed at understanding whether the use of multispectral detection is helpful for metabolic imaging of cancer cells. We use two-photon spectral fluorescence lifetime imaging microscopy. Starting from model solutions, we switched to cell cultures treated by metabolic inhibitors and then studied the metabolism of cells within tumor spheroids. The use of a multispectral detector in combination with an excitation at a single wavelength of 750nm allows the identification of fluorescence signals from three components: free and bound NAD(P)H, and flavins based on the global fitting procedure. Multispectral data make it possible to assess not only the lifetime but also the spectral shifts of emission of flavins caused by chemical perturbations. Altogether, the informative parameters of the developed approach are the ratio of free and bound NAD(P)H amplitudes, the decay time of bound NAD(P)H, the amplitude of flavin fluorescence signal, the fluorescence decay time of flavins, and the spectral shift of the emission signal of flavins. Hence, with multispectral fluorescence lifetime imaging, we get five independent parameters, of which three are related to flavins. The approach to probe the metabolic state of cells in culture and spheroids using excitation at a single wavelength of 750nm and a fluorescence time-resolved spectral detection with the consequent global analysis of the data not only simplifies image acquisition protocol but also allows to disentangle the impacts of free and bound NAD(P)H, and flavin components evaluate changes in their fluorescence parameters (emission spectra and fluorescence lifetime) upon treating cells with metabolic inhibitors and sense metabolic heterogeneity within 3D tumor spheroids.

Dynamic Analysis and Approximate Solution of Transient Stability Targeting Fault Process in Power Systems

Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system’s power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system.

A deterministic fluid model for production and energy mode control of a single machine

Improving machines’ energy efficiency through dynamic energy mode control to meet demand requirements with minimal energy consumption is a promising approach. This study considers a machine operating in working, idle, off, and warmup energy modes with different energy consumption in each mode. A deterministic fluid model is developed to analyze an energy mode control policy that determines when to keep the machine working, off or idle, and switch to other modes based on the inventory/backlog level to minimize the total energy, inventory, and backlog costs. This approach facilitates the derivation of closed-form expressions for the optimal thresholds and the associated costs. This modeling approach allows us to prove that a policy that operates the machine between the working and off modes or the working and idle modes is always better than a hybrid policy that operates the machine in working, off, and idle modes simultaneously. We use the solution of the deterministic fluid model to propose an approximate policy for machines with stochastic production, warmup, and demand processes. We compare the results of the proposed approximation method with the optimal solution of a stochastic system where the production and warmup times are exponential and the demand inter-arrival times have Erlang distribution. The optimal solution for the stochastic system is determined by solving a Markovian Decision Process (MDP). Our numerical experiments show that the proposed approximation method predicts the optimal policy type for the stochastic case with a 89.3% accuracy, and the average error between the optimal cost and the cost obtained with the approximation method is 1.37% for 729 different cases tested. Furthermore, the computational efficiency of the proposed approximation is around 250 times better than the effort to determine the optimal policy using an MDP approach. We propose this approximation method where the control parameters are given in closed form as an easy-to-implement and effective policy to control energy modes to minimize the total energy, inventory, and backlog costs. Furthermore, we present the deterministic fluid modeling approach as a versatile approach to analyze energy mode control problems.