Solution Of Model Research Articles

Enhanced TomoSAR imaging method with complex least squares for 3D building reconstruction

ABSTRACT Synthetic aperture radar tomography (TomoSAR) has emerged as an advanced technology for the rapid acquisition of three-dimensional information, with model solutions dependent on a specific complex least squares adjustment criterion. We design two TomoSAR imaging algorithms based on two adjustment criterions minimizing the square sum of the real and imaginary components of observation vector residual, and minimizing the square sum of the L2-norm of observation vector residual. Additionally, we propose a strong scatterer recognition method that combines amplitude thresholding and density-based spatial clustering of applications with noise to alleviate the low efficiency and excessive noise in real images. The simulated and practical experiments are conducted to evaluate the performance of algorithms. Results suggested that two algorithms perform similarly in parameter estimation accuracy and noise immunity for buildings with simple structures and single scatterer. However, for buildings with multiple scatterers, the algorithm derived by minimizing the square sum of the L2-norm from the observation vector residual exhibits more robustly than the other algorithm, accurately distinguishing multiple scatterers within pixels and reconstructing 3D scenes mirroring the actual ones. The results verify the effectiveness of the proposed strong scatterer recognition method and the importance of the adjustment criterion in TomoSAR imaging.

Enhancing Supply Chain Sustainability and Reliability Through WSM and TOPSIS: A Symmetrical Real-World Case Study

Large corporations have recently demonstrated an increasing propensity to enhance the sustainability and reliability of their supply chains in order to comply with environmental regulations and improve customer satisfaction through on-time demand fulfillment. There are two phases to this study: mathematical modeling and model solution using precise techniques. In the first step, a mixed-integer linear programming model is developed. This model is an improvement of an existing supply chain model. Further, our suggested strategy is verified by using numerical data based on three criteria and four suppliers. The goals of the proposed model are to maximize supply chain reliability, economic profit, and social responsibilities by taking suppliers’ priorities into account. Modeled as a mixed-integer linear programming problem, the constraints on the problem include budget, emission, demand, allocation, facility, and shipping capacity. Power symmetry and information symmetry are incorporated in order to perform symmetric analysis. The weighted sum method (WSM) and the technique for order of preference by similarity to ideal solution (TOPSIS) are the two methods used in the second step of solving the model to identify the best supplier. In order to evaluate how well the proposed methodology was applied, a practical case was considered and implemented.

Heuristic Approaches for Using an Exact Model to Obtain the Placement of a Set of Rectangles on a Half-Strip

There is considered the problem of the compact orthogonal placement, which consists in placing of the set of rectangles on the half-strip and its solution by constructing an optimization model that reduces to solving a high-dimensional linear partial Boolean programming problem. The main method of solving the problem is the algorithm of branches and boundaries, providing consistent fiXation of the Boolean variables. The direct use of this algorithm represents significant computational difficulties and is used only for the small size of the initial set of rectangles. In this paper are proposes approaches that reduce the computational complexity of the solution of this optimization model by using heuristic approaches to fix individual Boolean variables. Most of the variables responsible for the relative arrangement of all pairs of rectangles relative to each other are fixed on the basis of generating the permutation of rectangles and special code that determines the direction by which the intersection of the location of the rectangles should be monitored. Thus, the direct computing complexity of the method of branches and the boundaries of solving the problem becomes insignificant. To generate pre-fixation of the Boolean variables, genetic algorithms and local search algorithms are used. Computational experiments showed that the used techniques of fixing the Boolean variables allowed to reduce the volume of calculations and the quality of the resulting approximate solution, in general, it turns out acceptable.

A Finite Difference-Based Adams-Type Approach for Numerical Solution of Nonlinear Fractional Differential Equations: A Fractional Lotka–Volterra Model as a Case Study

Abstract In this paper, we developed an efficient Adams-type predictor–corrector (PC) approach for the numerical solution of fractional differential equations (FDEs) with a power law kernel. The main idea of the proposed approach is to use a linear approximation to the nonlinear problem and then implement finite difference approximations of derivatives. Numerical comparisons with the fractional Adams method are made and simulation results are demonstrated to evaluate the approximation error of the proposed approach. The efficiency of this approach has been depicted by presenting numerical solutions of some test fractional calculus models. Numerical simulation of a fractional Lotka–Volterra model is provided, as a case study, using the proposed approach. The advantage of the proposed approach lies in its flexibility in providing approximate numerical solutions with high accuracy.

Influence of Additives on Crystallization of Calcium Phosphates from Prototypes of Blood Plasma

The paper presents the results of studies on the effect of additives on crystallization in solutions simulating the composition of human blood plasma. Synthesis from prototypes of human blood plasma in the presence of organic and inorganic additives was carried out, and it was found that the obtained solid phases consisted of octacalcium phosphate, B-type carbonate hydroxyapatite, and vitlocite. The effect of additives (magnesium ions, alanine, and glycine) on the crystallization of calcium phosphates was studied. It was found that the presence of additives in the model solution reduces the crystallite size and the fraction of carbonate hydroxyapatite in the solid phase. The bioactivity of synthetic samples was studied, and kinetic characteristics were established. A study of thermal transformations.

A comparison of stochastic and deterministic dynamics of tuberculosis model

Tuberculosis is a deadly infectious disease leading to a major health concern in Southern India while there are major obstacles to controlling its spread. Here, we present a mathematical model with five compartments. We categorize the infected compartment into two subcategories: latent TB-infected individuals and active TB-infected individuals. By introducing white noise in a deterministic system, we formulate a stochastic system. We investigate the model in deterministic and stochastic framework, followed by data calibration using TB infection data from Kanyakumari District in South India from 2019 to 2023. In the deterministic model, we derive the disease-free and endemic equilibrium points, compute the basic reproduction number, and examine their stability. Moreover, we perform sensitivity analysis to evaluate how variations in model parameters affect TB prevalence. In addition, we study the uniqueness of solutions of stochastic model. After that we derive the conditions for disease extinction and stochastic permanence, and execute extensive simulations to capture the variability and randomness in TB transmission dynamics. This study signifies that stochastic dynamics is richer than deterministic one in the way of mitigation TB transmission.

A fully coupled multiscale phase-change model at the porous interface for transpiration cooling: coupling dynamics pore-scale networks to continuum-scale free flow

Being a promising method for thermal protection system, transpiration cooling has received wide interest recently. Numerical simulation for transpiration cooling, however, has been limited due to the mis-matching between the pore-scale two-phase flow and external high-temperature aerothermodynamic environment, which induced by conventional decoupled or iterative one-way coupled simplification methods. In this work, a fully coupled continuum-scale and pore-scale model is established for transient transpiration cooling at the interface between boundary layer flow and porous medium through coupling Computational Fluid Dynamics (CFD) and Pore-Network Model (PNM), termed as the multiscale CFD-PNM coupled method. The coupled method allows to capture detailed displacement and phase change of two-phase flow at pore-scale, revealing the strong interaction of the water vapor with the external free flow within a high temperature boundary layer. After successfully validating the new coupled model by comparing with the Two-Phase Mixture Model (TPMM) solution, a number of cases mimicking the cooling at the interface of typical blunt bodies are simulated. The results show that the multiscale CFD-PNM coupled method can not only provide the thermal protection effect prediction, but also reveal many critical features that beyond the reach of continuum-scale studies. Some pore-scale phenomena that are important to the overall transpiration cooling effects are revealed, including transient phase change and composition variation of water vapor, imbibition and drainage of two-phase flow related to pore-scale capillary thresholds and applied boundary pressures, as well as the two-way mass transfer at the interface, such as the invasion of external hot air.

A novel micro ohmic heating cell for microorganism destruction kinetic studies: Performance validation

Ohmic heating cells used for microbial destruction are typically large compared with conventional capillary tubes. Limitations of commonly used large cells include large mass, high come-up-time (CUT), lack of uniform heating, and operation at atmospheric pressure. A new 3 mL Micro Ohmic Cell (MOC) was designed and fabricated for the kinetic study of microbial spore destruction. Two tiny titanium electrodes, mounted horizontally on a T-shaped cylindrical cell with a 3 cm gap, generate a rapid heating rate up to 140 °C. Fibre optic temperature sensors were used for direct temperature monitoring during CUT and holding time. Model solutions were heated under voltage gradients up to 90 V/cm. Uniform heating was achieved under stirring conditions with less than 1 °C variation across the cell volume, and the coldest spot was identified as the liquid-air interface. CUT was evaluated as influenced by both system and product parameters, resulting in less than 50 s comparable to those obtained using capillary tubes. The newly developed MOC was validated for microbial destruction kinetic study under ohmic heating conditions using Clostridium sporogenes spores in buffer and concentrated maple sap. With its small volume, short CUT, and uniform temperature similar to capillary tubes in conventional heating, the MOC has the potential to be considered as a standard device for kinetic studies under ohmic heating.

Modeling of the interaction of stressful components agricultural production

There is a completely natural, organic nonlinear relationship between crop production and animal husbandry, which are crucial components of agricultural production in Ukraine. Timely and appropriate management of these subsystems contributes to the stable growth of the country’s agriculture with minimal risk. This approach requires improvements in terms of the digitalization of the economy, particularly in the context of applying computer modeling to the nonlinear processes of interaction between these components. The article develops a modern methodology for computer modeling of an economic management object—a thorough study of a nonlinear dynamic model of the VolterraLotka class, featuring a component that characterizes the increase in livestock profitability due to feed supply. The model takes into account various influencing factors, allowing for the assessment of the efficiency of the interaction between crop production and animal husbandry at different stages of agricultural production. The study examines the behavior of the dynamic model in the vicinity of the leverage point, analyzing the modeled trend dependencies and statistical components: in the vicinity of the equilibrium point, there are oscillatory movements with a certain defined period, and the solutions of the mathematical model, i.e., integral curves, over time reflect the seasonal nature of the interaction between crop production and animal husbandry. The behavior of virtual scenarios—integral curves and phase portraits based on the mathematical model of nonlinear interaction of agricultural production components—wasstudied, showing the location of the equilibrium point, extreme points, and other critical points for the respective curves in a specific coordinate system. A transition to a dimensionless dynamic model and an economic interpretation of its implicit solution were indicated. Additionally, the impact of external economic factors on the stability of the system was analyzed, allowing for better forecasting of potential risks and the preparation of appropriate strategies to minimize them. For the first time, an approximate numerical estimate of the economic risk measure of the evolution of the interaction and interplay of agricultural subsystems over time was carried out in the study of the nonlinear dynamic model of the economic management object. The obtained results can be used to improve management strategies in the agricultural sector, particularly to enhance the stability of production processes and reduce economic risks in the context of market instability and climate change. This research provides new opportunities for effective planning and the implementation of innovations in Ukraine’s agricultural sector.

Analytical Model for Heat Transfer Around Energy Piles in Layered Soil With Interfacial Thermal Resistance by Integral Transform Method

ABSTRACTEnergy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles.

Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.

Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Bioproducts

Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into in silico tools and provide valuable information for human health risk assessment.

Cooperative energy and reserve trading strategies for multiple integrated energy systems based on asymmetric nash bargaining theory

To tackle the issues of cooperative energy and reserve trading as well as fair cooperative benefit allocation among multiple integrated energy systems (IESs), this paper proposes a two-stage cooperative energy and reserve trading model for multiple integrated energy systems (MIESs). Specifically, at day-ahead stage, MIESs aim to maximize their overall profit through cooperative electricity and heat trading. At real-time stage, MIESs trade demand response (DR) reserve to minimize the overall wind power deviation compensation cost. To reduce the complexity in model solution, we transform the model into two sub-problems. In sub-problem 1, we determine the energy and DR reserve trading volumes. Here, distributionally robust optimization (DRO) is utilized to manage the severe uncertainties in wind power distribution. In sub-problem 2, based on the outcomes from sub-problem 1, we settle the energy and DR reserve trading prices. To ensure the fairness of benefit allocation, asymmetric Nash bargaining theory is applied to assess each IES's contributions in trading volumes and profit growth. Interval adaptive alternating direction method of multipliers (IA-ADMM) is used to preserve each IES's privacy. Finally, simulation results demonstrate that, compared with independent operation, cooperative trading among MIESs increases profits for all IESs, thereby motivating their participation in cooperative trading.

Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method

The behavior of several particulate processes, such as cell interaction, blood clotting, bubble formation, grain breakage, and cheese formation from milk, have been studied using coagulation and fragmentation models (Fogelson and Guy, 2008 [1]; Pazmiño et al., 2022 [2]; Chen et al., [3]). Various studies utilize the linear fragmentation model to simplify the underlying physics. However, in real-life scenarios, particles form due to the collision of two particles, leading to a non-linear collisional breakage model. Unfortunately, the collisional breakage model is less explored due to its complex behavior. While analytical solutions are difficult to compute and are still missing in the literature, this article proposes an approximate solution for the model using the Laplace-based accelerated homotopy perturbation method. Further, coupling with Padé approximant, the accuracy of the solution is extended for the longer time. Considering various physically relevant kernels, the approximate series solutions are compared with the well known finite-volume solutions to measure the accuracy in terms of qualitative and quantitative errors. The article also encompasses theoretical convergence analysis and error estimations to enhance comprehension of the proposed formulation.

Enhanced removal of Fe, Cu, Ni, Pb, and Zn from acid mine drainage using food waste compost and its mechanisms

Heavy metals (HMs) in acid mine drainage (AMD) pose serious threats to aquatic life and soil. Biosorbents are promising materials to remove HMs from wastewater. Herein, food waste compost was used as a low-cost and sustainable biosorbent to remove Fe3+, Cu2+, Ni2+, Pb2+, and Zn2+ from an AMD and other model solutions with an initial pH of 2.24. Batch adsorption tests were conducted to systematically investigate the influences of initial pH, compost dose, the presence of Fe3+ and SO42− ions, and the pH-induced Fe precipitates on the removal performance. The involved removal mechanisms were explored by conducting stepwise precipitation tests, sequential extraction tests, and Fourier transform infrared spectroscopy (FTIR) characterization. It was found that the addition of the compost removed over 90% of Zn, Ni, Cu, and Pb at pH 5.80, 5.50, 4.50, and 3.00, respectively. At low compost doses, the presence of Fe3+ and SO42− ions hindered the removal since the competition effect of Fe3+ ion and lower absorbability of metal-sulfate complexes, respectively. Sequential extraction tests revealed that higher fractions of Fe, Cu, and Pb were strongly immobilized through complexation and precipitation relative to Ni and Zn. Additionally, the pH-induced Fe precipitates did not favor the removal of the HMs, probably due to the adsorption of organic components released from the compost. This study suggests that compost have the potential to remove HMs from acidic wastewater without pre-neutralization.

Numerical solution of fractional order model of measles disease with double dose vaccination

Numerical solution of fractional order model of measles disease with double dose vaccination

Existence and stability of boundary spike layer solutions of an attractive chemotaxis model with singular sensitivity and nonlinear consumption rate of chemical stimuli

Existence and stability of boundary spike layer solutions of an attractive chemotaxis model with singular sensitivity and nonlinear consumption rate of chemical stimuli

Variational inequalities of multilayer elastic contact systems with interlayer friction: Existence and uniqueness of solution and convergence of numerical solution

Inspired by the layered structure models in pavement mechanics research, in this study, a class of multilayer elastic contact systems with interlayer frictional contact conditions and deformable supporting frictional contact conditions on the foundation has been constructed. Based on the nonlinear elastic constitutive equations, the corresponding system of partial differential equations and variational inequalities are respectively introduced. Under the framework of variational inequalities, the existence and uniqueness of solutions for such models, along with the approximation properties of finite element numerical solutions, are proven and analyzed. The aforementioned conclusions provide fundamental and broadly applicable theoretical support for addressing mechanical problems in multilayer elastic contact systems within the framework of variational inequalities. Finally, the numerical experimental results based on the mixed finite element method also substantiate our theoretical conclusions.

A GRASP-based multi-objective approach for the tuna purse seine fishing fleet routing problem

Nowadays, the world’s fishing fleet uses 20% more fuel to catch the same amount of fish compared to 30 years ago. Addressing this negative environmental and economic performance is crucial due to stricter emission regulations, rising fuel costs, and predicted declines in fish biomass and body sizes due to climate change. Investment in more efficient engines, larger ships and better fuel has been the main response, but this is only feasible in the long term at high infrastructure cost. An alternative is to optimize operations such as the routing of a fleet, which is an extremely complex problem due to its dynamic (time-dependent) moving target characteristics. To date, no other scientific work has approached this problem in its full complexity, i.e., as a dynamic vehicle routing problem with multiple time windows and moving targets. In this paper, two bi-objective mixed linear integer programming (MIP) models are presented, one for the static variant and another for the time-dependent variant. The bi-objective approaches allow to trade off the economic (e.g., probability of high catches) and environmental (e.g., fuel consumption) objectives. To overcome the limitations of exact solutions of the MIP models, a greedy randomized adaptive search procedure for the multi-objective problem (MO-GRASP) is proposed. The computational experiments demonstrate the good performance of the MO-GRASP algorithm with clearly different results when the importance of each objective is varied. In addition, computational experiments conducted on historical data prove the feasibility of applying the MO-GRASP algorithm in a real context and explore the benefits of joint planning (collaborative approach) compared to a non-collaborative strategy. Collaborative approaches enable the definition of better routes that may select slightly worse fishing and planting areas (2.9%), but in exchange for a significant reduction in fuel consumption (17.3%) and time at sea (10.1%) compared to non-collaborative strategies. The final experiment examines the importance of the collaborative approach when the number of available drifting fishing aggregation devices (dFADs) per vessel is reduced.

Investigation of the Solution of a Smoking Model with Conformable Derivative

Investigation of the Solution of a Smoking Model with Conformable Derivative