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This paper proposes a novel method to address coherent interference (pilot contamination) in Massive MIMO by incorporating control over propagation environment through Intelligent Reflecting Surfaces. In earlier research it was established that each mobile device has unique spatial signature which can be used as identifier even if they are sharing same pilot sequence. However in certain circumstances when their signals are received at BS with same Angle of Arrival their spatial structure become similar thus their individual identity is lost. This situation adds error in acquisition of channel state information, the accuracy of which is the key to benefit from Massive MIMO. This paper present a method to resolve the mentioned accepted gap using mathematical basis and simulation methods. A mathematical model of Massive MIMO is presented which is widely accepted by the subject modeling community. The model is then used to generate the basis for the presented algorithm through further mathematical studies and simulations. The basic algorithm used for the resolution of pilot contamination problem is finally presented in this paper. The algorithm was simulated using MATLAB and simulation results are tabulated to identify the results of pilot de-contamination after incorporating signal propagation control. [ABSTRACT FROM AUTHOR]

This paper studies a cascaded flowshop joint scheduling problem that has critical applications in the electronic information equipment manufacturing industry but has received limited attention in the scheduling field. The cascaded flowshop joint scheduling problem encompasses both a distributed permutation flowshop scheduling problem and a hybrid flowshop scheduling problem. This paper investigates the efficient scheduling of a set of jobs in two heterogeneous flowshops to minimize the makespan. We present a mixed integer linear programming mathematical model and a shifting iterated greedy algorithm, which constantly changes its search space to explore different solution spaces. Based on the specific characteristics of the problem, a hybrid scheduling approach that combines forward and backward scheduling, a step-by-step destruction and reconstruction operator, and three adaptive reconstructive methods that combine coarse-tuning and fine-tuning are proposed to explore the near-optimal solution. Through comprehensive computational comparison and statistical analysis, the results demonstrate that the proposed shifting iterated greedy algorithm performs significantly better in relative deviation index values at the same CPU running time. [ABSTRACT FROM AUTHOR]

Tourist trip design is a fast-growing area of research. Tourist interest, budget, travel style, safety, and the existence of travelers with special needs (for example, wheelchair accessibility) are some of the elements to consider for obtaining personalized routes. Including these elements in a single mathematical model can considerably complicate the solution process. Also, route decision-making is affected by the context (health, social, political, economic, etc.) in which decisions are made. In this paper, the first aim is to propose a three-step methodology to obtain contextualized solutions to a tourist trip design problem (TTDP) with time-dependent recommendation factors. The methodology consists of (1) providing a basic TTDP model that avoids the complexity of including contextual information, (2) obtaining a set of solutions to the problem using a Modeling to Generate Alternatives (MGA) approach, and (3) using a recently developed a posteriori method to include the contextual information through fuzzy propositions. The second aim of the paper is to evaluate three algorithmic strategies for the MGA step. Lastly, considering a context for people with mobility impairments, an example is solved using real data. The results show the usefulness of the proposed methodology in solving the TTDP with contextual information. • A tourist trip design problem with time-dependent recommendations factors is solved. • A methodology to obtain contextualized solutions is developed. • An accessibility context is modeled with fuzzy propositions. • Solutions are obtained by using the modeling-to-generate-alternatives approach. • Best solutions are suitable for the accessibility context. [ABSTRACT FROM AUTHOR]

Composite materials are widely used in the aerospace industry thanks to their lightweight along with high stiffness and strength. Automated tape placement (ATP) is an important automated process used for the fabrication of large composite structures. In ATP, the layup paths of contiguous tapes are not parallel along their lengths due to the complex contour of the mandrel, which eventually introduces gaps or overlaps between the edges of tapes. Overlaps or excessive gaps are highly undesirable as they will weaken the resulting composite member. To date, little research reveals the generation and evolution principles of placement gaps on curved mold surfaces. A better understanding of the principles would help to adjust the layup trajectories to eliminate the deposition errors and ensure the layup quality. In this paper, the evolution law of layup gaps on mold surfaces is presented at first. Then, a placement gap model is established to predict the value of gaps in the trajectory planning stage. The gap model has been validated on a series of mold surfaces. One application of this model is to optimize the placement trajectories for ATP. • The evolution law of layup gaps in the trajectory planning for ATP is presented. • A mathematical model is established to predict the value of layup gap along the placement trajectory. • The accuracy of the gap model is validated on a series of mold surfaces. • The gap model could be adopted to optimize the layup trajectories such that eliminating excessive gaps. [ABSTRACT FROM AUTHOR]

An improved understanding of the cascading structure of recycling isimportant for increasing resource productivity. The cascading theory, developed to analyze resource cascading, has two major dimensions; resource quality and resource lifetime. The latter is the only dimension for which a quantitative evaluation has been carried out in the previous research. In this study, we propose new tools to quantify both dimensions. These tools enable statistical estimation of the times of utilization of the material cascaded. The pre-circulation index (pre-CI) counts how many times the material has been utilized before consumption. For material in which quality deterioration is measurable largely on the basis of the number of utilization times, pre-CI can be an index of resource quality. The post-circulation index (post-CI) counts how many times the material will be utilized after consumption. The higher the number of utilization times, the longer the lifetimeof the material. Thus, post-CI can be an index of resource lifetime.Total-circulation index (TCI) is the sum of pre- and post-CIs. This can be an overall index of resource productivity. We apply the methodpresented herein to an analysis of the paper recycling system in Japan. Some important features of the CIs are demonstrated by the results; certain potential remains for further improvements in paper recycling in Japan. In the case that two products have the same utilizationrates, their pre-CIs can still differ according to the positions they occupy in the cascade. In the case that two recycling policies achieve the same size of primary raw material reduction, they can still differ in their impact to the whole cascade. By the method described herein, the CIs can represent the structure of a material cascade quantitatively and offer important knowledge by which to increase resource productivity. [ABSTRACT FROM AUTHOR]

• The mathematical model of the reachable domain of the contingency return trajectories. • Reachable domain calculation method of the contingency return trajectories based on interval analysis. • Parameter characteristic analysis of reachable domain. The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple and fast shape transformation method. This method is based on the Allen-Cahn (AC) partial differential equation and uses the edge stop function to constrain evolution. We use the operator splitting method to control the equation for splitting, and use the explicit Euler's method to solve the discrete equation. Based on the source shape and the target shape, our phase-field model can perform rapid shape transformation when the appropriate parameters are selected. In order to verify the feasibility of our proposed phase-field model, numerical experiments on shape transformation are carried out in two-dimensional and three-dimensional space. The results show that the established mathematical model can not only perform shape transformation between simple shapes, but also have a good effect on shape transformation between complex shapes. We also propose a numerical solution using the Crank-Nicolson numerical scheme to handle the model we introduced. This numerical scheme utilizes the multigrid method and Gauss-Seidel iteration for solving. The results of the numerical experiments demonstrate the effectiveness of this numerical method in handling shape transformations in three-dimensional space. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel deep neural model for Mathematical Expression Recognition (MER). The proposed model uses encoder–decoder transformer architecture that is supported by additional pre/post-processing modules, to recognize the image of mathematical formula and convert it to a well-formed language. A novel pre-processing module based on domain prior knowledge is proposed to generate random pads around the formula's image to create more efficient feature maps and keeps all the encoder neurons active during the training process. Also, a new post-processing module is developed which uses a sliding window to extract additional position-based information from the feature map, that is proved to be useful in the recognition process. The recurrent decoder module uses the combination of feature maps and the additional position-based information, which takes advantage of a soft attention mechanism, to extract the formula context into the LaTeX well-formed language. Finally, a novel Reinforcement Learning (RL) module processes the decoder output and tunes its results by sending proper feedbacks to the previous steps. The experimental results on im2latex-100k benchmark dataset indicate that each devised pre/post-processing as well as the RL refinement module has a positive effect on the performance of the proposed model. The results also demonstrate the higher accuracy of the proposed model compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper introduces a new, stochastic mathematical model for the crystallization of emulsion in dispersed media. The mathematical model reads as a stochastic partial differential equation by combining the heat energy equation and the nucleation theory with specified drift and diffusion. We show the existence and uniqueness of the solution of the model by using techniques of stochastic partial differential equations. Numerical experiments are drawn to support the theoretical results. Moreover, comparison of numerical results to experimental ones is provided. [ABSTRACT FROM AUTHOR]

• A model for edema growth coupled with degradation and drug delivery from a PLGA intravitreal implant is proposed. • The edema growth model can be fitted with respect to one parameter to match patient-specific data. • The proposed methodology can be used to provide insights into the pharmacokinetics of a dexamethasone PLGA implant. • The model presented provides a general framework for the study of problems in tissue growth in other contexts. In this paper, we introduce a mathematical model for the drug release from an intravitreal implant and the subsequent effect of the drug on the inflammation process of macular edema. Coupling the drug transport problem with the growth of the edema, we compare the numerical simulations with patient-specific medical images. We fit the model with respect to one parameter and match the retinal thickness observed in the patient. After the validation of the proposed model, we perform numerical experiments regarding patient-specific treatments. In particular, we analyze the drug concentration in the different sub-domains (e.g., the implant and the retina) and simulate the scenario of edema recurrence and implant re-injection. The proposed mathematical model has the potential to provide important insights into the use of intravitreal dexamethasone implants and the treatment of macular edema. [ABSTRACT FROM AUTHOR]

• In this article, an optimal evaluation of re-opening policies for COVID-19 is developed. • The method provides effective re-opening policies using agent-based models and the whale optimization algorithm. • Agent-based models simulate the transmission risk in scenarios that are impossible to evaluate in real conditions. • The whale optimization algorithm is used to find the best scenario where the lowest risk of infection is reached. • Experiments demonstrate that the proposed approach delivers realistic predictions to formulate re-opening policies. A new contagious disease or unidentified COVID-19 variants could provoke a new collapse in the global economy. Under such conditions, companies, factories, and organizations must adopt reopening policies that allow their operations to reduce economic effects. Effective reopening policies should be designed using mathematical models that emulate infection chains through individual interactions. In contrast to other modeling approaches, agent-based schemes represent a computational paradigm used to characterize the person-to-person interactions of individuals inside a system, providing accurate simulation results. To evaluate the optimal conditions for a reopening policy, authorities and decision-makers need to conduct an extensive number of simulations manually, with a high possibility of losing information and important details. For this reason, the integration of optimization and simulation of reopening policies could automatically find the realistic scenario under which the lowest risk of infection was attained. In this paper, the metaheuristic technique of the Whale Optimization Algorithm is used to find the solution with the minimal transmission risk produced by an agent-based model that emulates a hypothetical re-opening context. Our scheme finds the optimal results of different generical activation scenarios. The experimental results indicate that our approach delivers practical knowledge and essential estimations for identifying optimal re-opening strategies with the lowest transmission risk. [ABSTRACT FROM AUTHOR]

In this paper, a novel four-dimensional autonomous chaotic system based on memristive diode bridge is presented, and it consists of a simple linear oscillation and a memristor. According to the mathematical model of the system, the equilibrium point is analyzed, and the phase portraits, time-domain sequences, bifurcation diagrams and Lyapunov exponent spectrums are numerically simulated. The rich dynamical behavior of proposed system is investigated. It includes multistability, offset boosting and chaotic bursting. In addition, the circuit simulation and Field-Programmable Gate Array (FPGA) hardware experiment are carried out to verify the feasibility of the system. Then the application of proposed system in chaotic image encryption is presented. By carrying out some security performance analyses, we show that the proposed system has good security performance. • A memristor chaotic system with simple circuit structure is proposed. • The memristive chaotic system presented in this paper has rich dynamical behaviors. • The dynamical behavior of offset boosting and multi-stable is proposed. [ABSTRACT FROM AUTHOR]

Intelligent Reflection Surface (IRS) will be widely used in future communication system construction to reduce construction costs and improve coverage. However, IRS systems are generally equipped with controllers to receive wireless signal instructions, this increases the vulnerability of future communications. In this paper, we present an attack tactic to provide a way of thinking for the future defense deployment. At the beginning, the hacker cannot know the whole communication system, then it continuously attacks the IRS system, monitor the communication system, and sequentially learns new information about the system in each attacking round in order to attack more effectively in the next round. A two-layer optimal mathematical model is presented to describe the BS and the hacker's decision. And the two-layer optimization which is difficult to solve is transformed into a single layer linear optimization by using equivalent transformation and dual transformation. A series of mathematical experiments are used to test different scenarios applicable to different monitoring style, and verify that the tactic proposed in this paper can effectively interfere with the system. [ABSTRACT FROM AUTHOR]

Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana–Baleanu derivatives. Moreover, future behaviors of the disease are investigated by considering the fractal–fractional operators that are very effective in modeling the real-life phenomena by virtue of their memory effect. The basic properties and steady states are also obtained. The threshold parameter for determining the spread of the disease is computed. Numerical results are presented for each fractal-fractional-order operator. The results obtained in the paper show that the numerical schemes are effective for predicting and analyzing complex phenomena. [ABSTRACT FROM AUTHOR]

This paper presents a dynamical analysis of a tethered aerostat using a multibody simulation tool called SimscapeMultibody™. Tethered aerostats are lighter than air vehicles that float in the air and are connected to the ground through the tether. Atmospheric winds are a source of disturbance to the aerostat. The wind produces drag force that causes the aerostat to displace from its mean position. This phenomenon is called blow-by. Solving the mathematical model of the motion dynamics with time step is the conventional method used for simulating the flight dynamics of the aerostat. This paper discusses the application of Simscape Multibody™ for the three-degrees-of-freedom flight dynamic simulation of spherical tethered aerostat. Simscape Multibody™, an extension of MATLAB®/Simulink, is a multibody modeling tool in which physical bodies and their interactions have to be defined to simulate the dynamics. The mathematical model of the defined system is automatically generated by the SimscapeMultibody™ solver, and the system dynamics is simulated. The simulation of dynamics using multibody modeling tools provides high fidelity simulation for the tethered aerostats. [ABSTRACT FROM AUTHOR]

This paper is the second in a two-part series on the concavity-convexity of the distribution system security region (DSSR). In Part I, the concave-convex characteristics and mechanism of DSSR are revealed by observing many case grids. In Part II (this paper), the concave-convex principle of DSSR is revealed through mathematical deduction. Firstly, the relevant concepts of sub-regions are proposed, and a DSSR model based on the union of sub-regions is developed. Secondly, the concave-convex principle of DSSR is proposed. The proposed criteria show that the security region of a distribution system with a single load transfer path for each feeder is convex, while that with multiple load transfer paths for some feeders can be concave or convex. Thirdly, the proposed criteria are deduced mathematically. Fourthly, based on the criteria, a method is proposed to judge whether a DSSR is concave or convex. Fifthly, the proposed criteria and method are verified through several cases, and the DSSR concavity-convexity of real distribution systems in China is also analyzed. Finally, the applications of DSSR concavity-convexity are illustrated. This work lays a mathematical foundation for the research of the topological properties of DSSR and is also useful for the application of DSSR. • The DSSR mathematical model based on the union of sub-regions is developed. • Three criteria are proposed and proved, revealing the concave-convex principle of DSSR. • A judgment method for DSSR concavity-convexity is proposed based on these criteria. • The DSSR concavity-convexity of real distribution systems in China is analyzed. • The application values of DSSR concavity-convexity are demonstrated. [ABSTRACT FROM AUTHOR]

With the development of economic globalization, distributed hybrid flow shop scheduling problem (DHFSSP) has become prevalent in realistic manufacturing systems. Moreover, to accord with the actual production scenarios and satisfy the requirement of manufacturing market, it is imperative to comprehensively explore various complex manufacturing scenarios (e.g., production assembly) and production-constrained resources (e.g., worker resources) in DHFSSP. However, the integration mode of DHFSSP, assembly shop problem (ASP), and dual-resource constraints (DRC) has not been reported in existing literature. Thus, to fill out this research gap, this paper first attempts to investigate DAHFSSP-DRC with minimization the total tardiness (T T D). To solve this problem, a mixed-integer linear programming (MILP) model and a knowledge-based iterated greedy algorithm (KBIG) are presented. The novelties of KBIG are as follows: (1) An efficient decoding is developed to improve the solution's quality; (2) A knowledge-based NEH (KB-NEH) initialization strategy is presented to generate an initial solution; (3) A knowledge-based destruction and construction is designed to improve the exploration capability; (4) A product-based local search is proposed to enhance the exploitation capability. Additionally, to validate the proposed model, we implement CPLEX to solve it on 24 small-sized instances. To verify the effectiveness of the proposed KBIG, extensive experiments are conducted to compare with other 7 comparison algorithms on 405 large-sized instances. Experimental results illustrate that KBIG is superior to its competitors. • This paper first investigates DAHFSSP-DRC with minimization TTD. • A MILP model and a KBIG are proposed for DAHFSSP-DRC. • The importance level of different knowledge is considered in KBIG. • Experimental results prove the effectiveness of MILP model and KBIG. [ABSTRACT FROM AUTHOR]

In the modern era, mathematical modeling is a promising tool to evaluate the forward osmosis (FO) and pressure retarded osmosis (PRO) systems process feasibility and check the outcome of performance parameters on the overall process without running it. The FO process is an energy-efficient and cost-effective desalination technique, and the PRO process is a promising renewable energy method that can generate energy by allowing different saline solutions to pass through a semipermeable membrane. This review paper critically analyses various mathematical models for FO and PRO processes. The paper provides an initial overview of FO and PRO, such as their operating principles, challenges, and potential applications. Then, it presents a detailed analysis of different mathematical models proposed for FO and PRO, highlighting their strengths and weaknesses. The review covers theoretical and experimental models and discusses the role of parameters and variables in the modeling process. The paper concludes with a discussion on future research directions and the potential for improving FO and PRO through innovative mathematical modeling. This study helps researchers in chemical engineering, membrane science, and renewable energy fields and can serve as a valuable reference for future studies on FO and PRO models to enhance system efficiency. [Display omitted] • Provides an overview of FO and PRO, their operating principles, challenges, and applications • Discusses theoretical and experimental models in FO and PRO processes • Presents the role of parameters and variables in the modeling process • Analyzes the future research directions for improving FO and PRO modeling [ABSTRACT FROM AUTHOR]

• The model allocates safety stocks in supply chains at minimum cost. • An MIQCP reformulation with piecewise approximation greatly improves computational efficiency. • The piecewise function yields an improved estimation for the fill rates. • The GSM is extended to handle non-normally distributed demands. • Real-world case studies solved to optimality within few seconds of computational time. This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time. [ABSTRACT FROM AUTHOR]

Abstract: Sonics and space are two topics which are not commonly considered together. However, sonic and ultrasonic models, devices and systems have space applications in both science and engineering, as well as showing promise in fields such as cleaning, healthcare and construction. This short paper describes some of these activities and appears as results start to come in from the Curiosity rover, which landed on Mars on the 6th of August, 2012, with over 20 piezoelectric and mechanically-resonant components on board. [Copyright &y& Elsevier]

Abstract: This paper concerns the modelling of an accumulator used in industrial elastic web processing plant such as paper mills, fabric, rolling mills etc. Accumulators are used to allow rewind or unwind core changes while the process continues at a constant web velocity. A new nonlinear model of a pneumatic actuated industrial accumulator including pneumatic jack model, static friction representation and web weight is first detailed which enables to deduce a linear model. These models are derived from physical laws that describe web tension and velocity dynamics in each web span. In a second part, the effects of time-varying mechanical parameters, such as web Young modulus, web length and rollers inertia on accumulator dynamics are presented. The performances of the modeled accumulator are illustrated by simulations in Matlab/Simulink software environment. [Copyright &y& Elsevier]

Abstract: A multivariate data analysis of cavitation indicators and parameters was carried out to improve the quantitative characterization of cavitation processes used in manufacturing and medical applications. The indicators were obtained from four model measurement methods applied to a 45kHz cleaning vessel. Together with experimental data such as temperature and electrical input power they form the data basis of a factor analysis. The loadings of three factors were calculated and the indicators, the parameters, and finally the data were depicted in factor space. The factors show relations between the variables and several overlapping indicators and parameters were identified. The coordinates of the data (data scores) indicate tendencies within the data and the assessment of the factors allows the finding of hidden relations. Using the factor analysis three representing indicators or parameters specific to the application case are identified which can be used for a complete description of the process. This characterization method can favourably be applied in quality management systems. [Copyright &y& Elsevier]

Gaseous flames and pulverized coal flames are considered to examine relationships between lab-scale flames, semi-industrial scale and industrial-scale flames. The experimental data spans the thermal input range from the lowest scale of 30 kW to the largest of 12 MW with several intermediate scales. The primary questions are whether effects observed in lab-scale flames are scalable to industrial applications and whether mathematical models developed on the basis of lab-scale data are directly applicable to industrial flames. It has been observed that disparity between the in-flame temperatures measured in lab-scale and in large-scale flames can be as large as 100–200 K due to different measurement techniques used. In lab-scale experiments one observes a strong interaction between turbulence and chemistry and the measured data is sensitive to small alterations to burner inputs and/or boundary conditions. The sensitivity almost disappears at large-scales since the convective mixings is the dominant (the slowest) mechanism. In other words, different effects are seen at small- and large-scales and different mechanisms are controlling. Although the paper is concerned with single flames, in our opinion, the conclusions are also relevant to gas turbines. Until genuine efforts are taken to develop a good understanding of combustion system scaling, the worlds of combustion science and combustion engineering will remain parted. • Turbulence- chemistry interaction determines structure of lab-scale flames whilst convective mixing is the controlling mechanism in industrial flames. • CFD-based models developed and validated using lab-scale data have to be substantially modified and tuned to provide accurate predictions of industrial flames. • Until genuine efforts are taken to developed a good understanding of combustion system scaling, the worlds of combustion science and engineering will remain parted. [ABSTRACT FROM AUTHOR]

Absorption machines are frequently used for cooling and heating. However, they must be improved to achieve high performance at a lower cost. Being a key component of these machines, this paper focuses on the absorber and specifically on falling film absorber configuration due to its compactness and simple geometry. This paper reviews the different analytical and numerical approaches used to analyze the thermal, mass and hydrodynamic phenomena occurring in falling films for both smooth and wavy-laminar regimes. It shows the significant progress made since 2000 in terms of mathematical models developed and coupling effect resolution. Research using thermodynamics to identify, locate and quantify the entropy generation sources in falling film absorbers is also presented. [ABSTRACT FROM AUTHOR]

The paper considers the process of imbibition in a porous medium under the action of capillary forces in microgravity. A description of experiments on the repeated imbibition of an artificial porous medium during parabolic flights is given. In some experiments, the porous medium is homogeneous; in others, the experimental cell contains regions with different permeability. The analysis of non-stationary and convective terms in the equation of momentum conservation and their influence on the imbibition process is carried out. The results of numerical modeling of the process of repeated imbibition under the action of capillary forces under microgravity in an inhomogeneous porous medium are presented. The results of numerical modeling are compared with experimental data. • The paper considers the imbibition of fluid into a porous medium in microgravity. • The mathematical model that takes into account hysteresis is proposed. • The experimental results for various porous media are described. • The results of numerical modeling are compared with experimental data. [ABSTRACT FROM AUTHOR]

• Determining the urban critical infrastructures in the event of an earthquake. • Designing Location-Routing-Inventory decisions in humanitarian relief chain. • Simulation of interaction of urban infrastructure in earthquake conditions. • Using a cooperative game to examine the manner of cooperation of disaster relief supply chain players. • Application of the model to a real-world disaster relief logistic case study. This paper describes a new simulation based mathematical model for locating distribution centres, vehicle routing, and inventory problems under earthquake conditions. In this paper, the proposed network includes affected areas, suppliers, distribution centres, and hospitals. Additionally, the basic infrastructures of the city, which are very fragile at the time of the earthquake, are identified. Then, the demand of each relief commodity is calculated depending on the different earthquake scenarios using simulation. The estimated demand is incorporated into the mathematical model as an uncertain parameter. The proposed methodology is designed as a two-stage model so that in the first stage the location and inventory of distribution centres are addressed. Thereafter, in the second stage the routing decisions are taken for the distribution of relief commodities from the distribution centres and suppliers to the affected areas. Due to the NP-hardness of the second stage model, this model is solved using multi-objective stochastic fractal search. This algorithm is one of the population-based and stochastic optimization techniques and inspired by the natural phenomenon of fractal growth. It should be noted that in the second stage, a cooperative game theory of coalition type is considered, which resulted in synergies that minimize the relief golden time. The kind of cooperation is the use of potential of co-operators' vehicle. In this stage, the possibility for the players to cooperate by sharing people and commodities transportation requests is considered. Also, to validate the model, a real case study is provided for a possible earthquake in Tehran. Finally, the comparison between the simulation results and the values obtained from the real system evaluates the performance of the implemented model. Considering normality and a 95% confidence interval, it can be concluded that the proposed model provides a precise representation of the real system's performance. [ABSTRACT FROM AUTHOR]

Renewable powered dc microgrid is more cost-effective, simple, reliable, highly efficient, and scalable than the traditional electric grid. This paper provides an overview of high gain dc converter topologies for dc microgrids. This research's primary objective is to impart a unique extensive, comparative, and perceptive analysis in high gain converter configurations. The most recently reported research articles are considered for discussion in this paper. Initially, based on the structural configurations, the converters are segregated and are grouped into four categories, such as Replacement, Reduced Redundant Power Processing (R2P2), Incorporation, Integration (R2I2) techniques. Secondly, based on the dynamic and steady-state analysis, the topological converter configurations are comparatively analyzed. A few topologies' mathematical modeling is also discussed to obtain a comprehensive insight into the converter's dynamic behavior. An extensive analysis, comparisons, and assessment of these converters with diverse configurations are acquainted with tables and figures are presented for choosing an appropriate converter suitable for dc grid application. The pros and cons of the topology derivation under each categorization are presented for benefitting the researchers in selecting the topological configuration method. In the end, the comparison results of the high gain converter clusters are summarized, and recommendations are given, which leads to the guidelines for selecting a significant high gain topology for a specific application. Furthermore, the constraints considered for topology derivation with the type of analysis carried out are presented. This gives a way to find the scope for future research under this area which is finally offered. This study will also provide an insight into the derivation of several configurations of the novel high gain dc-dc converter in the field of dc microgrid. [ABSTRACT FROM AUTHOR]

Abstract: The possibility to develop an absolute technique, independent from the paper conservation conditions, to date recent paper documents (i.e. less than 50 years old) for forensics purposes is discussed. We suggest the possibility to use the curve representing the strong increase in the atmospheric radiocarbon concentration induced in the last 50 years by nuclear weapons tests as reference to date paper documents, with a resolution down to a few months. The results obtained in the analysis of two known age documents are presented together with a first order mathematical model developed in order to take into account the contributions of the different tree rings employed in the paper production. [Copyright &y& Elsevier]

The recent outbreak of rabies virus has affected numerous individuals in the community, highlighting the importance of studying the disease mathematically in epidemiology. In this paper, we develop a mathematical model for the spread of rabies disease using the harmonic mean incidence rate and determine the reproduction number R 0 using the next generation matrix approach. The fractional dynamics of the model incorporate the interaction between infected individuals and environmental factors. We analyze the model using both Atangana-Baleanu-Caputo (ABC) and Caputo-Fabrizio (CF) techniques, drawing on both modern and classical approaches. For qualitative investigation using fractional operators, we utilize the Banach fixed-point theory and derive the Hyers-Ulam stability concept. We assign values to the model parameters and utilize the Newton interpolation technique to obtain a numerical scheme. Additionally, we perform sensitivity analysis on the model. In conclusion, our findings provide important insights for the study of epidemics. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization and set point tracking of the utility boiler is achieved via the Proportional-Integral-Derivative (PID) controller, tuned using the versions of metaheuristic Particle Swarm Optimization (PSO) algorithms. The utility boiler model dynamics are based on the Bell and Astrom boiler turbine system. Initially, the non-linear mathematical model is obtained using the first principles data from the plant model. Further, Taylor series approximation is applied to linearize the non-linear equations around the equilibrium point to implement a stable controller for the plant. Finally, the PID controller gains for the plant model are determined using the PSO algorithms to achieve the desired response. For tuning the PID controller, three PSO algorithms namely standard PSO, Adaptive PSO (APSO) and Improved Adaptive PSO (IAPSO) are proposed. The performance of the proposed PSO based PID control algorithms are evaluated using error metrics such as Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE) and Integral Square Error (ISE). The simulation results show that the proposed APSO and IAPSO algorithms have improved performance when compared to regular PSO algorithms and are capable of optimizing the control parameters. [ABSTRACT FROM AUTHOR]

Magnetic localization techniques are used in in vivo therapy, drug delivery, and surgical localization widely due to their ability to locate in an unobstructed environment precisely. The Levenberg-Marquardt (L-M) algorithm is one of the most common magnetic localization algorithms due to its fast optimization speed and high precision, but it requires high initial values such that improper initial values can easily lead to local optimization. In this paper, the performance of ten commonly used intelligent optimization algorithms is compared based on the mathematical model of the permanent magnet. The final position of the magnet is obtained by a fusion algorithm that uses the result of the intelligent optimization algorithm as the initial value of L-M. The real-time localization accuracy of this fusion algorithm is verified on a hardware platform and experiments demonstrate that the integration of the TSA algorithm and L-M algorithm fusion yields higher performance of the magnetic positioning system. [ABSTRACT FROM AUTHOR]

In this paper, wave power extraction from a floating Clam-type wave energy converter is investigated. The device is mainly composed of a Clam, which is formed from two pieces of floating flaps hinged at a submerged body. The Clam is closed by a flexible impermeable bag with the two hinged floating flaps kept apart by a Power Take-Off system. As waves propagate through the device, the Clam motion of the device is excited, which can be used to drive the Power Take-Off system to capture wave power. To evaluate the response and also the wave power absorption of the device, a mathematical model is developed based on the linear potential flow theory, in which a generalised mode method is adopted to model the Clam action. Theoretical expressions of the maximum wave power absorption and the corresponding optimised Power Take-Off system and mooring parameters are derived. Good agreement between the present numerical results of the device response and the physical observations is obtained. The validated model is then applied to do a series of case studies. It is revealed that the optimised Power Take-Off stiffness and mooring stiffness are independent of the Power Take-Off damping. The maximum wave power absorption can be achieved when the device is fixed in heave mode or free-floating without any constraints from the mooring system. • We developed a mathematical model to study the performance of a Clam-type device. • A generalised mode method was adopted to model the Clam action. • We derived the expressions of the maximum wave power output and the optimised PTO. • The numerical results agree well with the corresponding measured physical data. The optimised PTO stiffness and mooring stiffness are independent of the PTO damping. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the stability of hydro-turbine governing system (HTGS) with sloping ceiling tailrace tunnel (SCTT) and upstream surge tank (UST) considering nonlinear hydro-turbine characteristics (NHTCs). Firstly, the mathematical model of HTGS is presented based on nonlinear seventh-order state equation, which is verified by example analysis so as to study the stability of HTGS. Subsequently, the effect of HTGS parameters on the stability of the system is investigated with numerical simulation. Finally, the coupling effect mechanism of SCTT and UST on stability under the effect of NHTCs is revealed by using contrastive analysis. The results are summarized as follows: (1) T a , K d and T wt perform larger effect on the stability of HTGS, while the influence of F and T wy is mild; (2) the NHTCs are beneficial under negative load disturbance and unfavorable under positive load disturbance for the stability and dynamic performance of HTGS; (3) the coupling effect of SCTT and UST outperforms the results of SCTT or UST alone under all load disturbances; (4) the incorporation of UST to the established model plays a certain role in stability compensation, while the introduction of SCTT not only improves the stability but also achieves smaller amplitude and lower frequency. [ABSTRACT FROM AUTHOR]

Some interest has been recently directed towards analytic mathematical models for reproducing the current–voltage (I–V) characteristics of solar cells, mainly due to their convenient property of expressing current as an explicit function of voltage (which is not true for the traditional one-diode model). However, as is the case with the one-diode model itself, existing analytic models do not yield a good fit in the case of S-shaped I–V characteristics. In this brief paper, an analytic explicit model based on a three-piece quadratic curve is proposed that surpasses such difficulty and enables accurate representation of S-shaped curves. To evaluate the proposed model, validation was carried out against three empirical solar cell I–V characteristics. In all cases, simulation results show that the proposed approach is more accurate than other closed-form models in the literature. • Fully analytic mathematical model for S-shaped I–V characteristics. • Piecewise quadratic nature ensures high mathematical tractability. • Parameter extraction via closed-form equations. • Over 60% reduction in RMSE compared to previous model. • The maximum power point is fitted with zero error. [ABSTRACT FROM AUTHOR]

Within-host models describe the dynamics of immune cells when encountering a pathogen, and how these dynamics can lead to an individual-specific immune response. This systematic review aims to summarize which within-host methodology has been used to study and quantify antibody kinetics after infection or vaccination. In particular, we focus on data-driven and theory-driven mechanistic models. PubMed and Web of Science databases were used to identify eligible papers published until May 2022. Eligible publications included those studying mathematical models that measure antibody kinetics as the primary outcome (ranging from phenomenological to mechanistic models). We identified 78 eligible publications, of which 8 relied on an Ordinary Differential Equations (ODEs)-based modelling approach to describe antibody kinetics after vaccination, and 12 studies used such models in the context of humoral immunity induced by natural infection. Mechanistic modeling studies were summarized in terms of type of study, sample size, measurements collected, antibody half-life, compartments and parameters included, inferential or analytical method, and model selection. Despite the importance of investigating antibody kinetics and underlying mechanisms of (waning of) the humoral immunity, few publications explicitly account for this in a mathematical model. In particular, most research focuses on phenomenological rather than mechanistic models. The limited information on the age groups or other risk factors that might impact antibody kinetics, as well as a lack of experimental or observational data remain important concerns regarding the interpretation of mathematical modeling results. We reviewed the similarities between the kinetics following vaccination and infection, emphasising that it may be worth translating some features from one setting to another. However, we also stress that some biological mechanisms need to be distinguished. We found that data-driven mechanistic models tend to be more simplistic, and theory-driven approaches lack representative data to validate model results. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of the vane chattering phenomenon through measurements of the instantaneous working chamber pressure of the multi-vane Revolving Vane (RV) compressor. The paper presents the prototype design, measurement setup, and processing of the recorded data to support the phenomenon. The analysis confirmed that the vane chattering was originated by the two free vanes which were detached and re-collided with the cylinder inner wall repeatedly during the course of compressor operation in the 60°–135° and 190°–255° angular position regions, respectively. Reasons of vane chattering have been hypothesized through the data collected and further verified with the mathematical model describing the dynamic behaviour of the free vanes. [ABSTRACT FROM AUTHOR]

With the increase in solar energy penetration in electric power systems, it is necessary to predict future solar radiation. With this, the solar power generation capacity can be predicted, allowing accurate scheduling for other sources. The solar radiation or the clearness index (CI) prediction was already presented using classical time series methods, artificial intelligence algorithms, among other approaches. In this paper, two methods are proposed to predict the CI. The first one solves a stochastic realization problem to find a mathematical model for the stochastic process that describes the CI. Then, a state observer is implemented to predict its future values. The second one performs the k-Nearest Neighbors (k -NN) regression algorithm for time series forecasting using two different approaches: the traditional k -NN and a recursive version proposed by the authors. As far as the authors know, the statistical and the recursive k -NN methods are different from the ones found in the literature to predict the CI. The methods were implemented and compared for short and long-term predictions. The results illustrate that one approach is more accurate than the other, depending on the prediction horizon. The comparison between the methods for different horizons is another contribution of this paper. • Statistical and AI algorithms were implemented to forecast the Clearness Index. • The statistical algorithm is based on state space stochastic realization theory. • The AI algorithm is the k-NN, implemented in two different versions. • The algorithms were compared for short and long term predictions. [ABSTRACT FROM AUTHOR]

• A mathematical modelling approach is proposed to predict the matching probability and the expected ride/shared distance of each ridepooling order. • The model explains the complex mechanism that determines the matching probability of each OD pair. • The model generates fairly good predictions under diverse matching conditions and demand intensities. The popularity of smartphones and the advent of GPS positioning and wireless communication technologies in the recent decade have facilitated large-scale implementations of dynamic ridepooling services, such as Uber Pool, Lyft Line, and Didi Pinche. As in such services trips usually start before the appearance of pooling partners, knowing the probability of getting matching with another order (i.e., matching probability), the expected detour distance, and the expected shared distance before the start of each trip is essential for passengers to evaluate their willingness to pool and for ridepooling platforms to offer attractive discounts. In this paper, assuming that every ridepooling passenger shares vehicle space with at most one another during the entire trip, and ridepooling orders in each (origin-destination) OD pair appear following a Poisson process with a given rate, we propose a mathematical modeling approach to predict the matching probability, the expected ride distance, and the expected shared distance of each order under a first-come-first-serve strategy in dynamic ridepooling service. The method defines unmatched passengers at different locations along the exclusive-riding path of each OD pair into different seeker- and taker-states, formulates the complex interdependency of the matching probabilities, matching rates and arrival rates of (unmatched) passengers in different states into a system of nonlinear equations, and generates the matching probabilities and expected ride/shared distances of all OD pairs simultaneously. Under the same first-come-first-serve strategy, we simulated the occurrence, movements and state transitions of ridepooling orders based on a 30*30 grid network and the real network of Haikou City in China. In comparison with simulation results, we show that the method proposed in this paper can generate fairly satisfactory predictions under diverse matching conditions and demand intensities. [ABSTRACT FROM AUTHOR]

Achieving precision in the prediction of buildings' dynamic heat load is crucial for the advancement of smart heating systems. This research highlights the urgent need to enhance the accuracy of models predicting dynamic heat load. Through literature review, distinguished machine learning and regression algorithms were chosen to formulate prediction models. These models employ a data time-step adaptive strategy, a physics-guided loss function, and fundamental principles of heat transfer. Optimization algorithms of a mathematical nature were utilized to fine-tune the parameters and the framework of long short-term memory (LSTM) and multi-layer perceptron (MLP) models. An analytical comparison was undertaken between physics-guided models and those not guided by physics. Principal conclusions are: 1) Pelican optimization algorithm (POA)-LSTM model emerges as superior in heat load prediction accuracy of an office building, with percentage errors for actual and simulated datasets ranging from −6.7 % to 5.8 % and −5.2 %–4.5 %, respectively, and the mean absolute percentage error (MAPE) standing at 2.3 % and 1.3 %. 2) The linear regression model exhibits the lowest precision, with a MAPE of 17.5 % and 4.0 % for the 7-day prediction results in the actual and simulated datasets, respectively. These findings provide support for improving heat load prediction in heating systems. • The authors have implemented a total of 20 physically-guided models for predicting building thermal load, among which the POA-LSTM model demonstrates the highest accuracy. • The disparities in thermal load prediction accuracy between the physically-guided machine learning models and the physically-guided mathematical regression models have been identified. • The accuracy of thermal load prediction was compared between the five physical guidance models proposed in this paper and the five non-physical guidance models mentioned in other papers. [ABSTRACT FROM AUTHOR]

The problem of motion of coupled harmonic oscillators can be modeled in the terms of system of ordinary differential equations (SODEs). In the present paper, authors used Sawi transformation for finding the solution of SODEs with application to determine the concentration of chemical reactants of chemical reaction in series. Authors have considered four numerical problems and determined their solutions step by step for explaining the complete method. After it, authors have taken a problem of physical chemistry for determining the concentration of chemical reactants (substances) of chemical reaction in series. Authors have obtained the solution of this problem by developing its mathematical model in terms of SODEs and then applying Sawi transformation on it. Results of this problem are visualized using tables and graphs. Results of the present paper show that the Sawi transformation provides us the exact solution of SODEs without large computational work. [ABSTRACT FROM AUTHOR]

In an integrated electricity-gas system (IEGS), gas-fired units with flexibility response capabilities address the uncertainty associated with renewable energy by swiftly adapting their output, which may result in uncertain fluctuations in the gas withdrawal of gas-fired units, potentially posing risks to the security of IEGS. Hence, it is necessary to efficiently evaluate the dynamic security region (DSR) of natural gas systems in IEGS by considering the real-time dynamic characteristics of natural gas systems, which are not satisfactorily handled in state-of-the-art works. To bridge this gap, this paper first conceptionally verifies the necessity of the DSR and establishes its mathematical model. Then, a dimensionality reduction method is proposed for the efficient solution and visualization of the high-dimensional DSR evaluation model. A fast evaluation (FE) algorithm is developed to address the difficulties of the nonconvex dynamic constraints in the reduced DSR model. Finally, the necessity and notable advantages of the proposed DSR model and FE are verified based on small and relatively large test systems in comparison with common security region models and algorithms. To the best of our knowledge, this is the first paper that comprehensively presents models and efficient algorithms regarding the DSR of natural gas systems in IEGS. • This paper proposes the novel dynamic security region (DSR) of the natural gas system with natural gas system dynamics. • A dimensionality reduction method for the efficient solution and visualization of the high-dimensional DSR is proposed. • A fast evaluation (FE) algorithm is developed to address the nonconvex dynamic constraints in the DSR model. • Case studies confirm the necessity and effectiveness of the DSR, dimensionality reduction method, and FE. [ABSTRACT FROM AUTHOR]

Urban building layout has an important influence on the formation of shadows on building façades, and photovoltaic (PV) power generation performance is greatly affected by shadows. However, there is limited research on detailed modeling of the power generation of photovoltaic systems on facades with different building layouts. In this paper, according to different urban building layouts, an annual dynamic shadow model of the building and a mathematical model of PV array power generation were established and validated. Then the model was used to calculate the annual power generation hour by hour, optimize the PV array topology, and analyze the shadow shading ratio and PV power generation performance of different building layouts. The results show that 95 % of the best topologies of all partially shaded façades in the four layouts are Total-Cross-Tied (Vertical and Horizontal); the highest annual shading ratio is layout 4 with a value of 60.161 %, the largest annual power generation is layout 3, but layout 4 has the highest broad generation efficiency, with layouts 1, 2, and 3 lower than it by 4.29 %, 0.20 %, and 0.11 %, respectively. This paper provides new ideas for the early design of building layouts and the performance research of PV systems. • Yearly dynamic shadow and detailed PV models developed for urban layouts. • Optimized PV topologies under year-round dynamic shading. • 95 % optimal topologies are Total-Cross-Tied (Vertical and Horizontal). • Compared annual PV output and broad efficiency across building layouts. • Layout 4 excels in broad generation efficiency, leading by 4.29 %. [ABSTRACT FROM AUTHOR]

Grey prediction evolutionary algorithm (GPE) is an emerging category of meta-heuristic algorithm based on mathematical model. It generates offspring by predicting the macroscopic evolutionary trend of population series. On the contrary, the mining of local evolutionary trend are flawed. To address this imperfection, this paper introduces a quadratic function as a surrogate model to mine the local evolutionary trend of population series for the first time. Thereby an improved grey prediction evolutionary algorithm called grey prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (GPE-QI) is designed. The surrogate model based on quadratic interpolation is regarded as an external auxiliary tool to mine the local evolutionary trend of population series by using currently superior individuals. Through utilizing the mined local trend information, a donor population closer to the optimal solution is formed to improve the prediction direction of the algorithm. The performance of GPE-QI is tested on CEC2019, CEC2020 benchmark functions and six engineering design problems. The experimental results demonstrate the stronger competitiveness of GPE-QI to well-established algorithms in terms of solving accuracy and convergence rate. If this paper is accepted, MATLAB codes associated with this paper will be uploaded to https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE. • Improvement can be made by enhancing local search of grey prediction evolution. • Mine local evolutionary trend of population series by quadratic interpolation. • Construct a surrogate model by using the local evolutionary trend. • Design an improved grey prediction evolutionary algorithm with a surrogate model. • The proposed algorithm is more competitive than the well-established. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) power generation has become one of the key technologies to reach energy-saving and carbon reduction targets. However, dust accumulation will significantly affect the electrical, optical, and thermal performance of PV panels and cause some energy loss. For this reason, appropriate cleaning measures are needed to restore their performance and power output. Many researchers have reviewed the effects of dust on the performance of PV panels and cleaning methods, but their coverage is narrow and lacks more in-depth summarization, comparison, and critique of key quantitative results. Using the Web of Science database as the main search source, this paper provides a comprehensive overview of research results on the mechanisms and influencing factors of dust deposition on photovoltaic panels, photovoltaic performance loss and prediction models, cleaning methods, and dirt monitoring systems. The results found that the module power output degradation due to dust deposition is more serious in different regions, ranging from 7% to 98.13%. The automatic cleaning robot, as an emerging intelligent technology, has a better cleaning effect and can increase PV efficiency by up to 49.53%. This paper also proposes a comprehensive strategy for dust prevention on PV panels that integrates "real-time monitoring of dust accumulation - model prediction of losses - and optimization of cleaning solutions", emphasises the development of new intelligent cleaning methods represented by robots and drone cleaning, and suggests promoting the application of AI in the monitoring and cleaning of PV modules to accelerate the process of achieving carbon neutrality. [ABSTRACT FROM AUTHOR]

Periodic cleaning of photovoltaic (PV) panels, such as every three months, is a common industry practice. However, this fixed period may not be optimal for maximizing the profit of a PV power generation system, due to numerous time-variant influencing factors, such as weather, temperature, etc. To increase the overall profit of a solar farm, it is highly desirable to have a flexible cleaning schedule that considers time-variant influencing factors. For this requirement, a rolling-horizon cleaning recommendation system is presented in this paper. Within this cleaning recommendation system, a prediction model and profit model are proposed. The prediction model, called the ensemble long-term and nonlinear autoregressive, can provide a time-variant future horizon by analyzing and compressing the time-variant characteristics in historical information. The profit model based on mathematical constraints, can process time-variant future horizon output from prediction model to generate a flexible optimized recommendation for cleaning schedule. The effectiveness of the proposed system is validated in real farms and all data used in this paper is collected from real world. The two case studies in experiments show that the profit improvement can reach up to 6% and 30%, respectively. [Display omitted] • A rolling-horizon cleaning recommendation system for PV panels. • A novel long-term and nonlinear predictive method. • A concise profit model for easy deployment in industry. • Flexible cleaning schedule considering time-variant characteristics. • Improvements of 6% and 30% in two different real farms, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we address modelling and simulation of dynamics involved in docking of large marine vessels with aid of tugboats, with the aim of providing a tool for improved design of control algorithms for autonomous docking operations. Mathematical models of the docking vessel and tugboats in 3DOF are derived, with a special focus on realistic interactions through towline, contact and friction forces with stick–slip dynamics and time delays, which are typically not considered in previous publications on the topic. We also present the implementation of the developed models in the first step towards a Simulink simulator in which considers the special case of tugboat-assisted docking operations in the Narvik harbour. The developed simulator is available on GitHub (see Ørke et al. (2023)) and encompasses model dynamics, tugboat control and vessel control and guidance, although the scope of this paper is model dynamics. We present simulation results that show that we are indeed able to capture interaction dynamics in a realistic way. Finally, we include a discussion of our results and some ideas for further development, as well as some concluding remarks. [Display omitted] • Mathematical modelling of docking vessel and tugboats in 3DOF. • Modelling of interaction forces in pushing/pulling operations. • Model implementation in Simulink-developed simulator. • Simulation and discussion of interaction forces, and ideas for future work. [ABSTRACT FROM AUTHOR]

In this paper the aerothermal heating of a reusable launch vehicle is reconstructed on the basis of temperature measurements taken in the thermal protection system of this vehicle. The discussed integrated thermal protection system is composed of three layers. Mathematical model, describing the problem, takes into account the dependence on temperature of the material parameters as well as the thermal resistances occurring in the contact zones of the layers, which is a novelty in the proposed approach. For solving the direct problem, the implicit scheme of the finite difference method is applied. Next, by using the solution of the direct problem, the Tikhonov functional is created, which describes the error of the current approximate solution. Whereas for determining the solution of the inverse problem the Levenberg-Marquardt method, modified and adapted to the Tikhonov functional, is used. The paper presents the mathematical model of the problem and the method of solution together with the selected examples illustrating its exactness and stability. In order to better examination of the solution method some various values of parameters are taken in the demonstrated examples. • Reconstructing an aerothermal heating in space vehicle protection system with temperature dependent material properties. • Reconstructing an aerothermal heating taking into account the thermal resistance between layers. • Solving the problem for three layers model of the thermal protection system. • Inverse problem solved for input data taken from NASA measurements. • Heat flux measured by NASA reconstructed with good precision and stability. [ABSTRACT FROM AUTHOR]

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