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Abstract: A wide range of mathematical models for multiple effect evaporators in process industry including paper industry are well reported in the literature but not so extensive work on the dynamic behavior of MEE system is available in the literature. In the present study dynamic behavior of multi-effect evaporator system of a paper industry is obtained by disturbing the feed flow rate, feed concentration, live steam temperature and feed temperature. For this purpose an unsteady-state model for the multi-effect evaporator system is developed. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow. A generalized mathematical model which could be applied to any number of effects and all kinds of feeding arrangements like forward feed, backward feed, mixed feed and spilt feed in the MEE system with simple modifications was finally obtained. Finally model for mixed feed sextuple effect falling film evaporators system was solved using MATLAB. For the steady state and dynamic simulation the ‘fsolve’ and ‘ode45’ solvers in MATLAB source code is used respectively. [Copyright &y& Elsevier]

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract: In this work we present a mathematical model describing the coupled heat and moisture transport in paper. The model is solved numerically and the numerical solution is used to study the interdependency of the moisture and temperature distribution in paper. The results show that variation with temperature of the saturated water vapor concentration and the sorption isotherm parameters are both important for inducing moisture desorption. It is also found that for steep relative humidity ramps moisture sorption generates temperature increments that slow down the sorption process itself. The model is also used to study the moisture gradients in a paper sheet inside a printer from Océ Technologies, which contains a warm print surface. The results predict changes in moisture content of only 0.2%, which suggests that no deformations are induced on the printed sheet. [Copyright &y& Elsevier]

Abstract: Availability analysis has been an important issue in the design field of any Industrial system as the system structure has become more complicated. Also, the system availability is affected by many factors such as design, manufacturing, installation, etc., and so it may be extremely difficult to model, analyze and predict the failure behavior of the system. The purpose of this paper is to develop a new approach for computing various performance measures, namely reliability, availability, MTBF (mean time between failures), ENOF (expected number of failures), failure rate and repair time, for any industrial system. In the proposed approach, the failure rates and repair times of all constituent components are obtained using genetic algorithms and then various performance measures are computed using fuzzy lambda–tau methodology. Washing system, the major part of paper industry is the subject of study. The interactions among the working components are modeled using Petri nets. Failure and repair rates are represented using triangular fuzzy numbers as they allow expert opinion, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into system model. Based on calculated reliability parameters, a structured framework has been developed that may help the maintenance engineers to analyze and predict the system behavior. [Copyright &y& Elsevier]

Abstract: Using advanced machine learning techniques as an alternative to conventional double-entry volume equations, a regression model of the inside-bark volume (dependent variable) for standing Eucalyptus globulus trunks (or main stems) has been built as a function of the following three independent variables: age, height and outside-bark diameter at breast height (DBH). The experimental observed data (age, height, outside-bark DBH and inside-bark volume) for 142 trees (E. globulus) were measured and a nonlinear model was built using a data-mining methodology based on support vector machines (SVM) and multilayer perceptron networks (MLP) for regression problems. Coefficients of determination and Furnival’s indices indicate the superiority of the SVM with a radial kernel over the allometric regression models and the MLP. [Copyright &y& Elsevier]

• A mathematical model for inverse kinematics and shape modeling of continuum robots is presented. • The inverse kinematics algorithm performs very well in the accuracy and efficiency by simulation. • Shape modeling of continuum robots is verified by prototype experiment. A mathematical model for the inverse kinematics and shape modeling of continuum robots is presented in this paper. This method simplifies the forward kinematics derivation process by introducing a rotation axis. In the inverse kinematics solution, an iterative approach is employed to try different initial values, and the optimal initial value is obtained by computing the condition number of the Jacobian matrix. Simulation experiments are verified that optimized initial values can effectively enhance the efficiency of inverse kinematics solution. Based on the Euler-Bernoulli beam theory, the shape modeling of continuum robots is derived, and the mathematical model of the relationship between robot shape and end loads is established. Finally, the mathematical model is verified through prototype experiments, demonstrating that the established shape modeling can achieve accurate simulation of deformation within a range where the bending angle is less than 90°, with errors within 10 %. [ABSTRACT FROM AUTHOR]

The mealybug (Paracoccus marginatus) is one of the most important pests of papaya (Carica papaya L.). The high potential damage of this pest threatens papaya production. The objective of this paper is to explore the impact of biocontrol and temperature variations on the population dynamics of Paracoccus marginatus (P. marginatus). We first propose and study a mathematical model for the dynamics of P. marginatus within a papaya field. This model consists of a time-delayed non-autonomous system of differential equations that takes into account the egg incubation period, temperature variations, plant compensation and predators that are natural enemies of the papaya pest. We provide the basic properties of the model, compute the basic offspring number N 0 and show that there exists two threshold parameters N _ 0 and ξ 0 such that N _ 0 ≤ N 0 ≤ ξ 0 ≤ 1 and N 0 ≥ N _ 0 > 1 provide conditions for the extinction and persistence of the pest within the papaya field, respectively. After, we investigate the impact of biocontrol on the pest population. We found that the use of a control strategy based on constant releases of predators could reduce the pest population by 35.62 percent and increase the biomass by 77.50 percent, while the use of impulsive releases of predators result in a decrease of 96.31 percent of the pest population and an increases of 55.74 percent of the biomass. We also combine the use of continuous predator releases and bio-pesticides and discovered that a spray applied 90 days after germination could completely eliminate the pest population and boost the biomass by 81.58 percent. • The population dynamics of Paracoccus marginatus , papaya pest is modeled. • The model includes the egg incubation period, temperature variations and biocontrol. • The warm temperatures are favorable to the development and survival of the pest. • The use of impulsive releases of predators can reduce the pest by 96.31%. • The use of continuous releases of predators and bio-pesticides can eradicate the pest. [ABSTRACT FROM AUTHOR]

• Reviews the mathematics of the EOQ/EPQ-based reverse logistics models. • It provides a condensed review of the works that stemmed from the work of Schrady (1967). • It identifies significant research gaps and provides future research directions. This paper reviews the mathematics of the economic order/production quantity (EOQ/EPQ)-based models in the reverse logistics (RL) literature. It starts with the seminal work of Schrady (A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, 14(3), 1967, 391–398) up until December 31, 2022. It provides researchers with a road map of how the mathematics has evolved since the work of Schrady and saves them time and effort by avoiding the need to review the entire RL literature. As it unifies the notations for all reviewed models, it also provides some research pointers for promising topics to be pursued. [ABSTRACT FROM AUTHOR]

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]

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference. • Simple multiscroll chaotic system with various signal control features is proposed. • Complex dynamics, circuit implementation of the proposed system is studied. • New chaos-based image encryption algorithm with high security is designed. [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]

• 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]

• 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]

• Mathematical model to describe drug delivery to the posterior segment of the eye. • Efficacy of intravitreal (IVI), suprachoroidal (SCS) and subretinal (SRS) injections enhanced by iontophoresis. • Protocols based on the use of a series of electric pulses at fixed times, can lead to an optimized SRS or SCS release. • In case of choroidal, retinal or vitreous diseases, SRS injection is the right option. Drug and gene delivery to the eye, namely to the posterior segment of the eye, is one of the most challenging problems for ophthalmologists and pharmacologists. The reason lies in the fact that the eye is protected by multiple barriers that prevent the permeation of xenobiotics and consequently prevent drugs from permeating ocular tissues. Intravitreal injection (IVI), a procedure that releases the drug directly into the vitreous, has become the gold standard for the treatment of posterior diseases. However, due to its invasiveness, several complications can occur. Medical and pharmaceutical researchers are continuously looking for new compounds, new access routes and new ways of enhancing the release. In recent years, two less invasive routes, subretinal space (SRS) and suprachoroidal space (SCS), have received considerable attention, to target the posterior segment of the eye. The aim of the paper is to present a mathematical model that simulates the coupling of an electric field with SRS or SCS injections, and to show how drug distribution compares with the gold standard, IVI. The model is represented by coupled systems of parabolic and elliptic partial differential equations. The ocular barriers are described with a certain detail. A priori estimates establish qualitative properties of the total mass released. Numerical simulations, in different scenarios, illustrate the comparative behaviour of the three treatments for short and long times. The evolution of mean drug concentration in the different ocular tissues, with and without electrical assistance, is studied. [ABSTRACT FROM AUTHOR]

• A truly meshless method is extended in this paper for solving coupled bedload sediment transport equations. • The method can solve problems which their domains discretized by irregularly distributed nodes , and shows good accuracy. • The method is applicable to cope with complex geometry in practical problems. The discrete least squares meshless (DLSM) method is extended in this paper for solving coupled bedload sediment transport equations. The mathematical formulation of this model consists of shallow water equations for the hydrodynamical component and an Exner equation expressing sediment continuity for the bedload transport. This method uses the moving least squares (MLS) function approximation to construct the shape functions and the minimizing least squares functional method to discretize the system of equations. The method can be viewed as a truly meshless method as it does not need any mesh for both field variable approximation and the construction of system matrices; it also provides the symmetric coefficient matrix. In the present work, several benchmark problems are studied and compared with the work of other researchers; the proposed method shows good accuracy, high convergence rate, and high efficiency, even for irregularly distributed nodes. At the end, a real test problem is performed to show and verify the main benefit and applicability of the proposed method to cope with complex geometry in practical problems. [ABSTRACT FROM AUTHOR]

• Differential manifolds and their tangent spaces are used for motion modelling. • Motions of parallel mechanisms with different constraint singularities are modelled. • Constraint singularities of parallel mechanisms are classified into two kinds. • Singularities causing bifurcated motions, instantaneous DoFs are separated. • Two examples are given to verify the theoretical results. This paper presents investigations into classification and analysis of constraint singularities for parallel mechanisms. Parallel mechanisms (also called parallel manipulators or parallel robots) have wide applications in industry. The singularities tremendously affect their applications. Existing research works show that constraint singularity causes a mechanism to have instantaneous degree-of-freedoms (DoFs) or bifurcated finite motions. However, the intrinsic differences among the conditions under which the specific constraint singularities happen have not been discussed. This paper is focused on these topics by using differential manifolds as mathematical tools. Firstly, the general mathematical models of parallel mechanisms are formulated by respectively describing their finite motions and instantaneous motions in forms of differential manifolds and their tangent spaces. Then, parallel mechanisms having bifurcated finite motions and instantaneous DoFs are modelled accordingly, and the constraint singularities are thus classified into two kinds by considering their influences on motions of mechanisms in both finite and instantaneous motion levels. Finally, two examples are given to further illustrate the theoretical analysis. This paper lays foundations for mathematical modelling and applications of parallel mechanisms with constraint singularities. [ABSTRACT FROM AUTHOR]

• A general mathematical spiral model is deduced for forming the skeleton of rope. • Costello's conclusion is extended to suit universal cases with rigorous proofs. • A novel cross section method (SCM) is put forward and proofed strictly for solving adjacent wires overlapping problem. • A precise geometric modeling of wire rope strands procedure is proposed. • The critical graph of wire radius determination is obtained for simple straight strand. Based on the Frenet frame, this paper proposes a general mathematical spiral model with an arbitrary smooth space curve as the center path, which can accurately build complex skeleton lines of wire rope strands. From the aspect of geometry, all the wires are spatial cylinders and must meet the actual geometric requirements: 1. The center cylinder is tangent or separated from the spiral cylinder; 2. The adjacent spiral cylinders do not overlap each other. For requirement 1, Costello' conclusion is referenced and extended universally to suit an arbitrary smooth space central curve case with rigorous proofs. For requirement 2, the overlapping problem is described as obtaining the minimum distance between the two adjacent spatial path curves, which is deduced by a novel cross section method (SCM) with rigorous proofs and solved by the General Particle Swarm Optimization (PSO) algorithm. Based on the above models, the geometric modeling of wire rope strands procedure is proposed and implemented on the platforms of MATLAB and SolidWorks. Validations are conducted through geometric graphical representations, compared with those from some previous researches. For the simple straight strand case, when the number of spiral cylinders and spiral radius are given, the critical relationship between the ratio of spiral wire radius to spiral radius and the spiral angle is firstly obtained, which can be a precise dimension design reference of simple straight strand for eliminating initial geometric overlap. Further, to show the advance, some precise graphical examples of complex wire rope strands like independent wire rope core (IWRC) and multilayered rope are presented. The wire rope strands geometric modeling method proposed in this paper is precise enough averting initial geometric overlap between the wires for the benefit of subsequent mechanical computation accuracy and efficiency. [ABSTRACT FROM AUTHOR]

• A mathematical methodology to find the optimal NIR light protocol in transdermal drug delivery; • Strategy based on an optimization problem minimizing the difference between target and simulated drug absorption profile; • The optimization problem relies on a 2D mathematical model for NIR light controlled transdermal drug delivery; • Validation of the transdermal model against laboratory data; • Convergence and stability analysis of a finite difference spatial scheme for a generalization of the transdermal model. Near-infrared light-controlled transdermal drug delivery (NIRTDD) has several advantages over traditional delivery methods, and it is now undergoing extensive research. One prominent aspect of NIRTDD is the possibility of keeping the drug concentration in its optimal therapeutic window using a suitable near-infrared light protocol. The problem is that this ideal protocol is usually unknown. In this paper, we propose a computational tool that aims at solving this issue. The computational tool relies on an optimization problem involving the numerical simulation of a two-dimensional mathematical model for NIRTDD. We also analyze the convergence and stability of a finite difference spatial scheme for a generalized version of this mathematical model. [ABSTRACT FROM AUTHOR]

• An industrial cargo routing problem with split loads motivated from a major steel company is studied. • Cargo-cargo and cargo-ship compatibility and the minimum loading amount for using a ship are considered. • An efficient path flow-based mathematical model is proposed. • The proposed model can reduce the computation time by 67% compared to an arc flow model. This paper presents an industrial ship routing problem with split loads faced by a steel company that exports its steel products to neighboring countries. The problem considers two types of ships: ships with contracts of affreightment and spot ships. It also considers other practical constraints, such as cargo–cargo and cargo–ship compatibility and the minimum loading amount for using a ship. Due to high surcharges for multiple port visits, each ship is allowed to visit at most two loading and two unloading ports. Herein, arc flow-based and path flow-based mathematical models are proposed to solve the problem. Computational experiments show that the path flow model is more efficient than the arc flow model. The path flow model can reduce the computational time by 67% on average and find optimal solutions to real-world ship routing problems in acceptable computational time in most cases. [ABSTRACT FROM AUTHOR]

• Bike repositioning problem with service requirements for rental and return requests was studied. • A mathematical model with the goal of minimizing the travel and unsatisfied costs was developed. • An efficient two-phase heuristic approach based on linear programming was proposed. • The proposed approach performs better than CPLEX optimizer and a genetic algorithm-based method. • The effects of various system parameters on the system were also investigated. An approach to overcome the bike imbalance problem is to transfer excess bikes to branches with bike shortages. This study develops a constrained mathematical model to deal with a multi-vehicle bike-repositioning problem, and aims to minimize the sum of transportation and unmet demand costs over a planning horizon through bike-transfer strategies under a minimum service requirement. A two-phase heuristic based on linear programming was proposed to solve the problem and produce compromising solutions. In the first phase, the paper developed a linear programming model to quickly develop decisions related to bike inventory, unloading, and loading for all stations for each time slot. In the second phase, this paper proposed an iterative approach through two parameter sensitive mathematical models to sequentially reduce the problem scale to develop decisions related to bike transfers. Computational results show that the proposed approach is superior to a CPLEX optimizer and a hybrid heuristic based on a genetic algorithm. The proposed approach was used to analyze the bicycle system in Taiwan. The impacts of various system parameters on the system were also investigated. [ABSTRACT FROM AUTHOR]

• This paper presents mathematical models that address the simultaneous evacuation of victims and entrance of responders. • Solutions provide the optimal routes for evacuees and responders within a critical timeframe. • Four types of models are developed according to the three different degrees of the golden time. • A heuristic algorithm is developed by extending the capacity constrained route planner. This paper presents mathematical models and a heuristic algorithm that address a simultaneous evacuation and entrance planning. For the simultaneous evacuation and entrance planning, four types of mathematical models based on the discrete time dynamic network flow model are developed to provide the optimal routes for evacuees and responders within a critical timeframe. The optimal routes obtained by the mathematical models can minimize the densification of evacuees and responders into specific areas. However, the mathematical model has a weakness in terms of long computation time for the large-size problem. To overcome the limitation, we developed a heuristic algorithm. We also analyzed the characteristics of each model and the heuristic algorithm by conducting case studies. This study pioneers area related to evacuation planning by developing and analyzing four types of mathematical models and a heuristic algorithm which take into account simultaneous evacuation and entrance planning. [ABSTRACT FROM AUTHOR]

• Developing a novel mathematical inventory model for growing-mortal items. • Studying the proposed model for trout fish production in a two-echelon supply chain (case study). • Applying revenue-sharing contract as well as revenue and cost sharing contract into proposed model. • Proposing a new feeding function for rainbow trout. • Providing managerial insights into trout production in a coordinated supply chain. Unlike the extensive inventory models for both ameliorating and deteriorating items, incorporating some specific features of these products have mostly been neglected. To fill this research gap, providing an appropriate mathematical inventory model for both ameliorating and deteriorating items is of paramount importance. In this regard, this paper proposes a novel mathematical inventory model for products called growing-mortal items in a two-echelon supply chain consisting of one supplier and one farmer. The proposed inventory model is more precise than analogous inventory models due to the fact that the specific growth function for the item is considered as well as mortality rate. As a case study, the model is applied to rainbow trout, which can be used for other types of growing-mortal items. Moreover, a feeding function is first-ever proposed for rainbow trout regarding the case study. The goal of this paper is to study the growth period in the supplier and then in the farmer sites to maximize the profit of the supplier as a leader and farmer as a follower under a Stackelberg game. To demonstrate how to reduce the inventory system costs by two coordination mechanisms, namely revenue-sharing and revenue and cost sharing, the model is solved under centralized and decentralized cases. Finally, sensitivity analysis on key parameters is also conducted to derive some managerial insights. [ABSTRACT FROM AUTHOR]

Highlights • A comprehensive method is proposed to compute the mesh stiffness of the spur gear pairs. • Two coupling models are developed to obtain the mesh stiffness of helical gear pairs. • The novel methods present a more accurate result compared to previous methods. Abstract This paper presents a novel calculation method to accurately determine the mesh stiffness of spur and helical gears. Firstly, based on the integral potential energy method, a comprehensive method is proposed to compute the mesh stiffness of the spur, obtaining more accurate results compared to previously used methods. Secondly, the proposed method for spur gears is then used to develop two models, single coupling and double coupling models, to calculate the mesh stiffness of helical gear pairs. The effects of coupling stiffness in both the single coupling and double coupling models are investigated. The main conclusion is drawn that the methods proposed in this paper can be used to accurately compute the meshing stiffness of spur and helical gears. [ABSTRACT FROM AUTHOR]

Highlights • A topology-based rigid spherical quadrilateral mesh method is proposed in this paper. • The nondifferentiable problem of free-form surface is solved based on topological transformation. • The model of feature extraction for free-form surface based on topological transformation is built. • The tangent bundle of smooth free-form surface manifold is analyzed. Abstract Free-form surface reconstruction is the key technology of mathematical modeling of engineering. It is important for accurate reconstruction of the entity model that conforms to the design. In order to improve the measurement accuracy of the workpiece, a method for free-form surface feature recognition based on topological transformation is proposed in this paper. Firstly, the information of scanning points is expressed as the form of topological space. Based on this, a method of surface constructing that selects the natural-quadratic-surface as the manifold of free-form surface is proposed. Then, the free-form surface that is constructed from the original point cloud is transformed into a smooth free-form surface which is homeomorphic to the original free-form surface based on the theory of topological embedding. The features of the transformed free-form surface can be easily analyzed and recognized. Finally, the qualitative description of an arbitrary point on the surface is obtained by analyzing the tangent bundle of smooth free-form surface manifolds. The feature recognition of free-form surface for workpiece is realized. The experimental results on workpiece model are reported in this paper, which validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights • This paper considers a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate. • Sufficient conditions for extinction of the disease are established. • Criteria for the existence of a stationary distribution are given through constructing suitable Lyapunov functions. • A threshold value for the disease to disappear or prevail is obtained. Abstract In this paper, we consider a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate. Before exploring its long-time behavior we show that there is a global positive solution of this model. Then sufficient conditions for extinction of the disease are established. Moreover, we give sufficient conditions for the existence of a stationary distribution of the model through constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Therefore, a threshold value for the disease to disappear or prevail is obtained. Finally, some numerical examples are illustrated to support our theoretical results. [ABSTRACT FROM AUTHOR]

Highlights • The convergence of Nicholson’s blowflies models has been analyzed. • Sufficient conditions for the addressed system to be global convergence are verified. • It is shown that all solutions of the addressed model are convergent to an almost periodic function. • The method of this paper can be used to study other asymptotically almost periodic population dynamics models. Abstract This paper is concerned with a asymptotically almost periodic Nicholson’s blowflies model involving a nonlinear density-dependent mortality term.By combining Lyapunov function method with differential inequality techniques, some novel sufficient conditions are derived to guarantee the asymptotically almost periodicity of the addressed model. Especially, a numerical example with graphical illustration is present to show the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

• A model for the population dynamics of age-structured criminal gangs with correctional intervention measures is proposed. • The existence of backward bifurcation is determined by the adolescent population. • We fitted the gang model against the crime data and provide forecast for the cumulative number of reported cases. • Global sensitivity analysis is carried out to determine the parameters that strongly drive the dynamics of the model. • The existence of periodic trajectories (Hopf bifurcation) for the criminal gang model is studied. The prevalence of criminal gang activities in the society has continued to be a huge burden to mankind. Despite several attempts by the government and non-governmental organizations in curtailing the activities of criminal gangs, new criminal gangs are beginning to emerge with associated criminal cases on the high side, thereby causing social unrest. This paper examines the impact of correctional intervention measures on the population dynamics of the criminal gangs in Nigeria, following an age-structured paradigm. The existence of backward bifurcation is presented sequel to the coexistence of gang free equilibrium and gang endemic equilibrium when the reproduction number is less than unity. Also, the model exhibits periodic trajectories (Hopf bifurcation) as a result of coexistence among the criminal gang classes. Using the Nigeria crime data (from 1993 to 2013) as obtained from Elsevier Data in Brief, we analyze the criminal gang model quantitatively and provide the sociological implications of the results. The numerical results obtained from this work show that if at least 60 % of adolescents between 8–17 years who commit crimes are apprehended with prompt prosecution and correction, we can potentially eradicate adolescent delinquencies from the population and thus control the entire criminal gangs' population. [ABSTRACT FROM AUTHOR]

• A comprehensive mathematical model scheme is proposed for the duplex angular contact ball bearings with three configurations. • The analytical expression of the stiffness matrix is formulated based on the implicit differential method. • The detailed two layers iterative algorithm based on the Newton-Raphson method is given. • The impacts of angular misalignment on the stiffness characteristics of the bearing are analyzed. Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and the direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings. [ABSTRACT FROM AUTHOR]

• The vibration characters of conical-cylinder shells with local bolt missing were analyzed theoretically and experimentally. • The artificial spring(main and secondary spring) method was utilized to simulate the model under any boundary conditions. • The mathematical model was verified by a series of experiments on a self-design testbed. • The effect of bolt looseness degree, missing form and quantity on vibration characteristics of the structure were discussed. This paper explores the vibration characteristics of fiber-reinforced thin-walled conical-cylinder composite shells (FTCCS 1 1 fiber-reinforced thin-walled conical-cylinder composite shells) with local bolt missing connections by combining theory and experiment. Firstly, based on the classical lamination theory and Kirchhoff-Love assumption, the FTCCS with local bolt missing is modeled. In order to simulate the bolt connections, the artificial spring method is used to equivalently represent any boundary conditions at the joints, where the artificial spring is divided into two forms: main spring and sub-spring. Meanwhile, the orthogonal polynomial method, Rayleigh-Ritz method, and modal superposition method are used to solve the vibration characteristics of the FTCCS with local bolt missing. To verify the rationality of the model, TC300/epoxy resin-based the FTCCS are taken as the research object, and vibration tests such as impulse, sweep, and resonance excitation are carried out. The experimental results show that the errors between the natural frequency and response displacement calculated by the solving method and the test results are in the range of 0.66 %∼4.56 % and 0.26 %∼10.39 %, indicating the reliability of the mathematical model prediction. Finally, by changing the bolt connection status, the structural dynamic parameters under different conditions are calculated to evaluate the impact of complex bolt connections on the vibration characteristics of the composite shell. [ABSTRACT FROM AUTHOR]

The numerical modelling of the internal heat generation in passenger vehicle tyres using finite element analysis is a well-known numerical approach. However, this application is rather uncommon for earthmover tyres. This paper describes the development of a finite element model of a 23.5R25 earthmover tyre for the numerical modelling of the temperature distribution in the tyre cross-section at steady-state heat transfer conditions using an uncoupled analysis procedure. Considering the non-linear behaviour of the rubber compounds used for the manufacturing of these tyres, as well as the complexity associated with the composite structural aspects of the tyre, the material properties used for the proposed numerical model were established experimentally. In the analyses completed, the tyre behaviour was studied by simulations at various inflation pressures, loads and rolling velocities. The numerical tyre defection was within an 8% deviation from the actual tyre behaviour. Thermal simulation results were used to derive an equation that can be used to predict the maximum temperature that would occur in the tyre’s cross-section as a function of its vertical deflection, its forward rolling velocity and the ambient temperature of the surroundings. The numerical models and simulations presented in this paper were completed using MSC.Marc/Mentat. [ABSTRACT FROM AUTHOR]

This paper proposes a production and differential pricing decision model in a two-echelon supply chain that involves a demand from two or more market segments. In this framework, the retailer is allowed to set different prices during the planning horizon. While integrated production-marketing management has been a key research issue in supply chain management for a long time, little attention has been given to set prices and marketing expenditures in integrated multi-site (parallel) manufacturing systems and multiple demand classes. Generally, the presence of multiple demand classes induced by different market segments may impose demand leakage and then change production plan and ordering policies throughout the supply chain system. To tackle this problem, this paper develops a novel approach in order to provide an optimal aggregate production and marketing plan by interconnecting the sales channels of the retailer and demand. A non-linear model is established to determine optimal price differentiation, marketing expenditures and production plans of manufacturing sites in a multi-period, multi-product and multi-sale channels production planning problem by maximizing total profit of the supply chain. To handle the model and obtain solutions, we propose an efficient analytical model based upon convex hulls. Finally, we apply the proposed procedure to a clothing company in order to show usefulness and significance of the model and solution method. [ABSTRACT FROM AUTHOR]

This paper addresses a multi-stage inventory model that allows different order quantities among the selected suppliers to obtain the optimal solutions. To achieve the objective of the study, the single-objective and multi-objective methods are adopted for suitable real-world applications. With respect to a single-objective method, this paper aims to minimize the total ordering costs, holding costs, and purchasing costs, subject to the price, quality, and capacity. With respect to a multi-objective method, it focuses on cost minimization, as well as quality and capacity maximization. The proposed model not only considers the allocation of different order quantities among the selected suppliers, but also incorporates the multi-stage inventory problem. Furthermore, a numerical example is provided to illustrate the usefulness of the proposed model and a comparative understanding of various methods. In addition, a simulation test is performed to effectively validate the proposed model which outperforms the previous works. Finally, a sensitivity analysis is carried out to investigate the impact of supply chain cost. [ABSTRACT FROM AUTHOR]

• Investigation of multiphysics shear wave propagation through piezoelectric - hydrogel - elastic substrate composite • Derivation of analytical solutions for the transverse deflection and electric potential in all the mediums • Demonstrating the influence of fixed - charge concentration in hydrogel on wave propagation through the composite material This paper presents a mathematical modelling of a novel multiphysics (electro-mechanic coupling) problem of the shear wave propagation in laminated structures (piezoelectric - hydrogel - elastic substrate) using the wave mode method while finding the general solution for each medium. A dynamic mechanical equilibrium equation (for transverse deflection) and Maxwell equation (for electric potential) are solved in a coupled manner over each domain resulting a general closed-form solution. A specific analytical solution is then obtained enforcing the boundary conditions at the top of piezoelectric layer and the interface continuity requirements between each layer and the elastic half-space. A novel approach, to uncouple the coupled equations, is presented resulting in a final systematic solution. The effect of x coordinate (thickness) on the field variables is carefully examined for the electrically open and short cases. The jump in the stress and electric displacement components (causing delamination due to shearing mode of fracture) is present across all the interfaces due to the different bulk material constants. The key contribution of the current work is demonstrating the influence of fixed-charge concentration inside the hydrogel layer on the shear wave propagation. The present study thus provides a new concept for adjusting and controlling the elastic wave propagation in the composite structures, and provides a proper theoretical understanding of wave propagation in the damage tolerance-based design of piezotronics devices. [ABSTRACT FROM AUTHOR]

• Developing a time-fractional compartmental model that incorporates the effect of contact tracing for Covid-19. • Describe the effective reproduction number in terms of observable quantities. • Discuss effects of tracking, reporting and monitoring in contact tracing. • Monitoring proportion of reported cases which must be tracked to ensure that the reproduction number is below one. • Numerical simulations are done to discuss the impact of contact tracing on the pandemic. Contact Tracing (CT) is one of the measures taken by government and health officials to reduce the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths. In particular, our findings suggest that effective monitoring policy of tracked cases and tracking of traced contacts while incubating are more crucial than tracing more contacts. The use of CT coupled with other measures such as social distancing, use of face mask, self-isolation or quarantine and lockdowns will greatly reduce the spread of the epidemic as well as peak hospitalizations and total deaths. [ABSTRACT FROM AUTHOR]

• A competition model is coupled with an intraguild predation model via dispersal of intraguild prey. • Large dispersal rate would lead to the collapse of species coexistence. • Three modes of species coexistence are possible when the intraguild prey dispersal rate is not too large. • For certain range of dispersal rates, a stable interior equilibrium can coexist with a stable positive limit cycle. Predators can greatly influence the coexistence of competing prey species via direct consumptive effects as well as non-consumptive effects on prey behavior. This makes predicting the consequences of predator introduction on biodiversity and ecological structure very challenging. In this paper, inspired by recent experimental observations (Pringle et al., Nature, 570 (2019) 58–64), we develop a novel mathematical model that couples a competition model with an intraguild predation model via dispersal of intraguild prey driven by intraguild predator-avoidance. We show that a large dispersal rate would lead to the collapse of species coexistence, which is consistent with the reported experimental results. In addition, we show that three modes of species coexistence are possible when the intraguild prey dispersal rate is not too large. Moreover, for a certain range of dispersal rates, a stable interior equilibrium can coexist with a stable positive limit cycle. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results. [Copyright &y& Elsevier]

• The equivalent method from bolted connections to spectral problem is presented. • The integrable system equivalent to a bolted connection is established. • A novel mathematical model is proposed for evaluating bolt preload. • The proposed model considers the geometric and physical parameters. • The preload is especially sensitive to the geometric parameters of connected parts. Accurate evaluation of preload in system with double-bolted connections is critical for the service performance of engineering structures or equipment. However, the theoretical framework for assessing preload is imperfect. An equivalent approach from the tightening process of double-bolted joints to second-order spectral problem of the energy-dependent potential is firstly established. This paper proposes a novel nonlinear model of bolt preload considering physical and geometric parameters by proving the completely integrability of systems used bolted connections. The experimental device for hmeasuring displacement and bolt preload was developed to verify the accuracy of proposed model. Results show that the maximum relative error is not more than 3%. Finally, the influences of elastic modulus, density, holes spacing, and height on preload are analyzed. [ABSTRACT FROM AUTHOR]

• A numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. • A finite number of rigid bars and lumped masses joined by elastic springs simulate both bending and shear deformation. • The analysis of thick plates is performed through the adoption of the Reddy's third-order shear deformable plate theory. • The obtained results show both the versatility and the accuracy of the proposed approach. In this paper, a novel discrete differential geometry-based numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. In the proposed approach a plate is discretized using a finite number of rigid bars, lumped masses, and elastic rotational springs to simulate both bending and shear deformation responses, allowing the analysis of thick plates through the adoption of the Reddy's third-order shear deformable plate theory. An interesting analogy between the proposed model and the central finite difference method for solving a set of partial differential equations is also highlighted, showing how the former can be seen as the physical model behind the mathematical representation of the latter. The numerical results presented show both the versatility and the accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

A fraction-order total variation blind image restoration algorithm based on L1-norm was proposed for restoring the images blurred by unknown point spread function (PSF) during imaging. According to the form of total variation, this paper introduced an arithmetic operator of fraction-order total variation and generated a mathematical model of cost. Semi-quadratic regularization was used to solve the model iteratively so that the solution of this algorithm became easier. This paper also analyzed the convergence of this algorithm and then testified its feasibility in theory. The experimental results showed the proposed algorithm can increase the PSNR of the restored image by 1 dB in relation to the first order total variation blind restoration method and Bayesian blind restoration method. The details in real blurred image were also pretty well restored. The effectiveness of the proposed algorithm revealed that it was practical in the blind image restoration. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence of the traveling waves of the equations describing a diffusive SEIR model with non-local reaction between the infected and the susceptible. The existence of traveling waves depends on the basic reproduction rate S − ∞ β / γ and the minimal speed. We use the Schauder fixed point theorem and the Laplace transform to get the existence and non-existence of traveling waves in our paper. We also give some numerical results of the minimal wave speed. [ABSTRACT FROM AUTHOR]

In this paper we present a multiphysics simulation model of Halcyon, an autonomous unmanned surface vehicle (USV). The simulation model presented in this paper has been developed to rapidly progress the design, development and validation of Halcyon’s autonomy management system, particularly in challenging sea conditions. Using simulation for this purpose enables extensive testing across the full environmental operating envelope of the vessel, hence greatly reducing the need for real-world sea-trials. The simulator is comprised of a novel and comprehensive sea-surface wave environment model, a six degree of freedom nonlinear unified seakeeping and manoeuvring boat dynamics model, an actuation dynamics model, an autopilot and an interface with an autonomy management system. Results are presented that show good agreement between real-world and simulated sea-trials data. [ABSTRACT FROM AUTHOR]

This paper attempts to fill the gap in the literature by introducing and discussing an enhanced physical model of the MR damper. The essence of the presented model is to combine the effect of compressibility of the MR fluid enclosed in each chamber with the effect of blocking the flow between the chambers in the case of a low pressure difference. As it will be shown, the concurrence of both considered phenomena significantly affects mechanical behaviour of the damper, influences its dissipative characteristics, and in particular, it is the reason behind the distinctive ‘z-shaped’ force–velocity hysteresis loops observed in experiments. The paper presents explanation of the observed phenomena, detailed derivation of the thermodynamic equations governing response of the damper, their implementation for various constitutive models of the magnetorheological fluid and, finally, formulation of the corresponding reduced and parametric models. Experimental validation shows that proper identification of physical parameters of the proposed mathematical model yields the correct shapes of force–velocity hysteresis loops. [ABSTRACT FROM AUTHOR]

This paper proposes a new ranking algorithm based on comprehensive weighted clique degree (CWCDR) for ranking importance of nodes in complex network. Simulation results show that CWCDR algorithm can overcome the limitation of degree ranking algorithm and find important nodes in complex networks more precisely and effectively. To the shortage of small-world model and BA model, this paper proposes an evolutionary model of complex network based on CWCDR algorithms, named CWCDR model. Simulation results show that the CWCDR model accords with power-law distribution. Compared with BA model, this model has better average shortest path length and clustering coefficient. Therefore, the CWCDR model is more consistent with the real network. [ABSTRACT FROM AUTHOR]

The paper presents a diagnose analysis for an industrial fan having vertical axis rotation, which shows dangerous levels of vibration. The fan ejects the flue gases from a thermoelectric power plant. This is located and isolated on the roof of the power plant building by some elastic elements, in the form of some cassettes with coil springs. The cassettes are arranged symmetrically along the separation plane. The experimental research has been carried out in two steps. In the first step, we designed and we studied in laboratory a mathematical model to reproduce a real situation of the fan insulation. In the second step, we made experimental investigations on the spot. Comparing the measured vibration amplitudes to those obtained on mathematical model, we identified a hidden connection near one of cassettes with coil springs. The hidden connection has appeared during the cassettes mounting and so was created a mechanical asymmetry. Due to this, the dangerous levels of vibration have occurred and it was caused a temporary shutdown of the fan. The process for detecting and eliminating the mounting nonconformities it is presented in the paper. [ABSTRACT FROM AUTHOR]

Determination of the creep model parameters is a challenging task particularly when a non-linear elastic visco-plastic (EVP) model is adopted, mainly due to the limited test duration as well as the assumption of the reference time. Therefore, this paper presents an innovative numerical solution to find the EVP model parameters applying the trustregion reflective least square optimization algorithm. The developed approach involves several available laboratory consolidation test results in the optimization procedure with the adopted commencing time to creep as a unit of time. In this paper, the laboratory results of Ottawa clay were employed to demonstrate the limitation of the recent method to obtain model parameters. Furthermore, the developed method is verified against Skå-Edeby clay in the laboratory conditions. The EVP model parameters are obtained by applying the developed method to the available laboratory consolidation results of clay samples. The analysis results of vertical strains and excess pore water pressures demonstrate that the developed method can be a feasible tool to estimate the settlement properties of clays. [ABSTRACT FROM AUTHOR]

A biofilm is usually defined as a layer of bacterial cells anchored to a surface. These cells are embedded into a polymer matrix that keeps them attached to each other and to a solid surface. Among a large variety of biofilms, in this paper we consider batch cultures. The mathematical model is formulated in terms of a quasilinear system of diffusion- reaction equations for biomass and nutrients concentrations, which exhibits possible degeneracy and singularities in the nonlinear diffusion coefficient. In the present paper, we propose a set of efficient numerical methods that speeds up the solution of the model. Mainly, Crank-Nicolson finite differences techniques for discretisation are combined with a Newton algorithm for the nonlinearities. Moreover, some numerical examples show the expected behaviour of the biomass and nutrients concentrations and also clearly illustrate some theoretically proved qualitative properties related to exponential decays or convergence to a critical biomass concentration depending on the values of the model parameters. [ABSTRACT FROM AUTHOR]

• Mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials. • General mathematical formulation using the thermal strain effect and elliptic integrals. • Elaboration of thermo-electro-elastic Green's functions and integral equations formulations. • Well conditioned localization tensors based on block decompositions for stable and accurate modeling. • Computation of effective anisotropic thermal conductivity and thermo-electro-elastic coefficients. In the present paper, a mathematical modeling of effective properties of fully coupled thermo-electro-mechanical heterogeneous materials is elaborated. Constitutive equations combined with equilibrium equations lead to a coupled partial differential system. A methodological procedure is elaborated based on thermo-electro-elastic Green's functions, integral equations, and a micro-macro approach. Localization tensors are derived using the Mori–Tanaka mean-field assumptions and the fully coupled effective behavior is obtained through averaging techniques. Due to the large dispersion between elastic, dielectric, and piezoelectric coefficients ill-conditioned localization tensors are resulted. Block matrix decomposition is elaborated to overcome this drawback and the so-regularized localization tensor's inverses are used to get a well conditioned problem. Numerical computations are done in the general case of ellipsoidal inclusions and anisotropic behavior. Effective thermal conductivity and heat capacity coefficients are obtained with and without the heat strain effect for various volume fractions and types of inclusions. The global properties of thermo-electro-elastic reinforced composites are presented with respect to shape and volume fractions of inclusions. [ABSTRACT FROM AUTHOR]

• We proposed a mathematical pathogen-host model with a time delay for the dynamics of the banana black leaf streak disease. • Model accounted for the two reproduction means of the pathogen spores, seasonality and time delay to describe the incubation. • The basic reproduction number R0 does not depend on the time delay and is related to both sexual and asexual spore production. • The stability of the system was shown to not depend on the time delay, i.e. on the duration of the incubation period. • Results proved that the control of sexual spore production is not sufficient. We provide numerical simulations. Black Sigatoka Disease, also called Black Leaf Streak Disease (BLSD), is caused by the fungus Mycosphaerella fijiensis and is arguably one of the most important pathogens affecting the banana and plantain industries. Theoretical results on its dynamics are rare, even though theoretical descriptions of epidemics of plant diseases are valuable steps toward their efficient management. In this paper, we propose a mathematical model describing the dynamics of BLSD on banana or plantain leaves within a whole field of plants. The model consists of a system of periodic non-autonomous differential equations with a time delay that accounts for the time of incubation of M. fijiensis ' spores. We compute the basic reproduction number of the disease and show that it does not depend on the time delay, meaning that the persistence of BLSD would not qualitatively change even if the incubation period of the pathogen is perturbed. We derive local and global long-term dynamics of the disease and provide numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

• Influences of lining leakage and train loading on tunnel are analyzed by a mathematical modelling. • Terzaghi-Rendulic consolidation solution considering boltzmann rheology is obtained by complex conformal method. • Triangular cyclic loading is equivalently applied to tunnel lining based on semi-permeable boundary condition. • Accuracy of analytical solutions is verified by comparisons with observed data and existing numerical results. • Parametric analysis for soil-lining permeability and viscoelastic porous medium is conducted. The long-term leakage of lining under train loading has a significant impact on the consolidation settlements around shield tunnel and the rheological behaviour of viscoelastic porous soils will further exacerbate this consequence, which adversely affect the adjacent geo-environments and the subsidence of existing structures. At present, the assumptions of tunnel impermeable lining and liner-elastic clays are usually received to conduct on the consolidation settlements. Moreover, little attention is paid on the coupled influence of lining leakage and train loading. For better engineering serviceability in viscous porous clays, this paper presents a closed-form analytical solution for predicting the ground consolidation settlements under train loading considering the lining leakage and the rheological medium, with the scope of Terzaghi-Rendulic theory. By introducing semi-permeable boundary condition, the triangular cyclic loading is equivalently applied to the tunnel lining and the Boltzmann viscoelastic model is employed to simulate the rheological characteristic of the actual geology. The dissipation solution of excess pore water pressure and the ground responses in viscoelastic porous clays are derived using the conformal mapping. In addition, the accuracy of the analytical solutions is verified by comparisons with in-situ observed data and existing numerical simulation results from the engineering cases, showing reasonable alignments. The differences between the Kelvin and Boltzmann model are further analyzed to estimate the influences of rheological geology. Furthermore, a detailed sensitivity analysis is also implemented to investigate the performance of concerned parameters on the surface consolidation settlements, including the lining-soil permeability, the parameters of Boltzmann model (elasticity module E h in the Hoek body, elasticity module E k and viscosity coefficient η k in the Kelvin body), and the train loading. The interesting point and ingenious approach in this study are tracing the corresponding analytical solutions on the consideration for not only the coupled influence of lining leakage and train loading but also the rheological behaviour in the viscoelastic porous soils. [ABSTRACT FROM AUTHOR]