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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 presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional numerical (2D) model for analysing the full three-dimensional (3D) problem of heat transport problems in laminated composite plates. A 2D finite element model is enough for good representation of a 3D problem since each single node in the mesh has enough degrees of freedom associated with particular layers of the laminated plate. The 2D numerical model is quite simple and effective and it allows considering multi-layered structures in which individual layers are made of different materials and the structure may consist of a combination of thick and very thin layers without numerical instabilities. The method presented in this paper is combined with a specially tailored postprocessing procedure so that results from the planar mesh can be visualised as 3D graphics. The paper is illustrated with a set of examples in which stationary and non-stationary problems are considered. In these examples modelling of the laminated glass with three glass panes and thin layers of bonding material is presented. [ABSTRACT FROM AUTHOR]

Matt Blum conjectured that the- number of tilings of a hexagonal dungeon with side-lengths a , 2 a , b , a , 2 a , b (for b ≥ 2 a ) equals 1 3 2 a 2 1 4 ⌊ a 2 ∕ 2 ⌋ . Ciucu and the author of the present paper proved the conjecture by using Kuo’s graphical condensation method. In this paper, we investigate a 3-parameter refinement of the conjecture and its application to enumeration of tilings of several new types of the hexagonal dungeons. [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]

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]

Shared autonomous vehicles (SAVs) could provide low-cost service to travelers and possibly replace the need for personal vehicles. Previous studies found that each SAV could service multiple travelers, but many used unrealistic congestion models, networks, and/or travel demands. The purpose of this paper is to provide a method for future research to use realistic flow models to obtain more accurate predictions about SAV benefits. This paper presents an event-based framework for implementing SAV behavior in existing traffic simulation models. We demonstrate this framework in a cell transmission model-based dynamic network loading simulator. We also study a heuristic approach for dynamic ride-sharing. We compared personal vehicles and SAV scenarios on the downtown Austin city network. Without dynamic ride-sharing, the additional empty repositioning trips made by SAVs increased congestion and travel times. However, dynamic ride-sharing resulted in travel times comparable to those of personal vehicles because ride-sharing reduced vehicular demand. Overall, the results show that using realistic traffic flow models greatly affects the predictions of how SAVs will affect traffic congestion and travel patterns. Future work should use a framework such as the one in this paper to integrate SAVs with established traffic flow simulators. [ABSTRACT FROM AUTHOR]

• Present a novel method to quantitatively measure video frame distortion in a wavelet transformdomain. • Propose a mathematical model to describe the minimum video frame distortion problemas an optimization problem. • Choose the best positions to embed a watermark that can maximize peak signal to noise ratio. • Apply the mathematical model to embed a watermark in a real video and compare itwith the state-of-the-art approaches. • Demonstrate the imperceptibility and robustness of the proposed method when the videois under various noise attacks. Digital video watermark is widely used to protect copyright and content authentication. DWT-SVD based method, i.e., discrete wavelet transform (DWT) and singular value decomposition (SVD) based method, is one of the most popular state-of-the-art methods. There are two main criteria to evaluate it, i.e., imperceptibility and robustness. The former is measured via the peak signal to noise ratio (PSNR) and structural similarity (SSIM). They should be as high as possible after the watermark is embedded. Robustness measures how easy to restore the embedded watermark by the owner even if the watermarked video is damaged by an outside attacker. Current studies randomly choose embedded positions for watermark, which hardly achieves its highest imperceptibility and robustness. In this paper, we propose a more imperceptible and robust digital video watermarking method than the existing one. First, we introduce a method to measure video frame distortion in a wavelet transform domain. Second, we model the problem to achieve the minimum video frame distortion as an optimization problem, i.e., choose embedded positions that can maximize peak signal to noise ratio. Finally, we evaluate and compare our method with the state-of-the-art approaches by using real experiments and show its advantages in both imperceptibility and robustness. [ABSTRACT FROM AUTHOR]

Two kinds of fractional-order autonomous circuits are constructed by using fractional-order capacitor and fractional-order inductor respectively. The orders of the adopted fractional-order elements must be greater than one. The corresponding circuit simulations were developed and verified the proposed fractional-order autonomous circuits. • Two kinds of new fractional-order autonomous circuits are proposed. • The fractional-order autonomous circuits are based on fractional-order elements with order larger than one. • The operating frequency or resonant frequency of the circuits can be changed by adjusting the resistance. • The current and voltage of the circuits can be controlled by adjusting the orders of fractional-order elements. • The available simulations verify the effectiveness of the theoretical analysis. Fractional-order circuit is a kind of circuit which contains fractional-order elements. It has been proved that the fractional-order circuit has some characteristics which are hard to be achieved by integer-order circuits, such as higher degree of freedom in circuit design. For integer-order circuits, there are not only non-autonomous circuits, but also autonomous circuits. Since there are many applications of integral-order autonomous circuits in real world, it is also necessary to explore fractional-order autonomous circuits. However, few research focuses on fractional-order autonomous circuits. Therefore, this paper proposes two kinds of fractional-order autonomous circuits based on fractional-order elements with order larger than one. The corresponding mathematical models are also established based on fractional calculus and their characteristics are analyzed based on circuit theory. Finally, circuit simulation are performed to verify the correctness of theoretical analysis. [ABSTRACT FROM AUTHOR]

The paper addresses several existing versions of mathematical models describing stiffened shell structures (accounting for the interaction between stiffeners and skin "along a line", and "along a strip", and a method for "smearing" the stiffness of stiffeners over the entire structure). The authors suggest a new, most accurate version to account for stiffness properties of stiffeners, based on introducing various modular ratios along various coordinate axes. For stiffeners perpendicular to the direction under consideration, the authors introduce a modular ratio equal to the ratio between the width of stiffeners in this direction and the linear dimension of the shell in the direction under consideration. For analysis, the authors use an algorithm based on the Ritz method and the best parameter continuation method. Three versions of models, taking into account the discrete introduction of stiffeners, are compared. Analysis is performed for isotropic shallow doubly curved shells reinforced with an orthogonal grid of stiffeners. [ABSTRACT FROM AUTHOR]

We present and discuss a variety of mathematical models that have been proposed to capture the dynamic behavior of epidemic processes. We first present traditional group models for which no underlying graph structures are assumed, thus implying that instantaneous mixing between all members of a population occurs. Then we consider models driven by similar principles, but involving non-trivial networks where spreading occurs between connected nodes. We present stability analysis results for selected models from both classes, as well as simple least squares approaches for estimating the spreading parameters of the virus from data for each basic networked model structure. We also provide some simulation models. The paper should serve as a succinct, accessible guide for systems and control research efforts toward understanding and combating COVID-19 and future pandemics. [ABSTRACT FROM AUTHOR]

Tackling societal challenges relating to sustainability requires both an understanding of the underlying complex socio-ecological systems and participation of scientists as well as relevant stakeholders, such as practice experts, decision makers, and citizens. This paper introduces the Decision Theatre Triangle, a method which combines empirical information, mathematical modelling and simulation, and a format for dialogue between scientists and stakeholders. While it builds on previous Decision Theatre work, the new structuring into these three elements emphasizes what is needed for setting up a Decision Theatre for a given challenge. Based on experience with a specific example – sustainable mobility in Germany – it is argued that agent-based models are particularly suitable for Decision Theatres and that the method is useful not only for decision support but also for science communication and co-creation of a deeper knowledge of the system under discussion. As a step towards facilitating a broader use of the Decision Theatre Triangle method, the paper then sketches research needs for each of its three elements, with a focus on mathematical modelling and simulation. [Display omitted] • The Decision Theatre Triangle combines data, models, and stakeholder dialogues. • It enables decision support, science communication and co-production of research. • Agent-based modelling shows benefits in the Decision Theatre Triangle method. • Setting up Decision Theatre Triangles for societal challenges needs model structures. [ABSTRACT FROM AUTHOR]

• Analytical solution describing fluid extraction from an adsorption column. • Excellent agreement with a range of experimental data. • Proof that previous accepted models do not work. • Demonstration that to accurately characterise experiments both breakthrough and isotherm data are required. • Development of a novel analytical solution including a SIPS mass sink. In this paper we investigate the standard one-dimensional model for adsorption of a contaminant in a packed column. Initially we focus on two mass sink models: a full nonlinear Langmuir equation, including adsorption and desorption and the linearised version which neglects the local concentration. Travelling wave solutions are developed for both cases, providing exact analytical formulae for the concentration and adsorbed fraction throughout the column. Comparison is made with experimental data for the adsorption of toluene on activated carbon (dominated by physical adsorption) and Cr(III) on zeolite NaX (dominated by ion exchange). For toluene the nonlinear model provides good agreement but it is less accurate for Cr(III). The linear model apparently works well for Cr(III) but only at the expense of violating the model assumptions. This motivates extending the travelling wave solution to a Sips sink model, which has a power law dependence on local concentration. Comparison with data provides excellent agreement in all cases and also indicates why the previous models fail. Following from the investigation of the linear sink model, we prove that previously accepted results frequently fail due to a violation of assumptions made in their derivation. Specifically we challenge the belief that widely used models such as Bohart–Adams, Yoon–Nelson, Bed Depth Service Time, etc can accurately predict breakthrough data. Their success instead may be attributed to: at times, having a similar shape to the breakthrough curve rather than being the correct solution; treating measurable quantities as fitting parameters and a willingness to accept that constant parameters vary. In contrast to these previous models, the travelling wave solution of the present paper, based on a Sips sink, provides analytical solutions consistent with the model assumptions for a wide range of experimental data. [ABSTRACT FROM AUTHOR]

• Extensive UHPFRC mixtures acquired from the literature were analyzed. • Key factors affecting the strength of UHPFRC mixtures were discussed. • Mathematical and ANN models for strength of UHPFRC was established. This paper presents a quantitative analysis of the mechanical performance of ultra-high performance fiber-reinforced concrete (UHPFRC). UHPFRC shows great potential in the construction of the cities of tomorrow. However, establishing empirical formulas by incorporating existing data for the practical engineering design of UHPFRC remains a problem. To advance the understanding of UHPFRC, this paper qualitatively and quantitatively studied UHPFRC with an emphasis on its strength. Utilizing abundant data consisting of 111 different UHPFRC mixtures in literature, the key factors governing the strength of UHPFRC, e.g., the volumetric ratios and types of paste, aggregate, fibers and filler, were identified. Based on the key factors, a robust mathematical model for the strength prediction of UHPFRC was established. In addition, an artificial neural network model was constructed. This study shall provide useful guidelines for the mix design of sustainable and resilient UHPFRC. [ABSTRACT FROM AUTHOR]

The second-hand vessel market has quite different dynamics than the market of the new-building vessel, and highly complicated and conflicting criteria and many uncertainties affect the ship selection process. Therefore, it is required to use a robust mathematical model to solve these kinds of decision-making problems. For this purpose, this paper presents an extended version of WASPAS (Weighted Aggregated Sum Product ASsessment) techniques with the help of T2NN based on the Bonferroni function (T2NN WASPAS'B). The three main focal points of the proposed approach are (i) setting the influential criteria to select the appropriate Ro-Ro vessel in the second-hand vessel market; and (ii) presenting a flexible group decision-making approach, which is proper to real decision-making problems. (iii) detecting the interrelations among criteria and eliminating the negative impacts of undesirable and excessive values in input variables on the results. Practical use of the proposed approach is demonstrated to select the appropriate Ro-Ro vessel in the second-hand market. The analysis results show that the most effective and determinative factor is Trailer Lane length, and the most effective alternative is GREIFSWALD. Besides, the consistency and validity of the obtained results have been verified with the help of a stability and robustness check. The results prove that the proposed novel T2NN WASPAS'B model is robust, powerful, and reliable for making rational and realistic decisions. • The current paper presents the T2NN WASPAS'B approach strengthen with the help of T2NN based on the Bonferroni function. • The proposed model is applied to solve second-hand Ro-Ro vessel selection problems, which are highly complex and include uncertainties. • It has identified the selection criteria for second-hand Ro-Ro ships for the first time. • It presents a flexible decision-making approach, which is proper for real decision-making problems. • It demonstrates interrelations among factors to make it more understandable in complex situations. [ABSTRACT FROM AUTHOR]

An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under local strain differences. A few examples are presented of the effect of the anisotropy and moisture streaks under stretching and drying conditions on strain differences and buckling. The internal stresses were studied through a case in which the drying of different layers occurred at different stages. Both the anisotropy and moisture streaks were capable of rendering the buckling of the sample visible. The permanency of these defects highly depends on several process stages and tension conditions of the sheet, as demonstrated in this paper. The application possibilities of the hygro-elasto-plastic model are diverse, including investigation into several phenomena and defects appearing in drying, converting and printing process conditions. [ABSTRACT FROM AUTHOR]

• Three-dimensional finite element simulation of flood discharge atomization process was carried out by the numerical method. • The compressible fluid dynamics equation is solved by the finite element method with a suitable solution strategy. • The numerical simulation results of flood discharge atomization agree well with the measured results. Flood discharge atomization is a phenomenon of water fog diffusion caused by the discharge of water from a spillway structure, which brings strong wind and heavy rainfall. These unnatural winds and rainfall are harmful for the safe operation of hydropower stations with high water heads. Compared to the method of prototype observations, physical models and mathematical models, which are semi-theoretical and semi-empirical, numerical simulation methods have the advantage of being not limited by a similar scale and are more economical. A finite element model is presented to simulate flood discharge atomization based on water–air two-phase flow in this paper. Equations governing flood discharge atomization are composed of partial differential equations of mass and momentum conservation laws with unknowns for pressure, velocity and the water concentration. The finite element method is used to solve the governing equations by adopting appropriate solution strategies to increase the convergence and numerical stability. Then, the finite element model is applied to a practical project, the Shuibuya hydropower station, which experienced a flood discharge in 2016. Simulation results show that the proposed model can simulate flood discharge atomization with efficient convergence and numerical stability in three dimensions, and good agreement was observed between numerical simulations and prototype observational data. Based on the simulation results, the mechanism of flood discharge atomization was analyzed. [ABSTRACT FROM AUTHOR]

This paper presents an asymptotic method-based analysis of composite laminates having interfacial imperfections. In general, imperfect interfaces are simply modeled by introducing a linear, spring-layer model, which empirically assumes that the displacement jumps that occur at the weakened interface are proportional to the transverse shear stresses of interface positions. In this study, we propose a composite plate model derived by using asymptotic expansion that does not make any assumptions, other than the scaling of coordinate systems. Within the framework of the asymptotic analysis, the spring-layer model is introduced to describe the effect of weakened interfaces, which is realized by the separation of domains in the through-the-thickness direction, and the integration of piecewise continuous warping functions. As a result, we newly define a spring parameter that is exactly the same as the stiffness of a spring. Therefore, a set of spring elements are added to the through-the-thickness modeling of the microscopic analysis, and the plate equations derived in the macroscopic problem are the same as those of the perfectly bonded laminates. As a consequence, we also derive the proposed plate model with the mathematical rigor that the previous asymptotic models contain. We provide some numerical results verifying that the proposed method shows good agreement with the elasticity and 3D FEM solutions. [ABSTRACT FROM AUTHOR]

A Pareto eigenvalue of a matrix A of order n is a scalar λ ∈ R for which the complementarity problem 0 ⪯ x ⊥ (A x − λ x) ⪰ 0 admits a nonzero solution x ∈ R n. Pareto eigenvalues are also known as complementarity eigenvalues. They have found applications in graph theory, cone-constrained dynamical systems, and mathematical modeling in general. In this paper we continue our study on theoretical properties of Pareto spectra. Special attention is paid to classification of Pareto eigenvalues and cardinality issues. [ABSTRACT FROM AUTHOR]

• Construct an agent-target binding model based on stochastic differential equations. • Determine conditions to apply stochastic quasi steady state approximation. • Compare parameter estimation with maximum likelihood estimation and Euler–Maruyama approximation for sparse data. • Strengths and weaknesses of the reduced model for the endocytosis and lysosome processes using an age-structured model. • Comparing the reduced model with the full system of the released payload by identifying the mean retention time. In this paper, we propose mathematical models to describe receptor-mediated endocytosis processes. One is a stochastic differential model for the agent-target binding process. The mean extinction time and a standard variation over time profile are evaluated. The other is an age-structured model for demonstrating endocytosis and lysosome processes. A targeted drug delivery system has a complex process in how it is to deliver drug molecules in terms of administration, transportation in blood and across membranes to intracellular space, and inhibition to microtubule polymerization. In particular, receptor-mediated endocytosis of targeted therapeutic agents, such as antibody drug conjugates or ligand-targeted liposome encapsulated nanoparticles, is a key step in understanding the drug delivery mechanism. We discuss stochastic quasi steady state approximation when agent-target complex does not appreciably vary compared with the free agents. This reduces the number of the systems and the parameters; however, an initial time phase cannot be captured. In addition, we discuss the strengths and weaknesses when the age-structured model induces the reduced model compared with the full model that considers endocytosis and lysosome processes. If the total mean retention time until payload release in intracellular space is known, then the age-structured model with the Erlang distribution may fairly predict data of the released payload over time profile with far fewer parameters; however, induced compartments lose their physical meaning and describe only a delay. [ABSTRACT FROM AUTHOR]

With the increasing complexity in modern circuit designs, the 6T&6TPPNN circuits have become popular in advanced technologies for better trade-offs among routability, timing, power and performance. The 6TPPNN cells incur great challenges to layout designs, especially the legalization problem due to their complex minimum width (MW) constraints and the fragmentation effect (FE). In this paper, we address the mixed 6T&6TPPNN cell legalization problem considering both MW constraints and FE issues. Given a global placement result, we first align all cells to the correct rows/half-rows that satisfy the VDD/VSS alignment constraints, and then propose a clustering-based MW constraints solving method to eliminate all the MW violations. After that, we formulate the legalization problem with MW constraints as a quadratic programming (QP) problem, which not only satisfies the MW constraints, but also avoid causing excessive dead spaces. Finally, we integrate the FE issues into the formulated MW-aware QP model, and adopt the modulus-based matrix splitting iteration method (MMSIM) to solve the mathematical model effectively and efficiently. Experimental results show that our algorithm can resolve all MW constraints and mitigate the half-row fragmentation effect without any extra area overhead in a reasonable time. • We propose a clustering-based method to eliminate all the minimum width (MW) violations. • We formulate the legalization problem with MW constraints as a quadratic programming problem. • We further integrate the fragmentation effect (FE) issues into the formulated MWaware legalization model. • We adopt the modulus-based matrix splitting iteration method to solve the MW&FE-aware legalization problem effectively. • Experimental results show that our algorithm can resolve all MW constraints and mitigate the FE in reasonable runtime. [ABSTRACT FROM AUTHOR]

This paper presents a multi-satellite scheduling problem for very large area observation with given specific constraints, derived from satellite capacity and customer requests. It is assumed that the profit was proportional to the coverage of acquired area, and the objective is therefore to maximize the total profits of generated observation schedule. To address the satellite scheduling problem, we first demonstrate a detailed problem description and then transform the problem into set covering problem within several criteria and constraints. Based on that, a mathematical model is established. In order to solve the multi-satellite scheduling problem for large area observation, a new solving framework is proposed. The framework is composed of three phases. In the discretizing phase, an area discretization method is adopted to establish the evaluation system. In the target decomposing phase, area target is decomposed into strips and corresponding visible time windows are calculated. In the scheduling phase, with crossover, mutation and feasibility operators, a genetic algorithm is introduced to generate an optimal observation schedule. Through extensive computational experiments on realistically generated problem with Chinese satellite platform, the effectiveness and reliability of the proposed solving framework are verified. • Multi-satellite scheduling problem for very large area observation is introduced. • The proposed problem is transformed and modeled as a set covering problem with constraints. • A new three-phase solving method is developed, including discretizing, decomposing and scheduling. [ABSTRACT FROM AUTHOR]

• Networked systems with random perturbances in outputs and transmissions are studied. • Time-correlated channel noise affects the available data after transmission. • The time-differencing approach is used to deal with time-correlated channel noise. • Fusion filtering and smoothing algorithms are designed using covariance information. This paper is concerned with the fusion filtering and fixed-point smoothing problems for a class of networked systems with multiple random uncertainties in both the sensor outputs and the transmission connections. To deal with this kind of systems, random parameter matrices are considered in the mathematical models of both the sensor measurements and the data available after transmission. The additive noise in the transmission channel from each sensor is assumed to be sequentially time-correlated. By using the time-differencing approach, the available measurements are transformed into an equivalent set of observations that do not depend on the time-correlated noise. The innovation approach is then applied to obtain recursive distributed and centralized fusion estimation algorithms for the filtering and fixed-point smoothing estimators of the signal based on the transformed measurements, which are equal to the estimators based on the original ones. The derivation of the algorithms does not require the knowledge of the signal evolution model, but only the mean and covariance functions of the processes involved (covariance information). A simulation example illustrates the utility and effectiveness of the proposed fusion estimation algorithms, as well as the applicability of the current model to deal with different network-induced random phenomena. [ABSTRACT FROM AUTHOR]

• Design of a dynamic mathematical model for blood assignment problem. • Proposal of a symbiotic optimization search algorithm for the BAP. • Implementation of two hybrid SOSGA and SOSSA algorithms to solve the BAP. • Suggestions for further development and possible areas of improvement. The shortage and wastage of blood products have been identified as the major contending factors that are frequently encountered in the management of blood supply chain processes. In general, the blood which is considered an essential product for which human existence relies on, has perishability characteristics that allow it to be stored up to a limited number of days. Therefore, this feature constrains the quantity of blood that can be retained in hospitals and blood centers, because keeping excessive number of blood units on inventory may result in blood product wastage. On the other hand, failure to stockpile on inventory can lead to shortage of this resource, and as a result may cause the cancellation of important activities such as treatment of special cases like surgery, accident, disaster circumstance and, in a worst case scenario increases the fatality rates at hospitals. This paper presents a dynamic mathematical model with the goal of improving the efficiency of blood related activities that occur at the blood centers. The model also caters for the assignment of whole blood units of available blood types to various requests. A set of equations that incorporate both the ABO and Rhesus blood groups are derived and presented subsequently. This further extends the initial work where only the ABO blood group was considered. In an effort to implement the developed model, three metaheuristic algorithms namely, symbiotic organisms search, symbiotic organisms search genetic algorithm, and symbiotic organisms search simulated annealing algorithms are proposed to identify the optimal routing for each of the blood types. An extensive numerical study was carried out using datasets from a synthetic blood sample collection process to illustrate the potential of the three metaheuristic algorithms to solve the developed blood assignment model. Furthermore, experimental results show that the hybrid symbiotic organisms search algorithms not only achieve superior accuracy, but also exhibits a higher level of stability, with the hybrid symbiotic organisms search genetic algorithm having the overall best superior performance. [ABSTRACT FROM AUTHOR]

• Recently discovered oscillations during CO oxidation over Ni were modeled. • The first mathematical model producing oscillations in excess CO was developed. • The T range of the oscillations and their waveforms and amplitudes were simulated. • Ni color variation during oscillations is caused by the O dissolution in the bulk. This paper presents the first mathematical model simulating the recently discovered oscillatory behavior during CO oxidation on a Ni foil in a continuous-flow catalytic reactor. These oscillations occur in the presence of excess CO; thus, the well-known Sales–Turner–Maple model, simulating oscillations in oxygen excess, cannot be applied. We suggest a modification of the Sales–Turner–Maple model by introducing the precursor-mediated adsorption of CO. This made it possible to simulate the oscillations under reducing conditions. The suggested microkinetic model coupled with a continuous-flow reactor model predicts that the oscillations proceed on the partially oxidized catalyst because of the periodic formation and reduction of the surface oxide. The introduction of oxygen diffusion into the subsurface layers allows the description of the experimentally observed variation in Ni color during the oscillatory cycle. The developed model successfully reproduces experimental data as the temperature range of the oscillations together with their shape and amplitudes. [ABSTRACT FROM AUTHOR]

Pressure cartridge type separation devices which are widely used in fairing, stage separations of space launch systems, and many other aerospace fields generate much lower pyroshock and produce no high-speed debris compared to frangible explosive separation devices. However, because the operation is completed in a few milliseconds and the releasing mechanism is complicated, their separation behavior is difficult to experimentally identify. This paper presents a mathematical model to simulate the separation behaviors for a split-type separation bolt, one of the pressure cartridge type separation devices. The mathematical model includes a combustion model, buckling resisting model, split behavior model related to static and dynamic friction, O-ring friction model, contact force model, and slip angle model. Each composing models are obtained by mathematical formulation or numerical analysis. An efficient contact model is constructed by using virtual penetration model appropriately for complex contact phenomenon. To validate the established model, separation experiments were performed; the results are then compared with the mathematical model. Present study show that complex mechanical behaviors coupled with combustion of solid propellant charge can be efficiently simulated by the mathematical model. • Established a mathematical model for a low-shock separation device using pressure cartridge. • Analyzed complicated separation behavior of the low-shock separation device. • Simulation results were well compared with separation experimental results. [ABSTRACT FROM AUTHOR]

This paper deals with an application of the fault detection and diagnosis algorithm based on nonlinear Kalman filter methods for transient state of an open-cycle liquid propellant rocket engine. In order to develop the algorithm, we designed two types of the nonlinear Kalman filter which are the extended Kalman filter and unscented Kalman filter with non-linear model of the liquid propellant rocket engine. Then using the measurement data of some important parameters of the engine, the residuals from the nonlinear Kalman filters are obtained. Using the residuals, we can detect and diagnose faults in the components of the engine by using the multiple model method. To confirm the fault detection and diagnosis algorithm, we developed mathematical model of an open-cycle liquid propellant rocket engine and artificially injected various faults such as decreasing turbopump efficiency. And then, perform the fault detection and diagnosis algorithm and check the performance of the algorithm. This process is numerically demonstrated for the open-cycle liquid propellant rocket engine under start-up process by using the simulated measurement data from the mathematical model of the engine. • A mathematical model for the transient state of an open-cycle liquid propellant rocket engine (OPLPRE) is developed. • Two variations of the nonlinear Kalman filter are used for fault detection and diagnosis (FDD) algorithm of the OPLPRE. • The FDD algorithms can be applied to the transient state of the OPLPRE. • The performances of the FDD algorithms are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

• We establish the first mathematical model for portraying inner behaviors and computational procedures of mimic computing. • We propose a novel type of automata called mimic automata, i.e., the new model mentioned above. • The formal semantic and expressive ability of the new automata is obtained. • In an application scene, this new model is employed to address a problem on systematic structures of mimic computers. In this paper, we aim to establish a mathematical model for mimic computing. To this end, we present a novel automaton called a mimic automaton. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a computing unit, a sequential automaton is employed to describe some state transitions, a hierarchical automaton is employed to express the different granularities of some computing units, and a probabilistic automaton is used to depict some random changes of a computing unit. Second, a mimic automaton is obtained by combining the various types of automata mentioned above in a certain logical relationship. Compared with the existing models of mimic computing, the new model portrays the operational semantics for a mimic computing system, and it can directly describe the behaviors of a system. Furthermore, the new model possesses a stronger generality. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of determining the requirements for the maintenance of circular, displaced, non-Keplerian orbits around the Sun by means of a magnetic sail-based spacecraft. The magnetic sail is an exotic propellantless propulsion system that gains thrust from the magnetostatic interaction between the solar wind and an artificial magnetic field, which is generated on board by an electrical current flowing through a loop of conducting material. The propulsive requirements are given in terms of characteristic acceleration and thrust (cone) angle. The analysis is performed using a recent mathematical model in which the magnetic sail thrust vector is expressed as a function of the Sun-spacecraft distance and the sail attitude. Moreover, a linear stability analysis is carried out to identify the (marginally) stable displaced orbits when an error in the orbital insertion is assumed. [ABSTRACT FROM AUTHOR]

• A meta-plate with high-static-low-dynamic stiffness local resonators is proposed. • Mathematical modeling of the meta-plate is established and solved by plane-wave expansion method. • The band gaps are predicted analytically and validated by numerical simulations. • The meta-plate with HSLD resonators can generate very low-frequency band gaps. Aiming to attenuate very low-frequency flexural wave in a thin plate, this paper proposes a meta-plate model by periodically attaching high-static-low-dynamic-stiffness (HSLDS) resonators onto the thin plate. The HSLDS resonator consists of a linear spring with a negative stiffness mechanism (NSM) in parallel, and thus its stiffness can be adjusted to any low values within a range from zero to the stiffness of the linear spring. Using the plane-wave expansion (PWE) method, and considering the linearized stiffness of the resonator, the dispersion relation of the meta-plate can be derived and the band structure can be obtained. A dynamic model of the meta-plate with the original nonlinear stiffness under external excitations is also established. The numerical simulations are carried out by the Galerkin method to evaluate the band structure and study the propagation of the flexural wave along the meta-plate with different azimuth angles. The analytical results exhibit good agreement with the numerical ones, which indicates that the proposed meta-plate can create a very low-frequency band gap. [ABSTRACT FROM AUTHOR]

• We show that algebraic methods of Cárdenas-Barrón [2] are questionable. • We provide our improvements for algebraic methods of Cárdenas-Barrón [2]. • We indicate that Sphicas [1] already solved these models by algebraic methods. This study examines the paper of Cárdenas-Barrón, entitled "The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra." that was published in Applied Mathematical Modelling at 2011 to point out it contains questionable results. The algebraic geometry and algebra applied by Cárdenas-Barrón [2] violated the rule of the arithmetic-geometric mean (AGM) mentioned by Cárdenas-Barrón [74]. Moreover, we point out Sphicas [1] had already solved this kind of EOQ and EPQ models using algebraic methods. [ABSTRACT FROM AUTHOR]

• We study a new hot rolling scheduling problem from compact strip production. • We divide the problem into two sub-problems of minimizing virtual sheet strips and optimizing the sequence of sheet strips. • An improved heuristic is developed to minimize virtual sheet strips. • A multi-objective evolutionary algorithm is proposed to optimize the sequence of sheet strips. • The effectiveness of the presented algorithms is demonstrated by example instances from practice. This paper addresses a hot-rolling scheduling problem from compact strip production processes. At first, a mathematical model that consists of two coupled sub-problems is presented. The first sub-problem is the sheet-strip assignment problem that is about how to assign sheet-strips to rolling-turns with the objective of minimizing virtual sheet-strips. The second is the sheet-strip sequencing problem that is about how to sort the sheet-strips in each rolling-turn with the objective of minimizing the maximal changes in thickness between adjacent sheet-strips and the change times of the thickness so as to ensure high quality sheet-strips to be produced. And then, an improved hot-rolling scheduling heuristic is proposed to solve the sheet-strip assignment problem. A multi-objective evolutionary algorithm is developed to find the Pareto optimal or near-optimal solutions for the sheet-strip sequencing problem. Besides, the problem-specific knowledge is explored. The key operators including crossover operator, mutation operator and repair operator are designed for the multi-objective evolutionary algorithm. At last, extensive experiments based on real-world instances from a compact strip production process are carried out. The results demonstrate the effectiveness of the proposed algorithms for solving the hot-rolling scheduling problem under consideration. [ABSTRACT FROM AUTHOR]

• A model was developed for forced convection condensation in the presence of air. • Condensation influences the mixture flow only through the boundary condition. • The proposed model was verified using published experimental data. • The tube bundle case was viewed as more closely reflecting industrial devices. This paper presents a description and the results of verification of an unsteady model for forced convection condensation on a smooth single horizontal tube in the presence of noncondensables. The external flow is described by the two-dimensional (2D) unsteady Navier–Stokes equations for a laminar regime or by the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for a turbulent regime, and the condensate film is considered using a one-dimensional model. Details of the numerical implementation of the developed algorithm are described. The available literature data were employed to verify the proposed model for forced convection condensation for an arbitrary flow direction of vapour with and without noncondensables. The numerical results are in good agreement with the published experimental data. In the proposed model, condensation influences the air-vapour mixture flow only through the boundary condition; therefore, this model can be easily implemented using different computational fluid dynamics (CFD) codes (in this work, an "in-house" CFD code ANES) for modelling more complex configurations, like tube bundles. Results for condensation on five tubes in a tube bundle are also presented in this work. The influence of mutual irrigation of pipes by drops coming off was also approximated. [ABSTRACT FROM AUTHOR]

• Developing a multi-objective optimization model to redesign of GSBE-SNR considering incoterms. • Integrating social objectives into multi-objective model. • Greenhouse gas emission savings are maximized in the global sustainable bioenergy network. • Using GIS software to draw precise maps of the studied countries before and after redesigning. • Iran-o-Armenia case study with taking the sustainability conditions of each country into account. In today's industrial world, depletion of fossil resources and the adverse environmental effects of consuming fossil fuels have become one of the serious challenges in sustainable development of the societies. In recent years, substantial attention has been paid to using biomass for producing bioenergy in order to increase economic performance, reduce environmental effects, and providing new opportunities in different societies in pursuit of sustainable development. The complexities related to procurement, logistics, technology selection, raw material management (biomass), and product distribution planning are the main causes of using the optimization models to design the bioenergy supply chains. On the other hand, the globalization of economy and industry increased the significance of the subjects related to global logistics and the ecological and social objectives of the countries have undeniable influences on each other. Hence, in this paper, a mathematical model has been developed to redesign a global bioenergy supply network. This model has simultaneously studied the economic, environmental, and social objectives and the environmental coefficients of the model were calculated using SimaPro software. The multi-objective model was solved by augmented ɛ-constraint method and the decision makers were informed of the obtained Pareto solutions. Data taken from the study on Iran and Armenia was used to validate the model and the Geographic information system (GIS) software was used with the goal of studying the geographical map of each country more accurately. [ABSTRACT FROM AUTHOR]

The production of mixed municipal waste changes due to the increase of separation rate, urbanization and other factors. The future changes in the legislation and technology development influences the way the waste is being treated. Thus the method, location and capacity of processing sites are unknown. The realization of future projects can be supported by the developing of transportation infrastructure. Such a feature may be represented by a robust transfer station grid, which can be designed to handle all possible future realizations and technological solutions (establishment of waste treatment facilities). The paper presents an approach utilising a mathematical model for the design of transfer stations. It is formulated as a multi-objective two-stage mixed-integer stochastic programming problem, where the trade-off between the environmental aspect and the economic viability is considered. The model is tested through a case study for the Czech Republic, where the waste treatment of over 6,000 municipalities is analysed. The solutions for different preferences are assessed throughout the principle called out-of-sample stability with 10,000 scenarios. The optimal decision consists of the robust transfer station grid with selected locations and their respective capacity. The particular solution with respect to the potential trade-off suggests to save 1.148 mil of travelled kilometres with only 0.77 mil EUR. The output in the form of decision support can serve possible stakeholders from the field of waste management to plan more sustainable projects. • A transfer station grid designed to handle future realizations and developments. • The efficiency of waste transport was analysed for more than 6000 municipalities. • A trade-off between environmental aspects and the economic viability was considered. • A solution suggests to save travelled 1.148 mil km with only extra 0.77 mil EUR. • Introduction. [ABSTRACT FROM AUTHOR]

• We propose a model for direct contact membrane distillation that accounts for fouling. • We design an adaptive observer for descriptor systems. • We use the adaptive observer for the estimation of the thermal resistance of the fouling. • Simulations are presented to show the effectiveness of the approach. This paper develops a lumped parameter model-based method for membrane fouling detection in Direct Contact Membrane Distillation (DCMD) process. First, a previously published mathematical model of DCMD is extended to account for the thermal resistance of the fouling layer. Then, an adaptive nonlinear descriptor observer is developed. The adaptive observer estimates the thermal resistance of the fouling layer in addition to the temporal and spatial temperature distribution of the bulk feed and permeate solutions and at membrane interface layers. Simulation results are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Preload relaxation, caused by elastic interaction between tightened bolts, is one of the major reasons for non-uniformity of pretension force. But how to accurately assess the residual tension of a bolt is still extremely difficult. This paper considers two types of multiple bolted joint and six kinds of tightening sequence. Based on the deformation compatibility equation and elastic interaction stiffness, the generalized mathematical model for evaluating residual preload of bolts is established. Certain model parameters are obtained through numerical simulation. To analyze the influence of initial tightening torque, spacing between bolt holes, bolt material and gasket material on the elastic interaction stiffness, experimental devices and test procedures are developed. Furtherly, preload relaxation models are validated by tests conducted on six types of multi-bolted joint with the same surface roughness. Results of the proposed mathematical model of pretension force show a good consistency with those of corresponding experiment. • A mathematical model for estimating preload relaxation of bolted joint subjected to elastic interaction was established. • The elastic interaction stiffness between bolts was analyzed based on developed Experimental devices and test procedures. • The proposed mathematical model of pretension force shows a good consistency with the corresponding experiment. [ABSTRACT FROM AUTHOR]

• A 3D reconstruction for anisotropic media is proposed. • A double-layer and multi-grid system is proposed. • The updated pattern density function simulation is adopted. • Dimensionality for 3D reconstruction is reduced. The physical properties of porous media can be more effectively observed and understood when analyzing three-dimensional (3D) structures. The use of computer-based mathematical modeling methods has been proven effective for reconstructing 3D structures of porous media from two-dimensional (2D) images. However, reconstructing a heterogeneous 3D structure from a single 2D image is currently challenging for computer-based mathematical modeling methods. Focusing on the reconstruction of heterogeneous 3D structures from a single anisotropic training image (TI), this paper first introduces a morphological completeness analysis method , which presents a completely new approach to reconstruction in which only two sections are controlled. Then, to enhance the constraint on the simulation points in this new approach to reconstruction, a double-layer and multi-grid system (DLMGS) is proposed. The updated pattern density function simulation , based on the DLMGS, is then taken as the specific reconstruction algorithm in this work. Finally, our reconstruction method is tested using a core image, and the performance of the reconstruction result is assessed using multiple functions. Detailed experiments show that our method can successfully reconstruct a heterogeneous 3D structure from a single anisotropic image, which reduces the required dimensionality of input data for 3D reconstruction and extends the applicable scope. [ABSTRACT FROM AUTHOR]

• A mathematical model to bring symmetry in knee joints angle trajectories. • A comparison between grid search and optimization is reported. • Damping adjustment of microprocessor based prosthetic knee joint with minimum effort. • An automated and time-efficient method for adjusting damper's parameter. In this paper, we developed a mathematical model to find the parameters of prosthetic damper which will provide a similar trajectory for the prosthetic knee joint. Two popular searching methods namely grid searching and optimization are used to determine the damper's parameters. The proposed model is validated with a simulation process using the data of the able-body individuals. We utilized the ground reaction force of sound limb to determine the values of the damper parameters of a prosthetic knee joint for maximum symmetry. Symmetry between knee moments was also improved in the stance period with optimized parameters. Finally, optimization-based searching was observed to be more computationally efficient than the grid-based searching method. The present study will provide a virtual solution to set the prosthetic dampers parameters based on user needs. In the future, the present method can be used for adjusting damping of microprocessor prosthetic knee joint for symmetrical gait pattern. [ABSTRACT FROM AUTHOR]

• An integral methodological approach is proposed for the design and assessment of biorefineries. • Conceptual design and optimization are the main stages of proposed strategy. • The mathematical model includes a cogeneration system and a wastewater treatment. • The generic approach is applied to a study case of CCS biorefinery. This paper presents a generic and integral methodological approach for the design and assessment of multiproduct biorefineries. The proposed methodology has been developed based on 2-stage strategy, conceptual design and optimization. In the conceptual design stage, the theoretical data about the biorefinery are collected in order to build the superstructure. In the optimization stage, the formulated superstructure based on surrogate models, is optimized in order to generate the optimal biorefinery configuration where the utilities are produced internally from biomass via a cogeneration system. The proposed framework is applied to evaluate the optimal exploitation of Coffee Cut-Stems (CCS). The results show that ethanol is the most interesting product following dilute acid pretreatment and the fermentation of C5 and C6 sugars due to the large yield of the process. However, an alternative scenario where energy is the protagonist, results in the selection of power and heat as main products. [ABSTRACT FROM AUTHOR]

The paper deals with the studies of the forced impacting oscillator when taking into account the dry and viscous resistance as well as the generalized Hertz contact law during an impact. Numerical investigations of the mathematical model are accompanied by validations obtained with an experimental rig. To study the solutions of the mathematical model, the sequences of impacts, when the system evolves in periodic and chaotic modes, is used. The statistical properties of chaotic impact events are considered in detail. In particular, successive iterations of the impact map, autocorrelation function and coefficient of variation for the impact train, histograms for the inter-impact intervals and values of obstacle penetrations are analyzed. It is revealed that the impact sequence is stationary but non-Poissonian and contains temporal scales that do not relate to the external stimulus. This sequence can be described by a bimodal distribution. The findings are confirmed by the analysis of experimental data. • Mathematical model and experimental stand of a forced impacting oscillator are studied. • Impact event sequences are considered numerically and experimentally. • Statistical properties of event sequences are examined. • Agreement between properties of numerical and experimental model is shown. [ABSTRACT FROM AUTHOR]

We consider foliations given by deformations d F + ϵ ω of exact forms dF in C 2 in a neighborhood of a family of cycles γ (t) ⊂ F − 1 (t). In 1996 Françoise gave an algorithm for calculating the first nonzero term of the displacement function Δ along γ of such deformations. This algorithm recalls the well-known Godbillon–Vey sequences discovered in 1971 for investigation of integrability of a form ω. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon–Vey sequences to the Françoise algorithm settings. [ABSTRACT FROM AUTHOR]

It seems that the index theory for non-compact spaces has found its ultimate formulation in the realm of coarse spaces and K -theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and interesting examples of this program. In this paper we formulate a combination of these two theorems and establish a partitioned-relative index theorem. [ABSTRACT FROM AUTHOR]

We extend our analysis of divergence-free positive symmetric tensors (DPT) begun in a previous paper. On the one hand, we refine the statements and give more direct proofs. Next, we study the most singular DPTs, and use them to prove that the determinant is the only quantity that enjoys an improved integrability. Curiously, these singularities are intimately related to the Minkowski's Problem for convex bodys with prescribed Gaussian curvature. We then cover a list of models of mathematical physics that display a divergence-free symmetric tensor; the most interesting one is probably that of nonlinear Maxwell's equations in a relativistic frame. The case of the wave equation is the occasion to highlight the role of the positivity assumption. Last, but not least, we show that the Vlasov–Poisson equation for a plasma is eligible for our theory. [ABSTRACT FROM AUTHOR]

The mathematical modeling problem of a general turbofan aeroengine control system used in autonomous aircraft is investigated in this paper. Unlike the thermodynamics or physical mechanism-based modeling methods in the existing literature, a pure data-driven modeling approach is presented with high accuracy via online and offline data only. This is achieved by using the nonlinear autoregressive neural network with exogenous inputs (NARX) neural network. In comparison with the existing NARX-based MIMO modeling methods, the series–parallel structure and the parallel structure are integrated for the neural network training. Faster convergence and stability as well as higher modeling accuracy are thus achieved. Another feature of this approach is that it is independent of all the components' dynamics in the turbofan aeroengine. Simulation results are given to verify the effectiveness of the proposed modeling approach. This is further validated by experimental testing with the method applied to mini turbofan aeroengine testbed. [ABSTRACT FROM AUTHOR]

Epidemiological-Mathematical models are powerful tools for estimating the course of a pandemic and exploring different scenarios through pandemic intervention policies (PIPs). These models are commonly developed to provide decision-support tools for policymakers who are forced to make difficult decisions in a timely manner. Done properly, these models are able to provide a safe, quick, and cheap solution for this challenge. There are numerous types of mathematical models for epidemiological disease spread and control. However, in order to become applicative tools for decision-making, the modelers of these models are required to overcome three computational challenges: efficiently define the model, develop it as computer software, and fit it into historical data. Performed efficiently, one can use the obtained tool to explore possible scenarios and PIPs. In this paper, we present a critical review of models that extend the Susceptible–Infected–Recovered (SIR) model and explore the efficiency of these models, their software characteristics, and model performance on real-world data. We further provide a guide for epidemiological-mathematical model development and implementation, exploring several modeling approaches and their respective implementation options. Lastly, we outline the current trends, limitations, and opportunities in this field. In particular, we find that the spatial properties of a model play a critical role in its accuracy and ability to explain historical pandemic spread, especially in the context of airborne diseases. Moreover, we show that agent-based simulations are preferable over partial/ordinary differential solvers when considering a highly-realistic pandemic model or focusing on a relatively small population size. • Spatio-temporal extended SIR models are useful tools to predict pandemic spread. • Intervention policies investigated by extended SIR have to take economics into account. • Agent-based simulation outperforms ODE-based modeling for most of the cases. [ABSTRACT FROM AUTHOR]

• The thermodynamic compatibility of initial conditions is investigated. • Analytical solutions of the Guyer-Krumhansl equation is provided. • The maximum principle for the Guyer-Krumhansl equation is proved. • The results are supported by computational calculations. In the literature, one can find numerous heat conduction models with different backgrounds. In general, a heat equation beyond Fourier consists of additional time and spatial derivatives, which makes it more challenging to solve the mathematical model correctly. In the present paper, we revisit the famous Guyer-Krumhansl heat equation for which it has been reported earlier that can lead to negative temperatures by violating the maximum principle. We show that for proper initial and boundary conditions with thermodynamic compatibility, the maximum principle is fulfilled. Our work further emphasizes the importance of the thermodynamic origin of heat equations and their compatibility with the second law. Furthermore, we use two different approaches how to determine the initial state in a thermodynamically compatible way. Computational simulations support our results. [ABSTRACT FROM AUTHOR]

• Comprehensive review of mathematical programming models for shale oil & gas development. • Detailed comparison of publications in five major topic areas: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) LCA & sustainability. • Highlight of optimization deployment success stories in industry (i.e., optimization value proposition in oil & gas). • Perspective on outstanding research opportunities in the respective field of study. In this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas. [ABSTRACT FROM AUTHOR]