Mathematical modelling and dynamic simulation of multi-effect falling-film evaporator for milk powder production

Multiple-effect evaporators are widely used in dairies and food industries because they are appropriately suited for concentrating food solutions. Some mathematical models for multi-effect evaporators are reported in previous studies. But most of them are steady-state models, and there are no extensive studies on the dynamic behaviour of these evaporators. In this paper, two types of dynamic model, lumped and distributed, are developed for an industrial four-effect falling-film evaporator which is used to concentrate whole milk. These models are validated with data from an industrial unit. The results show that the distributed model has slightly better predictions than the lumped model, but the lumped model has comparable performance because its structure is simple and the needed simulation time is short in comparison with the distributed model.     

Developing a Visual Interactive Model for Corporate Cash Management

The operational research/management science journals contain an extensive literature that addresses the corporate cash management problem; yet few, if any, companies make use of any of this published work in their daily cash-management decision making. A review of the literature suggests that the reason for this lack of applications may well be poor problem formulation—the problems that are solved in the literature as ‘cash management’ problems evolve from a ‘hard systems’ view of real-world cash management. However, the problem as perceived by cash managers involves both dynamic and loosely structured components which are difficult to model using classical (i.e. ‘hard systems’) approaches.We therefore decided to approach the cash management problem as an experiment in the use of a novel visual interactive problem solving (VIPS) methodology. The aim of the experiment was to develop an implementable, visual interactive model to support daily cash management decision making. Working closely with a corporate cash manager, we first developed a visual model of his daily decision problem and then agreed on the feasible options and the interactive requirements. At this stage, the problem was sufficiently well defined for a mathematical model to be built and the visual model made ‘smart’.This paper discusses the results of this experiment and suggests that VIPS may have distinct advantages as a problem-solving technique in loosely structured, ‘messy’ problem situations.     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

The Development of a Mathematical Model of the Operations of a National Glass Manufacturer

In this paper, a mathematical model of the entire operations of a national glass manufacturer is developed. This includes the float glass manufacture, distribution, storage operations and the technical considerations dictated by the plant as well as the operating procedures. The model is initially for a planning year, and is generated from a ‘monthly model’. This monthly model interconnects with other monthly models primarily via stock flows. The mathematical model is formulated in a unique way that allows certain production aspects to be modelled using a ‘pseudo-continuous’ time frame, rather than a discrete one. The generation of the overall model (as a mixed integer linear programming problem) and its solution is also discussed.     

On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid

In this paper, the vibration characteristics of transversely isotropic magneto-electro-elastic (MEE) rectangular plates in contact with fluid are investigated. The mathematical formulation on the determination of added virtual mass for water-contacting MEE rectangular plates with uniform thickness is performed. Based on the recently proposed differential equation governing the dynamical responses of the MEE rectangular plates, a fluid-structure interaction model is established and analyzed. First of all, the added virtual mass incremental (AVMI) factor of the system is calculated by using the proposed approach and the added virtual mass can then be obtained, furthermore, the natural frequencies of the MEE rectangular plates in contact with fluid with different boundary conditions are also investigated. It is noted that the natural frequencies based on the proposed method are very useful for those engineers or researchers who are engaged in the vibration analysis and design of the MEE plate in contact with fluid.     

The dynamics of athletic performance,fitness and fatigue

We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the two well-known principles ‘train to failure’ and ‘use it or lose it’. The anabolic and catabolic processes are modelled with differential equations. Fitness is defined as muscle fitness. We model the work power of any muscle or set of muscles, and the muscle's maximum work power. Parameters are estimated and we present analytical and numerical results. The relationships between performance, fitness and fatigue are demonstrated for various activity scenarios. For example, the model quantifies the exact manner in which the optimal rest period can be determined to maximize the performance on a given day. The model provides realistic predictions, and constitutes a powerful tool which describes the processes by which performance, fitness and fatigue can be regulated and controlled.     

Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example

Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the system’s solutions only via numerical integration. In this work, we demonstrate utilization of the perturbation expansion method for analyzing a model example of mixed locomotion system—the twistcar toy vehicle, which is a variant of the well-studied roller-racer model. The system is investigated by assuming small-amplitude oscillatory inputs of either steering angle (kinematic) or steering torque (mechanical), and explicit expansions for the system’s solutions under both types of actuation are obtained. These expressions enable analyzing the dependence of the system’s dynamic behavior on the vehicle’s structural parameters and actuation type. In particular, we study the reversal in direction of motion under steering angle oscillations about the unfolded configuration, as well as influence of the choice of actuation type on convergence properties of the motion. Some of the findings are demonstrated qualitatively by reporting preliminary motion experiments with a modular robotic prototype of the vehicle.     

Model validation in operations research

Numerous articles have appeared in the literature expressing different degrees of concern with the methodology of OR in general and with the validation of OR models in particular. Suggestions have been formulated to remove some of the shortcomings of the methodology as currently practised and to introduce modifications in the approach because of the changing nature of the problems tackled. Advances in modeling capabilities and solution techniques have also had considerable impact on the way validation is perceived. Large scale computer-based mathematical models and especially simulation models have brought new dimensions to the notion of validation. Terms like ‘confidence’, ‘credibility and reliability’, ‘model assessment and evaluation’, ‘usefulness and usability of the model’ have become rather common. This paper is an attempt, through an interpretation of the literature, to put model validation and related issues in a framework that may be of use both to model-builders and to decision-makers.     

Micromixing effects on the dynamic behavior of continuous free-radical solution polymerization tank reactors

The degree of mixing in polymerization reactions can be influenced by various factors that can also affect the reactor performance. For this reason, a detailed micromixing model was implemented to study the effects of micromixing on the dynamic behavior of continuous free-radical solution polymerization tank reactors. The reactor model was used to perform the bifurcation analysis of the reacting system, paying special attention to the effect of micromixing parameters on the reactor behavior. The bifurcation study showed that multiple steady-states and periodic oscillations can be observed under partially segregated micromixing conditions. Moreover, the micromixing model was able to describe the dynamic responses presented by perfectly mixed and completely segregated reactors. These results indicate that this class of reactors can exhibit more complex dynamic behavior than shown until now.     

Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys

In this paper a thermomechanical model for the dynamics of structural phase transitions in the so-called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non-linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local-in-time existence of weak solutions is shown.     

Exact physical model of magnetorheological damper

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.     

Zur Gleichwertigkeit zweier Arten der Randomisierung

For the choice of a mathematical model describing randomized decisions it is important to make sure that given a ‘behavioral decision rule’ there exists an equivalent ‘randomized decision function’ (cf. [2], p. 24–26). This fact seems to be known only in some special cases (cf. [1], Th. 8.3.1 and [3]). Here we give a simple proof for the general case.     

On buffers with periodical input traffic

The paper considers an infinite discrete-time buffer system with one single output channel. Unlike most analyses of such a buffer system, the present study uses a ‘dynamic’ model for the arrival process of data units into the system. More specifically, the distribution of the number of arrivals per discrete time-unit is allowed to fluctuate in time, in a periodical fashion, whereas in classical models this distribution remains the same, as time goes by. The probability generating function of the number of data units in the buffer, at various time instants, is derived under such dynamic arrival conditions. An extended illustrating example, comparing ‘static’ and ‘dynamic’ arrival models, concludes the paper.     

On designing experiments for a dynamic response modeled by regression splines

Dynamic response systems are often found in science, engineering, and medical applications, but the discussion on experimental design for such a system is relatively rare in literature. For an experimenter, designing such experiments requires making decisions on (1) when or where to take response measurements along the dynamic variable and (2) how to choose the combination of experimental factors and their levels. The first consideration is unique for such experiments, especially when the measurement cost is high. In this paper, we present a design approach through the mixed‐effect linear model, which is based on a hierarchical B‐spline function for the dynamic response. We develop several theorems that can assist in finding a statistically efficient sampling plan and propose an algorithm for searching the D‐optimal design of a dynamic response system.     

Chattering in dynamic mathematical two-phase flow models

This paper presents a chattering problem which arises in a dynamic mathematical two-phase flow model. The real system under study is also introduced, the DISS test facility, a parabolic-trough solar thermal power plant. The heat transfer fluid in the DISS facility is the steam-water mixture. A dynamic model of this plant, using Modelica as the modeling language, was previously developed in order to study its behavior. Chattering arises in the pipe model reducing the computational performance and hence limiting the applicability of the model. The problem source is studied and analysed together with an approach to the problem which is based on the smooth interpolation of some thermodynamic properties.     

Comparative statics of a signaling game: An experimental study

In this paper a simple and basic signaling game is studied in an experimental environment. First, we check whether we can replicate some of the findings in the literature concerning equilibrium selection and the use and impact of costly signals. Second, and foremost, the comparative statics implications of the game are studied. The experimental results are related to the predictions of two competing behavioral models: a game model, in which subjects are assumed to behave in line with (refined) sequential equilibrium theory, and a decision model, in which subjects are assumed to behave as non-strategic decision makers. The experimental outcomes replicate the finding in the literature that costly messages are sent more frequently by ‘higher’ sender types (whose information is such that persuasion is also profitable to the responder), and that such messages have an impact on the behavior of the responder. These results are consistent with (versions of) both the game model and the decision model. The comparative statics results, however, clearly point in the direction of the decision model. Play is most strongly affected by ‘own’ payoff parameters, as predicted by the decision model, and less so by opponent's payoff parameters, as predicted by the mixed strategies of the refined sequential equilibrium. Particularly, a decision model in which players are assumed to adapt beliefs about opponents' choice probabilities in response to experience in previous play, appears to succeed best in organizing the data.     

Quantum electronic transport in graphene: A kinetic and fluid‐dynamic approach

We derive a fluid‐dynamic model for electron transport near a Dirac point in graphene. Starting from a kinetic model, based on spinorial Wigner functions, the derivation of the fluid model is based on the minimum entropy principle, which is exploited to close the moment system deduced from the Wigner equation. To this aim we make two main approximations: the usual semiclassical approximation (??1) and a new one, namely, the ‘strongly mixed state’ approximation, which allow to compute the closure explicitly. Particular solutions of the fluid‐dynamic equations are discussed which are of physical interest because of their connection with the Klein paradox phenomenon. Copyright © 2010 John Wiley & Sons, Ltd.