A short note on the solution of a multi-effect evaporator system employed in pulp and paper industry

In this short communication the solution of a steady state model of a sextuple evaporator system used in a paper industry has been presented. With the help of the residual values of model equations (a set of 12 nonlinear algebraic equations) it has been shown that the presently obtained results are superior to the previously published results. The importance of the number of significant digits in calculation are also briefly discussed.     

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.     

Modeling industry structure and economic performance

This paper presents a simultaneous equations model of profitability, concentration, advertising expenditures and research and development outlays. The data are subjected to regression diagnostics in an effort to ascertain the importance to the estimation results of a subset of the data that can have a disproportionate influence. The estimation results, especially for the advertising expenditures relationship and the research and development outlays equation, do change when a truncated data sample (based on the omission of the outliers) is used. This serves partially to explain why there is some disagreement in the literature on market structure and economic performance.     

Modeling, simulation and optimization in logistics

This text summarizes the PhD thesis defended by the author in March 2009 under the supervision of Pasquale Legato at the University of Calabria, Italy. The thesis is written in English and is available for download at the following URL: . It aims to explore friendly Operations Research tools for modeling and simulation of logistics processes, with particular interest for mathematical programming models combined with stochastic simulation tools. In particular key assignment and scheduling problems that arise in maritime container terminals are explored. Initially it is presented a study on different modeling paradigms devoted to the representation of logistical processes and the formalization of problems with complex scheduling/assignment constraints. Successively an IP model for managing the assignment of a pool of rail-mounted gantry cranes to berthed vessels is proposed. Then, according to a functional integration approach, a second model centered on the intra-ship scheduling of vessel container bulks to the assigned cranes is further formulated. Finally a simulation-based optimization approach is investigated and the effectiveness of recent search methods is evaluated by comparison with a commercial solver.     

Modeling and simulation of pollutants transport in rivers

This paper is devoted to mathematical modeling and computer simulation of diffusion and transport of chemicals in rivers. We present one-, two-, and three-dimensional models in terms of time-dependent convection–diffusion–reaction differential equations, further we give the finite difference approximation and appropriate numerical algorithms for these models, and finally we discuss briefly the computer implementation of this methodology in a user friendly software package. To verify the model and the computer code we have used it to study the diffusion and transport of chemicals, in this case NO₃ and PO₄, in two rivers in Western Georgia flowing into the Black Sea. Namely, we considered the river Khobistskali subject to pollution sources Ochkhomuri and Chanistskali river Choga polluted with NO₃.     

Modeling of spraying with time-dependent material feed rate

This paper presents a mathematical model for predicting the thickness of coatings deposited by means of spraying onto rotating parts with circular symmetry, for the case of time-dependent material feed rate. A procedure for calculating the material feed rate control law providing production of coatings with uniform thickness or coatings with a predefined law of thickness variation is developed. The proposed procedure was used to analyze the process of spraying onto the surface of a rotating disc. A material feed rate variation law providing production of uniform coatings and coatings with linear thickness variation is calculated. It is demonstrated that for the first case the optimal law of material feed rate variation is described by a linear function and for the second case it can be successfully approximated by a quadratic function. The proposed calculation technique can be easily used for the case of coatings with a more complex law of thickness variation.     

Modeling and simulation with operator scaling

Self-similar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries in two dimensions is given, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator self-similar processes.     

On positional simulation in dynamic systems

The problem of simulating delays and controls in a dynamic system described by ordinary differential-difference equations is examined. The simulation is carried out in real time by the feedback principle on the basis of information and the current phase states of the system, measurable with a certain error. The simulation algorithm proposed —an algorithm for reconstructing the unknown delays and controls —is a regularizing one in the sense that the simulation results become better the less the measurement errors in the system's phase positions. The ideological source of the proposed method of solving the problem is Krasovskii's extremal aiming principle /1, 2/. The paper extends the investigation in /3, 4/ and touches on /1–5/.     

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.     

Modeling and simulation of population balances in particulate systems

This article focuses on the modeling and simulation of population balance equations (PBEs) for simultaneous growth, nucleation and aggregation processes. Two numerical method are proposed for this purpose. The first method combines the method of characteristics (MOC) for growth process with a finite volume scheme (FVS) for aggregation process. The second method uses a high resolution finite volume scheme to solve the resulting PBEs. The numerical results show that both methods give accurate results. However, the first method is more efficient and accurate as compared to the second method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.     

Performance and learning in a simulation of oil industry dynamics

Experimental studies on decision making in dynamically complex simulated systems have shown that poor performance arises from decision makers’ failure to correctly interpret feedback information due to the confounding effects of stock accumulation, time delays between decisions and actions, and non-linearities between system elements.This experimental simulation study examines ways to improve performance through online information feedback that clarifies for subjects the task structure of their decisions including cause and effect. In order to test our ideas we devised an assignment for business school students using a microworld simulator representing the global oil industry. Subjects completed a set of six upstream investment tasks and their resulting financial performance was measured and recorded. The repeated measures factorial design included three different treatment groups, who received various task structure feedback during the first three trials only. A fourth control group received no task structure feedback at all.The results show that mean subject performance was significantly greater for the treatment groups during the first two trials, consistent with our view that task structure feedback is helpful. However, in later trials the performance of all groups, including the control group, eventually reached a similar plateau, some 30% below a behavioural benchmark. From these results conclusions are drawn about individual and team learning in complex dynamic systems.     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of dynamic sand dunes

The physics of granular materials is interesting from many points of view because they exhibit a wealth of phenomena that have both fluid and solid aspects [C.S. Campbell, Annu. Rev. Fluid. Mech. 22 (1990) 57, H.M. Jaeger, S.R. Nagel, R.P. Behringer, Phys. Today 494 (1996) 32]. Recently a difficult pattern was observed if sand falls in the space between two plates and passes an obstacle [Y. Amarouchene, J.F. Boudet, H. Kellay, Phys. Rev. Lett. 86 (2001) 4286]. The interesting behaviour occurs on top of the obstacle where a dynamic dune with a parabolic tip is formed. Inside this parabola, a triangular region of non- or very slow flowing sand is observed. Using factor analysis it is possible to extract latent parameters from a dynamic process. Applying a three factor model we can clearly identify the inner triangle (1st factor) and the outer parabolic pattern (3rd factor). The second factor we interpret as shock wave. Most interactions between particles take place in a relatively small region. We show that the pattern formation process depends on the restitution coefficients (particle–particle and particle–obstacle) and also on the particle size. These findings cannot be observed if standard velocity profiles are used to analyse the data. Our findings show, that most interactions take place in a relatively small area correlating with the particle size. If the interactions between different particles and particle–obstacle are elastic the formation of a non-flowing triangular region is more difficult as if inelastic collisions are used. The factor curves also clearly show that a pattern formation process has to be finished, before the next pattern can be formed.     

Modeling and simulation of chip formation in high speed cutting

The purpose of this short work is the thermomechanical modeling of shear band and chip formation during high-speed cutting. Shear bands develop in areas of maximal mechanical dissipation in which temperature-dependent softening dominates strainand strain-rate-dependent hardening. In the simulations, the well-known problem of the mesh-dependence of the shear-band development is addressed, involving both mesh size and mesh orientation. An example simulation is presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of the CLS cryogenic system

This paper presents results pertaining to the numerical modeling of the cryogenic system at the Canadian Light Source. The cryogenic system consists of a cryostat that houses a Radio Frequency (RF) cavity used for boosting the energy of an electron beam. For consistent operation of the RF cavity, it must be kept immersed in liquid helium at a constant level with the pressure in the gas space maintained to an accuracy of ±1 mbar. An improvement to the cryostat model suggested in [3] using control volumes is described. The model and numerical method developed for the liquid helium supply and gaseous helium return lines are validated using two different cases, viz., the liquid helium flow rate from the liquid helium transfer line and the gaseous helium flow rate from the cryostat for various heater power input settings. The numerical method described here is significantly more accurate, efficient, and flexible than that used in [1] based on an iterative bisection method.     

Mathematical model for waste minimization of a bleach plant in paper industry

In the present investigation a steady-state mathematical model is developed for a typical four stage CEHH bleaching sequence in Indian Pulp and Paper Industry. Each stage of the sequence is composed of chemical additions and mixing, reaction in a retention tower, and washing. Unit operation models were formulated using mass balances on liquor, fibres, kappa number, chemicals and COD based on the assumption of perfect mixing and quasi steady-state. The COD is used in this paper as an indication of the amount of effluent coming out from four bleaching stages. In order to validate the model, the simulated results are compared with the literature data; a good agreement is achieved between the simulated results with the literature data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dynamic model and simulation of system generation

Translated from Issledovaniya po Prikladnoi Matematike, No. 5, pp. 18–24, 1976.