Zbigniew Szwast

Complexity principle of extremality in evolution of living organisms by information-theoretic entropy

Abstract We consider evolution from a multiorgan (multistage) organism, which has a number of identical organs (e.g. a trilobite with many pairs of legs), to another organism, which has one organ modified (specialized) into a different part of the body (e.g. claws of a crab) at the expense of reduction in the number of non-modified organs. We observe that in early stages of evolution multiple organs (pairs of legs) may be created, and that extra organs may rapidly be reduced during later stages. We ask: Why do extra organs evolve during early stages of evolution? To answer the question we construct and then analyze a simple although basic model of evolution based on information-theoretic entropy. We show that an extremality principle is valid in which the increase in number of identical organs is led by the gradient of information entropy increasing with the number of these organs. On the other hand, the reduction in number of these organs, observed for later stages of evolution, results from catastrophes between submanifolds of evolution, the surfaces on which modifications (specializations) of organs may occur. Our conclusion is that modification (specialization) of organs, while in principle consistent with the entropy principle of extremality, may lead evolution to a region of catastrophes, and that these catastrophes may explain extinction of some species. The same mathematical model is applied for explanation of parallel evolution of animals and for some evolution problems of flowers.

Optimal temperature profiles for parallel-consecutive reactions with deactivating catalyst

Abstract A cocurrent tubular reactor with temperature profile control and recycle of moving deactivating catalyst has been investigated. For the temperature-dependent catalyst deactivation, the optimization problem has been formulated in which a maximum of a profit flux is achieved by the best choice of temperature profile and residence time of reactants for the set of catalytic reactions A+B→R and R+B→S with desired product R, the rates of reactions have been described separately for every reagent by the expressions containing (temperature dependent) reaction rate constants, concentrations of reagents, catalyst activity, as well as catalyst concentration in the reacting suspension and a measure of the slip between reagents and solid catalyst particles. The algorithms of maximum principle have been used for optimization. The optimal solutions show that a shape of the optimal temperature profile depends on the mutual relations between activation energies of reactions and catalyst deactivation. It has been proved that the optimal temperature profile is a result of the compromise between the overall production rate of desired reagent R (production rate in the first reaction minus disappearance rate in the second one), necessity of saving of reagents residence time (reactor volume) and necessity of saving catalyst; the most important influence on the optimal temperature profile is associated with necessity of saving the catalyst. When catalyst recycle ratio increases (mean number of catalyst particles residing in reactor increases), optimal temperatures save the catalyst, as the optimal profile is shifted in direction of lower temperatures. The same is observed when catalyst slip increases (catalyst residence time in reactor increases). Despite of variation in the catalyst concentration the optimal profile is practically the same because the decay rate is affected only by instantaneous activity of catalyst. When reactor unit volume price decreases, catalyst residence time increases, whereas optimal temperature profile is shifted to lower temperatures. When economic value of unit activity of outlet catalyst increases (catalyst with a residual activity still has an economic value), catalyst saving should be more and more intense. As far as possible, the optimal profile is shifted in direction of lower temperatures, whereas the optimal residence time is still the same. Then the optimal profile is isothermal at the level of minimum allowable temperature, whereas the catalyst is saved as its residence time in reactor decreases.

Optimization of multistage crosscurrent fluidized drying by a special algorithm of the discrete maximum principle with a constant hamiltonian

Abstract Optimization of minimum economic costs is formulated and solved for steady-state multistage fluidized drying. The optimized decision variables, which pertain to the inlet gas state at each stage, are temperatures, humidities and flows of gas. The original discrete algorithm, with a constant Hamiltonian for the multistage process, is used in optimal control computations. The optimal results are obtained numerically for the family of drying processes corresponding to various values of the parameter λ, which characterizes the sum of investment and gas pumping costs. The properties of the optimal solid and gas parameters are discussed. The optimization results for conventional drying processes (where the optimal decision values are the same for every stage) are also presented and compared with those found for unconventional (i.e. control) processes. For unconventional steady-state multistage crosscurrent fluidized drying the optimization problem has been formulated and solved. The decision variables (which pertained to the inlet gas state) were temperatures, humidities and gas flows. The optimum values of these quantities were chosen at each process stage. The economic effectiveness index, corresponding to the sum of the investment and operational costs, was accepted as a performance criterion. To express the cost of the drying gas in terms of the drying parameters (gas temperature and gas humidity) an economic balance of the dryers investigated was made. In this balance the so-called exergy tariff of prices was applied for the purpose of quantitative evaluations. Then, the expression describing the performance criterion was transformed into some special form in which, together with physiochemical variables, only one parameter λ, connected with the sum of the investment and gas pumping costs, appeared. The values of this parameter for a concrete drying process can be computed on the basis of formula (6) given in this paper (λ = λ e / e ). The original discrete algorithm, with the constant Hamiltonian of the multistage process, was used in the optimization computations. On this basis a computer program was developed and the optimization results were obtained for the family of drying processes corresponding to various values of the parameter λ. These results are quite general, since amongst the whole family of optimal solutions a special solution can always be found which pertains to the concrete value of λ calculated for the specified drying process. The computations were performed for the case of drying of silica gel in a three-stage cascade. From the computer outputs the properties of the optimal controls and the optimal trajectories were analysed and the following conclusions were reached: 1. (1) When the stage number increases (for λ = constant), the temperatures, humidities and flows of the inlet gas decrease. When λ increases (for n = constant), the process intensity also increases, i.e. humidities and flows of gas decrease and gas temperature increases (for large values of λ, the respective humidities reach their minimum allowable values). 2. (2) The largest decrease of solid moisture content is in the first stage of the cascade the lowest in the third one. This property becomes more noticeable as λ increases. For small λ, the temperatures of the solid decrease in the first stage and increase in the last one (for large λ the reverse situation occurs). For an intermediate stage, temperatures of the solid remain practically unchanged. 3. (3) A general result is that large energy. consumption is reasonable only in sufficiently costly apparatus. In addition, the optimization results were presented for the two conventional variants of drying in which the optimal decision variables were constrained to be the same for every stage. These results were compared with those found for unconventional (control) drying processes. For variant I the decision variables were the temperature, humidity and flow of the inlet gas. For variant II the decision variables were only the temperature and flow of the inlet gas, the inlet gas humidity being equal to the ambient humidity. It was found that the optimal costs for variant I of the conventional process are only slightly higher than those for the unconventional process, whereas the optimal costs for variant II are considerably higher. Hence, the optimal decision level is a dominant factor which makes it possible to improve the economics of the process. As the constant decision policy is easiest in practice, variant I of the conventional process may be recommended for the drying system considered in the computational range studied. For other ranges of input data (especially for low W k ), or for other drying systems, the superiority of the unconventional process may be more obvious. In such cases, the unconventional process, worked out here in detail, is recommended (it should be remembered that, in industry, even a small percentage increase in profit is usually important). Moreover, the computer program (Fig. 2) makes it possible to obtain optimization solutions for the following continuous processes: horizontal fluidized drying and batch fluidized drying when the number of process stages becomes sufficiently large.

Optimization of the reactor-regenerator system with catalytic parallel-consecutive reactions

Abstract The system with moving deactivating catalyst, composed of a cocurrent tubular reactor and a catalyst regenerator with an additional flux of a fresh catalyst, has been investigated. For the temperature dependent catalyst deactivation, the optimization problem has been formulated in which a maximum of a process profit flux is achieved by a best choice of temperature profile along tubular reactor, best catalyst recycle ratio and best catalyst activity after regeneration. The set of parallel–consecutive reactions, A+B→R and R+B→S, with desired product R has been taken into account. A relatively unknown, powerful discrete algorithm in which a suitably defined Hamiltonian is constant along the optimal path, has been applied for optimization. The optimal solutions have been discussed. In particular, it has been shown that an increase of the unit cost of catalyst regeneration or an increase of the catalyst recycle ratio causes such optimal temperatures in reactor which save the catalyst, as the optimal temperature profiles are then shifted towards lower temperatures. Finally these profiles reach isothermal shape at the level of minimum allowable temperature and then there is no further possibility to control the reactor process by the temperature profile. Thus the catalyst activity after regeneration, as well as an average catalyst activity in the reactor do decrease when the unit catalyst regeneration cost increases. This is a new form of catalyst saving, as the catalyst deactivation rate becomes reduced when an average catalyst activity is allowed to decrease. It is important that this form of catalyst saving appears in the region where any saving of the catalyst by an optimal choice of temperature profile is impossible. It has been also shown that for small values of the catalyst recycle ratio, the catalyst regenerator should be removed from the system. In such a case, the renewal of catalyst takes place due to a fresh catalyst input, exclusively.

5 – Uncontrolled Fluid–Solid Systems in Chemistry

In this chapter primary attention is paid to uncontrolled fluid–solid noncatalytic and catalytic systems with particulate solids. The scientific information is largely based on a book in Polish by Szarawara, J., Skrzypek, J., Gawdzik A. 1991. Podstawy Inzynierii Reaktorow Chemicznych ( Fundamentals of Chemical Reactor Engineering ), second ed. Warszawa, WNT, whose English counterpart is not available to date. Basic regimes of a heterogeneous processes (kinetic, diffusional, and intermediate) are distinguished. The notion of chemical resistance is defined and its significance for heterogeneous reactors is exemplified. The so-called model of shrinking grain is formulated and its main implications are described. Some special cases of this model are analytically solved and numerous application examples to industrial processes are presented. Statics and kinetics of sorption processes are considered. The equation of heterogeneous surface kinetics is derived and its “decelerating kinetics” is explained by the detrimental product rates in the denominator of this equation. Effects of concentration and temperature on the general rate of contact reaction are discussed for both exothermal reactions and exothermic reactions. Issues associated with diffusion in porous channels, Thiele modulus, and the influence of internal diffusion on the general chemical rate are discussed. The popular notion of effectiveness coefficient of a contact, attributed to the exploitation of the internal surface of grain, is defined. Charts characterizing internal diffusion under nonisothermal conditions are analyzed. While the effects of catalyst and sorbent deactivation are ignored, the chapter describes the main mechanisms of catalyst decay and, as such, it provides an introduction to further chapters which analyze systems with deactivating sorbents and catalysts to minimize the detrimental effect of catalyst deactivation.

Neural Networks for Emission Prediction of Dust Pollutants

We review the recent applications of artificial neural networks (ANNs) for predicting suspended particulate concentrations in urban air, taking into account meteorological conditions. Described calculations are based on pollution measurements taken in the city of Radom, Poland, in the period 2001–02. PM10 emission and primary meteorological data, which were obtained from the Inspectorate for Environmental Protection (IEP) in Radom, were used to train and test the applied network. Two different methods of emission calculation can be applied. Firstly, an artificial neural network method based on multilayer perceptron with unidirectional information flow is used. Secondly, a hybrid model based on a modified Gaussian model of Pasquilles type and artificial neural network with radial basis function (RBF) is applied. Network architecture and transition function types are described. Statistical assessment of the results is described. In addition, a hybrid model used results which are compared with emission calculations of dust pollution based on a Gaussian model, including various methods of calculation of pollution dispersion coefficients.

Maximum Power Yield in Homogeneous Chemical Systems

This chapter treats approaches, models, and analyzes the rise in optimization of power yield in chemical and biochemical reactors. Nonlinear kinetic models of reacting systems stem from kinetic mass action law, which leads to the identification of two competing unidirectional fluxes in each elementary step of the reaction. Near the thermodynamic equilibrium the approach converges to the standard linear kinetics governed by Onsagers equations. Using these models and methods we then extend to the chemical realm the method of thermodynamic optimization that was developed in earlier chapters for thermal machines. The extended method is aimed at the maximum production of power in isothermal and nonisothermal chemical systems. Some attention is given to analysis of derived dynamic programming algorithms and to development of a generalized approach for complex systems with internal dissipation. Chemical components of power yield are shown to be generated with lowered (imperfect) efficiencies, which are described by “reduced chemical affinities.”

Maximum Conversion in Processes With Chemical Reactions

This chapter reviews basic problems of maximum conversion encountered in typical systems with chemical reactions. The initial continuous problem of the optimal temperature profile for a single reversible reaction in a batch or tubular reactor is easily transformed into its corresponding multistage counterpart where a maximum conversion is sought for a discrete cascade. The experience gained helps to solve generalized optimization problems for parallel and consecutive-parallel reactions in a tubular or batch reactor. The analysis assumes that even a reaction is catalytic, the state of the catalyst remains unchanged when the reaction advances in time, i.e., any phenomena causing catalyst deactivation are absent in the system. Chapter 8 discusses the chemical reactions with catalyst deactivation as well as the associated catalyst regeneration problems.

Outline of Classical Optimization Methods

This chapter provides a brief description of contemporary optimization methods and approaches which are applied throughout this book to improve the performance of thermal, mechanical, chemical, and environmental systems. We optimize profit or cost criteria subject to equality and/or inequality constraints by applying search approaches, methods of static and dynamic optimization, and using some stochastic techniques. With these methods and approaches, we investigate unique optimal properties of neural networks, cascades, multilevel systems of complex topology, etc. Throughout the chapters of this book, optimization problems and goal criteria are formulated, and optimal solutions are found for unit operations and chemical reactors. Our concise review of optimization tools outlines the methods based on differential calculus, Lagrange multipliers, mathematical programming, iterative approaches, dynamic algorithms, and some stochastic optimization techniques. They are applied in the book to processes with energy yield and conversion, modeled with the help of classical and finite-time thermodynamics and second-law approaches. Throughout the book special attention is paid to fluid-solid catalytic systems with particulate solids as well as to complex multiphase reaction-regeneration systems with deactivated sorbents and catalysts.

Finite Rate Optimization of Steady Thermal Units

This chapter offers an advanced synthesizing approach to power yield and power limits in various thermal power generators, such as thermal and solar engines. Thermodynamic principles determine the converters efficiency and the generated power. Static and dynamical power systems are investigated. Dynamical models take into account the gradual downgrading of a resource, caused by power delivery. Analytical modeling includes conversion efficiencies expressed in terms of driving fluxes. Products of efficiencies and driving fluxes determine the power yield and power maxima. While the static optimization of industrial and practical systems requires the use of the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. The results of power maxima provide limiting indicators for thermal and solar power generators. They are more exact than classical reversible limits of thermal energy transformation. Following the present procedure, in later chapters ( Chapters 6 and 9 Chapter 6 Chapter 9 ), which deal with reacting mixtures, balances of mass and energy will serve to derive power yield in terms of the active part of chemical affinity. A generalized approach will then be applied to flow engines driven by fluxes of heat and chemical reagents.