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A model is considered that describes the interaction of predators and prey in a certain area. Moreover, the population of the prey does not leave the site, and the population of predators migrates from the site with an insufficient amount of food resources. The presence or absence of a population of predators in an area is determined by the value of a function that makes sense for the food attractiveness of the area for the population of predators. The model under study is a system of three differential equations, two of which describe the dynamics of the numbers of predators and prey, and one describes the dynamics of the food attractiveness of the site. The task of preserving the species structure of the biological community of the site is solved by the removal of individuals. The species structure of a biocommunity is understood as the set of species and types of interactions between them. A model of the periodic process of the external effect, which preserves the species structure of the biological community, is presented. A numerical method is developed and a program is created that implements the constructed model. The results of testing the program are presented. [ABSTRACT FROM AUTHOR]

Modelling of periodic processes of electromagnetic devices is a complex problem. The task of finding of periodic solutions of nonlinear differential equations is more complex than the Cauchy task of integrating of these equations because it imposes another condition on the solution - the condition of periodicity, that is it becomes a point-to-point T-periodic boundary value problem of nonlinear differential equations. Aim: The aim of the work is to simplify the computing method of the sensitivity matrix elements of the object parameters to their initial conditions by analytical solution of the equations of first variation. Materials and Methods: The author proposed to calculate the matrix elements of the sensitivity model to the initial conditions of the variational equations not through their joint numerical integration with the original equations in the period but to search for the common solution of these equations by means of using a transition state matrix. In this case the order of the equations of the object remains the same, restrictions on the method use for analysis of complex dynamical systems are removed and its efficiency improves significantly. Results: Due to the independence of differential equations in variations from external influence, they become a homogeneous system of linear differential equations. This approach greatly simplifies the analysis and removes the restrictions on the application of the method of sensitivity to initial conditions during the study of dynamical systems of any complexity.

An analytical solution is obtained for a system of differential equations consisting of the equation for diffusion and absorption of a component in adsorbent grains and the balance equation for this component moving in the adsorbent layer.The technique for calculation of steady-state periodic adsorption processes based on expansion of a concentration signal into Fourier series of eigenfrequencies of this adsorption process is proposed. After decomposition each of the eigenwaves independently of the others is passed through the adsorbent layer, and at the output from this layer all this solutions for individual eigenwaves are summed. The solution to a problem of passing an arbitrary periodic concentration signal through the adsorbent layer is obtained as a result of summing the solutions for individual eigenwaves.The proposed method takes into account nonstationary diffusion processes inside the adsorbent grains. It makes possible to analyze effect of the adsorbent grain sizes on a pressure swing adsorption processes.

The dynamical model describing several stages of interaction between populations of predators and preys in some area is proposed. The transition from one stage to another is determined by the values of the function which has the sense of trophical attractiveness of a species area. Under condition that the trophical attractiveness not less than threshold value the interaction of populations is desribed by the Volterra--Lotka system. Oterwise, the predator population transfers to a migration stage. The model also describes the process of colonization of the area by predators. The problem of species composition preserving by selection is solved. The selection intensity is considered as a control function. The control which permits to coordinate the anthropogenic impact with natural development of a biocommunity is constructed. As a result, the control process acquires the periodic or quasiperiodic nature which depends on the initial values of populations size. The proposed model is described by the three dimensional system of ordinary differential equations with variable structure.The qualitative analysis of the system is carried out.

An analytical solution is obtained for a system of differential equations consisting of the equation for diffusion and absorption of a component in adsorbent grains and the balance equation for this component moving in the adsorbent layer. The technique for calculation of steady-state periodic adsorption processes based on expansion of a concentration signal into Fourier series of eigenfrequencies of this adsorption process is proposed. After decomposition each of the eigenwaves independently of the others is passed through the adsorbent layer, and at the output from this layer all this solutions for individual eigenwaves are summed. The solution to a problem of passing an arbitrary periodic concentration signal through the adsorbent layer is obtained as a result of summing the solutions for individual eigenwaves. The proposed method takes into account nonstationary diffusion processes inside the adsorbent grains. It makes possible to analyze effect of the adsorbent grain sizes on a pressure swing adsorption processes. [ABSTRACT FROM AUTHOR]

This paper presents first principles model for operation of a plunger lift system in natural gas wells. The model consists of pressure and flow dynamics of fluids in annulus and the central tubing sections of the well, and dynamics of plunger fall and rise in the tubing. System dynamics switch on shutting or opening the production valve, and with autonomous events related to plunger motion. A nonlinear hybrid model is realized with nine states, switching though six stages (modes) of operation. This is the first instance of modeling complex system of plunger lift using a standard hybrid system model (HSM) framework. The resulting model is used to present insight into plunger lift operation, including an efficient simulation of multiple plunger cycles and analysis of effect of uncertainties on the well behavior. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal control problem for a continuous stirred tank reactor (CSTR) that represents a reaction of the type “ A → product”. The reactor dynamics is described by a nonlinear system of ordinary differential equations controlled by two inputs: the inlet concentration and the inlet temperature. We formulate the problem of maximizing the average product of this reactor for a fixed consumption of the input component over a period of time. This kind of isoperimetric optimal control problem is analyzed by using the Pontryagin maximum principle with Lagrange multipliers. We show that the optimal controls are bang-bang and propose an upper bound for the number of switchings for the linearized problem with periodic boundary conditions. Numerical simulations confirm that our control strategy can be used to improve the reactor performance over a specified period of time in comparison to the steady-state operation. [ABSTRACT FROM AUTHOR]

A comparative analysis of different versions of the Menter shear-stress transfer model, including with correction for the curvature of streamlines, has been performed as applied to a periodic flow around a semicircular airfoil with a zero angle of attack at Re = 45,000. A comparison of the calculated aerodynamic coefficients C and C and the surface distribution of the pressure coefficient, averaged over the period of oscillations of the lift coefficient C, with the corresponding experimental data has shown that the Menter shear-stress transfer model modified within the framework of the Rody-Leshtsiner-Isaev approach with the use of the inverse function of the Richardson number correcting the eddy viscosity of a flow with a semiempirical Isaev-Kharchenko-Usachov constant equal to 0.02 is preferred compared to the other versions of this model. The errors of the calculations performed with the use of the multiblock computational technologies based on intersecting structured meshes of different scales were analyzed. The interrelation between the evolution of the structure of the periodic flow around the semicircular airfoil and the distribution of its integral force characteristics in the period of C oscillations is discussed. [ABSTRACT FROM AUTHOR]

Speeded search of the periodic processes of dynamical systems. Modelling of periodic processes of electromagnetic devices is a complex problem. The task of finding of periodic solutions of nonlinear differential equations is more complex than the Cauchy task of integrating of these equations because it imposes another condition on the solution ⎯ the condition of periodicity, that is it becomes a point-to-point T-periodic boundary value problem of nonlinear differential equations. Aim: The aim of the work is to simplify the computing method of the sensitivity matrix elements of the object parameters to their conditions by analytical solution of the equations of first variation. Materials and Methods: The author proposed to calculate the matrix elements of the sensitivity model to the conditions of the variational equations not through their joint numerical integration with the original equations in the period but to search for the common solution of these equations by means of using a transition state matrix. In this case the order of the equations of the object remains the same, restrictions on the method use for analysis of complex dynamical systems are removed and its efficiency improves significantly. Results: Due to the independence of differential equations in variations from influence, they become a homogeneous system of linear differential equations. This approach greatly simplifies the analysis and removes the restrictions on the application of the method of sensitivity to conditions during the study of dynamical systems of any complexity. [ABSTRACT FROM AUTHOR]

We study nonautonomous linear difference equations via the corresponding abstract Cauchy problem. The domains of the associated operators are time dependent and do not contain a common core, so we have to prove wellposedness by a direct approach. In the periodic case we then investigate the asymptotics (in different topologies) of the corresponding evolution families using the Perron-Frobenius theory for positive matrices combined with spectral decomposition methods. Finally, we show how flows in time-dependent networks can be treated within this framework. [ABSTRACT FROM AUTHOR]

Abstract: The dynamic optimisation and optimal control of innovative cyclic chemical processes are challenging because these problems involve apart from temporal periodicity constraints often also Partial Differential Equation (PDE) models and multiple objectives. To allow a fast and efficient generation of the Pareto set, this paper presents a deterministic approach that integrates accurate scalarisation methods for multi-objective optimisation as Normal Boundary Intersection (NBI) and (Enhanced) Normalised Normal Constraint (E)NNC, with a fast direct multiple shooting approach for optimal control. The feasibility of the proposed approach is presented for a reverse flow reactor involving conflicting conversion and energy objectives. In addition, advantages of the NBI and (E)NNC methods over the classic Weighted Sum of the individual objectives have been illustrated. [Copyright &y& Elsevier]

For cyclic processes modeled by periodic motions of a continuous control system on a circle, we prove the uniqueness of a cycle maximizing the average one-period time profit in the case of discounting provided that the minimum and maximum velocities of the system coincide at some points only and the profit density is a differentiable function with a finite number of critical points. The uniqueness theorem is an analog of Arnold's theorem on the uniqueness of such a cycle in the case when the profit gathered along the cycle is not discounted. [ABSTRACT FROM AUTHOR]

Abstract: The performance of a stirred tank bioreactor operated in sequencing batch operation mode (SBR) to treat diesel waste from storage tanks, was investigated. The SBR run in four cycles of 72 h, using optimized setpoints for pH, initial waste load, C:N ratio and agitation speed. Optimal conditions allowed the system to reach biodegradation percentages of 53.3, 96.0, 76.2 and 75.0% at the end of cycles one, two three and four, respectively. Investigations of microbial diversity showed changes in the microbial community members at the end of the cycle one. Significant reductions in the relative ecotoxicity were observed beginning with cycle two, and the reductions extended until the end of process. The SBR operation mode proved to be an efficient method for treating the diesel waste, allowing relevant reductions in the hydrocarbon content of the waste along with an increase in its environmental quality. [Copyright &y& Elsevier]

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Abstract: Almost CO-free hydrogen gas, which could be directly used as a feed for a PEM fuel cell, can be produced by a novel steam reforming process of methane in a fixed bed reactor which contains two different catalysts layers which go through a periodic reduction/re-oxidation cycle. During the reduction phase, water-free methane is converted at the first layer (Pt–Ce0.5Zr0.5O2) into a mixture of СО and Н2 by partial oxidation. This mixture is fed directly to a second layer of Fe2O3–Ce0.5Zr0.5O2 where the products of the methane partial oxidation reduce the iron-containing catalyst whereby giving CO2 and H2O. During the re-oxidation phase of the cycle, the two-layer reactor is fed with pure steam which is converted into a CO-free hydrogen gas whereby leading to the re-oxidation of the catalytic materials in both layers so that that they can be reused in the next redox cycle. The present study reports the preparation and characterization of suitable catalytic materials, related activity tests and kinetic studies which demonstrate the feasibility of the proposed process concept. [Copyright &y& Elsevier]

The US Army is pilot testing the neutralization of VX nerve agent stockpiled at Newport, Indiana using caustic hydrolysis in a Sequencing Batch Reactor (SBR). The resulting hydrolysate was tested at the bench-scale for treatment with activated sludge biodegradation in two distinct studies, one in the SBR and another, in the PACT® process. The feed to both biological systems was pretreated to enhance the biodegradability of the hydrolysis products. Both biodegradation studies demonstrated that the hydrolysate could easily meet the Chemical Weapons Convention treaty and US environmental regulations following pretreatment. [ABSTRACT FROM AUTHOR]

For a couple of years, unsteady state processing has been discussed to be possibly advantageous for chemical process engineering. Specifically periodic changes of reaction parameters are expected to enhance the rates of certain reactions [Chem. Eng. Commun. (1973) 111]. For different reaction systems, concentration cycling has been performed [P.L. Silveston, Composition Modulation of Catalytic Reactors, Gordon and Breach, Amsterdam, 1998]. In contrast, a fast periodic modulation of the reactor temperature, even though potentially beneficial, has long been considered to be beyond reach because of the large thermal masses and the poor surface-to-volume ratio which restrict the heat exchange between conventional reactor systems (e.g. fixed bed reactors) and heating/cooling systems. Recently, microstructure devices for fast temperature cycling have been described [J.J. Brandner, G. Emig, M. Fichtner, M.A. Liauw, K. Schubert, A new microstructure device for fast temperature cycling for chemical reactions, in: M. Matlosz, W. Ehrfeld, J.P. Baselt (Eds.), Proceedings of the Fifth International Conference on Microreaction Technology, IMRET 5, Springer, Berlin, 2001, pp. 164–174; Chem. Eng. Sci. 56 (2001) 1419; Gen. Eng. News 22 (11), 42]. The devices make it possible to obtain a periodic temperature change by 100 K in the second to subsecond range. A method for catalyst integration into microstructure devices will be described briefly. First results on the stability of catalyst carrier layers with respect to fast temperature changes are very promising. The oxidation of carbon monoxide was chosen as model reaction. Under fast temperature cycling conditions, a considerably higher yield compared to the steady state could be observed. [Copyright &y& Elsevier]

Activation phenomenon has been observed with two sets of enzymes under the conditions of low dosage irradiation. Activation was registered for angiotensin-converting enzyme under in vitro γ-irradiation (0.662 MeV, pulse duration approx 10s) at dose levels of 1–3 Gy and under X-ray irradiation (approx 9 keV, pulseduration approx 10−9s) at dose levels of 2×10−5 Gy. An activation effect has also occurred for native and recombinant horseradish peroxidase and tobacco peroxidase under γ-irradiation. The phenomenon observed is rationalized in terms of a kinetic model suggesting the existence of at least one activated enzyme conformation induced by radiolysis. The activity oscillations registered in dense plasma focus experiments were rationalized using the same model with the corresponding kinetic equation converted into the form describing the decaying oscillations caused by exciting force. The model analysis is presented. [ABSTRACT FROM AUTHOR]

The role of storage in buffering a process train from the effects of periodically reoccuring equipment failure is studied. The effects of deterministic and stochastic variations in the failure frequency and recovery time on the required size of intermediate storage are investigated. A dynamic operating policy is proposed to accommodate process variations in concern with the use of intermediate storage. Dynamic operation offers an increase in the average production rate of the process while using only modest levels of intermediate storage. [ABSTRACT FROM AUTHOR]

The problem of calculating the stationary modes in nonlinear electrical circuits with reactive elements that are under periodic disturbances is considered. The problem is solved as a boundary value problem for a system of differential equations with periodic boundary conditions, which describe the dynamic steady state that can have obtained dependencies of state variables on the period without resorting to solving the problem in the time domain. Presentation in algebraic form system of differential equations is performed using projection method of spline approximation. The resulting system of nonlinear algebraic equations is solved by the method of continuation parameter that allows investigating the influence on the nature of periodic dependencies of coordinates as value of a periodic disturbances, and any other parameter of electric circuit. [ABSTRACT FROM AUTHOR]