P. Érdi, J. Tóth: Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic models. A volume in the series: Nonlinear Science, Theory and Application. Manchester University Press, Manchester (U.K.) 1989. 259 Seiten

1989 ◽  
Vol 93 (12) ◽  
pp. 1501-1502 ◽  
Author(s):  
Peter Schuster
Author(s):  
N. Anbazhagan

Supply Chain Management (SCM) is the practice of coordinating the flow of goods, services, information and finances as they move from raw materials to parts supplier to manufacturer to wholesaler to retailer to consumer. Different supply chains have been designed for a variety of firms and this chapter discusses some issues in this regard. This chapter attempts to find why we require different supply chain for different companies. In this chapter we discuss the role of stochastic models in supply chain management system, and also discuss other mathematical models for SCM.


1983 ◽  
Vol 20 (04) ◽  
pp. 877-883
Author(s):  
Peter Hall

Several stochastic models have been proposed to describe the kinetic theory of reversible chemical reactions. However, in macroscopic systems the effects of stochastic variability are often outweighed by mean effects. In the present paper we show that some observed phenomena can be explained quite adequately by a stochastic model in which the stochastic variability is not negligible in comparison with mean effects. Our argument involves approximations to a stochastic model for competing chemical reactions.


2019 ◽  
Vol 110 ◽  
pp. 02041
Author(s):  
Irina Zaychenko ◽  
Nadezhda Grashchenko ◽  
Tatiana Saurenko ◽  
Vladimir Anisimov ◽  
Evgeniy Anisimov ◽  
...  

Achieving energy security by preventing and timely eliminating the consequences of accidents at energy facilities and in energy supply systems of enterprises is one of the important tasks of energy management. The basis for planning appropriate energy security measures is the prediction of damage from these accidents. The purpose of forecasting is to assess the possibility of an accident occurring at some point in time and leading to a particular damage, and to assess the magnitude of this damage. The article proposed methodological approaches to the construction of mathematical models of such prediction. In this case, as an indicator of damage, the economic losses caused by these accidents are taken. The simulation is based on the representation of this indicator in the form of a step change function of the magnitude of losses in the event of an accident. Depending on the amount of information available in the period prior to forecasting, the mathematical representation of the forecasting problem is reduced to the construction of conditionally determined or stochastic models. Conditionally determined models allow obtaining acceptable damage estimates with a short period of retrospection and small amounts of information, and stochastic models with significantly large amounts. At the same time, the principle of “maximum uncertainty” formalized in the form of maximum entropy is the basis for removing uncertainty in the construction of both conditionally determined and stochastic models. Its use has allowed increasing the objectivity of forecasts by minimizing the subjective information used in modeling. The proposed approaches to the construction of mathematical models for predicting accidents at energy facilities and power supply systems of enterprises are the basis for creating specific techniques for solving relevant energy management tasks both at the micro level at the scale of individual enterprises and at the macro level at the scale of industries, regions and the state as a whole.


1990 ◽  
Vol 43 (12) ◽  
pp. 297-309 ◽  
Author(s):  
A. T. Winfree

Three-dimensional continua capable of recurrent local activation are observed—both in the laboratory and in mathematical models—to support persistent self-organizing patterns of activity most conveniently described in terms of vortex lines. These lines generally close in rings, which may be linked and knotted. In some cases they adopt stable configurations resembling tiny dynamos of millimeter dimensions. The dynamics of these “organizing centers” has been investigated in certain chemical reactions, in heart muscle, and numerically in digital computers. The pertinent mathematical principles appear to entail consequences of local reaction and neighborhood diffusion, in the form of a dependency of the vortex filament’s lateral motion upon its local geometry and, when too closely approached by another segment of vortex filament, upon the distance and orientation involved.


2004 ◽  
Vol 41 (2) ◽  
pp. 593-596 ◽  
Author(s):  
A. Yu. Mitrophanov

It is shown that the method of deriving bounds on the rate of convergence for birth–death processes developed by Zeifman can be effectively applied to stochastic models of chemical reactions.


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