Mathematical Models of Chemical Reactions

Author(s):  
Ludwig Arnold
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.


1996 ◽  
Vol 06 (02) ◽  
pp. 245-268 ◽  
Author(s):  
L. RONDONI

Modeling and analysis of models of complex chemical reactions constitute wide branches of research in chemistry, physics and mathematics. Here a model is proposed which is amenable to rigorous mathematical study, which makes clear the dynamics of the systems described by such a model. In particular, only combinations of chemical reactions which preserve the number of particles, and which have equal forward and backward reaction rates are allowed. Reactions which do not satisfy such requirements can be considered, provided they are suitably modified. Also, it is required that the densities of the chemicals in the reactions be low, so that the applicability of the theory is restricted to mixtures of gases.


2006 ◽  
Vol 16 (05) ◽  
pp. 1419-1434 ◽  
Author(s):  
V. GONTAR ◽  
O. GRECHKO

An automatic procedure for generating colored two-dimensional symmetrical images based on the chemical reactions discrete chaotic dynamics (CRDCD) is proposed. The inverse problem of derivation of symmetrical images from CRDCD mathematical models was formulated and solved using a special type of genetic algorithm. Different symmetrical images corresponding to the solutions of a CRDCD mathematical model for which the parameters were obtained automatically by the proposed method are presented.


Author(s):  
Tomás Aquino Portes

The aims was to use mathematical models to analyze the interconversion between the amount of organic matter produced and the consequent variation in the concentration of CO2 in the atmosphere and to discuss, supported by the data presented and the literature, possible changes in the Earth's environment. Scientific findings and evidence indicate that the concentrations of CO2 and O2 varied throughout the existence of the Earth. These variations were a consequence of the existing environment in different Eras, resulting in changes in all other processes that depended on these gases. Chemical reactions occurred and organic products such as petroleum arose abiotically. These products gave origin to organic chemistry and drastically reduced the concentration of CO2 and elevated O2 in the atmosphere. In the current plants, for each O2 produced in the photochemical step of photosynthesis, one CO2 is assimilated in the biochemical step. Supported by this relationship and by the results presented in this work, it can be inferred that the first photosynthetic organisms originated on Earth when the concentration of CO2 was possibly at a concentration below 1000 ppm. Biochemistry started with these organisms. The results suggest that the reduction in CO2 concentration was linear in relation to the age of the Earth, before the origin of photosynthetic organisms. This relationship changed with origin of these organisms, due to the major changes that occurred in the environment. There is evidence that in certain periods, CO2 concentrations have been reduced below the CO2 compensation point for certain plants resulting in the extinction of these plants and the organisms that depended on them.


2020 ◽  
Author(s):  
D. Nicolas Quiros ◽  
Luis S. Mayorga

ABSTRACTCell biology is evolving to become a more formal and quantitative science. In particular, several mathematical models have been proposed to address Golgi self-organization and protein and lipid transport. However, most scientific articles about the Golgi apparatus are still using static cartoons to represent their findings that miss the dynamism of this organelle. In this report, we show that schematic drawings of Golgi trafficking can be easily translated into an Agent-Based Model (ABM) using the Repast platform. The simulations generate an active interplay among cisternae and vesicles rendering quantitative predictions about Golgi stability and transport of soluble and membrane-associated cargoes. The models can incorporate complex networks of molecular interactions and chemical reactions by association with COPASI, a software that handles Ordinary Differential Equations. The strategy described provides a simple, flexible, and multiscale support to analyze Golgi transport. The simulations can be used to address issues directly linked to the mechanism of transport or as a way to incorporate the complexity of trafficking to other cellular processes that occur in dynamic organelles.


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