Equations Of Chemical Kinetics Research Articles

Optimization of thick rubber part curing cycles

Thick rubber part moulding is a process, during which coupling between heat and chemical kinetic equations is strong. Automatic tooling control, therefore, is the guarantee of achieving proper curing within the mould. This article initially presents a detailed method for curing optimization. With this aim in view, the optimum temperature cycle for the desired curing state is examined. The use, here, of the conjugate gradient method implies to determine the solution of both adjoin and sensitivity equations. A sensitivity study is also conducted in order to improve the kinetic model. Finally, some optimization examples are discussed.

Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry

In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.

Construction of solutions to quasilinear partial differential equations

We propose a method for constructing solutions to a class of quasilinear parabolic partial differential equations (PDEs) basing on a new property of these equations. The method applies to quasilinear hyperbolic and elliptic equations as well. The results of this article broaden the class of exact solutions to the quasilinear equations, in particular, to the nonlinear heat equations, the equations of chemical kinetics and mathematical biology.

Magnetogasdynamic generation of electrical energy in models of aircraft with a high-speed jet engine

The possibility of generating electric power in a plane model of an integral high-speed hydrogen-burning jet engine by mounting a magnetogasdynamic (MHD) generator at the combustion chamber exit is discussed. Attention is concentrated on clarifying the effect of MHD energy extraction from the stream on the aircraft’s thrust characteristics. The internal and external flows are simulated numerically. The two-dimensional supersonic gasdynamic flow inside the engine (in the air-intake, combustion chamber, MHD generator, and nozzle) and the supersonic flow past the aircraft are described on the basis of the complete averaged system of Navier-Stokes equations (in the presence of turbulence), which includes MHD force and heat sources, a one-parameter turbulence model, the electrodynamic equations for an ideal segmented MHD generator, and the equations of the detailed chemical kinetics of hydrogen burning in air. The numerical solution is obtained by means of a computer program that uses a relaxation scheme and an implicit higher-order version of the Godunov method. It is shown that MHD electric power generation can be realized without disturbing the positive balance in the relation between the thrust and the drag of the aircraft with the engine operating with allowance for the MHD drag, but with some loss of effective thrust.

STEPS: reaction-diffsion simulation in complex 3D geometries

STEPS (STochastic Engine for Pathway Simulation) wasdeveloped as a tool for simulating reaction-diffusion sys-tems, such as the signaling pathways involved in synapticplasticity. We aim to provide the tools to allow investiga-tion of the effects of morphology and stochastic fluctua-tions in such systems, since it is widely believed suchfeatures may play an important role in biological function[1]. STEPS is written almost entirely in C++ for high per-formance, but maintains a user interface in Python toallow for greater interactivity and control. The softwareruns on various platforms, including Unix, Mac OS X andWindows. By writing relatively straightforward Pythonscripts the modeler can create the molecular species in thesystem, set up the reaction-diffusion kinetics, define thegeometry of the system, set the initial conditions, importa 3D tetrahedral mesh, run and control the simulationand visualize and/or save the simulation results.STEPS currently includes three solvers, allowing the userto choose the most efficient solution that can accuratelydescribe their model:-WmDirect: Stochastic solver, based on the GillespieDirect Method [2].Recommended for systems that can be assumed to bewell-mixed and where any species is in a sufficiently lowconcentration that the probabilistic nature of the systembecomes significant and a stochastic description is neces-sary [1,3]. The modeler can adapt their Python script torun the simulation a number of times to see the stochasticfluctuations in the system.-WmRK4: Deterministic solver, based on the fourth-orderRunge-Kutta method.Recommended for systems that can be assumed to bewell-mixed and where molecular populations are largeenough that system behavior can be approximated bysolving classical chemical kinetics equations. This is usu-ally the quickest solver as the simulation need only be runonce.-TetExact: Stochastic solver extended for simulating diffu-sion by implementing a 3D tetrahedral mesh.Allows for the investigation of the effects of morphologi-cal aspects such as concentration gradients and chemicalcompartmentalization. This solver requires constructionof a high-quality computational tetrahedral mesh that canadequately represent the relevant morphological features.STEPS currently supports meshes generated by TetGenhttp://tetgen.berlios.de, which is freely available forresearch use. In addition, we aim to implement mesh-gen-eration in STEPS in the future based on the algorithm in[4]. These meshes can then be used for simulation byextending Gillespie's Direct Method [2] to deal with spa-tial processes. Each voxel is treated as a well-mixed vol-ume in which reactions can occur and are coupled to theirneighboring voxels by diffusive fluxes and to neighboring

Unusual Antioxidant Behavior of α- and γ-Terpinene in Protecting Methyl Linoleate, DNA, and Erythrocyte

The antioxidant effects of alpha-terpinene (alpha-TH) and gamma-terpinene (gamma-TH) on the oxidation of methyl linoleate (LH), DNA, and erythrocytes induced by 2,2'-azobis(2-amidinopropane hydrochloride) (AAPH) were investigated. The results from erythrocytes and DNA were treated by means of chemical kinetic equations. It was found that either alpha- or gamma-TH was able to scavenge approximately 0.4 radicals when they protected DNA. alpha-TH can trap approximately 0.7 radicals when protecting erythrocytes and can trap approximately 0.5 radicals when protecting LH. gamma-TH can trap approximately 1.2 radicals when protecting erythrocytes and LH. Therefore, the antioxidant effectiveness of gamma-TH was higher than alpha-TH. gamma-TH contained a nonconjugated diene, and the diene in alpha-TH was conjugated. The obtained results implied that the nonconjugated diene benefited for antioxidant capacity more than a conjugated diene. Moreover, the reactions of alpha- and gamma-TH with 2,2'-azinobis(3-ethylbenzothiazoline-6-sulfonate) cation radical (ABTS(+) (*)) and 2,2'-diphenyl-1-picrylhydrazyl (DPPH) implicated that alpha- and gamma-TH were able to scavenge radicals directly. However, alpha- and gamma-TH promoted AAPH-induced hemolysis with a high concentration employed.

How many peroxyl radicals can be scavenged by hydroxyl‐substituted Schiff bases in the oxidation of linoleic acid?

AbstractEleven hydroxyl‐substituted Schiff bases (SchOHs) were synthesized by the reaction between hydroxyl‐substituted benzaldehydes and hydroxyl‐substituted anilines, and their antioxidant effects on the oxidation of linoleic acid (dissolved in sodium dodecyl sulfate micelle) induced by 2,2′‐azobis(2‐amidinopropane hydrochloride) (AAPH) were investigated. The relationships between the period of the oxidation inhibited by SchOHs (tinh) and their concentrations ([SchOHs]) were measured firstly, and then treated by a chemical kinetic equation, tinh = (n/Ri)[SchOH], to obtain the number (n) of the oxidative chains terminated by one molecule of SchOH. Therefore, the antioxidant activities of SchOHs can be expressed quantitatively by the n value. Finally, the spin‐densities (SD) on O atom in the radical of SchOH (SchO.) were calculated by quantum chemical method, and, to some extent, SD provided an explanation to the difference of the antioxidant effects among various SchOH. Therefore, the obtained results provided an attempt to bridge the kinetic measurement and quantum calculation in the study on the property of an antioxidant. Copyright © 2008 John Wiley & Sons, Ltd.

Characteristics of Transcriptional Activity in Nonlinear Dynamics of Genetic Regulatory Networks

Microarray measurements of mRNA abundances is a standard tool for evaluation of transcriptional activity in functional genomics. The methodology underlying these measurements assumes existence of a direct link between transcription levels, that is, gene-specific mRNA copy numbers present in the cell, and transcription rates, that is, the numbers of gene-specific mRNA molecules synthesized per unit of time. In this paper, the question of whether or not such a tight interdependence may exist is examined in the context of nonlinear dynamics of genetic regulatory networks. Using the equations of chemical kinetics, a model has been constructed that is capable of explicitly taking into consideration nonlinear interactions between the genes through the teamwork of transcription factors. Jacobian analysis of stability has shown that steady state equilibrium is impossible in such systems. However, phase space compressibility is found to be negative, thus suggesting that asymptotic stability may exist and assume either the form of limit cycle or of a chaotic attractor. It is argued that in rapidly fluctuating or chaotic systems, direct evaluation of transcription rates through transcription levels is highly problematic. It is also noted that even if a hypothetical steady state did exist, the knowledge of transcription levels alone would not be sufficient for the evaluation of transcription rates; an additional set of parameters, namely the mRNA decay rates, would be required. An overall conclusion of the work is that the measurements of mRNA abundances are not truly representative of the functionality of genes and structural fidelity of the genetic codes.

A dynamic adaptive chemistry scheme for reactive flow computations

An on-the-fly kinetic mechanism reduction scheme, referred to as dynamic adaptive chemistry (DAC), has been developed to incorporate detailed chemical kinetics into reactive flow computations with high efficiency and accuracy. The procedure entails reducing a detailed mechanism to locally and instantaneously accurate sub-mechanisms at each hydrodynamic time step of the calculation, and consequently no a priori information regarding simulation conditions is needed. The reduction utilizes an extended version of the directed relation graph (DRG) method in which the edges are weighted by a value that measures the dependence of the tail species (vertex) on the head species. An R-value is then defined at each vertex as the maximum of the products of these weights along all paths to that vertex from an initiating species. Active species are identified by their R-values exceeding a threshold value, εR, using a modified breadth-first search (BFS) that starts from a pre-defined set of initiating species. Chemical kinetics equations are then formulated with respect to the active species, with the inactive species considered only as third body collision partners. The DAC method is implemented into CHEMKIN and tested by simulating homogeneous charge compression ignition (HCCI) combustion using detailed and pre-reduced n-heptane mechanisms (578 species and 178 species, respectively) as the full mechanisms. The DAC scheme reproduces with high accuracy the pressure curves and species mass fractions obtained using the full mechanisms. The on-the-fly mechanism reduction scheme introduces minimal computational overhead and achieves more than 30-fold time reduction in calculations using the 578-species mechanism.

Chapter 5 Discrete Stochastic Simulation Methods for Chemically Reacting Systems

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

Non-isothermal kinetic model for reduction of ferrous oxide with hydrogen and carbon monoxide

A non-isothermal mathematical model has been developed for study of the reduction process of ferrous oxide with gases. The model includes heterogeneous chemical kinetic expressions and equations of heat and mass transfer. The numerical scheme based on the finite volume method in an implicit formulation is used for solving the differential equations. The model has been validated with experimental results from the literature. The numerical results indicated reaction enthalpy was influenced transiently by temperature. The gas concentration profile inside ferrous oxide particle developing with an elapse of time can also be simulated by the model.

Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks

The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh-Hurwitz, Lyapunov criteria, Feinberg's Deficiency Zero theorem) would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.

Current Equation for Hopping Ions on a Lattice under High Driving Force and Nondilute Concentration

The current density equation of hopping ions (and localized electrons) is evaluated for high driving forces originating both from high internal electric fields and high gradients in the particle concentrations. Both high concentration of the ions and the dilute limit are discussed. Interaction between the mobile ions is included. Attention is paid to details of the derivation. It requires the discussion of local thermal equilibrium, as opposed to chemical equilibrium, of local exchange current, hopping probability, and conductivity. A comparison with other equations aimed at coping with higher driving forces is given. In particular, the results are compared with those of irreversible thermodynamics and the substitution of activity instead of concentration in a chemical kinetic rate equation. The latter is shown to be inaccurate, yet to recover the correct dependence on the difference in the electrochemical potential of the ions. Additional topics that come up during the evaluation and are discussed are the interaction potential between the ions, the activity of building elements and of structure elements, and the effect of frequency on the hopping probability.

Positivity preserving chemical Langevin equations

Chemical kinetic equations for cellular biochemical systems generally include stochastic contributions which arise as a consequence of Brownian buffeting of the small numbers of participating molecules. The precise structure of these kinetic equations is not known with complete certainty, but at present some arguments favor equations of chemical Langevin form. Unfortunately, these equations sometimes predict negative concentrations. Here we explore a way of modifying the chemical Langevin equations such that they preserve positivity. To test the validity of this approach we apply the original and modified equations to two representative biochemical problems. Numerical solutions are obtained using a recently developed algorithm for stochastic differential equations. We find that positivity is indeed obtained for the modified equations without distortion of the interesting qualitative aspects of the original solutions.

Multilevel modeling of the influence of surface transport peculiarities on growth, shaping, and doping of Si nanowires

The growth, shaping, and doping of silicon nanowires in a catalyst-mediated CVD process are analyzed within the framework of a multilevel modeling procedure. At an atomistic level, surface transport processes and adsorption are considered by MC simulations. At the macroscopic level, numerical solutions of chemical kinetics equations are used to describe nanowire elongation growth and doping. Both atomistic and kinetic considerations complementing each other reveal the importance of surface transport and the role of low-mobility impurities present on the catalyst surface in the nanowire growth process. In particular, a controllable shaping and selective doping of nanowires is possible by means of well-directed effects on the surface transport of both silicon and impurity adatoms. Some nonlinear effects in the growth and doping caused by percolation-related phenomena are demonstrated.

Modeling and simulation of evaporation–pyrolysis processes of a naturally smoldering cylindrical cellulosic materials rod: Effect of smoldering rate on product concentrations

This study developed the mathematical model of the simultaneous transport and chemical processes inside naturally smoldering cellulosic materials. Matlab is employed for solving heat and mass transfer model as well as chemical kinetic model equations represented by a Distributed Activation Energy Model (DAEM). Simulations are carried out for the smoldering rate ranging from 0.18 cm/min to 0.4 cm/min and a final fixed pyrolysis temperature of 450 °C. On the basis of the model, the product yields, the evolution rate, and the influences of smoldering rate on the 22 selected volatile species out of 45 pyrolysis precursors are predicted.

Effect of reaction heat on Maxwellian distribution functions and rate of reactions

A binary gaseous mixture undergoing a reversible reaction of type is modeled with the chemical kinetic Boltzmann equation, assuming hard sphere crosssections for elastic collisions, and two different models with activation energy forreactive interactions, namely the line-of-centers and step cross-section models.The Chapman–Enskog method and Sonine polynomial representation of thedistribution functions are used to obtain the solution of the Boltzmann equationin a chemical regime for which the reactive interactions are less frequent thanthe elastic collisions, i.e. in the early stage of the reaction when the constituentA is in a large amountwith respect to B and the affinity of the reaction tends to infinity. The aim of this paper is twofold: (i) toevaluate the effect of the reaction heat on the Maxwellian distribution functions and on theproduction terms of both particle number densities and mixture energy density; (ii) toanalyze spatially homogeneous solutions for the particle number density and temperatureof the reactants when the chemical reaction advances. It is shown that the reaction heatchanges the Maxwellian distribution functions, the production terms and hencethe trend to equilibrium of the particle number density and temperature of thereactants. Moreover, these changes differ for exothermic and endothermic reactions.

Ring-opening polymerization of decamethylcyclopentasiloxane initiated by a superbase: Kinetics and rheology

The use of phosphazene bases in combination with water was proved to be efficient in order to obtain polysiloxane polymers from cyclic monomers. Only a few minutes are necessary to obtain polymer chains with a monomer concentration of 5% at the equilibrium. For that purpose the space which is between a rheometer's plates is the most convenient device to monitor this reaction concerning a chemical and viscoelastic point of view. Therefore, here is proposed a chemo-rheology study that leads in the same time to the chemical kinetics equations and to the variation of the viscoelastic functions during the polymerization. In this way different catalysts are used and their efficiencies are compared as a function of their “basicity tank”. Whatever the experimental conditions involved are, viscosity versus polymer concentration or conversion shows a master curve for catalysts suitable to be used under extrusive conditions. Thus, only a few experiments are needed in order to develop a model which can be used to foresee the variation of the viscosity during the reaction.

Characterization of an atmospheric pressure dc plasma jet

The fluxes of chemical active particles in the effluent of plasma jets are very important parameters for different applications. Herein, we present a method of measurement and an algorithm to obtain plasma parameters and particle fluxes from the atmospheric pressure direct current (dc) plasma jet operated in nitrogen/oxygen mixtures. We determine the atom and radical steady state densities and particles fluxes by means of emission spectroscopy and numerical modelling. The plasma parameters, electron density ne and electron velocity distribution function, are obtained by means of emission spectroscopy, microphotography and solutions of the Boltzmann equation. The steady state densities of particles in the effluent region are calculated by solving transport equations (thermal conductivity and diffusion) and chemical kinetics equations. The calculated densities of nitrogen atoms are compared with emission spectroscopy measurements at various positions outside the nozzle of the plasma source. The measurements confirm model results. The fluxes of chemically active particles are determined by means of steady state particle densities and known gas flow rate.

Antioxidative effect of melatonin on DNA and erythrocytes against free-radical-induced oxidation

The aim of this work is to investigate the antioxidative effect of melatonin ( N-acetyl-5-methoxytryptamine) on the oxidation of DNA and human erythrocytes induced by 2,2′-azobis(2-amidinopropane hydrochloride) (AAPH). First, the 50% inhibition concentration (IC 50) of melatonin is measured by reacting with two radical species, i.e., 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonate) radical cation (ABTS +) and 2,2′-diphenyl-1-picrylhydrazyl (DPPH). The IC 50 of melatonin are 75 μM and 300 μM when melatonin reacts with ABTS + and DPPH, respectively. Especially, the reactions of melatonin with ABTS + and DPPH are the direct evidence for melatonin to trap radicals. Then, melatonin is applied to protect DNA and human erythrocytes against oxidative damage and hemolysis induced by 2,2′-azobis(2-amidinopropane hydrochloride) (AAPH). The presence of melatonin prolongs the occurrence of the oxidative damage of DNA and hemolysis of erythrocytes, generating an inhibition period ( t inh). The proportional relationship between t inh and the concentration of melatonin ([MLT]) is treated by the chemical kinetic equation, t inh = ( n/ R i)[MLT], in which n means the number of peroxyl radical trapped by an antioxidant, and R i stands for the initiation rate of the radical reaction. It is found that every molecule of melatonin can trap almost two radicals in protecting DNA and erythrocytes. Furthermore, quantum calculation proves that the indole-type radical derived from melatonin is much stable than amide-type radical. Finally, melatonin is able to accelerate hemolysis of erythrocytes induced by hemin, indicating that melatonin leads to the collapse of the erythrocyte membrane in the presence of hemin. This may provide detailed information for the usage of melatonin and helpful reference for the design of indole-related drugs.