Kinetic Rules Research Articles

Introduction of a scalable three-dimensional cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena

Abstract The paper introduces a scalable three-dimensional (3D) kinetic cellular automaton model with a probabilistic switching rule for the spatial and crystallographic prediction of mesoscale transformation phenomena that involve orientational field variables and the motion of sharp interfaces, such as encountered in the field of recrystallization. The automaton is discrete in time, physical space and Euler orientation space. It is defined on a regular 3D cubic lattice considering the first-, second- and third-neighbour shells for the calculation of the local driving forces. The kinetic transformation rule is formulated as a probabilistic analogue of the classical linearized symmetric Turnbull rate equation for grain-boundary segment motion. It is used to calculate the switching probability of each grid point as a function of its previous state and the state of the neighbouring grid points. The actual decision about a switching event is made by evaluating the local switching probability using a Monte Ca...

Ordering and transport in generalized continua with arbitrary order parameters

With reference to two phase solids, Gurtin has recently formulated a unified framework for Ginzburg-Landau's and Cahn-Hilliard's equations. The present paper deals with its possible extension to generalized continua described by arbitrary tensor-order parameters. The role of the configurational entropy is discussed in detail. Such an entropy allows to obtain kinetic rules even in the theoretical limit case of frictionless materials.

A Principal of Linear Covariance for Quantum Mechanics and Its Consequences Taking one Beyond Symmetry

Abstract A Principle of Linear Covariance is stated which follows from the "superposition principle" of quantum mechanics. Accordingly, quantum mechanical equations should be written in linearly covariant form which makes them look the same under non-unitary as well as unitary transformations. The principle leads to a non-unitary classification of all molecules (and clusters and solids) into distinct equivalence classes giving hitherto unknown relations between isomeric molecules. One also gets kinetic and thermic selection rules for chemical reactions. All these are independent of, and far more general than any unitary or point group symmetries. The invariants found for each class of molecules or clusters allow qualitative electronic deductions and are more generally applicable than symmetry based quantum numbers.

Study of the Structure and Characteristics of Epitaxial T-grains Along Their Edges

AbstractEpitaxial tabular silver halide emulsions with tabular grains of AgBrl, containing iodine in the range of 0—10.9 mol% and with epitaxial ledges, were prepared in the presence of a suitable growth modifier. The host microcrystals were pure AgBr, The epitaxial tabular grain silver halide emulsions were studied by scanning electronic microscope (SEM). Ionic conductivity of the emulsion decreases duetoepitaxial growth of the host tabular grains. The photoelectron decay processes for both host and epitaxial emulsions obey a first-order kinetic rule, the photoelectron lifetime of epitaxial grain emulsion becomes longer than the host.

Features in the kinetics of lateral zone crystallization of semiconductor crystals in a temperature gradient field

Theoretical and experimental investigations of the kinetics of a lateral zone crystallization process in a temperature gradient field are given. Kinetic rules for the method are established which allow one to control the rate of the process and the configuration of the crystallization channel.

General Kinetic Rules for Rapid Thermal Processing

AbstractUp to now, kinetic effects in rapid thermal processing (RTP) have been assessed qualitatively and rather vaguely through the concept of thermal budget. We discuss the shortcomings associated with thermal budget and present an alternate conceptual framework that explicitly treats selectivity between desired and undesired physical phenomena. This framework is quite simple and is intended for rapidly assessing the qualitative effects of various heating programs. From a purely kinetic perspective, selecting the best program involves only comparing the activation energies for the desired and undesired rate phenomena. We cite examples where application of the thermal budget approach gives incorrect guidance for minimizing the undesired process. Such deficiencies are rectified by the framework presented here.

95/05054 Study of general rule of combustion kinetics of coal char

95/05054 Study of general rule of combustion kinetics of coal char

Binary nucleation kinetics. I. Self-consistent size distribution

Using the principle of detailed balance, we derive a new self-consistency requirement, termed the kinetic product rule, relating the evaporation coefficients and equilibrium cluster distribution for a binary system. We use this result to demonstrate and resolve an inconsistency for an idealized Kelvin model of nucleation in a simple binary mixture. We next examine several common forms for the equilibrium distribution of binary clusters based on the capillarity approximation and ideal vapor behavior. We point out fundamental deficiencies for each expression. We also show that each distribution yields evaporation coefficients that formally satisfy the new kinetic product rule but are physically unsatisfactory because they depend on the monomer vapor concentrations. We then propose a new form of the binary distribution function that is free of the deficiencies of the previous functions except for its reliance on the capillarity approximation. This new self-consistent classical (SCC) size distribution for binary clusters has the following properties: It satisfies the law of mass action; it reduces to an SCC unary distribution for clusters of a single component; and it produces physically acceptable evaporation rate coefficients that also satisfy the new kinetic product rule. Since it is possible to construct other examples of similarly well-behaved distributions, our result is not unique in this respect, but it does give reasonable predictions. As an illustrative example, we calculate binary nucleation rates and vapor activities for the ethanol–hexanol system at 260 K using the new SCC distribution and compare them to experimental results. The theoretical rates are uniformly higher than the experimental values over the entire vapor composition range. Although the predicted activities are lower, we find good agreement between the measured and theoretical slope of the critical vapor activity curve at a constant nucleation rate of 107 cm−3 s−2.

Two-Phase Stefan Problem with Supercooling

Both one-dimensional two-phase Stefan problems with the thermodynamic equilibrium condition $\theta (R(t),t) = 0$, and with the kinetic rule $\theta (R(t),t) = - \varepsilon \dot R(t)$ at the moving boundary $x = R(t)$ are considered. We study the properties of the regular solutions of the problem with equilibrium condition. They are obtained as a limit of solutions of the problem with the kinetic law as $\varepsilon \to 0$. The peculiarity of our problem is the partial supercooling of the liquid phase $(\theta 0$ exactly equal to the interval in which $\theta (x,\bar t - 0) \leq - L$. He...

MATHEMATICAL MODELLING OF CELLULAR RESPONSES TO EXTERNAL SIGNALS

An empirical mathematical model is proposed to describe the response (growth rate, metabolic activity etc.) of a cell population to various intensities of an external signal (hormone, antibody, pharmacon etc.). The model is based on the assumption that the signal causes the target system to pass consecutively through i=1, …, N distinct population states having response coefficients Ri. Describing the interaction of the system with the signal according to the rules of chemical kinetics by two phenomenological parameters (k - sensitivity, n - cooperativity index) one arrives at a series expansion for Ri which is linear in the Ri’s but nonlinear with respect to k and n (“R-decomposition”). The pattern of expansion coefficients Ri is characteristic of a given signal and can be used to reveal similarities in the responses of the cell population to various signals. A user-friendly microcomputer program has been developed to fit the model equation to experimental data by means of constraint nonlinear regression analysis and to determine all characteristic curve parameters (number and location of extremal values, inflection points etc.). The robustness and benefit of the model is demonstrated by applications to various types of “exotic” dose-reponse-curves obtained from a neutral-red assay of fibroblasts. Similarities between response curves are studied.

Mathematical Modeling of Action Mechanisms of Some Aromatic Amine Class Inhibitors for Polymers

Abstract The kinetic rules of inhibited oxidation of n-hexadecane have been investigated in presence of aromatic amine inhibitors. The studies were carried out in autooxidative conditions at different rates of oxidation initiation. The study included a wide range of inhibitor concentrations and hydroperoxides at different partial pressures of oxygen. A mathematical model of the investigated process has been worked out that describes the main rules of the process and quantitatively predicts the experimental data.

Structural kinetic rules governing the thermal decomposition of pyridine N-oxides

The Arrhenius parameters of the thermal composition of pyridine N-oxides in the liquid phase have been determined. The conclusion has been reached that the formation of an oxaziridine activated complex can be considered as the initial act of the thermolysis. A correlation has been found to exist between the rate constants of the thermal decomposition and the calculated values of the fractional electron charge at the oxygen of the N-oxide, and the length of the N- O bonds.

Photoreduction dehalogenation of polychlorobenzenes by ethanol

It has been demonstrated that in ethanolic solutions in the presence of oxygen the photochemical and photocatalytic consecutive dehalogenation of hexachlorobenzene to benzene can take place. The kinetic rules governing the processes have been established and the possible mechanisms discussed.

Plant growth modelling without integrating mechanisms

ABSTRACTThe integration of root and shoot activity for resource acquisition and allocation is a central problem both in experimental physiology and in mathematical growth modelling. A key feature in all proposed solutions is the mechanism by which roots and shoot communicate their resource status, their needs or their demands. In experimental studies, chemical messengers (hormones or nutrients) have been central. In mathematical models, partitioning or productivity functions of one form or another have been incorporated to fill a similar role. In this paper, the central hypothesis is that growth and resource allocation can be based solely on local, internal, non‐structural resource concentrations and local kinetic rules, without the need for additional mechanisms to integrate activities at the organis‐mal level. The specific objective was to develop a formal model using the classical two‐compartment, two‐resource framework which did not include direct intercompartmental coordinating or communicating mechanisms or resource partitioning functions. The formalization effort was successful based on two criteria. First, the ‘plants’ grow at steady and balanced rates when ‘growth conditions’ are constant; and second, challenged with experimental manipulations such as pruning or limitations in resource acquisition, their growth responses mimic those of real plants. Analysis of the results indicates that the complex integrated growth patterns of the modelled plants are emergent properties – having no direct or indirect mechanistic basis – of the simple system. They imply that similar ‘mechanism‐less’ integration is possible in real plants as an emergent property of strictly local, cellular‐level activities.

Thiol group identification at or near the agonist binding site of the vascular dopamine receptor

Cultured mesenteric artery vascular smooth muscle cells derived from male Wistar rats, expressing both β 2-adrenoceptors and dopamine DA 1 receptors, were prelabelled for 2 h with [ 3H]adenine. [ 3H]cAMP formation stimulated by the addition of dopamine (plus propranolol 10 μM), isoprenaline or forskolin, in the presence of the phosphodiesterase inhibitor 3-isobutyl-1-methylxanthine (IBMX) (0.5 mM) was then determined. Exposure of cells to the thiol-oxidizing agent DTNB (5.5′-dithiobis-2-nitrobenzoic acid) following prelabelling, and prior to cAMP assay, resulted in time-dependent inhibition of dopamine (0.1 mM-induced cAMP formation, which obeyed the rules of first-order kinetics, being complete by 60 min. This inhibitory effect was observed to be dose related with 50% inhibition achieved at a concentration of 0.5 mM. Exposure to DTNB (5 mM) for 45 min abolished the cAMP response to dopamine (0.1 mM) with little effect on the response to forskolin (10 μM) or isoprenaline (10 μM). Prior addition of the dopamine DA 1/D 1 receptor selective partial agonist (+)-SKF 38393 (1 μM) preserved the dopamine induced cAMP formation despite DTNB exposure, while its stereo-enantiomer (−)-SKF 38393 (1 μM) protected only 25% of the response. Sequential exposure of cells to DTNB (5 mM) and then either vehicle or DTT (DL-dithiothreitol; 1 mM), each for 20 min periods, resulted in a 70% inhibition of dopamine induced cAMP formation which was almost completely reversed by the disulphide bridge cleaving compound DTT. Our data indicate that dopamine receptors coupled to adenylate cyclase expressed by rat mesenteric artery vascular smooth muscle cells in culture posses a thiol group at or near the agonist binding site, the integrity of which is vital for normal receptor-ligand interaction to take place.

Schematic methods for probabilistic enzyme kinetics

The theory of steady-state enzyme processes which avoids using the mass action law of chemical kinetics and consistently describes catalytic mechanisms by probabilistic concepts has recently been proposed (Mazur, 1991, J. theor. Biol. 148, 229-242). To facilitate the analysis of complex reaction graphs by this theory the possibility of constructing schematic rules similar to those used in classical kinetics is studied. It is found that due to the similarity of algebraic procedures the popular method of King & Altman can be applied in probabilistic kinetics in addition to the earlier proposed rule based on enumeration of cycles of the reaction graph. This similarity also allows one to adapt many other shortcut methods of classical kinetics for probabilistic reaction graphs. The paper considers separately the possibility of transforming reaction mechanisms so that the initial graph is replaced by a simpler but equivalent one. It is shown that there are few cases when a group of states can be replaced by one united state, with earlier known rules such as the rule of Cha for equilibrium stages being particular cases of a more general procedure. In addition a novel method is proposed which performs step-by-step reduction of any reaction graph. All the new methods can be adapted for traditional kinetics as well. The results obtained demonstrate that many schematic rules of classical kinetics are of probabilistic origin.

Simultaneous transport of parent and daughter compounds in aquifers with linear first-order sorption kinetics

In soils, daughter compounds may be generated from a parent compound by microbial metabolism, chemical reactions, radioactive decay, or other mechanisms. These daughter compounds are also acted upon by soil physical, chemical and biological processes. A system often referred to as a cascade or chain of compounds system results. While a great deal of attention has been given to this problem with the linear equilibrium assumption applied uniformly to all transport and reacting compounds, little attention has been given to the simultaneous transport and fate of a parent-daughter chain with a first-order rate assumed for the adsorption-desorption kinetics of each compound and with the soil partitioned into three sorption classes. A general one-dimensional cascade or chain model for the simultaneous transport of parent and daughter compounds in sorbing, homogeneous, water table aquifers is presented. The model is based on an advective-dispersive mass accounting formulation for both compounds and includes: (a) first-order rate of conversion of parent to daughter; (2) first-order rates of loss of either parent or daughter or both due to metabolism, chemical reaction and/or irreversible processes; (3) partitioning of the aquifer material into three sorption classes, namely mildly sorbing, strongly sorbing and organic matter; (4) linear first-order kinetic rules for adsorption and desorption operating on each of the sorbing soil fractions for each compound; (5) constantly emitting sources of rectangular shape of parent compound; and (6) mass accounting boundary conditions; and a tailorable initial distribution on [0, ∞). Mathematical analysis yields a coupled, linear system of equations including two transport and fate equations, initial and boundary data, and six kinetic rules, namely three each for parent and daughter compound. A numerical scheme for solving the system of equations was developed using readily available procedures since analytical solutions could not be found. Solutions for scenarios based on leaking underground sources are presented.

Hydrolysis and alkylating reactivity of aromatic nitrogen mustards

Rate constants for the hydrolysis of a series of aromatic nitrogen mustards Ar–X–C6H4-N(CH2CH2Cl)2(X = O, CH2, CONH, S, CO and SO2) in buffered aqueous acetone mixtures have been obtained using an HPLC technique which allows evaluation of the rate constants for hydrolytic displacement of both chlorines in consecutive reactions. Hydrolysis has a general-base-catalysed component and is accompanied by external chloride ion return. An aziridinium ion intermediate is implicated in at least one pathway. The mustards also alkylate the nucleophiles thiourea and 4-(4-nitrobenzyl)pyridine (NBP) and again the aziridinium ion intermediate is involved since the kinetic behaviour rules out a direct SN2 pathway.

An inverse correlation between activation energies and the heats of formation for the thermal oxidation of metals

All clean metal surfaces (with the possible exception of gold exposed to dry air at room temperature) react with oxygen and/or moisture to form a surface oxide when brought in contact with the ambient atmosphere. The data on the thermodynamic tendency (as represented by the heats of formation per equivalent,-ΔH e) and the kinetic tendency (as signified by the activation energy for thermal oxide formation, E) for the oxidation of a number of common metals is examined with a view to explore a possible interconnection between the two. An inverse correlation between -ΔH e and E is found to exist: this would indicate that the thermodynamic ease of oxidation ( i.e., a high-ΔH e value) tends to be associated with the kinetic ease of oxidation ( i.e., low E value). This would appear to be at variance with the Brönsted's rule of reaction kinetics in which a linear relation between -ΔH an E is expected to operate.

Presence of ghost doublets of coded neuronal patterns: relation to synaptic memory storage.

Recent evidence demonstrates that controlled visual stimuli cause the generation, in the primary visual cortex of rhesus monkey cells, of large numbers of very precisely replicating copies of complex patterns of discharge consisting of three or more spikes, the patterns of which presumedly code for specific qualities of the stimuli presented. We present evidence that the copies of precisely replicating triplets of spikes, generally not exceeding 100 ms in duration, occur in close time proximity to many copies of highly precise "ghost" doublets. These doublets are defined as patterns consisting of two pulses, with precise separations in time, specifically those that would be generated if any one of the pulses making up a given replicating triplet were missing. In striking contrast, nonreplicating triplets (also present in these records)--that is, triplets made up of intervals that are not present in replicating triplets--are not accompanied by such ghost doublets. The persistence (memory) of capacity to produce such ghost doublets decays according to two independent kinetic rules. The first of these results in the disappearance of such doublets within about 0.1 s as measured by two independent methods, whereas the second disappears only after several minutes or longer. These results provide strong evidence consistent with the notion that at least some parts of the brain transmit, store representations of, and retrieve qualitative information through the use of a code consisting of specific patterns of nerve discharges in time.