Low-dimensional manifolds in reaction-diffusion equations. 2. Numerical analysis and method development

Calculations are undertaken to study the approach to equilibrium for systems of reaction-diffusion equations on bounded domains. It is demonstrated that a number of systems approach equilibrium along attractive low-dimensional manifolds over significant ranges of parameter space. Numerical methods for generating the manifolds are adapted from methods that were developed for systems of ordinary differential equations. The truncation of the infinite spectrum of the partial differential equations makes it necessary to devise a new version of one of these methods, the well-known algorithm of Maas and Pope.     

Spatial dynamics of steady flames 2. Low-dimensional manifolds and the role of transport processes

The study of the spatial dynamics of steady one-dimensional H 2/O 2 flames is continued. Algorithms for generating low-dimensional manifolds for these systems are presented and used to find low-dimensional manifolds for the flames and the corresponding adiabatic, isobaric chemical-kinetic systems. It is demonstrated that these algorithms generate manifolds that are more accurate than the ILDM algorithm for two-dimensional manifolds of the flames. The manifolds are then employed to study the relationship between the manifolds of the flame and the manifolds of the chemical-kinetic system. It is shown that the one-dimensional manifolds of the flame match well with the composite manifolds of the chemical kinetics, but that for two-dimensional manifolds there are discrepancies between the flame manifolds and the chemical-kinetic manifolds.     

A singular pertubation theory for reaction-diffusion equations

A pertubation theory is developed for the probability density for the displacement in reaction-diffusion equations of the form ∂p/∂τ = ε (∂/∂y) [f(y)∂p/∂y] − (∂/∂y) [v(y)p] − κ(yp. In this equation f(y), v(y) and κ(y) are dimensionless functions of y taken to be O(1), and ε is a dimensionless parameter which, in the diffusion-dominated regime satisfies ε 1. We briefly also discuss the case in which v(y) is also proportional to ε. Our results are then applied to an exactly solvable example.     

Correction factors for boundary diffusion in reaction-diffusion master equations

The reaction-diffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDME-based trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particle-based methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007); R. Erban and S. J. Chapman, Phys. Biol. 6, 46001 (2009); D. Fange, O. G. Berg, P. Sjo?berg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A. 107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate--and possibly unphysical--results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semi-permeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.     

Fundamental aspects of electrocatalysis

A theory for electrochemical electron transfer is proposed which explicitly accounts for the electronic structure of the electrode; it applies both to simple and to bond-breaking reactions. Interactions with narrow d-bands lead to changes in the local density of states of the reactant as its electronic level fluctuates due to solvent reorganization. More importantly, it can significantly reduce activation barriers, and in extreme cases induce dissociative adsorption. The model gives some justification to recent suggestions that the center of the d-band is a key factor for electrocatalysis, and it offers a route for calculating reaction rates using results from ab initio calculations as input.     

Fundamental aspects of rubber-elasticity in real networks

Based on the van der Waals-equation of state a characterization of the elastic properties of molecular networks in the total range of strain is presented by the use of Mooney-Rivlin plots. This discussion elucidates the importance of finite chain extensibility as well as global interactions for a quantitative interpretation of the deformation properties of molecular networks. An interpretation of the so-called Mooney-Rivlin coefficients in terms of the van der Waals-parameters delivers at least a novel, yet very consistent understanding of simple extension of swollen networks.     

Theory of damped quantum rotation in NMR spectra. I. Fundamental aspects

The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the "degree of classicality" represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work.     

Amplitude equations for breathing spiral waves in a forced reaction-diffusion system

Based on a multiple scale analysis of a forced reaction-diffusion system leading to amplitude equations, we explain the existence of spiral wave and its photo-induced spatiotemporal behavior in chlorine dioxide-iodine-malonic acid system. When the photo-illumination intensity is modulated, breathing of spiral is observed in which the period of breathing is identical to the period of forcing. We have also derived the condition for breakup and suppression of spiral wave by periodic illumination. The numerical simulations agree well with our analytical treatment.     

Cathodic electrodeposition of ceramic and organoceramic materials. Fundamental aspects

Electrodeposition of ceramic materials can be performed by electrophoretic (EPD) or electrolytic (ELD) deposition. Electrophoretic deposition is achieved via motion of charged particles towards an electrode under an applied electric field. Electrolytic deposition produces colloidal particles in cathodic reactions for subsequent deposition. Various electrochemical strategies and deposition mechanisms have been developed for electrodeposition of ceramic and organoceramic films, and are discussed in the present article. Electrode-position of ceramic and organoceramic materials includes mass transport, accumulation of particles near the electrode and their coagulation to form a cathodic deposit. Various types of interparticle forces that govern colloidal stability in the absence and presence of processing additives are discussed. Novel theoretical contributions towards an interpretation of particle coagulation near the electrode surface are reviewed. Background information is given on the methods of particle charging, stabilization of colloids in aqueous and non-aqueous media, electrophoretic mobility of ceramic particles and polyelectrolytes, and electrode reactions. This review also covers recent developments in the electrodeposition of ceramic and organoceramic materials.     

Crystallization in oriented poly(ethylene terephthalate) fibers. I. Fundamental aspects

The nature of crystallization- and mobility-induced changes during annealing of melt-spun poly(ethylene terephthalate) precursor fibers of a range of orientations has been examined. The kinetics of crystallization and the accompanying orientational changes have been studied under conditions of constant, low tensile stress, with the accompanying dimensional changes and under a constraint against shrinkage in length, with the stress developed being monitored. The effects of precursor orientation and externally imposed constraints on the course of the fundamental crystallization and orientational relaxation processes are revealed. Oriented crystallization has been shown to have a significant effect on the stress developed and on the dimensions of oriented precursor fibers, with a strong tendency to spontaneously extend as a consequence of the reorientation of crystallizing segments predominantly along the preferred fiber direction. The sequence in which crystallization and major orientational relaxation, if any, occur is found to have a profound effect on the structure and thus the deformability of oriented fibers after annealing above the glass transition temperature.     

Fundamental aspects of chiral separations by capillary electrophoresis

A review is presented that surveys the basic theory of direct separation of enantiomers by capillary electrophoretic (CE) techniques. These separations are based on the formation of diastereomeric complexes between the enantiomeric analytes and a chiral selector added to the electrolyte solution. The review covers a comprehensive treatment of the equations needed for optimization of selectivity coefficients, resolution and analysis time in the zone electrophoretic mode. In this context, it takes into account combined equilibria of complexation and protonation/deprotonation as well as complexation and paritition into micelles. On the basis of these equations, the benefits of charged selectors and the optimization potential inherent to pH tuning can be documented. In addition, the review deals with some basic aspects of chiral isoelectric focusing and briefly discusses indirect enantioseparation. In a subsequent section a survey is given on particularfeatures of the various types of chiral selectors. Finally, the recent developments in preparative enantioseparation in continuous free-flow system and by use of isoelectric membranes are discussed.     

Fundamental aspects of oxidation of electroexplosive nickel nanopowder

Fundamental aspects of the process in which a nickel nanopowder produced by an electric explosion of conductors is oxidized under heating in air at a linearly increasing temperature and in the isothermal mode were studied. It is shown that the dispersion composition of the powder, structure of the metallic core of nickel particles, and characteristics of the oxide shell affect the kinetic parameters of the process. An explanation is suggested for specific features of the macrokinetic reaction mode caused by the joint influence exerted by the relative amounts of fractions of different-size particles in the powder and by the characteristic of the oxide layer. The reaction kinetics is simulated, with the size distribution function of nickel particles taken into account.     

Fundamental aspects of electrospray droplet impact/SIMS

A new ionization method, electrospray droplet impact ionization (EDI), has been developed for matrix-free secondary-ion mass spectrometry (SIMS). The charged droplets formed by electrospraying 1 M acetic acid aqueous solution are sampled through an orifice with a diameter of 400 microm into the first vacuum chamber, transported into a quadrupole ion guide, and accelerated by 10 kV after exiting the ion guide. The droplets impact on a dry solid sample (no matrix used) deposited on a stainless steel substrate. The secondary ions formed by the impact are transported to a second quadrupole ion guide and mass-analyzed by an orthogonal time-of-flight mass spectrometer (TOF-MS). Ten pmol of gramicidin S could be detected with the presence of as much as 10 nmol of NaCl. The ion signal for arginine disappeared with decrease in the substrate temperature below 150 K owing to the formation of ice film over the sample surface. While 10 fmol of gramicidin S could be detected for 30 min, the ionization/desorption efficiency for EDI becomes smaller with an increase in the molecular weight (MW) of a biological sample. The largest protein samples detected to date are cytochrome c and lysozyme. The high sensitivity for EDI is due to the fact that samples only a few monolayers thick are subject to desorption/ionization by EDI, with little fragmentation. A coherent phonon excitation may be the main mechanism for the desorption/ionization of the solid sample.     

Fundamental aspects of the behavior of various lignosulfonates in solutions

Fundamental aspects of associative-dissociative and acid-base transformations of technical-grade high-and low-molecular mass lignosulfonates were identified by carrying out a set of physicochemical studies.     

Fundamental and engineering thermal aspects of energy and environment

Journal of Thermal Analysis and Calorimetry -     

Fundamental aspects and applications of fourier-transform ion-cyclotron resonance spectrometry

The operating principles, features, advantages, applications and potential of Foourier-transform ion-cyclotron resonance (F.t./i.c.r. or F.t.m.s.) mass spectrometry are discussed. It is shown that F.t./i.c.r. technology creates a high-performance mass spectrometer with high speed, high sensitivity, ultrahigh mass resolution, very wide mass range and unparalleled versatility.     

Fundamental aspects and applications of glow discharge spectrometric techniques

Glow discharges are kind of plasmas which are used in many fields of application, including analytical spectrometry. This review addresses both the fundamental aspects and analytical applications of glow discharges. In the first part, a systematic overview of the most important plasma processes is presented. To obtain better insight into the complexity of the glow discharge, both mathematical modeling and experimental plasma diagnostics can be carried out. Therefore, the models that were developed for a glow discharge are presented and typical results (e.g. three-dimensional density profiles, fluxes and energy distributions of the various plasma species, the electric field and potential distributions, information about collision processes in the plasma and about sputtering at the cathode, etc.) are summarized. Moreover, the most important plasma diagnostic techniques for glow discharges are discussed. In the second part, an overview is given of the various analytical applications of glow discharges.     

Fundamental aspects of initiated oxidation of tridecane and polyethylene in solutions

Specific features of the initiated oxidation of polyethylene and its low-molecular-weight analogue tridecane, associated with the occurrence of the process in the short-chain mode, were studied.