General Coupling Theory Research Articles

Coupling of diffusion and chemical stress: The case of ion exchange in glass

AbstractThe chemical strengthening of glass results from an ion exchange process in which smaller alkali ions in a glass are replaced with larger alkali ions from a molten salt bath. This interdiffusion process leads to a buildup of chemical stress in the glass. However, traditional modeling of the ion exchange process has not fully accounted for interaction effects between mass diffusion and the chemical stress developed during the process. In this study, we develop the general theory of coupling between diffusion and stress, resulting in a single flux equation with a concentration‐ and stress‐dependent interdiffusion coefficient. We apply the theory to the specific cases of chemically strengthened soda lime silicate and aluminosilicate glasses, demonstrating the impact of interaction terms on concentration profiles and interdiffusion coefficient. Following a phenomenological approach, this study demonstrates the effect of the interdiffusion on stress generation and vice versa to account for deviations from the simple expressions published hitherto in the literature.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations.

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Non-invasive measurement of eddy diffusion in very efficient liquid chromatography columns packed with sub-3 μm shell particles

Mass transfer kinetics in a particular column packed with 2.6 μ m Kinetex-C 18 particles was measured using a series of non-invasive methods. According to the manufacturer, this column was the most efficient one in a lot of 133 columns of the same dimensions, packed with particles of the same batch, with an efficiency about 6% larger than the lot average. The total eddy diffusion term of this column was determined by subtracting from the experimental HETP data (1) the longitudinal diffusion term (given by the peak parking method); (2) the trans-particle solid–liquid mass transfer resistance term (given by the peak parking method and an axial diffusion model); and (3) the external film mass transfer resistance term (derived from the Wilson and Geankoplis correlation). The results are analyzed based on the general coupling theory of eddy diffusion of Giddings and are compared to those previously obtained with a column packed with 2.7 μ m Halo-C 18 column, which also has a low eddy diffusion term. The particular column investigated shows no trans-column velocity bias and a smaller reduced short-range inter-channel eddy diffusion term than the Halo column. This result explains the unusual efficiency of this exceptionally well packed column.

Coupling of eigenvalues of complex matrices at diabolic and exceptional points

The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios. Two physical examples illustrate effectiveness and accuracy of the presented theory.

Coupling and convergence of random elements, processes, and regenerative processes

The paper starts by proving that a sequence of random elements can be coupled in such a way that the random elements eventually coincide if and only if liminf of their densities is a density. It continues with a survey of some general coupling theory for stochastic processes and applications to wide sense regenerative processes and Palm theory. Finally, a successful coupling and ɛ-coupling of wide sense regenerative processes is constructed without assuming that the inter-regeneration times have finite mean.

Theory and practice of coupled gas chromatographic columns

Serial coupled gas chromatographic columns, first introduced in 1958, remained neglected until quite recently when interest began to focus on the possibilities of linked capillaries. Analytical success was, however, not accompanied by conformity with the available theories tested and so the procedures adopted were, in the event, essentially empirical. Over the same period, Purnell and Williams have published a series of papers which establish the general theory of coupling of columns of any kind. We present here an example of its use in the optimisation of a sample analysis with serial columns which further establishes the quantitative validity of the theory and illustrates its practicality and simplicity in use.

Physical interpretations of various dynamic light scattering data, their interconnections and relations to other relaxation data

Dynamic light scattering has been proven to be a useful tool to study relaxations in polymeric and small molecular liquids, fused salts, ionic conductors, etc. We attempt to enhance the physical interpretations of the experimental data with the help of a general coupling theory of relaxations. It is demonstrated by many examples that the ideas and predictions of the coupling theory are matching very well to the experimental data. The relations between Brillouin scattering and photon correlation spectroscopy relaxation data are brought out. Physical meanings of the relaxation parameters become evident. Dynamic light scattering data then can be used to advantage in consideration of other physical phenomena and measurements.

Theory and practice of coupled gas chromatographic columns

Serial coupled gas chromatographic columns, first introduced in 1958, remained neglected until quite recently when interest began to focus on the possibilities of linked capillaries. Analytical success was, however, not accompanied by conformity with the available theories tested and so the procedures adopted were, in the event, essentially empirical. Over the same period, Purnell and Williams have published a series of papers which establish the general theory of coupling of columns of any kind. We present here an example of its use in the optimisation of a sample analysis with serial columns which further establishes the quantitative validity of the theory and illustrates its practicality and simplicity in use.

Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

AbstractDifferences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[−(tτ*)1−n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ0) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ* and τ0 predicted by the theory is confirmed also by the experimental data.

A GENERAL THEORY OF TAYLOR DISPERSION PHENOMENA IV. Direct Coupling Effects

Abstract A previous generalized theory of Taylor dispersion phenomena is here extended so as to include “coupling” phenomena. Such direct coupling arises from the fact that—in certain circumstances—global transport processes may be driven by local gradients, and conversely. An obvious example of such direct coupling effects arises in problems pertaining to the gravitational settling and concomitant “sedimentation dispersion” of asymmetric Brownian particles lacking a center of symmetry. In the presence of such asymmetry the parlicle's translational and rotational motions are inseparably coupled to one another. This specific problem will be ueated in a companion paper as an example of the general coupling theory developed herein.

An investigation of the magnetic transverse waves on an electron beam

An electron beam in the presence of an axial magnetic field supports four transverse waves; two cyclotron waves, and two synchronous waves. A general coupling theory is developed from an electronic equation and a circuit equation to describe how these waves can be coupled to traveling-wave circuits. The polarization and power flow characteristics of the waves are derived. The theory is applied to. the bifilar helix, a circuit which can couple selectively to each of the four modes. A bifilar helix traveling-wave tube was used to investigate experimentally the four beam modes and provide a quantitative check of the coupling theory.