Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to drift do not fall into a limited number of universality classes.Comment: 10 pages, tex, 3 figures, also available upon reques

Automated prediction of catalytic mechanism and rate law using graph-based reaction-path sampling

In a recent article [J. Chem. Phys., 143, 094106 (2015)], we have introduced a novel graph-based sampling scheme which can be used to generate chemical reaction paths in many-atom systems in an efficient and highly-automated manner. The main goal of this work is to demonstrate how this approach, when combined with direct kinetic modelling, can be used to determine the mechanism and phenomenological rate law of a complex catalytic cycle, namely cobalt-catalyzed hydroformylation of ethene. Our graph-based sampling scheme generates 31 unique chemical products and 32 unique chemical reaction pathways; these sampled structures and reaction paths en- able automated construction of a kinetic network model of the catalytic system when combined with density functional theory (DFT) calculations of free energies and resul- tant transition-state theory rate constants. Direct simulations of this kinetic network across a range of initial reactant concentrations enables determination of both the re- action mechanism and the associated rate law in an automated fashion, without the need for either pre-supposing a mechanism or making steady-state approximations in kinetic analysis. Most importantly, we find that the reaction mechanism which emerges from these simulations is exactly that originally proposed by Heck and Breslow; fur- thermore, the simulated rate law is also consistent with previous experimental and computational studies, exhibiting a complex dependence on carbon monoxide pres- sure. While the inherent errors of using DFT simulations to model chemical reactivity limit the quantitative accuracy of our calculated rates, this work confirms that our automated simulation strategy enables direct analysis of catalytic mechanisms from first principles

Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A

Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the distribution of distances between nearest particles. However, a full characterization of a particle system is only provided by the infinite hierarchy of multiple-point density correlation functions. We derive an exact description of the full hierarchy of correlation functions for the diffusion-limited irreversible coalescence process A + A -> A.Comment: 4 pages, 2 figures (postscript). Typeset with Revte

New evidence on Allyn Young's style and influence as a teacher

This paper publishes the hitherto unpublished correspondence between Allyn Abbott Young's biographer Charles Blitch and 17 of Young's former students or associates. Together with related biographical and archival material, the paper shows the way in which this adds to our knowledge of Young's considerable influence as a teacher upon some of the twentieth century's greatest economists. The correspondents are as follows: James W Angell, Colin Clark, Arthur H Cole, Lauchlin Currie, Melvin G de Chazeau, Eleanor Lansing Dulles, Howard S Ellis, Frank W Fetter, Earl J Hamilton, Seymour S Harris, Richard S Howey, Nicholas Kaldor, Melvin M Knight, Bertil Ohlin, Geoffrey Shepherd, Overton H Taylor, and Gilbert Walker

Geometrical Models of the Phase Space Structures Governing Reaction Dynamics

Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow \emph{bottlenecks} created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description of the phase space structures that are responsible for controlling transport in these problems. Of central importance is the existence of a \emph{Normally Hyperbolic Invariant Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient dimensionality to act as separatrices, partitioning energy surfaces into regions of qualitatively distinct behavior. This NHIM forms the natural (dynamical) equator of a (spherical) \emph{dividing surface} which locally divides an energy surface into two components (`reactants' and `products'), one on either side of the bottleneck. This dividing surface has all the desired properties sought for in \emph{transition state theory} where reaction rates are computed from the flux through a dividing surface. In fact, the dividing surface that we construct is crossed exactly once by reactive trajectories, and not crossed by nonreactive trajectories, and related to these properties, minimizes the flux upon variation of the dividing surface. We discuss three presentations of the energy surface and the phase space structures contained in it for 2-degree-of-freedom (DoF) systems in the threedimensional space $\R^3$, and two schematic models which capture many of the essential features of the dynamics for $n$-DoF systems. In addition, we elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function

Microcanonical rates, gap times, and phase space dividing surfaces

The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN $\rightleftharpoons$ CNH. Both algebraic (power law) and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Examination of the decay properties of subsensembles of trajectories that exit the HCN well through either of 2 available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short timescale $t \lesssim 0.5$ ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential (nonstatistical) decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.Comment: 44 pages, 9 figure

Imaging mass cytometry analysis of Becker muscular dystrophy muscle samples reveals different stages of muscle degeneration

\ua9 2024. The Author(s). Becker muscular dystrophy (BMD) is characterised by fiber loss and expansion of fibrotic and adipose tissue. Several cells interact locally in what is known as the degenerative niche. We analysed muscle biopsies of controls and BMD patients at early, moderate and advanced stages of progression using Hyperion imaging mass cytometry (IMC) by labelling single sections with 17 markers identifying different components of the muscle. We developed a software for analysing IMC images and studied changes in the muscle composition and spatial correlations between markers across disease progression. We found a strong correlation between collagen-I and the area of stroma, collagen-VI, adipose tissue, and M2-macrophages number. There was a negative correlation between the area of collagen-I and the number of satellite cells (SCs), fibres and blood vessels. The comparison between fibrotic and non-fibrotic areas allowed to study the disease process in detail. We found structural differences among non-fibrotic areas from control and patients, being these latter characterized by increase in CTGF and in M2-macrophages and decrease in fibers and blood vessels. IMC enables to study of changes in tissue structure along disease progression, spatio-temporal correlations and opening the door to better understand new potential pathogenic pathways in human samples