Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

We analyze both the spatiotemporal behavior of non-linear reaction models utilizing reaction-diffusion equations, and spatial transport problems on surfaces and in nanopores utilizing the relevant diffusion or Fokker-Planck equations. The non-linear reaction models involve spatial discrete systems where particles reside at the sites of a periodic lattice: particles, X, spontaneously annihilate (X-\u3eO) at a specified rate p, and are autocatalytically created given the presence of nearby pairs of particles (O+2X-\u3e3X) at rates depending on the local configuration. [This reaction model is equivalent to a spatial epidemic model where sick individuals spontaneously recover (S-\u3eH), and healthy individuals are infected by pairs of sick neighbors (H+2S-\u3e3S).] The model exhibits a non-equilibrium phase-transition from a populated state to a vacuum state (with no particles) with increasing p. Near this transition, one can consider the propagation of interfaces separating the two states. Planar interfaces exhibit an orientation-dependence (leading to so-called generic two-phase coexistence), and curved interfaces enclosing droplets exhibit even richer behavior. These phenomena are analyzed utilizing the appropriate set of discrete reaction-diffusion equations (corresponding to lattice differential equations). Diffusive transport of particles between islands or clusters of particles on a surface leads to coarsening of island arrays which can be analyzed by solution of an appropriate boundary value problem for the surface diffusion equation. We extend previous treatments to strongly anisotropic systems. Diffusion and passing of pairs of overdamped Langevin molecules in narrow nanopores can be described by the appropriate Fokker-Planck equations (corresponding to a high-dimensional diffusion equation). We provide the first analysis of this problem focusing on a characterization of the propensity of passing as a function of pore diameter

Uncovering Hierarchical Structure in Social Networks using Isospectral Reductions

We employ the recently developed theory of isospectral network reductions to analyze multi-mode social networks. This procedure allows us to uncover the hierarchical structure of the networks we consider as well as the hierarchical structure of each mode of the network. Additionally, by performing a dynamical analysis of these networks we are able to analyze the evolution of their structure allowing us to find a number of other network features. We apply both of these approaches to the Southern Women Data Set, one of the most studied social networks and demonstrate that these techniques provide new information, which complements previous findings.Comment: 17 pages, 5 figures, 5 table

Schloegl’s second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence

Schloegl\u27s second model on a (d ≥ 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, pf(d

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Threshold versions of Schloegl\u27s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior

Optimization of a Continuous Preparation Method of Arthrospira platensis γ-linolenic acid by supercritical carbon dioxide technology using response surface methodology

γ-linolenic acid is an essential omega-6 unsaturated fatty acid made in the human body from linoleic acid. It can be metabolized to various important eicosanoids and it is also a precursor of prostaglandin E and several other active substances that are associated with anti-inflammatory properties. Arthrospira platensis is known to contain relatively large quantities of γ-linolenic acid. The aim of this study was to investigate the optimal parameters under a continuous preparation method of γ-linolenic acid from A. platensis using supercritical carbon dioxide technology. A Box-Behnken experimental design and response surface methodology were used to optimize combinations among pressure (10, 20 and 30 MPa), temperature (40, 50 and 60°C) and flow rate of A. platensis extract liquor (1, 2 and 3 mL/min) for yield of γ-linolenic acid. The results showed that the extraction of γ-linolenic acid from A. platensis was optimized at a temperature of 60°C, a pressure of 30 MPa and a flow rate of 3 mL/min. These parameters could be used as a basis for facilitating future scale-up industrial applications

A CMMI-based approach for medical software project life cycle study

In terms of medical techniques, Taiwan has gained international recognition in recent years. However, the medical information system industry in Taiwan is still at a developing stage compared with the software industries in other nations. In addition, systematic development processes are indispensable elements of software development. They can help developers increase their productivity and efficiency and also avoid unnecessary risks arising during the development process. Thus, this paper presents an application of Light-Weight Capability Maturity Model Integration (LW-CMMI) to Chang Gung Medical Research Project (CMRP) in the Nuclear medicine field. This application was intended to integrate user requirements, system design and testing of software development processes into three layers (Domain, Concept and Instance) model. Then, expressing in structural System Modeling Language (SysML) diagrams and converts part of the manual effort necessary for project management maintenance into computational effort, for example: (semi-) automatic delivery of traceability management. In this application, it supports establishing artifacts of “requirement specification document”, “project execution plan document”, “system design document” and “system test document”, and can deliver a prototype of lightweight project management tool on the Nuclear Medicine software project. The results of this application can be a reference for other medical institutions in developing medical information systems and support of project management to achieve the aim of patient safety. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/2193-1801-2-266) contains supplementary material, which is available to authorized users

Kinetic Monte Carlo Simulation of Statistical Mechanical Models and Coarse-Grained Mesoscale Descriptions of Catalytic Reaction–Diffusion Processes: 1D Nanoporous and 2D Surface Systems

Traditional mean-field rate equations of chemical kinetics for spatially uniform systems1−3 and the corresponding reaction−diffusion equations describing spatial heterogeneity4−6 have proved immensely useful in elucidating catalytic processes. However, it is well-recognized that standard mean-field rate expressions neglect spatial correlations in the reactant and/or product distribution. It is less well appreciated that the standard treatment of diffusion is generally applicable only at low concentrations and in unrestricted environments

Langevin and Fokker-Planck Analyses of Inhibited Molecular Passing Processes Controlling Transport and Reactivity in Nanoporous Materials

Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P∼(R−Rc)σ, where passing is sterically blocked for R≤Rc, with σ below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules