Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

Halbig, Michael C.; Eckel, Andrew J.; Cawley, James D.

1999-01-01

Previous stressed oxidation tests of C/SiC composites at elevated temperatures (350 C to 1500 C) and sustained stresses (69 MPa and 172 MPa) have led to the development of a finite difference cracked matrix model. The times to failure in the samples suggest oxidation occurred in two kinetic regimes defined by the rate controlling mechanisms (i.e. diffusion controlled and reaction controlled kinetics). Microstructural analysis revealed preferential oxidation along as-fabricated, matrix microcracks and also suggested two regimes of oxidation kinetics dependent on the oxidation temperature. Based on experimental results, observation, and theory, a finite difference model was developed. The model simulates the diffusion of oxygen into a matrix crack bridged by carbon fibers. The model facilitates the study of the relative importance of temperature, the reaction rate constant, and the diffusion coefficient on the overall oxidation kinetics.

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

NASA Astrophysics Data System (ADS)

Deng, M. L.; Zhu, W. Q.

2007-10-01

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Itô stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

PubMed

Sheng, Yin; Zhang, Hao; Zeng, Zhigang

2017-10-01

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Crystallization kinetics of the borax decahydrate

NASA Astrophysics Data System (ADS)

Ceyhan, A. A.; Sahin, Ö.; Bulutcu, A. N.

2007-03-01

The growth and dissolution rates of borax decahydrate have been measured as a function of supersaturation for various particle sizes at different temperature ranges of 13 and 50 °C in a laboratory-scale fluidized bed crystallizer. The values of mass transfer coefficient, K, reaction rate constant, kr and reaction rate order, r were determined. The relative importances of diffusion and integration resistance were described by new terms named integration and diffusion concentration fraction. It was found that the overall growth rate of borax decahydrate is mainly controlled by integration (reaction) steps. It was also estimated that the dissolution region of borax decahydrate, apart from other materials, is controlled by diffusion and surface reaction. Increasing the temperature and particle size cause an increase in the values of kinetic parameters ( Kg, kr and K). The activation energies of overall, reaction and mass transfer steps were determined as 18.07, 18.79 and 8.26 kJmol -1, respectively.

Chemistry with spatial control using particles and streams†

PubMed Central

Kalinin, Yevgeniy V.; Murali, Adithya

2012-01-01

Spatial control of chemical reactions, with micro- and nanometer scale resolution, has important consequences for one pot synthesis, engineering complex reactions, developmental biology, cellular biochemistry and emergent behavior. We review synthetic methods to engineer this spatial control using chemical diffusion from spherical particles, shells and polyhedra. We discuss systems that enable both isotropic and anisotropic chemical release from isolated and arrayed particles to create inhomogeneous and spatially patterned chemical fields. In addition to such finite chemical sources, we also discuss spatial control enabled with laminar flow in 2D and 3D microfluidic networks. Throughout the paper, we highlight applications of spatially controlled chemistry in chemical kinetics, reaction-diffusion systems, chemotaxis and morphogenesis. PMID:23145348

Free-standing supramolecular hydrogel objects by reaction-diffusion

PubMed Central

Lovrak, Matija; Hendriksen, Wouter E. J.; Maity, Chandan; Mytnyk, Serhii; van Steijn, Volkert; Eelkema, Rienk; van Esch, Jan H.

2017-01-01

Self-assembly provides access to a variety of molecular materials, yet spatial control over structure formation remains difficult to achieve. Here we show how reaction–diffusion (RD) can be coupled to a molecular self-assembly process to generate macroscopic free-standing objects with control over shape, size, and functionality. In RD, two or more reactants diffuse from different positions to give rise to spatially defined structures on reaction. We demonstrate that RD can be used to locally control formation and self-assembly of hydrazone molecular gelators from their non-assembling precursors, leading to soft, free-standing hydrogel objects with sizes ranging from several hundred micrometres up to centimeters. Different chemical functionalities and gradients can easily be integrated in the hydrogel objects by using different reactants. Our methodology, together with the vast range of organic reactions and self-assembling building blocks, provides a general approach towards the programmed fabrication of soft microscale objects with controlled functionality and shape. PMID:28580948

Synthesis and Performance Characterization of a Nanocomposite Ternary Thermite: Al/Fe2O3/SiO2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prentice, D; Pantoya, M L; Clapsaddle, B J

2005-02-04

Making solid energetic materials requires the physical mixing of solid fuels and oxidizers or the incorporation of fuel and oxidizing moieties into a single molecule. The former are referred to as composite energetic materials (i.e., thermites, propellants, pyrotechnics) and the latter are deemed monomolecular energetic materials (i.e., explosives). Mass diffusion between the fuel and oxidizer is the rate controlling step for composite reactions while bond breaking and chemical kinetics control monomolecular reactions. Although composites have higher energy densities than monomolecular species, they release that energy over a longer period of time because diffusion controlled reactions are considerably slower than chemistrymore » controlled reactions. Conversely, monomolecular species exhibit greater power due to more rapid kinetics than physically mixed energetics. Reducing the diffusion distance between fuel and oxidizer species within an energetic composite would enhance the reaction rate. Recent advances in nanotechnology have spurred the development of nano-scale fuel and oxidizer particles that can be combined into a composite and effectively reduce diffusion distances to nano-scale dimensions or less. These nanocomposites have the potential to deliver the best of both worlds: high energy density of the physically mixed composite with the high power of the monomolecular species. Toward this end, researchers at Lawrence Livermore National Laboratory (LLNL) developed nano-particle synthesis techniques, based on sol-gel chemistry, for the production of thermite nanocomposites.« less

From conservative to reactive transport under diffusion-controlled conditions

NASA Astrophysics Data System (ADS)

Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.

2016-05-01

We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.

Erosion of stereochemical control with increasing nucleophilicity: O-glycosylation at the diffusion limit.

PubMed

Beaver, Matthew G; Woerpel, K A

2010-02-19

Nucleophilic substitution reactions of 2-deoxyglycosyl donors indicated that the reactivity of the oxygen nucleophile has a significant impact on stereoselectivity. Employing ethanol as the nucleophile resulted in a 1:1 (alpha:beta) ratio of diastereomers under S(N)1-like reaction conditions. Stereoselective formation of the 2-deoxy-alpha-O-glycoside was only observed when weaker nucleophiles, such as trifluoroethanol, were employed. The lack of stereoselectivity observed in reactions of common oxygen nucleophiles can be attributed to reaction rates of the stereochemistry-determining step that approach the diffusion limit. In this scenario, both faces of the prochiral oxocarbenium ion are subject to nucleophilic addition to afford a statistical mixture of diastereomeric products. Control experiments confirmed that all nucleophilic substitution reactions were performed under kinetic control.

Efficient Green's Function Reaction Dynamics (GFRD) simulations for diffusion-limited, reversible reactions

NASA Astrophysics Data System (ADS)

Bashardanesh, Zahedeh; Lötstedt, Per

2018-03-01

In diffusion controlled reversible bimolecular reactions in three dimensions, a dissociation step is typically followed by multiple, rapid re-association steps slowing down the simulations of such systems. In order to improve the efficiency, we first derive an exact Green's function describing the rate at which an isolated pair of particles undergoing reversible bimolecular reactions and unimolecular decay separates beyond an arbitrarily chosen distance. Then the Green's function is used in an algorithm for particle-based stochastic reaction-diffusion simulations for prediction of the dynamics of biochemical networks. The accuracy and efficiency of the algorithm are evaluated using a reversible reaction and a push-pull chemical network. The computational work is independent of the rates of the re-associations.

Control of transversal instabilities in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

2018-05-01

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

Travelling fronts of the CO oxidation on Pd(111) with coverage-dependent diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cisternas, Jaime, E-mail: jecisternas@miuandes.cl; Karpitschka, Stefan; Wehner, Stefan

2014-10-28

In this work, we study a surface reaction on Pd(111) crystals under ultra-high-vacuum conditions that can be modeled by two coupled reaction-diffusion equations. In the bistable regime, the reaction exhibits travelling fronts that can be observed experimentally using photo electron emission microscopy. The spatial profile of the fronts reveals a coverage-dependent diffusivity for one of the species. We propose a method to solve the nonlinear eigenvalue problem and compute the direction and the speed of the fronts based on a geometrical construction in phase-space. This method successfully captures the dependence of the speed on control parameters and diffusivities.

Product interactions and feedback in diffusion-controlled reactions

NASA Astrophysics Data System (ADS)

Roa, Rafael; Siegl, Toni; Kim, Won Kyu; Dzubiella, Joachim

2018-02-01

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.

Macromolecular crowding effect upon in vitro enzyme kinetics: mixed activation-diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase.

PubMed

Balcells, Cristina; Pastor, Isabel; Vilaseca, Eudald; Madurga, Sergio; Cascante, Marta; Mas, Francesc

2014-04-17

Enzyme kinetics studies have been usually designed as dilute solution experiments, which differ substantially from in vivo conditions. However, cell cytosol is crowded with a high concentration of molecules having different shapes and sizes. The consequences of such crowding in enzymatic reactions remain unclear. The aim of the present study is to understand the effect of macromolecular crowding produced by dextran of different sizes and at diverse concentrations in the well-known reaction of oxidation of NADH by pyruvate catalyzed by L-lactate dehydrogenase (LDH). Our results indicate that the reaction rate is determined by both the occupied volume and the relative size of dextran obstacles with respect to the enzyme present in the reaction. Moreover, we analyzed the influence of macromolecular crowding on the Michaelis-Menten constants, vmax and Km. The obtained results show that only high concentrations and large sizes of dextran reduce both constants suggesting a mixed activation-diffusion control of this enzymatic reaction due to the dextran crowding action. From our knowledge, this is the first experimental study that depicts mixed activation-diffusion control in an enzymatic reaction due to the effect of crowding.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Synchronization of hybrid coupled reaction-diffusion neural networks with time delays via generalized intermittent control with spacial sampled-data.

PubMed

Lu, Binglong; Jiang, Haijun; Hu, Cheng; Abdurahman, Abdujelil

2018-05-04

The exponential synchronization of hybrid coupled reaction-diffusion neural networks with time delays is discussed in this article. At first, a generalized intermittent control with spacial sampled-data is introduced, which is intermittent in time and data sampling in space. This type of control strategy not only can unify the traditional periodic intermittent control and the aperiodic case, but also can lower the update rate of the controller in both temporal and spatial domains. Next, based on the designed control protocol and the Lyapunov-Krasovskii functional approach, some novel and readily verified criteria are established to guarantee the exponential synchronization of the considered networks. These criteria depend on the diffusion coefficients, coupled strengths, time delays as well as control parameters. Finally, the effectiveness of the proposed control strategy is shown by a numerical example. Copyright © 2018 Elsevier Ltd. All rights reserved.

The rate constant of a quantum-diffusion-controlled bimolecular reaction

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

A quantum-mechanical equation is derived in the tight-bond approximation which describes the motion and chemical interaction of a pair of species A and B when their displacement in the matrix is caused by tunnelling. Within the framework of the discrete model of random walks, definitions are given of the probability and rate constant of a reaction A + B → P (products) proceeding in a condensed medium. A method is suggested for calculating the rate constant of a quantum-diffusion-controlled bimolecular reaction. By this method, an expression is obtained for the rate constant in the stationary spherically symmetrical case. An equation for the density matrix is also proposed which describes the motion and chemical interaction of a pair of species when the quantum and classical diffusion are competitive.

A model for the compositions of non-stoichiometric intermediate phases formed by diffusion reactions, and its application to Nb 3Sn superconductors

DOE PAGES

Xu, X.; Sumption, M. D.

2016-01-12

In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb 3Sn superconductors. In the first part, the governing equations for the bulk diffusion and interphase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether itmore » is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Lastly, we apply this model to the Nb 3Sn superconductors and propose approaches to control their compositions.« less

Reaction layer formation at the graphite/copper-chromium alloy interface

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1992-01-01

Sessile drop tests were used to obtain information about copper chromium alloys that suitably wet graphite. Characterization of graphite/copper-chromium alloy interfaces subjected to elevated temperatures were conducted using scanning electron micrography, energy dispersive spectroscopy, auger electron spectroscopy, and x ray diffraction analyses. These analyses indicate that during sessile drop tests conducted at 1130 C for one hour, copper alloys containing greater than 0.98 percent chromium form continuous reaction layers of approximately 10 micron thickness. The reaction layers adhere to the graphite surface. The copper wets the reaction layer to form a contact angle of 60 degrees or less. X ray diffraction results indicate that the reaction layer is chromium carbide. The kinetics of reaction layer formation were modelled in terms of bulk diffusion mechanisms. Reaction layer thickness is controlled initially by the diffusion of Cr out of Cu alloy and later by the diffusion of C through chromium carbide.

Reaction layer formation at the graphite/copper-chromium alloy interface

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1993-01-01

Sessile drop tests were used to obtain information about copper chromium alloys that suitably wet graphite. Characterization of graphite/copper-chromium alloy interfaces subjected to elevated temperatures were conducted using scanning electron micrography, energy dispersive spectroscopy, Auger electron spectroscopy, and X-ray diffraction analyses. These analyses indicate that during sessile drop tests conducted at 1130 C for one hour, copper alloys containing greater than 0.98 percent chromium form continuous reaction layers of approximately 10 micron thickness. The reaction layers adhere to the graphite surface. The copper wets the reaction layer to form a contact angle of 60 degrees or less. X-ray diffraction results indicate that the reaction layer is chromium carbide. The kinetics of reaction layer formation were modelled in terms of bulk diffusion mechanisms. Reaction layer thickness is controlled initially by the diffusion of Cr out of Cu alloy and later by the diffusion of C through chromium carbide.

Modeling transport kinetics in clinoptilolite-phosphate rock systems

NASA Technical Reports Server (NTRS)

Allen, E. R.; Ming, D. W.; Hossner, L. R.; Henninger, D. L.

1995-01-01

Nutrient release in clinoptilolite-phosphate rock (Cp-PR) systems occurs through dissolution and cation-exchange reactions. Investigating the kinetics of these reactions expands our understanding of nutrient release processes. Research was conducted to model transport kinetics of nutrient release in Cp-PR systems. The objectives were to identify empirical models that best describe NH4, K, and P release and define diffusion-controlling processes. Materials included a Texas clinoptilolite (Cp) and North Carolina phosphate rock (PR). A continuous-flow thin-disk technique was used. Models evaluated included zero order, first order, second order, parabolic diffusion, simplified Elovich, Elovich, and power function. The power-function, Elovich, and parabolic-diffusion models adequately described NH4, K, and P release. The power-function model was preferred because of its simplicity. Models indicated nutrient release was diffusion controlled. Primary transport processes controlling nutrient release for the time span observed were probably the result of a combination of several interacting transport mechanisms.

A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

To analyse the frequently encountered thermo-chemo-mechanical problems in chemically active material applications, we develop a thermodynamically-consistent continuum theory of coupled deformation, mass diffusion, heat conduction and chemical reaction. Basic balance equations of force, mass and energy are presented at first, and then fully coupled constitutive laws interpreting multi-field interactions and evolving equations governing irreversible fluxes are constructed according to the energy dissipation inequality and the chemical kinetics. To consider the essential distinction between mass diffusion and chemical reactions in affecting free energy and dissipations of a highly coupled system, we regard both the concentrations of diffusive species and the extent of reaction as independent state variables. This new formulation then distinguishes between the energy contribution from the diffusive species entering the solid and that from the subsequent chemical reactions occurring among these species and the host solid, which not only interact with stresses or strains in different manners and on different time scales, but also induce different variations of solid microstructures and material properties. Taking advantage of this new description, we further establish a specialized isothermal model to predict precisely the transient chemo-mechanical response of a swelling solid with a proposed volumetric constraint that accounts for material incompressibility. Coupled kinetics is incorporated to capture the volumetric swelling of the solid caused by imbibition of external species and the simultaneous dilation arised from chemical reactions between the diffusing species and the solid. The model is then exemplified with two numerical examples of transient swelling accompanied by chemical reaction. Various ratios of characteristic times of diffusion and chemical reaction are taken into account to shed light on the dependency on kinetic time scales of evolution patterns for a diffusion-reaction controlled deformable solid.

Pattern formation in mass conserving reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Brauns, Fridtjof; Halatek, Jacob; Frey, Erwin

We present a rigorous theoretical framework able to generalize and unify pattern formation for quantitative mass conserving reaction-diffusion models. Mass redistribution controls chemical equilibria locally. Separation of diffusive mass redistribution on the level of conserved species provides a general mathematical procedure to decompose complex reaction-diffusion systems into effectively independent functional units, and to reveal the general underlying bifurcation scenarios. We apply this framework to Min protein pattern formation and identify the mechanistic roles of both involved protein species. MinD generates polarity through phase separation, whereas MinE takes the role of a control variable regulating the existence of MinD phases. Hence, polarization and not oscillations is the generic core dynamics of Min proteins in vivo. This establishes an intrinsic mechanistic link between the Min system and a broad class of intracellular pattern forming systems based on bistability and phase separation (wave-pinning). Oscillations are facilitated by MinE redistribution and can be understood mechanistically as relaxation oscillations of the polarization direction.

Nonequilibrium Self-Assembly of π-Conjugated Oligopeptides in Solution.

PubMed

Li, Bo; Li, Songsong; Zhou, Yuecheng; Ardoña, Herdeline Ann M; Valverde, Lawrence R; Wilson, William L; Tovar, John D; Schroeder, Charles M

2017-02-01

Supramolecular assembly is a powerful method that can be used to generate materials with well-defined structures across multiple length scales. Supramolecular assemblies consisting of biopolymer-synthetic polymer subunits are specifically known to exhibit exceptional structural and functional diversity as well as programmable control of noncovalent interactions through hydrogen bonding in biopolymer subunits. Despite recent progress, there is a need to control and quantitatively understand assembly under nonequilibrium conditions. In this work, we study the nonequilibrium self-assembly of π-conjugated synthetic oligopeptides using a combination of experiments and analytical modeling. By isolating an aqueous peptide solution droplet within an immiscible organic layer, the rate of peptide assembly in the aqueous solution can be controlled by tuning the transport rate of acid that is used to trigger assembly. Using this approach, peptides are guided to assemble under reaction-dominated and diffusion-dominated conditions, with results showing a transition from a diffusion-limited reaction front to spatially homogeneous assembly as the transport rate of acid decreases. Interestingly, our results show that the morphology of self-assembled peptide fibers is controlled by the assembly kinetics such that increasingly homogeneous structures of self-assembled synthetic oligopeptides were generally obtained using slower rates of assembly. We further developed an analytical reaction-diffusion model to describe oligopeptide assembly, and experimental results are compared to the reaction-diffusion model across a range of parameters. Overall, this work highlights the importance of molecular self-assembly under nonequilibrium conditions, specifically showing that oligopeptide assembly is governed by a delicate balance between reaction kinetics and transport processes.

Determination of kinetic data for soot oxidation: Modeling of competition between oxygen diffusion and reaction during thermogravimetric analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilot, P.; Bonnefoy, F.; Marcuccilli, F.

1993-10-01

Kinetic data concerning carbon black oxidation in the temperature range between 600 and 900 C have been obtained using thermogravimetric analysis. Modeling of diffusion in a boundary layer above the pan and inside the porous medium coupled to oxygen reaction with carbon black is necessary to obtain kinetic constants as a function of temperature. These calculations require the knowledge of the oxidation rate at a given constant temperature as a function of the initial mass loading m[sub o]. This oxidation rate, expressed in milligrams of soot consumed per second and per milligram of initial soot loading, decreases when m[sub o]more » increases, in agreement with a reaction in an intermediary regime where the kinetics and the oxygen diffusion operate. The equivalent diffusivity of oxygen inside the porous medium is evaluated assuming two degrees of porosity: between soot aggregates and inside each aggregate. Below 700 C an activation energy of about 103 kJ/mol can be related to a combustion reaction probably kinetically controlled. Beyond 700 C the activation energy of about 20 kJ/ mol corresponds to a reaction essentially controlled by oxygen diffusion leading to a constant density oxidation with oxygen consumption at or near the particle surface. To validate these data, they are used in the modeling of a Diesel particulate trap regeneration. In this particular case, the oxidizing flux is forced across the carbon black deposit, oxygen diffusion being insignificant. A good agreement between experimental results and model predictions is obtained, proving the rate constants validity.« less

Escape and finite-size scaling in diffusion-controlled annihilation

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul L.

2016-12-16

In this paper, we study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial dimensions d>2 where a finite number of particles typically survive the annihilation process. Using scaling techniques we investigate the average number of surviving particles, M, as a function of the initial number of particles, N. In three dimensions, for instance, we find the scaling law M ~ N 1/3 in the asymptotic regime N»1. We show that two time scales govern the reaction kinetics: the diffusionmore » time scale, T ~ N 2/3, and the escape time scale, τ ~ N 4/3. The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale.« less

Reaction mechanism of chalcone isomerase. pH dependence, diffusion control, and product binding differences.

PubMed

Jez, Joseph M; Noel, Joseph P

2002-01-11

Chalcone isomerase (CHI) catalyzes the intramolecular cyclization of bicyclic chalcones into tricyclic (S)-flavanones. The activity of CHI is essential for the biosynthesis of flavanone precursors of floral pigments and phenylpropanoid plant defense compounds. We have examined the spontaneous and CHI-catalyzed cyclization reactions of 4,2',4',6'-tetrahydroxychalcone, 4,2',4'-trihydroxychalcone, 2',4'-dihydroxychalcone, and 4,2'-dihydroxychalcone into the corresponding flavanones. The pH dependence of flavanone formation indicates that both the non-enzymatic and enzymatic reactions first require the bulk phase ionization of the substrate 2'-hydroxyl group and subsequently on the reactivity of the newly formed 2'-oxyanion during C-ring formation. Solvent viscosity experiments demonstrate that at pH 7.5 the CHI-catalyzed cyclization reactions of 4,2',4',6'-tetrahydroxychalcone, 4,2',4'-trihydroxychalcone, and 2',4'-dihydroxychalcone are approximately 90% diffusion-controlled, whereas cyclization of 4,2'-dihydroxychalcone is limited by a chemical step that likely reflects the higher pK(a) of the 2'-hydroxyl group. At pH 6.0, the reactions with 4,2',4',6'-tetrahydroxychalcone and 4,2',4'-trihydroxychalcone are approximately 50% diffusion-limited, whereas the reactions of both dihydroxychalcones are limited by chemical steps. Comparisons of the 2.1-2.3 A resolution crystal structures of CHI complexed with the products 7,4'-dihydroxyflavanone, 7-hydroxyflavanone, and 4'-hydroxyflavanone show that the 7-hydroxyflavanones all share a common binding mode, whereas 4'-hydroxyflavanone binds in an altered orientation at the active site. Our functional and structural studies support the proposal that CHI accelerates the stereochemically defined intramolecular cyclization of chalcones into biologically active (2S)-flavanones by selectively binding an ionized chalcone in a conformation conducive to ring closure in a diffusion-controlled reaction.

Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

NASA Astrophysics Data System (ADS)

Camley, Brian A.; Zhao, Yanxiang; Li, Bo; Levine, Herbert; Rappel, Wouter-Jan

2017-01-01

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies.

PubMed

Hepburn, Iain; Chen, Weiliang; Wils, Stefan; De Schutter, Erik

2012-05-10

Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. We describe STEPS, a stochastic reaction-diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction-diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. STEPS simulates models of cellular reaction-diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2015-09-01

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jing; Ackerman, David M.; Lin, Victor S.-Y.

2013-04-02

Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reactionmore » and restricted transport.« less

Dichotomous-noise-induced pattern formation in a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Ray, Deb Shankar

2013-06-01

We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

Role of Water Activity on Intergranular Transport at High Pressure

NASA Astrophysics Data System (ADS)

Gasc, J.; Brunet, F.; Brantut, N.; Corvisier, J.; Findling, N.; Verlaguet, A.; Lathe, C.

2016-12-01

The kinetics of the reaction Ca(OH)2 + MgCO3 = CaCO3 + Mg(OH)2 were investigated at a pressure of 1.8 GPa and temperatures of 120-550°C, using synchrotron X-ray diffraction and analysis of reaction rims on recovered samples. Comparable reaction kinetics were obtained under water saturated ( 10 wt.%), intermediate (0.1-1 wt.%) and dry conditions at 150, 400 and 550°C, respectively, where, in the latter case, water activity was buffered below one (no free water). At a given temperature, these gaps imply differences of several orders of magnitude in terms of reaction kinetics. Microscopy analysis shows that intergranular transport of Ca controls the reaction progress. Grain boundary diffusivities were retrieved from measurements of reaction rim widths on recovered samples. In addition, an innovative reaction rim growth model was developed to simulate and fit kinetic data. The diffusion values thus obtained show that both dry and intermediate datasets are in fact consistent with a water saturated intergranular medium with different levels of connectivity. Diffusivity of Ca in the CaCO3 + Mg(OH)2 rims is found to be much larger than that of Mg in enstatite rims, which emphasizes the prominent role of interactions between diffusing species and mineral surfaces on diffusion. We suggest that diffusivity of major species (Mg, Ca) in low-porosity metamorphic rocks is not only water-content dependent but also strongly depends on the interaction between diffusing species and mineral surfaces. This parameter, which will vary from one rock-type to the other, needs to be considered when extrapolating (P,T,t, xH2O) laboratory diffusion data to metamorphic processes. The present study, along with previous data from the literature, will help quantify the tremendous effect of small water content variations, i.e., within the 0-1 wt. % range, on intergranular transport and reaction kinetics (Gasc et al., J. Pet., In press).

Contribution to an effective design method for stationary reaction-diffusion patterns.

PubMed

Szalai, István; Horváth, Judit; De Kepper, Patrick

2015-06-01

The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.

Pattern dynamics of the reaction-diffusion immune system.

PubMed

Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

2018-01-01

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

PubMed

Everaers, Ralf; Rosa, Angelo

2012-01-07

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

Diffusive confinement of free radical intermediates in the OH radical oxidation of semisolid aerosols

DOE PAGES

Wiegel, Aaron A.; Liu, Matthew J.; Hinsberg, William D.; ...

2017-02-07

Multiphase chemical reactions (gas + solid/liquid) involve a complex interplay between bulk and interface chemistry, diffusion, evaporation, and condensation. Reactions of atmospheric aerosols are an important example of this type of chemistry: the rich array of particle phase states and multiphase transformation pathways produce diverse but poorly understood interactions between chemistry and transport. Their chemistry is of intrinsic interest because of their role in controlling climate. Their characteristics also make them useful models for the study of principles of reactivity of condensed materials under confined conditions. Previously, we have reported a computational study of the oxidation chemistry of a liquidmore » aliphatic aerosol. In this study, we extend the calculations to investigate nearly the same reactions at a semisolid gas-aerosol interface. A reaction-diffusion model for heterogeneous oxidation of triacontane by hydroxyl radicals (OH) is described, and its predictions are compared to measurements of aerosol size and composition, which evolve continuously during oxidation. Our results are also explicitly compared to those obtained for the corresponding liquid system, squalane, to pinpoint salient elements controlling reactivity. The diffusive confinement of the free radical intermediates at the interface results in enhanced importance of a few specific chemical processes such as the involvement of aldehydes in fragmentation and evaporation, and a significant role of radical-radical reactions in product formation. The simulations show that under typical laboratory conditions semisolid aerosols have highly oxidized nanometer-scale interfaces that encapsulate an unreacted core and may confer distinct optical properties and enhanced hygroscopicity. This highly oxidized layer dynamically evolves with reaction, which we propose to result in plasticization. The validated model is used to predict chemistry under atmospheric conditions, where the OH radical concentration is much lower. The oxidation reactions are more strongly influenced by diffusion in the particle, resulting in a more liquid-like character.« less

Pair and triple correlations in the A+B-->B diffusion-controlled reaction

NASA Astrophysics Data System (ADS)

Kuzovkov, Vladimir; Kotomin, Eugene

1994-03-01

An exact solution for the one-dimensional kinetics of the diffusion-controlled reaction A+B-->B is obtained by means of the three-particle correlation functions. Because of a lattice discreteness each site could be occupied by a single particle only which leads to the so-called ``bus effect'': Recombination of any particle A is defined by a spatial configuration of two nearest particles B only surrounding A from its left and right. This results in the unusual algebraic decay law, n(t)~t-1, which asymptotically (as t-->∞) does not depend on the trap B concentration.

Evolutionary dynamics of enzymes.

PubMed

Demetrius, L

1995-08-01

This paper codifies and rationalizes the large diversity in reaction rates and substrate specificity of enzymes in terms of a model which postulates that the kinetic properties of present-day enzymes are the consequence of the evolutionary force of mutation and selection acting on a class of primordial enzymes with poor catalytic activity and broad substrate specificity. Enzymes are classified in terms of their thermodynamic parameters, activation enthalpy delta H* and activation entropy delta S*, in their kinetically significant transition states as follows: type 1, delta H* > 0, delta S* < 0; type 2, delta H* < or = 0, delta S* < or = 0; type 3, delta H* > 0, delta S* > 0. We study the evolutionary dynamics of these three classes of enzymes subject to mutation, which acts at the level of the gene which codes for the enzyme and selection, which acts on the organism that contains the enzyme. Our model predicts the following evolutionary trends in the reaction rate and binding specificity for the three classes of molecules. In type 1 enzymes, evolution results in random, non-directional changes in the reaction rate and binding specificity. In type 2 and 3 enzymes, evolution results in a unidirectional increase in both the reaction rate and binding specificity. We exploit these results in order to codify the diversity in functional properties of present-day enzymes. Type 1 molecules will be described by intermediate reaction rates and broad substrate specificity. Type 2 enzymes will be characterized by diffusion-controlled rates and absolute substrate specificity. The type 3 catalysts can be further subdivided in terms of their activation enthalpy into two classes: type 3a (delta H* small) and type 3b (delta H* large). We show that type 3a will be represented by the same functional properties that identify type 2, namely, diffusion-controlled rates and absolute substrate specificity, whereas type 3b will be characterized by non-diffusion-controlled rates and absolute substrate specificity. We infer from this depiction of the three classes of enzymes, a general relation between the two functional properties, reaction rate and substrate specificity, namely, enzymes with diffusion-controlled rates have absolute substrate specificity. By appealing to energetic considerations, we furthermore show that enzymes with diffusion-controlled rates (types 2 and 3a) form a small subset of the class of all enzymes. This codification of present-day enzymes derived from an evolutionary model, essentially relates the structural properties of enzymes, as described by their thermodynamic parameters, to their functional properties, as represented by the reaction rate and substrate specificity.

Link between alginate reaction front propagation and general reaction diffusion theory.

PubMed

Braschler, Thomas; Valero, Ana; Colella, Ludovica; Pataky, Kristopher; Brugger, Jürgen; Renaud, Philippe

2011-03-15

We provide a common theoretical framework reuniting specific models for the Ca(2+)-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differential equations that are traditionally solved numerically: the Mikkelsen-Elgsaeter model. Applying the traveling-wave hypothesis as a major simplification, we obtain an analytical solution. The solution indicates that the fundamental properties of the alginate reaction front are governed by a single dimensionless parameter λ. For small λ values, a large depletion zone accompanies the reaction front. For large λ values, the alginate reacts before having the time to diffuse significantly. We show that the λ parameter is of general importance beyond the alginate model system, as it can be used to classify known solutions for second-order reaction diffusion schemes, along with the novel solution presented here. For experimental validation, we develop a microchip model system, in which the alginate gel formation can be carried out in a highly controlled, essentially 1D environment. The use of a filter barrier enables us to rapidly renew the CaCl(2) solution, while maintaining flow speeds lower than 1 μm/s for the alginate compartment. This allows one to impose an exactly known bulk CaCl(2) concentration and diffusion resistance. This experimental model system, taken together with the theoretical development, enables the determination of the entire set of physicochemical parameters governing the alginate reaction front in a single experiment.

The influence of radiation-induced vacancy on the formation of thin-film of compound layer during a reactive diffusion process

NASA Astrophysics Data System (ADS)

Akintunde, S. O.; Selyshchev, P. A.

2016-05-01

A theoretical approach is developed that describes the formation of a thin-film of AB-compound layer under the influence of radiation-induced vacancy. The AB-compound layer is formed as a result of a chemical reaction between the atomic species of A and B immiscible layers. The two layers are irradiated with a beam of energetic particles and this process leads to several vacant lattice sites creation in both layers due to the displacement of lattice atoms by irradiating particles. A- and B-atoms diffuse via these lattice sites by means of a vacancy mechanism in considerable amount to reaction interfaces A/AB and AB/B. The reaction interfaces increase in thickness as a result of chemical transformation between the diffusing species and surface atoms (near both layers). The compound layer formation occurs in two stages. The first stage begins as an interfacial reaction controlled process, and the second as a diffusion controlled process. The critical thickness and time are determined at a transition point between the two stages. The influence of radiation-induced vacancy on layer thickness, speed of growth, and reaction rate is investigated under irradiation within the framework of the model presented here. The result obtained shows that the layer thickness, speed of growth, and reaction rate increase strongly as the defect generation rate rises in the irradiated layers. It also shows the feasibility of producing a compound layer (especially in near-noble metal silicide considered in this study) at a temperature below their normal formation temperature under the influence of radiation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiegel, Aaron A.; Liu, Matthew J.; Hinsberg, William D.

Multiphase chemical reactions (gas + solid/liquid) involve a complex interplay between bulk and interface chemistry, diffusion, evaporation, and condensation. Reactions of atmospheric aerosols are an important example of this type of chemistry: the rich array of particle phase states and multiphase transformation pathways produce diverse but poorly understood interactions between chemistry and transport. Their chemistry is of intrinsic interest because of their role in controlling climate. Their characteristics also make them useful models for the study of principles of reactivity of condensed materials under confined conditions. Previously, we have reported a computational study of the oxidation chemistry of a liquidmore » aliphatic aerosol. In this study, we extend the calculations to investigate nearly the same reactions at a semisolid gas-aerosol interface. A reaction-diffusion model for heterogeneous oxidation of triacontane by hydroxyl radicals (OH) is described, and its predictions are compared to measurements of aerosol size and composition, which evolve continuously during oxidation. Our results are also explicitly compared to those obtained for the corresponding liquid system, squalane, to pinpoint salient elements controlling reactivity. The diffusive confinement of the free radical intermediates at the interface results in enhanced importance of a few specific chemical processes such as the involvement of aldehydes in fragmentation and evaporation, and a significant role of radical-radical reactions in product formation. The simulations show that under typical laboratory conditions semisolid aerosols have highly oxidized nanometer-scale interfaces that encapsulate an unreacted core and may confer distinct optical properties and enhanced hygroscopicity. This highly oxidized layer dynamically evolves with reaction, which we propose to result in plasticization. The validated model is used to predict chemistry under atmospheric conditions, where the OH radical concentration is much lower. The oxidation reactions are more strongly influenced by diffusion in the particle, resulting in a more liquid-like character.« less

A generalized expression for lag-time in the gas-phase permeation of hollow tubes

NASA Technical Reports Server (NTRS)

Shah, K. K.; Nelson, H. G.; Johnson, D. L.; Hamaker, F. M.

1975-01-01

A generalized expression for the nonsteady-state parameter, lag-time, has been obtained from Fick's second law for gas-phase transport through hollow, cylindrical membranes. This generalized expression is simplified for three limiting cases of practical interest: (1) diffusion controlled transport, (2) phase boundary reaction control at the inlet surface, and (3) phase boundary reaction control at the outlet surface. In all three cases the lag-time expressions were found to be inversely proportional only to the diffusion coefficient and functionally dependent on the membrane radii. Finally, the lag-time expressions were applied to experimentally obtained lag-time data for alpha-phase titanium and alpha-phase iron.

Synthesis and materialization of a reaction-diffusion French flag pattern

NASA Astrophysics Data System (ADS)

Zadorin, Anton S.; Rondelez, Yannick; Gines, Guillaume; Dilhas, Vadim; Urtel, Georg; Zambrano, Adrian; Galas, Jean-Christophe; Estevez-Torres, André

2017-10-01

During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.

THE INTERPLAY BETWEEN GEOCHEMICAL REACTIONS AND ADVECTION-DISPERSION IN CONTAMINANT TRANSPORT AT A URANIUM MILL TAILINGS SITE

EPA Science Inventory

It is well known that the fate and transport of contaminants in the subsurface are controlled by complex processes including advection, dispersion-diffusion, and chemical reactions. However, the interplay between the physical transport processes and chemical reactions, and their...

Comparative analysis of nitrite uptake and hemoglobin-nitrite reactions in erythrocytes: sorting out uptake mechanisms and oxygenation dependencies.

PubMed

Jensen, Frank B; Rohde, Sabina

2010-04-01

Nitrite uptake into red blood cells (RBCs) precedes its intracellular reactions with hemoglobin (Hb) that forms nitric oxide (NO) during hypoxia. We investigated the uptake of nitrite and its reactions with Hb at different oxygen saturations (So(2)), using RBCs with (carp and rabbit) and without (hagfish and lamprey) anion exchanger-1 (AE1) in the membrane, with the aim to unravel the mechanisms and oxygenation dependencies of nitrite transport. Added nitrite rapidly diffused into the RBCs until equilibrium. The distribution ratio of nitrite across the membrane agreed with that expected from HNO(2) diffusion and AE1-mediated facilitated NO(2)(-) diffusion. Participation of HNO(2) diffusion was emphasized by rapid transmembrane nitrite equilibration also in the natural AE1 knockouts. Following the equilibration, nitrite was consumed by reacting with Hb, which created a continued inward diffusion controlled by intracellular reaction rates. Changes in nitrite uptake with So(2), pH, or species were accordingly explained by corresponding changes in reaction rates. In carp, nitrite uptake rates increased linearly with decreasing So(2) over the entire So(2) range. In rabbit, nitrite uptake rates were highest at intermediate So(2), producing a bell-shaped relationship with So(2). Nitrite consumption increased approximately 10-fold with a 1 unit decrease in pH, as expected from the involvement of protons in the reactions with Hb. The reaction of nitrite with deoxyhemoglobin was favored over that with oxyhemoglobin at intermediate So(2). We propose a model for RBC nitrite uptake that involves both HNO(2) diffusion and AE1-mediated transport and that explains both the present and previous (sometimes puzzling) results.

Modeling Bimolecular Reactive Transport With Mixing-Limitation: Theory and Application to Column Experiments

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

The challenge of determining mixing extent of solutions undergoing advective-dispersive-diffusive transport is well known. In particular, reaction extent between displacing and displaced solutes depends on mixing at the pore scale, that is, generally smaller than continuum scale quantification that relies on dispersive fluxes. Here a novel mobile-mobile mass transfer approach is developed to distinguish diffusive mixing from dispersive spreading in one-dimensional transport involving small-scale velocity variations with some correlation, such as occurs in hydrodynamic dispersion, in which short-range ballistic transports give rise to dispersed but not mixed segregation zones, termed here ballisticules. When considering transport of a single solution, this approach distinguishes self-diffusive mixing from spreading, and in the case of displacement of one solution by another, each containing a participant reactant of an irreversible bimolecular reaction, this results in time-delayed diffusive mixing of reactants. The approach generates models for both kinetically controlled and equilibrium irreversible reaction cases, while honoring independently measured reaction rates and dispersivities. The mathematical solution for the equilibrium case is a simple analytical expression. The approach is applied to published experimental data on bimolecular reactions for homogeneous porous media under postasymptotic dispersive conditions with good results.

Rhenium/Oxygen Interactions at Elevated Temperatures

NASA Technical Reports Server (NTRS)

Jacobson, Nathan; Myers, Dwight; Zhu, Dong-Ming; Humphrey, Donald

2000-01-01

The oxidation of pure rhenium is examined from 600-1400 C in oxygen/argon mixtures. Linear weight loss kinetics are observed. Gas pressures, flow rates, and temperatures are methodically varied to determine the rate controlling steps. The reaction at 600 and 800 C appears to be controlled by a chemical reaction step at the surface; whereas the higher temperature reactions appear to be controlled by gas phase diffusion of oxygen to the rhenium surface. Attack of the rhenium appears to be along grain boundaries and crystallographic planes.

Pore and Continuum Scale Study of the Effect of Subgrid Transport Heterogeneity on Redox Reaction Rates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yuanyuan; Liu, Chongxuan; Zhang, Changyong

2015-08-01

A micromodel system with a pore structure for heterogeneous flow and transport was used to investigate the effect of subgrid transport heterogeneity on redox reaction rates. Hematite reductive dissolution by injecting a reduced form of flavin mononucleotide (FMNH2) at variable flow rates was used as an example to probe the variations of redox reaction rates in different subgrid transport domains. Experiments, pore-scale simulations, and macroscopic modeling were performed to measure and simulate in-situ hematite reduction and to evaluate the scaling behavior of the redox reaction rates from the pore to macroscopic scales. The results indicated that the measured pore-scale ratesmore » of hematite reduction were consistent with the predictions from a pore scale reactive transport model. A general trend is that hematite reduction followed reductant transport pathways, starting from the advection-dominated pores toward the interior of diffusion-dominated domains. Two types of diffusion domains were considered in the micromodel: a micropore diffusion domain, which locates inside solid grains or aggregates where reactant transport is limited by diffusion; and a macropore diffusion domain, which locates at wedged, dead-end pore spaces created by the grain-grain contacts. The rate of hematite reduction in the advection-dominated domain was faster than those in the diffusion-controlled domains, and the rate in the macropore diffusion domain was faster than that in the micropore domain. The reduction rates in the advection and macropore diffusion domains increased with increasing flow rate, but were affected by different mechanisms. The rate increase in the advection domain was controlled by the mass action effect as a faster flow supplied more reactants, and the rate increase in the macropore domain was more affected by the rate of mass exchange with the advection domain, which increased with increasing flow rate. The hematite reduction rate in the micropore domain was, however, not affected by the flow rate because molecular diffusion limits reductant supply to the micropore domain interior. Domain-based macroscopic models were evaluated to scale redox reaction rates from the pore to macroscopic scales. A single domain model, which ignores subgrid transport heterogeneity deviated significantly from the pore-scale results. Further analysis revealed that the rate expression for hematite reduction was not scalable from the pore to porous media using the single domain model. A three-domain model, which effectively considers subgrid reactive diffusion in the micropore and macropore domains, significantly improved model description. Overall this study revealed the importance of subgrid transport heterogeneity in the manifestation of redox reaction rates in porous media and in scaling reactions from the pore to porous media. The research also supported that the domain-based scaling approach can be used to directly scale redox reactions in porous media with subgrid transport heterogeneity.« less

Aluminum/water reactions under extreme conditions

NASA Astrophysics Data System (ADS)

Hooper, Joseph

2013-03-01

We discuss mechanisms that may control the reaction of aluminum and water under extreme conditions. We are particularly interested in the high-temperature, high-strain regime where the native oxide layer is destroyed and fresh aluminum is initially in direct contact with liquid or supercritical water. Disparate experimental data over the years have suggested rapid oxidation of aluminum is possible in such situations, but no coherent picture has emerged as to the basic oxidation mechanism or the physical processes that govern the extent of reaction. We present theoretical and computational analysis of traditional metal/water reaction mechanisms that treat diffusion through a dynamic oxide layer or reaction limited by surface kinetics. Diffusion through a fresh solid oxide layer is shown to be far too slow to have any effect on the millisecond timescale (even at high temperatures). Quantum molecular dynamics simulations of liquid Al and water surface reactions show rapid water decomposition at the interface, catalyzed by adjacent water molecules in a Grotthus-like relay mechanism. The surface reaction barriers are far too low for this to be rate-limiting in any way. With these straightforward mechanisms ruled out, we investigate two more complex possibilities for the rate-limiting factor; first, we explore the possibility that newly formed oxide remains a metastable liquid well below its freezing point, allowing for diffusion-limited reactions through the oxide shell but on a much faster timescale. The extent of reaction would then be controlled by the solidification kinetics of alumina. Second, we discuss preliminary analysis on surface erosion and turbulent mixing, which may play a prominent role during hypervelocity penetration of solid aluminum projectiles into water.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: Non-nearest-neighbor effects

NASA Astrophysics Data System (ADS)

Bentz, Jonathan L.; Kozak, John J.; Nicolis, Gregoire

2005-08-01

The influence of non-nearest-neighbor displacements on the efficiency of diffusion-reaction processes involving one and two mobile diffusing reactants is studied. An exact analytic result is given for dimension d=1 from which, for large lattices, one can recover the asymptotic estimate reported 30 years ago by Lakatos-Lindenberg and Shuler. For dimensions d=2,3 we present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via the theory of finite Markov processes and supported by Monte Carlo simulations. Qualitatively different results are found between processes occurring on d=1 versus d>1 lattices, and between results obtained assuming nearest-neighbor (only) versus non-nearest-neighbor displacements.

In General, the Total Voltammetric Current from a Mixture of Redox-Active Substances will Not be the Sum of the Currents that Each Substance would Produce Independently at the Same Concentration as in the Mixture

NASA Technical Reports Server (NTRS)

Leventis, Nicholas; Oh, Woon Su; Gao, Xue-Rong; Rawashdeh, Abdel Monem M.

2003-01-01

At the potential range where both decamethylferrocene (dMeFc) and ferrocene (Fc) are oxidized with rates controlled by linear diffusion, electrogenerated Fc(+) radicals diffusing outwards from the electrode react quantitatively (K23 C=5.8 x 10(exp 8) with dMeFc diffusing towards the electrode and produce Fc and dMeFc. That reaction replaces dMeFc with Fc, whose diffusion coefficient is higher than that of dMeFc(+), and the total mass-transfer limited current from the mixture is increased by approximately 10%. Analogous observations are made when mass-transfer is controlled by convective-diffusion as in RDE voltammetry. Similar results have been obtained with another, and for all practical purposes randomly selected pair of redox-active substances, [Co(bipy)3](2+) and N - methylphenothiazine (MePTZ); reaction of MePTZ(+) with [Co(bipy)3](2+) replaces the latter with MePTZ, which diffuses faster and the current increases by approximately 20%. The experimental voltammograms have been simulated numerically and the role of (a) the rate constant of the homogeneous reaction; (b) the relative concentrations; and, (c) the diffusion coefficients of all species involved have been studied in detail. Importantly, it was also identified that within any given redox system the dependence of the mass-transfer limited current on the bulk concentrations of the redox-active species is expected to be non-linear. These findings are discussed in terms of their electroanalytical implications.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Steric effects on diffusion into bituminous coals

DOE Office of Scientific and Technical Information (OSTI.GOV)

John W. Larsen; Doyoung Lee

2006-02-01

The reactions of maleic anhydride, cis-maleate esters, and acetylenedicarboxylate esters with Pittsburgh No. 8 or Illinois No. 6 coal using o-xylene or o-dichlorobenzene solvent are diffusion controlled. Diffusion is Fickian in all cases. The measured activation energies are between 5.4 and 7.6 kcal/mol. Diffusion rates decrease slowly with increasing alkyl chain length and sharply with branching. Diffusion rates are slightly faster with o-xylene than when o-dichlorobenzene is used. 40 refs., 5 figs., 4 tabs.

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting.

PubMed

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2014-06-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

Solvent viscosity and friction in protein folding dynamics.

PubMed

Hagen, Stephen J

2010-08-01

The famous Kramers rate theory for diffusion-controlled reactions has been extended in numerous ways and successfully applied to many types of reactions. Its application to protein folding reactions has been of particular interest in recent years, as many researchers have performed experiments and simulations to test whether folding reactions are diffusion-controlled, whether the solvent is the source of the reaction friction, and whether the friction-dependence of folding rates generally can provide insight into folding dynamics. These experiments involve many practical difficulties, however. They have also produced some unexpected results. Here we briefly review the Kramers theory for reactions in the presence of strong friction and summarize some of the subtle problems that arise in the application of the theory to protein folding. We discuss how the results of these experiments ultimately point to a significant role for internal friction in protein folding dynamics. Studies of friction in protein folding, far from revealing any weakness in Kramers theory, may actually lead to new approaches for probing diffusional dynamics and energy landscapes in protein folding.

A COMPUTATIONAL ANALYSIS OF BONE FORMATION IN THE CRANIAL VAULT USING A COUPLED REACTION-DIFFUSION-STRAIN MODEL

PubMed Central

LEE, CHANYOUNG; RICHTSMEIER, JOAN T.; KRAFT, REUBEN H.

2017-01-01

Bones of the murine cranial vault are formed by differentiation of mesenchymal cells into osteoblasts, a process that is primarily understood to be controlled by a cascade of reactions between extracellular molecules and cells. We assume that the process can be modeled using Turing’s reaction-diffusion equations, a mathematical model describing the pattern formation controlled by two interacting molecules (activator and inhibitor). In addition to the processes modeled by reaction-diffusion equations, we hypothesize that mechanical stimuli of the cells due to growth of the underlying brain contribute significantly to the process of cell differentiation in cranial vault development. Structural analysis of the surface of the brain was conducted to explore the effects of the mechanical strain on bone formation. We propose a mechanobiological model for the formation of cranial vault bones by coupling the reaction-diffusion model with structural mechanics. The mathematical formulation was solved using the finite volume method. The computational domain and model parameters are determined using a large collection of experimental data that provide precise three dimensional (3D) measures of murine cranial geometry and cranial vault bone formation for specific embryonic time points. The results of this study suggest that mechanical strain contributes information to specific aspects of bone formation. Our mechanobiological model predicts some key features of cranial vault bone formation that were verified by experimental observations including the relative location of ossification centers of individual vault bones, the pattern of cranial vault bone growth over time, and the position of cranial vault sutures. PMID:29225392

Kinetics of dissolution of sapphire in melts in the CaO-Al2O3-SiO2 system

NASA Astrophysics Data System (ADS)

Shaw, Cliff S. J.; Klausen, Kim B.; Mao, Huahai

2018-05-01

The dissolution rate of sapphire in melts in the CAS system of varying silica activity, viscosity and degree of alumina saturation has been determined at 1600 °C and 1.5 GPa. After an initiation period of up to 1800 s, dissolution is controlled by diffusion of cations through the boundary layer adjacent to the dissolving sapphire. The dissolution rate decreases with increasing silica activity, viscosity and molar Al2O3/CaO. The calculated diffusion matrix for each solvent melt shows that CAS 1 and 9 which have molar Al2O3/CaO of 0.33 and 0.6 and dissolution rate constants of 0.65 × 10-6 and 0.59 × 10-6 m/s0.5 have similar directions and magnitudes of diffusive coupling: DCaO-Al2O3 and DAl2O3-CaO are both negative are approximately equal. The solvent with the fastest dissolution rate: CAS 4, which has a rate constant of 1.5 × 10-6 m/s0.5 and Al2O3/CaO of 0.31 has positive DCaO-Al2O3 and negative DAl2O3-CaO and the absolute values vary by a factor of 4. Although many studies show that aluminium is added to the melts via the reaction: Si4+ =Al3+ + 0.5Ca2+ the compositional profiles show that this reaction is not the only one involved in accommodating the aluminium added during sapphire dissolution. Rather, aluminium is incorporated as both tetrahedrally coordinated Al charge balanced by Ca and as aluminium not charge balanced by Ca (termed Alxs). This reaction: AlIV -Ca =Alxs +CaNBO where CaNBO is a non-bridging oxygen associated with calcium, may involve the formation of aluminium triclusters. The shape of the compositional profiles and oxide-oxide composition paths is controlled by the aluminium addition reaction. When Alxs exceeds 2%, CaO diffusion becomes increasingly anomalous and since the bond strength of Alxs correlates with CaO/CaO + Al2O3, the presence of more than 2% Alxs leads to significantly slower dissolution than when Alxs is absent or at low concentration. Thus, dissolution is controlled by diffusion of cations through the boundary layer, but this diffusion is itself controlled by the structural modifications required by the addition of new components to the melt. Comparison of quartz dissolution rates in similar melts shows that dissolution is much faster for quartz than for sapphire and that dissolution rates show the same correlation with silica activity and viscosity. We suggest that diffusive fluxes are related to changes in melt structure and the nature of the reaction that incorporates the added component. For the slow eigendirection, SiO2 addition occurs by a single reaction whereas Al2O3 addition requires a more complex two part reaction in which Al is accommodated by charge balance with Ca until Al is in excess of that which can be charge balanced. The Alxs incorporation reaction, is slower than the Si incorporation reaction which inhibits sapphire dissolution relative to quartz in melts of the same composition.

Reaction-diffusion pattern in shoot apical meristem of plants.

PubMed

Fujita, Hironori; Toyokura, Koichi; Okada, Kiyotaka; Kawaguchi, Masayoshi

2011-03-29

A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants.

Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants

PubMed Central

Fujita, Hironori; Toyokura, Koichi; Okada, Kiyotaka; Kawaguchi, Masayoshi

2011-01-01

A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants. PMID:21479227

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

Diffusion modulation of DNA by toehold exchange

NASA Astrophysics Data System (ADS)

Rodjanapanyakul, Thanapop; Takabatake, Fumi; Abe, Keita; Kawamata, Ibuki; Nomura, Shinichiro M.; Murata, Satoshi

2018-05-01

We propose a method to control the diffusion speed of DNA molecules with a target sequence in a polymer solution. The interaction between solute DNA and diffusion-suppressing DNA that has been anchored to a polymer matrix is modulated by the concentration of the third DNA molecule called the competitor by a mechanism called toehold exchange. Experimental results show that the sequence-specific modulation of the diffusion coefficient is successfully achieved. The diffusion coefficient can be modulated up to sixfold by changing the concentration of the competitor. The specificity of the modulation is also verified under the coexistence of a set of DNA with noninteracting base sequences. With this mechanism, we are able to control the diffusion coefficient of individual DNA species by the concentration of another DNA species. This methodology introduces a programmability to a DNA-based reaction-diffusion system.

A reaction-diffusion-based coding rate control mechanism for camera sensor networks.

PubMed

Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki

2010-01-01

A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.

Reaction-diffusion processes at the nano- and microscales

NASA Astrophysics Data System (ADS)

Epstein, Irving R.; Xu, Bing

2016-04-01

The bottom-up fabrication of nano- and microscale structures from primary building blocks (molecules, colloidal particles) has made remarkable progress over the past two decades, but most research has focused on structural aspects, leaving our understanding of the dynamic and spatiotemporal aspects at a relatively primitive stage. In this Review, we draw inspiration from living cells to argue that it is now time to move beyond the generation of structures and explore dynamic processes at the nanoscale. We first introduce nanoscale self-assembly, self-organization and reaction-diffusion processes as essential features of cells. Then, we highlight recent progress towards designing and controlling these fundamental features of life in abiological systems. Specifically, we discuss examples of reaction-diffusion processes that lead to such outcomes as self-assembly, self-organization, unique nanostructures, chemical waves and dynamic order to illustrate their ubiquity within a unifying context of dynamic oscillations and energy dissipation. Finally, we suggest future directions for research on reaction-diffusion processes at the nano- and microscales that we find hold particular promise for a new understanding of science at the nanoscale and the development of new kinds of nanotechnologies for chemical transport, chemical communication and integration with living systems.

Diffusion-controlled reactions: hydrodynamic interaction between charged, uniformly reactive spherical reactants.

PubMed

Allison, Stuart

2006-12-28

In this work, different models of hydrodynamic interaction (HI) are examined in the diffusion-controlled reaction between uniformly reactive charged spherical particles. In addition to Oseen "stick" and "slip" models of HI, one is considered that accounts for the disturbance of fluid flow by the ions around one reactive partner as they interact with a neighboring reactive species. This interaction is closely related to the "electrophoretic effect" in electrokinetics and can be described by a fairly simple electrophoretic, or E-tensor. These models are applied to the electron-transfer quenching reaction of Ru(bpy)3(2+) and methyl viologen (MV2+) over a wide range of NaCl concentrations (Chiorboli, C. et al., J. Phys. Chem. 1988, 92, 156). The back reaction is also considered. From a comparison of the salt dependence of the model and experimental rates, it is concluded that the "E-tensor" model works best and ignoring HI altogether works worst. The Oseen "stick" and "slip" models fall between these.

Integrating impairments in reaction time and executive function using a diffusion model framework

PubMed Central

Karalunas, Sarah L.; Huang-Pollock, Cynthia L.

2013-01-01

Using Ratcliff’s diffusion model and ex-Gaussian decomposition, we directly evaluate the role individual differences in reaction time (RT) distribution components play in the prediction of inhibitory control and working memory (WM) capacity in children with and without ADHD. Children with (n=92, x̄ age= 10.2 years, 67% male) and without ADHD (n=62, x̄ age=10.6 years, 46% male) completed four tasks of WM and a stop signal reaction time (SSRT) task. Children with ADHD had smaller WM capacities and less efficient inhibitory control. Diffusion model analyses revealed that children with ADHD had slower drift rates (v) and faster non-decision times (Ter), but there were no group differences in boundary separations (a). Similarly, using an ex-Gaussian approach, children with ADHD had larger τ values than non-ADHD controls, but did not differ in µ or σ distribution components. Drift rate mediated the association between ADHD status and performance on both inhibitory control and WM capacity. τ also mediated the ADHD-executive function impairment associations; however, models were a poorer fit to the data. Impaired performance on RT and executive functioning tasks has long been associated with childhood ADHD. Both are believed to be important cognitive mechanisms to the disorder. We demonstrate here that drift rate, or the speed at which information accumulates towards a decision, is able to explain both. PMID:23334775

Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

NASA Astrophysics Data System (ADS)

Plante, Ianik

2016-01-01

The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

Electrochemical oxidation of ciprofloxacin in two different processes: the electron transfer process on the anode surface and the indirect oxidation process in bulk solutions.

PubMed

Shen, Bo; Wen, Xianghua; Korshin, Gregory V

2018-05-14

Herein, the rotating disk electrode technique was used for the first time to investigate the effects of mass-transfer limitations and pH on the electrochemical oxidation of CPX, to determine the kinetics of CPX oxidation and to explore intrinsic mechanisms during the electron transfer process. Firstly, cyclic voltammetry revealed that an obvious irreversible CPX oxidation peak was observed within the potential window from 0.70 to 1.30 V at all pHs. Based on the Levich equation, the electrochemical oxidation of CPX in the electron transfer process was found to be controlled by both diffusion and kinetic processes when pH = 2, 5, 7 and 9; the diffusion coefficient of CPX at pH = 2 was calculated to be 1.5 × 10-7 cm2 s-1. Kinetic analysis indicated that the reaction on the electrode surface was adsorption-controlled compared to a diffusion process; the surface concentration of electroactive species was estimated to be 1.15 × 10-9 mol cm-2, the standard rate constant of the surface reaction was calculated to be 1.37 s-1, and CPX oxidation was validated to be a two-electron transfer process. Finally, a possible CPX oxidation pathway during the electron transfer process was proposed. The electrochemical degradation of CPX on a Ti-based anode was also conducted subsequently to investigate the electrochemical oxidation of CPX in the indirect oxidation process in bulk solutions. The effects of pH and current density were determined and compared to related literature results. The oxidation of CPX at different pHs is believed to be the result of a counterbalance between favorable and unfavorable factors, namely electromigration and side reactions of oxygen evolution, respectively. The effects of current density indicated a diffusion- and reaction-controlled process at low currents followed by a reaction-controlled process at high currents. The results presented in this study provide better understanding of the electrochemical oxidation of CPX and would enable the development of new treatment methods based on electrochemistry.

Light-induced spatial control of pH-jump reaction at smart gel interface.

PubMed

Techawanitchai, Prapatsorn; Ebara, Mitsuhiro; Idota, Naokazu; Aoyagi, Takao

2012-11-01

We proposed here a 'smart' control of an interface movement of proton diffusion in temperature- and pH-responsive hydrogels using a light-induced spatial pH-jump reaction. A photoinitiated proton-releasing reaction of o-nitrobenzaldehyde (NBA) was integrated into poly(N-isopropylacrylamide-o-2-carboxyisopropylacrylamide) (P(NIPAAm-co-CIPAAm)) hydrogels. NBA-integrated hydrogels demonstrated quick release of proton upon UV irradiation, allowing the pH inside the gel to decrease below the pK(a) of P(NIPAAm-co-CIPAAm) within a minute. The NBA-integrated gel was shown to shrink rapidly upon UV irradiation without polymer "skin layer" formation due to a uniform decrease of pH inside the gel. Spatial control of gel shrinking was also created by irradiating UV light to a limited region of the gel through a photomask. The interface of proton diffusion ("active interface") gradually moved toward non-illuminated area. The apparent position of "active interface", however, did not change remarkably above the LCST, while protons continuously diffused outward direction. This is because the "active interface" also moved inward direction as gel shrank above the LCST. As a result, slow movement of the apparent interface was observed. The NBA-integrated gel was also successfully employed for the controlled release of an entrapped dextran in a light controlled manner. This system is highly promising as smart platforms for triggered and programmed transportation of drugs. Copyright © 2011 Elsevier B.V. All rights reserved.

Micro/nanofabricated environments for synthetic biology.

PubMed

Collier, C Patrick; Simpson, Michael L

2011-08-01

A better understanding of how confinement, crowding and reduced dimensionality modulate reactivity and reaction dynamics will aid in the rational and systematic discovery of functionality in complex biological systems. Artificial microfabricated and nanofabricated structures have helped elucidate the effects of nanoscale spatial confinement and segregation on biological behavior, particularly when integrated with microfluidics, through precise control in both space and time of diffusible signals and binding interactions. Examples of nanostructured interfaces for synthetic biology include the development of cell-like compartments for encapsulating biochemical reactions, nanostructured environments for fundamental studies of diffusion, molecular transport and biochemical reaction kinetics, and regulation of biomolecular interactions as functions of microfabricated and nanofabricated topological constraints. Copyright © 2011 Elsevier Ltd. All rights reserved.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Kinetic phase evolution of spinel cobalt oxide during lithiation

DOE PAGES

Li, Jing; He, Kai; Meng, Qingping; ...

2016-09-15

Spinel cobalt oxide has been proposed to undergo a multiple-step reaction during the electrochemical lithiation process. Understanding the kinetics of the lithiation process in this compound is crucial to optimize its performance and cyclability. In this work, we have utilized a low-angle annular dark-field scanning transmission electron microscopy method to visualize the dynamic reaction process in real time and study the reaction kinetics at different rates. We show that the particles undergo a two-step reaction at the single-particle level, which includes an initial intercalation reaction followed by a conversion reaction. At low rates, the conversion reaction starts after the intercalationmore » reaction has fully finished, consistent with the prediction of density functional theoretical calculations. At high rates, the intercalation reaction is overwhelmed by the subsequently nucleated conversion reaction, and the reaction speeds of both the intercalation and conversion reactions are increased. Phase-field simulations show the crucial role of surface diffusion rates of lithium ions in controlling this process. Furthermore, this work provides microscopic insights into the reaction dynamics in non-equilibrium conditions and highlights the effect of lithium diffusion rates on the overall reaction homogeneity as well as the performance.« less

Kinetic phase evolution of spinel cobalt oxide during lithiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jing; He, Kai; Meng, Qingping

Spinel cobalt oxide has been proposed to undergo a multiple-step reaction during the electrochemical lithiation process. Understanding the kinetics of the lithiation process in this compound is crucial to optimize its performance and cyclability. In this work, we have utilized a low-angle annular dark-field scanning transmission electron microscopy method to visualize the dynamic reaction process in real time and study the reaction kinetics at different rates. We show that the particles undergo a two-step reaction at the single-particle level, which includes an initial intercalation reaction followed by a conversion reaction. At low rates, the conversion reaction starts after the intercalationmore » reaction has fully finished, consistent with the prediction of density functional theoretical calculations. At high rates, the intercalation reaction is overwhelmed by the subsequently nucleated conversion reaction, and the reaction speeds of both the intercalation and conversion reactions are increased. Phase-field simulations show the crucial role of surface diffusion rates of lithium ions in controlling this process. Furthermore, this work provides microscopic insights into the reaction dynamics in non-equilibrium conditions and highlights the effect of lithium diffusion rates on the overall reaction homogeneity as well as the performance.« less

Component mobility at 900 °C and 18 kbar from experimentally grown coronas in a natural gabbro

NASA Astrophysics Data System (ADS)

Keller, Lukas M.; Wunder, Bernd; Rhede, Dieter; Wirth, Richard

2008-09-01

Several approximately 100-μm-wide reaction zones were grown under experimental conditions of 900 °C and 18 kbar along former olivine-plagioclase contacts in a natural gabbro. The reaction zone comprises two distinct domains: (i) an irregularly bounded zone with idiomorphic grains of zoisite and minor corundum and kyanite immersed in a melt developed at the plagioclase side and (ii) a well-defined reaction band comprising a succession of mineral layers forming a corona structure around olivine. Between the olivine and the plagioclase reactant phases we observe the following layer sequence: olivine|pyroxene|garnet|partially molten domain|plagioclase. Within the pyroxene layer two micro-structurally distinct layers comprising enstatite and clinopyroxene can be discerned. Chemical potential gradients persisted for the CaO, Al 2O 3, SiO 2, MgO and FeO components, which drove diffusion of Ca, Al and Si bearing species from the garnet-matrix interface to the pyroxene-olivine interface and diffusion of Mg- and Fe-bearing species in the opposite direction. The systematic mineralogical organization and chemical zoning across the corona suggest that the olivine corona was formed by a "diffusion-controlled" reaction. We estimate a set of diffusion coefficients and conclude that LAlAl < LCaCa < ( LSiSi, LFeFe) < LMgMg during reaction rim growth.

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation.

PubMed

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S

2013-08-01

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

Overall adsorption rate of metronidazole, dimetridazole and diatrizoate on activated carbons prepared from coffee residues and almond shells.

PubMed

Flores-Cano, J V; Sánchez-Polo, M; Messoud, J; Velo-Gala, I; Ocampo-Pérez, R; Rivera-Utrilla, J

2016-03-15

This study analyzed the overall adsorption rate of metronidazole, dimetridazole, and diatrizoate on activated carbons prepared from coffee residues and almond shells. It was also elucidated whether the overall adsorption rate was controlled by reaction on the adsorbent surface or by intraparticle diffusion. Experimental data of the pollutant concentration decay curves as a function of contact time were interpreted by kinetics (first- and second-order) and diffusion models, considering external mass transfer, surface and/or pore volume diffusion, and adsorption on an active site. The experimental data were better interpreted by a first-order than second-order kinetic model, and the first-order adsorption rate constant varied linearly with respect to the surface area and total pore volume of the adsorbents. According to the diffusion model, the overall adsorption rate is governed by intraparticle diffusion, and surface diffusion is the main mechanism controlling the intraparticle diffusion, representing >90% of total intraparticle diffusion. Copyright © 2015 Elsevier Ltd. All rights reserved.

Effects of non-unity Lewis numbers in diffusion flames

NASA Technical Reports Server (NTRS)

Linan, A.; Orlandi, P.; Verzicco, R.; Higuera, F. J.

1994-01-01

The purpose of this work is to carry out direct numerical simulations of diffusion controlled combustion with non-unity Lewis numbers for the reactants and products, thus accounting for the differential diffusion effects of the temperature and concentration fields. We use a formulation based on combining the conservation equations in a way to eliminate the reaction terms similar to the method used by Burke and Schumann (1928) for unity Lewis numbers. We present calculations for an axisymmetric fuel jet and for a planar, time evolving mixing layer, leaving out the effects of thermal expansion and variations of the transport coefficients due to the heat release. Our results show that the front of the flame shifts toward the fuel or oxygen sides owing to the effect of the differential diffusion and that the location of maximum temperature may not coincide with the flame. The dependence of the distribution of the reaction products on their Lewis number has been investigated.

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

NASA Astrophysics Data System (ADS)

Naruemon, Rueangkham; Charin, Modchang

2016-04-01

Most biochemical processes in cells are usually modeled by reaction-diffusion (RD) equations. In these RD models, the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement (MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times. The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations. Project supported by the Thailand Research Fund and Mahidol University (Grant No. TRG5880157), the Thailand Center of Excellence in Physics (ThEP), CHE, Thailand, and the Development Promotion of Science and Technology.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

PubMed

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-04-08

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

PubMed Central

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-01-01

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems. DOI: http://dx.doi.org/10.7554/eLife.14022.001 PMID:27058171

A Computational Approach to Increase Time Scales in Brownian Dynamics–Based Reaction-Diffusion Modeling

PubMed Central

Frazier, Zachary

2012-01-01

Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Integrating impairments in reaction time and executive function using a diffusion model framework.

PubMed

Karalunas, Sarah L; Huang-Pollock, Cynthia L

2013-07-01

Using Ratcliff's diffusion model and ex-Gaussian decomposition, we directly evaluate the role individual differences in reaction time (RT) distribution components play in the prediction of inhibitory control and working memory (WM) capacity in children with and without ADHD. Children with (n = 91, [Formula: see text] age = 10.2 years, 67 % male) and without ADHD (n = 62, [Formula: see text] age = 10.6 years, 46 % male) completed four tasks of WM and a stop signal reaction time (SSRT) task. Children with ADHD had smaller WM capacities and less efficient inhibitory control. Diffusion model analyses revealed that children with ADHD had slower drift rates (v) and faster non-decision times (Ter), but there were no group differences in boundary separations (a). Similarly, using an ex-Gaussian approach, children with ADHD had larger τ values than non-ADHD controls, but did not differ in μ or σ distribution components. Drift rate mediated the association between ADHD status and performance on both inhibitory control and WM capacity. τ also mediated the ADHD-executive function impairment associations; however, models were a poorer fit to the data. Impaired performance on RT and executive functioning tasks has long been associated with childhood ADHD. Both are believed to be important cognitive mechanisms to the disorder. We demonstrate here that drift rate, or the speed at which information accumulates towards a decision, is able to explain both.

A reaction-diffusion malaria model with seasonality and incubation period.

PubMed

Bai, Zhenguo; Peng, Rui; Zhao, Xiao-Qiang

2018-07-01

In this paper, we propose a time-periodic reaction-diffusion model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. The basic reproduction number [Formula: see text] is derived, and it is shown that the disease-free periodic solution is globally attractive if [Formula: see text], while there is an endemic periodic solution and the disease is uniformly persistent if [Formula: see text]. Numerical simulations indicate that prolonging the EIP may be helpful in the disease control, while spatial heterogeneity of the disease transmission coefficient may increase the disease burden.

Organic influences on inorganic patterns of diffusion-controlled precipitation in gels

NASA Astrophysics Data System (ADS)

Barge, Laura M.; Nealson, Kenneth H.; Petruska, John

2010-06-01

The well-known AgNO 3/K 2CrO 4 reaction-diffusion system produces periodic bands of silver chromate precipitate in gelatin, but only randomly oriented crystals in agarose gel. We show that comparable bands can be produced in agarose gel by adding small amounts of simple organic acids (e.g., acetic acid, N-acetyl glycine, and N-acetyl alanine) that suppress crystal growth and promote formation of rounded particles of precipitate. These results indicate that α-carboxyl groups of amino acids or short peptides in gelatin under mildly acidic conditions can induce periodic band patterns in diffusion-controlled silver chromate precipitates.

4D porosity evolution during solid-solid replacement reaction in mineral system (KBr, KCl)

NASA Astrophysics Data System (ADS)

Beaudoin, Nicolas; Hamilton, Andrea; Koehn, Daniel; Shipton, Zoe

2017-04-01

An extensive understanding of the controlling mechanisms of phase transformation is key in geosciences to better predicting the evolution of the physical parameters of rocks (porosity, permeability, and rheology) from centimetre-scale (e.g. fingering in siltstones) to kilometer-scale (e.g. Dolostone geobodies), in both the diagenetic and metamorphic domains. This contribution reports the 4D monitoring of a KBr crystal at different time steps during an experimental, fluid-mediated replacement reaction with KCl. Volumes are reconstructed based on density contrast using non-destructive X-ray Computed Tomography (XCT) at a resolution of 3 microns. A sample of KBr was immersed in a static bath of saturated KCl at room temperature and pressure. 5 scans were performed during the reaction at 5, 10, 20, 35 and 55 minutes, until 50% of the original crystal was replaced. As a control experiment, two samples reacted continuously for 15 and 55 minutes, respectively. Each 3D dataset was reconstructed to visualize and quantify the different mineral phases, the porosity distribution and connectivity, along with the reaction front morphology. In the case of successive baths, results show that the front morphology evolves from rough with small fingers to flat and thick during the reaction, suggesting a switch between advection and diffusion controlled reactant distribution through time. This switch is also reflected in the mass evolution and the rate of propagation of the replaced zone, being rapid in the first 20 minutes before reaching steady state. The porosity develops perpendicular to the crystal wall, suggesting a self-organization process governed by advection, before connecting laterally. While the reaction changes from advection controlled to diffusion controlled, the direction of the connected pores becomes parallel to the crystal walls. This phenomenon is not observed when the crystal is reacting discontinuously for 55 minutes. In the latter case, self-organization similar to extended fingering is observed, suggesting the advection to diffusion switch is related to the successive stop of reaction progress for scanning. In both cases, when considering only the reacting zone of the crystal, we can estimate the porosity created by Br-Cl substitution at 30%. The evolution of connected porosity distribution helps to understand how fluid flow can migrate in a transforming rock, for example during dolomitisation, a phenomenon extensively observed in sedimentary basins.

Physarum machines: encapsulating reaction-diffusion to compute spanning tree

NASA Astrophysics Data System (ADS)

Adamatzky, Andrew

2007-12-01

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.

Application of Bogolyubov's theory of weakly nonideal Bose gases to the A+A, A+B, B+B reaction-diffusion system

NASA Astrophysics Data System (ADS)

Konkoli, Zoran

2004-01-01

Theoretical methods for dealing with diffusion-controlled reactions inevitably rely on some kind of approximation, and to find the one that works on a particular problem is not always easy. Here the approximation used by Bogolyubov to study a weakly nonideal Bose gas, referred to as the weakly nonideal Bose gas approximation (WBGA), is applied in the analysis of three reaction-diffusion models: (i) A+A→Ø, (ii) A+B→Ø, and (iii) A+A,B+B,A+B→Ø (the ABBA model). Two types of WBGA are considered, the simpler WBGA-I and the more complicated WBGA-II. All models are defined on the lattice to facilitate comparison with computer experiment (simulation). It is found that the WBGA describes the A+B reaction well, it reproduces the correct d/4 density decay exponent. However, it fails in the case of the A+A reaction and the ABBA model. (To cure the deficiency of WBGA in dealing with the A+A model, a hybrid of the WBGA and Kirkwood superposition approximations is suggested.) It is shown that the WBGA-I is identical to the dressed-tree calculation suggested by Lee [J. Phys. A 27, 2633 (1994)], and that the dressed-tree calculation does not lead to the d/2 density decay exponent when applied to the A+A reaction, as normally believed, but it predicts the d/4 decay exponent. Last, the usage of the small n0 approximation suggested by Mattis and Glasser [Rev. Mod. Phys. 70, 979 (1998)] is questioned if used beyond the A+B reaction-diffusion model.

Decontamination of chemical tracers in droplets by a submerging thin film flow

NASA Astrophysics Data System (ADS)

Landel, Julien R.; McEvoy, Harry; Dalziel, Stuart B.

2016-11-01

We investigate the decontamination of chemical tracers contained in small viscous drops by a submerging falling film. This problem has applications in the decontamination of hazardous chemicals, following accidental releases or terrorist attacks. Toxic droplets lying on surfaces are cleaned by spraying a liquid decontaminant over the surface. The decontaminant film submerges the droplets, without detaching them, in order to neutralize toxic chemicals in the droplets. The decontamination process is controlled by advection, diffusion and reaction processes near the drop-film interface. Chemical tracers dissolve into the film flow forming a thin diffusive boundary layer at the interface. The chemical tracers are then neutralized through a reaction with a chemical decontaminant transported in the film. We assume in this work that the decontamination process occurs mainly in the film phase owing to low solubility of the decontaminant in the drop phase. We analyze the impact of the reaction time scale, assuming first-order reaction, in relation with the characteristic advection and diffusion time scales in the case of a single droplet. Using theoretical, numerical and experimental means, we find that the reaction time scale need to be significantly smaller than the characteristic time scale in the diffusive boundary layer in order to enhance noticeably the decontamination of a single toxic droplet. We discuss these results in the more general case of the decontamination of a large number of droplets. This material is based upon work supported by the Defense Threat Reduction Agency under Contract No. HDTRA1-12-D-0003-0001.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

The Scales Of Chemical Transport During Dehydration Reactions: The Roles Of Diffusion And Fluid Expulsion

NASA Astrophysics Data System (ADS)

Bedford, J. D.; Wheeler, J.; Fusseis, F.; Leclere, H.; Faulkner, D.

2016-12-01

The growth of new minerals in response to disequilibrium is the most fundamental metamorphic process. However, the kinetics controls on metamorphic reactions, including the transport of chemical components to growing minerals, are poorly understood as direct observation has been impossible both in nature and experiments. Dehydration reactions are common during prograde metamorphism and require both the expulsion of H2O and the transport of solid chemical components to the product mineral(s) in order for reaction to proceed. The expulsion of H2O is particularly important in understanding when fluid overpressures might develop, which can in turn lead to sudden failure (earthquakes) if the fluid is unable to drain. Using time-resolved (4D) synchrotron X-ray microtomography we have imaged a complete dehydration reaction and show how chemical transport of both the solid and fluid phases evolves during reaction. The reaction analysed is the dehydration of gypsum to form bassanite and H2O - an analogue for silicate dehydration but with much faster and controllable reaction rate. Like most dehydration reactions, the breakdown of gypsum is associated with a solid volume reduction which generates pore space. This new porosity wraps around growing bassanite grains, producing fluid-filled moats, across which transport of dissolved solutes to the growing grains occurs via diffusion. As moats grow in width, diffusion and hence reaction rate slow down. Each new grain-moat pair evolves in relative isolation from each other indicating that the chemical transport of solid components occurs over relatively short distances. This is despite the overall pore network becoming connected during the early stages of reaction, thus allowing efficient expulsion of excess H2O. A dehydrating system can therefore act as an open system with respect to the fluid phase and in contrast be restricted to the grain-scale with respect to the dissolved chemicals. This is in accord with observations that many rocks appear to have preserved their chemistry during dehydration (apart from the loss of H2O).

Highly Viscous States Affect the Browning of Atmospheric Organic Particulate Matter

PubMed Central

2018-01-01

Initially transparent organic particulate matter (PM) can become shades of light-absorbing brown via atmospheric particle-phase chemical reactions. The production of nitrogen-containing compounds is one important pathway for browning. Semisolid or solid physical states of organic PM might, however, have sufficiently slow diffusion of reactant molecules to inhibit browning reactions. Herein, organic PM of secondary organic material (SOM) derived from toluene, a common SOM precursor in anthropogenically affected environments, was exposed to ammonia at different values of relative humidity (RH). The production of light-absorbing organonitrogen imines from ammonia exposure, detected by mass spectrometry and ultraviolet–visible spectrophotometry, was kinetically inhibited for RH < 20% for exposure times of 6 min to 24 h. By comparison, from 20% to 60% RH organonitrogen production took place, implying ammonia uptake and reaction. Correspondingly, the absorption index k across 280 to 320 nm increased from 0.012 to 0.02, indicative of PM browning. The k value across 380 to 420 nm increased from 0.001 to 0.004. The observed RH-dependent behavior of ammonia uptake and browning was well captured by a model that considered the diffusivities of both the large organic molecules that made up the PM and the small reactant molecules taken up from the gas phase into the PM. Within the model, large-molecule diffusivity was calculated based on observed SOM viscosity and evaporation. Small-molecule diffusivity was represented by the water diffusivity measured by a quartz-crystal microbalance. The model showed that the browning reaction rates at RH < 60% could be controlled by the low diffusivity of the large organic molecules from the interior region of the particle to the reactive surface region. The results of this study have implications for accurate modeling of atmospheric brown carbon production and associated influences on energy balance. PMID:29532020

Highly Viscous States Affect the Browning of Atmospheric Organic Particulate Matter.

PubMed

Liu, Pengfei; Li, Yong Jie; Wang, Yan; Bateman, Adam P; Zhang, Yue; Gong, Zhaoheng; Bertram, Allan K; Martin, Scot T

2018-02-28

Initially transparent organic particulate matter (PM) can become shades of light-absorbing brown via atmospheric particle-phase chemical reactions. The production of nitrogen-containing compounds is one important pathway for browning. Semisolid or solid physical states of organic PM might, however, have sufficiently slow diffusion of reactant molecules to inhibit browning reactions. Herein, organic PM of secondary organic material (SOM) derived from toluene, a common SOM precursor in anthropogenically affected environments, was exposed to ammonia at different values of relative humidity (RH). The production of light-absorbing organonitrogen imines from ammonia exposure, detected by mass spectrometry and ultraviolet-visible spectrophotometry, was kinetically inhibited for RH < 20% for exposure times of 6 min to 24 h. By comparison, from 20% to 60% RH organonitrogen production took place, implying ammonia uptake and reaction. Correspondingly, the absorption index k across 280 to 320 nm increased from 0.012 to 0.02, indicative of PM browning. The k value across 380 to 420 nm increased from 0.001 to 0.004. The observed RH-dependent behavior of ammonia uptake and browning was well captured by a model that considered the diffusivities of both the large organic molecules that made up the PM and the small reactant molecules taken up from the gas phase into the PM. Within the model, large-molecule diffusivity was calculated based on observed SOM viscosity and evaporation. Small-molecule diffusivity was represented by the water diffusivity measured by a quartz-crystal microbalance. The model showed that the browning reaction rates at RH < 60% could be controlled by the low diffusivity of the large organic molecules from the interior region of the particle to the reactive surface region. The results of this study have implications for accurate modeling of atmospheric brown carbon production and associated influences on energy balance.

Modeling precursor diffusion and reaction of atomic layer deposition in porous structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keuter, Thomas, E-mail: t.keuter@fz-juelich.de; Menzler, Norbert Heribert; Mauer, Georg

2015-01-01

Atomic layer deposition (ALD) is a technique for depositing thin films of materials with a precise thickness control and uniformity using the self-limitation of the underlying reactions. Usually, it is difficult to predict the result of the ALD process for given external parameters, e.g., the precursor exposure time or the size of the precursor molecules. Therefore, a deeper insight into ALD by modeling the process is needed to improve process control and to achieve more economical coatings. In this paper, a detailed, microscopic approach based on the model developed by Yanguas-Gil and Elam is presented and additionally compared with themore » experiment. Precursor diffusion and second-order reaction kinetics are combined to identify the influence of the porous substrate's microstructural parameters and the influence of precursor properties on the coating. The thickness of the deposited film is calculated for different depths inside the porous structure in relation to the precursor exposure time, the precursor vapor pressure, and other parameters. Good agreement with experimental results was obtained for ALD zirconiumdioxide (ZrO{sub 2}) films using the precursors tetrakis(ethylmethylamido)zirconium and O{sub 2}. The derivation can be adjusted to describe other features of ALD processes, e.g., precursor and reactive site losses, different growth modes, pore size reduction, and surface diffusion.« less

Rhenium-Oxygen Interactions at High Temperatures

NASA Technical Reports Server (NTRS)

Jacobson, Nathan S.; Myers, Dwight L.; Zhu, Dongming; Humphrey, Donald

2000-01-01

The reaction of pure rhenium metal with dilute oxygen/argon mixtures was studied from 600 to 1400 C. Temperature, oxygen pressure, and flow rates were systematically varied to determine the rate-controlling steps. At lower temperatures the oxygen/rhenium chemical reaction is rate limiting; at higher temperatures gas-phase diffusion of oxygen through the static boundary layer is rate limiting. At all temperatures post-reaction microstructures indicate preferential attack along certain crystallographic planes and defects.

Changes in Reactivity as Chemistry Becomes Confined to an Interface. The Case of Free Radical Oxidation of C 30H 62 Alkane by OH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Houle, Frances A.; Wiegel, Aaron A.; Wilson, Kevin R.

Here, we examine in a simple organic aerosol the transition between heterogeneous chemistry under well-mixed conditions to chemistry under interfacial confinement. A single reaction mechanism, shown to reproduce observed OH oxidation chemistry for liquid and semisolid C 30H 62, is used in reaction-diffusion simulations to explore reactivity over a broad viscosity range. The results show that when internal mixing of the aerosol is fast and the particle interface is enriched in C-H groups, ketone and alcohol products, formed via peroxy radical disproportionation, predominate. As viscosity increases the reactions become confined to a shell at the gas-aerosol interface. The confinement ismore » accompanied by emergence of acyloxy reaction pathways that are particularly active when the shell is 1 nm or less. We quantify this trend using a reaction-diffusion index, allowing the parts of the mechanism that control reactivity as viscosity increases to be identified.« less

Changes in Reactivity as Chemistry Becomes Confined to an Interface. The Case of Free Radical Oxidation of C 30H 62 Alkane by OH

DOE PAGES

Houle, Frances A.; Wiegel, Aaron A.; Wilson, Kevin R.

2018-02-14

Here, we examine in a simple organic aerosol the transition between heterogeneous chemistry under well-mixed conditions to chemistry under interfacial confinement. A single reaction mechanism, shown to reproduce observed OH oxidation chemistry for liquid and semisolid C 30H 62, is used in reaction-diffusion simulations to explore reactivity over a broad viscosity range. The results show that when internal mixing of the aerosol is fast and the particle interface is enriched in C-H groups, ketone and alcohol products, formed via peroxy radical disproportionation, predominate. As viscosity increases the reactions become confined to a shell at the gas-aerosol interface. The confinement ismore » accompanied by emergence of acyloxy reaction pathways that are particularly active when the shell is 1 nm or less. We quantify this trend using a reaction-diffusion index, allowing the parts of the mechanism that control reactivity as viscosity increases to be identified.« less

Changes in Effective Thermal Conductivity During the Carbothermic Reduction of Magnetite Using Graphite

NASA Astrophysics Data System (ADS)

Kiamehr, Saeed; Ahmed, Hesham; Viswanathan, Nurni; Seetharaman, Seshadri

2017-06-01

Knowledge of the effective thermal diffusivity changes of systems undergoing reactions where heat transfer plays an important role in the reaction kinetics is essential for process understanding and control. Carbothermic reduction process of magnetite containing composites is a typical example of such systems. The reduction process in this case is highly endothermic and hence, the overall rate of the reaction is greatly influenced by the heat transfer through composite compact. Using Laser-Flash method, the change of effective thermal diffusivity of magnetite-graphite composite pellet was monitored in the dynamic mode over a pre-defined thermal cycle (heating at the rate of 7 K/min to 1423 K (1150 °C), holding the sample for 270 minutes at this temperature and then cooling it down to the room temperature at the same rate as heating). These measurements were supplemented by Thermogravimetric Analysis under comparable experimental conditions as well as quenching tests of the samples in order to combine the impact of various factors such as sample dilatations and changes in apparent density on the progress of the reaction. The present results show that monitoring thermal diffusivity changes during the course of reduction would be a very useful tool in a total understanding of the underlying physicochemical phenomena. At the end, effort is made to estimate the apparent thermal conductivity values based on the measured thermal diffusivity and dilatations.

Local error estimates for adaptive simulation of the Reaction–Diffusion Master Equation via operator splitting

PubMed Central

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2015-01-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

NASA Astrophysics Data System (ADS)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Reaction Rate of Ti0.18Zr0.84Cr1.0Fe0.7Mn0.3Cu0.057 to Use for the Heat Driven Type Compact Metal Hydride Refrigerator

NASA Astrophysics Data System (ADS)

Bae, Sang-Chul; Katsuta, Masafumi

Our final goal of this study is to develop the heat driven type compact metal hydride (MH) refrigeration system for the vending machine and the show case, and to attain a refrigeration temperature of 243 K by using a heat source of about 423K. The reaction rate of the MH to use for the heat source, MH used for heat source is studied firstly because the MH refrigeration system consists of two MHs, one is used for the heat source and the other is used for the cooling load extracting. As for the reaction rate in the hydriding process, initially, a rapid surface reaction, governed by the relation 1-(1-F )1/3=kht . After the MH surface has been covered by hydride, the reaction becomes diffusion controlled with the relation 1-3(1-F ' )2/3+2(1-F ' )=k'ht . The reaction rates, kh and k'h , are exponentially proportional to the pressure difference and increase with temperature. And, as for the dehydriding process, it is found out that the rate-controlling step is uniquely diffusion reaction. The dehydriding reaction rate is exponentially proportional to the pressure difference and the initial reacted fraction, and increases with temperature. Finally, on the basis of these experimental results, the brand new rate correlations are reasonably derived. The predicted results for this correlation are in successfully agreement with the experimental ones.

Reaction-diffusion controlled growth of complex structures

NASA Astrophysics Data System (ADS)

Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna

2013-03-01

Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support

Enhanced diffusion on oscillating surfaces through synchronization

NASA Astrophysics Data System (ADS)

Wang, Jin; Cao, Wei; Ma, Ming; Zheng, Quanshui

2018-02-01

The diffusion of molecules and clusters under nanoscale confinement or absorbed on surfaces is the key controlling factor in dynamical processes such as transport, chemical reaction, or filtration. Enhancing diffusion could benefit these processes by increasing their transport efficiency. Using a nonlinear Langevin equation with an extensive number of simulations, we find a large enhancement in diffusion through surface oscillation. For helium confined in a narrow carbon nanotube, the diffusion enhancement is estimated to be over three orders of magnitude. A synchronization mechanism between the kinetics of the particles and the oscillating surface is revealed. Interestingly, a highly nonlinear negative correlation between diffusion coefficient and temperature is predicted based on this mechanism, and further validated by simulations. Our results provide a general and efficient method for enhancing diffusion, especially at low temperatures.

Theory of Neutron Chain Reactions: Extracts from Volume I, Diffusion and Slowing Down of Neutrons: Chapter I. Elementary Theory of Neutron Diffusion. Chapter II. Second Order Diffusion Theory. Chapter III. Slowing Down of Neutrons

DOE R&D Accomplishments Database

Weinberg, Alvin M.; Noderer, L. C.

1951-05-15

The large scale release of nuclear energy in a uranium fission chain reaction involves two essentially distinct physical phenomena. On the one hand there are the individual nuclear processes such as fission, neutron capture, and neutron scattering. These are essentially quantum mechanical in character, and their theory is non-classical. On the other hand, there is the process of diffusion -- in particular, diffusion of neutrons, which is of fundamental importance in a nuclear chain reaction. This process is classical; insofar as the theory of the nuclear chain reaction depends on the theory of neutron diffusion, the mathematical study of chain reactions is an application of classical, not quantum mechanical, techniques.

Large disparity between gallium and antimony self-diffusion in gallium antimonide.

PubMed

Bracht, H; Nicols, S P; Walukiewicz, W; Silveira, J P; Briones, F; Haller, E E

2000-11-02

The most fundamental mass transport process in solids is self-diffusion. The motion of host-lattice ('self-') atoms in solids is mediated by point defects such as vacancies or interstitial atoms, whose formation and migration enthalpies determine the kinetics of this thermally activated process. Self-diffusion studies also contribute to the understanding of the diffusion of impurities, and a quantitative understanding of self- and foreign-atom diffusion in semiconductors is central to the development of advanced electronic devices. In the past few years, self-diffusion studies have been performed successfully with isotopically controlled semiconductor heterostructures of germanium, silicon, gallium arsenide and gallium phosphide. Self-diffusion studies with isotopically controlled GaAs and GaP have been restricted to Ga self-diffusion, as only Ga has two stable isotopes, 69Ga and 71Ga. Here we report self-diffusion studies with an isotopically controlled multilayer structure of crystalline GaSb. Two stable isotopes exist for both Ga and Sb, allowing the simultaneous study of diffusion on both sublattices. Our experiments show that near the melting temperature, Ga diffuses more rapidly than Sb by over three orders of magnitude. This surprisingly large difference in atomic mobility requires a physical explanation going beyond standard diffusion models. Combining our data for Ga and Sb diffusion with related results for foreign-atom diffusion in GaSb (refs 8, 9), we conclude that the unusually slow Sb diffusion in GaSb is a consequence of reactions between defects on the Ga and Sb sublattices, which suppress the defects that are required for Sb diffusion.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

The kinetics of dolomite reaction rim growth under isostatic and non-isostatic pressure conditions

NASA Astrophysics Data System (ADS)

Helpa, V.; Rybacki, E.; Morales, L. G.; Abart, R.; Dresen, G. H.

2013-12-01

During burial and exhumation, rocks are simultaneously exposed to metamorphic reactions and tectonic stresses. Therefore, the reaction rate of newly formed minerals may depend on chemical and mechanical driving forces. Here, we investigate the reaction kinetics of dolomite (CaMg[CO3]2) rim growth by solid-state reactions experiments on oriented calcite (CaCO3) and magnesite (MgCO3) single crystals under isostatic and non-isostatic pressure conditions. Cylindrical samples of 3-5 mm length and 7 mm diameter were drilled and polished perpendicular to the rhombohedral cleavage planes of natural clear crystals. The tests were performed using a Paterson-type deformation apparatus at P = 400 MPa confining pressure, temperatures, T, between 750 and 850°C, and reaction durations, t, of 2 - 146 h to calculate the kinetic parameters of dolomite rim growth under isostatic stress conditions. For non-isostatic reaction experiments we applied in addition differential stresses, σ, up to 40 MPa perpendicular to the contact interface at T = 750°C for 4 - 171 h duration, initiating minor inelastic deformation of calcite. The thickness of the resulting dolomite reaction rims increases linearly with the square root of time, indicating a diffusion-controlled reaction. The rims consist of two different textural domains. Granular dolomite grains (≈ 2 -5 μm grain size) form next to calcite and elongated palisade-shaped grains (1-6 μm diameter) grow perpendicular to the magnesite interface. Texture measurements with the electron backscatter diffraction technique indicate that the orientations of dolomite grains are mainly influenced by the orientation of the calcite educt crystal, in particular in the granular rim. To some extent, the texture of dolomite palisades is also influenced by the orientation of magnesite. The thickness of the two individual layers increases with temperature. At 400 MPa isostatic pressure, T = 750°C and t = 29 hours, a 5 μm thick granular dolomite layer and a 7 μm thick palisade-shaped layer evolve. At similar conditions and a differential stress of 30 MPa, the rim thickness remains similar; consequently the effect of non-isostatic stress on dolomite rim growth is negligible. Platinum markers show that the initial calcite-magnesite interface is located between granular and palisade-forming dolomite, indicating that rim growth occurs by counter diffusion of MgO and CaO. Diffusion of MgO across the dolomite reaction rim into calcite forms additionally magnesio-calcite grains with diameters of ≈ 13 - 46 μm, depending on the experimental conditions and increasing with increasing distance to the dolomite boundary. At T = 750°C, t = 29 hours, the thickness of the magnesio-calcite layer is 32 μm (isostatic) - 35 μm (σ = 30 MPa). The experiments indicate that solid-state reaction rim growth of dolomite between calcite and magnesite is primarily controlled by diffusion of MgO and CaO, forming layers with different microstructures during growth into the educt phases. The kinetics of the reaction in the carbonate system are not significantly changed by differential stresses up to 40 MPa. We suggest that volume diffusion is the dominant transport mechanism, which is presumably less affected by non-isostatic stresses than grain boundary diffusion.

Efficient reactive Brownian dynamics

DOE PAGES

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-21

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Efficient reactive Brownian dynamics

NASA Astrophysics Data System (ADS)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-01

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.

Efficient reactive Brownian dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Mapping Ionic Currents and Reactivity on the Nanoscale: Electrochemical Strain Microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalinin, S.V.

2010-10-19

Solid-state electrochemical processes in oxides underpin a broad spectrum of energy and information storage devices, ranging from Li-ion and Li-air batteries, to solid oxide fuel cells (SOFC) to electroresistive and memristive systems. These functionalities are controlled by the bias-driven diffusive and electromigration transport of mobile ionic species, as well as intricate a set of electrochemical and defect-controlled reactions at interfaces and in bulk. Despite the wealth of device-level and atomistic studies, little is known on the mesoscopic mechanisms of ion diffusion and electronic transport on the level of grain clusters, individual grains, and extended defects. The development of the capabilitymore » for probing ion transport on the nanometer scale is a key to deciphering complex interplay between structure, functionality, and performance in these systems. Here we introduce Electrochemical Strain Microscopy, a scanning probe microscopy technique based on strong strain-bias coupling in the systems in which local ion concentrations are changed by electrical fields. The imaging capability, as well as time- and voltage spectroscopies analogous to traditional current based electrochemical characterization methods are developed. The reversible intercalation of Li and mapping electrochemical activity in LiCoO2 is demonstrated, illustrating higher Li diffusivity at non-basal planes and grain boundaries. In Si-anode device structure, the direct mapping of Li diffusion at extended defects and evolution of Li-activity with charge state is explored. The electrical field-dependence of Li mobility is studied to determine the critical bias required for the onset of electrochemical transformation, allowing reaction and diffusion processes in the battery system to be separated at each location. Finally, the applicability of ESM for probing oxygen vacancy diffusion and oxygen reduction/evolution reactions is illustrated, and the high resolution ESM maps are correlated with aberration corrected scanning transmission electron microscopy imaging. The future potential for deciphering mechanisms of electrochemical transformations on an atomically-defined single-defect level is discussed.« less

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, A. M.; Zheng, B.; Barajas-Solano, D. A.

2017-12-01

We propose an effective stochastic advection-diffusion-reaction (SADR) model. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, the mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a fickian diffusion with the effective diffusion coefficient. Both coefficients are given in terms of Peclet number (Pe) and the coefficient of molecular diffusion. We use the experimental results of to demonstrate that for transport and bimolecular reactions in porous media the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the mass of the reaction product by as much as 25%.

Interplay between inhibited transport and reaction in nanoporous materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ackerman, David Michael

2013-01-01

This work presents a detailed formulation of reaction and diffusion dynamics of molecules in confined pores such as mesoporous silica and zeolites. A general reaction-diffusion model and discrete Monte Carlo simulations are presented. Both transient and steady state behavior is covered. Failure of previous mean-field models for these systems is explained and discussed. A coarse-grained, generalized hydrodynamic model is developed that accurately captures the interplay between reaction and restricted transport in these systems. This method incorporates the non-uniform chemical diffusion behavior present in finite pores with multi-component diffusion. Two methods of calculating these diffusion values are developed: a random walkmore » based approach and a driven diffusion model based on an extension of Fick's law. The effects of reaction, diffusion, pore length, and catalytic site distribution are investigated. In addition to strictly single file motion, quasi-single file diffusion is incorporated into the model to match a range of experimental systems. The connection between these experimental systems and model parameters is made through Langevin dynamics modeling of particles in confined pores.« less

Reactive sintering process of ferromagnetic MnBi under high magnetic fields

NASA Astrophysics Data System (ADS)

Mitsui, Yoshifuru; Umetsu, Rie Y.; Takahashi, Kohki; Koyama, Keiichi

2018-05-01

The magnetic field effect on the reactive sintering process of MnBi was investigated. Magnetic-field-induced enhancement of the reaction was found to be exhibited at the initial stages. The coercivity field decreased with an increase in the in-field annealing time. The kinetics of the reaction were in good agreement with the diffusion-controlled reaction model. It is suggested that the decrease in activation energy at the initial stages of reaction increased the amount of formed MnBi phases, resulting in enhancement of the reaction Mn + Bi to MnBi phase by in-field reactive sintering.

Twisted multifilament superconductor

NASA Technical Reports Server (NTRS)

Coles, W. D. (Inventor)

1973-01-01

Masking selected portions of a ribbon and forming an intermetallic compound on the unmasked portions by a controlled diffusion reaction produces a twisted filamentary structure. The masking material prohibits the formation of superconductive material on predetermined areas of the substrate.

Kinetics of exciplex formation/dissipation in reaction following Weller Scheme II

NASA Astrophysics Data System (ADS)

Fedorenko, S. G.; Burshtein, A. I.

2014-09-01

Creation of exciplexes from the charged products of photoionization is considered by means of Integral Encounter Theory. The general kinetic equations of such a reaction following the Weller scheme II are developed. The special attention is given to the particular case of irreversible remote ionization of primary excited electron donor. Kinetics of exciplex formation is considered at fast biexponential geminate transformation of exciplexes in cage that gives way to subsequent bulk reaction of equilibrated reaction products controlled by power law recombination of ions. It is shown that the initial geminate stage of exciplex kinetics is observed only in diffusion controlled regime of the reaction and disappears with increasing mobility of ions in passing to kinetic regime. The quantum yield of exciplexes is studied along with their kinetics.

Kinetics of exciplex formation/dissipation in reaction following Weller Scheme II.

PubMed

Fedorenko, S G; Burshtein, A I

2014-09-21

Creation of exciplexes from the charged products of photoionization is considered by means of Integral Encounter Theory. The general kinetic equations of such a reaction following the Weller scheme II are developed. The special attention is given to the particular case of irreversible remote ionization of primary excited electron donor. Kinetics of exciplex formation is considered at fast biexponential geminate transformation of exciplexes in cage that gives way to subsequent bulk reaction of equilibrated reaction products controlled by power law recombination of ions. It is shown that the initial geminate stage of exciplex kinetics is observed only in diffusion controlled regime of the reaction and disappears with increasing mobility of ions in passing to kinetic regime. The quantum yield of exciplexes is studied along with their kinetics.

Diffusion modelling of metamorphic layered coronas with stability criterion and consideration of affinity

NASA Astrophysics Data System (ADS)

Ashworth, J. R.; Sheplev, V. S.

1997-09-01

Layered coronas between two reactant minerals can, in many cases, be attributed to diffusion-controlled growth with local equilibrium. This paper clarifies and unifies the previous approaches of various authors to the simplest form of modelling, which uses no assumed values for thermochemical quantities. A realistic overall reaction must be estimated from measured overall proportions of minerals and their major element compositions. Modelling is not restricted to a particular number of components S, relative to the number of phases Φ. IfΦ > S + 1, the overall reaction is a combination of simultaneous reactions. The stepwise method, solving for the local reaction at each boundary in turn, is extended to allow for recurrence of a mineral (its presence in two parts of the layer structure separated by a gap). The equations are also given in matrix form. A thermodynamic stability criterion is derived, determining which layer sequence is truly stable if several are computable from the same inputs. A layer structure satisfying the stability criterion has greater growth rate (and greater rate of entropy production) than the other computable layer sequences. This criterion of greatest entropy production is distinct from Prigogine's theorem of minimum entropy production, which distinguishes the stationary or quasi-stationary state from other states of the same layer sequence. The criterion leads to modification of previous results for coronas comprising hornblende, spinel, and orthopyroxene between olivine (Ol) and plagioclase (Pl). The outcome supports the previous inference that Si, and particularly Al, commonly behave as immobile relative to other cation-forming major elements. The affinity (-ΔG) of a corona-forming reaction is estimated, using previous estimates of diffusion coefficient and the duration t of reaction, together with a new model quantity (-ΔG) *. For an example of the Ol + Pl reaction, a rough calculation gives (-ΔG) > 1.7RT (per mole of P1 consumed, based on a 24-oxygen formula for Pl). At 600-700°C, this represents (-ΔG) > 10kJ mol -1 and departure from equilibrium temperature by at least ˜ 100°C. The lower end of this range is petrologically reasonable and, for t < 100Ma, corresponds to a Fick's-law diffusion coefficient for Al, DAl > 10 -25m 2s -1, larger than expected for lattice diffusion but consistent with fluid-absent grain-boundary diffusion and small concentration gradients.

Kinetic and Mechanism Study of Vanadium Acid Leaching from Black Shale Using Microwave Heating Method

NASA Astrophysics Data System (ADS)

Wang, Jing-peng; Zhang, Yi-min; Huang, Jing; Liu, Tao

2018-04-01

The leaching kinetics of the vanadium leaching process were investigated by the comparison of microwave heating and conventional heating methods. Microwave heating with CaF2 had a synergistic effect and improved the vanadium leaching efficiency. In contrast to conventional heating leaching, microwave heating accelerated the vanadium leaching rate by approximately 1-3% and by approximately 15% when CaF2 was also used. The kinetics analysis showed that the calculated activation energy decreased in the microwave heating method in the presence and absence of CaF2. The control procedure of leaching also changed from a chemical reaction control step to a mixed chemical diffusion control step upon the addition of CaF2. Microwave heating was shown to be suitable for leaching systems with diffusion or mixed chemical diffusion control steps when the target mineral does not have a microwave absorbing ability.

Kinetic and Mechanism Study of Vanadium Acid Leaching from Black Shale Using Microwave Heating Method

NASA Astrophysics Data System (ADS)

Wang, Jing-peng; Zhang, Yi-min; Huang, Jing; Liu, Tao

2018-06-01

The leaching kinetics of the vanadium leaching process were investigated by the comparison of microwave heating and conventional heating methods. Microwave heating with CaF2 had a synergistic effect and improved the vanadium leaching efficiency. In contrast to conventional heating leaching, microwave heating accelerated the vanadium leaching rate by approximately 1-3% and by approximately 15% when CaF2 was also used. The kinetics analysis showed that the calculated activation energy decreased in the microwave heating method in the presence and absence of CaF2. The control procedure of leaching also changed from a chemical reaction control step to a mixed chemical diffusion control step upon the addition of CaF2. Microwave heating was shown to be suitable for leaching systems with diffusion or mixed chemical diffusion control steps when the target mineral does not have a microwave absorbing ability.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

A Design Principle for an Autonomous Post-translational Pattern Formation.

PubMed

Sugai, Shuhei S; Ode, Koji L; Ueda, Hiroki R

2017-04-25

Previous autonomous pattern-formation models often assumed complex molecular and cellular networks. This theoretical study, however, shows that a system composed of one substrate with multisite phosphorylation and a pair of kinase and phosphatase can generate autonomous spatial information, including complex stripe patterns. All (de-)phosphorylation reactions are described with a generic Michaelis-Menten scheme, and all species freely diffuse without pre-existing gradients. Computational simulation upon >23,000,000 randomly generated parameter sets revealed the design motifs of cyclic reaction and enzyme sequestration by slow-diffusing substrates. These motifs constitute short-range positive and long-range negative feedback loops to induce Turing instability. The width and height of spatial patterns can be controlled independently by distinct reaction-diffusion processes. Therefore, multisite reversible post-translational modification can be a ubiquitous source for various patterns without requiring other complex regulations such as autocatalytic regulation of enzymes and is applicable to molecular mechanisms for inducing subcellular localization of proteins driven by post-translational modifications. Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Oxidation of Carbon Fibers in a Cracked Ceramic Matrix Composite Modeled as a Function of Temperature

NASA Technical Reports Server (NTRS)

Halbig, Michael C.; Cawley, James D.; Eckel, Andrew J.

2003-01-01

The oxidation model simulates the oxidation of the reinforcing carbon fibers within a ceramic matrix composite material containing as-fabricated microcracks. The physics-based oxidation model uses theoretically and experimentally determined variables as input for the model. The model simulates the ingress of oxygen through microcracks into a two-dimensional plane within the composite material. Model input includes temperature, oxygen concentration, the reaction rate constant, the diffusion coefficient, and the crack opening width as a function of the mechanical and thermal loads. The model is run in an iterative process for a two-dimensional grid system in which oxygen diffuses through the porous and cracked regions of the material and reacts with carbon in short time steps. The model allows the local oxygen concentrations and carbon volumes from the edge to the interior of the composite to be determined over time. Oxidation damage predicted by the model was compared with that observed from microstructural analysis of experimentally tested composite material to validate the model for two temperatures of interest. When the model is run for low-temperature conditions, the kinetics are reaction controlled. Carbon and oxygen reactions occur relatively slowly. Therefore, oxygen can bypass the carbon near the outer edge and diffuse into the interior so that it saturates the entire composite at relatively high concentrations. The kinetics are limited by the reaction rate between carbon and oxygen. This results in an interior that has high local concentrations of oxygen and a similar amount of consumed carbon throughout the cross section. When the model is run for high-temperature conditions, the kinetics are diffusion controlled. Carbon and oxygen reactions occur very quickly. The carbon consumes oxygen as soon as it is supplied. The kinetics are limited by the relatively slow rate at which oxygen is supplied in comparison to the relatively fast rate at which carbon and oxygen reactions occur. This results in a sharp gradient in oxygen concentration from the edge where it is supplied to the nearest source of carbon, which is where the oxygen is quickly consumed. A moving reaction front is seen in which the outlaying carbon is consumed before the next inner layer of carbon begins to react.

Asynchronous discrete event schemes for PDEs

NASA Astrophysics Data System (ADS)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

Abnormal growth kinetics of h-BN epitaxial monolayer on Ru(0001) enhanced by subsurface Ar species

NASA Astrophysics Data System (ADS)

Wei, Wei; Meng, Jie; Meng, Caixia; Ning, Yanxiao; Li, Qunxiang; Fu, Qiang; Bao, Xinhe

2018-04-01

Growth kinetics of epitaxial films often follows the diffusion-limited aggregation mechanism, which shows a "fractal-to-compact" morphological transition with increasing growth temperature or decreasing deposition flux. Here, we observe an abnormal "compact-to-fractal" morphological transition with increasing growth temperature for hexagonal boron nitride growth on the Ru(0001) surface. The unusual growth process can be explained by a reaction-limited aggregation (RLA) mechanism. Moreover, introduction of the subsurface Ar atoms has enhanced this RLA growth behavior by decreasing both reaction and diffusion barriers. Our work may shed light on the epitaxial growth of two-dimensional atomic crystals and help to control their morphology.

STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python

PubMed Central

Wils, Stefan; Schutter, Erik De

2008-01-01

We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code. PMID:19623245

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Multi-layer light-weight protective coating and method for application

NASA Technical Reports Server (NTRS)

Wiedemann, Karl E. (Inventor); Clark, Ronald K. (Inventor); Taylor, Patrick J. (Inventor)

1992-01-01

A thin, light-weight, multi-layer coating is provided for protecting metals and their alloys from environmental attack at high temperatures. A reaction barrier is applied to the metal substrate and a diffusion barrier is then applied to the reaction barrier. A sealant layer may also be applied to the diffusion barrier if desired. The reaction barrier is either non-reactive or passivating with respect to the metal substrate and the diffusion barrier. The diffusion barrier is either non-reactive or passivating with respect to the reaction barrier and the sealant layer. The sealant layer is immiscible with the diffusion barrier and has a softening point below the expected use temperature of the metal.

Nonlinear Chemical Dynamics and Synchronization

NASA Astrophysics Data System (ADS)

Li, Ning

Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.

Control of scroll wave turbulence in a three-dimensional reaction-diffusion system with gradient.

PubMed

Qiao, Chun; Wu, Yabi; Lu, Xiaochuan; Wang, Chunyan; Ouyang, Qi; Wang, Hongli

2008-06-01

In this paper, we summarize our recent experimental and theoretical works on observation and control of scroll wave (SW) turbulence. The experiments were conducted in a three-dimensional Belousov-Zhabotinsky reaction-diffusion system with chemical concentration gradients in one dimension. A spatially homogeneous external forcing was used in the experiments as a control; it was realized by illuminating white light on the light sensitive reaction medium. We observed that, in the oscillatory regime of the system, SW can appear automatically in the gradient system, which will be led to spatiotemporal chaos under certain conditions. A suitable periodic forcing may stabilize inherent turbulence of SW. The mechanism of the transition to SW turbulence is due to the phase twist of SW in the presence of chemical gradients, while modulating the phase twist with a proper periodic forcing can delay this transition. Using the FitzHugh-Nagumo model with an external periodic forcing, we confirmed the control mechanism with numerical simulation. Moreover, we also show in the simulation that adding temporal external noise to the system may have the same control effect. During this process, we observed a new state called "intermittent turbulence," which may undergo a transition into a new type of SW collapse when the noise intensity is further increased. The intermittent state and the collapse could be explained by a random process.

Time-delayed feedback control of breathing localized structures in a three-component reaction-diffusion system.

PubMed

Gurevich, Svetlana V

2014-10-28

The dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to time-delayed feedback is investigated. It is shown that variation of the delay time and the feedback strength can lead either to stabilization of the breathing or to delay-induced periodic or quasi-periodic oscillations of the localized structure. A bifurcation analysis of the system in question is provided and an order parameter equation is derived that describes the dynamics of the localized structure in the vicinity of the Andronov-Hopf bifurcation. With the aid of this equation, the boundaries of the stabilization domains as well as the dependence of the oscillation radius on delay parameters can be explicitly derived, providing a robust mechanism to control the behaviour of the breathing localized structure in a straightforward manner. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Dynamical spike solutions in a nonlocal model of pattern formation

NASA Astrophysics Data System (ADS)

Marciniak-Czochra, Anna; Härting, Steffen; Karch, Grzegorz; Suzuki, Kanako

2018-05-01

Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns.

Water-Rock Interaction Simulations of Iron Oxide Mobilization and Precipitation: Implications of Cross-diffusion Reactions for Terrestrial and Mars 'Blueberry' Hematite Concretions

NASA Astrophysics Data System (ADS)

Park, A. J.; Chan, M. A.; Parry, W. T.

2005-12-01

Modeling of how terrestrial concretions form can provide valuable insights into understanding water-rock interactions that led to the formation of hematite concretions at Meridiani Planum, Mars. Numerical simulations of iron oxide concretions in the Jurassic Navajo Sandstone of southern Utah provide physical and chemical input parameters for emulating conditions that may have prevailed on Mars. In the terrestrial example, iron oxide coatings on eolian sand grains are reduced and mobilized by methane or petroleum. Precipitation of goethite or hematite occurs as Fe interacts with oxygen. Conditions that produced Navajo Sandstone concretions can range from a regional scale that is strongly affected by advection of large pore volumes of water, to small sub-meter scale features that are dominantly controlled by diffusive processes. Hematite concretions are results of a small-scale cross-diffusional process, where Fe and oxygen are supplied from two opposite sides from the 'middle' zone of mixing where concretions precipitate. This is an ideal natural system where Liesegang banding and other self-organized patterns can evolve. A complicating variable here is the sedimentologic (both mineralogic and textural) heterogeneity that, in reality, may be the key factor controlling the nucleation and precipitation habits (including possible competitive growth) of hematite concretions. Sym.8 water-rock interaction simulator program was used for the Navajo Sandstone concretions. Sym.8 is a water-rock simulator that accounts for advective and diffusive mass-transfer, and equilibrium and kinetic reactions. The program uses a dynamic composite media texture model to address changing sediment composition and texture to be consistent with the reaction progress. Initial one-dimensional simulation results indicate precipitation heterogeneity in the range of sub-meters, e.g., possible banding and distribution of iron oxide nodules may be centimeters apart for published diffusivities and water chemistries of the solutes involved. This modeling effort underscores the importance of coupled reactions and mass-transfer in formation of iron oxide concretions in both terrestrial and Mars sediments. Methane is interpreted to be the reactive agent that mobilizes iron in Navajo Sandstone. On Mars volatile volcanic gases may be the reactive agents that mobilize iron from volcanic sediments. In both cases, subsequent diffusive and advective mass-transfer coupled to nonlinear chemical reactions produces localized precipitates.

A class of exact solutions for biomacromolecule diffusion-reaction in live cells.

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD-Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Predicting Upscaled Behavior of Aqueous Reactants in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

Wright, E. E.; Hansen, S. K.; Bolster, D.; Richter, D. H.; Vesselinov, V. V.

2017-12-01

When modeling reactive transport, reaction rates are often overestimated due to the improper assumption of perfect mixing at the support scale of the transport model. In reality, fronts tend to form between participants in thermodynamically favorable reactions, leading to segregation of reactants into islands or fingers. When such a configuration arises, reactions are limited to the interface between the reactive solutes. Closure methods for estimating control-volume-effective reaction rates in terms of quantities defined at the control volume scale do not presently exist, but their development is crucial for effective field-scale modeling. We attack this problem through a combination of analytical and numerical means. Specifically, we numerically study reactive transport through an ensemble of realizations of two-dimensional heterogeneous porous media. We then employ regression analysis to calibrate an analytically-derived relationship between reaction rate and various dimensionless quantities representing conductivity-field heterogeneity and the respective strengths of diffusion, reaction and advection.

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis.

PubMed

Zhang, Xuzhu; Poniewierski, Andrzej; Jelińska, Aldona; Zagożdżon, Anna; Wisniewska, Agnieszka; Hou, Sen; Hołyst, Robert

2016-10-04

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C 12 E 8 (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Turing instability in reaction-diffusion systems with nonlinear diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zemskov, E. P., E-mail: zemskov@ccas.ru

2013-10-15

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

The Development of a Compact Refrigeration System using Metal Hydrides

NASA Astrophysics Data System (ADS)

Bae, Sang-Chul; Ogawa, Masahito; Katsuta, Masafumi

The MH refrigeration systems are regarded as important and compact ones for solving energy and environmental issues. Our purposes are to develop the compact refrigeration system for the vending machine and the show case using MH, and to attain a refrigeration temperature of 243K by using a heat source of 403∼423K. The kinetics of MH hydriding and dehydriding reactions is of importance relative to their practical use as a refrigerator system. The kinetics of the reaction between hydrogen and MHHigh (Ti0.18Zr0.84Cr1.0FeO.7Mn0.3CuO.057)has been followed in this paper. A relatively rapid absorption of hydrogen takes place for values of relative composition to about 0.3∼0.4. It is evident that a hydrogen diffusion plays a minor role during this stage, as that part of the metal not covered by hydride is always in contact with hydrogen. The direct chemical reaction between the hydrogen and the exposed metal surface is therefore postulated as the rate-controlling process. The rate of the reaction then decreases, and for values of relative composition above about 0.8, the reaction becomes slow. After the metal particles have been completely covered by a hydride layer, the transport of materials through the layer by diffusion becomes rate controlling process

Genipin diffusion and reaction into a gelatin matrix for tissue engineering applications.

PubMed

Montemurro, Francesca; De Maria, Carmelo; Orsi, Gianni; Ghezzi, Lisa; Tinè, Maria Rosaria; Vozzi, Giovanni

2017-04-01

Genipin is a natural low-toxic cross-linker for molecules with primary amino groups, and its use with collagen and gelatin has shown a great potential in tissue engineering applications. The fabrication of scaffolds with a well-organized micro and macro topology using additive manufacturing systems requires an accurate control of working parameters, such as reaction rate, gelling time, and diffusion constant. A polymeric system of 5% w/v gelatin in PBS with 2 mg/mL collagen solutions in a 1:1 weight ratio was used as template to perform measurements varying genipin concentration in a range of 0.1-1.5% w/w with respect to gelatin. In the first part of this work, the reaction rate of the polymeric system was estimated using a new colorimetric analysis of the reaction. Then its workability time, closely related to the gelling time, was evaluated thanks to rheological analysis: finally, the quantification of static and dynamic diffusion constants of genipin across nonreacting and reacting membranes, made respectively by agarose and gelatin, was performed. It was shown that the colorimetric analysis is a good indicator of the reaction progress. The gelling time depends on the genipin concentration, but a workability window of 40 min guaranteed up to 0.5% w/w genipin. The dynamic diffusion constant of genipin in the proposed polymeric system is in the order of magnitude of 10 -7 . The obtained results indicated the possibility to use the genipin, gelatin, and collagen, in the proposed concentrations, to build well-defined hydrogel scaffolds with both extrusion-based and 3D ink-jet system. © 2015 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 473-480, 2017. © 2015 Wiley Periodicals, Inc.

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

PubMed

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

NASA Technical Reports Server (NTRS)

Plante, Ianik; Wu, Honglu

2014-01-01

Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.

The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems.

PubMed

Lampoudi, Sotiria; Gillespie, Dan T; Petzold, Linda R

2009-03-07

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm.

Sequestration of flue gas CO₂ by direct gas-solid carbonation of air pollution control system residues.

PubMed

Tian, Sicong; Jiang, Jianguo

2012-12-18

Direct gas-solid carbonation reactions of residues from an air pollution control system (APCr) were conducted using different combinations of simulated flue gas to study the impact on CO₂ sequestration. X-ray diffraction analysis of APCr determined the existence of CaClOH, whose maximum theoretical CO₂ sequestration potential of 58.13 g CO₂/kg APCr was calculated by the reference intensity ratio method. The reaction mechanism obeyed a model of a fast kinetics-controlled process followed by a slow product layer diffusion-controlled process. Temperature is the key factor in direct gas-solid carbonation and had a notable influence on both the carbonation conversion and the CO₂ sequestration rate. The optimal CO₂ sequestrating temperature of 395 °C was easily obtained for APCr using a continuous heating experiment. CO₂ content in the flue gas had a definite influence on the CO₂ sequestration rate of the kinetics-controlled process, but almost no influence on the final carbonation conversion. Typical concentrations of SO₂ in the flue gas could not only accelerate the carbonation reaction rate of the product layer diffusion-controlled process, but also could improve the final carbonation conversion. Maximum carbonation conversions of between 68.6% and 77.1% were achieved in a typical flue gas. Features of rapid CO₂ sequestration rate, strong impurities resistance, and high capture conversion for direct gas-solid carbonation were proved in this study, which presents a theoretical foundation for the applied use of this encouraging technology on carbon capture and storage.

Explosion investigation of asphalt-salt mixtures in a reprocessing plant.

PubMed

Hasegawa, K; Li, Y

2000-12-15

Cause investigation of a fire and explosion at the nuclear fuel waste reprocessing plant indicated that self-heating ignition of an asphalt-salt-waste, bituminized, mixture (AS) caused the disaster. A 220l drum was filled with the AS at a temperature of about 180 degrees C. About 20h later the drum ignited and burned as it was being cooled. It is estimated that the AS contained approximately 55wt.% blown asphalt, 25wt.% NaNO(3), 5wt.% NaNO(2), 8wt.% Na(2)CO(3), 2wt.% NaH(2)PO(4), 1wt.% Ba (OH)(2), 1wt.% K(4)[Fe(CN)(6)], and possibly 3wt.% of other materials. To determine the reaction promoting factors and pertinent chemical reaction rates, self-reaction of the AS has been investigated by the use of a C80D heat flux reaction calorimeter. The oxidizing reactions with asphalt are ruled by NaNO(2) rather than by NaNO(3), in spite of a lower concentration of NaNO(2). The kinetic rates of the interfacial reaction between salt particles and asphalt for the reaction controlled and diffusion controlled steps have been formulated as a function of salt particle size for both NaNO(2) and NaNO(3). Numerical solution of the heat balance equations formulating the heterogeneous reaction scheme indicates that a runaway reaction occurs when the AS-filling temperature is 208 degrees C for a drum filled with an AS mixture produced under standard operating conditions. Molecules containing intramolecular hydrogen, such as Na(2)HPO(4) and NaHCO(3), do not oxidize asphalt directly, however, their presence chemically promotes the oxidizing reaction of NaNO(2). Moreover, NaHCO(3) decomposition which produces gases creates many micro holes in the interior of the salt particles. This in turn promotes the oxidizing reactions that are diffusion controlled. Finally, the consequence of a runaway reaction at 180 degrees C or lower is qualitatively explained by taking into account the chemical effect of intramolecular hydrogen and the physical effect of the NaHCO(3) decomposition gases.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

A study on ?-dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Ali, M. Syed; Zhu, Quanxin; Pavithra, S.; Gunasekaran, N.

2018-03-01

This study examines the problem of dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays. This paper proposes a complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. By constructing a suitable Lyapunov-Krasovskii functional (LKF), utilisation of Jensen's inequality and reciprocally convex combination (RCC) approach, strictly ?-dissipative conditions of the addressed systems are derived. Finally, a numerical example is given to show the effectiveness of the theoretical results.

A fully coupled 3D transport model in SPH for multi-species reaction-diffusion systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adami, Stefan; Hu, X. Y.; Adams, N. A.

2011-08-23

Abstract—In this paper we present a fully generalized transport model for multiple species in complex two and threedimensional geometries. Based on previous work [1] we have extended our interfacial reaction-diffusion model to handle arbitrary numbers of species allowing for coupled reaction models. Each species is tracked independently and we consider different physics of a species with respect to the bulk phases in contact. We use our SPH model to simulate the reaction-diffusion problem on a pore-scale level of a solid oxide fuel cell (SOFC) with special emphasize on the effect of surface diffusion.

The role of electrostatic interactions in protease surface diffusion and the consequence for interfacial biocatalysis.

PubMed

Feller, Bob E; Kellis, James T; Cascão-Pereira, Luis G; Robertson, Channing R; Frank, Curtis W

2010-12-21

This study examines the influence of electrostatic interactions on enzyme surface diffusion and the contribution of diffusion to interfacial biocatalysis. Surface diffusion, adsorption, and reaction were investigated on an immobilized bovine serum albumin (BSA) multilayer substrate over a range of solution ionic strength values. Interfacial charge of the enzyme and substrate surface was maintained by performing the measurements at a fixed pH; therefore, electrostatic interactions were manipulated by changing the ionic strength. The interfacial processes were investigated using a combination of techniques: fluorescence recovery after photobleaching, surface plasmon resonance, and surface plasmon fluorescence spectroscopy. We used an enzyme charge ladder with a net charge ranging from -2 to +4 with respect to the parent to systematically probe the contribution of electrostatics in interfacial enzyme biocatalysis on a charged substrate. The correlation between reaction rate and adsorption was determined for each charge variant within the ladder, each of which displayed a maximum rate at an intermediate surface concentration. Both the maximum reaction rate and adsorption value at which this maximum rate occurs increased in magnitude for the more positive variants. In addition, the specific enzyme activity increased as the level of adsorption decreased, and for the lowest adsorption values, the specific enzyme activity was enhanced compared to the trend at higher surface concentrations. At a fixed level of adsorption, the specific enzyme activity increased with positive enzyme charge; however, this effect offers diminishing returns as the enzyme becomes more highly charged. We examined the effect of electrostatic interactions on surface diffusion. As the binding affinity was reduced by increasing the solution ionic strength, thus weakening electrostatic interaction, the rate of surface diffusion increased considerably. The enhancement in specific activity achieved at the lowest adsorption values is explained by the substantial rise in surface diffusion at high ionic strength due to decreased interactions with the surface. Overall, knowledge of the electrostatic interactions can be used to control surface parameters such as surface concentration and surface diffusion, which intimately correlate with surface biocatalysis. We propose that the maximum reaction rate results from a balance between adsorption and surface diffusion. The above finding suggests enzyme engineering and process design strategies for improving interfacial biocatalysis in industrial, pharmaceutical, and food applications.

Pattern formation in a model for mountain pine beetle dispersal: linking model predictions to data.

PubMed

Strohm, S; Tyson, R C; Powell, J A

2013-10-01

Pattern formation occurs in a wide range of biological systems. This pattern formation can occur in mathematical models because of diffusion-driven instability or due to the interaction between reaction, diffusion, and chemotaxis. In this paper, we investigate the spatial pattern formation of attack clusters in a system for Mountain Pine Beetle. The pattern formation (aggregation) of the Mountain Pine Beetle in order to attack susceptible trees is crucial for their survival and reproduction. We use a reaction-diffusion equation with chemotaxis to model the interaction between Mountain Pine Beetle, Mountain Pine Beetle pheromones, and susceptible trees. Mathematical analysis is utilized to discover the spacing in-between beetle attacks on the susceptible landscape. The model predictions are verified by analysing aerial detection survey data of Mountain Pine Beetle Attack from the Sawtooth National Recreation Area. We find that the distance between Mountain Pine Beetle attack clusters predicted by our model closely corresponds to the observed attack data in the Sawtooth National Recreation Area. These results clarify the spatial mechanisms controlling the transition from incipient to epidemic populations and may lead to control measures which protect forests from Mountain Pine Beetle outbreak.

Delay-induced wave instabilities in single-species reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Otto, Andereas; Wang, Jian; Radons, Günter

2017-11-01

The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

Diffusion Driven Combustion Waves in Porous Media

NASA Technical Reports Server (NTRS)

Aldushin, A. P.; Matkowsky, B. J.

2000-01-01

Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.

Reactive solid surface morphology variation via ionic diffusion.

PubMed

Sun, Zhenchao; Zhou, Qiang; Fan, Liang-Shih

2012-08-14

In gas-solid reactions, one of the most important factors that determine the overall reaction rate is the solid morphology, which can be characterized by a combination of smooth, convex and concave structures. Generally, the solid surface structure varies in the course of reactions, which is classically noted as being attributed to one or more of the following three mechanisms: mechanical interaction, molar volume change, and sintering. Here we show that if a gas-solid reaction involves the outward ionic diffusion of a solid-phase reactant then this outward ionic diffusion could eventually smooth the surface with an initial concave and/or convex structure. Specifically, the concave surface is filled via a larger outward diffusing surface pointing to the concave valley, whereas the height of the convex surface decreases via a lower outward diffusion flux in the vertical direction. A quantitative 2-D continuum diffusion model is established to analyze these two morphological variation processes, which shows consistent results with the experiments. This surface morphology variation by solid-phase ionic diffusion serves to provide a fourth mechanism that supplements the traditionally acknowledged solid morphology variation or, in general, porosity variation mechanisms in gas-solid reactions.

Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

2015-05-01

With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

Cooperativity to increase Turing pattern space for synthetic biology.

PubMed

Diambra, Luis; Senthivel, Vivek Raj; Menendez, Diego Barcena; Isalan, Mark

2015-02-20

It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction-diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells.1 The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose-response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction-diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

Solid-State Reaction Between Fe-Al-Ca Alloy and Al2O3-CaO-FeO Oxide During Heat Treatment at 1473 K (1200 °C)

NASA Astrophysics Data System (ADS)

Liu, Chengsong; Yang, Shufeng; Li, Jingshe; Ni, Hongwei; Zhang, Xueliang

2017-04-01

The aim of this study was to control the physicochemical characteristics of inclusions in steel through appropriate heat treatment. Using a confocal scanning laser microscope (CSLM) and pipe furnace, the solid-state reactions between Fe-Al-Ca alloy and Al2O3-CaO-FeO oxide during heat treatment at 1473 K (1200 °C) and the influence of these reactions on the compositions of and phases in the alloy and oxide were investigated by the diffusion couple method. Suitable pretreatment of the oxide using a CSLM and production of the diffusion couple of Fe-Al-Ca alloy and Al2O3-CaO-FeO oxide gave good contact between the alloy and oxide. The diffusion couple was then sealed in a quartz tube with a piece of Ti foil to lower oxygen partial pressure and a block of Fe-Al-Ca alloy was introduced to conduct heat treatment experiments. Solid-state reactions between the alloy and oxide during heat treatment at 1473 K (1200 °C) were analyzed and discussed. A dynamic model to calculate the width of the particle precipitation zone based on the Wagner model of internal oxidation of metal was proposed. This model was helpful to understand the solid-state reaction mechanism between Fe-Al-Ca alloy and Al2O3-CaO-FeO oxide.

Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2017-10-01

Ionizing radiation interacts with the water molecules of the tissues mostly by ionizations and excitations, which result in the formation of the radiation track structure and the creation of radiolytic species such as H.,.OH, H2, H2O2, and e-aq. After their creation, these species diffuse and may chemically react with the neighboring species and with the molecules of the medium. Therefore radiation chemistry is of great importance in radiation biology. As the chemical species are not distributed homogeneously, the use of conventional models of homogeneous reactions cannot completely describe the reaction kinetics of the particles. Actually, many simulations of radiation chemistry are done using the Independent Reaction Time (IRT) method, which is a very fast technique to calculate radiochemical yields but which do not calculate the positions of the radiolytic species as a function of time. Step-by-step (SBS) methods, which are able to provide such information, have been used only sparsely because these are time-consuming in terms of calculation. Recent improvements in computer performance now allow the regular use of the SBS method in radiation chemistry. The SBS and IRT methods are both based on the Green's functions of the diffusion equation (GFDE). In this paper, several sampling algorithms of the GFDE and for the IRT method are presented. We show that the IRT and SBS methods are exactly equivalent for 2-particles systems for diffusion and partially diffusion-controlled reactions between non-interacting particles. We also show that the results obtained with the SBS simulation method with periodic boundary conditions are in agreement with the predictions by classical reaction kinetics theory, which is an important step towards using this method for modelling of biochemical networks and metabolic pathways involved in oxidative stress. Finally, the first simulation results obtained with the code RITRACKS (Relativistic Ion Tracks) are presented.

Imaging and controlling intracellular reactions: Lysosome transport as a function of diameter and the intracellular synthesis of conducting polymers

NASA Astrophysics Data System (ADS)

Payne, Christine

2014-03-01

Eukaryotic cells are the ultimate complex environment with intracellular chemical reactions regulated by the local cellular environment. For example, reactants are sequestered into specific organelles to control local concentration and pH, motor proteins transport reactants within the cell, and intracellular vesicles undergo fusion to bring reactants together. Current research in the Payne Lab in the School of Chemistry and Biochemistry at Georgia Tech is aimed at understanding and utilizing this complex environment to control intracellular chemical reactions. This will be illustrated using two examples, intracellular transport as a function of organelle diameter and the intracellular synthesis of conducting polymers. Using single particle tracking fluorescence microscopy, we measured the intracellular transport of lysosomes, membrane-bound organelles, as a function of diameter as they underwent transport in living cells. Both ATP-dependent active transport and diffusion were examined. As expected, diffusion scales with the diameter of the lysosome. However, active transport is unaffected suggesting that motor proteins are insensitive to cytosolic drag. In a second example, we utilize intracellular complexity, specifically the distinct micro-environments of different organelles, to carry out chemical reactions. We show that catalase, found in the peroxisomes of cells, can be used to catalyze the polymerization of the conducting polymer PEDOT:PSS. More importantly, we have found that a range of iron-containing biomolecules are suitable catalysts with different iron-containing biomolecules leading to different polymer properties. These experiments illustrate the advantage of intracellular complexity for the synthesis of novel materials.

Buoyancy and Pressure Effects on Bulk Metal-Oxygen Reactions

NASA Technical Reports Server (NTRS)

Abbud-Madrid, A.; McKnight, C.; Branch, M. C.; Daily, J. W.; Friedman, R. (Technical Monitor)

1998-01-01

The combustion behavior of metal-oxygen reactions if a weakly buoyant environment is studied to understand the rate-controlling mechanisms in the homogeneous and heterogeneous combustion of bulk metals. Cylindrical titanium and magnesium specimens are ignited in pure-oxygen at pressures ranging from 0.1 to 4.0 atm. Reduced gravity is obtained from an aircraft flying parabolic trajectories. A weakly buoyant environment is generated at low pressures under normal gravity and also at 1 atm under reduced gravity (0.01g). The similarity between these two experimental conditions comes from the p(exp 2)g buoyancy scale extracted from the Grashof number. Lower propagation rates of the molten interface on titanium samples are found at progressively lower pressures at 1 g. These rates are compared to theoretical results from heat conduction analyses with a diffusion/convection controlled reaction. The close agreement found between experimental and theoretical values indicate the importance values indicate the importance of natural convection enhanced oxygen transport on combustion rates. For magnesium, progressively longer burning times are experienced at lower pressures and 1 g. Under reduced gravity conditions at 1 atm, a burning time twice as long as in 1 g is exhibited. However, in this case, the validity of the p(exp 2)g buoyancy scale remains untested due to the inability to obtain steady gas-phase burning of the magnesium sample at 0.1 atm. Nevertheless, longer burning times and larger flame standoff distance at low pressures and at low gravity points to a diffusion/convection controlled reaction.

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials

NASA Astrophysics Data System (ADS)

Zhang, XiaoLong; Zhong, Zheng

2017-08-01

In this paper, a general thermodynamic framework is developed to describe the thermo-chemo-mechanical interactions in elastic solids undergoing mechanical deformation, imbibition of diffusive chemical species, chemical reactions and heat exchanges. Fully coupled constitutive relations and evolving laws for irreversible fluxes are provided based on entropy imbalance and stoichiometry that governs reactions. The framework manifests itself with a special feature that the change of Helmholtz free energy is attributed to separate contributions of the diffusion-swelling process and chemical reaction-dilation process. Both the extent of reaction and the concentrations of diffusive species are taken as independent state variables, which describe the reaction-activated responses with underlying variation of microstructures and properties of a material in an explicit way. A specialized isothermal formulation for isotropic materials is proposed that can properly account for volumetric constraints from material incompressibility under chemo-mechanical loadings, in which inhomogeneous deformation is associated with reaction and diffusion under various kinetic time scales. This framework can be easily applied to model the transient volumetric swelling of a solid caused by imbibition of external chemical species and simultaneous chemical dilation arising from reactions between the diffusing species and the solid.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

A "desperation-reaction" model of medical diffusion.

PubMed Central

Warner, K E

1975-01-01

Knowledge about the adoption and diffusion of innovations is briefly reviewed. A model is then proposed to explain how certain innovations, intended to address dire medical problems, might diffuse in a manner not previously reported, with extensive diffusion occurring during what would be a period of small-scale experimentation and limited adoption in the conventional innovation-diffusion environment. The model is illustrated with findings from a case study of the diffusion of drug therapies for four types of leukemia. Possible implications of "desperation-reaction" diffusion are suggested. PMID:1065622

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Spatially explicit control of invasive species using a reaction-diffusion model

USGS Publications Warehouse

Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.

2016-01-01

Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.

Controlled surface diffusion in plasma-enhanced chemical vapor deposition of GaN nanowires.

PubMed

Hou, Wen Chi; Hong, Franklin Chau-Nan

2009-02-04

This study investigates the growth of GaN nanowires by controlling the surface diffusion of Ga species on sapphire in a plasma-enhanced chemical vapor deposition (CVD) system. Under nitrogen-rich growth conditions, Ga has a tendency to adsorb on the substrate surface diffusing to nanowires to contribute to their growth. The significance of surface diffusion on the growth of nanowires is dependent on the environment of the nanowire on the substrate surface as well as the gas phase species and compositions. Under nitrogen-rich growth conditions, the growth rate is strongly dependent on the surface diffusion of gallium, but the addition of 5% hydrogen in nitrogen plasma instantly diminishes the surface diffusion effect. Gallium desorbs easily from the surface by reaction with hydrogen. On the other hand, under gallium-rich growth conditions, nanowire growth is shown to be dominated by the gas phase deposition, with negligible contribution from surface diffusion. This is the first study reporting the inhibition of surface diffusion effects by hydrogen addition, which can be useful in tailoring the growth and characteristics of nanowires. Without any evidence of direct deposition on the nanowire surface, gallium and nitrogen are shown to dissolve into the catalyst for growing the nanowires at 900 degrees C.

Simulation studies of chemical erosion on carbon based materials at elevated temperatures

NASA Astrophysics Data System (ADS)

Kenmotsu, T.; Kawamura, T.; Li, Zhijie; Ono, T.; Yamamura, Y.

1999-06-01

We simulated the fluence dependence of methane reaction yield in carbon with hydrogen bombardment using the ACAT-DIFFUSE code. The ACAT-DIFFUSE code is a simulation code based on a Monte Carlo method with a binary collision approximation and on solving diffusion equations. The chemical reaction model in carbon was studied by Roth or other researchers. Roth's model is suitable for the steady state methane reaction. But this model cannot estimate the fluence dependence of the methane reaction. Then, we derived an empirical formula based on Roth's model for methane reaction. In this empirical formula, we assumed the reaction region where chemical sputtering due to methane formation takes place. The reaction region corresponds to the peak range of incident hydrogen distribution in the target material. We adopted this empirical formula to the ACAT-DIFFUSE code. The simulation results indicate the similar fluence dependence compared with the experiment result. But, the fluence to achieve the steady state are different between experiment and simulation results.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and themore » perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.« less

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

Analytical Solution for Transport with Bimolecular Reactions in Fracture-Matrix Systems with Application to In-Situ Chemical Oxidation

NASA Astrophysics Data System (ADS)

Rajaram, H.; Arshadi, M.

2016-12-01

In-situ chemical oxidation (ISCO) is an effective strategy for remediation of DNAPL contamination in fractured rock. During ISCO, an oxidant (e.g. permanganate) is typically injected through fractures and is consumed by bimolecular reactions with DNAPLs such as TCE and natural organic matter in the fracture and the adjacent rock matrix. Under these conditions, moving reaction fronts form and propagate along the fracture and into the rock matrix. The propagation of these reaction fronts is strongly influenced by the heterogeneity/discontinuity across the fracture-matrix interface (advective transport dominates in the fractures, while diffusive transport dominates in the rock matrix). We present analytical solutions for the concentrations of the oxidant, TCE and natural organic matter; and the propagation of the reaction fronts in a fracture-matrix system. Our approximate analytical solutions assume advection and reaction dominate over diffusion/dispersion in the fracture and neglect the latter. Diffusion and reaction with both TCE and immobile natural organic matter in the rock matrix are considered. The behavior of the reaction-diffusion equations in the rock matrix is posed as a Stefan problem where the diffusing oxidant reacts with both diffusing (TCE) and immobile (natural organic matter) reductants. Our analytical solutions establish that the reaction fronts propagate diffusively (i.e. as the square root of time) in both the matrix and the fracture. Our analytical solutions agree very well with numerical simulations for the case of uniform advection in the fracture. We also present extensions of our analytical solutions to non-uniform flows in the fracture by invoking a travel-time transformation. The non-uniform flow solutions are relevant to field applications of ISCO. The approximate analytical solutions are relevant to a broad class of reactive transport problems in fracture-matrix systems where moving reaction fronts occur.

Ion Diffusion Within Water Films in Unsaturated Porous Media.

PubMed

Tokunaga, Tetsu K; Finsterle, Stefan; Kim, Yongman; Wan, Jiamin; Lanzirotti, Antonio; Newville, Matthew

2017-04-18

Diffusion is important in controlling local solute transport and reactions in unsaturated soils and geologic formations. Although it is commonly assumed that thinning of water films controls solute diffusion at low water contents, transport under these conditions is not well understood. We conducted experiments in quartz sands at low volumetric water contents (θ) to quantify ion diffusion within adsorbed films. At the lowest water contents, we employed fixed relative humidities to control water films at nm thicknesses. Diffusion profiles for Rb + and Br - in unsaturated sand packs were measured with a synchrotron X-ray microprobe, and inverse modeling was used to determine effective diffusion coefficients, D e, as low as ∼9 × 10 -15 m 2 s -1 at θ = 1.0 × 10 -4 m 3 m -3 , where the film thickness = 0.9 nm. Given that the diffusion coefficients (D o ) of Rb + and Br - in bulk water (30 °C) are both ∼2.4 × 10 -9 m 2 s -1 , we found the impedance factor f = D e /(θD o ) is equal to 0.03 ± 0.02 at this very low saturation, in agreement with the predicted influence of interface tortuosity (τ a ) for diffusion along grain surfaces. Thus, reduced cross-sectional area (θ) and tortuosity largely accounted for the more than 5 orders of magnitude decrease in D e relative to D o as desaturation progressed down to nanoscale films.

Biochemical Frequency Control by Synchronisation of Coupled Repressilators: An In Silico Study of Modules for Circadian Clock Systems

PubMed Central

Hinze, Thomas; Schumann, Mathias; Bodenstein, Christian; Heiland, Ines; Schuster, Stefan

2011-01-01

Exploration of chronobiological systems emerges as a growing research field within bioinformatics focusing on various applications in medicine, agriculture, and material sciences. From a systems biological perspective, the question arises whether biological control systems for regulation of oscillatory signals and their technical counterparts utilise similar mechanisms. If so, modelling approaches and parameterisation adopted from building blocks can help to identify general components for frequency control in circadian clocks along with gaining insight into mechanisms of clock synchronisation to external stimuli like the daily rhythm of sunlight and darkness. Phase-locked loops could be an interesting candidate in this context. Both, biology and engineering, can benefit from a unified view resulting from systems modularisation. In a first experimental study, we analyse a model of coupled repressilators. We demonstrate its ability to synchronise clock signals in a monofrequential manner. Several oscillators initially deviate in phase difference and frequency with respect to explicit reaction and diffusion rates. Accordingly, the duration of the synchronisation process depends on dedicated reaction and diffusion parameters whose settings still lack to be sufficiently captured analytically. PMID:22046179

Effects of H{sub 2} and H preferential diffusion and unity Lewis number on superadiabatic flame temperatures in rich premixed methane flames

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Fengshan; Guelder, OEmer L.

2005-11-01

The structures of freely propagating rich CH{sub 4}/air and CH{sub 4}/O{sub 2} flames were studied numerically using a relatively detailed reaction mechanism. Species diffusion was modeled using five different methods/assumptions to investigate the effects of species diffusion, in particular H{sub 2} and H, on superadiabatic flame temperature. With the preferential diffusion of H{sub 2} and H accounted for, significant amount of H{sub 2} and H produced in the flame front diffuse from the reaction zone to the preheat zone. The preferential diffusion of H{sub 2} from the reaction zone to the preheat zone has negligible effects on the phenomenon ofmore » superadiabatic flame temperature in both CH{sub 4}/air and CH{sub 4}/O{sub 2} flames. It is therefore demonstrated that the superadiabatic flame temperature phenomenon in rich hydrocarbon flames is not due to the preferential diffusion of H{sub 2} from the reaction zone to the preheat zone as recently suggested by Zamashchikov et al. [V.V. Zamashchikov, I.G. Namyatov, V.A. Bunev, V.S. Babkin, Combust. Explosion Shock Waves 40 (2004) 32]. The suppression of the preferential diffusion of H radicals from the reaction zone to the preheat zone drastically reduces the degree of superadiabaticity in rich CH{sub 4}/O{sub 2} flames. The preferential diffusion of H radicals plays an important role in the occurrence of superadiabatic flame temperature. The assumption of unity Lewis number for all species leads to the suppression of H radical diffusion from the reaction zone to the preheat zone and significant diffusion of CO{sub 2} from the postflame zone to the reaction zone. Consequently, the degree of superadiabaticity of flame temperature is also significantly reduced. Through reaction flux analyses and numerical experiments, the chemical nature of the superadiabatic flame temperature phenomenon in rich CH{sub 4}/air and CH{sub 4}/O{sub 2} flames was identified to be the relative scarcity of H radical, which leads to overshoot of H{sub 2}O and CH{sub 2}CO in CH{sub 4}/air flames and overshoot of H{sub 2}O in CH{sub 4}/O{sub 2} flames.« less

How the contagion at links influences epidemic spreading

NASA Astrophysics Data System (ADS)

Ruan, Zhongyuan; Tang, Ming; Liu, Zonghua

2013-04-01

The reaction-diffusion (RD) model of epidemic spreading generally assume that contagion occurs only at the nodes of network, i.e., the links are used only for migration/diffusion of agents. However, in reality, we observe that contagion occurs also among the travelers staying in the same car, train or plane etc., which consist of the links of network. To reflect the contagious effect of links, we here present a traveling-contagion model where contagion occurs not only at nodes but also at links. Considering that the population density in transportation is generally much larger than that in districts, we introduce different infection rates for the nodes and links, respectively, whose two extreme cases correspond to the type-I and type-II reactions in the RD model [V. Colizza, R. Pastor-Satorras, A. Vespignani, Nat. Phys. 3, 276 (2007)]. Through studying three typical diffusion processes, we reveal both numerically and theoretically that the contagion at links can accelerate significantly the epidemic spreading. This finding is helpful in designing the controlling strategies of epidemic spreading.

Surface charge- and space-dependent transport of proteins in crowded environments of nanotailored posts.

PubMed

Choi, Chang Kyoung; Fowlkes, Jason D; Retterer, Scott T; Siuti, Piro; Iyer, Sukanya; Doktycz, Mitchel J

2010-06-22

The reaction and diffusion of molecules across barriers and through crowded environments is integral to biological system function and to separation technologies. Ordered, microfabricated post arrays are a promising route to creating synthetic barriers with controlled chemical and physical characteristics. They can be used to create crowded environments, to mimic aspects of cellular membranes, and to serve as engineered replacements of polymer-based separation media. Here, the translational diffusion of fluorescein isothiocyante and various forms of green fluorescent protein (GFP), including "supercharged" variants, are examined in a silicon-based post array environment. The technique of fluorescence recovery after photobleaching (FRAP) is combined with analytical approximations and numerical simulations to assess the relative effects of reaction and diffusion on molecular transport, respectively. FRAP experiments were conducted for 64 different cases where the molecular species, the density of the posts, and the chemical surface charge of the posts were varied. In all cases, the dense packing of the posts hindered the diffusive transport of the fluorescent species. The supercharged GFPs strongly interacted with oppositely charged surfaces. With similar molecular and surface charges, transport is primarily limited by hindered diffusion. For conventional, enhanced GFP in a positively charged surface environment, transport was limited by the coupled action of hindered diffusion and surface interaction with the posts. Quantification of the size-, space-, time-, and charge-dependent translational diffusion in the post array environments can provide insight into natural processes and guide the design and development of selective membrane systems.

Reaction-diffusion systems in natural sciences and new technology transfer

NASA Astrophysics Data System (ADS)

Keller, André A.

2012-12-01

Diffusion mechanisms in natural sciences and innovation management involve partial differential equations (PDEs). This is due to their spatio-temporal dimensions. Functional semi-discretized PDEs (with lattice spatial structures or time delays) may be even more adapted to real world problems. In the modeling process, PDEs can also formalize behaviors, such as the logistic growth of populations with migration, and the adopters’ dynamics of new products in innovation models. In biology, these events are related to variations in the environment, population densities and overcrowding, migration and spreading of humans, animals, plants and other cells and organisms. In chemical reactions, molecules of different species interact locally and diffuse. In the management of new technologies, the diffusion processes of innovations in the marketplace (e.g., the mobile phone) are a major subject. These innovation diffusion models refer mainly to epidemic models. This contribution introduces that modeling process by using PDEs and reviews the essential features of the dynamics and control in biological, chemical and new technology transfer. This paper is essentially user-oriented with basic nonlinear evolution equations, delay PDEs, several analytical and numerical methods for solving, different solutions, and with the use of mathematical packages, notebooks and codes. The computations are carried out by using the software Wolfram Mathematica®7, and C++ codes.

Domainal cleavage as an Anisotropic Reaction-diffusion Process

NASA Astrophysics Data System (ADS)

Mulchrone, Kieran; Meere, Patrick

2017-04-01

Domainal cleavage comprises zones dominated by quartz and feldspar (QF-domains) and zones dominated by Mica (M-domains) which form at low metamorphic grades. The protolith is typically fairly homogeneous mudstone, siltstone, sandstone or limestone. Wet diffusion or pressure solution along grain boundaries is a key mechanism in the development of domanial cleavage. However, this does not explain why M-domains become sub-regularly spaced, visually evident in coarser-grained rocks, and take on an anastomising morphology. The ratio of M to QF-domains by volume can range from 1 to 0.1 and lower i.e. in extreme cases M-domains are intermittent but regularly spaced. It is suggested here that an anisotropic reaction-diffusion process model can explain these features. The imposed stress field instantaneously leads to anisotropy of diffusion by narrowing intergranular channels perpendicular to the principal stress. This leads to a preferred diffusion of chemicals parallel to the principal stress direction and lower diffusion rates in the normal direction. Combining this with the chemical reaction of pressure solution produces an anisotropic reaction-diffusion system. Both isotropic and anistropic reaction diffusion systems lead to pattern formation as discovered by Alan Turing on the 1950's as an explanation for patterns found in animal skins such as spots and stripes. Thus domanial cleavage is a striped pattern induced by diffusion anisotropy combined with a chemical reaction. Furthermore, rates of chemical reaction in intergranular fluids is likely to be many orders of magnitude greater that rates of deformation. Therefore we expect domanial cleavage to form relatively rapidly. As deformation progresses the M-domains behave less competently and may be the site of enhanced shearing. An example from Co. Cork, Ireland demonstrates shear folding in low-grade metasedimentary rocks with reverse shear along M-domains at a high angle to the maximum compressive stress.

A Simple Demonstration of Convective Effects on Reaction-Diffusion Systems: A Burning Cigarette.

ERIC Educational Resources Information Center

Pojman, John A.

1990-01-01

Described is a demonstration that provides an introduction to nonequilibrium reaction-diffusion systems and the coupling of hydrodynamics to chemical reactions. Experiments that demonstrate autocatalytic behavior that are effected by gravity and convection are included. (KR)

Incorporating reaction-rate dependence in reaction-front models of wellbore-cement/carbonated-brine systems

DOE PAGES

Iyer, Jaisree; Walsh, Stuart D. C.; Hao, Yue; ...

2017-03-08

Contact between wellbore cement and carbonated brine produces reaction zones that alter the cement's chemical composition and its mechanical properties. The reaction zones have profound implications on the ability of wellbore cement to serve as a seal to prevent the flow of carbonated brine. Under certain circumstances, the reactions may cause resealing of leakage pathways within the cement or at cement-interfaces; either due to fracture closure in response to mechanical weakening or due to the precipitation of calcium carbonate within the fracture. In prior work, we showed how mechanical sealing can be simulated using a diffusion-controlled reaction-front model that linksmore » the growth of the cement reaction zones to the mechanical response of the fracture. Here, we describe how such models may be extended to account for the effects of the calcite reaction-rate. We discuss how the relative rates of reaction and diffusion within the cement affect the precipitation of calcium carbonate within narrow leakage pathways, and how such behavior relates to the formation of characteristic reaction modes in the direction of flow. In addition, we compare the relative impact of precipitation and mechanical deformation on fracture sealing for a range of flow conditions and fracture apertures. Here, we conclude by considering how the prior leaching of calcium from cement may influence the sealing behavior of fractures, and the implication of prior leaching on the ability of laboratory tests to predict long-term sealing.« less

Incorporating reaction-rate dependence in reaction-front models of wellbore-cement/carbonated-brine systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iyer, Jaisree; Walsh, Stuart D. C.; Hao, Yue

Contact between wellbore cement and carbonated brine produces reaction zones that alter the cement's chemical composition and its mechanical properties. The reaction zones have profound implications on the ability of wellbore cement to serve as a seal to prevent the flow of carbonated brine. Under certain circumstances, the reactions may cause resealing of leakage pathways within the cement or at cement-interfaces; either due to fracture closure in response to mechanical weakening or due to the precipitation of calcium carbonate within the fracture. In prior work, we showed how mechanical sealing can be simulated using a diffusion-controlled reaction-front model that linksmore » the growth of the cement reaction zones to the mechanical response of the fracture. Here, we describe how such models may be extended to account for the effects of the calcite reaction-rate. We discuss how the relative rates of reaction and diffusion within the cement affect the precipitation of calcium carbonate within narrow leakage pathways, and how such behavior relates to the formation of characteristic reaction modes in the direction of flow. In addition, we compare the relative impact of precipitation and mechanical deformation on fracture sealing for a range of flow conditions and fracture apertures. Here, we conclude by considering how the prior leaching of calcium from cement may influence the sealing behavior of fractures, and the implication of prior leaching on the ability of laboratory tests to predict long-term sealing.« less

Oxidation Kinetics of Copper: An Experiment in Solid State Chemistry.

ERIC Educational Resources Information Center

Ebisuzaki, Y.; Sanborn, W. B.

1985-01-01

Oxidation kinetics in metals and the role defects play in diffusion-controlled reactions are discussed as background for a junior/senior-level experiment in the physical or inorganic chemistry laboratory. Procedures used and typical data obtained are provided for the experiment. (JN)

Simultaneous removal of SO2 and trace SeO2 from flue gas: effect of SO2 on selenium capture and kinetics study.

PubMed

Li, Yuzhong; Tong, Huiling; Zhuo, Yuqun; Wang, Shujuan; Xu, Xuchang

2006-12-15

Sulfur dioxide (SO2) and trace elements are all pollutants derived from coal combustion. This study relates to the simultaneous removal of SO2 and trace selenium dioxide (SeO2) from flue gas by calcium oxide (CaO) adsorption in the moderate temperature range, especially the effect of SO2 presence on selenium capture. Experiments performed on a thermogravimetric analyzer (TGA) can reach the following conclusions. When the CaO conversion is relatively low and the reaction rate is controlled by chemical kinetics, the SO2 presence does not affect the selenium capture. When the CaO conversion is very high and the reaction rate is controlled by product layer diffusion, the SO2 presence and the product layer diffusion resistance jointly reduce the selenium capture. On the basis of the kinetics study, a method to estimate the trace selenium removal efficiency using kinetic parameters and the sulfur removal efficiency is developed.

Using rapid infrared forming to control interfaces in titanium-matrix composites

NASA Technical Reports Server (NTRS)

Warrier, Sunil G.; Lin, Ray Y.

1993-01-01

Control of the fiber-matrix reaction during composite fabrication is commonly achieved by shortening the processing time, coating the reinforcement with relatively inert materials, or adding alloying elements to retard the reaction. To minimize the processing time, a rapid IR forming (RIF) technique for metal-matrix composite fabrication has been developed. Experiments have shown that the RIF technique is a quick, simple, and low-cost process to fabricate titanium-alloy matrix composites reinforced with either silicon carbide or carbon fibers. Due to short processing times (typically on the order of 1-2 minutes in an inert atmosphere for composites with up to eight-ply reinforcements), the interfacial reaction is limited and well controlled. Composites fabricated by this technique have mechanical properties that are comparable to (in several cases, superior to) those made with conventional diffusion-bonding techniques.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations

NASA Astrophysics Data System (ADS)

Elperin, T.; Kleeorin, N.; Liberman, M.; Lipatnikov, A. N.; Rogachevskii, I.; Yu, R.

2017-11-01

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014), 10.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

The development and preliminary application of an invariant coupled diffusion and chemistry model

NASA Technical Reports Server (NTRS)

Hilst, G. R.; Donaldson, C. DUP.; Teske, M.; Contiliano, R.; Freiberg, J.

1973-01-01

In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

PubMed

Elperin, T; Kleeorin, N; Liberman, M; Lipatnikov, A N; Rogachevskii, I; Yu, R

2017-11-01

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Simulation tools for particle-based reaction-diffusion dynamics in continuous space

PubMed Central

2014-01-01

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. A physically realistic model, depending on the system at hand and the questions asked, would require different levels of modeling detail such as particle diffusion, geometrical confinement, particle volume exclusion or particle-particle interaction potentials. Higher levels of detail usually correspond to increased number of parameters and higher computational cost. Certain systems however, require these investments to be modeled adequately. Here we present a review on the current field of particle-based reaction-diffusion software packages operating on continuous space. Four nested levels of modeling detail are identified that capture incrementing amount of detail. Their applicability to different biological questions is discussed, arching from straight diffusion simulations to sophisticated and expensive models that bridge towards coarse grained molecular dynamics. PMID:25737778

STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

PubMed Central

2012-01-01

Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates models of cellular reaction–diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/ PMID:22574658

Multiscale Modeling of Diffusion in a Crowded Environment.

PubMed

Meinecke, Lina

2017-11-01

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

Study on Kinetic Mechanism of Bastnaesite Concentrates Decomposition Using Calcium Hydroxide

NASA Astrophysics Data System (ADS)

Cen, Peng; Wu, Wenyuan; Bian, Xue

2018-06-01

The thermal decomposition of bastnaesite concentrates using calcium hydroxide was studied. Calcium hydroxide can effectively inhibit the emission of fluorine during roasting by transforming it to calcium fluoride. The decomposition rate increased with increasing reaction temperature and amount of calcium hydroxide. The decomposition kinetics were investigated. The decomposition reaction was determined to be a heterogeneous gas-solid reaction, and it followed an unreacted shrinking core model. By means of the integrated rate equation method, the reaction was proven to be kinetically first order. Different reaction models were fit to the experimental data to determine the reaction control process. The chemical reaction at the phase interface controlled the reaction rate in the temperatures ranging from 673 K to 773 K (400 °C to 500 °C) with an apparent activation energy of 82.044 kJ·mol-1. From 773 K to 973 K (500 °C to 700 °C), diffusion through the solid product's layer became the determining step, with a lower activation energy of 15.841 kJ·mol-1.

Photo-Controlled Waves and Active Locomotion.

PubMed

Epstein, Irving R; Gao, Qingyu

2017-08-22

Waves of chemical concentration, created by the interaction between reaction and diffusion, occur in a number of chemical systems far from equilibrium. In appropriately chosen polymer gels, these waves generate mechanical forces, which can result in locomotion. When a component of the system is photosensitive, light can be used to modulate and control these waves. In this Concept article, we examine various forms of photo-control of such systems, focusing particularly on the Belousov-Zhabotinsky oscillating chemical reaction. The phenomena we consider include image storage and image processing, feedback-control and feedback-induced clustering of waves, and phototropic and photophobic locomotion. Several of these phenomena have analogues in or potential applications to biological systems. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Controlling three-dimensional vortices using multiple and moving external fields

NASA Astrophysics Data System (ADS)

Das, Nirmali Prabha; Dutta, Sumana

2017-08-01

Spirals or scroll wave activities in cardiac tissues are the cause of lethal arrhythmias. The external control of these waves is thus of prime interest to scientists and physicians. In this article, we demonstrate the spatial control of scroll waves by using external electric fields and thermal gradients in experiments with the Belousov-Zhabotinsky reaction. We show that a scroll ring can be made to trace cyclic trajectories under a rotating electric field. Application of a thermal gradient in addition to the electric field deflects the motion and changes the nature of the trajectory. Our experimental results are analyzed and corroborated by numerical simulations based on an excitable reaction diffusion model.

Computational methods for diffusion-influenced biochemical reactions.

PubMed

Dobrzynski, Maciej; Rodríguez, Jordi Vidal; Kaandorp, Jaap A; Blom, Joke G

2007-08-01

We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems. Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

PubMed

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping.

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

Cross-Diffusion Driven Instability for a Lotka-Volterra Competitive Reaction-Diffusion System

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2008-04-01

In this work we investigate the possibility of the pattern formation for a reaction-diffusion system with nonlinear diffusion terms. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-diffusion effects are responsible for the initiation of spatial patterns. Finally, we find a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation.

PubMed

Drawert, Brian; Lawson, Michael J; Petzold, Linda; Khammash, Mustafa

2010-02-21

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.

A simple reaction-rate model for turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Bangert, L. H.

1975-01-01

A simple reaction rate model is proposed for turbulent diffusion flames in which the reaction rate is proportional to the turbulence mixing rate. The reaction rate is also dependent on the mean mass fraction and the mean square fluctuation of mass fraction of each reactant. Calculations are compared with experimental data and are generally successful in predicting the measured quantities.

pH Wave-Front Propagation in the Urea-Urease Reaction

PubMed Central

Wrobel, Magdalena M.; Bánsági, Tamás; Scott, Stephen K.; Taylor, Annette F.; Bounds, Chris O.; Carranza, Arturo; Pojman, John A.

2012-01-01

The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ∼3) to base (pH ∼9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1−1 mm min−1. The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH. PMID:22947878

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2003-07-01

Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied.

The effects of diffuse and distinct affect.

PubMed

Stapel, Diederik A; Koomen, Willem; Ruys, Kirsten I

2002-07-01

In a series of suboptimal priming studies, it was shown that both affective and nonaffective reactions to a stimulus may occur without awareness. Moreover, it was demonstrated that affective information is detected earlier than nonaffective information. Therefore, early reactions to an affect-laden stimulus (e.g., a smiling man) are cognitively unappraised and thus diffuse (e.g., "positive"), whereas later affective reactions can be more specific and distinct (e.g., "a smiling man"). Through variations of prime exposure (extremely short, moderately short) the impact of early diffuse and late distinct affect on judgment was investigated. Findings show that distinctness (and prime-target similarity) is an essential determinant of whether the effect of affect is null, assimilation, or contrast. Furthermore, whether affect priming activates diffuse or distinct reactions is a matter of a fraction of seconds.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

Conceptual model analysis of interaction at a concrete-Boom Clay interface

NASA Astrophysics Data System (ADS)

Liu, Sanheng; Jacques, Diederik; Govaerts, Joan; Wang, Lian

In many concepts for deep disposal of high-level radioactive waste, cementitious materials are used in the engineered barriers. For example, in Belgium the engineered barrier system is based on a considerable amount of cementitious materials as buffer and backfill in the so-called supercontainer embedded in the hosting geological formation. A potential hosting formation is Boom Clay. Insight in the interaction between the high-pH pore water of the cementitious materials and neutral-pH Boom Clay pore water is required. Two problems are quite common for modeling of such a system. The first one is the computational cost due to the long timescale model assessments envisaged for the deep disposal system. Also a very fine grid (in sub-millimeter), especially at interfaces has to be used in order to accurately predict the evolution of the system. The second one is whether to use equilibrium or kinetic reaction models. The objectives of this paper are twofold. First, we develop an efficient coupled reactive transport code for this diffusion-dominated system by making full use of multi-processors/cores computers. Second, we investigate how sensitive the system is to chemical reaction models especially when pore clogging due to mineral precipitation is considered within the cementitious system. To do this, we selected two portlandite dissolution models, i.e., equilibrium (fastest) and diffusion-controlled model with precipitation of a calcite layer around portlandite particles (diffusion-controlled dissolution). The results show that with shrinking core model portlandite dissolution and calcite precipitation are much slower than with the equilibrium model. Also diffusion-controlled dissolution smooths out dissolution fronts compared to the equilibrium model. However, only a slight difference with respect to the clogging time can be found even though we use a very small diffusion coefficient (10-20 m2/s) in the precipitated calcite layer.

Characterization of Secondary Mineral Grain Coatings and their Role as Diffusion-controlled Sinks and Sources for Metal Contaminants

NASA Astrophysics Data System (ADS)

Davis, J. A.; Guo, H.; Lai, B.; Kemner, K. M.; Ercius, P.; Fox, P. M.; Singer, D. M.; Minor, A.; Waychunas, G.

2012-12-01

Many important geochemical reactions occur at the mineral-water interface, including sorption and desorption reactions of contaminants. Fundamental knowledge of the kinetics of these processes is based primarily on experimental observations of reactions at faces of single crystals or macroscopic data from pure mineral powder suspensions. Sorption reactions at crystal faces are generally very fast, on the order of microseconds or less, with reaction times often limited only by film diffusion at the mineral-water interface. In well-stirred suspensions of aquifer sediments, however, sorptive equilibrium can take many hours or days to achieve steady-state concentrations. We have examined the potential reasons for sorption rate limitation using uranium(VI) sorption by sediments from a sandy aquifer in Savannah River, South Carolina (USA). U(VI) sorption by sand-sized grains from the aquifer is dominated by reaction with secondary mineral coatings on quartz and feldspar grains. The coatings studied were on the order of 15 microns in thickness (i.e., from quartz grain to aqueous solution) and composed primarily of clay minerals and hematite of varying particle size. Microfocused-XRF imaging of elemental concentrations (e.g., U, Fe) of polished cross-sections of the grain/coating contact showed strong spatial correlations of U and Fe within the coatings, regardless of the length of reaction time (30 minutes to 4 weeks). The spatial resolution of the μ-XRF technique is of the order of 2 microns in horizontal directions, but the uncertainty of the observed spatial gradients is high due to grain curvature away from the polished surface and fluorescence contributed from the entire 30 micron thickness of a typical grain/epoxy thin section. TEM characterization of focused-ion-beam (FIB), vertically-extracted samples of the grain-coating contact shows that complex pore networks exist within the coatings of variable dimensions and unknown connectivity. Using scanning TEM (STEM) tomography, it can be seen that there are large numbers of pore throat sizes less than 10 nm within the coatings. We hypothesize that diffusion through these pores, which likely have electrically charged surfaces, controls the observed macroscopic rates of U(VI) sorption in batch experiments with sand grains. Evidence to support this hypothesis was observed by studying U and Fe fluorescence spatial variation within FIB samples (1 micron thick) at 200 nm spatial resolution. With this greater spatial resolution, it is possible to see U concentration variations within the coatings that are dependent on the time of sorption reaction, and illustrates how the coating environment constitutes a diffusion constraint to achieve adsorptive equilibrium between an aqueous phase and the mineral surfaces. Including this diffusion constraint within conceptual models for reactive contaminant transport may be significant at the field scale, because secondary mineral coatings are potentially both sinks and sources of contaminants depending on the history of a contaminated site. This is important in resolving long-term transport predictions at DOE sites, such as Hanford and Savannah River, where equilibrium versus kinetic reactive transport models are being evaluated.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

The rate of the deoxygenation reaction limits myoglobin- and hemoglobin-facilitated O₂ diffusion in cells.

PubMed

Endeward, Volker

2012-05-01

A mathematical model describing facilitation of O(2) diffusion by the diffusion of myoglobin and hemoglobin is presented. The equations are solved numerically by a finite-difference method for the conditions as they prevail in cardiac and skeletal muscle and in red cells without major simplifications. It is demonstrated that, in the range of intracellular diffusion distances, the degree of facilitation is limited by the rate of the chemical reaction between myglobin or hemoglobin and O(2). The results are presented in the form of relationships between the degree of facilitation and the length of the diffusion path on the basis of the known kinetics of the oxygenation-deoxygenation reactions. It is concluded that the limitation by reaction kinetics reduces the maximally possible facilitated oxygen diffusion in cardiomyoctes by ∼50% and in skeletal muscle fibers by ∼ 20%. For human red blood cells, a reduction of facilitated O(2) diffusion by 36% is obtained in agreement with previous reports. This indicates that, especially in cardiomyocytes and red cells, chemical equilibrium between myoglobin or hemoglobin and O(2) is far from being established, an assumption that previously has often been made. Although the "O(2) transport function" of myoglobin in cardiac muscle cells thus is severely limited by the chemical reaction kinetics, and to a lesser extent also in skeletal muscle, it is noteworthy that the speed of release of O(2) from MbO(2), the "storage function," is not limited by the reaction kinetics under physiological conditions.

Solid-State Diffusional Behaviors of Functional Metal Oxides at Atomic Scale.

PubMed

Chen, Jui-Yuan; Huang, Chun-Wei; Wu, Wen-Wei

2018-02-01

Metal/metal oxides have attracted extensive research interest because of their combination of functional properties and compatibility with industry. Diffusion and thermal reliability have become essential issues that require detailed study to develop atomic-scaled functional devices. In this work, the diffusional reaction behavior that transforms piezoelectric ZnO into magnetic Fe 3 O 4 is investigated at the atomic scale. The growth kinetics of metal oxides are systematically studied through macro- and microanalyses. The growth rates are evaluated by morphology changes, which determine whether the growth behavior was a diffusion- or reaction-controlled process. Furthermore, atom attachment on the kink step is observed at the atomic scale, which has important implications for the thermodynamics of functional metal oxides. Faster growth planes simultaneously decrease, which result in the predominance of low surface energy planes. These results directly reveal the atomic formation process of metal oxide via solid-state diffusion. In addition, the nanofabricated method provides a novel approach to investigate metal oxide evolution and sheds light on diffusional reaction behavior. More importantly, the results and phenomena of this study provide considerable inspiration to enhance the material stability and reliability of metal/oxide-based devices. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Calorimetric Studies of Precipitation and Dissolution Kinetics in Aluminum Alloys 2219 and 7075

NASA Astrophysics Data System (ADS)

Papazian, John M.

1982-05-01

Differential scanning calorimetry (DSC) was used to study the kinetics of precipitation and dissolution of metastable and stable phases in aluminum alloys 2219 and 7075. A comparison of DSC scans obtained at heating rates of 1, 5, 10, and 20 K per minute showed that, during a DSC scan, the rates of precipitation of θ' and θ in 2219 and η' and η in 7075 were limited by their reaction kinetics. Likewise, the rates of dissolution of GP zones, θ' and η', were found to be dominated by kinetics. In contrast, the dissolution of θ and η was dominated by the thermodynamic equilibrium between these phases and the matrix. Analysis of the kinetically dominated reaction peaks and their dependence on heating rate and particle size showed that the GP zone dissolution reaction could best be described by a three-dimensional volume diffusion limited rate expression with an activation energy equal to that for diffusion. The rate of formation of θ' was best described by an Avrami expression with n = 1.1, indicating that nucleation was not the rate controlling step. A pronounced dependence of the θ' formation rate on prior plastic deformation was observed and ascribed to the influence of the matrix dislocation density on diffusivity.

Consumption and diffusion of dissolved oxygen in sedimentary rocks.

PubMed

Manaka, M; Takeda, M

2016-10-01

Fe(II)-bearing minerals (e.g., biotite, chlorite, and pyrite) are a promising reducing agent for the consumption of atmospheric oxygen in repositories for the geological disposal of high-level radioactive waste. To estimate effective diffusion coefficients (D e , in m 2 s -1 ) for dissolved oxygen (DO) and the reaction rates for the oxidation of Fe(II)-bearing minerals in a repository environment, we conducted diffusion-chemical reaction experiments using intact rock samples of Mizunami sedimentary rock. In addition, we conducted batch experiments on the oxidation of crushed sedimentary rock by DO in a closed system. From the results of the diffusion-chemical reaction experiments, we estimated the values of D e for DO to lie within the range 2.69×10 -11

The influence of physical state on shikimic acid ozonolysis: a case for in situ microspectroscopy

NASA Astrophysics Data System (ADS)

Steimer, S. S.; Lampimäki, M.; Coz, E.; Grzinic, G.; Ammann, M.

2014-03-01

Atmospheric soluble organic aerosol material can become solid or semi-solid. Due to increasing viscosity and decreasing diffusivity, this can impact important processes such as gas uptake and reactivity within aerosols containing such substances. This work explores the dependence of shikimic acid ozonolysis on humidity and thereby viscosity. Shikimic acid, a proxy for oxygenated reactive organic material, reacts with O3 in a Criegee-type reaction. We used an environmental microreactor embedded in a Scanning Transmission X-ray Microscope (STXM) to probe this oxidation process. This technique facilitates in situ measurements with single micron-sized particles and allows to obtain Near Edge X-ray Absorption Fine Structure (NEXAFS) spectra with high spatial resolution. Thus, the chemical evolution of the interior of the particles can be followed under reaction conditions. The experiments show that the overall degradation rate of shikimic acid is depending on the relative humidity in a way that is controlled by the decreasing diffusivity of ozone with decreasing humidity. This decreasing diffusivity is most likely linked to the increasing viscosity of the shikimic acid-water mixture. The degradation rate was also depending on particle size, most congruent with a reacto-diffusion limited kinetic case where the reaction progresses only in a shallow layer within the bulk. No gradient in the shikimic acid concentration was observed within the bulk material at any humidity indicating that the diffusivity of shikimic acid is still high enough to allow its equilibration throughout the particles on the time scale of hours at higher humidity and that the thickness of the oxidized layer under dry conditions, where the particles are solid, is beyond the resolution of STXM.

The influence of physical state on shikimic acid ozonolysis: a case for in situ microspectroscopy

NASA Astrophysics Data System (ADS)

Steimer, S. S.; Lampimäki, M.; Coz, E.; Grzinic, G.; Ammann, M.

2014-10-01

Atmospheric soluble organic aerosol material can become solid or semi-solid. Due to increasing viscosity and decreasing diffusivity, this can impact important processes such as gas uptake and reactivity within aerosols containing such substances. This work explores the dependence of shikimic acid ozonolysis on humidity and thereby viscosity. Shikimic acid, a proxy for oxygenated reactive organic material, reacts with O3 in a Criegee-type reaction. We used an environmental microreactor embedded in a scanning transmission X-ray microscope (STXM) to probe this oxidation process. This technique facilitates in situ measurements with single micron-sized particles and allows to obtain near-edge X-ray absorption fine structure (NEXAFS) spectra with high spatial resolution. Thus, the chemical evolution of the interior of the particles can be followed under reaction conditions. The experiments show that the overall degradation rate of shikimic acid is depending on the relative humidity in a way that is controlled by the decreasing diffusivity of ozone with decreasing humidity. This decreasing diffusivity is most likely linked to the increasing viscosity of the shikimic acid-water mixture. The degradation rate was also depending on particle size, most congruent with a reacto-diffusion limited kinetic case where the reaction progresses only in a shallow layer within the bulk. No gradient in the shikimic acid concentration was observed within the bulk material at any humidity indicating that the diffusivity of shikimic acid is still high enough to allow its equilibration throughout the particles on the timescale of hours at higher humidity and that the thickness of the oxidized layer under dry conditions, where the particles are solid, is beyond the resolution of STXM.

Using rapid infrared forming to control interfaces in titanium-matrix composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warrier, S.G.; Lin, R.Y.

1993-03-01

Control of the fiber-matrix reaction during composite fabrication is commonly achieved by shortening the processing time, coating the reinforcement with relatively inert materials, or adding alloying elements to retard the reaction. To minimize the processing time, a rapid IR forming (RIF) technique for metal-matrix composite fabrication has been developed. Experiments have shown that the RIF technique is a quick, simple, and low-cost process to fabricate titanium-alloy matrix composites reinforced with either silicon carbide or carbon fibers. Due to short processing times (typically on the order of 1-2 minutes in an inert atmosphere for composites with up to eight-ply reinforcements), themore » interfacial reaction is limited and well controlled. Composites fabricated by this technique have mechanical properties that are comparable to (in several cases, superior to) those made with conventional diffusion-bonding techniques. 21 refs.« less

Synthesis of Refractory Compounds with Gasless Combustion Reactions.

DTIC Science & Technology

1983-09-01

either Al or Mg as the reducing agent. With Al as the reductant, the stoichiometric equation is 2Mo03 + B203 + 6 Al 2MoB + 3 A120 3 Using the methods...r. rr. . . ;. ., .s . , . . o. . - •-~~- ~- . . . .4 calculated to be 267.3 kcal/mole. With Mg as the reductant, the stoichio- metric equation for the...reaction conditions also are assumed for each model. Conservation of energy and heat diffusion equations are applied to a characteristic control volume

Effect of crowding and confinement on first-passage times: A model study

NASA Astrophysics Data System (ADS)

Antoine, C.; Talbot, J.

2016-06-01

We study the "color dynamics" of a hard-disk fluid confined in an annulus, as well as the corresponding hard-sphere system in three dimensions, using event-driven simulation in order to explore the effect of confinement and self-crowding on the search for targets. We compute the mean first-passage times (MFPTs) of red particles transiting from the outer to the inner boundary as well as those of blue particles passing from the inner to the outer boundary for different packing fractions and geometries. In the steady state the reaction rate, defined as the rate of collision of red particles with the inner boundary, is inversely proportional to the sum of the MFPTs. The reaction rate is wall mediated (ballistic) at low densities and diffusion controlled at higher densities and displays a maximum at intermediate densities. At moderate to high densities, the presence of layering has a strong influence on the search process. The numerical results for the reaction rate and MFPTs are compared with a ballistic model at low densities and a Smoluchowski approach with uniform diffusivities at higher densities. We discuss the reasons for the limited validity of the theoretical approaches. The maximum in the reaction rate is qualitatively well rendered by a Bosanquet-like approach that interpolates between the two regimes. Finally, we compute the position-dependent diffusivity from the MFPTs and observe that it is out of phase with the radial density.

TEMPO/viologen electrochemical heterojunction for diffusion-controlled redox mediation: a highly rectifying bilayer-sandwiched device based on cross-reaction at the interface between dissimilar redox polymers.

PubMed

Tokue, Hiroshi; Oyaizu, Kenichi; Sukegawa, Takashi; Nishide, Hiroyuki

2014-03-26

A couple of totally reversible redox-active molecules, which are different in redox potentials, 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) and viologen (V(2+)), were employed to give rise to a rectified redox conduction effect. Single-layer and bilayer devices were fabricated using polymers containing these sites as pendant groups per repeating unit. The devices were obtained by sandwiching the redox polymer layer(s) with indium tin oxide (ITO)/glass and Pt foil electrodes. Electrochemical measurements of the single-layer device composed of polynorbornene-bearing TEMPO (PTNB) exhibited a diffusion-limited current-voltage response based on the TEMPO(+)/TEMPO exchange reaction, which was almost equivalent to a redox gradient through the PTNB layer depending upon the thickness. The bilayer device gave rise to the current rectification because of the thermodynamically favored cross-reaction between TEMPO(+) and V(+) at the polymer/polymer interface. A current-voltage response obtained for the bilayer device demonstrated a two-step diffusion-limited current behavior as a result of the concurrent V(2+)/V(+) and V(+)/V(0) exchange reactions according to the voltage and suggested that the charge transport process through the device was most likely to be rate-determined by a redox gradient in the polymer layer. Current collection experiments revealed a charge transport balance throughout the device, as a result of the electrochemical stability and robustness of the polymers in both redox states.

Nanoparticle bioconjugates as "bottom-up" assemblies of artifical multienzyme complexes

NASA Astrophysics Data System (ADS)

Keighron, Jacqueline D.

2010-11-01

The sequential enzymes of several metabolic pathways have been shown to exist in close proximity with each other in the living cell. Although not proven in all cases, colocalization may have several implications for the rate of metabolite formation. Proximity between the sequential enzymes of a metabolic pathway has been proposed to have several benefits for the overall rate of metabolite formation. These include reduced diffusion distance for intermediates, sequestering of intermediates from competing pathways and the cytoplasm. Restricted diffusion in the vicinity of an enzyme can also cause the pooling of metabolites, which can alter reaction equilibria to control the rate of reaction through inhibition. Associations of metabolic enzymes are difficult to isolate ex vivo due to the weak interactions believed to colocalize sequential enzymes within the cell. Therefore model systems in which the proximity and diffusion of intermediates within the experiment system are controlled are attractive alternatives to explore the effects of colocalization of sequential enzymes. To this end three model systems for multienzyme complexes have been constructed. Direct adsorption enzyme:gold nanoparticle bioconjugates functionalized with malate dehydrogenase (MDH) and citrate synthase (CS) allow for proximity between to the enzymes to be controlled from the nanometer to micron range. Results show that while the enzymes present in the colocalized and non-colocalized systems compared here behaved differently overall the sequential activity of the pathway was improved by (1) decreasing the diffusion distance between active sites, (2) decreasing the diffusion coefficient of the reaction intermediate to prevent escape into the bulk solution, and (3) decreasing the overall amount of bioconjugate in the solution to prevent the pathway from being inhibited by the buildup of metabolite over time. Layer-by-layer (LBL) assemblies of MDH and CS were used to examine the layering effect of sequential enzymes found in multienzyme complexes such as the pyruvate dehydrogenase complex (PDC). By controlling the orientation of enzymes in the complex (i.e. how deeply embedded each enzyme is) it was hypothesized that differences in sequential activity would determine an optimal orientation for a multienzyme complex. It was determined during the course of these experiments that the polyelectrolyte (PE) assembly itself served to slow diffusion of intermediates, leading to a buildup of oxaloacetate within the PE layers to form a pool of metabolite that equalized the rate of sequential reaction between the different orientations tested. Hexahistidine tag -- Ni(II) nitriliotriacetic acid (NTA) chemistry is an attractive method to control the proximity between sequential enzymes because each enzyme can be bound in a specific orientation, with minimal loss of activity, and the interaction is reversible. Modifying gold nanoparticles or large unilamellar vesicles with this functionality allows for another class of model to be constructed in which proximity between enzymes is dynamic. Some metabolic pathways (such as the de novo purine biosynthetic pathway), have demonstrated dynamic proximity of sequential enzymes in response to specific cellular stimuli. Results indicate that Ni(II)NTA scaffolds immobilize histidine-tagged enzymes non-destructively, with a near 100% reversibility. This model can be used to demonstrate the possible implications of dynamic proximity such as pathway regulation. Insight into the benefits and mechanisms of sequential enzyme colocalization can enhance the general understanding of cellular processes, as well as allow for the development of new and innovative ways to modulate pathway activity. This may provide new designs for treatments of metabolic diseases and cancer, where metabolic pathways are altered.

A Role of the Reaction Kernel in Propagation and Stabilization of Edge Diffusion Flames of C1-C3 Hydrocarbons

NASA Technical Reports Server (NTRS)

Takahashi, Fumiaki; Katta, Viswanath R.

2003-01-01

Diffusion flame stabilization is of essential importance in both Earth-bound combustion systems and spacecraft fire safety. Local extinction, re-ignition, and propagation processes may occur as a result of interactions between the flame zone and vortices or fire-extinguishing agents. By using a computational fluid dynamics code with a detailed chemistry model for methane combustion, the authors have revealed the chemical kinetic structure of the stabilizing region of both jet and flat-plate diffusion flames, predicted the flame stability limit, and proposed diffusion flame attachment and detachment mechanisms in normal and microgravity. Because of the unique geometry of the edge of diffusion flames, radical back-diffusion against the oxygen-rich entrainment dramatically enhanced chain reactions, thus forming a peak reactivity spot, i.e., reaction kernel, responsible for flame holding. The new results have been obtained for the edge diffusion flame propagation and attached flame structure using various C1-C3 hydrocarbons.

A new approach for crystallization of copper(ii) oxide hollow nanostructures with superior catalytic and magnetic response

NASA Astrophysics Data System (ADS)

Singh, Inderjeet; Landfester, Katharina; Chandra, Amreesh; Muñoz-Espí, Rafael

2015-11-01

We report the synthesis of copper(ii) oxide hollow nanostructures at ambient pressure and close to room temperature by applying the soft templating effect provided by the confinement of droplets in miniemulsion systems. Particle growth can be explained by considering a mechanism that involves both diffusion and reaction control. The catalytic reduction of p-nitrophenol in aqueous media is used as a model reaction to prove the catalytic activity of the materials: the synthesized hollow structures show nearly 100 times higher rate constants than solid CuO microspheres. The kinetic behavior and the order of the reduction reaction change due to the increase of the surface area of the hollow structures. The synthesis also leads to modification of physical properties such as magnetism.We report the synthesis of copper(ii) oxide hollow nanostructures at ambient pressure and close to room temperature by applying the soft templating effect provided by the confinement of droplets in miniemulsion systems. Particle growth can be explained by considering a mechanism that involves both diffusion and reaction control. The catalytic reduction of p-nitrophenol in aqueous media is used as a model reaction to prove the catalytic activity of the materials: the synthesized hollow structures show nearly 100 times higher rate constants than solid CuO microspheres. The kinetic behavior and the order of the reduction reaction change due to the increase of the surface area of the hollow structures. The synthesis also leads to modification of physical properties such as magnetism. Electronic supplementary information (ESI) available: Associated structural and morphological analysis, XPS characterization, BET surface area, catalytic measurements, recycle tests of the catalyst, and magnetic characterizations. See DOI: 10.1039/c5nr05579b

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Flexible Hybrid Battery/Pseudocapacitor

NASA Technical Reports Server (NTRS)

Tucker, Dennis S.; Paley, Steven

2015-01-01

Batteries keep devices working by utilizing high energy density, however, they can run down and take tens of minutes to hours to recharge. For rapid power delivery and recharging, high-power density devices, i.e., supercapacitors, are used. The electrochemical processes which occur in batteries and supercapacitors give rise to different charge-storage properties. In lithium ion (Li+) batteries, the insertion of Li+, which enables redox reactions in bulk electrode materials, is diffusion controlled and can be slow. Supercapacitor devices, also known as electrical double-layer capacitors (EDLCs) store charge by adsorption of electrolyte ions onto the surface of electrode materials. No redox reactions are necessary, so the response to changes in potential without diffusion limitations is rapid and leads to high power. However, the charge in EDLCs is confined to the surface, so the energy density is lower than that of batteries.

Diffusion Limited Supercritical Water Oxidation (SCWO) in Microgravity Environments

NASA Technical Reports Server (NTRS)

Hicks, M. C.; Lauver, R. W.; Hegde, U. G.; Sikora, T. J.

2006-01-01

Tests designed to quantify the gravitational effects on thermal mixing and reactant injection in a Supercritical Water Oxidation (SCWO) reactor have recently been performed in the Zero Gravity Facility (ZGF) at NASA s Glenn Research Center. An artificial waste stream, comprising aqueous mixtures of methanol, was pressurized to approximately 250 atm and then heated to 450 C. After uniform temperatures in the reactor were verified, a controlled injection of air was initiated through a specially designed injector to simulate diffusion limited reactions typical in most continuous flow reactors. Results from a thermal mapping of the reaction zone in both 1-g and 0-g environments are compared. Additionally, results of a numerical model of the test configuration are presented to illustrate first order effects on reactant mixing and thermal transport in the absence of gravity.

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

A selection criterion for patterns in reaction–diffusion systems

PubMed Central

2014-01-01

Background Alan Turing’s work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided certain conditions are met. Ever since, extensive work on several kinds of pattern-generating reaction diffusion systems has been done. Nevertheless, prediction of specific patterns is far from being straightforward, and a great deal of interest in deciphering how to generate specific patterns under controlled conditions prevails. Results Techniques allowing one to predict what kind of spatial structure will emerge from reaction–diffusion systems remain unknown. In response to this need, we consider a generalized reaction diffusion system on a planar domain and provide an analytic criterion to determine whether spots or stripes will be formed. Our criterion is motivated by the existence of an associated energy function that allows bringing in the intuition provided by phase transitions phenomena. Conclusions Our criterion is proved rigorously in some situations, generalizing well-known results for the scalar equation where the pattern selection process can be understood in terms of a potential. In more complex settings it is investigated numerically. Our work constitutes a first step towards rigorous pattern prediction in arbitrary geometries/conditions. Advances in this direction are highly applicable to the efficient design of Biotechnology and Developmental Biology experiments, as well as in simplifying the analysis of morphogenetic models. PMID:24476200

Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling

DOE PAGES

Garcia, Andres; Wang, Jing; Windus, Theresa L.; ...

2016-05-20

Statistical mechanical modeling is developed to describe a catalytic conversion reaction A → B c or B t with concentration-dependent selectivity of the products, B c or B t, where reaction occurs inside catalytic particles traversed by narrow linear nanopores. The associated restricted diffusive transport, which in the extreme case is described by single-file diffusion, naturally induces strong concentration gradients. Hence, by comparing kinetic Monte Carlo simulation results with analytic treatments, selectivity is shown to be impacted by strong spatial correlations induced by restricted diffusivity in the presence of reaction and also by a subtle clustering of reactants, A.

Reactive Radial Diffusion Model for the Aging/Sequestration Process

NASA Astrophysics Data System (ADS)

Ginn, T. R.; Basagaoglu, H.; McCoy, B. J.; Scow, K. M.

2001-12-01

A radial diffusion model has been formulated to simulate age-dependent bioavailability of chemical compounds to micro-organisms residing outside (and/or inside) the porous soil particles. Experimental findings in the literature indicate that the sequestration and reduction in bioavailability of contaminants are controlled presumably by the diffusion-limited sorption kinetics and the time-variant desorption process. Here we combine radial-diffusion mass transfer modeling with the exposure-time concept to generate mass-balance equations for the intra- and extra-particle concentrations. The model accomodates reversible sorption kinetics involving sorption time-dependence of the rate coefficients, distinct intra- and extra-particle biodegradation rates; and a dynamic mass interaction between the intra- and extra-particle concentrations arising from the radial diffusion concept. The model explicitly treats multiple particle classes distributed in size and chemical properties in a bulk aquifer or soil volume, which allows the simulation of the sequestration and bioavailability of contaminants in different particle size classes that have distinct diffusion, reaction, and aging properties.

Application of Ionic Liquids in Pot-in-Pot Reactions.

PubMed

Çınar, Simge; Schulz, Michael D; Oyola-Reynoso, Stephanie; Bwambok, David K; Gathiaka, Symon M; Thuo, Martin

2016-02-26

Pot-in-pot reactions are designed such that two reaction media (solvents, catalysts and reagents) are isolated from each other by a polymeric membrane similar to matryoshka dolls (Russian nesting dolls). The first reaction is allowed to progress to completion before triggering the second reaction in which all necessary solvents, reactants, or catalysts are placed except for the starting reagent for the target reaction. With the appropriate trigger, in most cases unidirectional flux, the product of the first reaction is introduced to the second medium allowing a second transformation in the same glass reaction pot--albeit separated by a polymeric membrane. The basis of these reaction systems is the controlled selective flux of one reagent over the other components of the first reaction while maintaining steady-state catalyst concentration in the first "pot". The use of ionic liquids as tools to control chemical potential across the polymeric membranes making the first pot is discussed based on standard diffusion models--Fickian and Payne's models. Besides chemical potential, use of ionic liquids as delivery agent for a small amount of a solvent that slightly swells the polymeric membrane, hence increasing flux, is highlighted. This review highlights the critical role ionic liquids play in site-isolation of multiple catalyzed reactions in a standard pot-in-pot reaction.

Complementary methods for the determination of dissolved oxygen content in perfluorocarbon emulsions and other solutions.

PubMed

Fraker, Christopher A; Mendez, Armando J; Stabler, Cherie L

2011-09-08

Perfluorocarbons (PFCs) are compounds with increased oxygen solubility and effective diffusivity, making them ideal candidates for improving oxygen mass transfer in numerous biological applications. Historically, quantification of the mass transfer characteristics of these liquids has relied on the use of elaborate laboratory equipment and complicated methodologies, such as in-line gas chromatography coupled with temperature-controlled glass fritted diffusion cells. In this work, we present an alternative method for the determination of dissolved oxygen content in PFC emulsions and, by extrapolation, pure PFCs. We implemented a simple stirred oxygen consumption microchamber coupled with an enzymatic reaction for the quantitative determination of oxygen by optical density measurements. Chambers were also custom fitted with lifetime oxygen sensors to permit simultaneous measurement of internal chamber oxygen levels. Analyzing the consumption of oxygen during the enzymatic reaction via recorded oxygen depletion traces, we found a strong degree of correlation between the zero-order reaction rate and the total measured oxygen concentrations, relative to control solutions. The values obtained were in close agreement with published values in the literature, establishing the accuracy of this method. Overall, this method allows for easy, reliable, and reproducible measurements of oxygen content in aqueous solutions, including, but not limited to PFC emulsions.

Study of photosensitization reaction progress in a 96 well plate with photosensitizer rich condition using Talaporfin sodium

NASA Astrophysics Data System (ADS)

Ogawa, Emiyu; Takahashi, Mei; Arai, Tsunenori

2013-02-01

To quantitatively investigate photosensitization reaction in vitro against myocardial cells with photosensitizer rich condition in solution using Talaporfin sodium in the well of a 96 well plate, we studied photosensitization reaction progress in this well. We have proposed non-thermal conduction block of myocardium tissue using the photosensitization reaction with laser irradiation shortly after Talaporfin sodium injection. In above situation, the photosensitizer is located outside the myocardial cells in high concentration. To understand interaction of the photosensitization reaction in which the photosensitizer distributes outside cells, the photosensitization reaction progress in the well was studied. Talaporfin sodium (799.69 MW) solution and a 663 nm diode laser were used. The photosensitizer solution concentrations of 12.5-37.5 μM were employed. The photosensitizer fluorescence with 0.29 W/cm2 in irradiance, which was optimized in previous cell death study, was measured during the laser irradiation until 40 J/cm2. The photosensitizer solution absorbance and dissolved oxygen pressure after the laser irradiation were also measured. We found that the photosensitization reaction progress had 2 distinctive phases of different reaction rate: rapid photosensitization reaction consuming dissolved oxygen and gentle photosensitization reaction with oxygen diffusion from the solution-air boundary. The dissolved oxygen pressure and photosensitizer solution absorbance were 30% and 80% of the initial values after the laser irradiation, respectively. Therefore, oxygen was rate-controlling factor of the photosensitization reaction in the well with the photosensitizer rich condition. In the oxygen diffusion phase, the oxygen pressure was maintained around 40 mmHg until the laser irradiation of 40 J/cm2 and it is similar to that of myocardium tissue in vivo. We think that our 96 well plate in vitro system may simulate PDT in myocardial tissue with photosensitization reaction parameters mentioned above.

Structure dependence of the rate coefficients of hydroxyl radical+aromatic molecule reaction

NASA Astrophysics Data System (ADS)

Wojnárovits, László; Takács, Erzsébet

2013-06-01

The rate coefficients of hydroxyl radical addition to the rings of simple aromatic molecules (kOH) were evaluated based on the literature data. By analyzing the methods of kOH determination and the data obtained the most probable values were selected for the kOH's of individual compounds and thereby the most reliable dataset was created for monosubstituted aromatics and p-substituted phenols. For these compounds the rate coefficients fall in a narrow range between 2×109 mol-1 dm3 s-1 and 1×1010 mol-1 dm3 s-1. Although the values show some regular trend with the electron donating/withdrawing nature of the substituent, the log kOH-σp Hammett substituent constant plots do not give straight lines because these high kOH's are controlled by both, the chemical reactivity and the diffusion. However, the logarithms of the rate coefficients of the chemical reactivity controlled reactions (kchem), are calculated by the equation 1/kOH=1/kchem+1/kdiff, and accepting for the diffusion controlled rate coefficient kdiff=1.1×1010 mol-1 dm3 s-1, show good linear correlation with σp.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

Cure Kinetics of Benzoxazine/Cycloaliphatic Epoxy Resin by Differential Scanning Calorimetry

NASA Astrophysics Data System (ADS)

Gouni, Sreeja Reddy

Understanding the curing kinetics of a thermoset resin has a significant importance in developing and optimizing curing cycles in various industrial manufacturing processes. This can assist in improving the quality of final product and minimizing the manufacturing-associated costs. One approach towards developing such an understanding is to formulate kinetic models that can be used to optimize curing time and temperature to reach a full cure state or to determine time to apply pressure in an autoclave process. Various phenomenological reaction models have been used in the literature to successfully predict the kinetic behavior of a thermoset system. The current research work was designed to investigate the cure kinetics of Bisphenol-A based Benzoxazine (BZ-a) and Cycloaliphatic epoxy resin (CER) system under isothermal and nonisothermal conditions by Differential Scanning Calorimetry (DSC). The cure characteristics of BZ-a/CER copolymer systems with 75/25 wt% and 50/50 wt% have been studied and compared to that of pure benzoxazine under nonisothermal conditions. The DSC thermograms exhibited by these BZ-a/CER copolymer systems showed a single exothermic peak, indicating that the reactions between benzoxazine-benzoxazine monomers and benzoxazine-cycloaliphatic epoxy resin were interactive and occurred simultaneously. The Kissinger method and isoconversional methods including Ozawa-Flynn-Wall and Freidman were employed to obtain the activation energy values and determine the nature of the reaction. The cure behavior and the kinetic parameters were determined by adopting a single step autocatalytic model based on Kamal and Sourour phenomenological reaction model. The model was found to suitably describe the cure kinetics of copolymer system prior to the diffusion-control reaction. Analyzing and understanding the thermoset resin system under isothermal conditions is also important since it is the most common practice in the industry. The BZ-a/CER copolymer system with 75/25 wt% ratio which exhibited high glass transition temperature compared to polybenzoxazine was investigated under isothermal conditions. The copolymer system exhibited the maximum reaction rate at an intermediate degree of cure (20 to 40%), indicating that the reaction was autocatalytic. Similar to the nonisothermal cure kinetics, Kamal and Sourour phenomenological reaction model was adopted to determine the kinetic behavior of the system. The theoretical values based on the developed model showed a deviation from the obtained experimental values, which indicated the change in kinetics from a reaction-controlled mechanism to a diffusion-controlled mechanism with increasing reaction conversion. To substantiate the hypothesis, Fournier et al's diffusion factor was introduced into the model, resulting in an agreement between the theoretical and experimental values. The changes in cross-linking density and the glass transition temperature (Tg) with increasing epoxy concentration were investigated under Dynamic Mechanical Analyzer (DMA). The BZ-a/CER copolymer system with the epoxy content of less than 40 wt% exhibited the greatest Tg and cross-linking density compared to benzoxazine homopolymer and other ratios.

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

Modeling the suppression of boron transient enhanced diffusion in silicon by substitutional carbon incorporation

NASA Astrophysics Data System (ADS)

Ngau, Julie L.; Griffin, Peter B.; Plummer, James D.

2001-08-01

Recent work has indicated that the suppression of boron transient enhanced diffusion (TED) in carbon-rich Si is caused by nonequilibrium Si point defect concentrations, specifically the undersaturation of Si self-interstitials, that result from the coupled out-diffusion of carbon interstitials via the kick-out and Frank-Turnbull reactions. This study of boron TED reduction in Si1-x-yGexCy during 750 °C inert anneals has revealed that the use of an additional reaction that further reduces the Si self-interstitial concentration is necessary to describe accurately the time evolved diffusion behavior of boron. In this article, we present a comprehensive model which includes {311} defects, boron-interstitial clusters, a carbon kick-out reaction, a carbon Frank-Turnbull reaction, and a carbon interstitial-carbon substitutional (CiCs) pairing reaction that successfully simulates carbon suppression of boron TED at 750 °C for anneal times ranging from 10 s to 60 min.

The Time Dependent Propensity Function for Acceleration of Spatial Stochastic Simulation of Reaction-Diffusion Systems

PubMed Central

Wu, Sheng; Li, Hong; Petzold, Linda R.

2015-01-01

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. PMID:26609185

Efficient kinetic Monte Carlo method for reaction-diffusion problems with spatially varying annihilation rates

NASA Astrophysics Data System (ADS)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

PubMed Central

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Materials Outgassing Rate Decay in Vacuum at Isothermal Conditions

NASA Technical Reports Server (NTRS)

Huang, Alvin Y.; Kastanas, George N.; Kramer, Leonard; Soares, Carlos E.; Mikatarian, Ronald R.

2016-01-01

As a laboratory for scientific research, the International Space Station has been in Low Earth Orbit for nearly 20 years and is expected to be on-orbit for another 10 years. The ISS has been maintaining a relatively pristine contamination environment for science payloads. Materials outgassing induced contamination is currently the dominant source for sensitive surfaces on ISS and modeling the outgassing rate decay over a 20 to 30 year period is challenging. Materials outgassing is described herein as a diffusion-reaction process using ASTM E 1559 rate data. The observation of -1/2 (diffusion) or non-integers (reaction limited) as rate decay exponents for common ISS materials indicate classical reaction kinetics is unsatisfactory in modeling materials outgassing. Non-randomness of reactant concentrations at the interface is the source of this deviation from classical reaction kinetics. A diffusion limited decay was adopted as the result of the correlation of the contaminant layer thicknesses on returned ISS hardware, the existence of high outgassing silicone exhibiting near diffusion limited decay, and the confirmation of non-depleted material after ten years in the Low Earth Orbit.Keywords: Materials Outgassing, ASTM E 1559, Reaction Kinetics, Diffusion, Space Environments Effects, Contamination

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.

PubMed

Peng, Rui; Zhao, Xiao-Qiang

2016-02-01

In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.

A Modified Consumer Inkjet for Spatiotemporal Control of Gene Expression

PubMed Central

Cohen, Daniel J.; Morfino, Roberto C.; Maharbiz, Michel M.

2009-01-01

This paper presents a low-cost inkjet dosing system capable of continuous, two-dimensional spatiotemporal regulation of gene expression via delivery of diffusible regulators to a custom-mounted gel culture of E. coli. A consumer-grade, inkjet printer was adapted for chemical printing; E. coli cultures were grown on 750 µm thick agar embedded in micro-wells machined into commercial compact discs. Spatio-temporal regulation of the lac operon was demonstrated via the printing of patterns of lactose and glucose directly into the cultures; X-Gal blue patterns were used for visual feedback. We demonstrate how the bistable nature of the lac operon's feedback, when perturbed by patterning lactose (inducer) and glucose (inhibitor), can lead to coordination of cell expression patterns across a field in ways that mimic motifs seen in developmental biology. Examples of this include sharp boundaries and the generation of traveling waves of mRNA expression. To our knowledge, this is the first demonstration of reaction-diffusion effects in the well-studied lac operon. A finite element reaction-diffusion model of the lac operon is also presented which predicts pattern formation with good fidelity. PMID:19763256

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

DOE PAGES

Hong, Liang; Li, Linsen; Chen-Wiegart, Yuchen-Karen; ...

2017-10-30

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Liang; Li, Linsen; Chen-Wiegart, Yuchen-Karen

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Liang; Chen-Wiegart, Yu-Chen K.

2017-10-30

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism andmore » the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.« less

Intensification of the Process of Flame Combustion of a Pulverized Coal Fuel

NASA Astrophysics Data System (ADS)

Popov, V. I.

2017-11-01

Consideration is given to a method of mechanoactivation intensification of the flame combustion of a pulverized coal fuel through the formation of a stressed state for the microstructure of its particles; the method is based on the use of the regularities of their external (diffusion) and internal (relaxation) kinetics. A study has been made of mechanoactivation nonequilibrium processes that occur in fuel particles during the induced relaxation of their stressed state with a resumed mobility of the microstructure of the particles and intensify diffusion-controlled chemical reactions in them under the assumption that the time of these reactions is much shorter than the times of mechanical action on a particle and of stress relaxation in it. The influence of the diffusion and relaxation factors on the burnup time of a fuel particle and on the flame distance has been analyzed. Ranges of variation in the parameters of flame combustion have been singled out in which the flame distance is determined by the mechanisms of combustion of the fuel and of mixing of combustion products.

The Oxidation Kinetics of Continuous Carbon Fibers in a Cracked Ceramic Matrix Composite. Degree awarded by Case Western Reserve Univ., May 2000

NASA Technical Reports Server (NTRS)

Halbig, Michael C.

2001-01-01

Experimental observations and results suggest two primary regimes as a function of temperature, i.e., diffusion and reaction controlled kinetics. Thermogravimetric analysis of carbon fiber in flowing oxygen gave an activation energy of 64.1 kJ/mol in the temperature range of 500 to 600 C and an apparent activation energy of 7.6 kJ/mol for temperatures from 600 to 1400 C. When C/SiC composite material was unstressed, matrix effects at temperatures from 900 to 1400 C protected the internal fibers. When under stress, self-protection was not observed. Increasing the stress from 10 to 25 ksi caused a 67 to 82 percent reduction in times to failure at temperatures from 750 to 1500 C. Based on experimental results, observation, and theory, a finite difference model was developed, which simulates the diffusion of oxygen into a matrix crack that is bridged by carbon fibers. The model allows the influence of important variables on oxidation kinetics to be studied systematically, i.e., temperature, reaction rate constant, diffusion coefficient, environment, and sample geometry.

Chlorination of lanthanum oxide.

PubMed

Gaviría, Juan P; Navarro, Lucas G; Bohé, Ana E

2012-03-08

The reactive system La(2)O(3)(s)-Cl(2)(g) was studied in the temperature range 260-950 °C. The reaction course was followed by thermogravimetry, and the solids involved were characterized by X-ray diffraction, scanning electron microscopy, and energy dispersive spectroscopy. The results showed that the reaction leads to the formation of solid LaOCl, and for temperatures above 850 °C, the lanthanum oxychloride is chlorinated, producing LaCl(3)(l). The formation of the oxychloride progresses through a nucleation and growth mechanism, and the kinetic analysis showed that at temperatures below 325 °C the system is under chemical control. The influence of diffusive processes on the kinetics of production of LaOCl was evaluated by studying the effect of the reactive gas flow rate, the mass of the sample, and the chlorine diffusion through the boundary layer surrounding the solid sample. The conversion curves were analyzed and fitted according to the Johnson-Mehl-Avrami description, and the reaction order with respect to the chlorine partial pressure was obtained by varying this partial pressure between 10 and 70 kPa. The rate equation was obtained, which includes the influence of the temperature, chlorine partial pressure, and reaction degree.

The Kinetics of TiAl3 Formation in Explosively Welded Ti-Al Multilayers During Heat Treatment

NASA Astrophysics Data System (ADS)

Foadian, Farzad; Soltanieh, Mansour; Adeli, Mandana; Etminanbakhsh, Majid

2016-10-01

Metallic-intermetallic laminate (MIL) composites, including Ti/TiAl3 composite, are promising materials for many applications, namely, in the aerospace industry. One method to produce Ti/TiAl3 laminate composite is to provide close attachment between desired number of titanium and aluminum plates, so that by applying heat and/or pressure, the formation of intermetallic phases between the layers becomes possible. In this work, explosive welding was used to make a strong bond between six alternative Ti and Al layers. The welded samples were annealed at three different temperatures: 903 K, 873 K, and 843 K (630 °C, 600 °C, and 570 °C) in ambient atmosphere, and the variation of the intermetallic layer thickness was used to study the growth kinetics. Microstructural investigations were carried out on the welded and annealed samples using optical microscopy and scanning electron microscopy equipped with energy-dispersive X-ray spectrometer (EDS). X-ray diffraction (XRD) technique was used to identify the formed intermetallic phases. It was found that at each temperature, two different mechanisms govern the process: reaction controlled and diffusion controlled. The calculated values of activation energies for reaction-controlled and diffusion-controlled mechanisms are 232.1 and 17.4 kJ, respectively.

Reactions of Azine Anions with Nitrogen and Oxygen Atoms: Implications for Titan's Upper Atmosphere and Interstellar Chemistry.

PubMed

Wang, Zhe-Chen; Cole, Callie A; Demarais, Nicholas J; Snow, Theodore P; Bierbaum, Veronica M

2015-08-26

Azines are important in many extraterrestrial environments, from the atmosphere of Titan to the interstellar medium. They have been implicated as possible carriers of the diffuse interstellar bands in astronomy, indicating their persistence in interstellar space. Most importantly, they constitute the basic building blocks of DNA and RNA, so their chemical reactivity in these environments has significant astrobiological implications. In addition, N and O atoms are widely observed in the ISM and in the ionospheres of planets and moons. However, the chemical reactions of molecular anions with abundant interstellar and atmospheric atomic species are largely unexplored. In this paper, gas-phase reactions of deprotonated anions of benzene, pyridine, pyridazine, pyrimidine, pyrazine, and s-triazine with N and O atoms are studied both experimentally and computationally. In all cases, the major reaction channel is associative electron detachment; these reactions are particularly important since they control the balance between negative ions and free electron densities. The reactions of the azine anions with N atoms exhibit larger rate constants than reactions of corresponding chain anions. The reactions of azine anions with O atoms are even more rapid, with complex product patterns for different reactants. The mechanisms are studied theoretically by employing density functional theory; spin conversion is found to be important in determining some product distributions. The rich gas-phase chemistry observed in this work provides a better understanding of ion-atom reactions and their contributions to ionospheric chemistry as well as the chemical processing that occurs in the boundary layers between diffuse and dense interstellar clouds.

Radiosensitization of DNA by Cisplatin Adducts Results from an Increase in the Rate Constant for the Reaction with Hydrated Electrons and Formation of Pt(I).

PubMed

Behmand, B; Marignier, J-L; Mostafavi, M; Wagner, J R; Hunting, D J; Sanche, L

2015-07-30

Pulse radiolysis measurements of the decay of hydrated electrons in solutions containing different concentrations of the oligonucleotide GTG with and without a cisplatin adduct show that the presence of a cisplatin moiety accelerates the reaction between hydrated electrons and the oligonucleotide. The rate constant of the reaction is found to be 2.23 × 10(10) mol(-1) L s(-1), which indicates that it is diffusion controlled. In addition, we show for the first time the formation of a Pt(I) intermediate as a result of the reaction of hydrated electrons with GTG-cisplatin. A putative reaction mechanism is proposed, which may form the basis of the radiosensitization of cancer cells in concomitant chemoradiation therapy with cisplatin.

An electromechanical based deformable model for soft tissue simulation.

PubMed

Zhong, Yongmin; Shirinzadeh, Bijan; Smith, Julian; Gu, Chengfan

2009-11-01

Soft tissue deformation is of great importance to surgery simulation. Although a significant amount of research efforts have been dedicated to simulating the behaviours of soft tissues, modelling of soft tissue deformation is still a challenging problem. This paper presents a new deformable model for simulation of soft tissue deformation from the electromechanical viewpoint of soft tissues. Soft tissue deformation is formulated as a reaction-diffusion process coupled with a mechanical load. The mechanical load applied to a soft tissue to cause a deformation is incorporated into the reaction-diffusion system, and consequently distributed among mass points of the soft tissue. Reaction-diffusion of mechanical load and non-rigid mechanics of motion are combined to govern the simulation dynamics of soft tissue deformation. An improved reaction-diffusion model is developed to describe the distribution of the mechanical load in soft tissues. A three-layer artificial cellular neural network is constructed to solve the reaction-diffusion model for real-time simulation of soft tissue deformation. A gradient based method is established to derive internal forces from the distribution of the mechanical load. Integration with a haptic device has also been achieved to simulate soft tissue deformation with haptic feedback. The proposed methodology does not only predict the typical behaviours of living tissues, but it also accepts both local and large-range deformations. It also accommodates isotropic, anisotropic and inhomogeneous deformations by simple modification of diffusion coefficients.

Comparative study of silver nanoparticle permeation using Side-Bi-Side and Franz diffusion cells

NASA Astrophysics Data System (ADS)

Trbojevich, Raul A.; Fernandez, Avelina; Watanabe, Fumiya; Mustafa, Thikra; Bryant, Matthew S.

2016-03-01

Better understanding the mechanisms of nanoparticle permeation through membranes and packaging polymers has important implications for the evaluation of drug transdermal uptake, in food safety and the environmental implications of nanotechnology. In this study, permeation of 21 nm diameter silver nanoparticles (AgNPs) was tested using Side-Bi-Side and Franz static diffusion cells through hydrophilic 0.1 and 0.05 µm pore diameter 125 µm thick synthetic cellulose membranes, and 16 and 120 µm thick low-density polyethylene (LDPE) films. Experiments performed with LDPE films discarded permeation of AgNPs or Ag ions over the investigated time-frame in both diffusion systems. But controlled release of AgNPs has been quantified using semipermeable hydrophilic membranes. The permeation followed a quasi-linear time-dependent model during the experimental time-frame, which represents surface reaction-limited permeation. Diffusive flux, diffusion coefficients, and membrane permeability were determined as a function of pore size and diffusion model. Concentration gradient and pore size were key to understand mass transfer phenomena in the diffusion systems.

Osmotic propulsion: the osmotic motor.

PubMed

Córdova-Figueroa, Ubaldo M; Brady, John F

2008-04-18

A model for self-propulsion of a colloidal particle--the osmotic motor--immersed in a dispersion of "bath" particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.

Osmotic Propulsion: The Osmotic Motor

NASA Astrophysics Data System (ADS)

Córdova-Figueroa, Ubaldo M.; Brady, John F.

2008-04-01

A model for self-propulsion of a colloidal particle—the osmotic motor—immersed in a dispersion of “bath” particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.

Electron Conduction in Organic Solutions

DTIC Science & Technology

1991-11-10

solutions, both eq(3) and eq(4) are diffusion controlled reactions, in agreement with Geske and Maid’s polarographic study of NB 10 . The decrease in... Geske , D.H., Maki, A. H. J. Am. Chem. Soc. 1960, 82, 2671. 11. Keq is calculated using EI/2 values obtained in dilute solutions (ref. 10) for eq. (3) (El

A reaction-diffusion model of the Darien Gap Sterile Insect Release Method

NASA Astrophysics Data System (ADS)

Alford, John G.

2015-05-01

The Sterile Insect Release Method (SIRM) is used as a biological control for invasive insect species. SIRM involves introducing large quantities of sterilized male insects into a wild population of invading insects. A fertile/sterile mating produces offspring that are not viable and the wild insect population will eventually be eradicated. A U.S. government program maintains a permanent sterile fly barrier zone in the Darien Gap between Panama and Columbia to control the screwworm fly (Cochliomyia Hominivorax), an insect that feeds off of living tissue in mammals and has devastating effects on livestock. This barrier zone is maintained by regular releases of massive quantities of sterilized male screwworm flies from aircraft. We analyze a reaction-diffusion model of the Darien Gap barrier zone. Simulations of the model equations yield two types of spatially inhomogeneous steady-state solutions representing a sterile fly barrier that does not prevent invasion and a barrier that does prevent invasion. We investigate steady-state solutions using both phase plane methods and monotone iteration methods and describe how barrier width and the sterile fly release rate affects steady-state behavior.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Modelling and simulating reaction-diffusion systems using coloured Petri nets.

PubMed

Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming

2014-10-01

Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Interface Reactions and Synthetic Reaction of Composite Systems

PubMed Central

Park, Joon Sik; Kim, Jeong Min

2010-01-01

Interface reactions in composite systems often determine their overall properties, since product phases usually formed at interfaces during composite fabrication processing make up a large portion of the composites. Since most composite materials represent a ternary or higher order materials system, many studies have focused on analyses of diffusion phenomena and kinetics in multicomponent systems. However, the understanding of the kinetic behavior increases the complexity, since the kinetics of each component during interdiffusion reactions need to be defined for interpreting composite behaviors. From this standpoint, it is important to clarify the interface reactions for producing compatible interfaces with desired product phases. A thermodynamic evaluation such as a chemical potential of involving components can provide an understanding of the diffusion reactions, which govern diffusion pathways and product phase formation. A strategic approach for designing compatible interfaces is discussed in terms of chemical potential diagrams and interface morphology, with some material examples.

Reaction-diffusion processes and metapopulation models on duplex networks

NASA Astrophysics Data System (ADS)

Xuan, Qi; Du, Fang; Yu, Li; Chen, Guanrong

2013-03-01

Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps β→α and α+β→2β, on duplex networks where links are classified into two groups: α and β links used to transfer α and β particles, which, along with the corresponding nodes, consist of an α subnetwork and a β subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.

Kinetics of the solid-state carbothermic reduction of wessel manganese ores

NASA Astrophysics Data System (ADS)

Akdogan, Guven; Eric, R. Hurman

1995-02-01

Reduction of manganese ores from the Wessel mine of South Africa has been investigated in the temperature range 1100 °C to 1350 °C with pure graphite as the reductant under argon atmosphere. The rate and degree of reduction were found to increase with increasing temperature and decreasing particle sizes of both the ore and the graphite. The reduction was found to occur in two stages: (1) The first stage includes the rapid reduction of higher oxides of manganese and iron to MnO and FeO. The rate control appears to be mixed, both inward diffusion of CO and outward diffusion of CO2 across the porous product layer, and the reaction of carbon monoxide on the pore walls of the oxide phase play important roles. The values of effective CO-CO2 diffusivities generated by the mathematical model are in the range from 2.15 x 10-5 to 6.17 X 10-5 cm2.s-1 for different ores at 1300 °C. Apparent activation energies range from 81. 3 to 94.6 kJ/kg/mol. (2) The second stage is slower during which MnO and FeO are reduced to mixed carbide of iron and manganese. The chemical reaction between the manganous oxide and carbon dissolved in the metal phase or metal carbide seems to be the rate-controlling process The rate constant of chemical reaction between MnO and carbide on the surface of the impervious core was found to lie in the range from 1.53 x 10-8 to 1.32 x 10-7 mol . s-1 . cm-2. Apparent activation energies calculated are in the range from 102.1 to 141.7 kJ/kg/mol.

Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes.

PubMed

Chevalier, Michael W; El-Samad, Hana

2012-08-28

Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

Probing the type of anomalous diffusion with single-particle tracking.

PubMed

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

Many reactions in complex fluids, e.g. signaling cascades in the cytoplasm of living cells, are governed by a diffusion-driven encounter of reactants. Yet, diffusion in complex fluids often exhibits an anomalous characteristic ('subdiffusion'). Since different types of subdiffusion have distinct effects on timing and equilibria of chemical reactions, a thorough determination of the reactants' type of random walk is key to a quantitative understanding of reactions in complex fluids. Here we introduce a straightforward and simple approach for determining the type of subdiffusion from single-particle tracking data. Unlike previous approaches, our method also is sensitive to transient subdiffusion phenomena, e.g. obstructed diffusion below the percolation threshold. We validate our strategy with data from experiment and simulation.

Functional tooth restoration utilising split germs through re-regionalisation of the tooth-forming field

PubMed Central

Yamamoto, Naomi; Oshima, Masamitsu; Tanaka, Chie; Ogawa, Miho; Nakajima, Kei; Ishida, Kentaro; Moriyama, Keiji; Tsuji, Takashi

2015-01-01

The tooth is an ectodermal organ that arises from a tooth germ under the regulation of reciprocal epithelial-mesenchymal interactions. Tooth morphogenesis occurs in the tooth-forming field as a result of reaction-diffusion waves of specific gene expression patterns. Here, we developed a novel mechanical ligation method for splitting tooth germs to artificially regulate the molecules that control tooth morphology. The split tooth germs successfully developed into multiple correct teeth through the re-regionalisation of the tooth-forming field, which is regulated by reaction-diffusion waves in response to mechanical force. Furthermore, split teeth erupted into the oral cavity and restored physiological tooth function, including mastication, periodontal ligament function and responsiveness to noxious stimuli. Thus, this study presents a novel tooth regenerative technology based on split tooth germs and the re-regionalisation of the tooth-forming field by artificial mechanical force. PMID:26673152

Mathematical Modeling of Decarburization in Levitated Fe-Cr-C Droplets

NASA Astrophysics Data System (ADS)

Gao, Lei; Shi, Zhe; Yang, Yindong; Li, Donghui; Zhang, Guifang; McLean, Alexander; Chattopadhyay, Kinnor

2018-04-01

Using carbon dioxide to replace oxygen as an alternative oxidant gas has proven to be a viable solution in the decarburization process, with potential for industrial applications. In a recent study, the transport phenomena governing the carbon dioxide decarburization process through the use of electromagnetic levitation (EML) was examined. CO2/CO mass transfer was found to be the principal reaction rate control step, as a result gas diffusion has gained significant attention. In the present study, gas diffusion during decarburization process was investigated using computational fluid dynamics (CFD) modeling coupled with chemical reactions. The resulting model was verified through experimental data in a published paper, and employed to provide insights on phenomena typically unobservable through experiments. Based on the results, a new correction of the Frössling equation was presented which better represents the mass transfer phenomena at the metal-gas interface within the range of this research.

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.

PubMed

Yamada, H; Nakagaki, T; Baker, R E; Maini, P K

2007-06-01

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

Two-dimensional wave patterns of spreading depolarization: Retracting, re-entrant, and stationary waves

NASA Astrophysics Data System (ADS)

Dahlem, Markus A.; Graf, Rudolf; Strong, Anthony J.; Dreier, Jens P.; Dahlem, Yuliya A.; Sieber, Michaela; Hanke, Wolfgang; Podoll, Klaus; Schöll, Eckehard

2010-06-01

We present spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves that repeatedly spread across gyrencephalic feline cortex observed by laser speckle flowmetry. A mathematical framework of reaction-diffusion systems with augmented transmission capabilities is developed to explain the emergence and transitions between these patterns. Our prediction is that the observed patterns are reaction-diffusion patterns controlled and modulated by weak nonlocal coupling such as long-range, time-delayed, and global coupling. The described spatio-temporal characteristics of SD are of important clinical relevance under conditions of migraine and stroke. In stroke, the emergence of re-entrant SD waves is believed to worsen outcome. In migraine, retracting SD wave segments cause neurological symptoms and transitions to stationary SD wave patterns may cause persistent symptoms without evidence from noninvasive imaging of infarction.

Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca2 + and its dyes

NASA Astrophysics Data System (ADS)

Sigaut, Lorena; Villarruel, Cecilia; Ponce, María Laura; Ponce Dawson, Silvina

2017-06-01

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca2 +) and single-wavelength dyes that increase their fluorescence upon Ca2 + binding. We validate the approach with experiments performed in aqueous solutions containing Ca2 + and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids

NASA Astrophysics Data System (ADS)

Bratsun, Dmitry; Mizev, Alexey; Mosheva, Elena; Kostarev, Konstantin

2017-11-01

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A +B →S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

Distance-dependent diffusion-controlled reaction of •NO and O2•- at chemical equilibrium with ONOO-.

PubMed

Botti, Horacio; Möller, Matías N; Steinmann, Daniel; Nauser, Thomas; Koppenol, Willem H; Denicola, Ana; Radi, Rafael

2010-12-16

The fast reaction of (•)NO and O(2)(•-) to give ONOO(-) has been extensively studied at irreversible conditions, but the reasons for the wide variations in observed forward rate constants (3.8 ≤ k(f) ≤ 20 × 10(9) M(-1) s(-1)) remain unexplained. We characterized the diffusion-dependent aqueous (pH > 12) chemical equilibrium of the form (•)NO + O(2)(•-) = ONOO(-) with respect to its dependence on temperature, viscosity, and [ONOO(-)](eq) by determining [ONOO(-)](eq) and [(•)NO](eq). The equilibrium forward reaction rate constant (k(f)(eq)) has negative activation energy, in contrast to that found under irreversible conditions. In contradiction to the law of mass action, we demonstrate that the equilibrium constant depends on ONOO(-) concentration. Therefore, a wide range of k(f)(eq) values could be derived (7.5-21 × 10(9) M(-1) s(-1)). Of general interest, the variations in k(f) can thus be explained by its dependence on the distance between ONOO(-) particles (sites of generation of (•)NO and O(2)(•-)).

Reduction of carbon contamination during the melting process of Czochralski silicon crystal growth

NASA Astrophysics Data System (ADS)

Liu, Xin; Gao, Bing; Nakano, Satoshi; Kakimoto, Koichi

2017-09-01

Generation, incorporation, and accumulation of carbon (C) were investigated by transient global simulations of heat and mass transport during the melting process of Czochralski silicon (CZ-Si) crystal growth. Contact reaction between the quartz crucible and graphite susceptor was introduced as an extra origin of C contamination. The contribution of the contact reaction on C accumulation is affected by the back diffusion of C monoxide (CO) from the gap between the gas-guide and the crucible. The effect of the gas-guide coating on C reduction was elucidated by taking the reaction between the silicon carbide (SiC) coating and gaseous Si monoxide (SiO) into account. Application of the SiC coating on the gas-guide could effectively reduce the C contamination because of its higher thermochemical stability relative to that of graphite. Gas flow control on the back diffusion of the generated CO was examined by the parametric study of argon gas flow rate. Generation and back diffusion of CO were both effectively suppressed by the increase in the gas flow rate because of the high Péclet number of species transport. Strategies for C content reduction were discussed by analyzing the mechanisms of C accumulation process. According to the elucidated mechanisms of C accumulation, the final C content depends on the growth duration and contamination flux at the gas/melt interface.

Multi-Algorithm Particle Simulations with Spatiocyte.

PubMed

Arjunan, Satya N V; Takahashi, Koichi

2017-01-01

As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (filament), 2D (membrane), and 3D (cytosol) compartments. The implications of crowded regions in the cell can be investigated because each diffusing molecule has spatial dimensions. Spatiocyte adopts multi-algorithm and multi-timescale frameworks to simulate models that simultaneously employ deterministic, stochastic, and particle reaction-diffusion algorithms. Comparison of light microscopy images to simulation snapshots is supported by Spatiocyte microscopy visualization and molecule tagging features. Spatiocyte is open-source software and is freely available at http://spatiocyte.org .

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA.

PubMed

Turkin, Alexander; van Oijen, Antoine M; Turkin, Anatoliy A

2015-01-01

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Boundary mediated position control of traveling waves

NASA Astrophysics Data System (ADS)

Martens, Steffen; Ziepke, Alexander; Engel, Harald

Reaction control is an essential task in biological systems and chemical process industry. Often, the excitable medium supporting wave propagation exhibits an irregular shape and/or is limited in size. In particular, the analytic treatment of wave phenomena is notoriously difficult due to the spatial modulation of the domain's. Recently, we have provided a first systematic treatment by applying asymptotic perturbation analysis leading to an approximate description that involves a reduction of dimensionality; the 3D RD equation with spatially dependent NFBCs on the reactants reduces to a 1D reaction-diffusion-advection equation. Here, we present a novel method to control the position ϕ (t) of traveling waves in modulated domains according to a prespecified protocol of motion. Given this protocol, the ``optimal'' geometry of reactive domains Q (x) is found as the solution of the perturbatively derived equation of motion. Noteworthy, such a boundary control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary. German Science Foundation DFG through the SFB 910 ''Control of Self-Organizing Nonlinear Systems''.

Kinetic analysis of the interactions between calcium ferrite and coal char for chemical looping gasification applications: Identifying reduction routes and modes of oxygen transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riley, Jarrett; Siriwardane, Ranjani; Tian, Hanjing

Chemical Looping Gasification (CLG) is an emerging technology that shows promise for efficient coal gasification by eliminating the need for energy intensive gas separations to achieve a non-nitrogen diluted syngas stream. Oxygen from oxygen carriers, such as CaFe 2O 4, are used for coal gasification in place of conventionally produced gaseous oxygen from cryogenic separation of air. These oxygen carriers are unique for their ability to selectively oxidize coal to form syngas and show limited reactivity with syngas components (H 2, CO). To gain a deeper understanding of how these unique oxygen carriers perform and to offer a first attemptmore » at the reaction modeling of solid mediated interactions of this nature, this study was carried out to determine the kinetic parameters associated with the selective oxidation of coal derived char (Wyodak and Illinois #6) with a metal ferrite, CaFe 2O 4. Using thermogravimetric analysis (TGA) coupled with mass spectrometry, the selective oxygen release of metal ferrite in the presence of char by proximal contact was examined. The application of combinatory model fitting approaches was used to describe controlling resistances during oxygen release. A combination of the modified shrinking core model (SCM) with planar oxygen ion diffusion control and reaction order based models was used for kinetic parameter determination. CaFe 2O 4 particle size plays a major role in the prevailing mode of oxygen release. Particle sizes on the order of 40–50 μm tend to favor first order kinetically controlled regimes independent of geometric and diffusion controls. The probability for oxygen ion diffusion controlling regimes increased when the particle size range of the oxygen carrier was increased up to 350 μm. Char type also impacted the prevalence of the controlling regime. Higher ranked chars react in a slower manner, limiting the gradient for oxygen ion release from the oxygen carrier. Activation energies determined for this process range from 120–200kJ/mol and oxygen ion diffusion coefficients are on the order of 10-8 cm 2/s. It is suggested that oxygen ion movement is regulated by lattice diffusion out of partially reduced phases (Ca 2Fe 2O 5) and through reduced outer layers composed of CaO and Fe. The controlled movement of oxygen ions influences the rate of carbon oxidation in the char and therefore the selectivity towards partial oxidation products, which are desirable in CLG applications.« less

Kinetic analysis of the interactions between calcium ferrite and coal char for chemical looping gasification applications: Identifying reduction routes and modes of oxygen transfer

DOE PAGES

Riley, Jarrett; Siriwardane, Ranjani; Tian, Hanjing; ...

2017-05-20

Chemical Looping Gasification (CLG) is an emerging technology that shows promise for efficient coal gasification by eliminating the need for energy intensive gas separations to achieve a non-nitrogen diluted syngas stream. Oxygen from oxygen carriers, such as CaFe 2O 4, are used for coal gasification in place of conventionally produced gaseous oxygen from cryogenic separation of air. These oxygen carriers are unique for their ability to selectively oxidize coal to form syngas and show limited reactivity with syngas components (H 2, CO). To gain a deeper understanding of how these unique oxygen carriers perform and to offer a first attemptmore » at the reaction modeling of solid mediated interactions of this nature, this study was carried out to determine the kinetic parameters associated with the selective oxidation of coal derived char (Wyodak and Illinois #6) with a metal ferrite, CaFe 2O 4. Using thermogravimetric analysis (TGA) coupled with mass spectrometry, the selective oxygen release of metal ferrite in the presence of char by proximal contact was examined. The application of combinatory model fitting approaches was used to describe controlling resistances during oxygen release. A combination of the modified shrinking core model (SCM) with planar oxygen ion diffusion control and reaction order based models was used for kinetic parameter determination. CaFe 2O 4 particle size plays a major role in the prevailing mode of oxygen release. Particle sizes on the order of 40–50 μm tend to favor first order kinetically controlled regimes independent of geometric and diffusion controls. The probability for oxygen ion diffusion controlling regimes increased when the particle size range of the oxygen carrier was increased up to 350 μm. Char type also impacted the prevalence of the controlling regime. Higher ranked chars react in a slower manner, limiting the gradient for oxygen ion release from the oxygen carrier. Activation energies determined for this process range from 120–200kJ/mol and oxygen ion diffusion coefficients are on the order of 10-8 cm 2/s. It is suggested that oxygen ion movement is regulated by lattice diffusion out of partially reduced phases (Ca 2Fe 2O 5) and through reduced outer layers composed of CaO and Fe. The controlled movement of oxygen ions influences the rate of carbon oxidation in the char and therefore the selectivity towards partial oxidation products, which are desirable in CLG applications.« less

Optical calorimetry in microfluidic droplets.

PubMed

Chamoun, Jacob; Pattekar, Ashish; Afshinmanesh, Farzaneh; Martini, Joerg; Recht, Michael I

2018-05-29

A novel microfluidic calorimeter that measures the enthalpy change of reactions occurring in 100 μm diameter aqueous droplets in fluoropolymer oil has been developed. The aqueous reactants flow into a microfluidic droplet generation chip in separate fluidic channels, limiting contact between the streams until immediately before they form the droplet. The diffusion-driven mixing of reactants is predominantly restricted to within the droplet. The temperature change in droplets due to the heat of reaction is measured optically by recording the reflectance spectra of encapsulated thermochromic liquid crystals (TLC) that are added to one of the reactant streams. As the droplets travel through the channel, the spectral characteristics of the TLC represent the internal temperature, allowing optical measurement with a precision of ≈6 mK. The microfluidic chip and all fluids are temperature controlled, and the reaction heat within droplets raises their temperature until thermal diffusion dissipates the heat into the surrounding oil and chip walls. Position resolved optical temperature measurement of the droplets allows calculation of the heat of reaction by analyzing the droplet temperature profile over time. Channel dimensions, droplet generation rate, droplet size, reactant stream flows and oil flow rate are carefully balanced to provide rapid diffusional mixing of reactants compared to thermal diffusion, while avoiding thermal "quenching" due to contact between the droplets and the chip walls. Compared to conventional microcalorimetry, which has been used in this work to provide reference measurements, this new continuous flow droplet calorimeter has the potential to perform titrations ≈1000-fold faster while using ≈400-fold less reactants per titration.

An efficient hybrid method for stochastic reaction-diffusion biochemical systems with delay

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Ilie, Silvana

2017-12-01

Many chemical reactions, such as gene transcription and translation in living cells, need a certain time to finish once they are initiated. Simulating stochastic models of reaction-diffusion systems with delay can be computationally expensive. In the present paper, a novel hybrid algorithm is proposed to accelerate the stochastic simulation of delayed reaction-diffusion systems. The delayed reactions may be of consuming or non-consuming delay type. The algorithm is designed for moderately stiff systems in which the events can be partitioned into slow and fast subsets according to their propensities. The proposed algorithm is applied to three benchmark problems and the results are compared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm. The numerical results show that the new hybrid algorithm achieves considerable speed-up in the run time and very good accuracy.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

PubMed

Schuszter, Gábor; Gehér-Herczegh, Tünde; Szűcs, Árpád; Tóth, Ágota; Horváth, Dezső

2017-05-17

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H + -autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.

Reactive Minerals and Dechlorinating Communities: Mechanisms Governing the Degradation of Chlorinated Ethenes during Back Diffusion from Low Permeability Zones in Aerobic and Anaerobic Environments

NASA Astrophysics Data System (ADS)

Berns, E. C.; Zeng, R.; Singh, H.; Valocchi, A. J.; Sanford, R. A.; Strathmann, T. J.; Schaefer, C. E.; Werth, C. J.

2017-12-01

Low permeability zones (LPZs) comprised of silts and clays, and contaminated with chlorinated ethenes, can act as a long term source of contaminated groundwater by diffusion into adjacent high permeability zones (HPZs). Following initial remediation efforts, chlorinated ethenes that have diffused into LPZs will back diffuse and recontaminate HPZs. Because chlorinated ethenes are known to cause cancer and damage the liver, kidneys, and central nervous system, it is important to understand how they degrade in natural systems and how to model their fate and transport. Previous work has shown that anaerobic hydrogenolysis reactions are facilitated by both dechlorinating microorganisms and reactive minerals. Abiotic dichloro-elimination reactions with reactive minerals can also degrade chlorinated ethenes to acetylene, albeit at slower rates than biotic processes. More recently, studies have explored aerobic abiotic degradation of chlorinated ethenes to formate, glycolate, and carbon dioxide. This study focuses on these biotic and abiotic reactions and their contributions to chlorinated ethene degradation under aerobic and anaerobic conditions at the LPZ/HPZ interface. A two-dimensional flow cell was constructed to model this interface using clay and sand from Pease Air Force Base. The clay was inoculated with a dechlorinating enrichment culture. Tenax adsorbent beads equilibrated with trichloroethylene (TCE) were used as a chlorinated ethene source zone at the base of the clay. TCE and its degradation products diffused from the clay into the sand, where they were removed from the flow cell by groundwater at a rate of 50 mL/day. Volatile compounds were trapped in a sample loop and removed every 48 hours for analysis by GC-FID. Organic and inorganic ions in the effluent were analyzed on the HPLC and IC. The experiment was terminated by freezing the flow cell, and chemical profiles through the flow cell material were created to show the spatial distribution of degradation products. Chemical profiles through the clay were modeled using a 1D diffusion-reaction model, and the contributions of abiotic and biotic processes to TCE degradation were determined. The model and experimental data lend insights into transformation processes that control the fate and transport of chlorinated ethenes at contaminated sites.

Synthesis of alloys with controlled phase structure

DOEpatents

Guthrie, Stephen Everett; Thomas, George John; Bauer, Walter; Yang, Nancy Yuan Chi

1999-04-20

A method for preparing controlled phase alloys useful for engineering and hydrogen storage applications. This novel method avoids melting the constituents by employing vapor transport, in a hydrogen atmosphere, of an active metal constituent, having a high vapor pressure at temperatures .apprxeq.300 C. and its subsequent condensation on and reaction with the other constituent (substrate) of an alloy thereby forming a controlled phase alloy and preferably a single phase alloy. It is preferred that the substrate material be a metal powder such that diffusion of the active metal constituent, preferably magnesium, and reaction therewith can be completed within a reasonable time and at temperatures .apprxeq.300 C. thereby avoiding undesirable effects such as sintering, local compositional inhomogeneities, segregation, and formation of unwanted second phases such as intermetallic compounds.

Synthesis of alloys with controlled phase structure

DOEpatents

Guthrie, S.E.; Thomas, G.J.; Bauer, W.; Yang, N.Y.C.

1999-04-20

A method is described for preparing controlled phase alloys useful for engineering and hydrogen storage applications. This novel method avoids melting the constituents by employing vapor transport, in a hydrogen atmosphere, of an active metal constituent, having a high vapor pressure at temperatures {approx_equal}300 C and its subsequent condensation on and reaction with the other constituent (substrate) of an alloy thereby forming a controlled phase alloy and preferably a single phase alloy. It is preferred that the substrate material be a metal powder such that diffusion of the active metal constituent, preferably magnesium, and reaction therewith can be completed within a reasonable time and at temperatures {approx_equal}300 C thereby avoiding undesirable effects such as sintering, local compositional inhomogeneities, segregation, and formation of unwanted second phases such as intermetallic compounds. 4 figs.

Diffusional limits to the consumption of atmospheric methane by soils

USGS Publications Warehouse

Striegl, Robert G.

1993-01-01

Net transport of atmospheric gases into and out of soil systems is primarily controlled by diffusion along gas partial pressure gradients. Gas fluxes between soil and the atmosphere can therefore be estimated by a generalization of the equation for ordinary gaseous diffusion in porous unsaturated media. Consumption of CH4 by methylotrophic bacteria in the top several centimeters of soil causes the uptake of atmospheric CH4 by aerated soils. The capacity of the methylotrophs to consume CH4 commonly exceeds the potential of CH4 to diffuse from the atmosphere to the consumers. The maximum rate of uptake of atmospheric CH4 by soil is, therefore, limited by diffusion and can be calculated from soil physical properties and the CH4 concentration gradient. The CH4 concentration versus depth profile is theoretically described by the equation for gaseous diffusion with homogeneous chemical reaction in porous unsaturated media. This allows for calculation of the in situ rate of CH4 consumption within specified depth intervals.

Class of self-limiting growth models in the presence of nonlinear diffusion

NASA Astrophysics Data System (ADS)

Kar, Sandip; Banik, Suman Kumar; Ray, Deb Shankar

2002-06-01

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Neurocomputation by Reaction Diffusion

NASA Astrophysics Data System (ADS)

Liang, Ping

1995-08-01

This Letter demonstrates the possible role nonsynaptic diffusion neurotransmission may play in neurocomputation using an artificial neural network model. A reaction-diffusion neural network model with field-based information-processing mechanisms is proposed. The advantages of nonsynaptic field neurotransmission from a computational viewpoint demonstrated in this Letter include long-range inhibition using only local interaction, nonhardwired and changeable (target specific) long-range communication pathways, and multiple simultaneous spatiotemporal organization processes in the same medium.

Radiosensitization of DNA by Cisplatin Adducts Results from an Increase in the Rate Constant for the Reaction with Hydrated Electrons and Formation of PtI

PubMed Central

Behmand, B.; Marignier, J.-L.; Mostafavi, M.; Wagner, J. R.; Hunting, D. J.; Sanche, L.

2015-01-01

Pulse radiolysis measurements of the decay of hydrated electrons in solutions containing different concentrations of the oligonucleotide GTG with and without a cisplatin adduct show that the presence of a cisplatin moiety accelerates the reaction between hydrated electrons and the oligonucleotide. The rate constant of the reaction is found to be 2.23 × 1010 mol−1 L s−1, which indicates that it is diffusion controlled. In addition, we show for the first time the formation of a PtI intermediate as a result of the reaction of hydrated electrons with GTG-cisplatin. A putative reaction mechanism is proposed, which may form the basis of the radiosensitization of cancer cells in concomitant chemoradiation therapy with cisplatin. PMID:26098937

Diffusion and Surface Reaction in Heterogeneous Catalysis

ERIC Educational Resources Information Center

Baiker, A.; Richarz, W.

1978-01-01

Ethylene hydrogenation on a platinum catalyst, electrolytically applied to a tube wall, is a good system for the study of the interactions between diffusion and surface reaction in heterogeneous catalysis. Theoretical background, apparatus, procedure, and student performance of this experiment are discussed. (BB)

Parallel changes in serum proteins and diffusion tensor imaging in methamphetamine-associated psychosis.

PubMed

Breen, Michael S; Uhlmann, Anne; Ozcan, Sureyya; Chan, Man; Pinto, Dalila; Bahn, Sabine; Stein, Dan J

2017-03-02

Methamphetamine-associated psychosis (MAP) involves widespread neurocognitive and molecular deficits, however accurate diagnosis remains challenging. Integrating relationships between biological markers, brain imaging and clinical parameters may provide an improved mechanistic understanding of MAP, that could in turn drive the development of better diagnostics and treatment approaches. We applied selected reaction monitoring (SRM)-based proteomics, profiling 43 proteins in serum previously implicated in the etiology of major psychiatric disorders, and integrated these data with diffusion tensor imaging (DTI) and psychometric measurements from patients diagnosed with MAP (N = 12), methamphetamine dependence without psychosis (MA; N = 14) and healthy controls (N = 16). Protein analysis identified changes in APOC2 and APOH, which differed significantly in MAP compared to MA and controls. DTI analysis indicated widespread increases in mean diffusivity and radial diffusivity delineating extensive loss of white matter integrity and axon demyelination in MAP. Upon integration, several co-linear relationships between serum proteins and DTI measures reported in healthy controls were disrupted in MA and MAP groups; these involved areas of the brain critical for memory and social emotional processing. These findings suggest that serum proteomics and DTI are sensitive measures for detecting pathophysiological changes in MAP and describe a potential diagnostic fingerprint of the disorder.

Anomalous Impact in Reaction-Diffusion Financial Models

NASA Astrophysics Data System (ADS)

Mastromatteo, I.; Tóth, B.; Bouchaud, J.-P.

2014-12-01

We generalize the reaction-diffusion model A +B → /0 in order to study the impact of an excess of A (or B ) at the reaction front. We provide an exact solution of the model, which shows that the linear response breaks down: the average displacement of the reaction front grows as the square root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.

Convective instabilities in traveling fronts of addition polymerization

NASA Technical Reports Server (NTRS)

Pojman, John A.; Jones, Chris E.; Khan, Akhtar M.

1993-01-01

An autocatalytic reaction in an unstirred vessel can support a constant velocity wavefront resulting from the coupling of diffusion to the chemical reaction. A flare front is a common example in which heat is the autocatalytic species that diffuses into unreacted regions stimulating a reaction that produces more heat. Traveling fronts were studied in synthetic polymerization reactions under high pressure by workers in the former USSR. More recently, propagating fronts of methacrylic acid polymerization were studied under ambient conditions, both with video techniques and by NMR.

Geochemical modeling of leaching of Ca, Mg, Al, and Pb from cementitious waste forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martens, E., E-mail: evelien.martens@csiro.a; Jacques, D.; Van Gerven, T.

2010-08-15

Results from extraction tests on cement-waste samples were simulated with a thermodynamic equilibrium model using a consistent database, to which lead data were added. Subsequent diffusion tests were modeled by means of a 3D diffusive transport model combined with the geochemical model derived from the extraction tests. Modeling results of the leached major element concentrations for both uncarbonated and (partially) carbonated samples agreed well with the extraction test using the set of pure minerals and solid solutions present in the database. The observed decrease in Ca leaching with increasing carbonation level was qualitatively predicted. Simulations also revealed that Pb leachingmore » is not controlled by dissolution/precipitation only. The addition of the calcite-cerrusite solid solution and adsorption reactions on amorphous Fe- and Al-oxides improved the predictions and are considered to control the Pb leaching during the extractions tests. The dynamic diffusive leaching tests were appropriately modeled for Na, K, Ca and Pb.« less

Rotating disk electrode system for elevated pressures and temperatures.

PubMed

Fleige, M J; Wiberg, G K H; Arenz, M

2015-06-01

We describe the development and test of an elevated pressure and temperature rotating disk electrode (RDE) system that allows measurements under well-defined mass transport conditions. As demonstrated for the oxygen reduction reaction on polycrystalline platinum (Pt) in 0.5M H2SO4, the setup can easily be operated in a pressure range of 1-101 bar oxygen, and temperature of 140 °C. Under such conditions, diffusion limited current densities increase by almost two orders of magnitude as compared to conventional RDE setups allowing, for example, fuel cell catalyst studies under more realistic conditions. Levich plots demonstrate that the mass transport is indeed well-defined, i.e., at low electrode potentials, the measured current densities are fully diffusion controlled, while at higher potentials, a mixed kinetic-diffusion controlled regime is observed. Therefore, the setup opens up a new field for RDE investigations under temperature and current density conditions relevant for low and high temperature proton exchange membrane fuel cells.

Rotating disk electrode system for elevated pressures and temperatures

NASA Astrophysics Data System (ADS)

Fleige, M. J.; Wiberg, G. K. H.; Arenz, M.

2015-06-01

We describe the development and test of an elevated pressure and temperature rotating disk electrode (RDE) system that allows measurements under well-defined mass transport conditions. As demonstrated for the oxygen reduction reaction on polycrystalline platinum (Pt) in 0.5M H2SO4, the setup can easily be operated in a pressure range of 1-101 bar oxygen, and temperature of 140 °C. Under such conditions, diffusion limited current densities increase by almost two orders of magnitude as compared to conventional RDE setups allowing, for example, fuel cell catalyst studies under more realistic conditions. Levich plots demonstrate that the mass transport is indeed well-defined, i.e., at low electrode potentials, the measured current densities are fully diffusion controlled, while at higher potentials, a mixed kinetic-diffusion controlled regime is observed. Therefore, the setup opens up a new field for RDE investigations under temperature and current density conditions relevant for low and high temperature proton exchange membrane fuel cells.

How to Enhance Gas Removal from Porous Electrodes?

PubMed Central

Kadyk, Thomas; Bruce, David; Eikerling, Michael

2016-01-01

This article presents a structure-based modeling approach to optimize gas evolution at an electrolyte-flooded porous electrode. By providing hydrophobic islands as preferential nucleation sites on the surface of the electrode, it is possible to nucleate and grow bubbles outside of the pore space, facilitating their release into the electrolyte. Bubbles that grow at preferential nucleation sites act as a sink for dissolved gas produced in electrode reactions, effectively suctioning it from the electrolyte-filled pores. According to the model, high oversaturation is necessary to nucleate bubbles inside of the pores. The high oversaturation allows establishing large concentration gradients in the pores that drive a diffusion flux towards the preferential nucleation sites. This diffusion flux keeps the pores bubble-free, avoiding deactivation of the electrochemically active surface area of the electrode as well as mechanical stress that would otherwise lead to catalyst degradation. The transport regime of the dissolved gas, viz. diffusion control vs. transfer control at the liquid-gas interface, determines the bubble growth law. PMID:28008914

High-energy phosphate transfer in human muscle: diffusion of phosphocreatine.

PubMed

Gabr, Refaat E; El-Sharkawy, Abdel-Monem M; Schär, Michael; Weiss, Robert G; Bottomley, Paul A

2011-07-01

The creatine kinase (CK) reaction is central to muscle energetics, buffering ATP levels during periods of intense activity via consumption of phosphocreatine (PCr). PCr is believed to serve as a spatial shuttle of high-energy phosphate between sites of energy production in the mitochondria and sites of energy utilization in the myofibrils via diffusion. Knowledge of the diffusion coefficient of PCr (D(PCr)) is thus critical for modeling and understanding energy transport in the myocyte, but D(PCr) has not been measured in humans. Using localized phosphorus magnetic resonance spectroscopy, we measured D(PCr) in the calf muscle of 11 adults as a function of direction and diffusion time. The results show that the diffusion of PCr is anisotropic, with significantly higher diffusion along the muscle fibers, and that the diffusion of PCr is restricted to a ∼28-μm pathlength assuming a cylindrical model, with an unbounded diffusion coefficient of ∼0.69 × 10(-3) mm(2)/s. This distance is comparable in size to the myofiber radius. On the basis of prior measures of CK reaction kinetics in human muscle, the expected diffusion distance of PCr during its half-life in the CK reaction is ∼66 μm. This distance is much greater than the average distances between mitochondria and myofibrils. Thus these first measurements of PCr diffusion in human muscle in vivo support the view that PCr diffusion is not a factor limiting high-energy phosphate transport between the mitochondria and the myofibrils in healthy resting myocytes.

High-energy phosphate transfer in human muscle: diffusion of phosphocreatine

PubMed Central

Gabr, Refaat E.; El-Sharkawy, AbdEl-Monem M.; Schär, Michael; Weiss, Robert G.

2011-01-01

The creatine kinase (CK) reaction is central to muscle energetics, buffering ATP levels during periods of intense activity via consumption of phosphocreatine (PCr). PCr is believed to serve as a spatial shuttle of high-energy phosphate between sites of energy production in the mitochondria and sites of energy utilization in the myofibrils via diffusion. Knowledge of the diffusion coefficient of PCr (DPCr) is thus critical for modeling and understanding energy transport in the myocyte, but DPCr has not been measured in humans. Using localized phosphorus magnetic resonance spectroscopy, we measured DPCr in the calf muscle of 11 adults as a function of direction and diffusion time. The results show that the diffusion of PCr is anisotropic, with significantly higher diffusion along the muscle fibers, and that the diffusion of PCr is restricted to a ∼28-μm pathlength assuming a cylindrical model, with an unbounded diffusion coefficient of ∼0.69 × 10−3 mm2/s. This distance is comparable in size to the myofiber radius. On the basis of prior measures of CK reaction kinetics in human muscle, the expected diffusion distance of PCr during its half-life in the CK reaction is ∼66 μm. This distance is much greater than the average distances between mitochondria and myofibrils. Thus these first measurements of PCr diffusion in human muscle in vivo support the view that PCr diffusion is not a factor limiting high-energy phosphate transport between the mitochondria and the myofibrils in healthy resting myocytes. PMID:21368292

Pattern formation in the iodate-sulfite-thiosulfate reaction-diffusion system.

PubMed

Liu, Haimiao; Pojman, John A; Zhao, Yuemin; Pan, Changwei; Zheng, Juhua; Yuan, Ling; Horváth, Attila K; Gao, Qingyu

2012-01-07

Sodium polyacrylate-induced pH pattern formation and starch-induced iodine pattern formation were investigated in the iodate-sulfite-thiosulfate (IST) reaction in a one-side fed disc gel reactor (OSFR). As binding agents of the autocatalyst of hydrogen ions or iodide ions, different content of sodium polyacrylate or starch has induced various types of pattern formation. We observed pH pulses, striped patterns, mixed spots and stripes, and hexagonal spots upon increasing the content of sodium polyacrylate and observed iodine pulses, branched patterns, and labyrinthine patterns upon increasing the starch content in the system. Coexistence of a pH front and an iodine front was also studied in a batch IST reaction-diffusion system. Both pH and iodine front instabilities were observed in the presence of sodium polyacrylate, i.e., cellular fronts and transient Turing structures resulting from the decrease in diffusion coefficients of activators. The mechanism of multiple feedback may explain the different patterns in the IST reaction-diffusion system.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Recovery of lithium and cobalt from spent lithium-ion batteries using organic acids: Process optimization and kinetic aspects.

PubMed

Golmohammadzadeh, Rabeeh; Rashchi, Fereshteh; Vahidi, Ehsan

2017-06-01

An environmentally-friendly route based on hydrometallurgy was investigated for the recovery of cobalt and lithium from spent lithium ion batteries (LIBs) using different organic acids (citric acid, Dl-malic acid, oxalic acid and acetic acid). In this investigation, response surface methodology (RSM) was utilized to optimize leaching parameters including solid to liquid ratio (S/L), temperature, acid concentration, type of organic acid and hydrogen peroxide concentration. Based on the results obtained from optimizing procedure, temperature was recognized as the most influential parameter. In addition, while 81% of cobalt was recovered, the maximum lithium recovery of 92% was achieved at the optimum leaching condition of 60°C, S/L: 30gL -1 , citric acid concentration: 2M, hydrogen peroxide concentration: 1.25Vol.% and leaching time: 2h. Furthermore, results displayed that ultrasonic agitation will enhance the recovery of lithium and cobalt. It was found that the kinetics of cobalt leaching is controlled by surface chemical reaction at temperatures lower than 45°C. However, diffusion through the product layer at temperatures higher than 45°C controls the rate of cobalt leaching. Rate of lithium reaction is controlled by diffusion through the product layer at all the temperatures studied. Copyright © 2017 Elsevier Ltd. All rights reserved.

Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification.

PubMed

Loodts, V; Trevelyan, P M J; Rongy, L; De Wit, A

2016-10-01

Various spatial density profiles can develop in partially miscible stratifications when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B→C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the nonreactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it. We use this framework to predict various possible hydrodynamic instability scenarios inducing buoyancy-driven convection around such reaction fronts when they propagate parallel to the gravity field.

Carbon isotope discrepancy between precambrian stromatolites and their modern analogs: Inferences from hypersaline microbial mats of the sinai coast

NASA Astrophysics Data System (ADS)

Schidlowski, Manfred

1985-12-01

The isotopic composition of organic carbon from extant stromatolite-type microbial ecosystems is commonly slanted toward heavy δ13 C values as compared to respective compositions of average organic matter (including that from Precambrian stromatolites). This seems the more enigmatic as the bulk of primary producers from benthic microbial communities are known to fix carbon via the C3 pathway normally entailing the sizable fractionations of the RuBP carboxylase reaction. There is reason to believe that the small fractionations displayed by aquatic microorganisms result from the limitations of a diffusion-controlled assimilatory pathway in which the isotope effect of the enzymatic reaction is largely suppressed. Apart from the diffusion-control exercised by the aqueous environment, transport of CO2 to the photosynthetically active sites will be further impeded by the protective slime (polysaccharide) coatings commonly covering microbial mats in which gas diffusivities are extremely low. Ineffective discrimination against13C becomes, however, most pronounced in hypersaline environments where substantially reduced CO2 solubilities tend to push carbon into the role of a limiting nutrient (brine habitats constitute preferential sanctuaries of mat-forming microbenthos since the emergence of Metazoan grazers ˜ 0.7 Ga ago). As the same microbial communities had been free to colonize normal marine environments during the Precambrian, the CO2 concentration effect was irrelevant to the carbon-fixing pathway of these ancient forms. Therefore, it might not surprise that organic matter from Precambrian stromatolites displays the large fractionations commonly associated with C3 photosynthesis. Increased mixing ratios of CO2 in the Precambrian atmosphere may have additionally contributed to the elimination of the diffusion barrier in the carbon-fixing pathways of ancient mat-forming microbiota.

Confining the nucleation and overgrowth of Rh to the {111} facets of Pd nanocrystal seeds: the roles of capping agent and surface diffusion.

PubMed

Xie, Shuifen; Peng, Hsin-Chieh; Lu, Ning; Wang, Jinguo; Kim, Moon J; Xie, Zhaoxiong; Xia, Younan

2013-11-06

This article describes a systematic study of the spatially confined growth of Rh atoms on Pd nanocrystal seeds, with a focus on the blocking effect of a surface capping agent and the surface diffusion of adatoms. We initially used Pd cuboctahedrons as the seeds to illustrate the concept and to demonstrate the capabilities of our approach. Because the Pd{100} facets were selectively capped by a layer of chemisorbed Br(–) or I(–) ions, we were able to confine the nucleation and deposition of Rh atoms solely on the {111} facets of a Pd seed. When the synthesis was conducted at a relatively low temperature, the deposition of Rh atoms followed an island growth mode because of the high Rh–Rh interatomic binding energy. We also facilitated the surface diffusion of deposited Rh atoms by increasing the reaction temperature and decreasing the injection rate for the Rh precursor. Under these conditions, the deposition of Rh on the Pd{111} facets was switched to a layered growth mode. We further successfully extended this approach to a variety of other types of Pd polyhedral seeds that contained Pd{111} and Pd{100} facets in different proportions on the surface. As expected, a series of Pd–Rh bimetallic nanocrystals with distinctive elemental distributions were obtained. We could remove the Pd cores through selective chemical etching to generate Rh hollow nanoframes with different types and degrees of porosity. This study clearly demonstrates the importance of facet capping, surface diffusion, and reaction kinetics in controlling the morphologies of bimetallic nanocrystals during a seed-mediated process. It also provides a new direction for the rational design and synthesis of nanocrystals with spatially controlled distributions of elements for a variety of applications.

Substitutional and Interstitial Diffusion in alpha2-Ti3Al(O)

NASA Technical Reports Server (NTRS)

Copland, Evan; Young, David J.; Gleeson, Brian; Jacobson, Nathan

2007-01-01

The reaction between Al2O3 and alpha2-Ti3Al was studied with a series of Al2O3/alpha2-Ti3Al multiphase diffusion couples annealed at 900, 1000 and 1100 C. The diffusion-paths were found to strongly depend on alpha2- Ti3Al(O) composition. For alloys with low oxygen concentrations the reaction involved the reduction of Al2O3, the formation of a gamma-TiAl reaction-layer and diffusion of Al and O into the alpha2-Ti3Al substrate. Measured concentration profiles across the interaction-zone showed "up-hill" diffusion of O in alpha2-Ti3Al(O) indicating a significant thermodynamic interaction between O and Al, Ti or both. Diffusion coefficients for the interstitial O in alpha2-Ti3Al(O) were determined independently from the interdiffusion of Ti and Al on the substitutional lattice. Diffusion coefficients are reported for alpha2-Ti3Al(O) as well as gamma-TiAl. Interpretation of the results were aided with the subsequent measurement of the activities of Al, Ti and O in alpha 2-Ti3Al(O) by Knudsen effusion-cell mass spectrometry.

Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

PubMed Central

Mironova, Lidia A.; Mironov, Sergej L.

2008-01-01

Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

CCR scientists tease out mechanisms of immune cell communication | Center for Cancer Research

Cancer.gov

Researchers from the Cancer and Inflammation Program at the Center for Cancer Research and the Ben-Gurion University of the Negev in Israel have discovered that the simple processes of molecular diffusion and absorption control the spread of cytokines through dense body tissues. The simple control mechanisms enable the immune response to tailor itself to the nature and severity of a pathogenic attack and to prevent dangerous autoimmune reactions.  Read more...

Characterizations of the Core-Shell Structured MgB2/CARBON Fiber Synthesis by Rf-Sputtering and Thermal Evaporation

NASA Astrophysics Data System (ADS)

Park, Sung Chang; Lim, Yeong Jin; Lee, Tae-Keun; Kim, Cheol Jin

MgB2/carbon fibers have been synthesized by the combination of RF-sputtering of B and thermal evaporation of Mg, followed by co-evaporation. First, boron layer was deposited by RF-sputtering on the carbon fiber with average diameter of 7.1 μm. Later this coated layer of B was reacted with Mg vapor to transform into MgB2. Since the MgB2 reaction proceed with Mg diffusion into the boron layer, Mg vapor pressure and the diffusion time had to be controlled precisely to secure the complete reaction. Also the deposition rate of each element was controlled separately to obtain stoichiometric MgB2, since Mg was evaporated by thermal heating and B by sputtering system. The sintered B target was magnetron sputtered at the RF-power of ~200 W, which corresponded to the deposition rate of ~3.6 Å/s. With the deposition rate of B fixed, the vapor pressure of Mg was controlled by varying the temperature of tungsten boat with heating element control unit between 100 and 900°C. The MgB2 layers with the thickness of 200-950 nm could be obtained and occasionally MgO appeared as a second phase. Superconducting transition temperatures were measured around ~38 K depending on the deposition condition.

Finite Element Analysis Modeling of Chemical Vapor Deposition of Silicon Carbide

DTIC Science & Technology

2014-06-19

thesis primarily focuses on mass transport by gas -phase flow and diffusion , chemical reaction in gas phase and on solid surfaces, and thin film...chemical vapor deposition (CVD). This thesis primarily focuses on mass transport by gas -phase flow and diffusion , chemical reaction in gas phase and...9 Fluid Flow…………………………………………..…………………..…………….9 Thermodynamics………………………………………..………………….….…….11 Chemical Reaction and Diffusion

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock-fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

Parametric spatiotemporal oscillation in reaction-diffusion systems.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Parametric spatiotemporal oscillation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Diffusion and Interface Effects during Preparation of All-Solid Microstructured Fibers

PubMed Central

Jens, Kobelke; Jörg, Bierlich; Katrin, Wondraczek; Claudia, Aichele; Zhiwen, Pan; Sonja, Unger; Kay, Schuster; Hartmut, Bartelt

2014-01-01

All-solid microstructured optical fibers (MOF) allow the realization of very flexible optical waveguide designs. They are prepared by stacking of doped silica rods or canes in complex arrangements. Typical dopants in silica matrices are germanium and phosphorus to increase the refractive index (RI), or boron and fluorine to decrease the RI. However, the direct interface contact of stacking elements often causes interrelated chemical reactions or evaporation during thermal processing. The obtained fiber structures after the final drawing step thus tend to deviate from the targeted structure risking degrading their favored optical functionality. Dopant profiles and design parameters (e.g., the RI homogeneity of the cladding) are controlled by the combination of diffusion and equilibrium conditions of evaporation reactions. We show simulation results of diffusion and thermal dissociation in germanium and fluorine doped silica rod arrangements according to the monitored geometrical disturbances in stretched canes or drawn fibers. The paper indicates geometrical limits of dopant structures in sub-µm-level depending on the dopant concentration and the thermal conditions during the drawing process. The presented results thus enable an optimized planning of the preform parameters avoiding unwanted alterations in dopant concentration profiles or in design parameters encountered during the drawing process. PMID:28788219

Diffusion and Interface Effects during Preparation of All-Solid Microstructured Fibers.

PubMed

Jens, Kobelke; Jörg, Bierlich; Katrin, Wondraczek; Claudia, Aichele; Zhiwen, Pan; Sonja, Unger; Kay, Schuster; Hartmut, Bartelt

2014-09-25

All-solid microstructured optical fibers (MOF) allow the realization of very flexible optical waveguide designs. They are prepared by stacking of doped silica rods or canes in complex arrangements. Typical dopants in silica matrices are germanium and phosphorus to increase the refractive index (RI), or boron and fluorine to decrease the RI. However, the direct interface contact of stacking elements often causes interrelated chemical reactions or evaporation during thermal processing. The obtained fiber structures after the final drawing step thus tend to deviate from the targeted structure risking degrading their favored optical functionality. Dopant profiles and design parameters (e.g., the RI homogeneity of the cladding) are controlled by the combination of diffusion and equilibrium conditions of evaporation reactions. We show simulation results of diffusion and thermal dissociation in germanium and fluorine doped silica rod arrangements according to the monitored geometrical disturbances in stretched canes or drawn fibers. The paper indicates geometrical limits of dopant structures in sub-µm-level depending on the dopant concentration and the thermal conditions during the drawing process. The presented results thus enable an optimized planning of the preform parameters avoiding unwanted alterations in dopant concentration profiles or in design parameters encountered during the drawing process.

In situ imaging of the soldering reactions in nanoscale Cu/Sn/Cu and Sn/Cu/Sn diffusion couples

NASA Astrophysics Data System (ADS)

Yin, Qiyue; Gao, Fan; Gu, Zhiyong; Wang, Jirui; Stach, Eric A.; Zhou, Guangwen

2018-01-01

The soldering reactions of three-segmented Sn/Cu/Sn and Cu/Sn/Cu diffusion couples are monitored by in-situ transmission electron microscopy to reveal the metallurgical reaction mechanism and the associated phase transformation pathway. For Sn/Cu/Sn diffusion couples, there is no ɛ-Cu3Sn formation due to the relatively insufficient Cu as compared to Sn. Kirkendall voids form initially in the Cu segment and then disappear due to the volume expansion associated with the continued intermetallic compound (IMC) formation as the reaction progresses. The incoming Sn atoms react with Cu to form η-Cu6Sn5, and the continuous reaction then transforms the entire nanowire to η-Cu6Sn5 grains with remaining Sn. With continued heating slightly above the melting point of Sn, an Sn-rich liquid phase forms between η-Cu6Sn5 grains. By contrast, the reaction in the Cu/Sn/Cu diffusion couples results in the intermetallic phases of both Cu3Sn and Cu6Sn5 and the development of Cu6Sn5 bulges on Cu3Sn grains. Kirkendall voids form in the two Cu segments, which grow and eventually break the nanowire into multiple segments.

Computation Of Facilitated Transport of O2 In Hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1991-01-01

Report describes computations of unsteady facilitated transport of oxygen through liquid membrane of hemoglobin. Used here, "facilitated transport" means diffusion of permeant through membrane in which that diffusion enhanced by reversible chemical reaction between permeant and membrane. In this case, reversible reactions between hemoglobin and oxygen.

Convection-Diffusion Layer in an "Open Space" for Local Surface Treatment and Microfabrication using a Four-Aperture Microchemical Pen.

PubMed

Mao, Sifeng; Zhang, Yong; Zhang, Weifei; Zeng, Hulie; Nakajima, Hizuru; Lin, Jin-Ming; Uchiyama, Katsumi

2017-09-06

A four-aperture microchemical pen was used to produce a stable convection-diffusion layer in an "open space" for microreactions and microfabrication. The process represents a new method for microreactions and microfabrication in a convection-diffusion layer. To prove the concept of a convection-diffusion layer in an "open space", bovine serum albumin was labeled with 4-fluoro-7-nitro-2,1,3-benzoxadiazole to confirm that the small convection-diffusion layer was effective for local surface treatment. To demonstrate the potential for microfabrication, silver patterns were fabricated on a glass surface with a convection-diffusion layer by using the silver-mirror reaction. The widths of each silver pattern could be easily controlled from 10 to 60 μm. Patterned silver lines with uniform widths or gradient widths were prepared. This is the first proof of concept study of a convection-diffusion layer in an "open space" used in local surface treatment and microfabrication on a surface. The microchemical pen represents a potential method for the region-selective microtreatment of tissues, cells, and other biological interfaces. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Chemical morphogenesis: recent experimental advances in reaction–diffusion system design and control

PubMed Central

Szalai, István; Cuiñas, Daniel; Takács, Nándor; Horváth, Judit; De Kepper, Patrick

2012-01-01

In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction–diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries. PMID:23919126

Improvement of time-delayed feedback control by periodic modulation: analytical theory of Floquet mode control scheme.

PubMed

Just, Wolfram; Popovich, Svitlana; Amann, Andreas; Baba, Nilüfer; Schöll, Eckehard

2003-02-01

We investigate time-delayed feedback control schemes which are based on the unstable modes of the target state, to stabilize unstable periodic orbits. The periodic time dependence of these modes introduces an external time scale in the control process. Phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance. We illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the Rössler model. In addition we provide the analytical explanation for the observed control features.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Turing patterns and a stochastic individual-based model for predator-prey systems

NASA Astrophysics Data System (ADS)

Nagano, Seido

2012-02-01

Reaction-diffusion theory has played a very important role in the study of pattern formations in biology. However, a group of individuals is described by a single state variable representing population density in reaction-diffusion models and interaction between individuals can be included only phenomenologically. Recently, we have seamlessly combined individual-based models with elements of reaction-diffusion theory. To include animal migration in the scheme, we have adopted a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Thus, we have observed the transition of population patterns from an extinction mode, a stable mode, or an oscillatory mode to the chaotic mode as the population growth rate increases. We show our phase diagram of predator-prey systems and discuss the microscopic mechanism for the stable lattice formation in detail.

TEM Analysis of Diffusion-Bonded Silicon Carbide Ceramics Joined Using Metallic Interlayers

NASA Technical Reports Server (NTRS)

Ozaki, T.; Hasegawa, Y.; Tsuda, H.; Mori, S.; Halbig, M. C.; Asthana, R.; Singh, M.

2017-01-01

SiC fiber-bonded ceramics (SA-Tyrannohex: SA-THX) diffusion-bonded with TiCu metallic interlayers were investigated. Thin samples of the ceramics were prepared with a focused ion beam (FIB) and the interfacial microstructure of the prepared samples was studied by transmission electron microscopy (TEM) and scanning TEM (STEM). In addition to conventional microstructure observation, for detailed analysis of reaction compounds in diffusion-bonded area, we performed STEM-EDS measurements and selected area electron diffraction (SAD) experiments. The TEM and STEM experiments revealed the diffusion-bonded area was composed of only one reaction layer, which was characterized by TiC precipitates in Cu-Si compound matrix. This reaction layer was in good contact with the SA-THX substrates, and it is concluded that the joint structure led to the excellent bonding strength.

Diffusion-controlled garnet growth in siliceous dolomites of the Adamello contact aureole, N-Italy

NASA Astrophysics Data System (ADS)

Muller, T.; Fiebich, E.; Foster, C. T.

2012-12-01

Texture forming processes are controlled by many factors, such as material transport through polycrystalline materials, surface kinetics, fluid flow, and many others. In metamorphic rocks, texture forming processes typically involve local reactions linked to net mass transfer which allows constraining the actual reaction path in more detail. In this study, we present geochemical data combined with textural modeling to constrain the conditions and reaction mechanism during contact metamorphic garnet growth in siliceous dolomites in the southern Adamello Massif, Italy. The metamorphic garnet porphyroblasts are poikiloblastic and idiomorphic in shape with a typical grain size ranging between 0.6-1 cm in diameter sitting in a matrix of calcite+diopside+anorthite+wollastonite. Inclusions in the grossular-rich garnets are almost uniquely diopside. On the hand specimen, garnets are surrounded by visible rims of about 0.6 mm indicating a diffusion-limited reaction mechanism to be responsible for the garnet formation. In the course of this study samples have been characterized by polarization microscopy, element x-ray maps using EMPA, cathodulominescence images and stable isotope analyses of carbon and oxygen of matrix carbonates. In addition, pseudosections have been calculated using the software package PerpleX (Connolly, 2005) based on the bulk chemistry of collected samples. Results indicate that the visible margin consists of a small rim (< 1 mm) purely consisting of recrystallized calcite adjacent to the garnet edge. The major part of the observed halo, however, is characterized by the absence of anorthite and wollastonite. The observed texture of garnet porphyroblasts growing and simultaneously forming an anorthite and wollastonite free margin can successfully be reproduced using the SEG program (Foster, 1993), which assumes diffusive mass transport. Therefore the model constrains the diffusive fluxes of Ca, Mg, Al and Si by mass balance and the local Gibbs-Duhem equations on the reaction site. Assuming that the pore fluid is not saturated in CO2, which is justified for the assumption of fluid-infiltration during contact metamorphism, the model predicts the wollastonite halo to be about the same size as the anorthite halo. Interestingly, the model also predicts the small diopside-free calcite margin surrounding the garnet interface, which is also observed in the thin section of the natural sample. Taken together, we interpret the garnet growth to be the consequence of the breakdown of anorthite + wollastonite + calcite at water-rich (XCO2 < 0.2) conditions around 600 °C. Preliminary modeling results suggest that the effective relative diffusion coefficients for Si, Mg and Al are not equal producing the diopside-free calcite rim surrounding the garnet edge. Connolly, J.A.D., 2005, Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation. EPSL, 236 : p. 524-541. Foster, C.T., 1993, SEG93: A program to model metamorphic textures: Geological Society of America Abstracts with Programs, v. 25, no. 6, p. A264.

Analysis of opposed jet hydrogen-air counter flow diffusion flame

NASA Technical Reports Server (NTRS)

Ho, Y. H.; Isaac, K. M.

1989-01-01

A computational simulation of the opposed-jet diffusion flame is performed to study its structure and extinction limits. The present analysis concentrates on the nitrogen-diluted hydrogen-air diffusion flame, which provides the basic information for many vehicle designs such as the aerospace plane for which hydrogen is a candidate as the fuel. The computer program uses the time-marching technique to solve the energy and species equations coupled with the momentum equation solved by the collocation method. The procedure is implemented in two stages. In the first stage, a one-step forward overal chemical reaction is chosen with the gas phase chemical reaction rate determined by comparison with experimental data. In the second stage, a complete chemical reaction mechanism is introduced with detailed thermodynamic and transport property calculations. Comparison between experimental extinction data and theoretical predictions is discussed. The effects of thermal diffusion as well as Lewis number and Prandtl number variations on the diffusion flame are also presented.

Breakdown of the reaction-diffusion master equation with nonelementary rates

NASA Astrophysics Data System (ADS)

Smith, Stephen; Grima, Ramon

2016-05-01

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.

Fungal bioleaching of WPCBs using Aspergillus niger: Observation, optimization and kinetics.

PubMed

Faraji, Fariborz; Golmohammadzadeh, Rabeeh; Rashchi, Fereshteh; Alimardani, Navid

2018-07-01

In this study, Aspergillus niger (A. niger) as an environmentally friendly agent for fungal bioleaching of waste printed circuit boards (WPCBs) was employed. D-optimal response surface methodology (RSM) was utilized for optimization of the bioleaching parameters including bioleaching method (one step, two step and spent medium) and pulp densities (0.5 g L -1 to 20 g L -1 ) to maximize the recovery of Zn, Ni and Cu from WPCBs. According to the high performance liquid chromatography analysis, citric, oxalic, malic and gluconic acids were the most abundant organic acids produced by A.niger in 21 days experiments. Maximum recoveries of 98.57% of Zn, 43.95% of Ni and 64.03% of Cu were achieved based on acidolysis and complexolysis dissolution mechanisms of organic acids. Based on the kinetic studies, the rate controlling mechanism for Zn dissolution at one step approach was found to be diffusion through liquid film, while it was found to be mixed control for both two step and spent medium. Furthermore, rate of Cu dissolution which is controlled by diffusion in one step and two step approaches, detected to be controlled by chemical reaction at spent medium. It was shown that for Ni, the rate is controlled by chemical reaction for all the methods studied. Eventually, it was understood that A. niger is capable of leaching 100% of Zn, 80.39% of Ni and 85.88% of Cu in 30 days. Copyright © 2018 Elsevier Ltd. All rights reserved.

Kinetics of heterogeneous chemical reactions: a theoretical model for the accumulation of pesticides in soil.

PubMed

Lin, S H; Sahai, R; Eyring, H

1971-04-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method.

Kinetics of Heterogeneous Chemical Reactions: A Theoretical Model for the Accumulation of Pesticides in Soil

PubMed Central

Lin, S. H.; Sahai, R.; Eyring, H.

1971-01-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method. PMID:5279519

Synthesis, characterization and electrochemical investigations of mixed-ligand copper(II)-organic supramolecular frameworks

NASA Astrophysics Data System (ADS)

Singh, Sandeep K.; Srivastava, Ashish Kumar; Srivastava, Krishna; Banerjee, Rahul; Prasad, Jagdish

2017-11-01

Two mixed-ligand copper(II)-organic coordination compounds with 5,5‧-dimethyl-2,2‧-bipyridine (5,5‧-Me2bpy) as a primary ligand while aliphatic malonate (Hmal) and aromatic 2-hydroxynicotinate (2-OHNA) as secondary ligands, were synthesized. These complexes are formulated as: [Cu(Hmal)(5,5‧-Me2bpy)(H2O)](ClO4) 1 and [Cu2(2-OHNA)2(5,5‧-Me2bpy)2(NO3)](NO3) 2. These two complexes were structurally characterized by single crystal X-ray diffraction analysis. Characterization was further supported by powder X-ray diffraction analysis, elemental analyses, FT-IR, FAB-MASS and TGA, DSC studies. Cyclic voltammetric and UV-visible spectral studies of these two complexes have also been done. The electrochemical studies of complex 1 in DMSO and DMF have shown that this complex undergoes quasi-reversible diffusion-controlled one-electron transfer reaction without any chemical complication while complex 2 in DMSO undergoes quasi-reversible diffusion-controlled one electron transfer reaction, following EC mechanism. The electrochemical behaviour of complex 2 in DMF is complicated probably due to presence of more than one species in solution phase.

First stage of reaction of molten Al with MgO substrate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morgiel, J., E-mail: j.morgiel@imim.pl; Sobczak, N.; Motor Transport Institute, 80 Jagiellońska St., 03-301 Warsaw

The Al/MgO couple was produced in vacuum (~ 5 × 10{sup −} {sup 4} Pa) by contact heating from RT up to 1000 °C and holding at that temperature for 1 h of a small 4 × 4 × 4 mm aluminium (5 N) sample placed on the [100] MgO single crystal substrate. TEM observations backed with electron diffraction analysis indicated that the interaction between liquid aluminium and MgO starts from a redox reaction producing a continuous layer of MgAl{sub 2}O{sub 4} spinel on the substrate surface. Its growth is controlled by solid state out-diffusion of magnesium and oxygen towardsmore » the surface being in contact with liquid metal. The thickening of spinel layer is accompanied by its cracking and infiltration with aluminium. The above process enables local dissolution of the MgO substrate and formation in it of a thin region of interpenetrating metallic channels walled with spinel. The removal of dissolved magnesium through open aluminium channels towards the drop and to vacuum locally produces areas of aluminium enriched with dissolved oxygen, which results in the nucleation of α-Al{sub 2}O{sub 3} at spinel clad walls. The growth of α-Al{sub 2}O{sub 3} is controlled only by the dissolution rate of MgO by aluminium, liquid state diffusion of Mg to drop/vacuum and oxygen to the front of the of α-Al{sub 2}O{sub 3} crystallites growing into MgO substrate. - Highlights: • New unique evidence of first stages of interaction of liquid Al with MgO substrates • Interaction of liquid Al with MgO starts with the formation of a layer MgAl{sub 2}O{sub 4}. • Growth of MgAl{sub 2}O{sub 4} is slow as controlled by solid state out-diffusion of Mg and O. • MgAl{sub 2}O{sub 4} serves as a nucleation site for Al{sub 2}O{sub 3} and consumed by it soon after. • Growth of Al{sub 2}O{sub 3} is fast as controlled by diffusion in liquid state.« less

Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (1 0 0) surfaces

NASA Astrophysics Data System (ADS)

Liu, Da-Jiang; Evans, James W.

2013-12-01

A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (1 0 0) or M(1 0 0) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(1 0 0) and O/M(1 0 0), as well as the interaction and reaction between different reactant species in mixed adlayers, such as (CO + O)/M(1 0 0). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(1 0 0) and O/M(1 0 0) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(1 0 0) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction-diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis.

Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (100) surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Dajiang; Evans, James W.

2013-12-01

A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (100) or M(100) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(100) and O/M(100), as well as the interaction and reaction between different reactant species in mixed adlayers,more » such as (CO + O)/M(100). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(100) and O/M(100) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(100) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis. (C) 2013 Elsevier Ltd. All rights reserved.« less

Controlled Hydrogen Peroxide Decomposition for a Solid Oxide Fuel Cell (SOFC) Oxidant Source with a Microreactor Model

DTIC Science & Technology

2007-10-01

established assuming first order kinetics weighted via an inputted catalyst mass, Mcat (equation 2). catrxn MCk *−=22OHr (2) The...H2O2 (0-50%w/w) solution heat capacity(J/kg*K) M cat Mcat 0.03 Mass of Catalyst (g) Deffhh2o 7.85E-10 Average effective diffusivity of H2O2 into... Mcat *c Rate Law for Elementary 1st Order Irreversible Reaction (mol/((s*m^3)) r H2O rtb -rt Rate Law for Elementary 1st Order Irreversible Reaction

High temperature alkali corrosion of ceramics in coal gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pickrell, G.R.; Sun, T.; Brown, J.J.

1992-02-24

The high temperature alkali corrosion kinetics of SiC have been systematically investigated from 950 to 1100[degrees]C at 0.63 vol % alkali vapor concentration. The corrosion rate in the presence of alkaliis approximately 10[sup 4] to 10[sup 5] times faster than the oxidation rate of SiC in air. The activation energy associated with the alkali corrosion is 406 kJ/mol, indicating a highly temperature-dependent reaction rate. The rate-controlling step of the overall reaction is likely to be the dissolution of silica in the sodium silicate liquid, based on the oxygen diffusivity data.

Spontaneous Symmetry Breaking Turing-Type Pattern Formation in a Confined Dictyostelium Cell Mass

NASA Astrophysics Data System (ADS)

Sawai, Satoshi; Maeda, Yasuo; Sawada, Yasuji

2000-09-01

We have discovered a new type of patterning which occurs in a two-dimensionally confined cell mass of the cellular slime mold Dictyostelium discoideum. Besides the longitudinal structure reported earlier, we observed a spontaneous symmetry breaking spot pattern whose wavelength shows similar strain dependency to that of the longitudinal pattern. We propose that these structures are due to a reaction-diffusion Turing instability similar to the one which has been exemplified by CIMA (chlorite-iodide-malonic acid) reaction. The present finding may exhibit the first biochemical Turing structure in a developmental system with a controllable boundary condition.

Strain-based diffusion solver for realistic representation of diffusion front in physical reactions

PubMed Central

2017-01-01

When simulating fluids, such as water or fire, interacting with solids, it is a challenging problem to represent details of diffusion front in physical reaction. Previous approaches commonly use isotropic or anisotropic diffusion to model the transport of a quantity through a medium or long interface. We have identified unrealistic monotonous patterns with previous approaches and therefore, propose to extend these approaches by integrating the deformation of the material with the diffusion process. Specifically, stretching deformation represented by strain is incorporated in a divergence-constrained diffusion model. A novel diffusion model is introduced to increase the global rate at which the solid acquires relevant quantities, such as heat or saturation. This ensures that the equations describing fluid flow are linked to the change of solid geometry, and also satisfy the divergence-free condition. Experiments show that our method produces convincing results. PMID:28448591

Analysis of transformations of the ultrafast electron transfer photoreaction mechanism in liquid solutions by the rate distribution approach.

PubMed

Kuzmin, Michael G; Soboleva, Irina V

2014-05-01

Representation of the experimental reaction kinetics in the form of rate distribution is shown to be an effective method for the analysis of the mechanisms of these reactions and for comparisons of the kinetics with QC calculations, as well as with the experimental data on the medium mobility. The rate constant distribution function P(k) can be obtained directly from the experimental kinetics N(t) by an inverse Laplace transform. The application of this approach to kinetic data for several excited-state electron transfer reactions reveals the transformations of their rate control factors in the time domain of 1-1000 ps. In neat electron donating solvents two components are observed. The fastest component (k > 1 ps(-1)) was found to be controlled by the fluctuations of the overall electronic coupling matrix element, involving all the reactant molecules, located inside the interior of the solvent shell, rather than for specific pairs of reactant molecules. The slower component (1 > k > 0.1 ps(-1)) is controlled by the medium reorganization (longitudinal relaxation times, τL). A substantial contribution from the non-stationary diffusion controlled reaction is observed in diluted solutions ([Q] < 1 M). No contribution from the long-distance electron transfer (electron tunneling) proposed earlier for the excited-state electron transfer between perylene and tetracyanoethylene in acetonitrile is observed. The rate distribution approach provides a simple and efficient method for the quantitative analysis of the reaction mechanism and transformation of the rate control factors in the course of the reactions.

Multistep Reduction Kinetics of Fine Iron Ore with Carbon Monoxide in a Micro Fluidized Bed Reaction Analyzer

NASA Astrophysics Data System (ADS)

Chen, Hongsheng; Zheng, Zhong; Chen, Zhiwei; Yu, Wenzhou; Yue, Junrong

2017-04-01

The reduction kinetics of Brazilian hematite by CO is investigated in a Micro Fluidized Bed Reaction Analyzer (MFBRA) using an analyzing method based on Johnson-Mehl-Avrami (JMA) model at temperatures of 973 K (700 °C), 1023 K (750 °C), 1073 K (800 °C), and 1123 K (850 °C). The solid products at different reduction stages are evaluated by SEM/EDS and XRD technologies. Results indicate that the reduction process is better to be discussed in terms of a parallel reaction model that consists of the reactions of hematite to wüstite and wüstite to iron, rather than a stepwise route. Meanwhile, the controlling mechanism of the reduction process is found to vary with temperature and the degree of conversion. The overall process is controlled by the gas-solid reaction occurring at the iron/wüstite interface in the initial stages, and then is limited by the nucleation of wüstite, and finally shifts to diffusion control. Moreover, the reactions of hematite to wüstite and wüstite to iron take place simultaneously but with different time dependences, and the apparent activation energies of hematite to wüstite and wüstite to iron are determined as 83.61 and 80.40 KJ/mol, respectively.

Review of problems in application of supersonic combustion

NASA Technical Reports Server (NTRS)

Ferri, A.

1977-01-01

The problem of air-breathing engines capable of flying at very high Mach numbers is described briefly. Possible performance of supersonic combustion ramjets is outlined briefly and the supersonic combustion process is described. Two mechanisms of combustion are outlined: one is supersonic combustion controlled by convection process, and the second is controlled by diffusion. The parameters related to the combustion process are discussed in detail. Data and analyses of reaction rates and mixing phenomena are represented; the flame mechanism is discussed, and experimental results are presented.

Multi-scale continuum modeling of biological processes: from molecular electro-diffusion to sub-cellular signaling transduction

NASA Astrophysics Data System (ADS)

Cheng, Y.; Kekenes-Huskey, P.; Hake, J. E.; Holst, M. J.; McCammon, J. A.; Michailova, A. P.

2012-01-01

This paper presents a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales (http://mccammon.ucsd.edu/smol/, http://FETK.org) by numerical solution of the time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times, with increasing ionic strength, and demonstrate the role of an enzyme's electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a nonlinear, reaction-diffusion system describing Ca2+ ligand buffering and diffusion in experimentally derived rodent ventricular myocyte geometries. Results reveal the important role of mobile and stationary Ca2+ buffers, including Ca2+ indicator dye. We found that alterations in Ca2+-binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate sub-cellular Ca2+ signals. The model predicts that reduced off-rate in the whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca2+ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for the integration of molecular-scale information into simulations of cellular-scale systems.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Mechanochemical mechanism for reaction of aluminium nano- and micrometre-scale particles.

PubMed

Levitas, Valery I

2013-11-28

A recently suggested melt-dispersion mechanism (MDM) for fast reaction of aluminium (Al) nano- and a few micrometre-scale particles during fast heating is reviewed. Volume expansion of 6% during Al melting produces pressure of several GPa in a core and tensile hoop stresses of 10 GPa in an oxide shell. Such stresses cause dynamic fracture and spallation of the shell. After spallation, an unloading wave propagates to the centre of the particle and creates a tensile pressure of 3-8 GPa. Such a tensile pressure exceeds the cavitation strength of liquid Al and disperses the melt into small, bare clusters (fragments) that fly at a high velocity. Reaction of the clusters is not limited by diffusion through a pre-existing oxide shell. Some theoretical and experimental results related to the MDM are presented. Various theoretical predictions based on the MDM are in good qualitative and quantitative agreement with experiments, which resolves some basic puzzles in combustion of Al particles. Methods to control and improve reactivity of Al particles are formulated, which are exactly opposite to the current trends based on diffusion mechanism. Some of these suggestions have experimental confirmation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wujcik, Kevin H.; Wang, Dunyang Rita; Pascal, Tod A.

Lithium sulfur (Li-S) batteries are well known for their high theoretical specific capacities, but are plagued with scientific obstacles that make practical implementation of the technology impossible. The success of Li-S batteries will likely necessitate the use of thick sulfur cathodes that enable high specific energy densities. However, little is known about the fundamental reaction mechanisms and chemical processes that take place in thick cathodes, as most research has focused on studying thinner cathodes that enable high performance. In this study, in situ X-ray absorption spectroscopy at the sulfur K-edge is used to examine the back of a 115 μmmore » thick Li-S cathode during discharge. Our results show that in such systems, where electrochemical reactions between sulfur and lithium are likely to proceed preferentially toward the front of the cathode, lithium polysulfide dianions formed in this region diffuse to the back of the cathode during discharge. We show that high conversion of elemental sulfur is achieved by chemical reactions between elemental sulfur and polysulfide dianions of intermediate chain length (Li 2S x, 4 ≤ x ≤ 6). Our work suggests that controlling the formation and diffusion of intermediate chain length polysulfide dianions is crucial for insuring full utilization of thick sulfur cathodes.« less

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems

PubMed Central

Hummer, Gerhard

2015-01-01

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions. PMID:26005592

Reaction-diffusion basis of retroviral infectivity

NASA Astrophysics Data System (ADS)

Sadiq, S. Kashif

2016-11-01

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env3) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env3 molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env3 diffuses comparably to Gag-absent Env3. Initial immobility of Env3 is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env3 diffusion, and permits Env3 clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Reactive diffusion in the presence of a diffusion barrier: Experiment and model

NASA Astrophysics Data System (ADS)

Mangelinck, D.; Luo, T.; Girardeaux, C.

2018-05-01

Reactions in thin films and diffusion barriers are important for applications such as protective coatings, electrical contact, and interconnections. In this work, the effect of a barrier on the kinetics of the formation for a single phase by reactive diffusion is investigated from both experimental and modeling point of views. Two types of diffusion barriers are studied: (i) a thin layer of W deposited between a Ni film and Si substrate and (ii) Ni alloy films, Ni(1%W) and Ni(5%Pt), that form a diffusion barrier during the reaction with the Si substrate. The effect of the barriers on the kinetics of δ-Ni2Si formation is determined by in situ X ray diffraction and compared to models that explain the kinetic slowdown induced by both types of barrier. A linear parabolic growth is found for the deposited barrier with an increasing linear contribution for increasing barrier thickness. On the contrary, the growth is mainly parabolic for the barrier formed by the reaction between an alloy film and the substrate. The permeability of the two types of barrier is determined and discussed. The developed models fit well with the dedicated model experiments, leading to a better understanding of the barrier effect on the reactive diffusion and allowing us to predict the barrier behaviour in various applications.

Dual-channel microreactor for gas-liquid syntheses.

PubMed

Park, Chan Pil; Kim, Dong-Pyo

2010-07-28

A microreactor consisting of two microfluidic channels that are separated by a thin membrane is devised for intimate contact between gas and liquid phases. Gas flowing in one microchannel can diffuse into the liquid flowing in the other microchannel through the thin membrane. An oxidative Heck reaction carried out in the dual-channel (DC) microreactor, in which gaseous oxygen plays a key role in the catalytic reaction, shows the significant improvement that can be made over the traditional batch reactor and the conventional segmental microreactor in terms of yield, selectivity, and reaction time. It also allows independent control of the flow of the gaseous reagent. The proposed DC microreactor should prove to be a powerful tool for fully exploring gas-liquid microchemistry.

Wavefronts for a global reaction-diffusion population model with infinite distributed delay

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

We consider a global reaction-diffusion population model with infinite distributed delay which includes models of Nicholson's blowflies and hematopoiesis derived by Gurney, Mackey and Glass, respectively. The existence of monotone wavefronts is derived by using the abstract settings of functional differential equations and Schauder fixed point theory.

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

Mechanism of spiral formation in heterogeneous discretized excitable media.

PubMed

Kinoshita, Shu-ichi; Iwamoto, Mayuko; Tateishi, Keita; Suematsu, Nobuhiko J; Ueyama, Daishin

2013-06-01

Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.

Electrochemical hydrogenation of thiophene on SPE electrodes

NASA Astrophysics Data System (ADS)

Huang, Haiyan; Yuan, Penghui; Yu, Ying; Chung, Keng H.

2017-01-01

Electrochemical reduction desulfurization is a promising technology for petroleum refining which is environmental friendly, low cost and able to achieve a high degree of automation. Electrochemical hydrogenation of thiophene was performed in a three-electrode system which SPE electrode was the working electrode. The electrochemical desulfurization was studied by cyclic voltammetry and bulk electrolysis with coulometry (BEC) techniques. The results of cyclic voltammetry showed that the electrochemical hydrogenation reduction reaction occurred at -0.4V. The BEC results showed that the currents generated from thiophene hydrogenation reactions increased with temperature. According to Arrhenius equation, activation energy of thiophene electrolysis was calculated and lower activation energy value indicated it was diffusion controlled reaction. From the products of electrolytic reactions, the mechanisms of electrochemical hydrogenation of thiophene were proposed, consisting of two pathways: openingring followed by hydrogenation, and hydrogenation followed by ring opening.

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.; McManus, Hugh L.

1996-01-01

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

Adenovirus type 5 intrinsic adsorption rates measured by surface plasmon resonance.

PubMed

Roper, D Keith; Nakra, Shamit

2006-01-01

Intrinsic adsorption rates of whole adenovirus type 5 (Ad5) onto a diethylaminoethyl (DEAE) anion exchange surface are measured for the first time by surface plasmon resonance (SPR). Fitting SPR sensorgrams to a two-compartment mass transport reaction model distinguishes intrinsic adsorption rates from slow diffusive Ad5 mass transport. Ad5 is a widely used viral vector for gene therapy that binds electrostatically to surfaces of cells and synthetics such as membranes, chromatographic resins, and glass. Increasing NaCl concentration from 4.8 to 14.4mM shifts binding of whole Ad5 from diffusion control to a regime where both sorption and diffusion affect binding. Intrinsic adsorption rates for Ad5-DEAE interaction are 16 times faster than intrinsic adsorption rates for Ad5 fiber knob interacting with soluble extracellular domain of coxsackievirus adenovirus receptors (s-CAR).

Hydrodynamic fingering instability induced by a precipitation reaction

NASA Astrophysics Data System (ADS)

De Wit, Anne; Nagatsu, Yuichiro

2014-05-01

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the build-up of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A+B → C type of reaction when a solution containing one of the reactant is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Finger-like precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice-versa. A mathematical modeling of the underlying mobility profile in the cell reconstructed on the basis of one-dimensional reaction-diffusion concentration profiles confirms that the instability originates from a local decrease in mobility driven by the precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns.

Unsteady Spherical Diffusion Flames in Microgravity

NASA Technical Reports Server (NTRS)

Atreya, Arvind; Berhan, S.; Chernovsky, M.; Sacksteder, Kurt R.

2001-01-01

The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and (mu-g) flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (i) It reduces the complexity by making the problem one-dimensional; (ii) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame. (iii) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in mu-g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in mu-g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Multiphase chemical kinetics of OH radical uptake by molecular organic markers of biomass burning aerosols: humidity and temperature dependence, surface reaction, and bulk diffusion.

PubMed

Arangio, Andrea M; Slade, Jonathan H; Berkemeier, Thomas; Pöschl, Ulrich; Knopf, Daniel A; Shiraiwa, Manabu

2015-05-14

Multiphase reactions of OH radicals are among the most important pathways of chemical aging of organic aerosols in the atmosphere. Reactive uptake of OH by organic compounds has been observed in a number of studies, but the kinetics of mass transport and chemical reaction are still not fully understood. Here we apply the kinetic multilayer model of gas-particle interactions (KM-GAP) to experimental data from OH exposure studies of levoglucosan and abietic acid, which serve as surrogates and molecular markers of biomass burning aerosol (BBA). The model accounts for gas-phase diffusion within a cylindrical coated-wall flow tube, reversible adsorption of OH, surface-bulk exchange, bulk diffusion, and chemical reactions at the surface and in the bulk of the condensed phase. The nonlinear dependence of OH uptake coefficients on reactant concentrations and time can be reproduced by KM-GAP. We find that the bulk diffusion coefficient of the organic molecules is approximately 10(-16) cm(2) s(-1), reflecting an amorphous semisolid state of the organic substrates. The OH uptake is governed by reaction at or near the surface and can be kinetically limited by surface-bulk exchange or bulk diffusion of the organic reactants. Estimates of the chemical half-life of levoglucosan in 200 nm particles in a biomass burning plume increase from 1 day at high relative humidity to 1 week under dry conditions. In BBA particles transported to the free troposphere, the chemical half-life of levoglucosan can exceed 1 month due to slow bulk diffusion in a glassy matrix at low temperature.

Helium diffusion in carbonates

NASA Astrophysics Data System (ADS)

Amidon, W. H.; Cherniak, D. J.; Watson, E. B.; Hobbs, D.

2013-12-01

The abundance and large grain size of carbonate minerals make them a potentially attractive target for 4He thermochronology and 3He cosmogenic dating, although the diffusive properties of helium in carbonates remain poorly understood. This work characterizes helium diffusion in calcite and dolomite to better understand the crystal-chemical factors controlling He transport and retentivity. Slabs of cleaved natural calcite and dolomite, and polished sections of calcite cut parallel or normal to c, were implanted with 3He at 3 MeV with a dose of 5x1015/cm2. Implanted carbonates were heated in 1-atm furnaces, and 3He distributions following diffusion anneals were profiled with Nuclear Reaction Analysis using the reaction 3He(d,p)4He. For 3He transport normal to cleavage surfaces in calcite, we obtain the following Arrhenius relation over the temperature range 78-300°C: Dcalcite = 9.0x10-9exp(-55 × 6 kJ mol-1/RT) m2sec-1. Diffusion in calcite exhibits marked anisotropy, with diffusion parallel to c about two orders of magnitude slower than diffusion normal to cleavage faces. He diffusivities for transport normal to the c-axis are similar in value to those normal to cleavage surfaces. Our findings are broadly consistent with helium diffusivities from step-heating measurements of calcite by Copeland et al. (2007); these bulk degassing data may reflect varying effects of diffusional anisotropy. Helium diffusion normal to cleavage surfaces in dolomite is significantly slower than diffusion in calcite, and has a much higher activation energy for diffusion. For dolomite, we obtain the following Arrhenius relation for He diffusion over the temperature range 150-400°C: Ddolomite = 9.0x10-8exp(-92 × 9 kJ mol-1/RT) m2sec-1. The role of crystallographic structure in influencing these differences among diffusivities was evaluated using the maximum aperture approach of Cherniak and Watson (2011), in which crystallographic structures are sectioned along possible diffusion directions and the maximum interstitial apertures in each 'slice' in the structure are identified. Preliminary results show that observed differences in diffusivities are consistent with the size of the smallest maximum aperture along each diffusion direction. In calcite, the smallest maximum apertures are ~0.92 and ~0.66 angstroms for cleavage-normal and c-axis parallel directions respectively. In dolomite, the smallest maximum aperture is ~0.78 angstroms for the cleavage normal direction. Work is in progress on characterizing helium diffusion for other orientations in dolomite, and in other carbonates, including aragonite and magnesite, and in implementing these diffusion findings in the interpretation and modeling of bulk volume diffusion in heterogeneous calcite crystals common in many geologic applications. Copeland et al. (2007) GCA 71, 4488-4511 Cherniak and Watson, (2011) Chem. Geo. 288, 149-161

Irreversible reactions and diffusive escape: Stationary properties

DOE PAGES

Krapivsky, Paul L.; Ben-Naim, Eli

2015-05-01

We study three basic diffusion-controlled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by particles, while the complementary half-line is empty. We show that the total number of particles that infiltrate the initially empty half-line is finite and has a stationary distribution. We determine the evolution of the average density from which we derive the average total number N of particles in the initially empty half-line; e.g. for annihilationmore » $$\\langle N\\rangle = \\frac{3}{16}+\\frac{1}{4\\π}$$ . For the coalescence process, we devise a procedure that in principle allows one to compute P(N), the probability to find exactly N particles in the initially empty half-line; we complete the calculations in the first non-trivial case (N = 1). As a by-product we derive the distance distribution between the two leading particles.« less

[Rapid bioluminescent antibiotic susceptibility assay].

PubMed

Frundzhian, V G; Ugarova, N N; Blatun, L A; Terekhova, R P; Rusanova, E V

2009-01-01

Rapid testing of pathogen susceptibility to antibiotics is of great practical value for rational chemotherapy of pyoinflammatory deseases and postoperative complications of microbial etiology. The standard microbiological methods, i.e., the disk diffusion method and the method of serial dilutions are labour- and time-consuming (not less than 18-36 hours). The method of the authors is based on measuring bioluminescence resulting from interaction of adenosine-5'-triphosphate (ATP) and ATP reagent, a standard reaction mixture of firefly luciferase (an enzyme) and luciferin. The bioluminescence intensity is proportional to the ATP concentration in the reaction mixture and the ATP concentration is proportional to the number of the pathogen viable cells in the sample. The bioluminescence intensity value in the pathogen suspension aliquots with and without (control) the antibiotic were compared after the incubation for 5 hours and the coefficient of the microbial cell growth inhibition was calculated. Satisfactory correlation (R2 > 88%) of the results of the bioluminescent assay and the assay with the disk diffusion method and the method of serial dilutions was observed.

Evaluation of shrinking core model in leaching process of Pomalaa nickel laterite using citric acid as leachant at atmospheric conditions

NASA Astrophysics Data System (ADS)

Wanta, K. C.; Perdana, I.; Petrus, H. T. B. M.

2016-11-01

Most of kinetics studies related to leaching process used shrinking core model to describe physical phenomena of the process. Generally, the model was developed in connection with transport and/or reaction of reactant components. In this study, commonly used internal diffusion controlled shrinking core model was evaluated for leaching process of Pomalaa nickel laterite using citric acid as leachant. Particle size was varied at 60-70, 100-120, -200 meshes, while the operating temperature was kept constant at 358 K, citric acid concentration at 0.1 M, pulp density at 20% w/v and the leaching time was for 120 minutes. Simulation results showed that the shrinking core model was inadequate to closely approach the experimental data. Meanwhile, the experimental data indicated that the leaching process was determined by the mobility of product molecules in the ash layer pores. In case of leaching resulting large product molecules, a mathematical model involving steps of reaction and product diffusion might be appropriate to develop.

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

Surface morphology and molecular bonding of CaCO3 nanocrystallites by gas diffusion method

NASA Astrophysics Data System (ADS)

Sulimai, N. H.; Rani, Rozina Abdul; Khusaimi, Z.; Abdullah, S.; Salifairus, M. J.; Alrokayan, Salman; Khan, Haseeb; Rusop, M.

2018-05-01

Calcium carbonate with the chemical formula of (CaCO3) is the most abundant element in the world. Its usage on certain applications is largely affected by its properties. The best means to control its properties is through controlled preparation of CaCO3. This study uses diffusion method between the precursors Calcium Chloride and Ammonium Carbonate. Instead of using water, ethanol was used to prepare the salt. Reaction was done in room temperature (RT) for 6h-24h. Smallest average crystallite size measured by FESEM micrograph is 500nm produced by synthesis of CaCO3 reacted for 168 hours. From energy-dispersive X-ray spectrum also indicated the smallest particle size is by CaCO3 reacted for 168 hours. Changes was seen for element Ca at 3.7keV.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes.

PubMed

Xu, Jingjie; Xie, Yan; Lu, Benzhuo; Zhang, Linbo

2016-08-25

The Debye-Hückel limiting law is used to study the binding kinetics of substrate-enzyme system as well as to estimate the reaction rate of a electrostatically steered diffusion-controlled reaction process. It is based on a linearized Poisson-Boltzmann model and known for its accurate predictions in dilute solutions. However, the substrate and product particles are in nonequilibrium states and are possibly charged, and their contributions to the total electrostatic field cannot be explicitly studied in the Poisson-Boltzmann model. Hence the influences of substrate and product on reaction rate coefficient were not known. In this work, we consider all the charged species, including the charged substrate, product, and mobile salt ions in a Poisson-Nernst-Planck model, and then compare the results with previous work. The results indicate that both the charged substrate and product can significantly influence the reaction rate coefficient with different behaviors under different setups of computational conditions. It is interesting to find that when substrate and product are both considered, under an overall neutral boundary condition for all the bulk charged species, the computed reaction rate kinetics recovers a similar Debye-Hückel limiting law again. This phenomenon implies that the charged product counteracts the influence of charged substrate on reaction rate coefficient. Our analysis discloses the fact that the total charge concentration of substrate and product, though in a nonequilibrium state individually, obeys an equilibrium Boltzmann distribution, and therefore contributes as a normal charged ion species to ionic strength. This explains why the Debye-Hückel limiting law still works in a considerable range of conditions even though the effects of charged substrate and product particles are not specifically and explicitly considered in the theory.

Origins and implications of the ordering of oxygen vacancies and localized electrons on partially reduced CeO 2(111)

DOE PAGES

Sutton, Jonathan E.; Beste, Ariana; Steven H. Overbury

2015-10-12

In this study, we use density functional theory to explain the preferred structure of partially reduced CeO 2(111). Low-energy ordered structures are formed when the vacancies are isolated (maximized intervacancy separation) and the size of the Ce 3+ ions is minimized. Both conditions help minimize disruptions to the lattice around the vacancy. The stability of the ordered structures suggests that isolated vacancies are adequate for modeling more complex (e.g., catalytic) systems. Oxygen diffusion barriers are predicted to be low enough that O diffusion between vacancies is thermodynamically controlled at room temperature. The O-diffusion-reaction energies and barriers are decreased when onemore » Ce f electron hops from a nearest-neighbor Ce cation to a next-nearest-neighbor Ce cation, with a barrier that has been estimated to be slightly less than the barrier to O diffusion in the absence of polaron hopping. In conculsion, this indicates that polaron hopping plays a key role in facilitating the overall O diffusion process, and depending on the relative magnitudes of the polaron hopping and O diffusion barriers, polaron hopping may be the kinetically limiting process.« less

Diffusion and binding constants for acetylcholine derived from the falling phase of miniature endplate currents.

PubMed Central

Land, B R; Harris, W V; Salpeter, E E; Salpeter, M M

1984-01-01

In previous papers we studied the rising phase of a miniature endplate current (MEPC) to derive diffusion and forward rate constants controlling acetylcholine (AcCho) in the intact neuromuscular junction. The present study derives similar values (but with smaller error ranges) for these constants by including experimental results from the falling phase of the MEPC. We find diffusion to be 4 X 10(-6) cm2 s-1, slightly slower than free diffusion, forward binding to be 3.3 X 10(7) M-1 s-1, and the distance from an average release site to the nearest exit from the cleft to be 1.6 micron. We also estimate the back reaction rates. From our values we can accurately describe the shape of MEPCs under different conditions of receptor and esterase concentration. Since we suggest that unbinding is slower than isomerization, we further predict that there should be several short "closing flickers" during the total open time for an AcCho-ligated receptor channel. PMID:6584895

Proposed uses of laser light scattering instruments for polymerization studies

NASA Technical Reports Server (NTRS)

Mathias, Lon J.; Hoyle, Charles E.; Mclaughlin, Kevin; Mcmanus, Samuel P.; Caruthers, James M.; Runge, Michael L.

1989-01-01

Microgravity offers a unique environment for studying polymer diffusion and polymer polymerization reactions. The absence of convection currents, which are the major mode of mixing at the molecular level on Earth, are eliminated or reduced in the microgravity environment. More importantly, the prediction of unique copolymer composition development in microgravity allows controlled formation of new compositions of matter. The absence of mixing at the molecular level should produce unique short block copolymers available for the first time for comonomer compositions which normally lead to random or long block copolymer under good mixing. The investigation of fundamental polymer diffusion and polymer polymerization processes in microgravity is proposed. This effort will involve fundamental studies of monomer and polymer diffusion; their effects on initiation, propagation, and especially termination kinetics rate constant; and the accurate evaluation of copolymerization reactivity ratios in microgravity. The experimental design is presented for these studies along with an evaluation technique for in situ monitoring of polymer diffusion and polymerization kinetics.

A hydrogen fuel cell for rapid, enzyme-catalysed organic synthesis with continuous monitoring.

PubMed

Wan, Lei; Megarity, Clare F; Siritanaratkul, Bhavin; Armstrong, Fraser A

2018-01-23

A one-pot fuel cell for specific, enzyme-catalysed organic synthesis, with continuous monitoring of rate and reaction progress, combines an electrode catalysing rapid, reversible and diffusion-controlled interconversion of NADP + and NADPH with a Pt electrode catalysing 2H + /H 2 interconversion. This Communication demonstrates its performance and characteristics using the reductive amination of 2-oxoglutarate as a test system.

Catalytic conversion in nanoporous materials: Concentration oscillations and spatial correlations due to inhibited transport and intermolecular interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, Andres; Evans, James W.

2016-11-03

We show that steady-state catalytic conversion in nanoporous materials can occur in a quasi-counter-diffusion mode with the reactant (product) concentration strongly decaying (growing) into the pore, but also with oscillations in the total concentration. These oscillations reflect the response of the fluid to the transition from an extended to a confined environment near the pore opening. We focus on the regime of strongly inhibited transport in narrow pores corresponding to single-file diffusion. Here, limited penetration of the reactant into the pores and the associated low reaction yield is impacted by strong spatial correlations induced by both reaction (non-equilibrium correlations) andmore » also by intermolecular interactions (thermodynamic correlations). We develop a generalized hydrodynamic formulation to effectively describe inhibited transport accounting for the effect of these correlations, and incorporate this description of transport into appropriate reaction-diffusion equations. These equations accurately describe both shorter-range concentration oscillations near the pore opening and the longer-range mesoscale variation of concentration profiles in the pore (and thus also describe reaction yield). Success of the analytic theory is validated by comparison with a precise kinetic Monte Carlo simulation of an appropriate molecular-level stochastic reaction-diffusion model. As a result, this work elucidates unconventional chemical kinetics in interacting confined systems.« less

Numerical Study of Pressure Influence on Methane-Oxygen Laminar Counterflow Diffusion Flames

NASA Astrophysics Data System (ADS)

Iino, Kimio; Akamatsu, Fumiteru; Katsuki, Masashi

We carried out numerical studies on methane/oxygen diffusion flames of counter-flow configuration to elucidate the influence of pressure on flame structure, heat release rate and reaction mechanisms. The chemistry in gas-phase was based on GRI-Mech 3.0 database. The thickness of diffusion flame became thinner with increasing strain rate a , with its characteristic flame thickness varying inversely with √a, especially its relation became significant with increasing pressure. Flame temperature increased with increasing pressure. Enhanced H2O production reactions, especially chain terminal reactions for H2O production, were found to be important in determining the flame temperature at high pressures. The small reduction in the flame temperature with increasing strain rate at high pressures, compared to the atmospheric pressure, is caused by the capacitor effect of product dissociation. From QRPDs, the third body dependent reactions were enhanced in high pressure conditions, hence C2 pathway was enhanced.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

NASA Astrophysics Data System (ADS)

Ivanov, Konstantin L.; Sadovsky, Vladimir M.; Lukzen, Nikita N.

2015-08-01

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N.; Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090

2015-08-28

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression formore » the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.« less

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

NASA Astrophysics Data System (ADS)

Straube, Ronny; Ward, Michael J.; Falcke, Martin

2007-10-01

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP3 receptor channels (IP3R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate `inner' and `outer' asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP3R. This supports the idea that clusters are formed by a purely diffusion limited process.

Inward propagating chemical waves in Taylor vortices.

PubMed

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

In Situ X-ray Absorption Spectroscopy Studies of Discharge Reactions in a Thick Cathode of a Lithium Sulfur Battery

DOE PAGES

Wujcik, Kevin H.; Wang, Dunyang Rita; Pascal, Tod A.; ...

2016-12-01

Lithium sulfur (Li-S) batteries are well known for their high theoretical specific capacities, but are plagued with scientific obstacles that make practical implementation of the technology impossible. The success of Li-S batteries will likely necessitate the use of thick sulfur cathodes that enable high specific energy densities. However, little is known about the fundamental reaction mechanisms and chemical processes that take place in thick cathodes, as most research has focused on studying thinner cathodes that enable high performance. In this study, in situ X-ray absorption spectroscopy at the sulfur K-edge is used to examine the back of a 115 μmmore » thick Li-S cathode during discharge. Our results show that in such systems, where electrochemical reactions between sulfur and lithium are likely to proceed preferentially toward the front of the cathode, lithium polysulfide dianions formed in this region diffuse to the back of the cathode during discharge. We show that high conversion of elemental sulfur is achieved by chemical reactions between elemental sulfur and polysulfide dianions of intermediate chain length (Li 2S x, 4 ≤ x ≤ 6). Our work suggests that controlling the formation and diffusion of intermediate chain length polysulfide dianions is crucial for insuring full utilization of thick sulfur cathodes.« less

Multispecies reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Fatollahi, A. H.; Khorrami, M.; Shariati, A.

2000-10-01

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Compatibility of buffered uranium carbides with tungsten.

NASA Technical Reports Server (NTRS)

Phillips, W. M.

1971-01-01

Results of compatibility tests between tungsten and hyperstoichiometric uranium carbide alloys run at 1800 C for 1000 and 2500 hours. These tests compared tungsten-buffered uranium carbide with tungsten-buffered uranium-zirconium carbide. The zirconium carbide addition appeared to widen the homogeneity range of the uranium carbide, making additional carbon available for reaction. Reaction layers could be formed by either of two diffusion paths, one producing UWC2, while the second resulted in the formation of W2C. UWC2 acts as a diffusion barrier for carbon and slows the growth of the reaction layer with time, while carbon diffusion is relatively rapid in W2C, allowing equilibrium to be reached in less than 2500 hours at a temperature of 1800 C.

Modeling the Impact of Heterogeneous Spatial Distribution of Soil Microbes on Pesticide Biodegradation at the Centimeter Scale

NASA Astrophysics Data System (ADS)

Babey, T.; De Dreuzy, J. R.; Pinheiro, M.; Garnier, P.; Vieublé-Gonod, L.; Rapaport, A.

2015-12-01

Micro-organisms and substrates may be heterogeneously distributed in soils. This repartition as well as transport mechanisms bringing them into contact are expected to impact the biodegradation rates. Pinheiro et al [2015] have measured in cm-large reconstructed soil cores the fate of an injection of 2,4-D pesticide for different injection conditions and initial distributions of soil pesticide degraders. Through the calibration of a reactive transport model of these experiments, we show that: i) biodegradation of diffusion-controlled pesticide fluxes is favored by a high Damköhler number (high reaction rate compared to flux rate); ii) abiotic sorption processes are negligible and do not interact strongly with biodegradation; iii) biodegradation is primarily governed by the initial repartition of pesticide and degraders for diffusion-controlled transport, as diffusion greatly limits the flux of pesticide reaching the microbial hotspot due to dilution. These results suggest that for biodegradation to be substantial, a spatial heterogeneity in the repartition of microbes and substrate has to be associated with intermittent and fast transport processes to mix them.

Direct induction of molecular alignment in liquid crystal polymer network film by photopolymerization

NASA Astrophysics Data System (ADS)

Hisano, K.; Aizawa, M.; Ishizu, M.; Kurata, Y.; Shishido, A.

2016-09-01

Liquid crystal (LC) is the promising material for the fabrication of high-performance soft, flexible devices. The fascinating and useful properties arise from their cooperative effect that inherently allows the macroscopic integration and control of molecular alignment through various external stimuli. To date, light-matter interaction is the most attractive stimuli and researchers developed photoalignment through photochemical or photophysical reactions triggered by linearly polarized light. Here we show the new choice based on molecular diffusion by photopolymerization. We found that photopolymerization of a LC monomer and a crosslinker through a photomask enables to direct molecular alignment in the resultant LC polymer network film. The key generating the molecular alignment is molecular diffusion due to the difference of chemical potentials between irradiated and unirradiated regions. This concept is applicable to various shapes of photomask and two-dimensional molecular alignments can be fabricated depending on the spatial design of photomask. By virtue of the inherent versatility of molecular diffusion in materials, the process would shed light on the fabrication of various high-performance flexible materials with molecular alignment having controlled patterns.

Confinement regulates complex biochemical networks: initiation of blood clotting by "diffusion acting".

PubMed

Shen, Feng; Pompano, Rebecca R; Kastrup, Christian J; Ismagilov, Rustem F

2009-10-21

This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da(2), was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as "diffusion acting", which is distinct from "diffusion sensing". The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological "on" and "off" processes that are controlled by thresholds.

Brain microstructural correlates of visuospatial choice reaction time in children.

PubMed

Madsen, Kathrine Skak; Baaré, William F C; Skimminge, Arnold; Vestergaard, Martin; Siebner, Hartwig R; Jernigan, Terry L

2011-10-15

The corticospinal tracts and the basal ganglia continue to develop during childhood and adolescence, and indices of their maturation can be obtained using diffusion-weighted imaging. Here we show that a simple measure of visuomotor function is correlated with diffusion parameters in the corticospinal tracts and neostriatum. In a cohort of 75 typically-developing children aged 7 to 13years, mean 5-choice reaction times (RTs) were assessed. We hypothesised that children with faster choice RTs would show lower mean diffusivity (MD) in the corticospinal tracts and neostriatum and higher fractional anisotropy (FA) in the corticospinal tracts, after controlling for age, gender, and handedness. Mean MD and/or FA were extracted from the right and left corticospinal tracts, putamen, and caudate nuclei. As predicted, faster 5-choice RTs were associated with lower MD in the corticospinal tracts, putamen, and caudate. MD effects on RT were bilateral in the corticospinal tracts and putamen, whilst right caudate MD was more strongly related to performance than was left caudate MD. Our results suggest a link between motor performance variability in children and diffusivity in the motor system, which may be related to: individual differences in the phase of fibre tract and neostriatal maturation in children of similar age, individual differences in motor experience during childhood (i.e., use-dependent plasticity), and/or more stable individual differences in the architecture of the motor system. Copyright © 2011 Elsevier Inc. All rights reserved.

Fluid flow and reaction fronts: characterization of physical processes at the microscale using SEM analyses

NASA Astrophysics Data System (ADS)

Beaudoin, Nicolas; Koehn, Daniel; Toussaint, Renaud; Gomez-Rivas, Enrique; Bons, Paul; Chung, Peter; Martín-Martín, Juan Diego

2014-05-01

Fluid migrations are the principal agent for mineral replacement in the upper crust, leading to dramatic changes in the porosity and permeability of rocks over several kilometers. Consequently, a better understanding of the physical parameters leading to mineral replacement is required to better understand and model fluid flow and rock reservoir properties. Large-scale dolostone bodies are one of the best and most debated examples of such fluid-related mineral replacement. These formations received a lot of attention lately, and although genetic mechanics and implications for fluid volume are understood, the mechanisms controlling the formation and propagation of the dolomitization reaction front remain unclear. This contribution aims at an improvement of the knowledge about how this replacement front propagates over space and time. We study the front sharpness on hand specimen and thin section scale and what the influence of advection versus diffusion of material is on the front development. In addition, we demonstrate how preexisting heterogeneities in the host rock affect the propagation of the reaction front. The rock is normally not homogeneous but contains grain boundaries, fractures and stylolites, and such structures are important on the scale of the front width. Using Scanning Electron Microscopy and Raman Spectroscopy we characterized the reaction front chemistry and morphology in different context. Specimens of dolomitization fronts, collected from carbonate sequences of the southern Maestrat Basin, Spain and the Southwestern Scottish Highlands suggest that the front thickness is about several mm being relatively sharp. Fluid infiltrated grain boundaries and fractures forming mm-scale transition zone. We study the structure of the reaction zone in detail and discuss implications for fluid diffusion-advection models and mineral replacement. In addition we formulate a numerical model taking into account fluid flow, diffusion and advection of the mobile reactive species, reaction rates, disorder in the location of the potential replacement seeds, and permeability heterogeneities. The goal of this model is to compare the shape of the resulting patterns, notably in terms of thickness, and eventually roughness or fractal dimension.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Daily, Michael; Baker, Nathan A.

2015-05-07

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Effect of integral membrane proteins on the lateral mobility of plastoquinone in phosphatidylcholine proteoliposomes.

PubMed

Blackwell, M F; Whitmarsh, J

1990-11-01

PYRENE FLUORESCENCE QUENCHING BY PLASTOQUINONE WAS USED TO ESTIMATE THE RATE OF PLASTOQUINONE LATERAL DIFFUSION IN SOYBEAN PHOSPHATIDYLCHOLINE PROTEOLIPOSOMES CONTAINING THE FOLLOWING INTEGRAL MEMBRANE PROTEINS: gramicidin D, spinach cytochrome bf complex, spinach cytochrome f, reaction centers from Rhodobacter sphaeroides, beef heart mitochondrial cytochrome bc(1), and beef heart mitochondrial cytochrome oxidase. The measured plastoquinone lateral diffusion coefficient varied between 1 and 3 . 10(-7) cm(2) s(-1) in control liposomes that lacked protein. When proteins were added, these values decreased: a 10-fold decrease was observed when 16-26% of the membrane surface area was occupied by protein for all the proteins but gramicidin. The larger protein complexes (cytochrome bf, Rhodobacter sphaeroides reaction centers, cytochrome bc(1), and cytochrome oxidase), whose hydrophobic volumes were 15-20 times as large as that of cytochrome f and the gramicidin transmembrane dimer, were 15-20 times as effective in decreasing the lateral-diffusion coefficient over the range of concentrations studied. These proteins had a much stronger effect than that observed for bacteriorhodopsin in fluorescence photobleaching recovery measurements. The effect of high-protein concentrations in gramicidin proteoliposomes was in close agreement with fluorescence photobleaching measurements. The results are compared with the predictions of several theoretical models of lateral mobility as a function of integral membrane concentration.

Effect of integral membrane proteins on the lateral mobility of plastoquinone in phosphatidylcholine proteoliposomes

PubMed Central

Blackwell, Mary F.; Whitmarsh, John

1990-01-01

Pyrene fluorescence quenching by plastoquinone was used to estimate the rate of plastoquinone lateral diffusion in soybean phosphatidylcholine proteoliposomes containing the following integral membrane proteins: gramicidin D, spinach cytochrome bf complex, spinach cytochrome f, reaction centers from Rhodobacter sphaeroides, beef heart mitochondrial cytochrome bc1, and beef heart mitochondrial cytochrome oxidase. The measured plastoquinone lateral diffusion coefficient varied between 1 and 3 · 10-7 cm2 s-1 in control liposomes that lacked protein. When proteins were added, these values decreased: a 10-fold decrease was observed when 16-26% of the membrane surface area was occupied by protein for all the proteins but gramicidin. The larger protein complexes (cytochrome bf, Rhodobacter sphaeroides reaction centers, cytochrome bc1, and cytochrome oxidase), whose hydrophobic volumes were 15-20 times as large as that of cytochrome f and the gramicidin transmembrane dimer, were 15-20 times as effective in decreasing the lateral-diffusion coefficient over the range of concentrations studied. These proteins had a much stronger effect than that observed for bacteriorhodopsin in fluorescence photobleaching recovery measurements. The effect of high-protein concentrations in gramicidin proteoliposomes was in close agreement with fluorescence photobleaching measurements. The results are compared with the predictions of several theoretical models of lateral mobility as a function of integral membrane concentration. PMID:19431774

A Reaction-Diffusion Model for Synapse Growth and Long-Term Memory

NASA Astrophysics Data System (ADS)

Liu, Kang; Lisman, John; Hagan, Michael

Memory storage involves strengthening of synaptic transmission known as long-term potentiation (LTP). The late phase of LTP is associated with structural processes that enlarge the synapse. Yet, synapses must be stable, despite continual subunit turnover, over the lifetime of an encoded memory. These considerations suggest that synapses are variable-size stable structure (VSSS), meaning they can switch between multiple metastable structures with different sizes. The mechanisms underlying VSSS are poorly understood. While experiments and theory have suggested that the interplay between diffusion and receptor-scaffold interactions can lead to a preferred stable size for synaptic domains, such a mechanism cannot explain how synapses adopt widely different sizes. Here we develop a minimal reaction-diffusion model of VSSS for synapse growth, incorporating the recent observation from super-resolution microscopy that neural activity can build compositional heterogeneities within synaptic domains. We find that introducing such heterogeneities can change the stable domain size in a controlled manner. We discuss a potential connection between this model and experimental data on synapse sizes, and how it provides a possible mechanism to structurally encode graded long-term memory. We acknowledge the support from NSF INSPIRE Award number IOS-1526941 (KL, MFH, JL) and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR- 1420382 (MFH).

Carbon isotope exchange between gaseous CO2 and thin solution films: Artificial cave experiments and a complete diffusion-reaction model

NASA Astrophysics Data System (ADS)

Hansen, Maximilian; Scholz, Denis; Froeschmann, Marie-Louise; Schöne, Bernd R.; Spötl, Christoph

2017-08-01

Speleothem stable carbon isotope (δ13C) records provide important paleoclimate and paleo-environmental information. However, the interpretation of these records in terms of past climate or environmental change remains challenging because of various processes affecting the δ13C signals. A process that has only been sparsely discussed so far is carbon isotope exchange between the gaseous CO2 of the cave atmosphere and the dissolved inorganic carbon (DIC) contained in the thin solution film on the speleothem, which may be particularly important for strongly ventilated caves. Here we present a novel, complete reaction diffusion model describing carbon isotope exchange between gaseous CO2 and the DIC in thin solution films. The model considers all parameters affecting carbon isotope exchange, such as diffusion into, out of and within the film, the chemical reactions occurring within the film as well as the dependence of diffusion and the reaction rates on isotopic mass and temperature. To verify the model, we conducted laboratory experiments under completely controlled, cave-analogue conditions at three different temperatures (10, 20, 30 °C). We exposed thin (≈0.1 mm) films of a NaHCO3 solution with four different concentrations (1, 2, 5 and 10 mmol/l, respectively) to a nitrogen atmosphere containing a specific amount of CO2 (1000 and 3000 ppmV). The experimentally observed temporal evolution of the pH and δ13C values of the DIC is in good agreement with the model predictions. The carbon isotope exchange times in our experiments range from ca. 200 to ca. 16,000 s and strongly depend on temperature, film thickness, atmospheric pCO2 and the concentration of DIC. For low pCO2 (between 500 and 1000 ppmV, as for strongly ventilated caves), our time constants are substantially lower than those derived in a previous study, suggesting a potentially stronger influence of carbon isotope exchange on speleothem δ13C values. However, this process should only have an influence in case of very long drip intervals and slow precipitation rates.

Hydrodynamically induced fluid transfer and non-convective double-diffusion in microgravity sliding solvent diffusion cells

NASA Technical Reports Server (NTRS)

Pollmann, Konrad W.; Stodieck, Louis S.; Luttges, Marvin W.

1994-01-01

Microgravity can provide a diffusion-dominated environment for double-diffusion and diffusion-reaction experiments otherwise disrupted by buoyant convection or sedimentation. In sliding solvent diffusion cells, a diffusion interface between two liquid columns is achieved by aligning two offset sliding wells. Fluid in contact with the sliding lid of the cavities is subjected to an applied shear stress. The momentum change by the start/stop action of the well creates an additional hydrodynamical force. In microgravity, these viscous and inertial forces are sufficiently large to deform the diffusion interface and induce hydrodynamic transfer between the wells. A series of KC-135 parabolic flight experiments were conducted to characterize these effects and establish baseline data for microgravity diffusion experiments. Flow visualizations show the diffusion interface to be deformed in a sinusoidal fashion following well alignment. After the wells were separated again in a second sliding movement, the total induced liquid transfer was determined and normalized by the well aspect ratio. The normalized transfer decreased linearly with Reynolds number from 3.3 to 4.0% (w/v) for Re = 0.4 (Stokes flow) to a minimum of 1.0% for Re = 23 to 30. Reynolds numbers that provide minimum induced transfers are characterized by an interface that is highly deformed and unsuitable for diffusion measurements. Flat diffusion interfaces acceptable for diffusion measurements are obtained with Reynolds numbers on the order of 7 to 10. Microgravity experiments aboard a sounding rocket flight verified counterdiffusion of different solutes to be diffusion dominated. Ground control experiments showed enhanced mixing by double-diffusive convection. Careful selection of experimental parameters improves initial conditions and minimizes induced transfer rates.

An experimental design method leading to chemical Turing patterns.

PubMed

Horváth, Judit; Szalai, István; De Kepper, Patrick

2009-05-08

Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

Chlorination Kinetics of Titanium Nitride for Production of Titanium Tetrachloride from Nitrided Ilmenite

NASA Astrophysics Data System (ADS)

Ahmadi, Eltefat; Rezan, Sheikh Abdul; Baharun, Norlia; Ramakrishnan, Sivakumar; Fauzi, Ahmad; Zhang, Guangqing

2017-10-01

The kinetics of chlorination of titanium nitride (TiN) was investigated in the temperature range of 523 K to 673 K (250 °C to 400 °C). The results showed that the extent of chlorination slightly increased with increasing temperature and decreasing particle size of titanium nitride at constant flow rate of N2-Cl2 gas mixture. At 523 K (250 °C), the extent of chlorination was 85.6 pct in 60 minutes whereas at 673 K (400 °C), it was 97.7 pct investigated by weight loss measurement and confirmed by ICP analyses. The experimental results indicated that a shrinking unreacted core model with mixed-control mechanism governed the chlorination rate. It was observed that the surface chemical reaction of chlorine gas on the surface of TiN particles was rate controlling in the initial stage and, during later stage, internal (pore) diffusion through the intermediate product layer was rate controlling step. Overall the process follows the mixed-control model incorporating both chemical reaction and internal diffusion control. The activation energy for the chlorination of TiN was found to be about 10.97 kJ mol-1. In processing TiCl4 from TiN and TiO0.02C0.13N0.85, the solids involved in the chlorination process were characterized by X-ray diffraction (XRD), Scanning electron microscopy (SEM) and Energy-dispersive X-ray spectrometer (EDX). The SEM/EDX results demonstrated the consumption of TiN particles with extent of chlorination that showed shrinking core behavior.

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

[Study on electrochemical mechanism of coronary stent used austenitic stainless steel in flowing artificial body fluid].

PubMed

Liang, Chenghao; Guo, Liang; Chen, Wan; Wang, Hua

2005-08-01

The electrochemical mechanism of austenitic stainless steel (SUS316L and SUS317L) coronary stents in flowing artificial body fluid has been investigated with electrochemical technologies. The results indicated that the flowing medium coursed the samples' pitting potential Eb shift negatively, increased the pitting corrosion sensitivity, accelerated its anodic dissolution, but had little effects on repassivated potential. The flowing environment had great effects on cathodic process. The oxygen reaction on the samples' surface became faster as the cathodic process was not controlled by oxygen diffusion but by mixed diffusion and electrochemical process. With the increase of velocity of solution, the pitting corrosion becomes liable to occur under this circumstance.

Molybdate transport in a chemically complex aquifer: Field measurements compared with solute-transport model predictions

USGS Publications Warehouse

Stollenwerk, Kenneth G.

1998-01-01

A natural-gradient tracer test was conducted in an unconfined sand and gravel aquifer on Cape Cod, Massachusetts. Molybdate was included in the injectate to study the effects of variable groundwater chemistry on its aqueous distribution and to evaluate the reliability of laboratory experiments for identifying and quantifying reactions that control the transport of reactive solutes in groundwater. Transport of molybdate in this aquifer was controlled by adsorption. The amount adsorbed varied with aqueous chemistry that changed with depth as freshwater recharge mixed with a plume of sewage-contaminated groundwater. Molybdate adsorption was strongest near the water table where pH (5.7) and the concentration of the competing solutes phosphate (2.3 micromolar) and sulfate (86 micromolar) were low. Adsorption of molybdate decreased with depth as pH increased to 6.5, phosphate increased to 40 micromolar, and sulfate increased to 340 micromolar. A one-site diffuse-layer surface-complexation model and a two-site diffuse-layer surface-complexation model were used to simulate adsorption. Reactions and equilibrium constants for both models were determined in laboratory experiments and used in the reactive-transport model PHAST to simulate the two-dimensional transport of molybdate during the tracer test. No geochemical parameters were adjusted in the simulation to improve the fit between model and field data. Both models simulated the travel distance of the molybdate cloud to within 10% during the 2-year tracer test; however, the two-site diffuse-layer model more accurately simulated the molybdate concentration distribution within the cloud.

The Melting Characteristics and Interfacial Reactions of Sn-ball/Sn-3.0Ag-0.5Cu-paste/Cu Joints During Reflow Soldering

NASA Astrophysics Data System (ADS)

Huang, J. Q.; Zhou, M. B.; Zhang, X. P.

2017-03-01

In this work, the melting characteristics and interfacial reactions of Sn-ball/Sn-3.0Ag-0.5Cu-paste/Cu (Sn/SAC305-paste/Cu) structure joints were studied using differential scanning calorimetry, in order to gain a deeper and broader understanding of the interfacial behavior and metallurgical combination among the substrate (under-bump metallization), solder ball and solder paste in a board-level ball grid array (BGA) assembly process, which is often seen as a mixed assembly using solder balls and solder pastes. Results show that at the SAC305 melting temperature of 217°C, neither the SAC305-paste nor the Sn-ball coalesce, while an interfacial reaction occurs between the SAC305-paste and Cu. A slight increase in reflow temperature (from 217°C to 218°C) results in the coalescence of the SAC305-paste with the Sn-ball. The Sn-ball exhibits premelting behavior at reflow temperatures below its melting temperature, and the premelting direction is from the bottom to the top of the Sn-ball. Remarkably, at 227°C, which is nearly 5°C lower than the melting point of pure Sn, the Sn-ball melts completely, resulting from two eutectic reactions, i.e., the reaction between Sn and Cu and that between Sn and Ag. Furthermore, a large amount of bulk Cu6Sn5 phase forms in the solder due to the quick dissolution of Cu substrate when the reflow temperature is increased to 245°C. In addition, the growth of the interfacial Cu6Sn5 layer at the SAC305-paste/Cu interface is controlled mainly by grain boundary diffusion, while the growth of the interfacial Cu3Sn layer is controlled mainly by bulk diffusion.

Recovery of valuable metals from waste diamond cutters through ammonia-ammonium sulfate leaching

NASA Astrophysics Data System (ADS)

Xue, Ping; Li, Guang-qiang; Yang, Yong-xiang; Qin, Qin-wei; Wei, Ming-xing

2017-12-01

Copper and zinc were recovered from waste diamond cutters through leaching with an ammonia-ammonium sulfate system and air as an oxidant. The effects of experimental parameters on the leaching process were investigated, and the potential-pH ( E-pH) diagrams of Cu-NH3-SO4 2--H2O and Zn-NH3-SO4 2--H2O at 25°C were drawn. Results showed that the optimal parameters for the leaching reaction are as follows: reaction temperature, 45°C; leaching duration, 3 h; liquid-to-solid ratio, 50:1 (mL/g); stirring speed, 200 r/min; ammonia concentration, 4.0 mol/L; ammonium sulfate concentration, 1.0 mol/L; and air flow rate, 0.2 L/min. The results of the kinetics study indicated that the leaching is controlled by the surface chemical reaction at temperatures below 35°C, and the leaching is controlled by diffusion through the product layer at temperatures above 35°C.

Coupling between geochemical reactions and multicomponent gas and solute transport in unsaturated media: A reactive transport modeling study

USGS Publications Warehouse

Molins, S.; Mayer, K.U.

2007-01-01

The two‐way coupling that exists between biogeochemical reactions and vadose zone transport processes, in particular gas phase transport, determines the composition of soil gas. To explore these feedback processes quantitatively, multicomponent gas diffusion and advection are implemented into an existing reactive transport model that includes a full suite of geochemical reactions. Multicomponent gas diffusion is described on the basis of the dusty gas model, which accounts for all relevant gas diffusion mechanisms. The simulation of gas attenuation in partially saturated landfill soil covers, methane production, and oxidation in aquifers contaminated by organic compounds (e.g., an oil spill site) and pyrite oxidation in mine tailings demonstrate that both diffusive and advective gas transport can be affected by geochemical reactions. Methane oxidation in landfill covers reduces the existing upward pressure gradient, thereby decreasing the contribution of advective methane emissions to the atmosphere and enhancing the net flux of atmospheric oxygen into the soil column. At an oil spill site, methane oxidation causes a reversal in the direction of gas advection, which results in advective transport toward the zone of oxidation both from the ground surface and the deeper zone of methane production. Both diffusion and advection contribute to supply atmospheric oxygen into the subsurface, and methane emissions to the atmosphere are averted. During pyrite oxidation in mine tailings, pressure reduction in the reaction zone drives advective gas flow into the sediment column, enhancing the oxidation process. In carbonate‐rich mine tailings, calcite dissolution releases carbon dioxide, which partly offsets the pressure reduction caused by O2 consumption.

Ballistic Motion of Enzymes that Catalyze Highly Exothermic Reactions

NASA Astrophysics Data System (ADS)

Tsekouras, Konstantinos; Pressé, Steve

Recently we proposed that the experimentally observed enhanced diffusion of enzymes catalyzing highly exothermic reactions is a consequence of their mechanism for dissipating reaction energy. More specifically, we proposed that reaction energy spreads out from the reaction site in the form of an acoustic wave which causes the enzyme to asymmetrically deform into the solvent. The solvent reaction propels the enzyme. However, it has been noted that in water, high viscosity should reduce enzyme momentum to zero within a few ps, so any diffusion increase should not be observable. Here we provide a model explaining how small volumetric expansions of biomolecules inside water may cause fluid compression that in turn creates regions of low fluid density around the biomolecule. We then investigate the dynamics of the biomolecule in the presence of these perturbations.

Engineering the Interfaces of Superadsorbing Graphene-Based Electrodes with Gas and Electrolyte to Boost Gas Evolution and Activation Reactions.

PubMed

Zhang, Jun-Jun; Lv, Li-Bing; Zhao, Tian-Jian; Lin, Yun-Xiao; Yu, Qiu-Ying; Su, Juan; Hirano, Shin-Ichi; Li, Xin-Hao; Chen, Jie-Sheng

2018-05-30

Electrochemical gas evolution and activation reactions are complicated processes, involving not only active electrocatalysts but also the interaction among solid electrodes, electrolyte, and gas-phase products and reactants. In this study, multiphase interfaces of superadsorbing graphene-based electrodes were controlled without changing the active centers to significantly facilitate mass diffusion kinetics for superior performance. The achieved in-depth understanding of how to regulate the interfacial properties to promote the electrochemical performance could provide valuable clues for electrode manufacture and for the design of more active electrocatalysts. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Buoyancy effects on smoldering combustion

NASA Technical Reports Server (NTRS)

Dosanjh, S.; Peterson, J.; Fernandez-Pello, A. C.; Pagni, P. J.

1985-01-01

The effect of buoyancy on the rate of spread of a concurrent smolder reaction through a porous combustible material is investigated theoretically and experimentally. In the experiments, buoyant forces are controlled by varying the density difference, and the smolder rate spread through porous alpha cellulose (0.83 void fraction) is measured as a function of the ambient air pressure. The smolder velocity is found to increase with the ambient pressure; extinction occurs when the buoyancy forces cannot overcome the drag forces, indicating that diffusion by itself cannot support the spread of a smolder reaction. Theoretical predictions are found to be in good qualitative agreement with the experimental results.

Quantum Yield of Cyclobutane Pyrimidine Dimer Formation Via the Triplet Channel Determined by Photosensitization.

PubMed

Liu, Lizhe; Pilles, Bert M; Gontcharov, Julia; Bucher, Dominik B; Zinth, Wolfgang

2016-01-21

UV-induced formation of the cyclobutane pyrimidine dimer (CPD) lesion is investigated by stationary and time-resolved photosensitization experiments. The photosensitizer 2'-methoxyacetophenone with high intersystem crossing efficiency and large absorption cross-section in the UV-A range was used. A diffusion controlled reaction model is presented. Time-resolved experiments confirmed the validity of the reaction model and provided information on the dynamics of the triplet sensitization process. With a series of concentration dependent stationary illumination experiments, we determined the quantum efficiency for CPD formation from the triplet state of the thymine dinucleotide TpT to be 4 ± 0.2%.

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Use of ion beams to simulate reaction of reactor fuels with their cladding

NASA Astrophysics Data System (ADS)

Birtcher, R. C.; Baldo, P.

2006-01-01

Processes occurring within reactor cores are not amenable to direct experimental observation. Among major concerns are damage, fission gas accumulation and reaction between the fuel and its cladding all of which lead to swelling. These questions can be investigated through simulation with ion beams. As an example, we discuss the irradiation driven interaction of uranium-molybdenum alloys, intended for use as low-enrichment reactor fuels, with aluminum, which is used as fuel cladding. Uranium-molybdenum coated with a 100 nm thin film of aluminum was irradiated with 3 MeV Kr ions to simulate fission fragment damage. Mixing and diffusion of aluminum was followed as a function of irradiation with RBS and nuclear reaction analysis using the 27Al(p,γ)28Si reaction which occurs at a proton energy of 991.9 keV. During irradiation at 150 °C, aluminum diffused into the uranium alloy at a irradiation driven diffusion rate of 30 nm2/dpa. At a dose of 90 dpa, uranium diffusion into the aluminum layer resulted in formation of an aluminide phase at the initial interface. The thickness of this phase grew until it consumed the aluminum layer. The rapid diffusion of Al into these reactor fuels may offer explanation of the observation that porosity is not observed in the fuel particles but on their periphery.

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

2009-06-01

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

Microfluidic droplet trapping array as nanoliter reactors for gas-liquid chemical reaction.

PubMed

Zhang, Qingquan; Zeng, Shaojiang; Qin, Jianhua; Lin, Bingcheng

2009-09-01

This article presents a simple method for trapping arrays of droplets relying on the designed microstructures of the microfluidic device, and this has been successfully used for parallel gas-liquid chemical reaction. In this approach, the trapping structure is composed of main channel, lateral channel and trapping region. Under a negative pressure, array droplets can be generated and trapped in the microstructure simultaneously, without the use of surfactant and the precise control of the flow velocity. By using a multi-layer microdevice containing the microstructures, single (pH gradient) and multiple gas-liquid reactions (metal ion-NH3 complex reaction) can be performed in array droplets through the transmembrane diffusion of the gas. The droplets with quantitative concentration gradient can be formed by only replacing the specific membrane. The established method is simple, robust and easy to operate, demonstrating the potential of this device for droplet-based high-throughput screening.

Patchy reaction-diffusion and population abundance: the relative importance of habitat amount and arrangement

Treesearch

Curtis H. Flather; Michael Bevers

2002-01-01

A discrete reaction-diffusion model was used to estimate long-term equilibrium populations of a hypothetical species inhabiting patchy landscapes to examine the relative importance of habitat amount and arrangement in explaining population size. When examined over a broad range of habitat amounts and arrangements, population size was largely determined by a pure amount...

Evidence of a kinetic isotope effect in nanoaluminum and water combustion.

PubMed

Tappan, Bryce C; Dirmyer, Matthew R; Risha, Grant A

2014-08-25

The normally innocuous combination of aluminum and water becomes violently reactive on the nanoscale. Research in the field of the combustion of nanoparticulate aluminum has important implications in the design of molecular aluminum clusters, hydrogen storage systems, as well as energetic formulations which could use extraterrestrial water for space propulsion. However, the mechanism that controls the reaction speed is poorly understood. While current models for micron-sized aluminum water combustion reactions place heavy emphasis on diffusional limitations, as reaction scales become commensurate with diffusion lengths (approaching the nanoscale) reaction rates have long been suspected to depend on chemical kinetics, but have never been definitely measured. The combustion analysis of nanoparticulate aluminum with H2O or D2O is presented. Different reaction rates resulting from the kinetic isotope effect are observed. The current study presents the first-ever observed kinetic isotope effect in a metal combustion reaction and verifies that chemical reaction kinetics play a major role in determining the global burning rate. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

NASA Astrophysics Data System (ADS)

Vidal-Henriquez, Estefania; Zykov, Vladimir; Bodenschatz, Eberhard; Gholami, Azam

2017-10-01

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

A Luenberger observer for reaction-diffusion models with front position data

NASA Astrophysics Data System (ADS)

Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe

2015-11-01

We propose a Luenberger observer for reaction-diffusion models with propagating front features, and for data associated with the location of the front over time. Such models are considered in various application fields, such as electrophysiology, wild-land fire propagation and tumor growth modeling. Drawing our inspiration from image processing methods, we start by proposing an observer for the eikonal-curvature equation that can be derived from the reaction-diffusion model by an asymptotic expansion. We then carry over this observer to the underlying reaction-diffusion equation by an ;inverse asymptotic analysis;, and we show that the associated correction in the dynamics has a stabilizing effect for the linearized estimation error. We also discuss the extension to joint state-parameter estimation by using the earlier-proposed ROUKF strategy. We then illustrate and assess our proposed observer method with test problems pertaining to electrophysiology modeling, including with a realistic model of cardiac atria. Our numerical trials show that state estimation is directly very effective with the proposed Luenberger observer, while specific strategies are needed to accurately perform parameter estimation - as is usual with Kalman filtering used in a nonlinear setting - and we demonstrate two such successful strategies.

Controlling Complex Systems and Developing Dynamic Technology

NASA Astrophysics Data System (ADS)

Avizienis, Audrius Victor

In complex systems, control and understanding become intertwined. Following Ilya Prigogine, we define complex systems as having control parameters which mediate transitions between distinct modes of dynamical behavior. From this perspective, determining the nature of control parameters and demonstrating the associated dynamical phase transitions are practically equivalent and fundamental to engaging with complexity. In the first part of this work, a control parameter is determined for a non-equilibrium electrochemical system by studying a transition in the morphology of structures produced by an electroless deposition reaction. Specifically, changing the size of copper posts used as the substrate for growing metallic silver structures by the reduction of Ag+ from solution under diffusion-limited reaction conditions causes a dynamical phase transition in the crystal growth process. For Cu posts with edge lengths on the order of one micron, local forces promoting anisotropic growth predominate, and the reaction produces interconnected networks of Ag nanowires. As the post size is increased above 10 microns, the local interfacial growth reaction dynamics couple with the macroscopic diffusion field, leading to spatially propagating instabilities in the electrochemical potential which induce periodic branching during crystal growth, producing dendritic deposits. This result is interesting both as an example of control and understanding in a complex system, and as a useful combination of top-down lithography with bottom-up electrochemical self-assembly. The second part of this work focuses on the technological development of devices fabricated using this non-equilibrium electrochemical process, towards a goal of integrating a complex network as a dynamic functional component in a neuromorphic computing device. Self-assembled networks of silver nanowires were reacted with sulfur to produce interfacial "atomic switches": silver-silver sulfide junctions, which exhibit complex dynamics (e.g. both short- and long-term changes in conductivity) in response to applied voltage signals. Characterization of these atomic switch networks (ASNs) brought out interesting parallels to biological neural networks, including power-law scaling in the statistics of electrical signal propagation and dynamic self-organization of differentiated subnetworks. A reservoir computing (RC) strategy was employed to utilize measurements of electrical signals dynamically generated in ASNs to perform time-series memory and manipulation tasks including a parity test and arbitrary waveform generation. These results represent the useful integration of a complex network into a dynamic physical RC device.

The relationship between the surface composition and electrical properties of corrosion films formed on carbon steel in alkaline sour medium: an XPS and EIS study.

PubMed

Galicia, Policarpo; Batina, Nikola; González, Ignacio

2006-07-27

This work studies the evolution of 1018 carbon steel surfaces during 3-15 day immersion in alkaline sour medium 0.1 M (NH4)2S and 10 ppm CN(-) as (NaCN). During this period of time, surfaces were jointly characterized by electrochemical techniques in situ (electrochemical impedance spectroscopy, EIS) and spectroscopic techniques ex situ (X-ray photoelectron spectroscopy, XPS). The results obtained by these techniques allowed for a description of electrical and chemical properties of the films of corrosion products formed at the 1018 steel surface. There is an interconversion cycle of chemical species that form films of corrosion products whose conversion reactions favor two different types of diffusions inside the films: a chemical diffusion of iron cations and a typical diffusion of atomic hydrogen. These phenomena jointly control the passivity of the interface attacked by the corrosive medium.

Two-dimensional enzyme diffusion in laterally confined DNA monolayers.

PubMed

Castronovo, Matteo; Lucesoli, Agnese; Parisse, Pietro; Kurnikova, Anastasia; Malhotra, Aseem; Grassi, Mario; Grassi, Gabriele; Scaggiante, Bruna; Casalis, Loredana; Scoles, Giacinto

2011-01-01

Addressing the effects of confinement and crowding on biomolecular function may provide insight into molecular mechanisms within living organisms, and may promote the development of novel biotechnology tools. Here, using molecular manipulation methods, we investigate restriction enzyme reactions with double-stranded (ds)DNA oligomers confined in relatively large (and flat) brushy matrices of monolayer patches of controlled, variable density. We show that enzymes from the contacting solution cannot access the dsDNAs from the top-matrix interface, and instead enter at the matrix sides to diffuse two-dimensionally in the gap between top- and bottom-matrix interfaces. This is achieved by limiting lateral access with a barrier made of high-density molecules that arrest enzyme diffusion. We put forward, as a possible explanation, a simple and general model that relates these data to the steric hindrance in the matrix, and we briefly discuss the implications and applications of this strikingly new phenomenon.

Reaction between aminoalkyl radicals and akyl halides: Dehalogenation by electron transfer?

NASA Astrophysics Data System (ADS)

Lalevée, J.; Fouassier, J. P.; Blanchard, N.; Ingold, K. U.

2011-07-01

Aminoalkyl radicals, such as Et2NCrad HCH3, have low oxidation potentials and are therefore powerful reducing agents. We have found that Et2NCrad HCH3 reacts with CCl4 and CBr4 in di-tert-butyl peroxide with bimolecular rate constants (measured by LFP) close, or equal, to the diffusion-controlled limit. For the less reactive halide, CH2Br2, the reaction rate is increased substantially by the addition of acetonitrile as a co-solvent. It is tentatively concluded that these reactions occur by electron-transfer from the aminoalkyl to the organohalide with formation of the iminium ion, Et2N+dbnd CHCH3 (NMR detection), halide ion and a halomethyl radical, e.g., rad CCl3 and rad CHCl2 (ESR, spin-trapping detection).

Rigorous results for the minimal speed of Kolmogorov-Petrovskii-Piscounov monotonic fronts with a cutoffa)

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Depassier, M. Cristina; Loss, Michael

2012-12-01

We study the effect of a cutoff on the speed of pulled fronts of the one-dimensional reaction diffusion equation. To accomplish this, we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles. This existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut-off parameter ɛ. From these bounds we estimate the range of validity of the Brunet-Derrida formula for a general class of reaction terms.

GOBF-ARMA based model predictive control for an ideal reactive distillation column.

PubMed

Seban, Lalu; Kirubakaran, V; Roy, B K; Radhakrishnan, T K

2015-11-01

This paper discusses the control of an ideal reactive distillation column (RDC) using model predictive control (MPC) based on a combination of deterministic generalized orthonormal basis filter (GOBF) and stochastic autoregressive moving average (ARMA) models. Reactive distillation (RD) integrates reaction and distillation in a single process resulting in process and energy integration promoting green chemistry principles. Improved selectivity of products, increased conversion, better utilization and control of reaction heat, scope for difficult separations and the avoidance of azeotropes are some of the advantages that reactive distillation offers over conventional technique of distillation column after reactor. The introduction of an in situ separation in the reaction zone leads to complex interactions between vapor-liquid equilibrium, mass transfer rates, diffusion and chemical kinetics. RD with its high order and nonlinear dynamics, and multiple steady states is a good candidate for testing and verification of new control schemes. Here a combination of GOBF-ARMA models is used to catch and represent the dynamics of the RDC. This GOBF-ARMA model is then used to design an MPC scheme for the control of product purity of RDC under different operating constraints and conditions. The performance of proposed modeling and control using GOBF-ARMA based MPC is simulated and analyzed. The proposed controller is found to perform satisfactorily for reference tracking and disturbance rejection in RDC. Copyright © 2015 Elsevier Inc. All rights reserved.

Reaction rates for mesoscopic reaction-diffusion kinetics

DOE PAGES

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2015-02-23

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In thismore » paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. Finally, we show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.« less

Reaction rates for mesoscopic reaction-diffusion kinetics

PubMed Central

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2016-01-01

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results. PMID:25768640

Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models.

PubMed

Drugowitsch, Jan

2016-02-11

We present a new, fast approach for drawing boundary crossing samples from Wiener diffusion models. Diffusion models are widely applied to model choices and reaction times in two-choice decisions. Samples from these models can be used to simulate the choices and reaction times they predict. These samples, in turn, can be utilized to adjust the models' parameters to match observed behavior from humans and other animals. Usually, such samples are drawn by simulating a stochastic differential equation in discrete time steps, which is slow and leads to biases in the reaction time estimates. Our method, instead, facilitates known expressions for first-passage time densities, which results in unbiased, exact samples and a hundred to thousand-fold speed increase in typical situations. In its most basic form it is restricted to diffusion models with symmetric boundaries and non-leaky accumulation, but our approach can be extended to also handle asymmetric boundaries or to approximate leaky accumulation.

Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions

NASA Astrophysics Data System (ADS)

Yeh, Gour-Tsyh (George); Siegel, Malcolm D.; Li, Ming-Hsu

2001-02-01

The couplings among chemical reaction rates, advective and diffusive transport in fractured media or soils, and changes in hydraulic properties due to precipitation and dissolution within fractures and in rock matrix are important for both nuclear waste disposal and remediation of contaminated sites. This paper describes the development and application of LEHGC2.0, a mechanistically based numerical model for simulation of coupled fluid flow and reactive chemical transport, including both fast and slow reactions in variably saturated media. Theoretical bases and numerical implementations are summarized, and two example problems are demonstrated. The first example deals with the effect of precipitation/dissolution on fluid flow and matrix diffusion in a two-dimensional fractured media. Because of the precipitation and decreased diffusion of solute from the fracture into the matrix, retardation in the fractured medium is not as large as the case wherein interactions between chemical reactions and transport are not considered. The second example focuses on a complicated but realistic advective-dispersive-reactive transport problem. This example exemplifies the need for innovative numerical algorithms to solve problems involving stiff geochemical reactions.

Two dimensional, transient catalytic combustion of CO-air on platinum

NASA Technical Reports Server (NTRS)

Sinha, N.; Bruno, C.; Bracco, F. V.

1985-01-01

The light off transient of catalytic combustion of lean CO-air mixtures in a platinum coated channel of a honeycomb monolith is studied with a model that resolves transient radial and axial gradients in both the gas and the solid. For the conditions studied it is concluded that: the initial heat release occurs near the entrance at the gas-solid interface and is controlled by heterogeneous reactions; large spatial and temporal temperature gradients occur in the solid near the entrance controlled mostly by the availability of fuel; the temperature of the solid near the entrance achieves almost its steady state value before significant heating of the back; heterogeneous reactions and the gas heated up front and flowing downstream heat the back of the solid; the overall transient time is controlled by the thermal inertia of the solid and by forced convection; radiation significantly influences both transient and steady state particularly near the entrance; the oxidation of CO occurs mostly on the catalyst and becomes diffusion controlled soon into the transient.

Induced polarization: Simulation and inversion of nonlinear mineral electrodics

NASA Astrophysics Data System (ADS)

Agunloye, Olu

1983-02-01

Graph-theoretic representations are used to model nonlinear electrodics, while forward and inverse simulations are based on reaction rate theory. The electrodic responses are presented as distorted elliptical Lissajous shapes obtained from dynamic impedance over a full cycle. Simulations show that asymmetry in reaction energy barrier causes slight asymmetry in the shape of the response ellipse and hardly affects the phase angle of the complex electrode impedance. The charge transfer resistance and the diffusion constraints tend to have opposite effects. The former causes reduction in the phase angle, tending to make the impedance purely resistive. Both of these mechanisms show saturation effects. Charge transfer resistance at its limit forces a thin S-type symmetry on the Lissajous patterns, while with diffusion control the size of the Lissajous patterns begins to reduce after saturation. The fixed layer causes substantial increase in the phase angle and tends to “enlarge” the Lissajous patterns. It is responsible for the hysteresis-like shapes of the Lissajous patterns when superimposed on strong charge transfer resistance. This study shows that it is quite possible to deduce the mechanisms that control the electrodic processes by inverting electrodic parameters from “observed” distorted, nonelliptical Lissajous patterns characteristic of nonlinear electrodics. The results and qualities of the inversion technique are discussed.

The chemistry and diffusion of aircraft exhausts in the lower stratosphere during the first few hours after fly-by. [with attention to ozone depletion by SST exhaust plumes

NASA Technical Reports Server (NTRS)

Hilst, G. R.

1974-01-01

An analysis of the hydrogen-nitrogen-oxygen reaction systems in the lower stratosphere as they are initially perturbed by individual aircraft engine exhaust plumes was conducted in order to determine whether any significant chemical reactions occur, either among exhaust chemical species, or between these species and the environmental ozone, while the exhaust products are confined to intact plume segments at relatively high concentrations. The joint effects of diffusive mixing and chemical kinetics on the reactions were also studied, using the techniques of second-order closure diffusion/chemistry models. The focus of the study was on the larger problem of the potential depletion of ozone by supersonic transport aircraft exhaust materials emitted into the lower stratosphere.

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

NASA Astrophysics Data System (ADS)

Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

2017-05-01

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Partial melting kinetics of plagioclase-diopside pairs

NASA Astrophysics Data System (ADS)

Tsuchiyama, Akira

1985-09-01

Partial melting experiments on plagioclase (An60) and diopside have been carried out using pairs of large crystals to investigate textures and kinetics of melting. The experiments were done at one atmosphere pressure as a function of temperature (1,190 1,307° C) and time (1.5 192 h). Melting took place mainly at the plagioclase-diopside contact planes. Reaction zones composed of fine mixtures of calcic plagioclase and melt were developed from the surface of the plagioclase crystal inward. There exists a critical temperature, below which only a few % melting can occur over the duration of the experiments. This sluggish melting is caused by slow NaSi-CaAl diffusion in plagioclase, because the plagioclase crystal must change its composition to produce albite-rich cotectic melts. Diffusion in the solid also affects the chemical composition of the melts. During initial melting, potassium is preferentially extracted from plagioclase because K-Na diffusion in plagioclase is faster than that of NaSi-CaAl. This also causes a shift in the cotectic compositions. Above the “critical temperature”, on the other hand, melting is promoted by a metastable reaction in which the plagioclase composition does not change, and which produces melts with compositional gradients along the original An60-diopside tie line. The critical temperature is determined by the intersection of the cotectic and the An60-diopside tie line. Interdiffusion coefficients of plagioclase-diopside components in the melt are estimated from melting rates above the critical temperature by using a simplified steady-state diffusion model (e.g., 10-8 cm2/sec at 1,300° C). Many examples of reaction zones due to partial melting have been described as spongy or fingerprint-like textures in xenoliths. Metastable melting above the critical temperature is considered to take place in natural melting where there is a high degree of melting. However, we cannot exclude the possibility of disequilibrium created by sluggish melting controlled by diffusion in the minerals. If melting occurs close to the solidus, this process can be important even for partial melting in the upper mantle.

Nitric oxide diffusion to red blood cells limits extracellular, but not intraphagosomal, peroxynitrite formation by macrophages.

PubMed

Prolo, Carolina; Álvarez, María Noel; Ríos, Natalia; Peluffo, Gonzalo; Radi, Rafael; Romero, Natalia

2015-10-01

Macrophage-derived nitric oxide ((•)NO) participates in cytotoxic mechanisms against diverse microorganisms and tumor cells. These effects can be mediated by (•)NO itself or (•)NO-derived species such as peroxynitrite formed by its diffusion-controlled reaction with NADPH oxidase-derived superoxide radical anion (O(2)(•-)). In vivo, the facile extracellular diffusion of (•)NO as well as different competing consumption routes limit its bioavailability for the reaction with O(2)(•-) and, hence, peroxynitrite formation. In this work, we evaluated the extent by which (•)NO diffusion to red blood cells (RBC) can compete with activated macrophages-derived O(2)(•-) and affect peroxynitrite formation yields. Macrophage-dependent peroxynitrite production was determined by boron-based probes that react directly with peroxynitrite, namely, coumarin-7-boronic acid (CBA) and fluorescein-boronate (Fl-B). The influence of (•)NO diffusion to RBC on peroxynitrite formation was experimentally analyzed in co-incubations of (•)NO and O(2)(•-)-forming macrophages with erythrocytes. Additionally, we evaluated the permeation of (•)NO to RBC by measuring the intracellular oxidation of oxyhemoglobin to methemoglobin. Our results indicate that diluted RBC suspensions dose-dependently inhibit peroxynitrite formation, outcompeting the O(2)(•-) reaction. Computer-assisted kinetic studies evaluating peroxynitrite formation by its precursor radicals in the presence of RBC are in accordance with experimental results. Moreover, the presence of erythrocytes in the proximity of (•)NO and O(2)(•-)-forming macrophages prevented intracellular Fl-B oxidation pre-loaded in L1210 cells co-cultured with activated macrophages. On the other hand, Fl-B-coated latex beads incorporated in the macrophage phagocytic vacuole indicated that intraphagosomal probe oxidation by peroxynitrite was not affected by nearby RBC. Our data support that in the proximity of a blood vessel, (•)NO consumption by RBC will limit the extracellular formation (and subsequent cytotoxic effects) of peroxynitrite by activated macrophages, while the intraphagosomal yield of peroxynitrite will remain unaffected. Copyright © 2015. Published by Elsevier Inc.

Intraparticle diffusion limitations in the hydrogenation of monounsaturated edible oils and their fatty acid methyl esters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jonker, G.H.; Veldsink, J.W.; Beenackers, A.A.C.M.

1998-12-01

Intraparticle diffusion limitation in the hydrogenation and isomerization of fatty acid methyl esters (FAMEs) and edible oils (triacylglycerol, TAG) in porous nickel catalyst was investigated both under reactive and under inert conditions. Under reactive conditions, the diffusion coefficients were determined from the best fits of the model simulations applying the intrinsic reacting kinetics of monounsaturated FAME hydrogenation to experiments under diffusion limited conditions. Due to the absence of reaction (hydrogenation of double bonds), the obtained effective H{sub z} diffusion coefficient (D{sub e}) with the HPLC technique is volume averaged and thereby determined by the larger intercrystalline pores (<30% of themore » total pore volume) only. Moreover, D{sub e} measured under reaction conditions reflected the influence of the micropores, resulting in a 10-fold lower value.« less

Product selectivity control induced by using liquid-liquid parallel laminar flow in a microreactor.

PubMed

Amemiya, Fumihiro; Matsumoto, Hideyuki; Fuse, Keishi; Kashiwagi, Tsuneo; Kuroda, Chiaki; Fuchigami, Toshio; Atobe, Mahito

2011-06-07

Product selectivity control based on a liquid-liquid parallel laminar flow has been successfully demonstrated by using a microreactor. Our electrochemical microreactor system enables regioselective cross-coupling reaction of aldehyde with allylic chloride via chemoselective cathodic reduction of substrate by the combined use of suitable flow mode and corresponding cathode material. The formation of liquid-liquid parallel laminar flow in the microreactor was supported by the estimation of benzaldehyde diffusion coefficient and computational fluid dynamics simulation. The diffusion coefficient for benzaldehyde in Bu(4)NClO(4)-HMPA medium was determined to be 1.32 × 10(-7) cm(2) s(-1) by electrochemical measurements, and the flow simulation using this value revealed the formation of clear concentration gradient of benzaldehyde in the microreactor channel over a specific channel length. In addition, the necessity of the liquid-liquid parallel laminar flow was confirmed by flow mode experiments.

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

NASA Astrophysics Data System (ADS)

Dahlem, Markus A.; Schneider, Felix M.; Schöll, Eckehard

2008-06-01

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of ˜3mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.

A diffusion modelling approach to understanding contextual cueing effects in children with ADHD

PubMed Central

Weigard, Alexander; Huang-Pollock, Cynthia

2014-01-01

Background Strong theoretical models suggest implicit learning deficits may exist among children with Attention Deficit Hyperactivity Disorder (ADHD). Method We examine implicit contextual cueing (CC) effects among children with ADHD (n=72) and non-ADHD Controls (n=36). Results Using Ratcliff’s drift diffusion model, we found that among Controls, the CC effect is due to improvements in attentional guidance and to reductions in response threshold. Children with ADHD did not show a CC effect; although they were able to use implicitly acquired information to deploy attentional focus, they had more difficulty adjusting their response thresholds. Conclusions Improvements in attentional guidance and reductions in response threshold together underlie the CC effect. Results are consistent with neurocognitive models of ADHD that posit sub-cortical dysfunction but intact spatial attention, and encourage the use of alternative data analytic methods when dealing with reaction time data. PMID:24798140

Strain localization and fabric development in polycrystalline anorthite + melt by water diffusion in an axial deformation experiment

NASA Astrophysics Data System (ADS)

Fukuda, Jun-ichi; Muto, Jun; Nagahama, Hiroyuki

2018-01-01

We performed two axial deformation experiments on synthetic polycrystalline anorthite samples with a grain size of 3 μm and 5 vol% Si-Al-rich glass at 900 °C, a confining pressure of 1.0 GPa, and a strain rate of 10-4.8 s-1. One sample was deformed as-is (dry); in the other sample, two half-cut samples (two cores) with 0.15 wt% water at the boundary were put together in the apparatus. The mechanical data for both samples were essentially identical with a yield strength of 700 MPa and strain weakening of 500 MPa by 20% strain. The dry sample appears to have been deformed by distributed fracturing. Meanwhile, the water-added sample shows plastic strain localization in addition to fracturing and reaction products composed of zoisite grains and SiO2 materials along the boundary between the two sample cores. Infrared spectra of the water-added sample showed dominant water bands of zoisite. The maximum water content was 1500 wt ppm H2O at the two-core boundary, which is the same as the added amount. The water contents gradually decreased from the boundaries to the sample interior, and the gradient fitted well with the solution of the one-dimensional diffusion equation. The determined diffusion coefficient was 7.4 × 10-13 m2/s, which agrees with previous data for the grain boundary diffusion of water. The anorthite grains in the water-added sample showed no crystallographic preferred orientation. Textural observations and water diffusion indicate that water promotes the plastic deformation of polycrystalline anorthite by grain-size-sensitive creep as well as simultaneous reactions. We calculated the strain rate evolution controlled by water diffusion in feldspar aggregates surrounded by a water source. We assumed water diffusion in a dry rock mass with variable sizes. Diffused water weakens a rock mass with time under compressive stress. The calculated strain rate decreased from 10-10 to 10-15 s-1 with an increase in the rock mass size to which water is supplied from < 1 m to 1 km and an increase in the time of water diffusion from < 1 to 10,000 years. This indicates a decrease in the strain rate in a rock mass with increasing deformation via water diffusion.

The Effectiveness of Surface Coatings on Preventing Interfacial Reaction During Ultrasonic Welding of Aluminum to Magnesium

NASA Astrophysics Data System (ADS)

Panteli, Alexandria; Robson, Joseph D.; Chen, Ying-Chun; Prangnell, Philip B.

2013-12-01

High power ultrasonic spot welding (USW) is a solid-state joining process that is advantageous for welding difficult dissimilar material couples, like magnesium to aluminum. USW is also a useful technique for testing methods of controlling interfacial reaction in welding as the interface is not greatly displaced by the process. However, the high strain rate deformation in USW has been found to accelerate intermetallic compound (IMC) formation and a thick Al12Mg17 and Al3Mg2 reaction layer forms after relatively short welding times. In this work, we have investigated the potential of two approaches for reducing the IMC reaction rate in dissimilar Al-Mg ultrasonic welds, both involving coatings on the Mg sheet surface to (i) separate the join line from the weld interface, using a 100- μm-thick Al cold spray coating, and (ii) provide a diffusion barrier layer, using a thin manganese physical vapor deposition (PVD) coating. Both methods were found to reduce the level of reaction and increase the failure energy of the welds, but their effectiveness was limited due to issues with coating attachment and survivability during the welding cycle. The effect of the coatings on the joint's interface microstructure, and the fracture behavior have been investigated in detail. Kinetic modeling has been used to show that the benefit of the cold spray coating can be attributed to the reaction rate reverting to that expected under static conditions. This reduces the IMC growth rate by over 50 pct because at the weld line, the high strain rate dynamic deformation in USW normally enhances diffusion through the IMC layer. In comparison, the thin PVD barrier coating was found to rapidly break up early in USW and become dispersed throughout the deformation layer reducing its effectiveness.

Finite element procedures for time-dependent convection-diffusion-reaction systems

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Park, Y. J.; Deans, H. A.

1988-01-01

New finite element procedures based on the streamline-upwind/Petrov-Galerkin formulations are developed for time-dependent convection-diffusion-reaction equations. These procedures minimize spurious oscillations for convection-dominated and reaction-dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations. As a special application problem, the single-well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests.

Influence of the baking process for chemically amplified resist on CD performance

NASA Astrophysics Data System (ADS)

Sasaki, Shiho; Ohfuji, Takeshi; Kurihara, Masa-aki; Inomata, Hiroyuki; Jackson, Curt A.; Murata, Yoshio; Totsukawa, Daisuke; Tsugama, Naoko; Kitano, Naoki; Hayashi, Naoya; Hwang, David H.

2002-12-01

CD uniformity and MTT (Mean to Target) control are very important in mask production for the 90nm node and beyond. Although it is well known that baking temperatures influence CD control in the CAR (chemically amplified resist) process for mask patterning, we found that 2 other process factors, which are related to acid diffusion and CA- reaction, greatly affect CD performance. We used a commercially available, negative CAR material and a 50kV exposure tool. We focused on the baking process for both PB (Pre Baking) and PEB (Post Exposure Bake). Film densification strength was evaluated from film thickness loss during PB. Plate temperature distribution was monitored with a thermocouple plate and IR camera. CA-reactions were also monitored with in-situ FTIR during PEB. CD uniformity was used to define the process influence. In conclusion, we found that airflow control and ramping temperature control in the baking process are very important factors to control CD in addition to conventional temperature control. These improvements contributed to a 30 % of reduction in CD variation.

High Temperature Degradation Mechanisms in Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.

1996-01-01

Polymer matrix composites are increasingly used in demanding structural applications in which they may be exposed to harsh environments. The durability of such materials is a major concern, potentially limiting both the integrity of the structures and their useful lifetimes. The goal of the current investigation is to develop a mechanism-based model of the chemical degradation which occurs, such that given the external chemical environment and temperatures throughout the laminate, laminate geometry, and ply and/or constituent material properties, we can calculate the concentration of diffusing substances and extent of chemical degradation as functions of time and position throughout the laminate. This objective is met through the development and use of analytical models, coupled to an analysis-driven experimental program which offers both quantitative and qualitative information on the degradation mechanism. Preliminary analyses using a coupled diffusion/reaction model are used to gain insight into the physics of the degradation mechanisms and to identify crucial material parameters. An experimental program is defined based on the results of the preliminary analysis which allows the determination of the necessary material coefficients. Thermogravimetric analyses are carried out in nitrogen, air, and oxygen to provide quantitative information on thermal and oxidative reactions. Powdered samples are used to eliminate diffusion effects. Tests in both inert and oxidative environments allow the separation of thermal and oxidative contributions to specimen mass loss. The concentration dependency of the oxidative reactions is determined from the tests in pure oxygen. Short term isothermal tests at different temperatures are carried out on neat resin and unidirectional macroscopic specimens to identify diffusion effects. Mass loss, specimen shrinkage, the formation of degraded surface layers and surface cracking are recorded as functions of exposure time. Geometry effects in the neat resin, and anisotropic diffusion effects in the composites, are identified through the use of specimens with different aspect ratios. The data is used with the model to determine reaction coefficients and effective diffusion coefficients. The empirical and analytical correlations confirm the preliminary model results which suggest that mass loss at lower temperatures is dominated by oxidative reactions and that these reaction are limited by diffusion of oxygen from the surface. The mechanism-based model is able to successfully capture the basic physics of the degradation phenomena under a wide range of test conditions. The analysis-based test design is successful in separating out oxidative, thermal, and diffusion effects to allow the determination of material coefficients. This success confirms the basic picture of the process; however, a more complete understanding of some aspects of the physics are required before truly predictive capability can be achieved.

Insights into thermal diffusion of germanium and oxygen atoms in HfO{sub 2}/GeO{sub 2}/Ge gate stacks and their suppressed reaction with atomically thin AlO{sub x} interlayers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogawa, Shingo, E-mail: Shingo-Ogawa@trc.toray.co.jp; Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871; Asahara, Ryohei

2015-12-21

The thermal diffusion of germanium and oxygen atoms in HfO{sub 2}/GeO{sub 2}/Ge gate stacks was comprehensively evaluated by x-ray photoelectron spectroscopy and secondary ion mass spectrometry combined with an isotopic labeling technique. It was found that {sup 18}O-tracers composing the GeO{sub 2} underlayers diffuse within the HfO{sub 2} overlayers based on Fick's law with the low activation energy of about 0.5 eV. Although out-diffusion of the germanium atoms through HfO{sub 2} also proceeded at the low temperatures of around 200 °C, the diffusing germanium atoms preferentially segregated on the HfO{sub 2} surfaces, and the reaction was further enhanced at high temperatures withmore » the assistance of GeO desorption. A technique to insert atomically thin AlO{sub x} interlayers between the HfO{sub 2} and GeO{sub 2} layers was proven to effectively suppress both of these independent germanium and oxygen intermixing reactions in the gate stacks.« less

The influence of cladding on fission gas release from irradiated U-Mo monolithic fuel

NASA Astrophysics Data System (ADS)

Burkes, Douglas E.; Casella, Amanda J.; Casella, Andrew M.

2017-04-01

The monolithic uranium-molybdenum (U-Mo) alloy has been proposed as a fuel design capable of converting the world's highest power research reactors from use of high enriched uranium to low enriched uranium. However, a zirconium (Zr) diffusion barrier must be used to eliminate interactions that form between the U-Mo monolith and aluminum alloy 6061 (AA6061) cladding during fabrication and are enhanced during irradiation. One aspect of fuel development and qualification is to demonstrate an appropriate understanding of the extent of fission product release from the fuel under anticipated service environments. An exothermic reaction has previously been observed between the AA6061 cladding and Zr diffusion layer. In this paper, two fuel segments with different irradiation history were subjected to specified thermal profiles under a controlled atmosphere using a thermogravimetric/differential thermal analyzer coupled with a mass spectrometer inside a hot cell. Samples from each segment were tested with cladding and without cladding to investigate the effect, if any, that the exothermic reaction has on fission gas release mechanisms. Measurements revealed there is an instantaneous effect of the cladding/Zr exothermic reaction, but not necessarily a cumulative effect above approximately 973 K (700 °C). The mechanisms responsible for fission gas release events are discussed.

The influence of cladding on fission gas release from irradiated U-Mo monolithic fuel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burkes, Douglas E.; Casella, Amanda J.; Casella, Andrew M.

2017-04-01

The monolithic uranium-molybdenum (U-Mo) alloy has been proposed as a fuel design capable of converting the world’s highest power research reactors from use of high enriched uranium to low enriched uranium. However, a zirconium (Zr) diffusion barrier must be used to eliminate interactions that form during fabrication and are enhanced during irradiation between the U-Mo monolith and aluminum alloy 6061 (AA6061) cladding. One aspect of fuel development and qualification is to demonstrate appropriate understanding of the extent of fission product release from the fuel under anticipated service environments. An exothermic reaction has previously been observed between the AA6061 cladding andmore » Zr diffusion layer. In this paper, two fuel segments with different irradiation history were subjected to specified thermal profiles under a controlled atmosphere using a thermogravimetric/differential thermal analyzer coupled with a mass spectrometer inside a hot cell. Samples from each segment were tested with cladding and without cladding to investigate the effect, if any, that the exothermic reaction has on fission gas release mechanisms. Measurements revealed there is an instantaneous effect of the cladding/Zr exothermic reaction, but not necessarily a cumulative effect above approximately 973 K (700 oC). The mechanisms responsible for fission gas release events are discussed.« less

A new necessary condition for Turing instabilities.

PubMed

Elragig, Aiman; Townley, Stuart

2012-09-01

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community. Copyright © 2012 Elsevier Inc. All rights reserved.

Microfabricated valveless devices for thermal bioreactions based on diffusion-limited evaporation.

PubMed

Wang, Fang; Yang, Ming; Burns, Mark A

2008-01-01

Microfluidic devices that reduce evaporative loss during thermal bioreactions such as PCR without microvalves have been developed by relying on the principle of diffusion-limited evaporation. Both theoretical and experimental results demonstrate that the sample evaporative loss can be reduced by more than 20 times using long narrow diffusion channels on both sides of the reaction region. In order to further suppress the evaporation, the driving force for liquid evaporation is reduced by two additional techniques: decreasing the interfacial temperature using thermal isolation and reducing the vapor concentration gradient by replenishing water vapor in the diffusion channels. Both thermal isolation and vapor replenishment techniques can limit the sample evaporative loss to approximately 1% of the reaction content.

Interfacial reactions between metal and gallium arsenide

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, J.C.; Schulz, K.J.; Hsieh, K.C.

1989-10-01

The phase formation sequence for GaAs/metal ternary diffusion couples is discussed. The diffusion path concept is introduced and is used with the phase diagram to understand interfacial reactions between GaAs and metal. The correlation between growth kinetics and interface morphology is discussed. Studies of bulk and thin film couples in two systems, GaAs/Pd and GaAs/Pt, are given to illustrate these concepts.

Hydration kinetics of cementitious materials composed of red mud and coal gangue

NASA Astrophysics Data System (ADS)

Zhang, Na; Li, Hong-xu; Liu, Xiao-ming

2016-10-01

To elucidate the intrinsic reaction mechanism of cementitious materials composed of red mud and coal gangue (RGC), the hydration kinetics of these cementitious materials at 20°C was investigated on the basis of the Krstulović-Dabić model. An isothermal calorimeter was used to characterize the hydration heat evolution. The results show that the hydration of RGC is controlled by the processes of nucleation and crystal growth (NG), interaction at phase boundaries (I), and diffusion (D) in order, and the pozzolanic reactions of slag and compound-activated red mud-coal gangue are mainly controlled by the I process. Slag accelerates the clinker hydration during NG process, whereas the compound-activated red mud-coal gangue retards the hydration of RGC and the time required for I process increases with increasing dosage of red mud-coal gangue in RGC.

Hot chemistry in the diffuse medium: spectral signature in the H2 rotational lines

NASA Astrophysics Data System (ADS)

Verstraete, L.; Falgarone, E.; Pineau des Forets, G.; Flower, D.; Puget, J. L.

1999-03-01

Most of the diffuse interstellar medium is cold, but it must harbor pockets of hot gas to explain the large observed abundances of molecules like CH+ and HCO+. Because they dissipate locally large amounts of kinetic energy, MHD shocks and coherent vortices in turbulence can drive endothermic chemical reactions or reactions with large activation barriers. We predict the spectroscopic signatures in the H2 rotational lines of MHD shocks and vortices and compare them to those observed with the ISO-SWS along a line of sight through the Galaxy which samples 20 magnitudes of mostly diffuse gas.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

Stability and Hopf Bifurcation in a Reaction-Diffusion Model with Chemotaxis and Nonlocal Delay Effect

NASA Astrophysics Data System (ADS)

Li, Dong; Guo, Shangjiang

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction-diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov-Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

Permanganate diffusion and reaction in sedimentary rocks.

PubMed

Huang, Qiuyuan; Dong, Hailiang; Towne, Rachael M; Fischer, Timothy B; Schaefer, Charles E

2014-04-01

In situ chemical oxidation using permanganate has frequently been used to treat chlorinated solvents in fractured bedrock aquifers. However, in systems where matrix back-diffusion is an important process, the ability of the oxidant to migrate and treat target contaminants within the rock matrix will likely determine the overall effectiveness of this remedial approach. In this study, a series of diffusion experiments were performed to measure the permanganate diffusion and reaction in four different types of sedimentary rocks (dark gray mudstone, light gray mudstone, red sandstone, and tan sandstone). Results showed that, within the experimental time frame (~2 months), oxidant migration into the rock was limited to distances less than 500 μm. The observed diffusivities for permanganate into the rock matrices ranged from 5.3 × 10(-13) to 1.3 × 10(-11) cm(2)/s. These values were reasonably predicted by accounting for both the rock oxidant demand and the effective diffusivity of the rock. Various Mn minerals formed as surface coatings from reduction of permanganate coupled with oxidation of total organic carbon (TOC), and the nature of the formed Mn minerals was dependent upon the rock type. Post-treatment tracer testing showed that these Mn mineral coatings had a negligible impact on diffusion through the rock. Overall, our results showed that the extent of permanganate diffusion and reaction depended on rock properties, including porosity, mineralogy, and organic carbon. These results have important implications for our understanding of long-term organic contaminant remediation in sedimentary rocks using permanganate. Copyright © 2014 Elsevier B.V. All rights reserved.

Electron-stimulated reactions in layered CO/H2O films: Hydrogen atom diffusion and the sequential hydrogenation of CO to methanol

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petrik, Nikolay G.; Monckton, Rhiannon J.; Koehler, Sven

Low-energy (100 eV) electron-stimulated reactions in layered H2O/CO/H2O ices are investigated. For CO trapped within approximately 50 ML of the vacuum interface in the amorphous solid water (ASW) films, both oxidation and reduction reactions are observed. However for CO buried more deeply in the film, only the reduction of CO to methanol is observed. Experiments with layered films of H2O and D2O show that the hydrogen atoms participating in the reduction of the buried CO originate in region from ~10 – 40 ML below the surface of the ASW films and subsequently diffuse through the film. For deeply buried COmore » layers, the CO reduction reactions quickly increase with temperature above ~60 K. We present a simple chemical kinetic model that treats the diffusion of hydrogen atoms in the ASW and sequential hydrogenation of the CO to methanol that accounts for the observations.« less

Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks

NASA Astrophysics Data System (ADS)

Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.

2018-04-01

Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.

Mesoscopic Modeling of Blood Clotting: Coagulation Cascade and Platelets Adhesion

NASA Astrophysics Data System (ADS)

Yazdani, Alireza; Li, Zhen; Karniadakis, George

2015-11-01

The process of clot formation and growth at a site on a blood vessel wall involve a number of multi-scale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and flow. To model these processes we have incorporated advection-diffusion-reaction (ADR) of multiple species into an extended version of Dissipative Particle Dynamics (DPD) method which is considered as a coarse-grained Molecular Dynamics method. At the continuum level this is equivalent to the Navier-Stokes equation plus one advection-diffusion equation for each specie. The chemistry of clot formation is now understood to be determined by mechanisms involving reactions among many species in dilute solution, where reaction rate constants and species diffusion coefficients in plasma are known. The role of blood particulates, i.e. red cells and platelets, in the clotting process is studied by including them separately and together in the simulations. An agonist-induced platelet activation mechanism is presented, while platelets adhesive dynamics based on a stochastic bond formation/dissociation process is included in the model.

On the Chemistry of Hydrides of N Atoms and O+ Ions

NASA Astrophysics Data System (ADS)

Awad, Zainab; Viti, Serena; Williams, David A.

2016-08-01

Previous work by various authors has suggested that the detection by Herschel/HIFI of nitrogen hydrides along the low-density lines of sight toward G10.6-0.4 (W31C) cannot be accounted for by gas-phase chemical models. In this paper we investigate the role of surface reactions on dust grains in diffuse regions, and we find that formation of the hydrides by surface reactions on dust grains with efficiency comparable to that for H2 formation reconciles models with observations of nitrogen hydrides. However, similar surface reactions do not contribute significantly to the hydrides of O+ ions detected by Herschel/HIFI that are present along many sight lines in the Galaxy. The O+ hydrides can be accounted for by conventional gas-phase chemistry either in diffuse clouds of very low density with normal cosmic-ray fluxes or in somewhat denser diffuse clouds with high cosmic-ray fluxes. Hydride chemistry in dense dark clouds appears to be dominated by gas-phase ion-molecule reactions.

Lack of detection of feline leukemia and feline sarcoma viruses in diffuse iris melanomas of cats by immunohistochemistry and polymerase chain reaction.

PubMed

Cullen, Cheryl L; Haines, Deborah M; Jackson, Marion L; Grahn, Bruce H

2002-07-01

Diffuse iris melanoma was confirmed by light-microscopic examination in 10 formalin-fixed, paraffin-embedded globes from 10 cats. To determine if feline leukemia virus or a replication defective feline leukemia virus, feline sarcoma virus, was present in these anterior uveal melanomas, immunohistochemistry and polymerase chain reaction for feline leukemia virus were utilized. Immunohistochemical staining for feline leukemia virus glycoprotein 70 was performed on all 10 tumors using an avidin-biotin complex technique. The DNA was extracted from each specimen and a 166-base pair region of the feline leukemia virus long terminal repeat was targeted by polymerase chain reaction. Immunohistochemical staining for feline leukemia virus glycoprotein 70 and polymerase chain reaction amplification of a feline leukemia virus long terminal repeat region were negative in all cases. Feline leukemia virus/feline sarcoma virus was not detected in any neoplasms and therefore was unlikely to play a role in the tumorigenesis of these feline diffuse iris melanomas.

Escarpment evolution on high-elevation rifted margins: Insights derived from a surface processes model that combines diffusion, advection and reaction

NASA Technical Reports Server (NTRS)

Kooi, Henk; Beaumont, Christopher

1994-01-01

Experiments with a surface processes model of large-scale (1-1000 km) long-term (1-100 m.y.) erosional denudation are used to establish the controls on the evolution of a model escarpment that is related to the rifting of a continent. The mdoel describes changes in topographic form as a result of sumultaneous short- and long-range mass transport representing hillslope (diffusive) processes and fluvial transport (advection), repsectively. Fluvial entrainment is modeled as a first-order kinetic reaction which reflects the erodibility of the substrate, and therefore the fluvial system is not necessarily carrying at capacity. One dimensional and planform models demonstrate that the principal controls on the evolution of an initially steep model escarpment are (1) antecedent topography/drainage; (2) the timesale (or equivalently a length scale) in the fluvial entrainment reaction; (3) the flexural response of the lithosphere to denudation; and (4) the relative efficiencies of the short- and long-range transport processes. When rainfall and substrate lithology are uniform, a significant amount of discharge draining over the escarpment top causes it to degrade. Only when the top of the model escarpment coincides with a drainage divide can escarpment retreat occur for these conditions. An additional requirement for retreat of a model escarpment without decline is a long reaction time scale for fluvial entrainment. This corresponds to a substrate that is hard to detach by flucial erosion, and therefore to fluvial erosion that is not transport limited. Coninuous backtilting of an escarpment due ot flexural isostatic uplift in response to denudational unloading helps maintain the scarp top as a divide. It is essntial if the escarpment gradient is to be preserved during retreat in a uniform lithology. Low flexural rigidieties propote steep and slowly retreating escarpments. For given rainfall and substrate conditions, the morphology of a retraeating model escarpment is determined by the ratio of hte short-range diffusive and long range advective transport efficiencies. A low ration (which is interpreted to correspond to a more humid, temperate climate) produces a convex upper slope, and concave lower slope morphology and only major escarpments are predicted to preserve a high scarp gradient. Lithological contrasts in hte model produce more complex morphologies and predict the formation of scarps crowned by an erosionaly resistant caprock. However, resistant caprocks are not an essential requirement for model scarps to retreat. We conclude that the inferred controls and model behavior are both consistent with the present-day morphology of rifted continental margins and with modern conceptual models of landscape evolution.

Chemical desorption and diffusive dust chemistry

NASA Astrophysics Data System (ADS)

Dulieu, Francois; Pirronello, Valerio; Minissale, Marco; Congiu, Emanuele; Baouche, Saoud; Chaabouni, Henda; Moudens, Audrey; Accolla, Mario; Cazaux, Stephanie; Manicò, Giulio

In molecular clouds, gaseous species can accrete efficiently on the cold surfaces of dust grains. As for radical-radical reactions, the surface of the grains acts as a third body, and changes dramatically the efficiency of the reactions (i.e., H2 formation), or lowers considerably the barrier to formation (i.e., H2O synthesis) in comparison with gas phase reaction processes. These properties make dust grains efficient catalytic templates. However, the chemical role of dust grains depends on the diffusive properties of the reactive partners. Over the last years, we have developed experimental tools and methods to explore the chemistry occurring on cold (6-50K) surfaces. We have obtained some hints about the diffusivity of H on amorphous ice, and studied in detail the diffusion of O atoms. The latter species appears to have a hopping rate in the range 0.01-100 hops/sec. The diffusion rate of O atoms is dependent on the surface morphology and on the surface temperature. The diffusion law is compatible with a diffusion dominated by quantum tunnelling rather than classical thermal hopping. Using H, O, N atoms and, indirectly, OH and HCO radicals, we have begun to explore many chemical reactive networks. In this presentation, I will focus on the formation of H2O and CO2, and will propose many possible formation routes to obtain these chemical traps. The molecules formed on surfaces have a certain probability of desorbing upon their formation. This non-thermal desorption mechanism, or chemical desorption, has been proposed to explain why some molecules can be detected in the gas phase of those region where they were believed to be part of the icy mantles covering dust grains. We have shown that this process can be very efficient, but is very sensitive to the substrate and the surroundings of the reaction site, is dependent on the kind of molecule formed and its chemical pathway. In my presentation I will present how the surface coverage and the type of reaction can play a major role in the chemical desorption process. I will discuss of possible key parameters that rule this process.

Heat Diffusion in Gases, Including Effects of Chemical Reaction

NASA Technical Reports Server (NTRS)

Hansen, C. Frederick

1960-01-01

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.