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

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...

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

Generalized Hydrodynamic Treatment of the Interplay between Restricted Transport and Catalytic Reactions in Nanoporous Materials

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

Ackerman, David M.; Wang, Jing; Evans, James W.

2012-05-30

Behavior of catalytic reactions in narrow pores is controlled by a delicate interplay between fluctuations in adsorption-desorption at pore openings, restricted diffusion, and reaction. This behavior is captured by a generalized hydrodynamic formulation of appropriate reaction-diffusion equations (RDE). These RDE incorporate an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The RDE elucidate the nonexponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth.

Generalized hydrodynamic treatment of the interplay between restricted transport and catalytic reactions in nanoporous materials.

PubMed

Ackerman, David M; Wang, Jing; Evans, James W

2012-06-01

Behavior of catalytic reactions in narrow pores is controlled by a delicate interplay between fluctuations in adsorption-desorption at pore openings, restricted diffusion, and reaction. This behavior is captured by a generalized hydrodynamic formulation of appropriate reaction-diffusion equations (RDE). These RDE incorporate an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The RDE elucidate the nonexponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth.

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/

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.

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.

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.

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.

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.

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.

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.

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/

Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent diffusion coefficient.

PubMed

Chen, Juan; Cui, Baotong; Chen, YangQuan

2018-06-11

This paper presents a boundary feedback control design for a fractional reaction diffusion (FRD) system with a space-dependent (non-constant) diffusion coefficient via the backstepping method. The contribution of this paper is to generalize the results of backstepping-based boundary feedback control for a FRD system with a space-independent (constant) diffusion coefficient to the case of space-dependent diffusivity. For the boundary stabilization problem of this case, a designed integral transformation treats it as a problem of solving a hyperbolic partial differential equation (PDE) of transformation's kernel, then the well posedness of the kernel PDE is solved for the plant with non-constant diffusivity. Furthermore, by the fractional Lyapunov stability (Mittag-Leffler stability) theory and the backstepping-based boundary feedback controller, the Mittag-Leffler stability of the closed-loop FRD system with non-constant diffusivity is proved. Finally, an extensive numerical example for this closed-loop FRD system with non-constant diffusivity is presented to verify the effectiveness of our proposed controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

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.

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.

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.

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 .

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.

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

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.

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

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.

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

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.

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.

A Transition in the Cumulative Reaction Rate of Two Species Diffusion with Bimolecular Reaction

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

Diffusion and bimolecular reaction between two initially separated reacting species is a prototypical small-scale description of reaction induced by transverse mixing. It is also relevant to diffusion controlled transport regimes as encountered in low-permeability matrix blocks in fractured media. In previous work, the reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), which predicts that front motion scales as √t, and the cumulative reaction rate scales as 1/√t-. We present a general non-dimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the cumulative reaction rate scales as √t- rather than 1/√t. The duration of this early time regime (where the cumulative rate is kinetically rather than diffusion controlled) depends on the rate parameter, in a manner that is consistently predicted by our non-dimensionalization. We also present results on the scaling of the reaction front width. We present numerical simulations in homogeneous and heterogeneous porous media to demonstrate the limited influence of heterogeneity on the behavior of the reaction-diffusion system. We illustrate applications to the practical problem of in-situ chemical oxidation of TCE and PCE by permanganate, which is employed to remediate contaminated sites where the DNAPLs are largely dissolved in the rock matrix.

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)

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.

Incomplete Mixing and Reactions - A Lagrangian Approach in a Pure Shear Flow

NASA Astrophysics Data System (ADS)

Paster, A.; Aquino, T.; Bolster, D.

2014-12-01

Incomplete mixing of reactive solutes is well known to slow down reaction rates relative to what would be expected from assuming perfect mixing. As reactions progress in a system and deplete reactant concentrations, initial fluctuations in the concentrations of reactions can be amplified relative to mean background concentrations and lead to spatial segregation of reactants. As the system evolves, in the absence of sufficient mixing, this segregation will increase, leading to a persistence of incomplete mixing that fundamentally changes the effective rate at which overall reactions will progress. On the other hand, non-uniform fluid flows are known to affect mixing between interacting solutes. Thus a natural question arises: Can non-uniform flows sufficiently enhance mixing to suppress incomplete mixing effects, and if so, under what conditions? In this work we address this question by considering one of the simplest possible flows, a laminar pure shear flow, which is known to significantly enhance mixing relative to diffusion alone. To study this system we adapt a novel Lagrangian particle-based random walk method, originally designed to simulate reactions in purely diffusive systems, to the case of advection and diffusion in a shear flow. To interpret the results we develop a semi-analytical solution, by proposing a closure approximation that aims to capture the effect of incomplete mixing. The results obtained via the Lagrangian model and the semi-analytical solutions consistently highlight that if shear effects in the system are not sufficiently strong, incomplete mixing effects initially similar to purely diffusive systems will occur, slowing down the overall reaction rate. Then, at some later time, dependent on the strength of the shear, the system will return to behaving as if it were well-mixed, but represented by a reduced effective reaction rate. If shear effects are sufficiently strong, the incomplete mixing regime never emerges and the system can behave as well-mixed at all times.

Incomplete Mixing and Reactions - A Lagrangian Approach in a Pure Shear Flow

NASA Astrophysics Data System (ADS)

Paster, Amir; Bolster, Diogo; Aquino, Tomas

2015-04-01

Incomplete mixing of reactive solutes is well known to slow down reaction rates relative to what would be expected from assuming perfect mixing. As reactions progress in a system and deplete reactant concentrations, initial fluctuations in the concentrations of reactions can be amplified relative to mean background concentrations and lead to spatial segregation of reactants. As the system evolves, in the absence of sufficient mixing, this segregation will increase, leading to a persistence of incomplete mixing that fundamentally changes the effective rate at which overall reactions will progress. On the other hand, nonuniform fluid flows are known to affect mixing between interacting solutes. Thus a natural question arises: Can non-uniform flows sufficiently enhance mixing to suppress incomplete mixing effects, and if so, under what conditions? In this work we address this question by considering one of the simplest possible flows, a laminar pure shear flow, which is known to significantly enhance mixing relative to diffusion alone. To study this system we adapt a novel Lagrangian particle-based random walk method, originally designed to simulate reactions in purely diffusive systems, to the case of advection and diffusion in a shear flow. To interpret the results we develop a semi-analytical solution, by proposing a closure approximation that aims to capture the effect of incomplete mixing. The results obtained via the Lagrangian model and the semi-analytical solutions consistently highlight that if shear effects in the system are not sufficiently strong, incomplete mixing effects initially similar to purely diffusive systems will occur, slowing down the overall reaction rate. Then, at some later time, dependent on the strength of the shear, the system will return to behaving as if it were well-mixed, but represented by a reduced effective reaction rate. If shear effects are sufficiently strong, the incomplete mixing regime never emerges and the system can behave as well-mixed at all times.

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.

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

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.

Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows

NASA Astrophysics Data System (ADS)

Lenarda, Pietro; Paggi, Marco; Ruiz Baier, Ricardo

2017-09-01

We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-diffusion-reaction systems and incompressible, viscous flow. The space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction, advection, and diffusion processes, considering the global system as a number of sequentially linked sets of partial differential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

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.

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.

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

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

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.

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.

Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming; Wu, Jianhong

Reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity. For such non-monotone dynamical systems, we develop a general comparison principle and show how this general comparison principle, coupled with some existing results for monotone dynamical systems, can be used to establish results on the asymptotic speeds of spread and travelling waves. We illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain, with the non-monotone nonlinearities including the Ricker birth function and the Mackey-Glass hematopoiesis feedback.

Emergent structures in reaction-advection-diffusion systems on a sphere.

PubMed

Krause, Andrew L; Burton, Abigail M; Fadai, Nabil T; Van Gorder, Robert A

2018-04-01

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

Emergent structures in reaction-advection-diffusion systems on a sphere

NASA Astrophysics Data System (ADS)

Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.

2018-04-01

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

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.

Mathematical approach to nonlocal interactions using a reaction-diffusion system.

PubMed

Tanaka, Yoshitaro; Yamamoto, Hiroko; Ninomiya, Hirokazu

2017-06-01

In recent years, spatial long range interactions during developmental processes have been introduced as a result of the integration of microscopic information, such as molecular events and signaling networks. They are often called nonlocal interactions. If the profile of a nonlocal interaction is determined by experiments, we can easily investigate how patterns generate by numerical simulations without detailed microscopic events. Thus, nonlocal interactions are useful tools to understand complex biosystems. However, nonlocal interactions are often inconvenient for observing specific mechanisms because of the integration of information. Accordingly, we proposed a new method that could convert nonlocal interactions into a reaction-diffusion system with auxiliary unknown variables. In this review, by introducing biological and mathematical studies related to nonlocal interactions, we will present the heuristic understanding of nonlocal interactions using a reaction-diffusion system. © 2017 Japanese Society of Developmental Biologists.

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 \

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.

Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns

NASA Astrophysics Data System (ADS)

Konishi, Keiji; Hara, Naoyuki

2018-05-01

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.

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

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.

Event-triggered synchronization for reaction-diffusion complex networks via random sampling

NASA Astrophysics Data System (ADS)

Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng

2018-04-01

In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.

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

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.

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.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

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.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

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.

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.

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.

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.

Rethinking pattern formation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Halatek, J.; Frey, E.

2018-05-01

The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

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

NASA Astrophysics Data System (ADS)

Ghosh, Pushpita; Ray, Deb Shankar

2011-09-01

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

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.

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

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

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.

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.

Effect of the universal acid-base indicator on the formation of the concentration-dependent diffusion instability

NASA Astrophysics Data System (ADS)

Mosheva, E. A.; Shmyrov, A. V.

2017-06-01

The effect of the universal acid-base indicator on the pattern formation and mass transfer in a two-layer system composed of two reactive miscible liquids in a vertical Hele-Shaw cell is studied experimentally. The reaction we study is a neutralization one. It turns out that the presence of the indicator leads to a change in the spatio-temporal characteristics of the system and even in the mass transfer mechanism near the reaction front—from diffusive to convective. The conditions, where the universal indicator does not affect the reaction and can be used as a visualizing mean, are reported.

Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.

PubMed

Tsyganov, M A; Ivanitsky, G R; Zemskov, E P

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Wave reflection in a reaction-diffusion system: Breathing patterns and attenuation of the echo

NASA Astrophysics Data System (ADS)

Tsyganov, M. A.; Ivanitsky, G. R.; Zemskov, E. P.

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

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

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.

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.

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.

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.

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

PubMed

Wang, Hongli; Ouyang, Qi

2007-11-23

The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

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

PubMed

Ghosh, Pushpita; Ray, Deb Shankar

2011-09-14

Based on a multiple scale analysis of a forced reaction-diffusion system leading to amplitude equations, we explain the existence of spiral wave and its photo-induced spatiotemporal behavior in chlorine dioxide-iodine-malonic acid system. When the photo-illumination intensity is modulated, breathing of spiral is observed in which the period of breathing is identical to the period of forcing. We have also derived the condition for breakup and suppression of spiral wave by periodic illumination. The numerical simulations agree well with our analytical treatment. © 2011 American Institute of Physics

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions

NASA Astrophysics Data System (ADS)

Fujieda, S.; Mori, Y.; Nakazawa, A.; Mogami, Y.

2001-01-01

Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.

Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach.

PubMed

Dharani, S; Rakkiyappan, R; Cao, Jinde; Alsaedi, Ahmed

2017-08-01

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.

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.

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.

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

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.

Hopping Conduction and Bacteria: Transport Properties of Disordered Reaction-Diffusion Systems

NASA Astrophysics Data System (ADS)

Missel, Andrew; Dahmen, Karin

2008-03-01

Reaction-diffusion (RD) systems are used to model everything from the formation of animal coat patterns to the spread of genes in a population to the seasonal variation of plankton density in the ocean. In all of these problems, disorder plays a large role, but determining its effects on transport properties in RD systems has been a challenge. We present here both analytical and numerical studies of a particular disordered RD system consisting of particles which are allowed to diffuse and compete for resources (2A->A) with spatially homogeneous rates, reproduce (A->2A) in certain areas (``oases''), and die (A->0) everywhere else (the ``desert''). In the low oasis density regime, transport is mediated through rare ``hopping events'' in which a small number of particles diffuse through the desert from one oasis to another; the situation is mathematically analogous to hopping conduction in doped semiconductors, and this analogy, along with some ideas from first passage percolation theory, allows us to make some quantitative predictions about the transport properties of the system on a large scale.

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

Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

NASA Astrophysics Data System (ADS)

Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.

2018-01-01

Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.

Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2

NASA Astrophysics Data System (ADS)

Niu, Hong-Tao; Wang, Zhi-Cheng; Bu, Zhen-Hui

2018-05-01

In this paper we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in R2 by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in R2.

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.

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

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.

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.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Scalar dissipation rates in non-conservative transport systems

PubMed Central

Engdahl, Nicholas B.; Ginn, Timothy R.; Fogg, Graham E.

2014-01-01

This work considers how the inferred mixing state of diffusive and advective-diffusive systems will vary over time when the solute masses are not constant over time. We develop a number of tools that allow the scalar dissipation rate to be used as a mixing measure in these systems without calculating local concentration gradients. The behavior of dissipation rates are investigated for single and multi-component kinetic reactions and a commonly studied equilibrium reaction. The scalar dissipation rate of a tracer experiencing first order decay can be determined exactly from the decay constant and the dissipation rate of a passive tracer, and the mixing rate of a conservative component is not the superposition of the solute specific mixing rates. We then show how the behavior of the scalar dissipation rate can be determined from a limited subset of an infinite domain. Corrections are derived for constant and time dependent limits of integration the latter is used to approximate dissipation rates in advective-diffusive systems. Several of the corrections exhibit similarities to the previous work on mixing, including non-Fickian mixing. This illustrates the importance of accounting for the effects that reaction systems or limited monitoring areas may have on the inferred mixing state. PMID:23584457

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

PubMed

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.

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.

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.

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

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

PubMed

Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi

2014-04-11

Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.

Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system.

PubMed

Berenstein, Igal; Muñuzuri, Alberto P; Yang, Lingfa; Dolnik, Milos; Zhabotinsky, Anatol M; Epstein, Irving R

2008-08-01

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems

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

Padgett, Jill M. A.; Ilie, Silvana, E-mail: silvana@ryerson.ca

2016-03-15

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating themore » solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.« less

Spatiotemporal patterns in reaction-diffusion system and in a vibrated granular bed

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

Swinney, H.L.; Lee, K.J.; McCormick, W.D.

Experiments on a quasi-two-dimensional reaction-diffusion system reveal transitions from a uniform state to stationary hexagonal, striped, and rhombic spatial patterns. For other reactor conditions lamellae and self-replicating spot patterns are observed. These patterns form in continuously fed thin gel reactors that can be maintained indefinitely in well-defined nonequilibrium states. Reaction-diffusion models with two chemical species yield patterns similar to those observed in the experiments. Pattern formation is also being examined in vertically oscillated thin granular layers (typically 3-30 particle diameters deep). For small acceleration amplitudes, a granular layer is flat, but above a well-defined critical acceleration amplitude, spatial patterns spontaneouslymore » form. Disordered time-dependent granular patterns are observed as well as regular patterns of squares, stripes, and hexagons. A one-dimensional model consisting of a completely inelastic ball colliding with a sinusoidally oscillating platform provides a semi-quantitative description of most of the observed bifurcations between the different spatiotemporal regimes.« less

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling

PubMed Central

Kekenes-Huskey, Peter M.; Eun, Changsun; McCammon, J. A.

2015-01-01

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion “barriers” arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to “compartments” of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways. PMID:26342355

Numerical simulation of the interaction of transport, diffusion and chemical reactions in an urban plume

NASA Technical Reports Server (NTRS)

Vogel, Bernhard; Vogel, Heike; Fiedler, Franz

1994-01-01

A model system is presented that takes into account the main physical and chemical processes on the regional scale here in an area of 100x100 sq km. The horizontal gridsize used is 2x2 sq km. For a case study, it is demonstrated how the model system can be used to separate the contributions of the processes advection, turbulent diffusion, and chemical reactions to the diurnal cycle of ozone. In this way, typical features which are visible in observations and are reproduced by the numerical simulations can be interpreted.

Square Turing patterns in reaction-diffusion systems with coupled layers

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

Li, Jing; Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn; Center for Quantitative Biology, Peking University, Beijing 100871

Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

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.

Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle.

PubMed

Kinsey, Stephen T; Locke, Bruce R; Dillaman, Richard M

2011-01-15

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.

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.

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.

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

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.

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

PubMed Central

2014-01-01

Background Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system’s set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This “code-based” approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. Results As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. Conclusions The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts. PMID:24725437

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

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

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

A Simple and Accurate Method To Calculate Free Energy Profiles and Reaction Rates from Restrained Molecular Simulations of Diffusive Processes.

PubMed

Ovchinnikov, Victor; Nam, Kwangho; Karplus, Martin

2016-08-25

A method is developed to obtain simultaneously free energy profiles and diffusion constants from restrained molecular simulations in diffusive systems. The method is based on low-order expansions of the free energy and diffusivity as functions of the reaction coordinate. These expansions lead to simple analytical relationships between simulation statistics and model parameters. The method is tested on 1D and 2D model systems; its accuracy is found to be comparable to or better than that of the existing alternatives, which are briefly discussed. An important aspect of the method is that the free energy is constructed by integrating its derivatives, which can be computed without need for overlapping sampling windows. The implementation of the method in any molecular simulation program that supports external umbrella potentials (e.g., CHARMM) requires modification of only a few lines of code. As a demonstration of its applicability to realistic biomolecular systems, the method is applied to model the α-helix ↔ β-sheet transition in a 16-residue peptide in implicit solvent, with the reaction coordinate provided by the string method. Possible modifications of the method are briefly discussed; they include generalization to multidimensional reaction coordinates [in the spirit of the model of Ermak and McCammon (Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352-1360)], a higher-order expansion of the free energy surface, applicability in nonequilibrium systems, and a simple test for Markovianity. In view of the small overhead of the method relative to standard umbrella sampling, we suggest its routine application in the cases where umbrella potential simulations are appropriate.

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.

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

Management of the diffusion of 4-methylumbelliferone across phases in microdroplet-based systems for in vitro protein evolution.

PubMed

Wu, Nan; Courtois, Fabienne; Zhu, Yonggang; Oakeshott, John; Easton, Chris; Abell, Chris

2010-09-01

Fluorongenic reagents based on 4-methylumbelliferone (4-MU) have been widely used for the detection of phosphatase, sulfatase, esterase, lipase and glycosidase activities in conventionally formatted enzyme assay systems. However, the sensitivity of assays based on these substrates is also potentially very useful in the microdroplet formats now being developed for high throughput in vitro evolution experiments. In this article, we report the investigation of diffusion of 4-MU as a model dye from water-in-oil droplets and the internal aqueous phase of water-in-oil-in-water droplets in microfluidics. The effect of BSA in the aqueous phase on the diffusion of 4-MU is also discussed. Based on these results, we provided here proof-of-concept of the reaction of the enzyme OpdA with the substrate coumaphos in water-in-oil-in-water droplets. In this double-emulsion system, the reaction of OpdA and coumaphos was achieved by allowing coumaphos to diffuse from the continuous aqueous phase across the oil phase into the internal aqueous droplets.

Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics

NASA Astrophysics Data System (ADS)

Wen, Zijuan; Fu, Shengmao

2009-08-01

In this paper, an n-species strongly coupled cooperating diffusive system is considered in a bounded smooth domain, subject to homogeneous Neumann boundary conditions. Employing the method of energy estimates, we obtain some conditions on the diffusion matrix and inter-specific cooperatives to ensure the global existence and uniform boundedness of a nonnegative solution. The globally asymptotical stability of the constant positive steady state is also discussed. As a consequence, all the results hold true for multi-species Lotka-Volterra type competition model and prey-predator model.

Introduction to the Focus Issue: Chemo-Hydrodynamic Patterns and Instabilities

NASA Astrophysics Data System (ADS)

De Wit, A.; Eckert, K.; Kalliadasis, S.

2012-09-01

Pattern forming instabilities are often encountered in a wide variety of natural phenomena and technological applications, from self-organization in biological and chemical systems to oceanic or atmospheric circulation and heat and mass transport processes in engineering systems. Spatio-temporal structures are ubiquitous in hydrodynamics where numerous different convective instabilities generate pattern formation and complex spatiotemporal dynamics, which have been much studied both theoretically and experimentally. In parallel, reaction-diffusion processes provide another large family of pattern forming instabilities and spatio-temporal structures which have been analyzed for several decades. At the intersection of these two fields, "chemo-hydrodynamic patterns and instabilities" resulting from the coupling of hydrodynamic and reaction-diffusion processes have been less studied. The exploration of the new instability and symmetry-breaking scenarios emerging from the interplay between chemical reactions, diffusion and convective motions is a burgeoning field in which numerous exciting problems have emerged during the last few years. These problems range from fingering instabilities of chemical fronts and reactive fluid-fluid interfaces to the dynamics of reaction-diffusion systems in the presence of chaotic mixing. The questions to be addressed are at the interface of hydrodynamics, chemistry, engineering or environmental sciences to name a few and, as a consequence, they have started to draw the attention of several communities including both the nonlinear chemical dynamics and hydrodynamics communities. The collection of papers gathered in this Focus Issue sheds new light on a wide range of phenomena in the general area of chemo-hydrodynamic patterns and instabilities. It also serves as an overview of the current research and state-of-the-art in the field.

Nonlinear Systems.

ERIC Educational Resources Information Center

Seider, Warren D.; Ungar, Lyle H.

1987-01-01

Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…

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

Step-by-Step Simulation of Radiation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions

NASA Technical Reports Server (NTRS)

Plante, Ianik; Cucinotta, Francis A.

2011-01-01

The irradiation of biological systems leads to the formation of radiolytic species such as H(raised dot), (raised dot)OH, H2, H2O2, e(sup -)(sub aq), etc.[1]. These species react with neighboring molecules, which result in damage in biological molecules such as DNA. Radiation chemistry is there for every important to understand the radiobiological consequences of radiation[2]. In this work, we discuss an approach based on the exact Green Functions for diffusion-influenced reactions which may be used to simulate radiation chemistry and eventually extended to study more complex systems, including DNA.

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

Drosophila segmentation: supercomputer simulation of prepattern hierarchy.

PubMed

Hunding, A; Kauffman, S A; Goodwin, B C

1990-08-09

Spontaneous prepattern formation in a two level hierarchy of reaction-diffusion systems is simulated in three space co-ordinates and time, mimicking gap gene and primary pair-rule gene expression. The model rests on the idea of Turing systems of the second kind, in which one prepattern generates position dependent rate constants for a subsequent reaction-diffusion system. Maternal genes are assumed responsible for setting up gradients from the anterior and posterior ends, one of which is needed to stabilize a double period prepattern suggested to underly the read out of the gap genes. The resulting double period pattern in turn stabilizes the next prepattern in the hierarchy, which has a short wavelength with many characteristics of the stripes seen in actual primary pair-rule gene expression. Without such hierarchical stabilization, reaction-diffusion mechanisms yield highly patchy short wave length patterns, and thus unreliable stripes. The model yields seven stable stripes located in the middle of the embryo, with the potential for additional expression near the poles, as observed experimentally. The model does not rely on specific chemical reaction kinetics, rather the effect is general to many such kinetic schemes. This makes it robust to parameter changes, and it has good potential for adapting to size and shape changes as well. The study thus suggests that the crucial organizing principle in early Drosophila embryogenesis is based on global field mechanisms, not on particular local interactions.

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

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Theory of bi-molecular association dynamics in 2D for accurate model and experimental parameterization of binding rates

PubMed Central

Yogurtcu, Osman N.; Johnson, Margaret E.

2015-01-01

The dynamics of association between diffusing and reacting molecular species are routinely quantified using simple rate-equation kinetics that assume both well-mixed concentrations of species and a single rate constant for parameterizing the binding rate. In two-dimensions (2D), however, even when systems are well-mixed, the assumption of a single characteristic rate constant for describing association is not generally accurate, due to the properties of diffusional searching in dimensions d ≤ 2. Establishing rigorous bounds for discriminating between 2D reactive systems that will be accurately described by rate equations with a single rate constant, and those that will not, is critical for both modeling and experimentally parameterizing binding reactions restricted to surfaces such as cellular membranes. We show here that in regimes of intrinsic reaction rate (ka) and diffusion (D) parameters ka/D > 0.05, a single rate constant cannot be fit to the dynamics of concentrations of associating species independently of the initial conditions. Instead, a more sophisticated multi-parametric description than rate-equations is necessary to robustly characterize bimolecular reactions from experiment. Our quantitative bounds derive from our new analysis of 2D rate-behavior predicted from Smoluchowski theory. Using a recently developed single particle reaction-diffusion algorithm we extend here to 2D, we are able to test and validate the predictions of Smoluchowski theory and several other theories of reversible reaction dynamics in 2D for the first time. Finally, our results also mean that simulations of reactive systems in 2D using rate equations must be undertaken with caution when reactions have ka/D > 0.05, regardless of the simulation volume. We introduce here a simple formula for an adaptive concentration dependent rate constant for these chemical kinetics simulations which improves on existing formulas to better capture non-equilibrium reaction dynamics from dilute to dense systems. PMID:26328828

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

Reaction Kernel Structure of a Slot Jet Diffusion Flame in Microgravity

NASA Technical Reports Server (NTRS)

Takahashi, F.; Katta, V. R.

2001-01-01

Diffusion flame stabilization in normal earth gravity (1 g) has long been a fundamental research subject in combustion. Local flame-flow phenomena, including heat and species transport and chemical reactions, around the flame base in the vicinity of condensed surfaces control flame stabilization and fire spreading processes. Therefore, gravity plays an important role in the subject topic because buoyancy induces flow in the flame zone, thus increasing the convective (and diffusive) oxygen transport into the flame zone and, in turn, reaction rates. Recent computations show that a peak reactivity (heat-release or oxygen-consumption rate) spot, or reaction kernel, is formed in the flame base by back-diffusion and reactions of radical species in the incoming oxygen-abundant flow at relatively low temperatures (about 1550 K). Quasi-linear correlations were found between the peak heat-release or oxygen-consumption rate and the velocity at the reaction kernel for cases including both jet and flat-plate diffusion flames in airflow. The reaction kernel provides a stationary ignition source to incoming reactants, sustains combustion, and thus stabilizes the trailing diffusion flame. In a quiescent microgravity environment, no buoyancy-induced flow exits and thus purely diffusive transport controls the reaction rates. Flame stabilization mechanisms in such purely diffusion-controlled regime remain largely unstudied. Therefore, it will be a rigorous test for the reaction kernel correlation if it can be extended toward zero velocity conditions in the purely diffusion-controlled regime. The objectives of this study are to reveal the structure of the flame-stabilizing region of a two-dimensional (2D) laminar jet diffusion flame in microgravity and develop a unified diffusion flame stabilization mechanism. This paper reports the recent progress in the computation and experiment performed in microgravity.

Evidence of negative-index refraction in nonlinear chemical waves.

PubMed

Yuan, Xujin; Wang, Hongli; Ouyang, Qi

2011-05-06

The negative index of refraction of nonlinear chemical waves has become a recent focus in nonlinear dynamics researches. Theoretical analysis and computer simulations have predicted that the negative index of refraction can occur on the interface between antiwaves and normal waves in a reaction-diffusion (RD) system. However, no experimental evidence has been found so far. In this Letter, we report our experimental design in searching for such a phenomenon in a chlorite-iodide-malonic acid (CIMA) reaction. Our experimental results demonstrate that competition between waves and antiwaves at their interface determines the fate of the wave interaction. The negative index of refraction was only observed when the oscillation frequency of a normal wave is significantly smaller than that of the antiwave. All experimental results were supported by simulations using the Lengyel-Epstein RD model which describes the CIMA reaction-diffusion system.

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.

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

NASA Astrophysics Data System (ADS)

Sirohi, Anuj Kumar; Banerjee, Malay; Chakraborti, Anirban

2015-09-01

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.

Measuring Hydrogen Concentrations in Metals

NASA Technical Reports Server (NTRS)

Danford, M. D.

1985-01-01

Commercial corrosion-measurement system adapted to electrochemical determination of hydrogen concentrations in metals. New technique based on diffusion of hydrogen through foil specimen of metal. In sample holder, hydrogen produced on one side of foil, either by corrosion reaction or by cathodic current. Hydrogen diffused through foil removed on other side by constant anode potential, which leads to oxidation of hydrogen to water. Anode current is measure of concentration of hydrogen diffusing through foil. System used to study hydrogen uptake, hydrogen elimination by baking, effect of heat treatment, and effect of electroplating on high-strength steels.

Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: the case of a color indicator.

PubMed

Kuster, S; Riolfo, L A; Zalts, A; El Hasi, C; Almarcha, C; Trevelyan, P M J; De Wit, A; D'Onofrio, A

2011-10-14

Buoyancy-driven hydrodynamic instabilities of acid-base fronts are studied both experimentally and theoretically in the case where an aqueous solution of a strong acid is put above a denser aqueous solution of a color indicator in the gravity field. The neutralization reaction between the acid and the color indicator as well as their differential diffusion modifies the initially stable density profile in the system and can trigger convective motions both above and below the initial contact line. The type of patterns observed as well as their wavelength and the speed of the reaction front are shown to depend on the value of the initial concentrations of the acid and of the color indicator and on their ratio. A reaction-diffusion model based on charge balances and ion pair mobility explains how the instability scenarios change when the concentration of the reactants are varied.

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

NASA Astrophysics Data System (ADS)

Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar

2018-02-01

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

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.

Lateral diffusion study of the Pt-Al system using the NAC nuclear microprobe.

NASA Astrophysics Data System (ADS)

de Waal, H.; Pretorius, R.

1999-10-01

In this study a nuclear microprobe (NMP) was used to analyse phase formation during reaction in Pt-Al lateral diffusion couples. Phase identification was done by Rutherford backscattering spectroscopy. These results were compared with phase formation during conventional thin film Pt-Al interactions. The co-existence of multiple phases in lateral diffusion couples is discussed with reference to the effective heat of formation (EHF) model.

Effect of Cr contents on the diffusion behavior of Te in Ni-based alloy

NASA Astrophysics Data System (ADS)

Jia, Yanyan; Li, Zhefu; Ye, Xiangxi; Liu, Renduo; Leng, Bin; Qiu, Jie; Liu, Min; Li, Zhijun

2017-12-01

The embrittlement of Ni-based structural alloys caused by fission production Te is one of the major challenges for molten salt reactors. It has been reported that solution element Cr can prevent the situation of intergranular cracks caused by Te. However, there is no detailed mechanism explanation on this phenomenon. In this study, the effect of Cr on Te diffusion in Ni-Cr binary system was investigated by diffusion experiments at 800 °C for 100 h. Results show that Te reacts with the alloy mainly forming Ni3Te2, and strip shaped Cr3Te4 is only found on the surface of Ni-15%Cr alloy. According to the discussion of thermodynamic chemical reaction process, Cr3Te4 exhibits the best stability and preferential formation compound in Te/Ni-Cr system as its Gibbs free energy of formation is the lowest. With the increase of Cr content in the alloy, the diffusion depth of Te along grain boundaries significantly decreases. Moreover, the formation process of reaction product and diffusion process are described. The diffusion of Te can be suppressed by high content of Cr in Ni-Cr alloy due to the formation of Cr3Te4 and thus the grain boundary is protected from Te corroding.

Wave Phenomena in Reaction-Diffusion Systems

NASA Astrophysics Data System (ADS)

Steinbock, Oliver; Engel, Harald

2013-12-01

Pattern formation in excitable and oscillatory reaction-diffusion systems provides intriguing examples for the emergence of macroscopic order from molecular reaction events and Brownian motion. Here we review recent results on several aspects of excitation waves including anomalous dispersion, vortex pinning, and three-dimensional scroll waves. Anomalies in the speed-wavelength dependence of pulse trains include nonmonotonic behavior, bistability, and velocity gaps. We further report on the hysteresis effects during the pinning-depinning transition of twodimensional spiral waves. The pinning of three-dimensional scroll waves shows even richer dynamic complexity, partly due to the possibility of geometric and topological mismatches between the unexcitable, pinning heterogeneities and the one-dimensional rotation backbone of the vortex. As examples we present results on the pinning of scroll rings to spherical, C-shaped, and genus-2-type heterogeneities. We also review the main results of several experimental studies employing the Belousov-Zhabotinsky reaction and briefly discuss the biomedical relevance of this research especially in the context of cardiology.

Diffusion Flame Stabilization

NASA Technical Reports Server (NTRS)

Takahashi, Fumiaki; Katta, V. R.

2006-01-01

Diffusion flames are commonly used for industrial burners in furnaces and flares. Oxygen/fuel burners are usually diffusion burners, primarily for safety reasons, to prevent flashback and explosion in a potentially dangerous system. Furthermore, in most fires, condensed materials pyrolyze, vaporize, and burn in air as diffusion flames. As a result of the interaction of a diffusion flame with burner or condensed-fuel surfaces, a quenched space is formed, thus leaving a diffusion flame edge, which plays an important role in flame holding in combustion systems and fire spread through condensed fuels. Despite a long history of jet diffusion flame studies, lifting/blowoff mechanisms have not yet been fully understood, compared to those of premixed flames. In this study, the structure and stability of diffusion flames of gaseous hydrocarbon fuels in coflowing air at normal earth gravity have been investigated experimentally and computationally. Measurements of the critical mean jet velocity (U(sub jc)) of methane, ethane, or propane at lifting or blowoff were made as a function of the coflowing air velocity (U(sub a)) using a tube burner (i.d.: 2.87 mm). By using a computational fluid dynamics code with 33 species and 112 elementary reaction steps, the internal chemical-kinetic structures of the stabilizing region of methane and propane flames were investigated. A peak reactivity spot, i.e., reaction kernel, is formed in the flame stabilizing region due to back-diffusion of heat and radical species against an oxygen-rich incoming flow, thus holding the trailing diffusion flame. The simulated flame base moved downstream under flow conditions close to the measured stability limit.

Diffusion Flame Stabilization

NASA Technical Reports Server (NTRS)

Takahashi, Fumiaki; Katta, Viswanath R.

2007-01-01

Diffusion flames are commonly used for industrial burners in furnaces and flares. Oxygen/fuel burners are usually diffusion burners, primarily for safety reasons, to prevent flashback and explosion in a potentially dangerous system. Furthermore, in most fires, condensed materials pyrolyze, vaporize, and burn in air as diffusion flames. As a result of the interaction of a diffusion flame with burner or condensed-fuel surfaces, a quenched space is formed, thus leaving a diffusion flame edge, which plays an important role in flame holding in combustion systems and fire spread through condensed fuels. Despite a long history of jet diffusion flame studies, lifting/blowoff mechanisms have not yet been fully understood, compared to those of premixed flames. In this study, the structure and stability of diffusion flames of gaseous hydrocarbon fuels in coflowing air at normal earth gravity have been investigated experimentally and computationally. Measurements of the critical mean jet velocity (U(sub jc)) of methane, ethane, or propane at lifting or blowoff were made as a function of the coflowing air velocity (U(sub a)) using a tube burner (i.d.: 2.87 mm) (Fig. 1, left). By using a computational fluid dynamics code with 33 species and 112 elementary reaction steps, the internal chemical-kinetic structures of the stabilizing region of methane and propane flames were investigated (Fig. 1, right). A peak reactivity spot, i.e., reaction kernel, is formed in the flame stabilizing region due to back-diffusion of heat and radical species against an oxygen-rich incoming flow, thus holding the trailing diffusion flame. The simulated flame base moved downstream under flow conditions close to the measured stability limit.

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

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.

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.

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.

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.

Soot Formation in Hydrocarbon/Air Laminar Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Sunderland, P. B.; Faeth, G. M.

1994-01-01

Soot processes within hydrocarbon/air diffusion flames are important because they affect the durability and performance of propulsion systems, the hazards of unwanted fires, the pollutant and particulate emissions from combustion processes, and the potential for developing computational combustion. Motivated by these observations, this investigation involved an experimental study of the structure and soot properties of round laminar jet diffusion flames, seeking an improved understanding of soot formation (growth and nucleation) within diffusion flames. The present study extends earlier work in this laboratory concerning laminar smoke points (l) and soot formation in acetylene/air laminar jet diffusion flames (2), emphasizing soot formation in hydrocarbon/air laminar jet diffusion flames for fuels other than acetylene. In the flame system, acetylene is the dominant gas species in the soot formation region and both nucleation and growth were successfully attributed to first-order reactions of acetylene, with nucleation exhibiting an activation energy of 32 kcal/gmol while growth involved negligible activation energy and a collision efficiency of O.53%. In addition, soot growth in the acetylene diffusion flames was comparable to new soot in premixed flame (which also has been attributed to first-order acetylene reactions). In view of this status, a major issue is the nature of soot formation processes in diffusion flame involving hydrocarbon fuels other than acetylene. In particular, information is needed about th dominant gas species in the soot formation region and the impact of gas species other than acetylene on soot nucleation and growth.

Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle

PubMed Central

Kinsey, Stephen T.; Locke, Bruce R.; Dillaman, Richard M.

2011-01-01

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction–diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction–diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle. PMID:21177946

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback

NASA Astrophysics Data System (ADS)

Gurevich, Svetlana V.

2013-05-01

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

Mean-field hierarchical equations for some A+BC catalytic reaction models

NASA Astrophysics Data System (ADS)

Cortés, Joaquín; Puschmann, Heinrich; Valencia, Eliana

1998-10-01

A mean-field study of the (A+BC→AC+1/2B2) system is developed from hierarchical equations, considering mechanisms that include dissociation, reaction with finite rates, desorption, and diffusion of the adsorbed species. The phase diagrams are compared to Monte Carlo simulations.

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

PubMed

Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

2016-04-01

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Application of gas diffusion electrodes in bioelectrochemical syntheses and energy conversion.

PubMed

Horst, Angelika E W; Mangold, Klaus-Michael; Holtmann, Dirk

2016-02-01

Combining the advantages of biological components (e.g., reaction specificity, self-replication) and electrochemical techniques in bioelectrochemical systems offers the opportunity to develop novel efficient and sustainable processes for the production of a number of valuable products. The choice of electrode material has a great impact on the performance of bioelectrochemical systems. In addition to the redox process at the electrodes, interactions of biocatalysts with electrodes (e.g., enzyme denaturation or biofouling) need to be considered. In recent years, gas diffusion electrodes (GDEs) have proved to be very attractive electrodes for bioelectrochemical purposes. GDEs are porous electrodes, that posses a large three-phase boundary surface. At this interface, a solid catalyst supports the electrochemical reaction between gaseous and liquid phase. This mini-review discusses the application of GDEs in microbial and enzymatic fuel cells, for microbial electrolysis, in biosensors and for electroenzymatic synthesis reactions. © 2015 Wiley Periodicals, Inc.

Restoration of rhythmicity in diffusively coupled dynamical networks.

PubMed

Zou, Wei; Senthilkumar, D V; Nagao, Raphael; Kiss, István Z; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen

2015-07-15

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.

The heat released during catalytic turnover enhances the diffusion of an enzyme

PubMed Central

Riedel, Clement; Gabizon, Ronen; Wilson, Christian A. M.; Hamadani, Kambiz; Tsekouras, Konstantinos; Marqusee, Susan; Pressé, Steve; Bustamante, Carlos

2015-01-01

Recent studies have shown that the diffusivity of enzymes increases in a substrate-dependent manner during catalysis1,2. Although this observation has been reported and characterized for several different systems3–10, the precise origin of this phenomenon is unknown. Calorimetric methods are often used to determine enthalpies from enzyme-catalysed reactions and can therefore provide important insight into their reaction mechanisms11,12. The ensemble averages involved in traditional bulk calorimetry cannot probe the transient effects that the energy exchanged in a reaction may have on the catalyst. Here we obtain single-molecule fluorescence correlation spectroscopy data and analyse them within the framework of a stochastic theory to demonstrate a mechanistic link between the enhanced diffusion of a single enzyme molecule and the heat released in the reaction. We propose that the heat released during catalysis generates an asymmetric pressure wave that results in a differential stress at the protein–solvent interface that transiently displaces the centre-of-mass of the enzyme (chemoacoustic effect). This novel perspective on how enzymes respond to the energy released during catalysis suggests a possible effect of the heat of reaction on the structural integrity and internal degrees of freedom of the enzyme. PMID:25487146

The heat released during catalytic turnover enhances the diffusion of an enzyme

DOE PAGES

Riedel, Clement; Gabizon, Ronen; Wilson, Christian A. M.; ...

2014-12-10

Recent studies have shown that the diffusivity of enzymes increases in a substrate-dependent manner during catalysis. Although this observation has been reported and characterized for several different systems, the precise origin of this phenomenon is unknown. Calorimetric methods are often used to determine enthalpies from enzyme-catalysed reactions and can therefore provide important insight into their reaction mechanisms. The ensemble averages involved in traditional bulk calorimetry cannot probe the transient effects that the energy exchanged in a reaction may have on the catalyst. Here we obtain single-molecule fluorescence correlation spectroscopy data and analyse them within the framework of a stochastic theorymore » to demonstrate a mechanistic link between the enhanced diffusion of a single enzyme molecule and the heat released in the reaction. We propose that the heat released during catalysis generates an asymmetric pressure wave that results in a differential stress at the protein-solvent interface that transiently displaces the centre-of-mass of the enzyme (chemoacoustic effect). We find this novel perspective on how enzymes respond to the energy released during catalysis suggests a possible effect of the heat of reaction on the structural integrity and internal degrees of freedom of the enzyme.« less

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

Kinetics of DNA-mediated docking reactions between vesicles tethered to supported lipid bilayers

PubMed Central

Chan, Yee-Hung M.; Lenz, Peter; Boxer, Steven G.

2007-01-01

Membrane–membrane recognition and binding are crucial in many biological processes. We report an approach to studying the dynamics of such reactions by using DNA-tethered vesicles as a general scaffold for displaying membrane components. This system was used to characterize the docking reaction between two populations of tethered vesicles that display complementary DNA. Deposition of vesicles onto a supported lipid bilayer was performed by using a microfluidic device to prevent mixing of the vesicles in bulk during sample preparation. Once tethered onto the surface, vesicles mixed via two-dimensional diffusion. DNA-mediated docking of two reacting vesicles results in their colocalization after collision and their subsequent tandem motion. Individual docking events and population kinetics were observed via epifluorescence microscopy. A lattice-diffusion simulation was implemented to extract from experimental data the probability, Pdock, that a collision leads to docking. For individual vesicles displaying small numbers of docking DNA, Pdock shows a first-order relationship with copy number as well as a strong dependence on the DNA sequence. Both trends are explained by a model that includes both tethered vesicle diffusion on the supported bilayer and docking DNA diffusion over each vesicle's surface. These results provide the basis for the application of tethered vesicles to study other membrane reactions including protein-mediated docking and fusion. PMID:18025472

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

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.

Investigation of Reaction Mechanism on the Lime-Free Roasting of Chromium-Containing Slag

NASA Astrophysics Data System (ADS)

Yu, Kai-ping; Zhang, Hong-ling; Chen, Bo; Xu, Hong-bin; Zhang, Yi

2015-12-01

The lime-free roasting process of trivalent chromium-containing slag was investigated. The effect of Fe and liquid phase on the conversion reaction of chromium was discussed. The oxidation of trivalent chromium depends greatly on the diffusion of Na+ and O2. Both the raw material Na2CO3 and the intermediate product NaFeO2 serve as the carriers of Na+. The Na+ diffusion is improved by the binary liquid phase of Na2CrO4-Na2CO3, whereas excess liquid phase results in a low conversion rate of chromium by hindering the diffusion of oxygen towards the reaction interface. With the increasing of liquid volume, the controlled step of chromium oxidation changes from Na+ diffusion to oxygen diffusion. The mechanism study showed that the volume of liquid phase increased while raising the reaction temperature or prolonging the reaction time. Based on the role of both liquid phase and Fe, the oxidation process of chromium was summarized as a three-stage model: the Na+ diffusion-controlled stage, the O2 diffusion-controlled stage, and the oxidation reaction halted stage.

Characterization of a Dynamic String Method for the Construction of Transition Pathways in Molecular Reactions

PubMed Central

Johnson, Margaret E.; Hummer, Gerhard

2012-01-01

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion, and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method. PMID:22616575

Mode Reduction and Upscaling of Reactive Transport Under Incomplete Mixing

NASA Astrophysics Data System (ADS)

Lester, D. R.; Bandopadhyay, A.; Dentz, M.; Le Borgne, T.

2016-12-01

Upscaling of chemical reactions in partially-mixed fluid environments is a challenging problem due to the detailed interactions between inherently nonlinear reaction kinetics and complex spatio-temporal concentration distributions under incomplete mixing. We address this challenge via the development of an order reduction method for the advection-diffusion-reaction equation (ADRE) via projection of the reaction kinetics onto a small number N of leading eigenmodes of the advection-diffusion operator (the so-called "strange eigenmodes" of the flow) as an N-by-N nonlinear system, whilst mixing dynamics only are projected onto the remaining modes. For simple kinetics and moderate Péclet and Damkhöler numbers, this approach yields analytic solutions for the concentration mean, evolving spatio-temporal distribution and PDF in terms of the well-mixed reaction kinetics and mixing dynamics. For more complex kinetics or large Péclet or Damkhöler numbers only a small number of modes are required to accurately quantify the mixing and reaction dynamics in terms of the concentration field and PDF, facilitating greatly simplified approximation and analysis of reactive transport. Approximate solutions of this low-order nonlinear system provide quantiative predictions of the evolving concentration PDF. We demonstrate application of this method to a simple random flow and various mass-action reaction kinetics.

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

Multiscale simulations of patchy particle systems combining Molecular Dynamics, Path Sampling and Green's Function Reaction Dynamics

NASA Astrophysics Data System (ADS)

Bolhuis, Peter

Important reaction-diffusion processes, such as biochemical networks in living cells, or self-assembling soft matter, span many orders in length and time scales. In these systems, the reactants' spatial dynamics at mesoscopic length and time scales of microns and seconds is coupled to the reactions between the molecules at microscopic length and time scales of nanometers and milliseconds. This wide range of length and time scales makes these systems notoriously difficult to simulate. While mean-field rate equations cannot describe such processes, the mesoscopic Green's Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. The recently developed multiscale Molecular Dynamics Green's Function Reaction Dynamics (MD-GFRD) approach combines GFRD for simulating the system at the mesocopic scale where particles are far apart, with microscopic Molecular (or Brownian) Dynamics, for simulating the system at the microscopic scale where reactants are in close proximity. The association and dissociation of particles are treated with rare event path sampling techniques. I will illustrate the efficiency of this method for patchy particle systems. Replacing the microscopic regime with a Markov State Model avoids the microscopic regime completely. The MSM is then pre-computed using advanced path-sampling techniques such as multistate transition interface sampling. I illustrate this approach on patchy particle systems that show multiple modes of binding. MD-GFRD is generic, and can be used to efficiently simulate reaction-diffusion systems at the particle level, including the orientational dynamics, opening up the possibility for large-scale simulations of e.g. protein signaling networks.

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.

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.

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

Transport-induced shifts in condensate dew-point and composition in multicomponent systems with chemical reaction

NASA Technical Reports Server (NTRS)

Rosner, D. E.; Nagarajan, R.

1985-01-01

Partial heterogeneous condensation phenomena in multicomponent reacting systems are analyzed taking into consideration the chemical element transport phenomena. It is demonstrated that the dew-point surface temperature in chemically reactive systems is not a purely thermodynamic quantity, but is influenced by the multicomponent diffusion and Soret-mass diffusion phenomena. Several distinct dew-points are shown to exist in such systems and, as a result of transport constraints, the 'sharp' locus between two chemically distinct condensates is systematically moved to a difference mainstream composition.

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%.

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

Laser Spot Detection Based on Reaction Diffusion.

PubMed

Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad

2016-03-01

Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

Interdiffusion and reactions between U-Mo and Zr at 650 °C as a function of time

NASA Astrophysics Data System (ADS)

Park, Y.; Keiser, D. D.; Sohn, Y. H.

2015-01-01

Development of monolithic U-Mo alloy fuel (typically U-10 wt.%Mo) for the Reduced Enrichment for Research and Test Reactors (RERTR) program entails a use of Zr diffusion barrier to eliminate the interdiffusion-reactions between the fuel alloy and Al-alloy cladding. The application of Zr barrier to the U-Mo fuel system requires a co-rolling process that utilizes a soaking temperature of 650 °C, which represents the highest temperature the fuel system is exposed to during both fuel manufacturing and reactor application. Therefore, in this study, development of phase constituents, microstructure and diffusion kinetics of U-10 wt.%Mo and Zr was examined using solid-to-solid diffusion couples annealed at 650 °C for 240, 480 and 720 h. Phase constituents and microstructural development were analyzed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Concentration profiles were mapped as diffusion paths on the isothermal ternary phase diagram. Within the diffusion zone, single-phase layers of β-Zr and β-U were observed along with a discontinuous layer of Mo2Zr between the β-Zr and β-U layers. In the vicinity of Mo2Zr phase, islands of α-Zr phases were also found. In addition, acicular α-Zr and U6Zr3Mo phases were observed within the γ-U(Mo) terminal alloy. Growth rate of the interdiffusion-reaction zone was determined to be 7.75 (± 5.84) × 10-16 m2/s at 650 °C, however with an assumption of a certain incubation period.

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.

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

Cluster geometry and survival probability in systems driven by reaction diffusion dynamics

NASA Astrophysics Data System (ADS)

Windus, Alastair; Jensen, Henrik J.

2008-11-01

We consider a reaction-diffusion model incorporating the reactions A→phi, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.

Summer Work Experience: Determining Methane Combustion Mechanisms and Sub-Scale Diffuser Properties for Space Transporation System Engine Testing

NASA Technical Reports Server (NTRS)

Williams, Powtawche N.

1998-01-01

To assess engine performance during the testing of Space Shuttle Main Engines (SSMEs), the design of an optimal altitude diffuser is studied for future Space Transportation Systems (STS). For other Space Transportation Systems, rocket propellant using kerosene is also studied. Methane and dodecane have similar reaction schemes as kerosene, and are used to simulate kerosene combustion processes at various temperatures. The equations for the methane combustion mechanism at high temperature are given, and engine combustion is simulated on the General Aerodynamic Simulation Program (GASP). The successful design of an altitude diffuser depends on the study of a sub-scaled diffuser model tested through two-dimensional (2-D) flow-techniques. Subroutines given calculate the static temperature and pressure at each Mach number within the diffuser flow. Implementing these subroutines into program code for the properties of 2-D compressible fluid flow determines all fluid characteristics, and will be used in the development of an optimal diffuser design.

Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers

NASA Astrophysics Data System (ADS)

Bandopadhyay, Aditya; Le Borgne, Tanguy; Méheust, Yves; Dentz, Marco

2017-02-01

Mixing fronts, where fluids of different chemical compositions mix with each other, are known to represent hotspots of chemical reaction in hydrological systems. These fronts are typically subjected to velocity gradients, ranging from the pore scale due to no slip boundary conditions at fluid solid interfaces, to the catchment scale due to permeability variations and complex geometry of the Darcy velocity streamlines. A common trait of these processes is that the mixing interface is strained by shear. Depending on the Péclet number Pe , which represents the ratio of the characteristic diffusion time to the characteristic shear time, and the Damköhler number Da , which represents the ratio of the characteristic diffusion time to the characteristic reaction time, the local reaction rates can be strongly impacted by the dynamics of the mixing interface. So far, this impact has been characterized mostly either in kinetics-limited or in mixing-limited conditions, that is, for either low or high Da. Here the coupling of shear flow and chemical reactivity is investigated for arbitrary Damköhler numbers, for a bimolecular reaction and an initial interface with separated reactants. Approximate analytical expressions for the global production rate and reactive mixing scale are derived based on a reactive lamella approach that allows for a general coupling between stretching enhanced mixing and chemical reactions. While for Pe < Da , reaction kinetics and stretching effects are decoupled, a scenario which we name "weak stretching", for Pe > Da , we uncover a "strong stretching" scenario where new scaling laws emerge from the interplay between reaction kinetics, diffusion, and stretching. The analytical results are validated against numerical simulations. These findings shed light on the effect of flow heterogeneity on the enhancement of chemical reaction and the creation of spatially localized hotspots of reactivity for a broad range of systems ranging from kinetic limited to mixing limited situations.

Minimal wave speed for a class of non-cooperative reaction-diffusion systems of three equations

NASA Astrophysics Data System (ADS)

Zhang, Tianran

2017-05-01

In this paper, we study the traveling wave solutions and minimal wave speed for a class of non-cooperative reaction-diffusion systems consisting of three equations. Based on the eigenvalues, a pair of upper-lower solutions connecting only the invasion-free equilibrium are constructed and the Schauder's fixed-point theorem is applied to show the existence of traveling semi-fronts for an auxiliary system. Then the existence of traveling semi-fronts of original system is obtained by limit arguments. The traveling semi-fronts are proved to connect another equilibrium if natural birth and death rates are not considered and to be persistent if these rates are incorporated. Then non-existence of bounded traveling semi-fronts is obtained by two-sided Laplace transform. Then the above results are applied to some disease-transmission models and a predator-prey model.

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.

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

PubMed

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.

PubMed

Maybank, Philip J; Whiteley, Jonathan P

2014-02-01

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

Coupling of active motion and advection shapes intracellular cargo transport.

PubMed

Khuc Trong, Philipp; Guck, Jochen; Goldstein, Raymond E

2012-07-13

Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such cargo-motor motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.

Flow/Soot-Formation Interactions in Nonbuoyant Laminar Diffusion Flames

NASA Technical Reports Server (NTRS)

Dai, Z.; Lin, K.-C.; Sunderland, P. B.; Xu, F.; Faeth, G. M.

2002-01-01

This is the final report of a research program considering interactions between flow and soot properties within laminar diffusion flames. Laminar diffusion flames were considered because they provide model flame systems that are far more tractable for theoretical and experimental studies than more practical turbulent diffusion flames. In particular, understanding the transport and chemical reaction processes of laminar flames is a necessary precursor to understanding these processes in practical turbulent flames and many aspects of laminar diffusion flames have direct relevance to turbulent diffusion flames through application of the widely recognized laminar flamelet concept of turbulent diffusion flames. The investigation was divided into three phases, considering the shapes of nonbuoyant round laminar jet diffusion flames in still air, the shapes of nonbuoyant round laminar jet diffusion flames in coflowing air, and the hydrodynamic suppression of soot formation in laminar diffusion flames.

On a nonlocal reaction-diffusion-advection system modelling the growth of phytoplankton with cell quota structure

NASA Astrophysics Data System (ADS)

Hsu, Sze-Bi; Mei, Linfeng; Wang, Feng-Bin

2015-11-01

Phytoplankton species in a water column compete for mineral nutrients and light, and the existing models usually neglect differences in the nutrient content and the amount of light absorbed of individuals. In this current paper, we examine a size-structured and nonlocal reaction-diffusion-advection system which describes the dynamics of a single phytoplankton species in a water column where the species depends simply on light for its growth. Our model is under the assumption that the amount of light absorbed by individuals is proportional to cell size, which varies for populations that reproduce by simple division into two equally-sized daughters. We first establish the existence of a critical death rate and our analysis indicates that the phytoplankton survives if and only if its death rate is less than the critical death rate. The critical death rate depends on a general reproductive rate, the characteristics of the water column (e.g., turbulent diffusion rate, sinking, depth), cell growth, cell division, and cell size.

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.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things

PubMed Central

Akan, Ozgur B.

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics. PMID:29415019

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

PubMed

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Modeling the transport of chemical warfare agents and simulants in polymeric substrates for reactive decontamination

NASA Astrophysics Data System (ADS)

Pearl, Thomas; Mantooth, Brent; Varady, Mark; Willis, Matthew

2014-03-01

Chemical warfare agent simulants are often used for environmental testing in place of highly toxic agents. This work sets the foundation for modeling decontamination of absorbing polymeric materials with the focus on determining relationships between agents and simulants. The correlations of agents to simulants must consider the three way interactions in the chemical-material-decontaminant system where transport and reaction occur in polymer materials. To this end, diffusion modeling of the subsurface transport of simulants and live chemical warfare agents was conducted for various polymer systems (e.g., paint coatings) with and without reaction pathways with applied decontamination. The models utilized 1D and 2D finite difference diffusion and reaction models to simulate absorption and reaction in the polymers, and subsequent flux of the chemicals out of the polymers. Experimental data including vapor flux measurements and dynamic contact angle measurements were used to determine model input parameters. Through modeling, an understanding of the relationship of simulant to live chemical warfare agent was established, focusing on vapor emission of agents and simulants from materials.

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.

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.

PubMed

Poznanski, R R

2010-09-01

A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.

Propagating gene expression fronts in a one-dimensional coupled system of artificial cells

NASA Astrophysics Data System (ADS)

Tayar, Alexandra M.; Karzbrun, Eyal; Noireaux, Vincent; Bar-Ziv, Roy H.

2015-12-01

Living systems employ front propagation and spatiotemporal patterns encoded in biochemical reactions for communication, self-organization and computation. Emulating such dynamics in minimal systems is important for understanding physical principles in living cells and in vitro. Here, we report a one-dimensional array of DNA compartments in a silicon chip as a coupled system of artificial cells, offering the means to implement reaction-diffusion dynamics by integrated genetic circuits and chip geometry. Using a bistable circuit we programmed a front of protein synthesis propagating in the array as a cascade of signal amplification and short-range diffusion. The front velocity is maximal at a saddle-node bifurcation from a bistable regime with travelling fronts to a monostable regime that is spatially homogeneous. Near the bifurcation the system exhibits large variability between compartments, providing a possible mechanism for population diversity. This demonstrates that on-chip integrated gene circuits are dynamical systems driving spatiotemporal patterns, cellular variability and symmetry breaking.

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.

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

Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when onemore » or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.« less

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.

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.

Lithium manganese oxide spinel electrodes

NASA Astrophysics Data System (ADS)

Darling, Robert Mason

Batteries based oil intercalation eletrodes are currently being considered for a variety of applications including automobiles. This thesis is concerned with the simulation and experimental investigation of one such system: spinel LiyMn2O4. A mathematical model simulating the behavior of an electrochemical cell containing all intercalation electrode is developed and applied to Li yMn2O4 based systems. The influence of the exchange current density oil the propagation of the reaction through the depth of the electrode is examined theoretically. Galvanostatic cycling and relaxation phenomena on open circuit are simulated for different particle-size distributions. The electrode with uniformly sized particles shows the best performance when the current is on, and relaxes towards equilibrium most quickly. The impedance of a porous electrode containing a particle-size distribution at low frequencies is investigated with all analytic solution and a simplified version of the mathematical model. The presence of the particle-size distribution leads to an apparent diffusion coefficient which has all incorrect concentration dependence. A Li/1 M LiClO4 in propylene carbonate (PC)/ LiyMn 2O4 cell is used to investigate the influence of side reactions oil the current-potential behavior of intercalation electrodes. Slow cyclic voltammograms and self-discharge data are combined to estimate the reversible potential of the host material and the kinetic parameters for the side reaction. This information is then used, together with estimates of the solid-state diffusion coefficient and main-reaction exchange current density, in a mathematical model of the system. Predictions from the model compare favorably with continuous cycling results and galvanostatic experiments with periodic current interruptions. The variation with respect to composition of' the diffusion coefficient of lithium in LiyMn2O4 is estimated from incomplete galvanostatic discharges following open-circult periods. The results compared favorably with those available in the literature. Dynamic Monte Carlo simulations were conducted to investigate the concentration dependence of the diffusion coefficient fundamentally. The dynamic Monte Carlo predictions compare favorably with the experimental data.

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).

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.

Microchemical Pen: An Open Microreactor for Region-Selective Surface Modification.

PubMed

Mao, Sifeng; Sato, Chiho; Suzuki, Yuma; Yang, Jianmin; Zeng, Hulie; Nakajima, Hizuru; Yang, Ming; Lin, Jin-Ming; Uchiyama, Katsumi

2016-10-18

Various micro surface-modification approaches including photolithography, dip-pen lithography and ink-jet systems have been developed and used to extend the functionalities of solid surfaces. While those approaches work in the "open space", push-pull systems which work in solutions have recently drawn considerable attention. However, the confining flows performed by push-pull systems have realized only the dispense process, while microscale, region-selective chemical reactions have remained unattainable. This study reports a microchemical pen that enables region-selective chemical reactions for the micro surface modification/patterning. The chemical pen is based on the principle of microfluidic laminar flows and the resulting mixing of reagents by the mutual diffusion. The tiny diffusion layer performs as the working region. This report represents the first demonstration of an open microreactor in which two different reagents react on a real solid sample. The multifunctional characteristics of the microchemical pen are confirmed by different types of reactions in many research areas, including inorganic chemistry, polymer science, electrochemistry and biological sample treatment. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Connecting localized DNA strand displacement reactions

NASA Astrophysics Data System (ADS)

Mullor Ruiz, Ismael; Arbona, Jean-Michel; Lad, Amitkumar; Mendoza, Oscar; Aimé, Jean-Pierre; Elezgaray, Juan

2015-07-01

Logic circuits based on DNA strand displacement reactions have been shown to be versatile enough to compute the square root of four-bit numbers. The implementation of these circuits as a set of bulk reactions faces difficulties which include leaky reactions and intrinsically slow, diffusion-limited reaction rates. In this paper, we consider simple examples of these circuits when they are attached to platforms (DNA origamis). As expected, constraining distances between DNA strands leads to faster reaction rates. However, it also induces side-effects that are not detectable in the solution-phase version of this circuitry. Appropriate design of the system, including protection and asymmetry between input and fuel strands, leads to a reproducible behaviour, at least one order of magnitude faster than the one observed under bulk conditions.Logic circuits based on DNA strand displacement reactions have been shown to be versatile enough to compute the square root of four-bit numbers. The implementation of these circuits as a set of bulk reactions faces difficulties which include leaky reactions and intrinsically slow, diffusion-limited reaction rates. In this paper, we consider simple examples of these circuits when they are attached to platforms (DNA origamis). As expected, constraining distances between DNA strands leads to faster reaction rates. However, it also induces side-effects that are not detectable in the solution-phase version of this circuitry. Appropriate design of the system, including protection and asymmetry between input and fuel strands, leads to a reproducible behaviour, at least one order of magnitude faster than the one observed under bulk conditions. Electronic supplementary information (ESI) available. See DOI: 10.1039/C5NR02434J

Phase Equilibria of the Sn-Ni-Si Ternary System and Interfacial Reactions in Sn-(Cu)/Ni-Si Couples

NASA Astrophysics Data System (ADS)

Fang, Gu; Chen, Chih-chi

2015-07-01

Interfacial reactions in Sn/Ni-4.5 wt.%Si and Sn-Cu/Ni-4.5 wt.%Si couples at 250°C, and Sn-Ni-Si ternary phase equilibria at 250°C were investigated in this study. Ni-Si alloys, which are nonmagnetic, can be regarded as a diffusion barrier layer material in flip chip packaging. Solder/Ni-4.5 wt.%Si interfacial reactions are crucial to the reliability of soldered joints. Phase equilibria information is essential for development of solder/Ni-Si materials. No ternary compound is present in the Sn-Ni-Si ternary system at 250°C. Extended solubility of Si in the phases Ni3Sn2 and Ni3Sn is 3.8 and 6.1 at.%, respectively. As more Si dissolves in these phases their lattice constants decrease. No noticeable ternary solubility is observed for the other intermetallics. Interfacial reactions in solder/Ni-4.5 wt.%Si are similar to those for solder/Ni. Si does not alter the reaction phases. No Si solubility in the reaction phases was detected, although rates of growth of the reaction phases were reduced. Because the alloy Ni-4.5 wt.%Si reacts more slowly with solders than pure Ni, the Ni-4.5 wt.%Si alloy could be a potential new diffusion barrier layer material for flip chip packaging.

Significance of vapor phase chemical reactions on CVD rates predicted by chemically frozen and local thermochemical equilibrium boundary layer theories

NASA Technical Reports Server (NTRS)

Gokoglu, Suleyman A.

1988-01-01

This paper investigates the role played by vapor-phase chemical reactions on CVD rates by comparing the results of two extreme theories developed to predict CVD mass transport rates in the absence of interfacial kinetic barrier: one based on chemically frozen boundary layer and the other based on local thermochemical equilibrium. Both theories consider laminar convective-diffusion boundary layers at high Reynolds numbers and include thermal (Soret) diffusion and variable property effects. As an example, Na2SO4 deposition was studied. It was found that gas phase reactions have no important role on Na2SO4 deposition rates and on the predictions of the theories. The implications of the predictions of the two theories to other CVD systems are discussed.

Removal of PCB and Other Halogenated Organic Contaminants found in Ex Situ Structures

NASA Technical Reports Server (NTRS)

Quinn, Jacqueline (Inventor); Clausen, Christian (Inventor); Geiger, Cherie L. (Inventor); Coon, Christina (Inventor); Berger, Cristina M. (Inventor); Filipek, Laura B. (Inventor); Milum, Kristen M. (Inventor)

2007-01-01

Emulsified systems or a surfactant-stabilized, biodegradable water-in-solvent emulsion with bimetallic particles contained with the emulsion droplets are useful at removing PCBs from ex situ structures. The hydrophobic emulsion system draws PCBs through the solvent/surfactant membrane. Once inside the membrane, the PCBs diffuse into the bimetallic particles and undergo degradation. The PCBs continue to enter, diffuse, degrade, and biphenyl will exit the particle maintaining a concentration gradient across the membrane and maintaining a driving force of the reaction.

Removal of PCB and other halogenated organic contaminants found in ex situ structures

NASA Technical Reports Server (NTRS)

Quinn, Jacqueline (Inventor); Clausen, Christian (Inventor); Geiger, Cherie L. (Inventor); Coon, Christina (Inventor); Berger, Cristina M. (Inventor); Filipek, Laura B. (Inventor); Milum, Kristen M. (Inventor)

2007-01-01

Emulsified systems of a surfactant-stabilized, biodegradable water-in-solvent emulsion with bimetallic particles contained with the emulsion droplets are useful at removing PCBs from ex situ structures. The hydrophobic emulsion system draws PCBs through the solvent/surfactant membrane. Once inside the membrane, the PCBs diffuse into the bimetallic particles and undergo degradation. The PCBs continue to enter, diffuse, degrade, and biphenyl will exit the particle maintaining a concentration gradient across the membrane and maintaining a driving force of the reaction.

Removal of PCB and other halogenated organic contaminants found in ex situ structures

NASA Technical Reports Server (NTRS)

Clausen, Christian A. (Inventor); Milum, Kristen M. (Inventor); Quinn, Jacqueline W. (Inventor); Berger, Cristina M. (Inventor); Geiger, Cherie L. (Inventor); Filipek, Laura B. (Inventor); Coon, Christina (Inventor)

2009-01-01

Emulsified systems of a surfactant-stabilized, biodegradable water-in-solvent emulsion with bimetallic particles contained with the emulsion droplets are useful at removing PCBs from ex situ structures. The hydrophobic emulsion system draws PCBs through the solvent/surfactant membrane. Once inside the membrane, the PCBs diffuse into the bimetallic particles and undergo degradation. The PCBs continue to enter, diffuse, degrade, and biphenyl will exit the particle maintaining a concentration gradient across the membrane and maintaining a driving force of the reaction.

A reaction-diffusion model of CO2 influx into an oocyte

PubMed Central

Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela

2012-01-01

We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674

Effect of isospin diffusion on the production of neutron-rich nuclei in multinucleon transfer reactions

NASA Astrophysics Data System (ADS)

Niu, Fei; Chen, Peng-Hui; Guo, Ya-Fei; Ma, Chun-Wang; Feng, Zhao-Qing

2018-03-01

The isospin dissipation dynamics in multinucleon transfer reactions has been investigated within the dinuclear system model. Production cross sections of neutron-rich isotopes around projectile-like and target-like fragments are estimated in collisions of Ni,6458+208Pb and 78.86,91Kr +198Pt near Coulomb barrier energies. The isospin diffusion in the nucleon transfer process is coupled to the dissipation of relative motion energy and angular momentum of colliding system. The available data of projectile-like fragments via multinucleon transfer reactions are nicely reproduced. It is found that the light projectile-like fragments are produced in the neutron-rich region because of the isospin equilibrium in two colliding nuclei. However, the heavy target-like fragments tend to be formed on the neutron-poor side above the β -stability line. The neutron-rich projectiles move the maximal yields of heavy nuclei to the neutron-rich domain and are available for producing the heavy exotic isotopes, in particular around the neutron shell closure of N =126 .

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.

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.

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

NASA Astrophysics Data System (ADS)

Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

2015-09-01

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations

PubMed Central

Hallock, Michael J.; Stone, John E.; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida

2014-01-01

Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems. PMID:24882911

Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations.

PubMed

Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida

2014-05-01

Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.

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.

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.

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.

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.

[Function of alveoles as a result of evolutionary development of respiratory system in mammals].

PubMed

Ivanov, K P

2013-01-01

Reaction of hemoglobin oxygenation is known to occur for 40 femtoseconds (40 x 10(-15) s). However, the process of oxygen diffusion to hemoglobin under physiologic conditions decelerated this reaction approximately billion times. In mammalian lungs, blood is moving at a high rate and in a relatively high amount. The human lung mass is as low as 600 g, but the complete cardiac output approaches 6 1/min. In rat, from 20 to 40 ml of blood is passed for q min through the lung whose mass is about 1.5 g. Such blood flow rate is possible, as in lungs of high animals there exists a dense network of relatively large microvessels with diameter from 20 to 40 microm and more. In spite of a large volume and a high blood flow rate hampering oxygen diffusion, the complete blood oxygenation occurs in lung alveoli. This is due to peculiar mechanisms that facilitate markedly the oxygen diffusion and that developed in alveoli of mammals in the course of many million years of evolution of their respiratory system. Thus, alveolus is not a bubble with air, but a complex tool of fight with inertness of diffusion. It is interesting that in lungs of the low vertebrates, neither such system of blood vessels nor alveoli exist, and their blood flow rate is much lower than in mammals.

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

Propagation failures, breathing pulses, and backfiring in an excitable reaction-diffusion system.

PubMed

Manz, Niklas; Steinbock, Oliver

2006-09-01

We report results from experiments with a pseudo-one-dimensional Belousov-Zhabotinsky reaction that employs 1,4-cyclohexanedione as its organic substrate. This excitable system shows traveling oxidation pulses and pulse trains that can undergo complex sequences of propagation failures. Moreover, we present examples for (i) breathing pulses that undergo periodic changes in speed and size and (ii) backfiring pulses that near their back repeatedly generate new pulses propagating in opposite direction.

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.

Mathematical model for the growth of phases in binary multiphase systems upon isothermic annealing

NASA Astrophysics Data System (ADS)

Molokhina, L. A.; Rogalin, V. E.; Filin, S. A.; Kaplunov, I. A.

2017-09-01

A phenomenological mathematical model of the formation and growth of phases in a binary multiphase system with allowance for factors influencing the process of diffusion in a binary system is presented. It is shown that phases can grow for a certain time at different ratios between diffusion parameters according to a parabolic law that depends on the duration of isothermic annealing. They then slow their growth after successor phases appear at their interface with one component and can completely disappear from a diffusion layer or begin to grow again, but only at a rate slower than during their initial formation. The dependence of the thickness of each phase layer in a multiphase diffusion zone on the duration of isothermic annealing and the ratio between the diffusion parameters in neighboring phases is obtained. It is established that a certain ratio between the phase growth and rates of dissolution with allowance for the coefficients of diffusion in each phase and the periods of incubation can result in the complete disappearance of one phase as early as the onset of the growth of phase nuclei and be interpreted as a process of reaction diffusion.

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

Surface diffusion of adsorbates is difficult to measure on realistic systems, yet it is of fundamental interest in catalysis and coating reactions. quasielastic neutron scattering (QENS) was used to investigate the diffusion of cyclohexane and benzene adsorbed on a nickel metal sponge catalyst. Molecular dynamics simulations of benzene on a model (111) nickel surface showed localised motion with diffusion by intermittent jumps. The experimental data was therefore fitted to the Singwi-Sjölander model and activation energies for diffusion of 4.0 kJ mol-1 for benzene and 4.3 kJ mol-1 for cyclohexane were calculated for the two dimensional model. Limited motion out-of plane was seen in the dynamics simulations and is discussed, although the resolution of the scattering experiment is insufficient to quantify this. Good agreement is seen between the use of a perfect crystal as a model for a disordered system over short time scales, suggesting that simple models are adequate to describe diffusion over polycrystalline metal surfaces on the timescale of QENS measurement.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

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.

Nanowire membrane-based nanothermite: towards processable and tunable interfacial diffusion for solid state reactions.

PubMed

Yang, Yong; Wang, Peng-peng; Zhang, Zhi-cheng; Liu, Hui-ling; Zhang, Jingchao; Zhuang, Jing; Wang, Xun

2013-01-01

Interfacial diffusion is of great importance in determining the performance of solid-state reactions. For nanometer sized particles, some solid-state reactions can be triggered accidently by mechanical stress owing to their large surface-to-volume ratio compared with the bulk ones. Therefore, a great challenge is the control of interfacial diffusion for solid state reactions, especially for energetic materials. Here we demonstrate, through the example of nanowire-based thermite membrane, that the thermite solid-state reaction can be easily tuned via the introduction of low-surface-energy coating layer. Moreover, this silicon-coated thermite membrane exhibit controlled wetting behavior ranging from superhydrophilic to superhydrophobic and, simultaneously, to significantly reduce the friction sensitivity of thermite membrane. This effect enables to increase interfacial resistance by increasing the amount of coating material. Indeed, our results described here make it possible to tune the solid-state reactions through the manipulation of interfacial diffusion between the reactants.

Nanowire Membrane-based Nanothermite: towards Processable and Tunable Interfacial Diffusion for Solid State Reactions

NASA Astrophysics Data System (ADS)

Yang, Yong; Wang, Peng-Peng; Zhang, Zhi-Cheng; Liu, Hui-Ling; Zhang, Jingchao; Zhuang, Jing; Wang, Xun

2013-04-01

Interfacial diffusion is of great importance in determining the performance of solid-state reactions. For nanometer sized particles, some solid-state reactions can be triggered accidently by mechanical stress owing to their large surface-to-volume ratio compared with the bulk ones. Therefore, a great challenge is the control of interfacial diffusion for solid state reactions, especially for energetic materials. Here we demonstrate, through the example of nanowire-based thermite membrane, that the thermite solid-state reaction can be easily tuned via the introduction of low-surface-energy coating layer. Moreover, this silicon-coated thermite membrane exhibit controlled wetting behavior ranging from superhydrophilic to superhydrophobic and, simultaneously, to significantly reduce the friction sensitivity of thermite membrane. This effect enables to increase interfacial resistance by increasing the amount of coating material. Indeed, our results described here make it possible to tune the solid-state reactions through the manipulation of interfacial diffusion between the reactants.

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.

Oscillation of a polymer gel entrained with a periodic force.

PubMed

Shiota, Takaya; Ikura, Yumihiko S; Nakata, Satoshi

2013-02-21

The oscillation of a polymer gel induced by the Belousov-Zhabotinsky (BZ) reaction was investigated under an external force composed of a square wave. The oscillation of the BZ reaction entrained to the periodic force and the features of this entrainment changed depending on the period and duty cycle of the square wave. The experimental results suggest that the change in the volume of the gel also gave feedback to the BZ reaction. The mechanism of entrainment is discussed in relation to the compression of the gel and the reaction-diffusion system in the BZ 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.

Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.

PubMed

Dematté, Lorenzo

2012-01-01

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

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.

Periodic stripe formation by a Turing-mechanism operating at growth zones in the mammalian palate

PubMed Central

Economou, Andrew D.; Ohazama, Atsushi; Porntaveetus, Thantrira; Sharpe, Paul T.; Kondo, Shigeru; Basson, M. Albert; Gritli-Linde, Amel; Cobourne, Martyn T.; Green, Jeremy B.A.

2012-01-01

We present direct evidence of an activator-inhibitor system in the generation of the regularly spaced transverse ridges of the palate. We show that new ridges, or rugae, marked by stripes of Sonic hedgehog (Shh) expression, appear at two growth zones where the space between previously laid-down rugae increases. However, inter-rugal growth is not absolutely required: new stripes still appear when growth is inhibited. Furthermore, when a ruga is excised new Shh expression appears, not at the cut edge but as bifurcating stripes branching from the neighbouring Shh stripe, diagnostic of a Turing-type reaction-diffusion mechanism. Genetic and inhibitor experiments identify Fibroblast Growth Factor (FGF) and Shh as an activator-inhibitor pair in this system. These findings demonstrate a reaction-diffusion mechanism likely to be widely relevant in vertebrate development. PMID:22344222

Enzymes containing porous polymersomes as nano reaction vessels for cascade reactions.

PubMed

Kuiper, Suzanne M; Nallani, Madhavan; Vriezema, Dennis M; Cornelissen, Jeroen J L M; van Hest, Jan C M; Nolte, Roeland J M; Rowan, Alan E

2008-12-07

Polystyrene(40)-b-poly(isocyanoalanine(2-thiophen-3-yl-ethyl)amide)(50) (PS-PIAT) polymersomes have the unique property of being sufficiently porous to allow diffusion of small (organic) substrates while retaining large biomolecules such as enzymes inside. Herein we report on the encapsulation and protection of glucose oxidase (GOx) and horse radish peroxidase (HRP) in PS-PIAT polymersomes and the successful employment of these functionalised nanoreactors in a cascade reaction. The demonstrated concept allows for further application in other enzymatic cascade reactions, bio-organic hybrid systems and biosensing devices.

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.

Reaction paths in the system Al 2O 3-hBN-Y

NASA Astrophysics Data System (ADS)

Reichert, K.; Oreshina, O.; Cremer, R.; Neuschütz, D.

2001-07-01

As part of the investigations on the suitability of a new concept for a tailored fiber-matrix interface in sapphire fiber reinforced NiAl matrix composites for application as a high-temperature structural material, the interfacial reactions in the system alumina-hexagonal boron nitride-yttrium (Al 2O 3-hBN-Y) have been examined in the temperature range of 1100-1300°C. For this, alumina substrates were coated with hBN by means of CVD and subsequently with sputter deposited yttrium. Afterwards the samples were annealed for up to 16 h under inert atmosphere. Grazing incidence X-ray diffraction (GIXRD) served to analyze the phases formed by diffusion processes in the reaction zone. The peak intensities in these diffraction patterns were used to evaluate the sequence of phases formed due to diffusion and reaction. After the initial formation of YN and YB 2, the phases Y 2O 3, Al 2Y, and YB 4 were observed. Even longer annealing times or higher temperatures, respectively, led to the formation of the ternary oxides YAlO 3 and Y 3Al 5O 12 as well as metallic aluminum.

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.

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

Dynamic coupling between coordinates in a model for biomolecular isomerization

NASA Astrophysics Data System (ADS)

Ma, Ao; Nag, Ambarish; Dinner, Aaron R.

2006-04-01

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C7eq→αR transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.

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.

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.

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.

Reaction-diffusion theory in the presence of an attractive harmonic potential

NASA Astrophysics Data System (ADS)

Spendier, K.; Sugaya, S.; Kenkre, V. M.

2013-12-01

Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reaction-diffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.

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

Capurro, O. A.; Niello, J. O. Fernandez; Pacheco, A. J.

We have investigated experimental quasielastic cross sections measured at backward angles and at deep sub-barrier energies for the {sup 35}Cl+{sup 105,106,110}Pd and {sup 32}S+{sup 110}Pd systems. Since coupling effects are almost negligible at very low bombarding energies, the quasielastic data allow one to determine the diffuseness parameter of the ion-ion potential. For the analyzed reactions we have obtained a surface diffuseness parameter value around 0.58{+-}0.04 fm.

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

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.

Formation of amorphous materials

DOEpatents

Johnson, William L.; Schwarz, Ricardo B.

1986-01-01

Metastable amorphous or fine crystalline materials are formed by solid state reactions by diffusion of a metallic component into a solid compound or by diffusion of a gas into an intermetallic compound. The invention can be practiced on layers of metals deposited on an amorphous substrate or by intermixing powders with nucleating seed granules. All that is required is that the diffusion of the first component into the second component be much faster than the self-diffusion of the first component. The method is practiced at a temperature below the temperature at which the amorphous phase transforms into one or more crystalline phases and near or below the temperature at which the ratio of the rate of diffusion of the first component to the rate of self-diffusion is at least 10.sup.4. This anomalous diffusion criteria is found in many binary, tertiary and higher ordered systems of alloys and appears to be found in all alloy systems that form amorphous materials by rapid quenching. The method of the invention can totally convert much larger dimensional materials to amorphous materials in practical periods of several hours or less.

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).

Reaction diffusion in the nickel-chromium-aluminum and cobalt-chromium-aluminum systems

NASA Technical Reports Server (NTRS)

Levine, S. R.

1977-01-01

The effects of MCrAl coating-substrate interdiffusion on oxidation life and the general mutliphase, multicomponent diffusion problem were examined. Semi-infinite diffusion couples that had sources representing coatings and sinks representing gas turbine alloys were annealed at 1,000, 1,095, 1,150, or 1,205 C for as long as 500 hours. The source and sink aluminum and chromium contents and the base metal (cobalt or nickel) determined the parabolic diffusion rate constants of the couples and predicted finite coating lives. The beta source strength concept provided a method (1) for correlating beta recession rate constants with composition; (2) for determining reliable average total, diffusion, and constitutional activation energies; and (3) for calculating interdiffusion coefficients.

The mechanism of myrmekite formation deduced from steady-diffusion modeling based on petrography: Case study of the Okueyama granitic body, Kyushu, Japan

NASA Astrophysics Data System (ADS)

Yuguchi, Takashi; Nishiyama, Tadao

2008-12-01

Myrmekite is an intergrowth texture consisting of vermicular quartz and albitic plagioclase (Ab 93An 7 in this study), typically occurring between K-feldspar and plagioclase. It occurs ubiquitously in both metamorphic and granitic rocks; however, its genesis has been an enigma. This paper describes myrmekite's petrography and discusses its genesis from the Okueyama granitic body (OKG), which is a young (14 Ma) granite in Southwest Japan with no evidence of deformation after solidification. The genesis of a newly observed texture, the 'reaction rim', will be also discussed in relation to myrmekite. The reaction rim is an albite layer (Ab 95An 5) with no vermicular quartz between K-feldspar and plagioclase, and it occasionally makes a composite texture with myrmekite. Both myrmekite and the reaction rim are accompanied by a diffusive boundary layer (Olg-layer) with a mean composition of oligoclase (Ab 75An 25) in the rim of neighboring plagioclase rim. The overall reactions in an open system for the formation of myrmekite and that for the reaction rim are derived based on the following two models: 1) one based on the assumption of conservation of solid volume with arbitrarily specified closure components, and 2) the other based on the assumption of closure of AlO 3/2 together with an arbitrarily specified volume factor. Steady diffusion modeling in an open system based on the overall reaction thus derived defines the stability field of myrmekite and of the reaction rim in terms of the ratios of phenomenological coefficients ( L-ratios). The steady diffusion models for the above two models have essentially the same features. Myrmekite is stable for large values (> 10) of LAlAl/ LCaCa, for moderate values of LAlAl/ LSiSi, and for only small values (< 1) of LAlAl/ LNaNa. In the case of the reaction rim, the stability field is much wider in a plot of LAlAl/ LCaCa vs. LAlAl/ LNaNa, and its dependence on LAlAl/ LSiSi is stronger than that of myrmekite. The reaction rim is stable only for large values of LAlAl/ LCaCa, which is consistent with the case of myrmekite. Exchange cycles for myrmekite and the reaction rim show that the essential formation mechanism is albitization of K-feldspar: KAlSi 3O 8 + NaO 1/2 = NaAlSi 3O 8 + KO 1/2, which is coupled with albitization of plagioclase via diffusive transport of NaO 1/2 and SiO 2: CaAl 2Si 2O 8 + NaO 1/2 + SiO 2 = NaAlSi 3O 8 + CaO + AlO 3/2. Formation of myrmekite requires more SiO 2 than development of the reaction rim; some of the SiO 2 is given by decomposition of K-feldspar and some is supplied from the environment to the boundary between K-feldspar and plagioclase.

Illustrating Chemical Concepts through Food Systems: Introductory Chemistry Experiments.

ERIC Educational Resources Information Center

Chambers, E., IV; Setser, C. S.

1980-01-01

Demonstrations involving foods that illustrate chemical concepts are described, including vaporization of liquids and Graham's law of diffusion, chemical reaction rates, adsorption, properties of solutions, colloidal dispersions, suspensions, and hydrogen ion concentration. (CS)

2D Lattice Boltzmann Simulation Of Chemical Reactions Within Rayleigh-Bénard And Poiseuille-Bénard Convection Systems

NASA Astrophysics Data System (ADS)

Amaya-Ventura, Gilberto; Rodríguez-Romo, Suemi

2011-09-01

This paper deals with the computational simulation of the reaction-diffusion-advection phenomena emerging in Rayleigh-Bénard (RB) and Poiseuille-Bénard reactive convection systems. We use the Boussinesq's approximation for buoyancy forces and the Lattice Boltzmann method (LBM). The first kinetic mesoscopic model proposed here is based on the discrete Boltzmann equation needed to solve the momentum balance coupled with buoyancy forces. Then, a second lattice Boltzmann algorithm is applied to solve the reaction-diffusion-advection equation to calculate the evolution of the chemical species concentration. We use a reactive system composed by nitrous oxide (so call laughing gas) in air as an example; its spatio-temporal decomposition is calculated. Two cases are considered, a rectangular enclosed cavity and an open channel. The simulations are performed at low Reynolds numbers and in a steady state between the first and second thermo-hydrodynamic instabilities. The results presented here, for the thermo-hydrodynamic behavior, are in good agreement with experimental data; while our| chemical kinetics simulation yields expected results. Some applications of our approach are related to chemical reactors and atmospheric phenomena, among others.

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.

Effect of static porosity fluctuations on reactive transport in a porous medium

NASA Astrophysics Data System (ADS)

L'Heureux, Ivan

2018-02-01

Reaction-diffusive transport phenomena in porous media are ubiquitous in engineering applications, biological and geochemical systems. The porosity field is usually random in space, but most models consider the porosity field as a well-defined deterministic function of space and time and ignore the porosity fluctuations. They use a reaction-diffusion equation written in terms of an average porosity and average concentration fields. In this contribution, we treat explicitly the effect of spatial porosity fluctuations on the dynamics of a concentration field for the case of a one-dimensional reaction-transport system with nonlinear kinetics. Three basic assumptions are considered. (i) The porosity fluctuations are assumed to have Gaussian properties and an arbitrary variance; (ii) we assume that the noise correlation length is small compared to the relevant macroscopic length scale; (iii) and we assume that the kinetics of the reactive term in the equations for the fluctuations is a self-consistently determined constant. Elimination of the fluctuating part of the concentration field from the dynamics leads to a renormalized equation involving the average concentration field. It is shown that the noise leads to a renormalized (generally smaller) diffusion coefficient and renormalized kinetics. Within the framework of the approximations used, numerical simulations are in agreement with our theory. We show that the porosity fluctuations may have a significant effect on the transport of a reactive species, even in the case of a homogeneous average porosity.

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.

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.

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

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.

PTFE effect on the electrocatalysis of the oxygen reduction reaction in membraneless microbial fuel cells.

PubMed

Guerrini, Edoardo; Grattieri, Matteo; Faggianelli, Alessio; Cristiani, Pierangela; Trasatti, Stefano

2015-12-01

Influence of PTFE in the external Gas Diffusion Layer (GDL) of open-air cathodes applied to membraneless microbial fuel cells (MFCs) is investigated in this work. Electrochemical measurements on cathodes with different PTFE contents (200%, 100%, 80% and 60%) were carried out to characterize cathodic oxygen reduction reaction, to study the reaction kinetics. It is demonstrated that ORR is not under diffusion-limiting conditions in the tested systems. Based on cyclic voltammetry, an increase of the cathodic electrochemical active area took place with the decrease of PTFE content. This was not directly related to MFC productivity, but to the cathode wettability and the biocathode development. Low electrodic interface resistances (from 1 to 1.5 Ω at the start, to near 0.1 Ω at day 61) indicated a negligible ohmic drop. A decrease of the Tafel slopes from 120 to 80 mV during productive periods of MFCs followed the biological activity in the whole MFC system. A high PTFE content in the cathode showed a detrimental effect on the MFC productivity, acting as an inhibitor of ORR electrocatalysis in the triple contact zone.

Effects of the fluid flows on enzymatic chemical oscillations

NASA Astrophysics Data System (ADS)

Shklyaev, Oleg; Yashin, Victor; Balazs, Anna

2017-11-01

Chemical oscillations are ubiquitous in nature and have a variety of promising applications. Usually, oscillating chemical systems are analyzed within the context of a reaction-diffusion framework. Here, we examine how fluid flows carrying the reactants can be utilized to modulate the negative feedback loops and time delays that promote chemical oscillations. We consider a model where a chemical reaction network involves two species, X and Y, which undergo transformations catalyzed by respective enzymes immobilized at the bottom wall of a fluid-filled microchamber. The reactions with the enzymes provide a negative feedback in the chemically oscillating system. In particular, the first enzyme, localized on the first patch, promotes production of chemical X, while the second enzyme, immobilized on the second patch, promotes production of chemical Y, which inhibits the production of chemical X. The separation distance between the enzyme-coated patches sets the time delay required for the transportation of X and Y. The chemical transport is significantly enhanced if convective fluxes accompany the diffusive ones. Therefore, the parameter region where oscillations are present is modified. The findings provide guidance to designing micro-scale chemical reactors with improved functionalities.

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

Cell adhesion and mechanics as drivers of tissue organization and differentiation: local cues for large scale organization.

PubMed

Wickström, Sara A; Niessen, Carien M

2018-06-01

Biological patterns emerge through specialization of genetically identical cells to take up distinct fates according to their position within the organism. How initial symmetry is broken to give rise to these patterns remains an intriguing open question. Several theories of patterning have been proposed, most prominently Turing's reaction-diffusion model of a slowly diffusing activator and a fast diffusing inhibitor generating periodic patterns. Although these reaction-diffusion systems can generate diverse patterns, it is becoming increasingly evident that cell shape and tension anisotropies, mediated via cell-cell and/or cell-matrix contacts, also facilitate symmetry breaking and subsequent self-organized tissue patterning. This review will highlight recent studies that implicate local changes in adhesion and/or tension as key drivers of cell rearrangements. We will also discuss recent studies on the role of cadherin and integrin adhesive receptors in mediating and responding to local tissue tension asymmetries to coordinate cell fate, position and behavior essential for tissue self-organization and maintenance. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

Patterns and Oscillations in Reaction-Diffusion Systems with Intrinsic Fluctuations

NASA Astrophysics Data System (ADS)

Giver, Michael; Goldstein, Daniel; Chakraborty, Bulbul

2013-03-01

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, biochemical reactions within cells, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Initially motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional systems with the ultimate goals of understanding the role of noise in spatially structured systems and engineering novel patterns and attractors induced by fluctuations. In the zero dimensional system, we observe a noise induced switching between small and large amplitude oscillations when a separation of time scales is present, while the spatially extended system displays a similar switching between a stationary Turing pattern and uniform oscillations.

Nanowire Membrane-based Nanothermite: towards Processable and Tunable Interfacial Diffusion for Solid State Reactions

PubMed Central

Yang, Yong; Wang, Peng-peng; Zhang, Zhi-cheng; Liu, Hui-ling; Zhang, Jingchao; Zhuang, Jing; Wang, Xun

2013-01-01

Interfacial diffusion is of great importance in determining the performance of solid-state reactions. For nanometer sized particles, some solid-state reactions can be triggered accidently by mechanical stress owing to their large surface-to-volume ratio compared with the bulk ones. Therefore, a great challenge is the control of interfacial diffusion for solid state reactions, especially for energetic materials. Here we demonstrate, through the example of nanowire-based thermite membrane, that the thermite solid-state reaction can be easily tuned via the introduction of low-surface-energy coating layer. Moreover, this silicon-coated thermite membrane exhibit controlled wetting behavior ranging from superhydrophilic to superhydrophobic and, simultaneously, to significantly reduce the friction sensitivity of thermite membrane. This effect enables to increase interfacial resistance by increasing the amount of coating material. Indeed, our results described here make it possible to tune the solid-state reactions through the manipulation of interfacial diffusion between the reactants. PMID:23603809

Target Patterns in Reaction-Diffusion Systems,

DTIC Science & Technology

1981-01-01

Riol. 37 (1974), 225-235. 8. M. H. COHEN AND S. A. ROBERTSON, Wave propagation in the early stages of aggregation of cellular slime molds . J. Theoret...the Zaikin-Zhabotinskii-Winfree reagent, Chem. Educ. 56 (1979), 574. 5. F. ALCANTARA AND M. MONK, Signal propagation during aggregation in the slime ... mold Dit’resteltu n discoideum. J. Gen. Microbiol. 85 (1974). 321-334. 6. M. S. COHEN AND P. S. HAGAN, Diffusion induced morphogenesis in the

Dynamical patterns and regime shifts in the nonlinear model of soil microorganisms growth

NASA Astrophysics Data System (ADS)

Zaitseva, Maria; Vladimirov, Artem; Winter, Anna-Marie; Vasilyeva, Nadezda

2017-04-01

Dynamical model of soil microorganisms growth and turnover is formulated as a system of nonlinear partial differential equations of reaction-diffusion type. We consider spatial distributions of concentrations of several substrates and microorganisms. Biochemical reactions are modelled by chemical kinetic equations. Transport is modelled by simple linear diffusion for all chemical substances, while for microorganisms we use different transport functions, e.g. some of them can actively move along gradient of substrate concentration, while others cannot move. We solve our model in two dimensions, starting from uniform state with small initial perturbations for various parameters and find parameter range, where small initial perturbations grow and evolve. We search for bifurcation points and critical regime shifts in our model and analyze time-space profile and phase portraits of these solutions approaching critical regime shifts in the system, exploring possibility to detect such shifts in advance. This work is supported by NordForsk, project #81513.

Death wins against life in a spatially extended model of the caspase-3/8 feedback loop.

PubMed

Daub, M; Waldherr, S; Allgöwer, F; Scheurich, P; Schneider, G

2012-01-01

Apoptosis is an important physiological process which enables organisms to remove unwanted or damaged cells. A mathematical model of the extrinsic pro-apoptotic signaling pathway has been introduced by Eissing et al. (2007) and a bistable behavior with a stable death state and a stable life state of the reaction system has been established. In this paper, we consider a spatial extension of the extrinsic pro-apoptotic signaling pathway incorporating diffusion terms and make a model-based, numerical analysis of the apoptotic switch in the spatial dimension. For the parameter regimes under consideration it turns out that for this model diffusion homogenizes rapidly the concentrations which afterward are governed by the original reaction system. The activation of effector-caspase 3 depends on the space averaged initial concentration of pro-caspase 8 and pro-caspase 3 at the beginning of the process. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

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.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Non-cooperative Fisher-KPP systems: traveling waves and long-time behavior

NASA Astrophysics Data System (ADS)

Girardin, Léo

2018-01-01

This paper is concerned with non-cooperative parabolic reaction-diffusion systems which share structural similarities with the scalar Fisher-KPP equation. These similarities make it possible to prove, among other results, an extinction and persistence dichotomy and, when persistence occurs, the existence of a positive steady state, the existence of traveling waves with a half-line of possible speeds and a positive minimal speed and the equality between this minimal speed and the spreading speed for the Cauchy problem. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.

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.

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.

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

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

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.

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.

Coadsorbate-Induced Reversal of Solid-Liquid Interface Dynamics.

PubMed

Rahn, Björn; Wen, Rui; Deuchler, Lukas; Stremme, Johannes; Franke, Andreas; Pehlke, Eckhard; Magnussen, Olaf M

2018-05-22

Coadsorbed anions are well-known to influence surface reactivity and dynamics at solid-liquid interfaces. Here we demonstrate that the chemical nature of these spectator species can entirely determine the microscopic dynamic behavior. Quantitative in situ video-STM data on the surface diffusion of adsorbed sulfur atoms on Cu(100) electrodes in aqueous solution covered by bromide and chloride spectators, respectively, reveal in both cases a strong exponential potential dependence, but with opposite sign. This reversal is highly surprising in view of the isostructural adsorbate arrangement in the two systems. Detailed DFT studies suggest an anion-induced difference in the sulfur diffusion mechanism, specifically an exchange diffusion on the Br-covered surface. Experimental evidence for the latter is provided by the observation of Cu vacancy formation in the Br system, which can be rationalized by a side reaction of the sulfur exchange diffusion. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

PubMed

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-10-15

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

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.

A diffusion-reaction scheme for modeling ignition and self-propagating reactions in Al/CuO multilayered thin films

NASA Astrophysics Data System (ADS)

Lahiner, Guillaume; Nicollet, Andrea; Zapata, James; Marín, Lorena; Richard, Nicolas; Rouhani, Mehdi Djafari; Rossi, Carole; Estève, Alain

2017-10-01

Thermite multilayered films have the potential to be used as local high intensity heat sources for a variety of applications. Improving the ability of researchers to more rapidly develop Micro Electro Mechanical Systems devices based on thermite multilayer films requires predictive modeling in which an understanding of the relationship between the properties (ignition and flame propagation), the multilayer structure and composition (bilayer thicknesses, ratio of reactants, and nature of interfaces), and aspects related to integration (substrate conductivity and ignition apparatus) is achieved. Assembling all these aspects, this work proposes an original 2D diffusion-reaction modeling framework to predict the ignition threshold and reaction dynamics of Al/CuO multilayered thin films. This model takes into consideration that CuO first decomposes into Cu2O, and then, released oxygen diffuses across the Cu2O and Al2O3 layers before reacting with pure Al to form Al2O3. This model is experimentally validated from ignition and flame velocity data acquired on Al/CuO multilayers deposited on a Kapton layer. This paper discusses, for the first time, the importance of determining the ceiling temperature above which the multilayers disintegrate, possibly before their complete combustion, thus severely impacting the reaction front velocity and energy release. This work provides a set of heating surface areas to obtain the best ignition conditions, i.e., with minimal ignition power, as a function of the substrate type.

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.

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.

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.

Orthotropic and time-dependent moisture diffusion measurements in polymer matrix composites using nuclear reaction analysis

NASA Astrophysics Data System (ADS)

Pilli, Siva P.

Moisture plays a significant role in influencing the mechanical behavior and long-term durability of composites. The objective of this dissertation was to understand the basic concepts of moisture transport in polymeric composites. Humidity test chambers were used in combination with D2O water to characterize the diffusion of D2O using Nuclear Reaction Analysis (NRA). Moisture content was measured as a function of through-thickness depth using NRA. In this study a novel method to measure the orthotropic diffusivities of polymer matrix composites has been demonstrated. This was achieved by soaking the samples in D2O vapor and subsequently characterizing the diffusion of D2O at all edges of the coupon using NRA. The diffusivity through the surface was 3½ times higher than the diffusivity through the edges. A direct comparison of experimental data with models using orthotropic diffusivities was in relatively good agreement. Surface moisture content was also measured as a function of time using NRA. It was shown that the surface concentration reaches an intermediate value of 79% Mm very rapidly and is followed by a slow linear increase to the saturation level (Mm). This research also interrogates the effect of pressure on diffusion. Test chambers were built to maintain a constant relative humidity of 80% at 60°C at three different pressures (0.101 MPa, 0.517 MPa and 1.034 MPa) including a liquid water immersion test chamber at 60°C. In this study it was observed that the time to saturation increased with increasing chamber pressure. This was primarily due to the increased maximum moisture content at higher pressures. Liquid immersion of the test samples provided the upper bound for maximum moisture content and a lower bound for time to saturation. The effects of material systems and layups on humidity measurements were also studied using two different polymer composite material systems, Cycom and Toray. Diffusivity results were identical for different layups whereas differences were observed for different material systems. Finally three-dimensional numeric models were developed, using ANSYS, to compare with the measured moisture content. Models incorporating the time-dependent and 3-D diffusion have shown an improved correlation with experiments.

Clinopyroxene dissolution in basaltic melt

NASA Astrophysics Data System (ADS)

Chen, Yang; Zhang, Youxue

2009-10-01

The history of magmatic systems may be inferred from reactions between mantle xenoliths and host basalt if the thermodynamics and kinetics of the reactions are quantified. To study diffusive and convective clinopyroxene dissolution in silicate melts, diffusive clinopyroxene dissolution experiments were conducted at 0.47-1.90 GPa and 1509-1790 K in a piston-cylinder apparatus. Clinopyroxene saturation is found to be roughly determined by MgO and CaO content. The effective binary diffusivities, DMgO and DCaO, and the interface melt saturation condition, C0MgO×C0CaO, are extracted from the experiments. DMgO and DCaO show Arrhenian dependence on temperature. The pressure dependence is small and not resolved within 0.47-1.90 GPa. C0MgO×C0CaO in the interface melt increases with increasing temperature, but decreases with increasing pressure. Convective clinopyroxene dissolution, where the convection is driven by the density difference between the crystal and melt, is modeled using the diffusivities and interface melt saturation condition. Previous studies showed that the convective dissolution rate depends on the thermodynamics, kinetics and fluid dynamics of the system. Comparing our results for clinopyroxene dissolution to results from a previous study on convective olivine dissolution shows that the kinetic and fluid dynamic aspects of the two minerals are quite similar. However, the thermodynamics of clinopyroxene dissolution depends more strongly on the degree of superheating and composition of the host melt than that of olivine dissolution. The models for clinopyroxene and olivine dissolution are tested against literature experiments on mineral-melt interaction. They are then applied to previously proposed reactions between Hawaii basalts and mantle minerals, mid-ocean ridge basalts and mantle minerals, and xenoliths digestion in a basalt at Kuandian, Northeast China.

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.

An Adaptive Method of Lines with Error Control for Parabolic Equations of the Reaction-Diffusion Type.

DTIC Science & Technology

1984-06-01

space discretization error . 1. I 3 1. INTRODUCTION Reaction- diffusion processes occur in many branches of biology and physical chemistry. Examples...to model reaction- diffusion phenomena. The primary goal of this adaptive method is to keep a particular norm of the space discretization error less...AD-A142 253 AN ADAPTIVE MET6 OFD LNES WITH ERROR CONTROL FOR 1 INST FOR PHYSICAL SCIENCE AND TECH. I BABUSKAAAO C7 EA OH S UMR AN UNVC EEP R

Dynamical System Approach for Edge Detection Using Coupled FitzHugh-Nagumo Neurons.

PubMed

Li, Shaobai; Dasmahapatra, Srinandan; Maharatna, Koushik

2015-12-01

The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network.

Synthesis of Biofluidic Microsystems (SYNBIOSYS)

DTIC Science & Technology

2007-10-01

reaction system. 58 FIGURE 41. The micro reactor is represented by a PFR network model. The calculation of reaction and convection is conducted in...one column of PFRs and the calculation of diffusional mixing is conducted between two columns of PFRs. 59 FIGURE 42. Apply the numerical method of...lines to calculate the diffusion in the channel width direction. Here, we take 10 discretized concentration points in the channel: ci1 - ci10. Points

On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems.

DTIC Science & Technology

1982-02-01

I. Diaz. "Soluciones con soporte compacto para alguno. problemas semilineales". Collect. Math. 30 (1979), 141-179. -26- [121 J. I. Diaz. Tecnica de ...supersoluciones locales para problemas estacionarios no lineales: applicacion al estudio de flujoe subsonicos. Memory of the Real Academia de Ciencias...nonlinearity, nonlinear boundary conditions, dead core set, chemical reactions Work Unit Number I - Applied Analysis (1) Seccion de Matematicas

Post-Self-Assembly Cross-Linking to Integrate Molecular Nanofibers with Copolymers in Oscillatory Hydrogels

DTIC Science & Technology

2013-05-09

The BZ reaction provides a model system to mimic a variety of complex processes, such as biological morphogenesis, in monodisperse microemulsions .15...surfaces, ion-exchange resins, membranes, and microemulsions . For example, in addition to minimizing the hydrodynamic effects and formation of bubbles...Reaction-Diffusion Microemulsions Reveals Three-Dimensional Tu- ring Patterns. Science (Washington, DC, U.S.) 2011, 331, 1309−1312. (16) Agladze, K. I

Symmetrization of conservation laws with entropy for high-temperature hypersonic computations

NASA Technical Reports Server (NTRS)

Chalot, F.; Hughes, T. J. R.; Shakib, F.

1990-01-01

Results of Hughes, France, and Mallet are generalized to conservation law systems taking into account high-temperature effects. Symmetric forms of different equation sets are derived in terms of entropy variables. First, the case of a general divariant gas is studied; it can be specialized to the usual Navier-Stokes equations, as well as to situations where the gas is vibrationally excited, and undergoes equilibrium chemical reactions. The case of gas in thermochemical nonequilibrium is considered next. Transport phenomena, and in particular mass diffusion, are examined in the framework of symmetric advective-diffusive systems.

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.

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.

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

NASA Astrophysics Data System (ADS)

Zhang, Linghai

2017-10-01

The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 < 2 (1 + αγ) θ < αβγ; the existence and stability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and γ2 ε > 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 <γ2 ε < 1; the existence and instability of an upside down standing pulse solution if 0 < (1 + αγ) θ < αβγ < 2 (1 + αγ) θ. To establish the bifurcation for the scalar equation, we will study the existence and stability of a traveling wave front as well as the existence and instability of a standing pulse solution if 0 < 2 θ < β; the existence and stability of two standing wave fronts if 2 θ = β; the existence and stability of a traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 < θ < β < 2 θ. By the way, we will also study the existence and stability of a traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 < 2 θ < β. To achieve the main goals, we will make complete use of the special structures of the model equations and we will construct Evans functions and apply them to study the eigenvalues and eigenfunctions of several eigenvalue problems associated with several linear differential operators. It turns out that a complex number λ0 is an eigenvalue of the linear differential operator, if and only if λ0 is a zero of the Evans function. The stability, instability and bifurcations of the nonlinear waves follow from the zeros of the Evans functions. A very important motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

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.

First-principles study of transition-metal nitrides as diffusion barriers against Al

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

Mei, Zhi-Gang; Yacout, Abdellatif M.; Kim, Yeon Soo

2016-04-01

Using density-functional theory based first-principles calculations we provided a comparative study of the diffusion barrier properties of TiN, ZrN, and HfN against Al for U-Mo dispersion fuel applications. We firstly examined the thermodynamic stability of these transition-metal nitrides with Al. The calculated heats of reaction show that both TiN and ZrN are thermodynamically unstable diffusion barrier materials, which might be decomposed by Al at relatively high temperatures. As a comparison, HfN is a stable diffusion barrier material for Al. To evaluate the kinetic stability of these nitride systems against Al diffusion, we investigated the diffusion mechanisms of Al in TiN,more » ZrN and HfN using atomic scale simulations. The effect of non-stoichiometry on the defect formation and Al migration was systematically studied. (C) 2015 ELSEVIER B.V. All rights reserved« less

Diffusion kinetics of the glucose/glucose oxidase system in swift heavy ion track-based biosensors

NASA Astrophysics Data System (ADS)

Fink, Dietmar; Vacik, Jiri; Hnatowicz, V.; Muñoz Hernandez, G.; Garcia Arrelano, H.; Alfonta, Lital; Kiv, Arik

2017-05-01

For understanding of the diffusion kinetics and their optimization in swift heavy ion track-based biosensors, recently a diffusion simulation was performed. This simulation aimed at yielding the degree of enrichment of the enzymatic reaction products in the highly confined space of the etched ion tracks. A bunch of curves was obtained for the description of such sensors that depend only on the ratio of the diffusion coefficient of the products to that of the analyte within the tracks. As hitherto none of these two diffusion coefficients is accurately known, the present work was undertaken. The results of this paper allow one to quantify the previous simulation and hence yield realistic predictions of glucose-based biosensors. At this occasion, also the influence of the etched track radius on the diffusion coefficients was measured and compared with earlier prediction.

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

NASA Astrophysics Data System (ADS)

Meerson, Baruch

2015-05-01

Suppose that a point-like steady source at x = 0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with mean \\bar{N} predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N. We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N.

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.

Reactions of SO 2 on hydrated cement particle system for atmospheric pollution reduction: A DRIFTS and XANES study

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

Ramakrishnan, Girish; Wu, Qiyuan; Moon, Juhyuk

An investigation of the adsorptive property of hydrated cement particle system for sulfur dioxide (SO2) removal was conducted. In situ and ex situ experiments using Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS) and X-ray Absorption Near Edge Spectroscopy (XANES) characterization techniques were employed to identify surface species formed during the exposure to SO2. Oxidation of SO2 to sulfate and sulfite species observed during these experiments indicated dominant reaction pathways for SO2 reaction with concrete constituents, such as calcium hydroxide, which were also moderated by adsorption on porous surfaces of crushed aggregates. The impact of variable composition of concrete on itsmore » adsorption capacity and reaction mechanisms was also proposed in this work.« less

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

Notch-mediated lateral inhibition regulates proneural wave propagation when combined with EGF-mediated reaction diffusion

PubMed Central

Sato, Makoto; Yasugi, Tetsuo; Minami, Yoshiaki; Miura, Takashi; Nagayama, Masaharu

2016-01-01

Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or “proneural wave” accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation. PMID:27535937

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.

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

Riedel, Clement; Gabizon, Ronen; Wilson, Christian A. M.

Recent studies have shown that the diffusivity of enzymes increases in a substrate-dependent manner during catalysis. Although this observation has been reported and characterized for several different systems, the precise origin of this phenomenon is unknown. Calorimetric methods are often used to determine enthalpies from enzyme-catalysed reactions and can therefore provide important insight into their reaction mechanisms. The ensemble averages involved in traditional bulk calorimetry cannot probe the transient effects that the energy exchanged in a reaction may have on the catalyst. Here we obtain single-molecule fluorescence correlation spectroscopy data and analyse them within the framework of a stochastic theorymore » to demonstrate a mechanistic link between the enhanced diffusion of a single enzyme molecule and the heat released in the reaction. We propose that the heat released during catalysis generates an asymmetric pressure wave that results in a differential stress at the protein-solvent interface that transiently displaces the centre-of-mass of the enzyme (chemoacoustic effect). We find this novel perspective on how enzymes respond to the energy released during catalysis suggests a possible effect of the heat of reaction on the structural integrity and internal degrees of freedom of the enzyme.« less

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.

Ultrasound and polar homogeneous reactions.

PubMed

Tuulmets, A

1997-04-01

The effect of ultrasound on the rates of homogeneous heterolytic reactions not switched to a free radical pathway can be explained by the perturbation of the molecular organization of or the solvation in the reacting system. A quantitative analysis of the sonochemical acceleration on the basis of the microreactor concept was carried out. It was found that (1) the Diels-Alder reaction cannot be accelerated by ultrasound except when SET or free radical processes are promoted, (2) the rectified diffusion during cavitation cannot be responsible for the acceleration of reactions, and (3) the sonochemical acceleration of polar homogeneous reactions takes place in the bulk reaction medium. This implies the presence of a 'sound-field' sonochemistry besides the 'hot-spot' sonochemistry. The occurrence of a sonochemical deceleration effect can be predicted.

Modeling diffusion and reaction in soils: 9. The Buckingham-Burdine-Campbell equation for gas diffusivity in undisturbed soil

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

Moldrup, P.; Olesen, T.; Yamaguchi, T.

1999-08-01

Accurate description of gas diffusivity (ratio of gas diffusion coefficients in soil and free air, D{sub s}/D{sub 0}) in undisturbed soils is a prerequisite for predicting in situ transport and fate of volatile organic chemicals and greenhouse gases. Reference point gas diffusivities (R{sub p}) in completely dry soil were estimated for 20 undisturbed soils by assuming a power function relation between gas diffusivity and air-filled porosity ({epsilon}). Among the classical gas diffusivity models, the Buckingham (1904) expression, equal to the soil total porosity squared, best described R{sub p}. Inasmuch, as their previous works implied a soil-type dependency of D{sub s}/D{submore » 0}({epsilon}) in undisturbed soils, the Buckingham R{sub p} expression was inserted in two soil-type-dependent D{sub s}/D{sub 0}({epsilon}) models. One D{sub s}/D{sub 0}({epsilon}) model is a function of pore-size distribution (the Campbell water retention parameter used in a modified Burdine capillary tube model), and the other is a calibrated, empirical function of soil texture (silt + sand fraction). Both the Buckingham-Burdine-Campbell (BBC) and the Buckingham/soil texture-based D{sub s}/D{sub 0}({epsilon}) models described well the observed soil type effects on gas diffusivity and gave improved predictions compared with soil type independent models when tested against an independent data set for six undisturbed surface soils. This study emphasizes that simple but soil-type-dependent power function D{sub s}/D{sub 0}({epsilon}) models can adequately describe and predict gas diffusivity in undisturbed soil. The authors recommend the new BBC model as basis for modeling gas transport and reactions in undisturbed soil systems.« less

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.

Characterization of Magma-Driven Hydrothermal Systems at Oceanic Spreading Centers

NASA Astrophysics Data System (ADS)

Farough, A.; Lowell, R. P.; Corrigan, R.

2012-12-01

Fluid circulation in high-temperature hydrothermal systems involves complex water-rock chemical reactions and phase separation. Numerical modeling of reactive transport in multi-component, multiphase systems is required to obtain a full understanding of the characteristics and evolution of hydrothermal vent systems. We use a single-pass parameterized model of high-temperature hydrothermal circulation at oceanic spreading centers constrained by observational parameters such as vent temperature, heat output, and vent field area, together with surface area and depth of the sub-axial magma chamber, to deduce fundamental hydrothermal parameters such as mass flow rate, bulk permeability, conductive boundary layer thickness at the base of the system, magma replenishment rate, and residence time in the discharge zone. All of these key subsurface characteristics are known for fewer than 10 sites out of 300 known hydrothermal systems. The principal limitations of this approach stem from the uncertainty in heat output and vent field area. For systems where data are available on partitioning of heat and chemical output between focused and diffuse flow, we determined the fraction of high-temperature vent fluid incorporated into diffuse flow using a two-limb single pass model. For EPR 9°50` N and ASHES, the diffuse flow temperatures calculated assuming conservative mixing are nearly equal to the observed temperatures indicating that approximately 80%-90% of the hydrothermal heat output occurs as high-temperature flow derived from magmatic heat even though most of the heat output appears as low-temperature diffuse discharge. For the Main Endeavour Field and Lucky Strike, diffuse flow fluids show significant conductive cooling and heating respectively. Finally, we calculate the transport of various geochemical constituents in focused and diffuse flow at the vent field scale and compare the results with estimates of geochemical transports from the Rainbow hydrothermal field where diffuse flow is absent.

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.

Effect of micro-stirring on enzymatic reaction kinetics inside a biomimetic container

NASA Astrophysics Data System (ADS)

Gozen, Irep; Horowitz, Viva; Chambers, Zachary; Manoharan, Vinothan

The intracellular environment is dynamic, influenced by the motion of active machinery such as cytoskeleton filaments and molecular motors. To understand whether and how such activity affects the rates of diffusion-limited reactions, we construct a model system consisting of a phospholipid vesicle encapsulating a small number of micro- or nanoparticles, the active motion of which can be induced by chemical or magnetic cues. We aim to determine a relation between active motion of particles and rates of enzymatic reactions in the confined volume. Our findings might illuminate how active motion influences cytoplasmic reaction dynamics, or may have played a role in protocell genetics.

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.

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.

A review on symmetries for certain Aedes aegypti models

NASA Astrophysics Data System (ADS)

Freire, Igor Leite; Torrisi, Mariano

2015-04-01

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

MODELING NITROGEN-CARBON CYCLING AND OXYGEN CONSUMPTION IN BOTTOM SEDIMENTS

EPA Science Inventory

A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffus...

Kinetic limitations of the Mg(2)Si system for reversible hydrogen storage.

PubMed

Kelly, Stephen T; Van Atta, Sky L; Vajo, John J; Olson, Gregory L; Clemens, B M

2009-05-20

Despite the promising thermodynamics and storage capacities of many destabilized metal hydride hydrogen storage material systems, they are often kinetically limited from achieving practical and reversible behavior. Such is the case with the Mg2Si system. We investigated the kinetic mechanisms responsible for limiting the reversibility of the MgH2+Si system using thin films as a controlled research platform. We observed that the reaction MgH2 + 1/2Mg2Si + H2 is limited by the mass transport of Mg and Si into separate phases. Hydrogen readily diffuses through the Mg2Si material and nucleating MgH2 phase growth does not result in reaction completion. By depositing and characterizing multilayer films of Mg2Si and Mg with varying Mg2Si layer thicknesses, we conclude that the hydrogenation reaction consumes no more than 1 nm of Mg2Si, making this system impractical for reversible hydrogen storage.

Pattern Formation on Networks: from Localised Activity to Turing Patterns

PubMed Central

McCullen, Nick; Wagenknecht, Thomas

2016-01-01

Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed system-scale patterns are investigated computationally using numerical continuation methods. These techniques are also used to help reveal a much larger portion of of the full number of solutions that exist in the system at different parameter values. The importance of network structure is also highlighted, with a key role being played by nodes with a certain so-called optimal degree, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system. PMID:27273339

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

Soliton solutions, stability analysis and conservation laws for the brusselator reaction diffusion model with time- and constant-dependent coefficients

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Hashemi, M. S.

2018-05-01

This paper studies the brusselator reaction diffusion model (BRDM) with time- and constant-dependent coefficients. The soliton solutions for BRDM with time-dependent coefficients are obtained via first integral (FIM), ansatz, and sine-Gordon expansion (SGEM) methods. Moreover, it is well known that stability analysis (SA), symmetry analysis and conservation laws (CLs) give several information for modelling a system of differential equations (SDE). This is because they can be used for investigating the internal properties, existence, uniqueness and integrability of different SDE. For this reason, we investigate the SA via linear stability technique, symmetry analysis and CLs for BRDM with constant-dependent coefficients in order to extract more physics and information on the governing equation. The constraint conditions for the existence of the solutions are also examined. The new solutions obtained in this paper can be useful for describing the concentrations of diffusion problems of the BRDM. It is shown that the examined dependent coefficients are some of the factors that are affecting the diffusion rate. So, the present paper provides much motivational information in comparison to the existing results in the literature.

Diffusional falsification of kinetic constants on Lineweaver-Burk plots.

PubMed

Ghim, Y S; Chang, H N

1983-11-07

The effect of mass transfer resistances on the Lineweaver-Burk plots in immobilized enzyme systems has been investigated numerically and with analytical approximate solutions. While Hamilton, Gardner & Colton (1974) studied the effect of internal diffusion resistances in planar geometry, our study was extended to the combined effect of internal and external diffusion in cylindrical and spherical geometries as well. The variation of Lineweaver-Burk plots with respect to the geometries was minimized by modifying the Thiele modulus and the Biot number with the shape factor. Especially for a small Biot number all the three Lineweaver-Burk plots fell on a single line. As was discussed by Hamilton et al. (1974), the curvature of the line for large external diffusion resistances was small enough to be assumed linear, which was confirmed from the two approximate solutions for large and small substrate concentrations. Two methods for obtaining intrinsic kinetic constants were proposed: First, we obtained both maximum reaction rate and Michaelis constant by fitting experimental data to a straight line where external diffusion resistance was relatively large, and second, we obtained Michaelis constant from apparent Michaelis constant from the figure in case we knew maximum reaction rate a priori.

Bistable traveling waves for a competitive-cooperative system with nonlocal delays

NASA Astrophysics Data System (ADS)

Tian, Yanling; Zhao, Xiao-Qiang

2018-04-01

This paper is devoted to the study of bistable traveling waves for a competitive-cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach.

A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Radszuweit, M.; Engel, H.; Bär, M.

2010-12-01

A mechano-chemical model for the spatiotemporal dynamics of free calcium and the thickness in protoplasmic droplets of the true slime mold Physarum polycephalum is derived starting from a physiologically detailed description of intracellular calcium oscillations proposed by Smith and Saldana (Biopys. J. 61, 368 (1992)). First, we have modified the Smith-Saldana model for the temporal calcium dynamics in order to reproduce the experimentally observed phase relation between calcium and mechanical tension oscillations. Then, we formulate a model for spatiotemporal dynamics by adding spatial coupling in the form of calcium diffusion and advection due to calcium-dependent mechanical contraction. In another step, the resulting reaction-diffusion model with mechanical coupling is simplified to a reaction-diffusion model with global coupling that approximates the mechanical part. We perform a bifurcation analysis of the local dynamics and observe a Hopf bifurcation upon increase of a biochemical activity parameter. The corresponding reaction-diffusion model with global coupling shows regular and chaotic spatiotemporal behaviour for parameters with oscillatory dynamics. In addition, we show that the global coupling leads to a long-wavelength instability even for parameters where the local dynamics possesses a stable spatially homogeneous steady state. This instability causes standing waves with a wavelength of twice the system size in one dimension. Simulations of the model in two dimensions are found to exhibit defect-mediated turbulence as well as various types of spiral wave patterns in qualitative agreement with earlier experimental observation by Takagi and Ueda (Physica D, 237, 420 (2008)).

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.

Transport with Bimolecular Reactions: Applications to In-Situ Chemical Oxidation of DNAPLs by Permanganate in Fractured Rock

NASA Astrophysics Data System (ADS)

Arshadi, Masoud

Chemical oxidation of dense nonaqueous-phase liquids (DNAPLs) by permanganate has emerged as an effective remediation strategy in fractured rock. Our objectives in this research were to carry out a sequence of experimental, computational and theoretical tasks aimed at improving current understanding of permanganate oxidation in fractured rock systems, and also develop modeling tools that can be used for preliminary design of oxidation schemes at field sites. Our research focused on both free-phase entrapped DNAPL in variable-aperture fractures and dissolved DNAPL in the rock matrix. In the first section of our research, we present high-resolution experimental investigations in transparent analog variable-aperture fractures to improve understanding of chemical oxidation of residual entrapped trichloroethylene (TCE) in fractures. Four experiments were performed with different permanganate concentrations, flow rates, and initial TCE phase geometry. The initial aperture field and evolving entrapped-phase geometry were measured quantitatively. We present results on the time-evolution of fracture-scale TCE consumption and DNAPL removal rates for all the experiments. In the next part of this work, we developed theoretical understanding of the reaction front dynamics in the case of chemical oxidation of aqueous-phase DNAPL within fracture-matrix system, backed up by numerical simulations. We also consider the influence of NOD consumption and contaminant sorption to solid aquifer materials in our models. Based on the results from this task we are able to propose simple strategies for remediation design (e.g. the time needed to degrade DNAPL inside the fracture-matrix system and the permanganate injection pattern) for a given set of conditions. Our numerical simulations of diffusion with bimolecular reaction in the rock matrix demonstrated a transition in the spatially integrated reaction rate - increasing with time initially, and transitioning to a decrease with time. We developed a general non-dimensionalization of the problem and a perturbation analysis to show that there is always an early time regime where the spatially integrated reaction rate scales as √t rather than 1/√t. The duration of this early time regime (where the total reaction rate is kinetically rather than diffusion controlled) is shown to depend on the kinetic rate parameters, diffusion coefficients and initial concentrations of the two species.

Making it stick: convection, reaction and diffusion in surface-based biosensors.

PubMed

Squires, Todd M; Messinger, Robert J; Manalis, Scott R

2008-04-01

The past decade has seen researchers develop and apply novel technologies for biomolecular detection, at times approaching hard limits imposed by physics and chemistry. In nearly all sensors, the transport of target molecules to the sensor can play as critical a role as the chemical reaction itself in governing binding kinetics, and ultimately performance. Yet rarely does an analysis of the interplay between diffusion, convection and reaction motivate experimental design or interpretation. Here we develop a physically intuitive and practical understanding of analyte transport for researchers who develop and employ biosensors based on surface capture. We explore the qualitatively distinct behaviors that result, develop rules of thumb to quickly determine how a given system will behave, and derive order-of-magnitude estimates for fundamental quantities of interest, such as fluxes, collection rates and equilibration times. We pay particular attention to collection limits for micro- and nanoscale sensors, and highlight unexplained discrepancies between reported values and theoretical limits.

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

We study a simple model for metal corrosion controlled by the reaction rate of the metal with an anionic species and the diffusion of that species in the growing passive film between the solution and the metal. A crossover from the reaction-controlled to the diffusion-controlled growth regime with different roughening properties is observed. Scaling arguments provide estimates of the crossover time and film thickness as functions of the reaction and diffusion rates and the concentration of anionic species in the film-solution interface, including a nontrivial square-root dependence on that concentration. At short times, the metal-film interface exhibits Kardar-Parisi-Zhang (KPZ) scaling, which crosses over to a diffusion-limited erosion (Laplacian growth) regime at long times. The roughness of the metal-film interface at long times is obtained as a function of the rates of reaction and diffusion and of the KPZ growth exponent. The predictions have been confirmed by simulations of a lattice version of the model in two dimensions. Relations with other erosion and corrosion models and possible applications are discussed.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

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

Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

2015-12-01

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. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated atmore » 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. 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

Theorems and application of local activity of CNN with five state variables and one port.

PubMed

Xiong, Gang; Dong, Xisong; Xie, Li; Yang, Thomas

2012-01-01

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

A living mesoscopic cellular automaton made of skin scales.

PubMed

Manukyan, Liana; Montandon, Sophie A; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C

2017-04-12

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

A living mesoscopic cellular automaton made of skin scales

NASA Astrophysics Data System (ADS)

Manukyan, Liana; Montandon, Sophie A.; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C.

2017-04-01

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

Spatial model for transmission of mosquito-borne diseases

NASA Astrophysics Data System (ADS)

Kon, Cynthia Mui Lian; Labadin, Jane

2015-05-01

In this paper, a generic model which takes into account spatial heterogeneity for the dynamics of mosquito-borne diseases is proposed. The dissemination of the disease is described by a system of reaction-diffusion partial differential equations. Host human and vector mosquito populations are divided into susceptible and infectious classes. Diffusion is considered to occur in all classes of both populations. Susceptible humans are infected when bitten by infectious mosquitoes. Susceptible mosquitoes bite infectious humans and become infected. The biting rate of mosquitoes is considered to be density dependent on the total human population in different locations. The system is solved numerically and results are shown.

Electrochemical force microscopy

DOEpatents

Kalinin, Sergei V.; Jesse, Stephen; Collins, Liam F.; Rodriguez, Brian J.

2017-01-10

A system and method for electrochemical force microscopy are provided. The system and method are based on a multidimensional detection scheme that is sensitive to forces experienced by a biased electrode in a solution. The multidimensional approach allows separation of fast processes, such as double layer charging, and charge relaxation, and slow processes, such as diffusion and faradaic reactions, as well as capturing the bias dependence of the response. The time-resolved and bias measurements can also allow probing both linear (small bias range) and non-linear (large bias range) electrochemical regimes and potentially the de-convolution of charge dynamics and diffusion processes from steric effects and electrochemical reactivity.

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.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

NASA Astrophysics Data System (ADS)

Shiraiwa, Manabu; Pfrang, Christian; Pöschl, Ulrich

2010-05-01

Aerosols are ubiquitous in the atmosphere and have strong effects on climate and public health. Gas-particle interactions can significantly change the physical and chemical properties of aerosols such as toxicity, reactivity, hygroscopicity and radiative properties. Chemical reactions and mass transport lead to continuous transformation and changes in the composition of atmospheric aerosols ("chemical aging"). Resistor model formulations are widely used to describe and investigate heterogeneous reactions and multiphase processes in laboratory, field and model studies of atmospheric chemistry. The traditional resistor models, however, are usually based on simplifying assumptions such as steady state conditions, homogeneous mixing, and limited numbers of non-interacting species and processes. In order to overcome these limitations, Pöschl, Rudich and Ammann have developed a kinetic model framework (PRA framework) with a double-layer surface concept and universally applicable rate equations and parameters for mass transport and chemical reactions at the gas-particle interface of aerosols and clouds [1]. Based on the PRA framework, we present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB) [2]. The model includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory studies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial transport and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (C=C double bonds) can reach chemical life-times of multiple hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (~10-10 cm2 s-1). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models. References [1] Pöschl et al., Atmos. Chem. and Phys., 7, 5989-6023 (2007). [2] Shiraiwa et al., Atmos. Chem. Phys. Discuss., 10, 281-326 (2010).

Positive feedback can lead to dynamic nanometer-scale clustering on cell membranes

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

Wehrens, Martijn; Rein ten Wolde, Pieter; Mugler, Andrew, E-mail: amugler@purdue.edu

2014-11-28

Clustering of molecules on biological membranes is a widely observed phenomenon. A key example is the clustering of the oncoprotein Ras, which is known to be important for signal transduction in mammalian cells. Yet, the mechanism by which Ras clusters form and are maintained remains unclear. Recently, it has been discovered that activated Ras promotes further Ras activation. Here we show using particle-based simulation that this positive feedback is sufficient to produce persistent clusters of active Ras molecules at the nanometer scale via a dynamic nucleation mechanism. Furthermore, we find that our cluster statistics are consistent with experimental observations ofmore » the Ras system. Interestingly, we show that our model does not support a Turing regime of macroscopic reaction-diffusion patterning, and therefore that the clustering we observe is a purely stochastic effect, arising from the coupling of positive feedback with the discrete nature of individual molecules. These results underscore the importance of stochastic and dynamic properties of reaction diffusion systems for biological behavior.« less

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.

A Model for Selection of Eyespots on Butterfly Wings.

PubMed

Sekimura, Toshio; Venkataraman, Chandrasekhar; Madzvamuse, Anotida

2015-01-01

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

Using supercritical fluids to refine hydrocarbons

DOEpatents

Yarbro, Stephen Lee

2015-06-09

A system and method for reactively refining hydrocarbons, such as heavy oils with API gravities of less than 20 degrees and bitumen-like hydrocarbons with viscosities greater than 1000 cp at standard temperature and pressure, using a selected fluid at supercritical conditions. A reaction portion of the system and method delivers lightweight, volatile hydrocarbons to an associated contacting unit which operates in mixed subcritical/supercritical or supercritical modes. Using thermal diffusion, multiphase contact, or a momentum generating pressure gradient, the contacting unit separates the reaction products into portions that are viable for use or sale without further conventional refining and hydro-processing techniques.

International Conference on Chemical Kinetics: Program and Abstracts Held in Gaithersburg, Maryland on 17-19 June 1985.

DTIC Science & Technology

1985-06-01

relative to reactant and with the free energy of reaction. The correlation equations were derived from hyperbolic paraboloid models of the energy...obtained the differen- tial equations which define the best dividing surfaces of this type for both microcanonical and canonical cases. We have...is now generalized to non-uniform reaction systems. For kinetics-diffusion problems the equations of the generalized PAM were (similar in form to

Numerical quantification of habitability in serpentinizing systems

NASA Astrophysics Data System (ADS)

Som, S.; Alperin, M. J.; Hoehler, T. M.

2012-12-01

The likely presence of liquid water in contact with olivine-bearing rocks on Mars, the detection of serpentine minerals and of methane emissions possibly consistent with serpentinization, and the observation of serpentine-associated methane-cycling communities on Earth have all led to excitement over the potential of such systems to host life on Mars, even into the present day. However, the habitability of subsurface serpentinizing systems on Mars does not necessarily follow from these qualitative observations. In particular, while the production of H2 during serpentinization could provide methanogens with a needed substrate, the alkaline conditions and corresponding potential for carbon limitation that arise in concert are negatives against which H2 supply must be balanced. We considered this balance via a coupled geochemical-bioenergetic model that weighs the outputs of serpentinization against the metabolic requirements of methanogenesis, in an energetic frame of reference. Serpentinization is modeled using the "Geochemist's Workbench" (GWB) whereby ultramafic harzburgite rocks are reacted with oxygen and sulfate depleted seawater. Reaction kinetics are not explicitly considered, but comparable effects of partial reaction are approximated by assuming post-reaction dilution of equilibrated fluids. The output of GWB serves as the input to the bioenergetic model, which calculates methanogenic energy yields based on spherically-symmetrical diffusion of substrates to a cell followed by reaction at the diffusion-limited rate. Membrane selectivity for substrate transport is explicitly considered. Results will be report updates for two scenarios: (i) High temperature serpentinization followed by cooling and transport of equilibrated fluid to a lower temperature regime accessible to biology; (ii) Serpentinization within the biologically-tolerated range of temperatures. Such coupled models demonstrate that environmental variability with respect to both water-rock reaction, temperature, and biologically-mediated methanogenesis drive orders of magnitude variability in the energy available in methanogenic metabolism.

Modeling the rate-controlled sorption of hexavalent chromium

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1985-01-01

Sorption of chromium VI on the iron-oxide- and hydroxide-coated surface of alluvial material was numerically simulated with rate-controlled reactions. Reaction kinetics and diffusional processes, in the form of film, pore, and particle diffusion, were simulated and compared with experimental results. The use of empirically calculated rate coefficients for diffusion through the reacting surface was found to simulate experimental data; pore or particle diffusion is believed to be a possible rate-controlling mechanism. The use of rate equations to predict conservative transport and rate- and local-equilibrium-controlled reactions was shown to be feasible.

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

The mechanistic basis of internal conductance: a theoretical analysis of mesophyll cell photosynthesis and CO2 diffusion.

PubMed

Tholen, Danny; Zhu, Xin-Guang

2011-05-01

Photosynthesis is limited by the conductance of carbon dioxide (CO(2)) from intercellular spaces to the sites of carboxylation. Although the concept of internal conductance (g(i)) has been known for over 50 years, shortcomings in the theoretical description of this process may have resulted in a limited understanding of the underlying mechanisms. To tackle this issue, we developed a three-dimensional reaction-diffusion model of photosynthesis in a typical C(3) mesophyll cell that includes all major components of the CO(2) diffusion pathway and associated reactions. Using this novel systems model, we systematically and quantitatively examined the mechanisms underlying g(i). Our results identify the resistances of the cell wall and chloroplast envelope as the most significant limitations to photosynthesis. In addition, the concentration of carbonic anhydrase in the stroma may also be limiting for the photosynthetic rate. Our analysis demonstrated that higher levels of photorespiration increase the apparent resistance to CO(2) diffusion, an effect that has thus far been ignored when determining g(i). Finally, we show that outward bicarbonate leakage through the chloroplast envelope could contribute to the observed decrease in g(i) under elevated CO(2). Our analysis suggests that physiological and anatomical features associated with g(i) have been evolutionarily fine-tuned to benefit CO(2) diffusion and photosynthesis. The model presented here provides a novel theoretical framework to further analyze the mechanisms underlying diffusion processes in the mesophyll.

The Mechanistic Basis of Internal Conductance: A Theoretical Analysis of Mesophyll Cell Photosynthesis and CO2 Diffusion1[W][OA

PubMed Central

Tholen, Danny; Zhu, Xin-Guang

2011-01-01

Photosynthesis is limited by the conductance of carbon dioxide (CO2) from intercellular spaces to the sites of carboxylation. Although the concept of internal conductance (gi) has been known for over 50 years, shortcomings in the theoretical description of this process may have resulted in a limited understanding of the underlying mechanisms. To tackle this issue, we developed a three-dimensional reaction-diffusion model of photosynthesis in a typical C3 mesophyll cell that includes all major components of the CO2 diffusion pathway and associated reactions. Using this novel systems model, we systematically and quantitatively examined the mechanisms underlying gi. Our results identify the resistances of the cell wall and chloroplast envelope as the most significant limitations to photosynthesis. In addition, the concentration of carbonic anhydrase in the stroma may also be limiting for the photosynthetic rate. Our analysis demonstrated that higher levels of photorespiration increase the apparent resistance to CO2 diffusion, an effect that has thus far been ignored when determining gi. Finally, we show that outward bicarbonate leakage through the chloroplast envelope could contribute to the observed decrease in gi under elevated CO2. Our analysis suggests that physiological and anatomical features associated with gi have been evolutionarily fine-tuned to benefit CO2 diffusion and photosynthesis. The model presented here provides a novel theoretical framework to further analyze the mechanisms underlying diffusion processes in the mesophyll. PMID:21441385

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.

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

DOE PAGES

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; ...

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. Here in this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion inmore » microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

PubMed Central

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-01-01

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer. PMID:26419420

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity.

PubMed

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Goryunov, V. E.; Kolesov, A. Yu

2018-01-01

We consider the problem of mathematical modeling of oxidation-reduction oscillatory chemical reactions based on the mechanism of Belousov reaction. The process of the main components interaction in such reaction can be interpreted by a phenomenologically similar to it “predator-prey” model. Thereby, we consider a parabolic boundary value problem consisting of three Volterra-type equations, which is a mathematical model of this reaction. We carry out a local study of the neighborhood of the system’s non-trivial equilibrium state and construct the normal form of the considering system. Finally, we do a numerical analysis of the coexisting chaotic oscillatory modes of the boundary value problem in a flat area, which have different nature and occur as the diffusion coefficient decreases.

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.

Diffusion Bonding of Silicon Carbide for MEMS-LDI Applications

NASA Technical Reports Server (NTRS)

Halbig, Michael C.; Singh, Mrityunjay; Shpargel, Tarah P.; Kiser, J. Douglas

2007-01-01

A robust joining approach is critically needed for a Micro-Electro-Mechanical Systems-Lean Direct Injector (MEMS-LDI) application which requires leak free joints with high temperature mechanical capability. Diffusion bonding is well suited for the MEMS-LDI application. Diffusion bonds were fabricated using titanium interlayers between silicon carbide substrates during hot pressing. The interlayers consisted of either alloyed titanium foil or physically vapor deposited (PVD) titanium coatings. Microscopy shows that well adhered, crack free diffusion bonds are formed under optimal conditions. Under less than optimal conditions, microcracks are present in the bond layer due to the formation of intermetallic phases. Electron microprobe analysis was used to identify the reaction formed phases in the diffusion bond. Various compatibility issues among the phases in the interlayer and substrate are discussed. Also, the effects of temperature, pressure, time, silicon carbide substrate type, and type of titanium interlayer and thickness on the microstructure and composition of joints are discussed.

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.

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.

Terrestrial Fe-oxide Concretions and Mars Blueberries: Comparisons of Similar Advective and Diffusive Chemical Infiltration Reaction Mechanisms

NASA Astrophysics Data System (ADS)

Park, A. J.; Chan, M. A.

2006-12-01

Abundant iron oxide concretions occurring in Navajo Sandstone of southern Utah and those discovered at Meridiani Planum, Mars share many common observable physical traits such as their spheriodal shapes, occurrence, and distribution patterns in sediments. Terrestrial concretions are products of interaction between oxygen-rich aquifer water and basin-derived reducing (iron-rich) water. Water-rock interaction simulations show that diffusion of oxygen and iron supplied by slow-moving water is a reasonable mechanism for producing observed concretion patterns. In short, southern Utah iron oxide concretions are results of Liesegang-type diffusive infiltration reactions in sediments. We propose that the formation of blueberry hematite concretions in Mars sediments followed a similar diagenetic mechanism where iron was derived from the alteration of volcanic substrate and oxygen was provided by the early Martian atmosphere. Although the terrestrial analog differs in the original host rock composition, both the terrestrial and Mars iron-oxide precipitation mechanisms utilize iron and oxygen interactions in sedimentary host rock with diffusive infiltration of solutes from two opposite sources. For the terrestrial model, slow advection of iron-rich water is an important factor that allowed pervasive and in places massive precipitation of iron-oxide concretions. In Mars, evaporative flux of water at the top of the sediment column may have produced a slow advective mass-transfer mechanism that provided a steady source and the right quantity of iron. The similarities of the terrestrial and Martian systems are demonstrated using a water-rock interaction simulator Sym.8, initially in one-dimensional systems. Boundary conditions such as oxygen content of water, partial pressure of oxygen, and supply rate of iron were varied. The results demonstrate the importance of slow advection of water and diffusive processes for producing diagenetic iron oxide concretions.

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.

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

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

Analysis on a diffusive SIS epidemic model with logistic source

NASA Astrophysics Data System (ADS)

Li, Bo; Li, Huicong; Tong, Yachun

2017-08-01

In this paper, we are concerned with an SIS epidemic reaction-diffusion model with logistic source in spatially heterogeneous environment. We first discuss some basic properties of the parabolic system, including the uniform upper bound of solutions and global stability of the endemic equilibrium when spatial environment is homogeneous. Our primary focus is to determine the asymptotic profile of endemic equilibria (when exist) if the diffusion (migration) rate of the susceptible or infected population is small or large. Combined with the results of Li et al. (J Differ Equ 262:885-913, 2017) where the case of linear source is studied, our analysis suggests that varying total population enhances persistence of infectious disease.

Transition of spiral calcium waves between multiple stable patterns can be triggered by a single calcium spark in a fire-diffuse-fire model

PubMed Central

Tang, Ai-Hui; Wang, Shi-Qiang

2009-01-01

Spiral patterns have been found in various nonequilibrium systems. The Ca2+-induced Ca2+ release system in single cardiac cells is unique for highly discrete reaction elements, each giving rise to a Ca2+ spark upon excitation. We imaged the spiral Ca2+ waves in isolated cardiac cells and numerically studied the effect of system excitability on spiral patterns using a two-dimensional fire-diffuse-fire model. We found that under certain conditions, the system was able to display multiple stable patterns of spiral waves, each exhibiting different periods and distinct routines of spiral tips. Transition between these different patterns could be triggered by an internal fluctuation in the form of a single Ca2+ spark. PMID:19792039

Transition of spiral calcium waves between multiple stable patterns can be triggered by a single calcium spark in a fire-diffuse-fire model.

PubMed

Tang, Ai-Hui; Wang, Shi-Qiang

2009-09-01

Spiral patterns have been found in various nonequilibrium systems. The Ca(2+)-induced Ca(2+) release system in single cardiac cells is unique for highly discrete reaction elements, each giving rise to a Ca(2+) spark upon excitation. We imaged the spiral Ca(2+) waves in isolated cardiac cells and numerically studied the effect of system excitability on spiral patterns using a two-dimensional fire-diffuse-fire model. We found that under certain conditions, the system was able to display multiple stable patterns of spiral waves, each exhibiting different periods and distinct routines of spiral tips. Transition between these different patterns could be triggered by an internal fluctuation in the form of a single Ca(2+) spark.

Coexistence of wave propagation and oscillation in the photosensitive Belousov-Zhabotinsky reaction on a circular route.

PubMed

Nakata, Satoshi; Morishima, Sayaka; Ichino, Takatoshi; Kitahata, Hiroyuki

2006-12-21

The photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated on a circular ring, which was drawn using computer software and then projected on a film soaked with BZ solution using a liquid-crystal projector. Under the initial conditions, a chemical wave propagated with a constant velocity on the black ring under a bright background. When the background was rapidly changed to dark, coexistence of the oscillation on part of the ring and propagation of the chemical wave on the other part was observed. These experimental results are discussed in relation to the nature of the photosensitive BZ reaction and theoretically reproduced based on a reaction-diffusion system using the modified Oregonator model.

Ultrafast lithium diffusion in bilayer graphene

NASA Astrophysics Data System (ADS)

Kühne, Matthias; Paolucci, Federico; Popovic, Jelena; Ostrovsky, Pavel M.; Maier, Joachim; Smet, Jurgen H.

2017-09-01

Solids that simultaneously conduct electrons and ions are key elements for the mass transfer and storage required in battery electrodes. Single-phase materials with a high electronic and high ionic conductivity at room temperature are hard to come by, and therefore multiphase systems with separate ion and electron channels have been put forward instead. Here we report on bilayer graphene as a single-phase mixed conductor that demonstrates Li diffusion faster than in graphite and even surpassing the diffusion of sodium chloride in liquid water. To measure Li diffusion, we have developed an on-chip electrochemical cell architecture in which the redox reaction that forces Li intercalation is localized only at a protrusion of the device so that the graphene bilayer remains unperturbed from the electrolyte during operation. We performed time-dependent Hall measurements across spatially displaced Hall probes to monitor the in-plane Li diffusion kinetics within the graphene bilayer and measured a diffusion coefficient as high as 7 × 10-5 cm2 s-1.

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

Optimizing laboratory-based radon flux measurements for sediments.

PubMed

Chanyotha, Supitcha; Kranrod, Chutima; Kritsananuwat, Rawiwan; Lane-Smith, Derek; Burnett, William C

2016-07-01

Radon flux via diffusion from sediments and other materials may be determined in the laboratory by circulating air through the sample and a radon detector in a closed loop. However, this approach is complicated by the necessity of having to determine the total air volume in the system and accounting for any small air leaks that can arise if using extended measurement periods. We designed a simple open-loop configuration that includes a measured mass of wet sediment and water inside a gas-tight reaction flask connected to a drying system and a radon-in-air analyzer. Ambient air flows through two charcoal columns before entering the reaction vessel to eliminate incoming radon. After traveling through the reaction flask, the air passes the drier and the radon analyzer and is then vented. After some time, the radon activity will reach a steady state depending upon the airflow rate. With this approach, the radon flux via diffusion is simply the product of the steady-state radon activity (Bq/m(3)) multiplied by the airflow rate (mL/min). We demonstrated that this setup could produce good results for materials that produce relatively high radon fluxes. We also show that a modified closed system approach, including radon removal of the incoming air by charcoal filtration in a bypass, can produce very good results including samples with very low emission rates. Copyright © 2016 Elsevier Ltd. All rights reserved.

Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system

NASA Astrophysics Data System (ADS)

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

2018-01-01

In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (sub T mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of sub T -mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Irradiation resistance of silicon carbide joint at light water reactor–relevant temperature

DOE PAGES

Koyanagi, T.; Katoh, Y.; Kiggans, J. O.; ...

2017-03-10

We fabricated and irradiated monolithic silicon carbide (SiC) to SiC plate joints with neutrons at 270–310 °C to 8.7 dpa for SiC. The joining methods included solid state diffusion bonding using titanium and molybdenum interlayers, SiC nanopowder sintering, reaction sintering with a Ti-Si-C system, and hybrid processing of polymer pyrolysis and chemical vapor infiltration (CVI). All the irradiated joints exhibited apparent shear strength of more than 84 MPa on average. Significant irradiation-induced cracking was found in the bonding layers of the Ti and Mo diffusion bonds and Ti-Si-C reaction sintered bond. Furthermore, the SiC-based bonding layers of the SiC nanopowdermore » sintered and hybrid polymer pyrolysis and CVI joints all showed stable microstructure following the irradiation.« less

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.

Real-time dielectric studies of polymerizing systems

NASA Astrophysics Data System (ADS)

Williams, G.; Smith, I. K.; Holmes, P. A.; Varma, S.

1999-03-01

The use of real-time dielectric relaxation spectroscopy (DRS) for monitoring changes in molecular mobility during reaction for thermosetting systems is described together with phenomenological and molecular theories of the time-dependent relaxation functions that are involved. Reduced molecular mobility normally leads to the diffusion control of a reaction and ultimately to glass formation at the polymerization temperature 0953-8984/11/10A/004/img7. We present new DRS results for a boroxine/epoxide system that show glass formation below a `floor temperature' 0953-8984/11/10A/004/img8 and very different behaviour above 0953-8984/11/10A/004/img8, when the dielectric properties become independent of time and an elastomer is formed.

Cyanide does more to inhibit heme enzymes, than merely serving as an active-site ligand.

PubMed

Parashar, Abhinav; Venkatachalam, Avanthika; Gideon, Daniel Andrew; Manoj, Kelath Murali

2014-12-12

The toxicity of cyanide is hitherto attributed to its ability to bind to heme proteins' active site and thereby inhibit their activity. It is shown herein that the long-held interpretation is inadequate to explain several observations in heme-enzyme reaction systems. Generation of cyanide-based diffusible radicals in heme-enzyme reaction milieu could shunt electron transfers (by non-active site processes), and thus be detrimental to the efficiency of oxidative outcomes. Copyright © 2014 Elsevier Inc. All rights reserved.

Time-delayed reaction-diffusion fronts

NASA Astrophysics Data System (ADS)

Isern, Neus; Fort, Joaquim

2009-11-01

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one.

Highly effective synthesis of a cobalt(ii) metal-organic coordination polymer by using continuous flow chemistry.

PubMed

Gong, Chunhua; Zhang, Junyong; Zeng, Xianghua; Xie, Jingli

2016-12-20

The coordination polymer [Co 2 L 4 (H 2 O) 2 ]·CH 3 CN·H 2 O (HL = (E)-2-[2-(4-chlorophenyl)vinyl]-8-hydroxyquinoline) has been achieved with 95% yield by using an Asia flow synthesis system (chip reactor). Compared with the conventional batch-type methods such as diffusion, reflux and solvothermal reactions, higher yielding reactions carried out in a flow reactor have demonstrated that this technique is a powerful strategy to obtain coordination compounds.

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.

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

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Byproduct-free mass production of compound semiconductor nanowires: zinc phosphide

NASA Astrophysics Data System (ADS)

Chen, Yixi; Polinnaya, Rakesh; Vaddiraju, Sreeram

2018-05-01

A method for the mass production of compound semiconductor nanowires that involves the direct reaction of component elements in a chemical vapor deposition chamber (CVD) is presented. This method results in nanowires, without the associated production of any other byproducts such as nanoparticles or three-dimensional (3D) bulk crystals. Furthermore, no unreacted reactants remain mixed with the nanowire product in this method. This byproduct-free nanowire production thus circumvents the need to tediously purify and collect nanowires from a mixture of products/reactants after their synthesis. Demonstration made using zinc phosphide (Zn3P2) material system as an example indicated that the direct reaction of zinc microparticles with phosphorus supplied via the vapor phase results in the production of gram quantities of nanowires. To enhance thermal transport and achieve the complete reaction of zinc microparticles, while simultaneously ensuring that the microparticles do not agglomerate into macroscale zinc particles and partly remain unreacted (owing to diffusion limitations), pellets composed of mixtures of zinc and a sacrificial salt, NH4Cl, were employed as the starting material. The sublimation by decomposition of NH4Cl in the early stages of the reaction leaves a highly porous pellet of zinc composed of only zinc microparticles, which allows for inward diffusion of phosphorus/outward diffusion of zinc and the complete conversion of zinc into Zn3P2 nanowires. NH4Cl also aids in removal of any native oxide layer present on the zinc microparticles that may prevent their reaction with phosphorus. This method may be used to mass produce many other nanowires in a byproduct-free manner, besides Zn3P2.

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.

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.

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

National treatment systems in global perspective.

PubMed

Klingemann, H

1999-09-01

Drug policy development is mostly viewed as emerging within the nation state. Processes of diffusion of innovative policies have been neglected to a large extent. The comparative study of public policy has demonstrated, however, that diffusion is an important predictor of early policy adaptation. Thus, the analysis asks the general question of the relative importance of endogenous and exogenous effects on the development of drug policies in various countries. Specifically it describes the Swiss debate leading to the popular initiative on 'Youth Without Drugs' as well as the international reactions regarding its liberal outcome. Results of an expert survey show two broad types of reactions. There is one set of countries where chances for the introduction of limited heroin-prescription trials during the next 5 years are considered probable and a second set of countries which seems to be strictly status quo oriented. In the concluding section a model is suggested which systematically considers endogenous as well as exogenous predictors of 'soft' or 'hard' drug policy adoption. Results of a first tentative test of the model are encouraging for future empirical research on diffusion processes of drug policies.

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

Development of morphogen gradient: The role of dimension and discreteness

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

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuummore » descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.« 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

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

Biomimicry Promotes the Efficiency of a 10-Step Sequential Enzymatic Reaction on Nanoparticles, Converting Glucose to Lactate.

PubMed

Mukai, Chinatsu; Gao, Lizeng; Nelson, Jacquelyn L; Lata, James P; Cohen, Roy; Wu, Lauren; Hinchman, Meleana M; Bergkvist, Magnus; Sherwood, Robert W; Zhang, Sheng; Travis, Alexander J

2017-01-02

For nanobiotechnology to achieve its potential, complex organic-inorganic systems must grow to utilize the sequential functions of multiple biological components. Critical challenges exist: immobilizing enzymes can block substrate-binding sites or prohibit conformational changes, substrate composition can interfere with activity, and multistep reactions risk diffusion of intermediates. As a result, the most complex tethered reaction reported involves only 3 enzymes. Inspired by the oriented immobilization of glycolytic enzymes on the fibrous sheath of mammalian sperm, here we show a complex reaction of 10 enzymes tethered to nanoparticles. Although individual enzyme efficiency was higher in solution, the efficacy of the 10-step pathway measured by conversion of glucose to lactate was significantly higher when tethered. To our knowledge, this is the most complex organic-inorganic system described, and it shows that tethered, multi-step biological pathways can be reconstituted in hybrid systems to carry out functions such as energy production or delivery of molecular cargo. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Biomimicry promotes the efficiency of a 10-step sequential enzymatic reaction on nanoparticles, converting glucose to lactate

PubMed Central

Mukai, Chinatsu; Gao, Lizeng; Nelson, Jacquelyn L.; Lata, James P.; Cohen, Roy; Wu, Lauren; Hinchman, Meleana M.; Bergkvist, Magnus; Sherwood, Robert W.; Zhang, Sheng; Travis, Alexander J.

2016-01-01

For nanobiotechnology to achieve its potential, complex organic-inorganic systems must grow to utilize the sequential functions of multiple biological components. Critical challenges exist: immobilizing enzymes can block substrate-binding sites or prohibit conformational changes, substrate composition can interfere with activity, and multistep reactions risk diffusion of intermediates. As a result, the most complex tethered reaction reported involves only 3 enzymes. Inspired by the oriented immobilization of glycolytic enzymes on the fibrous sheath of mammalian sperm, here we show a complex reaction of 10 enzymes tethered to nanoparticles. Although individual enzyme efficiency was higher in solution, the efficacy of the 10-step pathway measured by conversion of glucose to lactate was significantly higher when tethered. To our knowledge, this is the most complex organic-inorganic system described, and it shows that tethered, multi-step biological pathways can be reconstituted in hybrid systems to carry out functions such as energy production or delivery of molecular cargo. PMID:27901298

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.

Population dynamics, information transfer, and spatial organization in a chemical reaction network under spatial confinement and crowding conditions

NASA Astrophysics Data System (ADS)

Bellesia, Giovanni; Bales, Benjamin B.

2016-10-01

We investigate, via Brownian dynamics simulations, the reaction dynamics of a generic, nonlinear chemical network under spatial confinement and crowding conditions. In detail, the Willamowski-Rossler chemical reaction system has been "extended" and considered as a prototype reaction-diffusion system. Our results are potentially relevant to a number of open problems in biophysics and biochemistry, such as the synthesis of primitive cellular units (protocells) and the definition of their role in the chemical origin of life and the characterization of vesicle-mediated drug delivery processes. More generally, the computational approach presented in this work makes the case for the use of spatial stochastic simulation methods for the study of biochemical networks in vivo where the "well-mixed" approximation is invalid and both thermal and intrinsic fluctuations linked to the possible presence of molecular species in low number copies cannot be averaged out.

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.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-Reaction Rates

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582

Reaction diffusion in the NiCrAl and CoCrAl systems

NASA Technical Reports Server (NTRS)

Levine, S. R.

1978-01-01

The paper assesses the effect of overlay coating and substrate composition on the kinetics of coating depletion by interdiffusion. This is accomplished by examining the constitution, kinetics and activation energies for a series of diffusion couples primarily of the NiCrAl/Ni-10Cr or CoCrAl/Ni-10Cr type annealed at temperatures in the range 1000-1205 C for times up to 500 hr. A general procedure is developed for analyzing diffusion in multicomponent multiphase systems. It is shown that by introducing the concept of beta-source strength, which can be determined from appropriate phase diagrams, the Wagner solution for consumption of a second phase in a semiinfinite couple is successfully applied to the analysis of MCrAl couples. Thus, correlation of beta-recession rate constants with couple composition, total and diffusional activation energies, and interdiffusion coefficients are determined.

Physiological Environment Induces Quick Response – Slow Exhaustion Reactions

PubMed Central

Hiroi, Noriko; Lu, James; Iba, Keisuke; Tabira, Akito; Yamashita, Shuji; Okada, Yasunori; Flamm, Christoph; Oka, Kotaro; Köhler, Gottfried; Funahashi, Akira

2011-01-01

In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (ds), which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from fluorescence correlation spectroscopy (FCS) data with fractal dimensions derived from transmission electron microscopy (TEM) image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. Subsequent TEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension ds to be 1.39 ± 0.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated using TEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems. PMID:21960972

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D (0) = 0) and advection-degenerate (at h '(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h ( u ): (1)   h '( u ) is constant k , (2)   h '( u ) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.

Ligand diffusion in proteins via enhanced sampling in molecular dynamics.

PubMed

Rydzewski, J; Nowak, W

2017-12-01

Computational simulations in biophysics describe the dynamics and functions of biological macromolecules at the atomic level. Among motions particularly important for life are the transport processes in heterogeneous media. The process of ligand diffusion inside proteins is an example of a complex rare event that can be modeled using molecular dynamics simulations. The study of physical interactions between a ligand and its biological target is of paramount importance for the design of novel drugs and enzymes. Unfortunately, the process of ligand diffusion is difficult to study experimentally. The need for identifying the ligand egress pathways and understanding how ligands migrate through protein tunnels has spurred the development of several methodological approaches to this problem. The complex topology of protein channels and the transient nature of the ligand passage pose difficulties in the modeling of the ligand entry/escape pathways by canonical molecular dynamics simulations. In this review, we report a methodology involving a reconstruction of the ligand diffusion reaction coordinates and the free-energy profiles along these reaction coordinates using enhanced sampling of conformational space. We illustrate the above methods on several ligand-protein systems, including cytochromes and G-protein-coupled receptors. The methods are general and may be adopted to other transport processes in living matter. Copyright © 2017 Elsevier B.V. All rights reserved.

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h′(u) is constant k, (2)  h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems.

PubMed

Woolley, Thomas E; Baker, Ruth E; Gaffney, Eamonn A; Maini, Philip K; Seirin-Lee, Sungrim

2012-05-01

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases.

Bursting Regimes in a Reaction-Diffusion System with Action Potential-Dependent Equilibrium

PubMed Central

Meier, Stephen R.; Lancaster, Jarrett L.; Starobin, Joseph M.

2015-01-01

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed. PMID:25823018

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

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.

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.

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.

Time of Flight Electrochemistry: Diffusion Coefficient Measurements Using Interdigitated Array (IDA) Electrodes

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

Liu, Fei; Kolesov, Grigory; Parkinson, Bruce A.

2014-09-26

A simple and straightforward method for measuring diffusion coefficients using interdigitated array (IDA) electrodes is reported. The method does not require that the exact electrode area be known but depends only the size of the gap between the IDA electrode pairs. Electroactive molecules produced at the generator electrode of the IDA by a voltage step or scan can diffuse to the collector electrode and the time delay before the current for the reverse electrochemical reaction is detected at the collector is used to calculate the diffusion coefficient. The measurement of the diffusion rate of Ru(NH3)6+2 in aqueous solution has beenmore » used as an example measuring diffusion coefficients using this method. Additionally, a digital simulation of the electrochemical response of the IDA electrodes was used to simulate the entire current/voltage/time behavior of the system and verify the experimentally measured diffusion coefficients. This work was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the Department of Energy, Office of Science, Office of Basic Energy Sciences.« less

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.

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.

Estimation of the activation energy in the Belousov-Zhabotinsky reaction by temperature effect on excitable waves.

PubMed

Zhang, Jinzhong; Zhou, Luqun; Ouyang, Qi

2007-02-15

We report the temperature effect on the propagation of excitable traveling waves in a quasi-two-dimensional Belousov-Zhabotinsky reaction-diffusion system. The onset of excitable waves as a function of the sulfuric acid concentration and temperature is identified, on which the sulfuric acid concentration exhibits an Arrhenius dependence on temperature. On the basis of this experimental data, the activation energy of the self-catalyzed reaction in the Oregonator model is estimated to be 83-113 kJ/mol, which is further supported by our numerical simulations. The estimation proceeds without analyzing detailed reaction steps but rather through observing the global dynamic behaviors in the BZ reaction. For a supplement, the wave propagation velocities are calculated based on our results and compared with the experimental observations.

Implementation of glider guns in the light-sensitive Belousov-Zhabotinsky medium.

PubMed

de Lacy Costello, Ben; Toth, Rita; Stone, Christopher; Adamatzky, Andrew; Bull, Larry

2009-02-01

In cellular automata models a glider gun is an oscillating pattern of nonquiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical gates and thus realize universal computation. The glider gun is the only means of ensuring the negation operation without additional external input and therefore is an essential component of a collision-based computing circuit. We demonstrate the existence of glider-gun-like structures in both experimental and numerical studies of an excitable chemical system-the light-sensitive Belousov-Zhabotinsky reaction. These discoveries could provide the basis for future designs of collision-based reaction-diffusion computers.

Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).

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

Reaction front barriers in time aperiodic fluid flows

NASA Astrophysics Data System (ADS)

Locke, Rory; Mitchell, Kevin

2016-11-01

Many chemical and biological systems can be characterized by the propagation of a front that separates different phases or species. One approach to formalizing a general theory is to apply frameworks developed in nonlinear dynamics. It has been shown that invariant manifolds form barriers to passive transport in time-dependent or time-periodic fluid flows. More recently, analogous manifolds termed burning- invariant-manifolds (BIMs), have been shown to form one-sided barriers to reaction fronts in advection-reaction-diffusion (ARD) systems. To model more realistic time-aperiodic systems, recent theoretical work has suggested that similar one-sided barriers, termed burning Lagrangian coherent structures (bLCSs), exist for fluid velocity data prescribed over a finite time interval. In this presentation, we use a stochastic "wind" to generate time dependence in a double-vortex channel flow and demonstrate the (locally) most attracting or repelling curves are the bLCSs.

Finite-time barriers to reaction front propagation

NASA Astrophysics Data System (ADS)

Locke, Rory; Mahoney, John; Mitchell, Kevin

2015-11-01

Front propagation in advection-reaction-diffusion systems gives rise to rich geometric patterns. It has been shown for time-independent and time-periodic fluid flows that invariant manifolds, termed burning invariant manifolds (BIMs), serve as one-sided dynamical barriers to the propagation of reaction front. More recently, theoretical work has suggested that one-sided barriers, termed burning Lagrangian Coherent structures (bLCSs), exist for fluid velocity data prescribed over a finite time interval, with no assumption on the time-dependence of the flow. In this presentation, we use a time-varying fluid ``wind'' in a double-vortex channel flow to demonstrate that bLCSs form the (locally) most attracting or repelling fronts.

The nature and role of advection in advection-diffusion equations used for modelling bed load transport

NASA Astrophysics Data System (ADS)

Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

2016-04-01

The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

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

Computational Analyses of Complex Flows with Chemical Reactions

NASA Astrophysics Data System (ADS)

Bae, Kang-Sik

The heat and mass transfer phenomena in micro-scale for the mass transfer phenomena on drug in cylindrical matrix system, the simulation of oxygen/drug diffusion in a three dimensional capillary network, and a reduced chemical kinetic modeling of gas turbine combustion for Jet propellant-10 have been studied numerically. For the numerical analysis of the mass transfer phenomena on drug in cylindrical matrix system, the governing equations are derived from the cylindrical matrix systems, Krogh cylinder model, which modeling system is comprised of a capillary to a surrounding cylinder tissue along with the arterial distance to veins. ADI (Alternative Direction Implicit) scheme and Thomas algorithm are applied to solve the nonlinear partial differential equations (PDEs). This study shows that the important factors which have an effect on the drug penetration depth to the tissue are the mass diffusivity and the consumption of relevant species during the time allowed for diffusion to the brain tissue. Also, a computational fluid dynamics (CFD) model has been developed to simulate the blood flow and oxygen/drug diffusion in a three dimensional capillary network, which are satisfied in the physiological range of a typical capillary. A three dimensional geometry has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model for blood, the oxygen transport model including in oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study the diffusion of drugs and other materials in the capillary streams. Finally, a chemical kinetic mechanism of JP-10 has been compiled and validated for a wide range of combustion regimes, covering pressures of 1atm to 40atm with temperature ranges of 1,200 K--1,700 K, which is being studied as a possible Jet propellant for the Pulse Detonation Engine (PDE) and other high-speed flight applications such as hypersonic missiles. The comprehensive skeletal mechanism consists of 58 species and 315 reactions including in CPD, Benzene formation process by the theory for polycyclic aromatic hydrocarbons (PAH) and soot formation process on the constant volume combustor, premixed flame characteristics.

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

Bulk Diffusion via a ``kick-out'' method for Lithium in the decomposition reaction LiAlH4/Li3AlH6

NASA Astrophysics Data System (ADS)

Rolih, Biljana; Ozolins, Vidvuds; Ozolins Team

2013-03-01

In the pursuit to find a practical system for hydrogen storage, complex metal hydrides have long been considered as viable candidates due to their high hydrogen content. However, some of the challenges faced with these types of systems are poor thermodynamics or kinetics. The underlying mechanisms, and their limiting processes, for the decomposition of these materials need to be understood. From experimental work on the decomposition of hydrogen storage materials, it has been suggested that bulk diffusion of metal species is the bottleneck for hydrogen release. In this work is the dehydrogenation we investigated the system LiAlH4  LiAlH6 with favorable hydrogen release (5.3 wt %), at moderate temperatures. Using first-principles density functional theory we found the defects facilitating mass transport by calculating individual formation energies, highest concentrations, and activation barriers for defect mobility. The mass transport of Lithium is found to be mediated by a ``kick-out'' mechanism. The results are used to further our understanding of the fundamental mechanism of mass transport and evaluate the possibility of kinetics as the limiting process in this reaction.

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

PubMed

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org.

Direct methanol fuel cell and system

DOEpatents

Wilson, Mahlon S.

2004-10-26

A fuel cell having an anode and a cathode and a polymer electrolyte membrane located between anode and cathode gas diffusion backings uses a methanol vapor fuel supply. A permeable polymer electrolyte membrane having a permeability effective to sustain a carbon dioxide flux equivalent to at least 10 mA/cm.sup.2 provides for removal of carbon dioxide produced at the anode by reaction of methanol with water. Another aspect of the present invention includes a superabsorpent polymer material placed in proximity to the anode gas diffusion backing to hold liquid methanol or liquid methanol solution without wetting the anode gas diffusion backing so that methanol vapor from the liquid methanol or liquid methanol-water solution is supplied to the membrane.

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.

Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery for the Non-steady State Conditions.

PubMed

Mehala, N; Rajendran, L; Meena, V

2017-02-01

A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (V max ) and Michaelis-Menten constants for glucose and oxygen (K g and K ox ) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.

Isotachophoresis-Based Surface Immunoassay.

PubMed

Paratore, Federico; Zeidman Kalman, Tal; Rosenfeld, Tally; Kaigala, Govind V; Bercovici, Moran

2017-07-18

In the absence of amplification methods for proteins, the immune-detection of low-abundance proteins using antibodies is fundamentally limited by binding kinetic rates. Here, we present a new class of surface-based immunoassays in which protein-antibody reaction is accelerated by isotachophoresis (ITP). We demonstrate the use of ITP to preconcentrate and deliver target proteins to a surface decorated with specific antibodies, where effective utilization of the focused sample is achieved by modulating the driving electric field (stop-and-diffuse ITP mode) or applying a counter flow that opposes the ITP motion (counterflow ITP mode). Using enhanced green fluorescent protein (EGFP) as a model protein, we carry out an experimental optimization of the ITP-based immunoassay and demonstrate a 1300-fold improvement in limit of detection compared to a standard immunoassay, in a 6 min protein-antibody reaction. We discuss the design of buffer chemistries for other protein systems and, in concert with experiments, provide full analytical solutions for the two operation modes, elucidating the interplay between reaction, diffusion, and accumulation time scales and enabling the prediction and design of future immunoassays.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Guiding brine shrimp through mazes by solving reaction diffusion equations

NASA Astrophysics Data System (ADS)

Singal, Krishma; Fenton, Flavio

Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.

Cyanide does more to inhibit heme enzymes, than merely serving as an active-site ligand

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

Parashar, Abhinav; Venkatachalam, Avanthika; Gideon, Daniel Andrew

Highlights: • Cyanide (CN) is a well-studied toxic principle, known to inhibit heme-enzymes. • Inhibition is supposed to result from CN binding at the active site as a ligand. • Diverse heme enzymes’ CN inhibition profiles challenge prevailing mechanism. • Poor binding efficiency of CN at low enzyme concentrations and ligand pressures. • CN-based diffusible radicals cause ‘non-productive electron transfers’ (inhibition). - Abstract: The toxicity of cyanide is hitherto attributed to its ability to bind to heme proteins’ active site and thereby inhibit their activity. It is shown herein that the long-held interpretation is inadequate to explain several observations inmore » heme-enzyme reaction systems. Generation of cyanide-based diffusible radicals in heme-enzyme reaction milieu could shunt electron transfers (by non-active site processes), and thus be detrimental to the efficiency of oxidative outcomes.« less

Pattern formation in three-dimensional reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

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.