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.

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

PubMed

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

2009-03-07

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

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.

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.

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.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

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

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

2014-05-30

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

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 \

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.

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.

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.

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

Clustering and optimal arrangement of enzymes in reaction-diffusion systems.

PubMed

Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich

2013-05-17

Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.

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.

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.

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.

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.

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

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.

The oleic acid-ozone heterogeneous reaction system: products, kinetics, secondary chemistry, and atmospheric implications of a model system - a review

NASA Astrophysics Data System (ADS)

Zahardis, J.; Petrucci, G. A.

2007-02-01

The heterogeneous processing of organic aerosols by trace oxidants has many implications to atmospheric chemistry and climate regulation. This review covers a model heterogeneous reaction system (HRS): the oleic acid-ozone HRS and other reaction systems featuring fatty acids, and their derivatives. The analysis of the commonly observed aldehyde and organic acid products of ozonolysis (azelaic acid, nonanoic acid, 9-oxononanoic acid, nonanal) is described. The relative product yields are noted and explained by the observation of secondary chemical reactions. The secondary reaction products arising from reactive Criegee intermediates are mainly peroxidic, notably secondary ozonides and α-acyloxyalkyl hydroperoxide oligomers and polymers, and their formation is in accord with solution and liquid-phase ozonolysis. These highly oxygenated products are of low volatility and hydrophilic which may enhance the ability of particles to act as cloud condensation nuclei (CCN). The kinetic description of this HRS is critically reviewed. Most kinetic studies suggest this oxidative processing is either a near surface reaction that is limited by the diffusion of ozone or a surface based reaction. Internally mixed particles and coatings represent the next stage in the progression towards more realistic proxies of tropospheric organic aerosols and a description of the products and the kinetics resulting from the ozonolysis of these proxies, which are based on fatty acids or their derivatives, is presented. Finally, the main atmospheric implications of oxidative processing of particulate containing fatty acids are presented. These implications include the extended lifetime of unsaturated species in the troposphere facilitated by the presence of solids, semi-solids or viscous phases, and an enhanced rate of ozone uptake by particulate unsaturates compared to corresponding gas-phase organics. Ozonolysis of oleic acid enhances its CCN activity, which implies that oxidatively processed

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

ERIC Educational Resources Information Center

Pojman, John A.

1990-01-01

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

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.

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

The oleic acid-ozone heterogeneous reaction system: products, kinetics, secondary chemistry, and atmospheric implications of a model system a review

NASA Astrophysics Data System (ADS)

Zahardis, J.; Petrucci, G. A.

2006-11-01

The heterogeneous processing of organic aerosols by trace oxidants has many implications to atmospheric chemistry and climate regulation. This review covers a model heterogeneous reaction system (HRS): the oleic acid-ozone HRS and other reaction systems featuring fatty acids, and their derivatives. The analysis of the primary products of ozonolysis (azelaic acid, nonanoic acid, 9-oxononanoic acid, nonanal) is described. Anomalies in the relative product yields are noted and explained by the observation of secondary chemical reactions. The secondary reaction products arising from reactive Criegee intermediates are mainly peroxidic, notably secondary ozonides and α-acyloxyalkyl hydroperoxide polymers. These highly oxygenated products are of low volatility and hydrophilic which may enhance the ability of particles to act as cloud condensation nuclei. The kinetic description of this HRS is critically reviewed. Most kinetic studies suggest this oxidative processing is either a near surface reaction that is limited by the diffusion of ozone or a surface based reaction. Internally mixed particles and coatings represent the next stage in the progression towards more realistic proxies of tropospheric organic aerosols and a description of the products and the kinetics resulting from the ozonolysis of these proxies, which are based on fatty acids or their derivatives, is presented. Finally, a series of atmospheric implications of oxidative processing of particulate containing fatty acids is presented. These implications include the extended lifetime of unsaturated species in the troposphere facilitated by the presence of solids, semisolids or viscous phases, and an enhanced rate of ozone uptake by particulate unsaturates compared to corresponding gas phase organics. Ozonolysis of oleic acid enhances its CCN activity, which implies that oxidatively processed particulate may contribute to indirect forcing of radiation. Other effects, including the potential role of aldehydic

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.

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.

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

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

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.

Nuclemeter: A Reaction-Diffusion Column for Quantifying Nucleic Acids Undergoing Enzymatic Amplification

NASA Astrophysics Data System (ADS)

Bau, Haim; Liu, Changchun; Killawala, Chitvan; Sadik, Mohamed; Mauk, Michael

2014-11-01

Real-time amplification and quantification of specific nucleic acid sequences plays a major role in many medical and biotechnological applications. In the case of infectious diseases, quantification of the pathogen-load in patient specimens is critical to assessing disease progression, effectiveness of drug therapy, and emergence of drug-resistance. Typically, nucleic acid quantification requires sophisticated and expensive instruments, such as real-time PCR machines, which are not appropriate for on-site use and for low resource settings. We describe a simple, low-cost, reactiondiffusion based method for end-point quantification of target nucleic acids undergoing enzymatic amplification. The number of target molecules is inferred from the position of the reaction-diffusion front, analogous to reading temperature in a mercury thermometer. We model the process with the Fisher Kolmogoroff Petrovskii Piscounoff (FKPP) Equation and compare theoretical predictions with experimental observations. The proposed method is suitable for nucleic acid quantification at the point of care, compatible with multiplexing and high-throughput processing, and can function instrument-free. C.L. was supported by NIH/NIAID K25AI099160; M.S. was supported by the Pennsylvania Ben Franklin Technology Development Authority; C.K. and H.B. were funded, in part, by NIH/NIAID 1R41AI104418-01A1.

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

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/

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.

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.

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.

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.

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

PubMed

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

2016-09-01

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

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.

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.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

Naruemon, Rueangkham; Charin, Modchang

2016-04-01

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

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.

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.

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

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.

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...

Characterizing acid diffusion lengths in chemically amplified resists from measurements of deprotection kinetics

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

Patil, Abhijit A.; Pandey, Yogendra Narayan; Doxastakis, Manolis

2014-10-01

The acid-catalyzed deprotection of glassy poly(4-hydroxystyrene-co-tertbutyl acrylate) films was studied with infrared absorbance spectroscopy and stochastic simulations. Experimental data were interpreted with a simple description of subdiffusive acid transport coupled to second-order acid loss. This model predicts key attributes of observed deprotection rates, such as fast reaction at short times, slow reaction at long times, and a nonlinear dependence on acid loading. Fickian diffusion is approached by increasing the post-exposure bake temperature or adding plasticizing agents to the polymer resin. These findings demonstrate that acid mobility and overall deprotection kinetics are coupled to glassy matrix dynamics. To complement the analysismore » of bulk kinetics, acid diffusion lengths were calculated from the anomalous transport model and compared with nanopattern line widths. The consistent scaling between experiments and simulations suggests that the anomalous diffusion model could be further developed into a predictive lithography tool.« less

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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

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

Polymerase chain reaction system using magnetic beads for analyzing a sample that includes nucleic acid

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

Nasarabadi, Shanavaz

2011-01-11

A polymerase chain reaction system for analyzing a sample containing nucleic acid includes providing magnetic beads; providing a flow channel having a polymerase chain reaction chamber, a pre polymerase chain reaction magnet position adjacent the polymerase chain reaction chamber, and a post pre polymerase magnet position adjacent the polymerase chain reaction chamber. The nucleic acid is bound to the magnetic beads. The magnetic beads with the nucleic acid flow to the pre polymerase chain reaction magnet position in the flow channel. The magnetic beads and the nucleic acid are washed with ethanol. The nucleic acid in the polymerase chain reactionmore » chamber is amplified. The magnetic beads and the nucleic acid are separated into a waste stream containing the magnetic beads and a post polymerase chain reaction mix containing the nucleic acid. The reaction mix containing the nucleic acid flows to an analysis unit in the channel for analysis.« less

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

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.

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

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)

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.

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

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.

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.

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.

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

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.

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.

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.

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.

Interchange reaction of disulfides and denaturation of oxytocin by copper(II)/ascorbic acid/O2 system.

PubMed

Inoue, H; Hirobe, M

1987-05-29

The interchange reaction of disulfides was caused by the copper(II)/ascorbic acid/O2 system. The incubation of two symmetric disulfides, L-cystinyl-bis-L-phenylalanine (PP) and L-cystinyl-bis-L-tyrosine (TT), with L-ascorbic acid and CuSO4 in potassium phosphate buffer (pH 7.2, 50 mM) resulted in the formation of an asymmetric disulfide, L-cystinyl-L-phenylalanine-L-tyrosine (PT), and the final ratio of PP:PT:TT was 1:2:1. As the reaction was inhibited by catalase and DMSO only at the initial time, hydroxyl radical generated by the copper(II)/ascorbic acid/O2 system seemed to be responsible for the initiation of the reaction. Oxytocin and insulin were denatured by this system, and catalase and DMSO similarly inhibited these denaturations. As the composition of amino acids was unchanged after the reaction, hydroxyl radical was thought to cause the cleavage and/or interchange reaction of disulfides to denature the peptides.

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.

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).

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.

Modeling and simulation of enzymatic gluconic acid production using immobilized enzyme and CSTR-PFTR circulation reaction system.

PubMed

Li, Can; Lin, Jianqun; Gao, Ling; Lin, Huibin; Lin, Jianqiang

2018-04-01

Production of gluconic acid by using immobilized enzyme and continuous stirred tank reactor-plug flow tubular reactor (CSTR-PFTR) circulation reaction system. A production system is constructed for gluconic acid production, which consists of a continuous stirred tank reactor (CSTR) for pH control and liquid storage and a plug flow tubular reactor (PFTR) filled with immobilized glucose oxidase (GOD) for gluconic acid production. Mathematical model is developed for this production system and simulation is made for the enzymatic reaction process. The pH inhibition effect on GOD is modeled by using a bell-type curve. Gluconic acid can be efficiently produced by using the reaction system and the mathematical model developed for this system can simulate and predict the process well.

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.

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.

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

PubMed

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

2013-08-01

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

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.

Diffusion of uncharged probe reveals structural changes in polyacids initiated by their neutralization: poly(acrylic acids).

PubMed

Hyk, Wojciech; Masiak, Michal; Stojek, Zbigniew; Ciszkowska, Malgorzata

2005-03-17

Stokes-Einstein relation and, therefore, suggests that the changes in the probe diffusion rate are mainly due to the structural changes in the polyacrylate medium and the macromolecular rearrangements induced by the chemical, acid-base reaction. By adapting the obstruction model for diffusion in homogeneous gels, the transport characteristics of the probe were converted into the structural characteristics of the polyelectrolytic systems. It has been found that the most ordered structure of the polyelectrolyte, or in other words the most permeable structure, is obtained when poly(acrylic acid) is neutralized at 75-80%.

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.

Reaction-diffusion basis of retroviral infectivity

NASA Astrophysics Data System (ADS)

Sadiq, S. Kashif

2016-11-01

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env3) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env3 molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env3 diffuses comparably to Gag-absent Env3. Initial immobility of Env3 is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env3 diffusion, and permits Env3 clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Citric Acid-Modified Fenton's Reaction for the Oxidation of Chlorinated Ethylenes in Soil Solution Systems

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

Seol, Yongkoo; Javandel, Iraj

Fenton's reagent, a solution of hydrogen peroxide and ferrous iron catalyst, is used for an in-situ chemical oxidation of organic contaminants. Sulfuric acid is commonly used to create an acidic condition needed for catalytic oxidation. Fenton's reaction often involves pressure buildup and precipitation of reaction products, which can cause safety hazards and diminish efficiency. We selected citric acid, a food-grade substance, as an acidifying agent to evaluate its efficiencies for organic contaminant removal in Fenton's reaction, and examined the impacts of using citric acid on the unwanted reaction products. A series of batch and column experiments were performed with varyingmore » H{sub 2}O{sub 2} concentrations to decompose selected chlorinated ethylenes. Either dissolved iron from soil or iron sulfate salt was added to provide the iron catalyst in the batch tests. Batch experiments revealed that both citric and sulfuric acid systems achieved over 90% contaminant removal rates, and the presence of iron catalyst was essential for effective decontamination. Batch tests with citric acid showed no signs of pressure accumulation and solid precipitations, however the results suggested that an excessive usage of H{sub 2}O{sub 2} relative to iron catalysts (Fe{sup 2+}/H{sub 2}O{sub 2} < 1/330) would result in lowering the efficiency of contaminant removal by iron chelations in the citric acid system. Column tests confirmed that citric acid could provide suitable acidic conditions to achieve higher than 55% contaminant removal rates.« less

Citric acid-modified Fenton's reaction for the oxidation of chlorinated ethylenes in soil solution systems.

PubMed

Seol, Yongkoo; Javandel, Iraj

2008-06-01

Fenton's reagent, a solution of hydrogen peroxide and ferrous iron catalyst, is used for an in situ chemical oxidation of organic contaminants. Sulfuric acid is commonly used to create an acidic condition needed for catalytic oxidation. Fenton's reaction often involves pressure buildup and precipitation of reaction products, which can cause safety hazards and diminish efficiency. We selected citric acid, a food-grade substance, as an acidifying agent to evaluate its efficiencies for organic contaminant removal in Fenton's reaction, and examined the impacts of using citric acid on the unwanted reaction products. A series of batch and column experiments were performed with varying H2O2 concentrations to decompose selected chlorinated ethylenes. Either dissolved iron from soil or iron sulfate salt was added to provide the iron catalyst in the batch tests. Batch experiments revealed that both citric and sulfuric acid systems achieved over 90% contaminant removal rates, and the presence of iron catalyst was essential for effective decontamination. Batch tests with citric acid showed no signs of pressure accumulation and solid precipitations, however the results suggested that an excessive usage of H2O2 relative to iron catalysts (Fe2+/H2O2<1/330) would result in lowering the efficiency of contaminant removal by iron chelation in the citric acid system. Column tests confirmed that citric acid could provide suitable acidic conditions to achieve higher than 55% contaminant removal rates.

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.

Electrochemical Reduction of CO2 to Organic Acids by a Pd-MWNTs Gas-Diffusion Electrode in Aqueous Medium

PubMed Central

Lu, Guang; Bian, Zhaoyong; Liu, Xin

2013-01-01

Pd-multiwalled carbon nanotubes (Pd-MWNTs) catalysts for the conversion of CO2 to organic acids were prepared by the ethylene glycol reduction and fully characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), and cyclic voltammetry (CV) technologies. The amorphous Pd particles with an average size of 5.7 nm were highly dispersed on the surface of carbon nanotubes. Functional groups of the MWNTs played a key role in the palladium deposition. The results indicated that Pd-MWNTs could transform CO2 into organic acid with high catalytic activity and CO2 could take part in the reduction reaction directly. Additionally, the electrochemical reduction of CO2 was investigated by a diaphragm electrolysis device, using a Pd-MWNTs gas-diffusion electrode as a cathode and a Ti/RuO2 net as an anode. The main products in present system were formic acid and acetic acid identified by ion chromatograph. The selectivity of the products could be achieved by reaction conditions changing. The optimum faraday efficiencies of formic and acetic acids formed on the Pd-MWNTs gas-diffusion electrode at 4 V electrode voltages under 1 atm CO2 were 34.5% and 52.3%, respectively. PMID:24453849

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.

Diffusion-reaction modelling of early diagenesis of sediments affected by acid mine drainage.

NASA Astrophysics Data System (ADS)

Torres, E.; Ayora, C.; Arias, J. L.; Garcia Robledo, E.; Papaspyrou, S.; Corzo, A.

2012-04-01

The Sancho Reservoir (SW Spain) is a monomictic water reservoir affected by acid mine drainage. It has a pH of ~4, with high sulfate (200 ppm) and heavy metal concentrations in the water column. The reservoir develops reducing conditions at the bottom during the stratification period. A laboratory experiment was carried out to study the effect of this oxygen variation on the early diagenesis processes and the cycling of metals. Sediment cores and bottom water were collected during the stratification period and brought to the laboratory. The cores were maintained in an aquarium bubbled with nitrogen gas to maintain hypoxic conditions (~10 µmol O2 L-1) for 1 day. Then, oxic conditions were induced by bubbling with air and maintained for 50 days. Finally, hypoxia was re-established for 10 days. Triplicate cores were sliced in a anaerobic glove box at each stage. Pore water was extracted by centrifugation and: Eh, pH, DO, DOC, sulfate, Fe and trace metals were analyzed. The sediment was freeze-dried and a sequential extraction protocol was applied to determine the exchangeable, AVS, Fe-(oxy)hydroxides, Fe-oxides, organic matter, pyrite sulfur and residual phase iron fractions. Organic carbon and total C, N, H and S were also analyzed in the sediment. A reactive diffusion model has been used to obtain the rates of biogeochemical reactions by fitting to the experimental data. During hypoxic conditions sulfate and Fe-(oxy)hydroxides are reduced, due to the anaerobic oxidation of organic matter, at the very first few cm, releasing sulfide and Fe(II) which precipitate as iron sulfide. When oxygen diffuses in the sediment, sulfate-reduction and the sulfide peaks are displaced deeper into the sediment. Oxygen penetration depth and its consumption rates in the sediment increase quickly, resulting in the reoxidation of the iron sulfides that had precipitated during hypoxic conditions. Sulfide and Fe(II) are released and are again oxidized to Fe(III) and sulfate respectively

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

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.

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

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.

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.

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A.

2018-05-01

We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.

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.

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.

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.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Acid-$beta$-glycerophosphatase reaction products in the central nervous system mitochondria following x-ray irradiation

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

Roizin, L.; Orlovskaja, D.; Liu, J.C.

A survey of the literature to date on the enzyme histochemistry of intracellular organelles has not yielded any reference to the presence of acid phosphatase reaction products in the mammalian mitochondria of the central nervous system. A combination of Gomori's acid phosphatase method, however, with standard electron microscopy has disclosed the presence of enzyme reaction products in the mitochondria of the central nervous system of rats from 2 hr to 22 weeks after x-ray irradiation, as well as in a cerebral biopsy performed on a patient affected by Huntington's chorea. No enzyme reaction products, on the other hand, were observedmore » in serial sections that had been incubated in substrates either containing sodium fluoride or lacking in $beta$- glycerophosphate. The abnormal mitochondrial enzyme reaction (chemical lesion) is considered to be the consequence of the pathologic process affecting the ultrastructural-chemical organization of the organelle. (auth)« less

The Effect of Limited Diffusion and Wet–Dry Cycling on Reversible Polymerization Reactions: Implications for Prebiotic Synthesis of Nucleic Acids

PubMed Central

Higgs, Paul G.

2016-01-01

A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction. PMID:27338479

The Effect of Limited Diffusion and Wet-Dry Cycling on Reversible Polymerization Reactions: Implications for Prebiotic Synthesis of Nucleic Acids.

PubMed

Higgs, Paul G

2016-06-08

A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction.

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.

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.

Intraparticle diffusion limitations in the hydrogenation of monounsaturated edible oils and their fatty acid methyl esters

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

Jonker, G.H.; Veldsink, J.W.; Beenackers, A.A.C.M.

1998-12-01

Intraparticle diffusion limitation in the hydrogenation and isomerization of fatty acid methyl esters (FAMEs) and edible oils (triacylglycerol, TAG) in porous nickel catalyst was investigated both under reactive and under inert conditions. Under reactive conditions, the diffusion coefficients were determined from the best fits of the model simulations applying the intrinsic reacting kinetics of monounsaturated FAME hydrogenation to experiments under diffusion limited conditions. Due to the absence of reaction (hydrogenation of double bonds), the obtained effective H{sub z} diffusion coefficient (D{sub e}) with the HPLC technique is volume averaged and thereby determined by the larger intercrystalline pores (<30% of themore » total pore volume) only. Moreover, D{sub e} measured under reaction conditions reflected the influence of the micropores, resulting in a 10-fold lower value.« less

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.

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.

Macromolecular Crowding Studies of Amino Acids Using NMR Diffusion Measurements and Molecular Dynamics Simulations

NASA Astrophysics Data System (ADS)

Virk, Amninder; Stait-Gardner, Timothy; Willis, Scott; Torres, Allan; Price, William

2015-02-01

Molecular crowding occurs when the total concentration of macromolecular species in a solution is so high that a considerable proportion of the volume is physically occupied and therefore not accessible to other molecules. This results in significant changes in the solution properties of the molecules in such systems. Macromolecular crowding is ubiquitous in biological systems due to the generally high intracellular protein concentrations. The major hindrance to understanding crowding is the lack of direct comparison of experimental data with theoretical or simulated data. Self-diffusion is sensitive to changes in the molecular weight and shape of the diffusing species, and the available diffusion space (i.e., diffusive obstruction). Consequently, diffusion measurements are a direct means for probing crowded systems including the self-association of molecules. In this work, nuclear magnetic resonance measurements of the self-diffusion of four amino acids (glycine, alanine, valine and phenylalanine) up to their solubility limit in water were compared directly with molecular dynamics simulations. The experimental data were then analyzed using various models of aggregation and obstruction. Both experimental and simulated data revealed that the diffusion of both water and the amino acids were sensitive to the amino acid concentration. The direct comparison of the simulated and experimental data afforded greater insights into the aggregation and obstruction properties of each amino acid.

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.

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.

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.

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.

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.

Survivability and Abiotic Reactions of Selected Amino Acids in Different Hydrothermal System Simulators

NASA Astrophysics Data System (ADS)

Chandru, Kuhan; Imai, Eiichi; Kaneko, Takeo; Obayashi, Yumiko; Kobayashi, Kensei

2013-04-01

We tested the stability and reaction of several amino acids using hydrothermal system simulators: an autoclave and two kinds of flow reactors at 200-250 °C. This study generally showed that there is a variation in the individual amino acids survivability in the simulators. This is mainly attributed to the following factors; heat time, cold quenching exposure, metal ions and also silica. We observed that, in a rapid heating flow reactor, high aggregation and/or condensation of amino acids could occur even during a heat exposure of 2 min. We also monitored their stability in a reflow-type of simulator for 120 min at 20 min intervals. The non-hydrolyzed and hydrolyzed samples for this system showed a similar degradation only in the absence of metal ions.

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.

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

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.

Time-Dependent ATR-FTIR Spectroscopic Studies on Fatty Acid Diffusion and the Formation of Metal Soaps in Oil Paint Model Systems.

PubMed

Baij, Lambert; Hermans, Joen J; Keune, Katrien; Iedema, Piet

2018-06-18

The formation of metal soaps (metal complexes of saturated fatty acids) is a serious problem affecting the appearance and structural integrity of many oil paintings. Tailored model systems for aged oil paint and time-dependent attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy were used to study the diffusion of palmitic acid and subsequent metal soap crystallization. The simultaneous presence of free saturated fatty acids and polymer-bound metal carboxylates leads to rapid metal soap crystallization, following a complex mechanism that involves both acid and metal diffusion. Solvent flow, water, and pigments all enhance metal soap crystallization in the model systems. These results contribute to the development of paint cleaning strategies, a better understanding of oil paint degradation, and highlight the potential of time-dependent ATR-FTIR spectroscopy for studying dynamic processes in polymer films. © 2018 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

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.

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

Reaction Mechanisms and Structural and Physicochemical Properties of Caffeic Acid Grafted Chitosan Synthesized in Ascorbic Acid and Hydroxyl Peroxide Redox System.

PubMed

Liu, Jun; Pu, Huimin; Chen, Chong; Liu, Yunpeng; Bai, Ruyu; Kan, Juan; Jin, Changhai

2018-01-10

The ascorbic acid (AA) and hydroxyl peroxide (H 2 O 2 ) redox pair induced free radical grafting reaction is a promising approach to conjugate phenolic groups with chitosan (CS). In order to reveal the exact mechanisms of the AA/H 2 O 2 redox pair induced grafting reaction, free radicals generated in the AA/H 2 O 2 redox system were compared with hydroxyl radical ( • OH) produced in the Fe 2+ /H 2 O 2 redox system. Moreover, the structural and physicochemical properties of caffeic acid grafted CS (CA-g-CS) synthesized in these two redox systems were compared. Results showed that only ascorbate radical (Asc •- ) was produced in the AA/H 2 O 2 system. The reaction between Asc •- and CS produced novel carbon-centered radicals, whereas no new free radicals were detected when • OH reacted with CS. Thin layer chromatography, UV-vis, Fourier transform infrared, and nuclear magnetic resonance spectroscopic analyses all confirmed that CA was successfully grafted onto CS through Asc •- . However, CA could be hardly grafted onto CS via • OH. CA-g-CS synthesized through Asc •- exhibited lower thermal stability and crystallinity than the reaction product obtained through • OH. For the first time, our results demonstrated that the synthesis of CA-g-CS in the AA/H 2 O 2 redox system was mediated by Asc •- rather than • OH.

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

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.

Diffusivity of dicarboxylic acids molecules to secondary organic material governed by particle phase state

NASA Astrophysics Data System (ADS)

Han, Y.; Gong, Z.; Liu, P.; de Sá, S. S.; McKinney, K. A.; Martin, S. T.

2017-12-01

Atmospheric secondary organic material (SOM) from oxidation of volatile organic compounds can exist in amorphous solid, semisolid, and liquid states depending on a range of factors such as relative humidity (RH), temperature, and reaction history. The phase state of SOM affects the dynamic exchange and reactivity between particles and gas-phase molecules. Dicarboxylic acids are ubiquitous in ambient atmosphere and the uptake of which may lead to substantial changes in hygroscopicity, absorption property, and light scattering of aerosol particles. This study investigates the diffusivity of dicarboxylic acids to the matrix of SOM particles. SOM was generated from dark ozonolysis of a-pinene in Harvard Environmental Chamber. The produced SOM particles were passed through an ozone scrubber to remove gas-phase chemistry before being led into a flask reactor, where gas-phase dicarboxylic acid was injected continuously and RH was varied from 5% to 85%. The probe dicarboxylic acids molecules including malonic acid and a-ketoglutaric acid have been investigated for the uptake to SOM particles. Organic composition in the outflow of the flask was measured with a high-resolution time-of-flight aerosol mass spectrometer. The mass fractions of tracer ions in total organic mass for both malonic acid and a-ketoglutaric acid increased substantially with the increase of RH values. The tracer ions of malonic acid were also more abundant in a-pinene SOM particles with increased gas-phase concentrations. These results suggest that the diffusion of the studied dicarboxylic acids molecules to a-pinene SOM particles was enhanced at increased RH values, which is possibly due to the phase transition of a-pinene SOM particles from non-liquid to liquid states. Therefore, particle phase state may be an important factor governing the diffusivity of dicarboxylic acids molecules to a-pinene SOM. Further dicarboxylic acids with various functional groups will be investigated to understand the

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.

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.

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.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Investigating Students' Reasoning about Acid-Base Reactions

ERIC Educational Resources Information Center

Cooper, Melanie M.; Kouyoumdjian, Hovig; Underwood, Sonia M.

2016-01-01

Acid-base chemistry is central to a wide range of reactions. If students are able to understand how and why acid-base reactions occur, it should provide a basis for reasoning about a host of other reactions. Here, we report the development of a method to characterize student reasoning about acid-base reactions based on their description of…

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

Topics in Diffusion Limited Reaction Processes

NASA Astrophysics Data System (ADS)

Lin, Jian-Cheng

We study, both theoretically and numerically, the macroscopic particle concentration in a class of simple diffusion-limited reactions: one species coagulation A + A to A, reversible coagulation A + A rightleftharpoons A, A + A to A with particle input, A + A rightleftharpoons A with particle input, single species annihilation A + A to inert, and two species annihilation A + B to inert. The main interest is in the asymptotic behavior of the particle concentration. We review the standard mean-field theory, mass-reaction kinetics and the associated nonlinear rate and diffusion-reaction equations. Theoretically we study the concentration using several closure schemes for truncating the infinite hierarchy of the kinetic equations for the joint density functions. Our goal is to evaluate the quality of some nonsystematic approximations by comparison with exact solutions. It is found that these approximations are very good at capturing the asymptotic behavior of the particle concentrations in the irreversible reactions, while they fail to predict the far-from-equilibrium dynamic phase transition in the one dimensional reversible coagulation reaction predicted by exact results. Numerically we use Monte Carlo simulation to study concentrations in the single species reversible coagulation process. In one dimension the numerical results are in excellent agreement with the exact analytic results. In two dimensions, our simulation data in the transient states suggest an interesting scaling for the deviation of the concentration from its equilibrium value, delta C(t) ~ exp( -beta(C_0)t^{alpha(C_0) }), where alpha(C_0) and beta(C_0) are functions of the initial concentration C_0. However, it seems unlikely to be able to answer the question of the existence of a dynamic phase transition in two dimensions by Monte Carlo simulation within a reasonable CPU time due to the long persistence of the transient states. In an appendix we solve exactly an annihilation-related percolation

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.

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.

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.

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.

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

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.

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.

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.

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.

Koch–Haaf reaction of adamantanols in an acid-tolerant hastelloy-made microreactor

PubMed Central

Mukai, Yu

2011-01-01

Summary The Koch–Haaf reaction of adamantanols was successfully carried out in a microflow system at room temperature. By combining an acid-tolerant hastelloy-made micromixer, a PTFE tube, and a hastelloy-made microextraction unit, a packaged reaction-to-workup system was developed. By means of the present system, the multigram scale synthesis of 1-adamantanecarboxylic acid was achieved in ca. one hour operation. PMID:21977213

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.

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.

Conformation-dependent chemical reaction of formic acid with an oxygen atom.

PubMed

Khriachtchev, Leonid; Domanskaya, Alexandra; Marushkevich, Kseniya; Räsänen, Markku; Grigorenko, Bella; Ermilov, Alexander; Andrijchenko, Natalya; Nemukhin, Alexander

2009-07-23

Conformation dictates many physical and chemical properties of molecules. The importance of conformation in the selectivity and function of biologically active molecules is widely accepted. However, clear examples of conformation-dependent bimolecular chemical reactions are lacking. Here we consider a case of formic acid (HCOOH) that is a valuable model system containing the -COOH carboxyl functional group, similar to many biomolecules including the standard amino acids. We have found a strong case of conformation-dependent reaction between formic acid and atomic oxygen obtained in cryogenic matrices. The reaction surprisingly leads to peroxyformic acid only from the ground-state trans conformer of formic acid, and it results in the hydrogen-bonded complex for the higher-energy cis conformer.

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.

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.

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.

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.

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.

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.

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

NASA Astrophysics Data System (ADS)

Straube, Ronny; Ward, Michael J.; Falcke, Martin

2007-10-01

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP3 receptor channels (IP3R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate `inner' and `outer' asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP3R. This supports the idea that clusters are formed by a purely diffusion limited process.

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

Free-standing supramolecular hydrogel objects by reaction-diffusion

PubMed Central

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

2017-01-01

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

Interface proliferation and the growth of labyrinths in a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Goldstein, Raymond E.; Muraki, David J.; Petrich, Dean M.

1996-04-01

In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact "localized states." The formation of space-filling patterns from instabilities of such structures is studied in the context of a nonlocal contour dynamics model for the evolution of boundaries between high and low concentrations of the activator. An earlier heuristic derivation [D. M. Petrich and R. E. Goldstein,

Fe2P as a novel efficient catalyst promoter in Pd/C system for formic acid electro-oxidation in fuel cells reaction

NASA Astrophysics Data System (ADS)

Wang, Fulong; Xue, Huaiguo; Tian, Zhiqun; Xing, Wei; Feng, Ligang

2018-01-01

Developing catalyst promoter for Pd/C catalyst is significant for the catalytic ability improvement in energy transfer related electrochemical reactions. Herein, we demonstrate Fe2P as an efficient catalyst promoter in Pd/C catalyst system for formic acid electro-oxidation in fuel cells reactions. Adding Fe2P in the Pd/C catalyst system greatly increases the performances for formic acid oxidation by 3-4 times; the CO stripping technique displays two kinds of active sites formation in the Pd-Fe2P/C catalyst system coming from the interaction of Pd, Fe2P and Pd oxide species and both are more efficient for formic acid and CO-species electrooxidation. The smaller charge transfer resistance and Tafel slope for formic acid oxidation indicate the improvements in kinetics by Fe2P in the Pd-Fe2P/C system. The nanostructured hybrid units of Pd, Fe2P and carbon are evidently visible in the high resolution microscopy images and XPS technique confirmes the electronic effect in the catalyst system. The promotion effect of Fe2P in the catalyst system arising from the structure, composition and electronic effect changes is discussed with the help from multiple physical and electrochemical techniques. It is concluded that Fe2P as a significant catalyst promoter will have potential application in energy transfer related electrochemical reactions.

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.

Enhancing Cation Diffusion and Suppressing Anion Diffusion via Lewis-Acidic Polymer Electrolytes.

PubMed

Savoie, Brett M; Webb, Michael A; Miller, Thomas F

2017-02-02

Solid polymer electrolytes (SPEs) have the potential to increase both the energy density and stability of lithium-based batteries, but low Li + conductivity remains a barrier to technological viability. SPEs are designed to maximize Li + diffusivity relative to the anion while maintaining sufficient salt solubility. It is thus remarkable that poly(ethylene oxide) (PEO), the most widely used SPE, exhibits Li + diffusivity that is an order of magnitude smaller than that of typical counterions at moderate salt concentrations. We show that Lewis-basic polymers like PEO favor slow cation and rapid anion diffusion, while this relationship can be reversed in Lewis-acidic polymers. Using molecular dynamics, polyboranes are identified that achieve up to 10-fold increases in Li + diffusivities and significant decreases in anion diffusivities, relative to PEO in the dilute-ion regime. These results illustrate a general principle for increasing Li + diffusivity and transference number with chemistries that exhibit weaker cation and stronger anion coordination.

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.

Heat Diffusion in Gases, Including Effects of Chemical Reaction

NASA Technical Reports Server (NTRS)

Hansen, C. Frederick

1960-01-01

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

The influence of acid diffusion on the performance of lead-acid cells

NASA Astrophysics Data System (ADS)

Kappus, W.; Bohmann, J.

1983-11-01

A model for the discharge performance of the lead-acid cell is proposed. Diffusion of acid into the porous electrodes, which is connected with diffusio Curves of diffusional polarizations as a function of the discharge time are presented. Calculated discharge capacities show the influence of various pa

Adverse drug reactions induced by valproic acid.

PubMed

Nanau, Radu M; Neuman, Manuela G

2013-10-01

Valproic acid is a widely-used first-generation antiepileptic drug, prescribed predominantly in epilepsy and psychiatric disorders. VPA has good efficacy and pharmacoeconomic profiles, as well as a relatively favorable safety profile. However, adverse drug reactions have been reported in relation with valproic acid use, either as monotherapy or polytherapy with other antiepileptic drugs or antipsychotic drugs. This systematic review discusses valproic acid adverse drug reactions, in terms of hepatotoxicity, mitochondrial toxicity, hyperammonemic encephalopathy, hypersensitivity syndrome reactions, neurological toxicity, metabolic and endocrine adverse events, and teratogenicity. Copyright © 2013 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

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.

Experimental and theoretical study on chemical reactions and species diffusion by a nano-pulse discharged bubble for water treatment

NASA Astrophysics Data System (ADS)

He, Yuchen; Uehara, Satoshi; Takana, Hidemasa; Nishiyama, Hideya

2018-01-01

Advanced oxidation processes using hydroxyl radicals (ṡOH) generated inside bubbles in water has drawn widely interest for the high oxidation potential of OH radical to decompose persistent organic pollutants such as dioxins and humic acid for water purification. In this study, a two-dimensional diffusion model for a nano-pulse discharged bubble in water is established. Based on the experimental results of streamer propagation inside a bubble, the diffusion processes around the bubble interface and reactions of chemical species in liquids are simulated. The simulation results show that OH radicals can diffuse only several micrometers away from the bubble interface in water. Furthermore, the optimal operating voltage and frequency conditions for OH generation is obtained by comparing the OH concentration in water obtained from numerical simulation with that measured by spectroscopy in experiment.

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

Synthesis and materialization of a reaction-diffusion French flag pattern

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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.

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

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

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

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.

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.

Sub-millitesla magnetic field effects on the recombination reaction of flavin and ascorbic acid radicals

NASA Astrophysics Data System (ADS)

Evans, Emrys W.; Kattnig, Daniel R.; Henbest, Kevin B.; Hore, P. J.; Mackenzie, Stuart R.; Timmel, Christiane R.

2016-08-01

Even though the interaction of a <1 mT magnetic field with an electron spin is less than a millionth of the thermal energy at room temperature (kBT), it still can have a profound effect on the quantum yields of radical pair reactions. We present a study of the effects of sub-millitesla magnetic fields on the photoreaction of flavin mononucleotide with ascorbic acid. Direct control of the reaction pathway is achieved by varying the rate of electron transfer from ascorbic acid to the photo-excited flavin. At pH 7.0, we verify the theoretical prediction that, apart from a sign change, the form of the magnetic field effect is independent of the initial spin configuration of the radical pair. The data agree well with model calculations based on a Green's function approach that allows multinuclear spin systems to be treated including the diffusive motion of the radicals, their spin-selective recombination reactions, and the effects of the inter-radical exchange interaction. The protonation states of the radicals are uniquely determined from the form of the magnetic field-dependence. At pH 3.0, the effects of two chemically distinct radical pair complexes combine to produce a pronounced response to ˜500 μT magnetic fields. These findings are relevant to the magnetic responses of cryptochromes (flavin-containing proteins proposed as magnetoreceptors in birds) and may aid the evaluation of effects of weak magnetic fields on other biologically relevant electron transfer processes.

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

A Luenberger observer for reaction-diffusion models with front position data

NASA Astrophysics Data System (ADS)

Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe

2015-11-01

We propose a Luenberger observer for reaction-diffusion models with propagating front features, and for data associated with the location of the front over time. Such models are considered in various application fields, such as electrophysiology, wild-land fire propagation and tumor growth modeling. Drawing our inspiration from image processing methods, we start by proposing an observer for the eikonal-curvature equation that can be derived from the reaction-diffusion model by an asymptotic expansion. We then carry over this observer to the underlying reaction-diffusion equation by an ;inverse asymptotic analysis;, and we show that the associated correction in the dynamics has a stabilizing effect for the linearized estimation error. We also discuss the extension to joint state-parameter estimation by using the earlier-proposed ROUKF strategy. We then illustrate and assess our proposed observer method with test problems pertaining to electrophysiology modeling, including with a realistic model of cardiac atria. Our numerical trials show that state estimation is directly very effective with the proposed Luenberger observer, while specific strategies are needed to accurately perform parameter estimation - as is usual with Kalman filtering used in a nonlinear setting - and we demonstrate two such successful strategies.

40 CFR 721.10125 - Alkenedioic acid, dialkyl ester, reaction products with polyaminocarbomonocycle and alkenoic acid...

Code of Federal Regulations, 2010 CFR

2010-07-01

..., reaction products with polyaminocarbomonocycle and alkenoic acid alkyl ester (generic). 721.10125 Section... Substances § 721.10125 Alkenedioic acid, dialkyl ester, reaction products with polyaminocarbomonocycle and.... (1) The chemical substances identified generically as alkenedioic acid, dialkyl ester, reaction...

40 CFR 721.10125 - Alkenedioic acid, dialkyl ester, reaction products with polyaminocarbomonocycle and alkenoic acid...

Code of Federal Regulations, 2011 CFR

2011-07-01

..., reaction products with polyaminocarbomonocycle and alkenoic acid alkyl ester (generic). 721.10125 Section... Substances § 721.10125 Alkenedioic acid, dialkyl ester, reaction products with polyaminocarbomonocycle and.... (1) The chemical substances identified generically as alkenedioic acid, dialkyl ester, reaction...

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.

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.

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.

Theory of ion transport with fast acid-base equilibrations in bioelectrochemical systems.

PubMed

Dykstra, J E; Biesheuvel, P M; Bruning, H; Ter Heijne, A

2014-07-01

Bioelectrochemical systems recover valuable components and energy in the form of hydrogen or electricity from aqueous organic streams. We derive a one-dimensional steady-state model for ion transport in a bioelectrochemical system, with the ions subject to diffusional and electrical forces. Since most of the ionic species can undergo acid-base reactions, ion transport is combined in our model with infinitely fast ion acid-base equilibrations. The model describes the current-induced ammonia evaporation and recovery at the cathode side of a bioelectrochemical system that runs on an organic stream containing ammonium ions. We identify that the rate of ammonia evaporation depends not only on the current but also on the flow rate of gas in the cathode chamber, the diffusion of ammonia from the cathode back into the anode chamber, through the ion exchange membrane placed in between, and the membrane charge density.

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.

Chemical computing with reaction-diffusion processes.

PubMed

Gorecki, J; Gizynski, K; Guzowski, J; Gorecka, J N; Garstecki, P; Gruenert, G; Dittrich, P

2015-07-28

Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

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.

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

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

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

A 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.

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

Signatures of a quantum diffusion limited hydrogen atom tunneling reaction.

PubMed

Balabanoff, Morgan E; Ruzi, Mahmut; Anderson, David T

2017-12-20

We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH 2 ) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH 3 OH) isolated in solid pH 2 . Short-term irradiation of CH 3 OH at 1.8 K readily produces CH 2 O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH 3 O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH 2 OH growth. The CH 2 OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH 3 O with the pH 2 host, (ii) H atom reactions with the CH 2 O photofragment, and (iii) long-range migration of H atoms and reaction with CH 3 OH. We assign the rapid CH 2 OH growth to the following CH 3 O + H 2 → CH 3 OH + H → CH 2 OH + H 2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD 3 OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH 2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

Acid-functionalized polyolefin materials and their use in acid-promoted chemical reactions

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

Oyola, Yatsandra; Tian, Chengcheng; Bauer, John Christopher

An acid-functionalized polyolefin material that can be used as an acid catalyst in a wide range of acid-promoted chemical reactions, wherein the acid-functionalized polyolefin material includes a polyolefin backbone on which acid groups are appended. Also described is a method for the preparation of the acid catalyst in which a precursor polyolefin is subjected to ionizing radiation (e.g., electron beam irradiation) of sufficient power and the irradiated precursor polyolefin reacted with at least one vinyl monomer having an acid group thereon. Further described is a method for conducting an acid-promoted chemical reaction, wherein an acid-reactive organic precursor is contacted inmore » liquid form with a solid heterogeneous acid catalyst comprising a polyolefin backbone of at least 1 micron in one dimension and having carboxylic acid groups and either sulfonic acid or phosphoric acid groups appended thereto.« less

A computational study of ultrafast acid dissociation and acid-base neutralization reactions. I. The model.

PubMed

Maurer, Patrick; Thomas, Vibin; Rivard, Ugo; Iftimie, Radu

2010-07-28

Ultrafast, time-resolved investigations of acid-base neutralization reactions have recently been performed using systems containing the photoacid 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt (HPTS) and various Bronsted bases. Two conflicting neutralization mechanisms have been formulated by Mohammed et al. [Science 310, 83 (2005)] and Siwick et al. [J. Am. Chem. Soc. 129, 13412 (2007)] for the same acid-base system. Herein an ab initio molecular dynamics based computational model is formulated, which is able to investigate the validity of the proposed mechanisms in the general context of ground-state acid-base neutralization reactions. Our approach consists of using 2,4,6-tricyanophenol (exp. pKa congruent with 1) as a model for excited-state HPTS( *) (pKa congruent with 1.4) and carboxylate ions for the accepting base. We employ our recently proposed dipole-field/quantum mechanics (QM) treatment [P. Maurer and R. Iftimie, J. Chem. Phys. 132, 074112 (2010)] of the proton donor and acceptor molecules. This approach allows one to tune the free energy of neutralization to any desired value as well as model initial nonequilibrium hydration effects caused by a sudden increase in acidity, making it possible to achieve a more realistic comparison with experimental data than could be obtained via a full-QM treatment of the entire system. It is demonstrated that the dipole-field/QM model reproduces correctly key properties of the 2,4,6-tricyanophenol acid molecule including gas-phase proton dissociation energies and dipole moments, and condensed-phase hydration structure and pKa values.

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.

Accelerated isothermal nucleic acid amplification in betaine-free reaction.

PubMed

Ma, Cuiping; Wang, Yifan; Zhang, Pansong; Shi, Chao

2017-08-01

Betaine was used as a common additive to isothermal nucleic acid amplification reactions because of lowering the melting temperature (Tm) of DNA. Herein, we reported a novel finding that betaine was inhibiting the reaction efficiency of isothermal amplification reactions. In this work, we have verified this finding by classical loop-mediated isothermal amplification that the addition of 0.8 M betaine inhibited the efficiency of reaction dropping to approximately 1%. Additionally, we clarified the mechanism of betaine hindering isothermal amplification reactions with a molecular barrier to lower associate rate constant K1 for intermolecular hybridization. This finding would be very significant for studies on the interaction between small molecule substance and DNA, and the development of point-of-care testing because of simplifying reaction system and increasing reaction efficiency. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

Unified path integral approach to theories of diffusion-influenced reactions

NASA Astrophysics Data System (ADS)

Prüstel, Thorsten; Meier-Schellersheim, Martin

2017-08-01

Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

Diffusion-controlled reactions modeling in Geant4-DNA

NASA Astrophysics Data System (ADS)

Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Ivantchenko, A.; Mantero, A.; Nieminem, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.

2014-10-01

Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k-d tree data structure for quickly locating, for a given molecule, its closest reactants. The

Diffusion-controlled reactions modeling in Geant4-DNA

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

Karamitros, M., E-mail: matkara@gmail.com; CNRS, INCIA, UMR 5287, F-33400 Talence; Luan, S.

2014-10-01

Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing allmore » the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

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

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

Photochemical reaction of 2-(3-benzoylphenyl)propionic acid (ketoprofen) with basic amino acids and dipeptides.

PubMed

Suzuki, Tadashi; Shinoda, Mio; Osanai, Yohei; Isozaki, Tasuku

2013-08-22

Photoreaction of 2-(3-benzoylphenyl)propionic acid (ketoprofen, KP) with basic amino acids (histidine, lysine, and arginine) and dipeptides (carnosine and anserine) including a histidine moiety in phosphate buffer solution (pH 7.4) has been investigated with transient absorption spectroscopy. With UV irradiation KP(-) gave rise to a carbanion through a decarboxylation reaction, and the carbanion easily abstracted a proton from the surrounding molecule to yield a 3-ethylbenzophenone ketyl biradical (EBPH). The dipeptides as well as the basic amino acids were found to accelerate the proton transfer reaction whereas alanine and glycine had no effect on the reaction, revealing that these amino acids having a protonated side chain act as a proton donor. The formation quantum yield of EBPH was estimated to be fairly large by means of an actinometrical method with benzophenone, and the bimolecular reaction rate constant for the proton transfer between the carbanion and the protonated basic amino acids or the protonated dipeptides was successfully determined. It has become apparent that the bimolecular reaction rate constant for the proton transfer depended on the acid dissociation constant for the side chain of the amino acids for the first time. This reaction mechanism was interpreted by difference of the heat of reaction for each basic amino acid based on the thermodynamical consideration. These results strongly suggest that the side chain of the basic amino acid residue in protein should play an important role for photochemistry of KP in vivo.

Multiphase chemical kinetics of OH radical uptake by molecular organic markers of biomass burning aerosols: humidity and temperature dependence, surface reaction, and bulk diffusion.

PubMed

Arangio, Andrea M; Slade, Jonathan H; Berkemeier, Thomas; Pöschl, Ulrich; Knopf, Daniel A; Shiraiwa, Manabu

2015-05-14

Multiphase reactions of OH radicals are among the most important pathways of chemical aging of organic aerosols in the atmosphere. Reactive uptake of OH by organic compounds has been observed in a number of studies, but the kinetics of mass transport and chemical reaction are still not fully understood. Here we apply the kinetic multilayer model of gas-particle interactions (KM-GAP) to experimental data from OH exposure studies of levoglucosan and abietic acid, which serve as surrogates and molecular markers of biomass burning aerosol (BBA). The model accounts for gas-phase diffusion within a cylindrical coated-wall flow tube, reversible adsorption of OH, surface-bulk exchange, bulk diffusion, and chemical reactions at the surface and in the bulk of the condensed phase. The nonlinear dependence of OH uptake coefficients on reactant concentrations and time can be reproduced by KM-GAP. We find that the bulk diffusion coefficient of the organic molecules is approximately 10(-16) cm(2) s(-1), reflecting an amorphous semisolid state of the organic substrates. The OH uptake is governed by reaction at or near the surface and can be kinetically limited by surface-bulk exchange or bulk diffusion of the organic reactants. Estimates of the chemical half-life of levoglucosan in 200 nm particles in a biomass burning plume increase from 1 day at high relative humidity to 1 week under dry conditions. In BBA particles transported to the free troposphere, the chemical half-life of levoglucosan can exceed 1 month due to slow bulk diffusion in a glassy matrix at low temperature.

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.

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.

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.

Sub-millitesla magnetic field effects on the recombination reaction of flavin and ascorbic acid radicals

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

Evans, Emrys W.; Henbest, Kevin B.; Timmel, Christiane R., E-mail: christiane.timmel@chem.ox.ac.uk, E-mail: stuart.mackenzie@chem.ox.ac.uk

Even though the interaction of a <1 mT magnetic field with an electron spin is less than a millionth of the thermal energy at room temperature (k{sub B}T), it still can have a profound effect on the quantum yields of radical pair reactions. We present a study of the effects of sub-millitesla magnetic fields on the photoreaction of flavin mononucleotide with ascorbic acid. Direct control of the reaction pathway is achieved by varying the rate of electron transfer from ascorbic acid to the photo-excited flavin. At pH 7.0, we verify the theoretical prediction that, apart from a sign change, themore » form of the magnetic field effect is independent of the initial spin configuration of the radical pair. The data agree well with model calculations based on a Green’s function approach that allows multinuclear spin systems to be treated including the diffusive motion of the radicals, their spin-selective recombination reactions, and the effects of the inter-radical exchange interaction. The protonation states of the radicals are uniquely determined from the form of the magnetic field-dependence. At pH 3.0, the effects of two chemically distinct radical pair complexes combine to produce a pronounced response to ∼500 μT magnetic fields. These findings are relevant to the magnetic responses of cryptochromes (flavin-containing proteins proposed as magnetoreceptors in birds) and may aid the evaluation of effects of weak magnetic fields on other biologically relevant electron transfer processes.« less

40 CFR 721.4385 - Hydrofluoric acid, reaction products with heptane.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Hydrofluoric acid, reaction products... Specific Chemical Substances § 721.4385 Hydrofluoric acid, reaction products with heptane. (a) Chemical... hydrofluoric acid, reaction products with heptane (PMN P-98-1036; CAS No. 207409-71-0) is subject to reporting...

40 CFR 721.4385 - Hydrofluoric acid, reaction products with heptane.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Hydrofluoric acid, reaction products... Specific Chemical Substances § 721.4385 Hydrofluoric acid, reaction products with heptane. (a) Chemical... hydrofluoric acid, reaction products with heptane (PMN P-98-1036; CAS No. 207409-71-0) is subject to reporting...

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.

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

A fractional reaction-diffusion description of supply and demand

NASA Astrophysics Data System (ADS)

Benzaquen, Michael; Bouchaud, Jean-Philippe

2018-02-01

We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Reaction of atomic hydrogen with formic acid.

PubMed

Cao, Qian; Berski, Slawomir; Latajka, Zdzislaw; Räsänen, Markku; Khriachtchev, Leonid

2014-04-07

We study the reaction of atomic hydrogen with formic acid and characterize the radical products using IR spectroscopy in a Kr matrix and quantum chemical calculations. The reaction first leads to the formation of an intermediate radical trans-H2COOH, which converts to the more stable radical trans-cis-HC(OH)2via hydrogen atom tunneling on a timescale of hours at 4.3 K. These open-shell species are observed for the first time as well as a reaction between atomic hydrogen and formic acid. The structural assignment is aided by extensive deuteration experiments and ab initio calculations at the UMP2 and UCCSD(T) levels of theory. The simplest geminal diol radical trans-cis-HC(OH)2 identified in the present work as the final product of the reaction should be very reactive, and further reaction channels are of particular interest. These reactions and species may constitute new channels for the initiation and propagation of more complex organic species in the interstellar clouds.

Investigation and kinetic evaluation of the reactions of hydroxymethylfurfural with amino and thiol groups of amino acids.

PubMed

Hamzalıoğlu, Aytül; Gökmen, Vural

2018-02-01

In this study, reactions of hydroxymethylfurfural (HMF) with selected amino acids (arginine, cysteine and lysine) were investigated in HMF-amino acid (high moisture) and Coffee-amino acid (low moisture) model systems at 5, 25 and 50°C. The results revealed that HMF reacted efficiently and effectively with amino acids in both high and low moisture model systems. High-resolution mass spectrometry (HRMS) analyses of the reaction mixtures confirmed the formations of Michael adduct and Schiff base of HMF with amino acids. Calculated pseudo-first order reaction rate constants were in the following order; k Cysteine >k Arginine >k Lysine for high moisture model systems. Comparing to these rate constants, the k Cysteine decreased whereas, k Arginine and k Lysine increased under the low moisture conditions of Coffee-amino acid model systems. The temperature dependence of the rate constants was found to obey the Arrhenius law in a temperature range of 5-50°C under both low and high moisture conditions. Copyright © 2017 Elsevier Ltd. All rights reserved.

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 0diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Generating Textures for Arbitrary Surfaces Using Reaction-Diffusion

DTIC Science & Technology

1990-01-01

Review and Classification," Computer Aided Design, Vol. 20, No. 1, pp. 27-38 (January/February 1988). [ Hubel and Wiesel 79] Hubel , David H. and...columns found in mammals [ Hubel and Wiesel 791. Complex Patterns This section shows how we can generate more complex patterns using reaction-diffusion by... Torsten N. Wiesel , "Brain Mechanisms of Vision," Scientific American, Vol. 241, No. 3, pp. 150-162 (September 1979). [Hunding 90] Hunding, Axel, Stuart A

Model Experiment of Thermal Runaway Reactions Using the Aluminum-Hydrochloric Acid Reaction

ERIC Educational Resources Information Center

Kitabayashi, Suguru; Nakano, Masayoshi; Nishikawa, Kazuyuki; Koga, Nobuyoshi

2016-01-01

A laboratory exercise for the education of students about thermal runaway reactions based on the reaction between aluminum and hydrochloric acid as a model reaction is proposed. In the introductory part of the exercise, the induction period and subsequent thermal runaway behavior are evaluated via a simple observation of hydrogen gas evolution and…

Diffusion of U(VI) in Opalinus Clay: Influence of temperature and humic acid

NASA Astrophysics Data System (ADS)

Joseph, C.; Van Loon, L. R.; Jakob, A.; Steudtner, R.; Schmeide, K.; Sachs, S.; Bernhard, G.

2013-05-01

The diffusion of U(VI) (c0 = 1 × 10-6 mol/L) in compacted Opalinus Clay from the Mont Terri underground laboratory, Switzerland, was studied in the absence and presence of humic acid (10 mg/L) at two different temperatures (25 °C, 60 °C) under anaerobic conditions. As background electrolyte synthetic Opalinus Clay pore water (pH 7.6, I = 0.36 mol/L) was used. The diffusion-accessible porosity, ɛ, was determined for each Opalinus Clay bore core sample by through-diffusion experiments with tritiated water (HTO) before the U(VI) diffusion experiments were carried out. The values for the effective diffusion and distribution coefficients De and Kd obtained for U(VI) and humic acid at 25 °C as well as at 60 °C showed that humic acid has no significant influence on the U(VI) diffusion. The diffusion profiles of humic acid in Opalinus Clay at 25 and 60 °C indicate the contributions of two different humic acid particle size fractions (<1 kDa and 10-100 kDa). The small-sized humic acid fraction diffused through the whole Opalinus Clay samples at both temperatures within the 3 month duration of the U(VI) diffusion experiments. At 60 °C, diffusion profiles of two different U(VI) species were observed. In a separate experiment the U(VI) speciation in the source reservoir solution at 60 °C was analyzed by laser-induced fluorescence spectroscopy, photon correlation spectroscopy and scanning electron microscopy with an energy dispersive X-ray detector. The two diffusion profiles could be attributed to an unknown colloidal and a known aquatic U(VI) species (Ca2UO2(CO3)3(aq)). The diffusion results showed that the interaction of U(VI) and of the large-sized humic acid colloid fraction with the clay is stronger at 60 °C. An increase of Kd from 0.025 ± 0.003 m3/kg at 25 °C to 0.25 ± 0.05 m3/kg for U(VI)colloidal at 60 °C was determined. In addition, the value for De of U(VI) increased with increasing temperature. Using the De values at 25 and 60 °C, a preliminary

[Effect of phosphatidic acid on the reaction of linoleic acid oxidation by 5-lipooxygenase from potatoes].

PubMed

Skaterna, T D; Kharchenko, O V

2008-01-01

Influence of anionogenic phospholipid of phosphatidic acid (PA) on oxidation of linoleic acid by 5-lipoxygenase (5-LO) from Solanum tuberosum was studied. The influence of PA was studied in micellar system which consisted of mixed micelles of linolenic acid (LK), Lubrol PX and different quantity of enzyme effector PA. The reaction was initiated by addition of 5-LO. It was established that 5-LO had two pHopt. in the presence of 50 microM phosphatidic acid: pH 5.0 and 6.9. In concentration of 50 microM PA was able to activate 5-LO 15 times at pH 5.0. The reaction maximum velocity (Vmax) coincided with Vmax of lipoxygenase reaction without the effector at pH 6.9 under such conditions. It was found that 30-50 microM phospholipid in the reaction mixture decreased the concentration of half saturation by the substrate by 43-67%. The enzyme demonstrated positive cooperation in respect of the substrate, the reaction is described by the Hill equation. Hill coefficient value (h) of the substrate was 3.34 +/- 0.22 (pH 6.9) and 5.61 +/- 0.88 (pH 5.0), that is with the change of pH to acidic region the number of substrate molecules increased and they could interact with the enzyme molecule. In case of substrate insufficiency the enzyme demonstrated positive cooperation of PA, it added from 4 to 3 effectors' molecules at pH 5.0, that is the phospholipid acted as the allosteric regulator of 5-LO. A comparative analysis of the influence of 4-hydroxy-TEMPO displayed, that the level of nonenzymatic processes in the case of physiological pH values was lower by 15-50% in the presence of PA in the range of 30-80 microM than without the effector.

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.

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.

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.

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.

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.

In vitro antioxidant and cytoprotective properties of Maillard reaction products from phloridzin-amino acid model systems.

PubMed

Han, Linna; Li, Feng; Yu, Qijian; Li, Dapeng

2018-01-01

The aim of this study was to investigate in vitro antioxidant activities and cytoprotective effect of Maillard reaction products (MRPs) from phloridzin (Pz)-amino acid model systems. Their structures were also characterised by Fourier transform-infrared spectroscopy (FTIR). MRPs were prepared from the Pz-methionine (Met), Pz-lysine (Lys), Pz-isoleucine (Ile), Pz-histidine (His) or Pz-glutamic acid (Glu) model system. The Pz-Lys MRPs, rich in antioxidant potency, were subjected to ultrafiltration to yield four MRPs fractions with different molecular weights (Mw). The fraction with Mw 30-50 kDa had significantly (P < 0.05) higher antioxidant activity than other fractions. Moreover, it significantly (P < 0.05) attenuated the 2,2'-azobis(2-methylpropionamidine) dihydrochloride (AAPH)-elicited decrease in cell viability in HepG2 cells in a concentration-dependent manner. FTIR analysis indicated that the fraction with Mw 30-50 kDa had the strong stretching vibration for the OH, NH, CH, CO and CC groups, suggesting the formation of intermediate MRPs during Maillard reaction. The results obtained in this study may provide some basis for the purported health-promoting effects of MRPs and their potential application as antioxidant agents in food industry. Also, it is important for our understanding of the variation of bioactive substances in food during thermal processing. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

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.

Alcohols enhance the rate of acetic acid diffusion in S. cerevisiae: biophysical mechanisms and implications for acetic acid tolerance.

PubMed

Lindahl, Lina; Genheden, Samuel; Faria-Oliveira, Fábio; Allard, Stefan; Eriksson, Leif A; Olsson, Lisbeth; Bettiga, Maurizio

2017-12-01

Microbial cell factories with the ability to maintain high productivity in the presence of weak organic acids, such as acetic acid, are required in many industrial processes. For example, fermentation media derived from lignocellulosic biomass are rich in acetic acid and other weak acids. The rate of diffusional entry of acetic acid is one parameter determining the ability of microorganisms to tolerance the acid. The present study demonstrates that the rate of acetic acid diffusion in S. cerevisiae is strongly affected by the alcohols ethanol and n-butanol. Ethanol of 40 g/L and n-butanol of 8 g/L both caused a 65% increase in the rate of acetic acid diffusion, and higher alcohol concentrations caused even greater increases. Molecular dynamics simulations of membrane dynamics in the presence of alcohols demonstrated that the partitioning of alcohols to the head group region of the lipid bilayer causes a considerable increase in the membrane area, together with reduced membrane thickness and lipid order. These changes in physiochemical membrane properties lead to an increased number of water molecules in the membrane interior, providing biophysical mechanisms for the alcohol-induced increase in acetic acid diffusion rate. n-butanol affected S. cerevisiae and the cell membrane properties at lower concentrations than ethanol, due to greater and deeper partitioning in the membrane. This study demonstrates that the rate of acetic acid diffusion can be strongly affected by compounds that partition into the cell membrane, and highlights the need for considering interaction effects between compounds in the design of microbial processes.

Alcohols enhance the rate of acetic acid diffusion in S. cerevisiae: biophysical mechanisms and implications for acetic acid tolerance

PubMed Central

Lindahl, Lina; Genheden, Samuel; Faria-Oliveira, Fábio; Allard, Stefan; Eriksson, Leif A.; Olsson, Lisbeth; Bettiga, Maurizio

2017-01-01

Microbial cell factories with the ability to maintain high productivity in the presence of weak organic acids, such as acetic acid, are required in many industrial processes. For example, fermentation media derived from lignocellulosic biomass are rich in acetic acid and other weak acids. The rate of diffusional entry of acetic acid is one parameter determining the ability of microorganisms to tolerance the acid. The present study demonstrates that the rate of acetic acid diffusion in S. cerevisiae is strongly affected by the alcohols ethanol and n-butanol. Ethanol of 40 g/L and n-butanol of 8 g/L both caused a 65% increase in the rate of acetic acid diffusion, and higher alcohol concentrations caused even greater increases. Molecular dynamics simulations of membrane dynamics in the presence of alcohols demonstrated that the partitioning of alcohols to the head group region of the lipid bilayer causes a considerable increase in the membrane area, together with reduced membrane thickness and lipid order. These changes in physiochemical membrane properties lead to an increased number of water molecules in the membrane interior, providing biophysical mechanisms for the alcohol-induced increase in acetic acid diffusion rate. n-butanol affected S. cerevisiae and the cell membrane properties at lower concentrations than ethanol, due to greater and deeper partitioning in the membrane. This study demonstrates that the rate of acetic acid diffusion can be strongly affected by compounds that partition into the cell membrane, and highlights the need for considering interaction effects between compounds in the design of microbial processes. PMID:29354649

[Study of Reaction Dynamics between Bovine Serum Albumin and Folic Acid by Stopped-Flow/Fluorescence].

PubMed

Ye, San-xian; Luo, Yun-jing; Qiao, Shu-liang; Li, Li; Liu, Cai-hong; Shi, Jian-long; An, Xue-jing

2016-01-01

As a kind of coenzyme of one-carbon enzymes in vivo, folic acid belongs to B vitamins, which can interact with other vitamins and has great significance for converting among amino acids, dividing growth of cells and protein synthesis reactions. Half-life, concentration and reaction rate constant of drugs are important parameters in pharmacokinetic study. In this paper, by utilizing fluorescence spectrophotometer and stopped-flow spectrum analyzer, reaction kinetic parameters between bovine serum albumin(BSA) and folic acid in a bionic system have been investigated, which provide references for parameters of drug metabolism related to folic acid. By using Stern-Volmer equation dealing with fluorescence quenching experiments data, we concluded that under 25, 30, and 37 degrees C, the static quenching constants of folic acid to intrinsic fluorescence from bovine serum albumin were 2.455 x 10(10), 4.900 x 10(10) and 6.427 x 10(10) L x mol(-1) x s(-1) respectively; The results of kinetic reaction rate have shown that the reaction rate of BSA and folic acid are greater than 100 mol x L(-1) x s(-1) at different temperatures, pH and buffering media, illustrating that the quenching mechanism between BSA and folic acid is to form composite static quenching process. Reaction concentration of bovine serum albumin and its initial concentration were equal to the secondary reaction formula, and the correlation coefficient was 0.998 7, while the half-life (t1/2) was 0.059 s at physiological temperature. With the increase of folic acid concentration, the apparent rate constant of this reaction had a linear increasing trend, the BSA fluorescence quenching rate constant catalyzed by folic acid was 3.174 x 10(5) mol x L(-1) x s(-1). Furthermore, with different buffer, the apparent rate constant and reaction rate constant of BSA interacting with folic acid were detected to explore the influence on the reaction under physiological medium, which is of great significance to determine the

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.

Critical time scales for advection-diffusion-reaction processes.

PubMed

Ellery, Adam J; Simpson, Matthew J; McCue, Scott W; Baker, Ruth E

2012-04-01

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J. 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. E 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math. 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

40 CFR 721.9484 - Dimer acid/rosin amidoamine reaction product (generic).

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Dimer acid/rosin amidoamine reaction... Specific Chemical Substances § 721.9484 Dimer acid/rosin amidoamine reaction product (generic). (a... generically as Dimer acid/rosin amidoamine reaction product (PMN P-99-0143) is subject to reporting under this...

40 CFR 721.4461 - Hydrofluoric acid, reaction products with octane (generic).

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Hydrofluoric acid, reaction products... New Uses for Specific Chemical Substances § 721.4461 Hydrofluoric acid, reaction products with octane... identified generically as a hydrofluoric acid, reaction products with octane (PMN P-99-0052) is subject to...

40 CFR 721.4461 - Hydrofluoric acid, reaction products with octane (generic).

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Hydrofluoric acid, reaction products... New Uses for Specific Chemical Substances § 721.4461 Hydrofluoric acid, reaction products with octane... identified generically as a hydrofluoric acid, reaction products with octane (PMN P-99-0052) is subject to...

40 CFR 721.9484 - Dimer acid/rosin amidoamine reaction product (generic).

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Dimer acid/rosin amidoamine reaction... Specific Chemical Substances § 721.9484 Dimer acid/rosin amidoamine reaction product (generic). (a... generically as Dimer acid/rosin amidoamine reaction product (PMN P-99-0143) is subject to reporting under this...

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

Electro-fenton and photoelectro-fenton degradation of sulfanilic acid using a boron-doped diamond anode and an air diffusion cathode.

PubMed

El-Ghenymy, Abdellatif; Garrido, José Antonio; Centellas, Francesc; Arias, Conchita; Cabot, Pere Lluís; Rodríguez, Rosa María; Brillas, Enric

2012-04-05

The mineralization of sulfanilic acid has been studied by electro-Fenton (EF) and photoelectro-Fenton (PEF) reaction with UVA light using an undivided electrochemical cell with a boron-doped diamond (BDD) anode and an air diffusion cathode able to generate H(2)O(2). Organics were then oxidized by hydroxyl radicals formed at the anode surface from water oxidation and in the bulk from Fenton's reaction between generated H(2)O(2) and added Fe(2+). The UVA irradiation in PEF enhanced the production of hydroxyl radicals in the bulk, accelerating the removal of organics and photodecomposed intermediates like Fe(III)-carboxylate complexes. Partial decontamination of 1.39 mM sulfanilic acid solutions was achieved by EF until 100 mA cm(-2) at optimum conditions of 0.4 mM Fe(2+) and pH 3.0. The increase in current density and substrate content led to an almost total mineralization. In contrast, the PEF process was more powerful, yielding almost complete mineralization in less electrolysis time under comparable conditions. The kinetics for sulfanilic acid decay always followed a pseudo-first-order reaction. Hydroquinone and p-benzoquinone were detected as aromatic intermediates, whereas acetic, maleic, formic, oxalic, and oxamic acids were identified as generated carboxylic acids. NH(4)(+) ion was preferentially released in both treatments, along with NO(3)(-) ion in smaller proportion.

The reaction of iodobenzene-p-sulphonyl chloride (pipsyl chloride) with certain amino acids and peptides, and with insulin

PubMed Central

Fletcher, J. C.

1967-01-01

1. A system of separation using buffered Celite columns is described that enables the pipsyl derivatives of most of the common amino acids to be separated. 2. The reaction of pipsyl chloride with several amino acids not included in previous studies has been investigated. In particular, knowledge of the acid-soluble pipsyl derivatives of arginine, histidine, lysine, tyrosine and cysteic acid has been extended. 3. Reproducible factors have been obtained that enable corrections to be applied for the breakdown of pipsylamino acids on acid hydrolysis. 4. The reaction of pipsyl chloride with peptides has been studied under various conditions. 5. The extent of the reaction between pipsyl chloride and insulin depends on the nature of the solvent–buffer system, and under the best conditions so far found is about 75% complete. 6. In an Appendix, the separation of pipsylamino acids by thin-layer chromatography is described. PMID:16742498

Kinetics of intercalation of fluorescent probes in magnesium-aluminium layered double hydroxide within a multiscale reaction-diffusion framework

NASA Astrophysics Data System (ADS)

Saliba, Daniel; Al-Ghoul, Mazen

2016-11-01

We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

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.

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 0diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t). PMID:25693183

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Turing instability in reaction-diffusion models on complex networks

NASA Astrophysics Data System (ADS)

Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya

2016-09-01

In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.

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.

Effect of surface curvature on diffusion-limited reactions on a curved surface

NASA Astrophysics Data System (ADS)

Eun, Changsun

2017-11-01

To investigate how the curvature of a reactive surface can affect reaction kinetics, we use a simple model in which a diffusion-limited bimolecular reaction occurs on a curved surface that is hollowed inward, flat, or extended outward while keeping the reactive area on the surface constant. By numerically solving the diffusion equation for this model using the finite element method, we find that the rate constant is a non-linear function of the surface curvature and that there is an optimal curvature providing the maximum value of the rate constant, which indicates that a spherical reactant whose entire surface is reactive (a uniformly reactive sphere) is not the most reactive species for a given reactive surface area. We discuss how this result arises from the interplay between two opposing effects: the exposedness of the reactive area to its partner reactants, which causes the rate constant to increase as the curvature increases, and the competition occurring on the reactive surface, which decreases the rate constant. This study helps us to understand the role of curvature in surface reactions and allows us to rationally design reactants that provide a high reaction rate.

Transport dissipative particle dynamics model for mesoscopic advection- diffusion-reaction problems

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

Zhen, Li; Yazdani, Alireza; Tartakovsky, Alexandre M.

2015-07-07

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic DPD framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between particles, and an analytical formula is proposed to relate the mesoscopic concentration friction to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPDmore » simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers.« less

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.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

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.

The chemisorption and reactions of formic acid on Cu films on ZnO (000 overline1)-O

NASA Astrophysics Data System (ADS)

Ludviksson, A.; Zhang, R.; Campbell, Charles T.; Griffiths, K.

1994-06-01

The adsorption and reactions of formic acid (HCOOD : HCOOH = 3:1) on the oxygen-terminated ZnO(0001¯)-O surface and on thin Cu films deposited on the ZnO(0001¯)-O surface have been studied with temperature programmed desorption (TPD) and XPS. Small amounts of formic acid dissociate at defect sites on clean ZnO(0001¯)-O to yield surface formate (HCOO). The acid D(H) from this dissociation does not reappear in TPD, and is lost to the ZnO bulk, as confirmed by nuclear reaction analysis. The surface HCOO decomposes to yield nearly simultaneous CO 2 (37%), CO (63%) and H 2 TPD peaks at 560 K. Substantial amounts of D (˜ 20%) are incorporated in this hydrogen TPD peak resulting from formate decomposition at ZnO defects, indicating that bulk D is readily accessible. Submonolayer and multilayer Cu films that are deposited at 130 K and partially cover the ZnO surface as 2D and 3D islands adsorb formic acid and decompose it into formate and hydrogen much like the Cu(110) surface. The surface formate from the Cu film decomposes at 470-500 K to give primarily CO 2 and H 2, also much like Cu(110), although atom-thin Cu islands also give ˜ 40% CO. Annealed Cu films give formate decomposition peaks at 25-50 K lower in temperature, attributed to thickening and ordering of the Cu islands to form Cu(111)-like sites. The acid D(H) atom from the formic acid is partially lost by hydrogen spillover from the Cu islands into the ZnO substrate, especially for thin Cu films. This effect partially desorbs and is enhanced upon preannealing the Cu layers, due to increased H diffusion rates across the annealed Cu islands, and/or the decrease in island size. Bulk D(H) is slowly removed as D 2, HD and H 2 above 400 K in diffusion-limited desorption, catalyzed by Cu.

Imino Acids in the Murchison Meteorite: Evidence of Strecker Reactions

NASA Technical Reports Server (NTRS)

Lerner, N. R.; Cooper, G. W.

2003-01-01

Both alpha-amino acids and alpha-hydroxy acids occur in aqueous extracts of the Murchison carbonaceous meteorite. The Strecker-cyanohydrin reaction, the reaction of carbonyl compounds, cyanide, and ammonia to produce amino and hydroxy acids, has been proposed as a source of such organic acids in meteorites. Such syntheses are consistent with the suggestion that interstellar precursors of meteoritic organic compounds accreted on the meteorite parent body together with other ices. Subsequent internal heating of the parent body melted these ices and led to the formation of larger compounds in synthetic reactions during aqueous alteration, which probably occurred at temperatures between 273K and 298K. In the laboratory, imino acids are observed as important by-products of the Strecker synthesis.

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

Interplay between inhibited transport and reaction in nanoporous materials

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

Ackerman, David Michael

2013-01-01

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

A theoretical study of concentration of profiles of primary cytochemical-enzyme reaction products in membrane-bound cell organelles and its application to lysosomal acid phosphatase.

PubMed

Cornelisse, C J; Hermens, W T; Joe, M T; Duijndam, W A; van Duijn, P

1976-11-01

A numerical method was developed for computing the steady-state concentration gradient of a diffusible enzyme reaction product in a membrane-limited compartment of a simplified theoretical cell model. In cytochemical enzyme reactions proceeding according to the metal-capture principle, the local concentration of the primary reaction product is an important factor in the onset of the precipitation process and in the distribution of the final reaction product. The following variables were incorporated into the model: enzyme activity, substrate concentration, Km, diffusion coefficient of substrate and product, particle radius and cell radius. The method was applied to lysosomal acid phosphatase. Numerical values for the variables were estimated from experimental data in the literature. The results show that the calculated phosphate concentrations inside lysosomes are several orders of magnitude lower than the critical concentrations for efficient phosphate capture found in a previous experimental model study. Reasons for this apparent discrepancy are discussed.

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.

[Effects of low molecular weight organic acids on redox reactions of mercury].

PubMed

Zhao, Shi-Bo; Sun, Rong-Guo; Wang, Ding-Yong; Wang, Xiao-Wen; Zhang, Cheng

2014-06-01

To study the effects of the main component of vegetation root exudates-low molecular weight organic acids on the redox reactions of mercury, laboratory experiments were conducted to investigate the roles of tartaric, citric, and succinic acid in the redox reactions of mercury, and to analyze their interaction mechanism. The results indicated that tartaric acid significantly stimulated the mercury reduction reaction, while citric acid had inhibitory effect. Succinic acid improved the reduction rate at low concentration, and inhibited the reaction at high concentration. The mercury reduction rate by tartaric acid treatment was second-order with respect to Hg2+ concentration, ranging from 0.0014 L x (ng x min)(-1) to 0.005 6 L x (ng x min)(-1). All three organic acids showed a capacity for oxidating Hg(0) in the early stage, but the oxidized Hg(0) was subsequently reduced. The oxidation capacity of the three organic acids was in the order of citric acid > tartaric acid > succinic acid.

Kinetics of browning and correlations between browning degree and pyrazine compounds in l-ascorbic acid/acidic amino acid model systems.

PubMed

Yu, Ai-Nong; Zhou, Yong-Yan; Yang, Yi-Ni

2017-04-15

The kinetics of browning and the correlation between browning products (BPs) and pyrazine compounds were investigated by heating equimolar l-ascorbic acid (ASA)/acidic amino acids under weak alkaline conditions at 120-150°C for 10-120min. The formations of BPs and pyrazine compounds from the reaction were monitored by UV-vis and SPME-GC-FID, respectively. The formation of BPs in both ASA/l-glutamic acid and ASA/l-aspartic acid model reaction systems followed zero order reaction kinetics with activation energies (E a ) of 90.13 and 93.38kJ/mol, respectively. ASA/l-aspartic acid browned at a slightly higher rate than ASA/l-glutamic acid. The total concentration of pyrazine compounds was highly and positively correlated with that of BPs. Based on the observed kinetic data, the formation mechanisms of BPs and pyrazine compounds were proposed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Fluorogenic, catalytic, photochemical reaction for amplified detection of nucleic acids.

PubMed

Dutta, Subrata; Fülöp, Annabelle; Mokhir, Andriy

2013-09-18

Photochemical, nucleic acid-induced reactions, which are controlled by nontoxic red light, are well-suited for detection of nucleic acids in live cells, since they do not require any additives and can be spatially and temporally regulated. We have recently described the first reaction of this type, in which a phenylselenyl derivative of thymidine (5'-PhSeT-ODNa) is cleaved in the presence of singlet oxygen (Fülöp, A., Peng, X., Greenberg, M. M., Mokhir, A. (2010) A nucleic acid directed, red light-induced chemical reaction. Chem. Commun. 46, 5659-5661). The latter reagent is produced upon exposure of a photosensitizer 3'-PS-ODNb (PS = Indium(III)-pyropheophorbide-a-chloride: InPPa) to >630 nm light. In 2012 we reported on a fluorogenic version of this reaction (Dutta, S., Flottmann, B., Heilemann, M., Mokhir, A. (2012) Hybridization and reaction-based, fluorogenic nucleic acid probes. Chem. Commun. 47, 9664-9666), which is potentially applicable for the detection of nucleic acids in cells. Unfortunately, its yield does not exceed 25% and no catalytic turnover could be observed in the presence of substrate excess. This problem occurs due to the efficient, competing oxidation of the substrate containing an electron rich carbon-carbon double bonds (SCH═CHS) in the presence of singlet oxygen with formation of a noncleavable product (SCH═CHSO). Herein we describe a related, but substantially improved photochemical, catalytic transformation of a fluorogenic, organic substrate, which consists of 9,10-dialkoxyanthracene linked to fluorescein, with formation of a bright fluorescent dye. In highly dilute solution this reaction occurs only in the presence of a nucleic acid template. We developed three types of such a reaction and demonstrated that they are high yielding and generate over 7.7 catalytic turnovers, are sensitive to single mismatches in nucleic acid targets, and can be applied for determination of both the amount of nucleic acids and potentially their

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

Critical time scales for advection-diffusion-reaction processes

NASA Astrophysics Data System (ADS)

Ellery, Adam J.; Simpson, Matthew J.; McCue, Scott W.; Baker, Ruth E.

2012-04-01

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J.BIOJAU0006-349510.1016/j.bpj.2010.07.045 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.051906 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/47.2.193 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

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.

Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks

NASA Astrophysics Data System (ADS)

Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.

2018-04-01

Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.

Glucose Sensing with Phenylboronic Acid Functionalized Hydrogel-Based Optical Diffusers

PubMed Central

2018-01-01

Phenylboronic acids have emerged as synthetic receptors that can reversibly bind to cis-diols of glucose molecules. The incorporation of phenylboronic acids in hydrogels offers exclusive attributes; for example, the binding process with glucose induces Donnan osmotic pressure resulting in volumetric changes in the matrix. However, their practical applications are hindered because of complex readout approaches and their time-consuming fabrication processes. Here, we demonstrate a microimprinting method to fabricate densely packed concavities in phenylboronic acid functionalized hydrogel films. A microengineered optical diffuser structure was imprinted on a phenylboronic acid based cis-diol recognizing motif prepositioned in a hydrogel film. The diffuser structure engineered on the hydrogel was based on laser-inscribed arrays of imperfect microlenses that focused the incoming light at different focal lengths and direction resulting in a diffused profile of light in transmission and reflection readout modes. The signature of the dimensional modulation was detected in terms of changing focal lengths of the microlenses due to the volumetric expansion of the hydrogel that altered the diffusion spectra and transmitted beam profile. The transmitted optical light spread and intensity through the sensor was measured to determine variation in glucose concentrations at physiological conditions. The sensor was integrated in a contact lens and placed over an artificial eye. Artificial stimulation of variation in glucose concentration allowed quantitative measurements using a smartphone’s photodiode. A smartphone app was utilized to convert the received light intensity to quantitative glucose concentration values. The developed sensing platform offers low cost, rapid fabrication, and easy detection scheme as compared to other optical sensing counterparts. The presented detection scheme may have applications in wearable real-time biomarker monitoring devices at point

Reaction-diffusion waves in neuronal tissue and the window of cortical excitability

NASA Astrophysics Data System (ADS)

Dahlem, M. A.; Müller, S. C.

2004-07-01

Spreading depression (SD) is a dynamic wave phenomenon occurring in all gray matter regions of the central nervous systems (CNS). It is characterized by a sudden breakdown of neuronal activity and accompanied by a massive influx and efflux of ions across the membrane of neurons. The retina is a constituent of the CNS in which one can easily observe the dynamic behavior of the SD wave fronts, because SD changes the optical properties of the tissue. There is ample evidence that SD belongs to the self-organization processes due to the coupling of reaction with diffusion in excitable medium. It is assumed that the occurrence of SD is associated with some neurological symptoms of migraine with aura. A frequently reported aura symptom is a traveling visual blind region (scotoma) with a preceding figure of scintillating line segments. The characteristic form and development of the scotoma suggests that the underlying phenomenon is a wave propagating through the primary visual cortex, most likely the cortical spreading depression. In this article we discuss similarities between SD waves and the migraine aura on the basis of properties of reaction-diffusion waves known from other excitable media. In particular, the propagation velocities, the shape and the dynamics of the waves are compared with each other. We find that the assumption of the neuronal tissue to be in a state of only weak excitability explains some properties of the migraine aura, such as the confined appearance and its propagation with a stable velocity.

Effects of phosphoric acid on the lead-acid battery reactions

NASA Astrophysics Data System (ADS)

Ikeda, Osamu; Iwakura, Chiaki; Yoneyama, Hiroshi; Tamura, Hideo

1986-10-01

The addition of a small amount of phosphoric acid to 5 M H2SO4 (commercial electrolyte of lead-acid batteries) results in various positive effects on the lead-acid battery reactions: (1) depression of the corrosion rate of the lead substrate through a preferential formation of alpha-PbO2 on the substrate surface; (2) retardation of hard sulfate formation or of deactivation of active materials; and (3) change in the crystal morphology of PbSO2 formed on the discharge of PbO2. Most of these effects results from chemisorption of phosphoric acid on PbSO4 crystals produced in the discharge process of PbO2.

Temperature influence on the malonic acid decomposition in the Belousov-Zhabotinsky reaction

NASA Astrophysics Data System (ADS)

Blagojević, S. M.; Anić, S. R.; Čupić, Ž. D.; Pejić, N. D.; Kolar-Anić, Lj. Z.

2009-09-01

The kinetic investigations of the malonic acid decomposition (8.00 × 10-3 mol dm-3 ≤ [CH2(COOH)2]0 ≤ 4.30 × 10-2 mol dm-3) in the Belousov-Zhabotinsky (BZ) system in the presence of bromate, bromide, sulfuric acid and cerium sulfate, were performed in the isothermal closed well stirred reactor at different temperatures (25.0°C ≤ T ≤ 45.0°C). The formal kinetics of the overall BZ reaction, and particularly kinetics in characteristic periods of BZ reaction, based on the analyses of the bromide oscillograms, was accomplished. The evolution as well as the rate constants and the apparent activation energies of the reactions, which exist in the preoscillatory and oscillatory periods, are also successfully calculated by numerical simulations. Simulations are based on the model including the Br2O species.

Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

PubMed

Lin, Zhongwei; Tropper, Carl; Mcdougal, Robert A; Patoary, Mohammand Nazrul Ishlam; Lytton, William W; Yao, Yiping; Hines, Michael L

2017-07-01

Cells exhibit stochastic behavior when the number of molecules is small. Hence a stochastic reaction-diffusion simulator capable of working at scale can provide a more accurate view of molecular dynamics within the cell. This paper describes a parallel discrete event simulator, Neuron Time Warp-Multi Thread (NTW-MT), developed for the simulation of reaction diffusion models of neurons. To the best of our knowledge, this is the first parallel discrete event simulator oriented towards stochastic simulation of chemical reactions in a neuron. The simulator was developed as part of the NEURON project. NTW-MT is optimistic and thread-based, which attempts to capitalize on multi-core architectures used in high performance machines. It makes use of a multi-level queue for the pending event set and a single roll-back message in place of individual anti-messages to disperse contention and decrease the overhead of processing rollbacks. Global Virtual Time is computed asynchronously both within and among processes to get rid of the overhead for synchronizing threads. Memory usage is managed in order to avoid locking and unlocking when allocating and de-allocating memory and to maximize cache locality. We verified our simulator on a calcium buffer model. We examined its performance on a calcium wave model, comparing it to the performance of a process based optimistic simulator and a threaded simulator which uses a single priority queue for each thread. Our multi-threaded simulator is shown to achieve superior performance to these simulators. Finally, we demonstrated the scalability of our simulator on a larger CICR model and a more detailed CICR model.

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

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.

Mathematical modeling of microbially induced crown corrosion in wastewater collection systems and laboratory investigation and modeling of sulfuric acid corrosion of concrete

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems

PubMed Central

Yazdani, Alireza; Tartakovsky, Alexandre; Karniadakis, George Em

2015-01-01

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between tDPD particles, and the advection is implicitly considered by the movements of these Lagrangian particles. An analytical formula is proposed to relate the tDPD parameters to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPD simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the conventional DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers. PMID:26156459

Aerosol-Forming Reactions of Glyoxal, Methylglyoxal and Amino Acids in Clouds

NASA Astrophysics Data System (ADS)

de Haan, D. O.; Smith, K. W.; Stroik, D. R.; Corrigan, A. L.; Lee, F. E.; Phan, J. T.; Conley, A. C.

2008-12-01

Glyoxal and methylglyoxal are two common aldehydes present in fog and cloud water. Amino acids are present in clouds at similar concentrations. Here we present bulk and aerosol mass spectroscopic data demonstrating that irreversible reactions between glyoxal and amino acids, triggered by droplet evaporation, produce N-derivatized imidazole compounds along with deeply colored Maillard reaction products. These reactions can occur in the dark and in the absence of oxidants. Reactions between methylglyoxal and amino acids produce analogous methylated products plus oligomers with masses up to m/z = 1000. These reactions, which go to completion on the 10-min-timescale of cloud processing, could be significant sources of secondary organic aerosol and humic-like substances (HULIS or brown carbon).

Lewis acid-Lewis acid heterobimetallic cooperative catalysis: mechanistic studies and application in enantioselective aza-Michael reaction.

PubMed

Yamagiwa, Noriyuki; Qin, Hongbo; Matsunaga, Shigeki; Shibasaki, Masakatsu

2005-09-28

The full details of a catalytic asymmetric aza-Michael reaction of methoxylamine promoted by rare earth-alkali metal heterobimetallic complexes are described, demonstrating the effectiveness of Lewis acid-Lewis acid cooperative catalysis. First, enones were used as substrates, and the 1,4-adducts were obtained in good yield (57-98%) and high ee (81-96%). Catalyst loading was successfully reduced to 0.3-3 mol % with enones. To broaden the substrate scope of the reaction to carboxylic acid derivatives, alpha,beta-unsaturated N-acylpyrroles were used as monodentate, carboxylic acid derivatives. With beta-alkyl-substituted N-acylpyrroles, the reaction proceeded smoothly and the products were obtained in high yield and good ee. Transformation of the 1,4-adducts from enones and alpha,beta-unsaturated N-acylpyrroles afforded corresponding chiral aziridines and beta-amino acids. Detailed mechanistic studies, including kinetics, NMR analysis, nonlinear effects, and rare earth metal effects, are also described. The Lewis acid-Lewis acid cooperative mechanism, including the substrate coordination mode, is discussed in detail.

The reaction of formic acid with RaneyTM copper

NASA Astrophysics Data System (ADS)

Callear, Samantha K.; Silverwood, Ian P.; Chutia, Arunabhiram; Catlow, C. Richard A.; Parker, Stewart F.

2016-04-01

The interaction of formic acid with RaneyTM Cu proves to be complex. Rather than the expected generation of a monolayer of bidentate formate, we find the formation of a Cu(II) compound. This process occurs by direct reaction of copper and formic acid; in contrast, previous methods are by solution reaction. This is a rare example of formic acid acting as an oxidant rather than, as more commonly found, a reductant. The combination of diffraction, spectroscopic and computational methods has allowed this unexpected process to be characterized.

MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

PubMed Central

BLANC, EMILIE; ENGBLOM, STEFAN; HELLANDER, ANDREAS; LÖTSTEDT, PER

2017-01-01

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again. PMID:29046618

Magnetite-supported sulfonic acid: a retrievable nanocatalyst for the Ritter reaction and multicomponent reactions

EPA Science Inventory

Magnetite-sulfonic acid (NanocatFe-OSO3H), prepared by wet-impregnation method, serves as a magnetically retrievable sustainable catalyst for the Ritter reaction which can be used in several reaction cycles without any loss of activity.

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.

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

PubMed

Jez, Joseph M; Noel, Joseph P

2002-01-11

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

Theoretical stusy of the reaction between 2,2',4' - trihydroxyazobenzene-5-sulfonic acid and zirconium

USGS Publications Warehouse

Fletcher, Mary H.

1960-01-01

Zirconium reacts with 2,2',4'-trihydroxyazobenzene-5-sulfonic acid in acid solutions to Form two complexes in which the ratios of dye to zirconium are 1 to 1 and 2 to 1. Both complexes are true chelates, with zirconium acting as a bridge between the two orthohydroxy dye groups. Apparent equilibrium constants for the reactions to form each of the complexes are determined. The reactions are used as a basis for the determination of the active component in the dye and a graphical method for the determination of reagent purity is described. Four absorption spectra covering the wave length region from 350 to 750 mu are given, which completely define the color system associated with the reactions in solutions where the hydrochloric acid concentration ranges from 0.0064N to about 7N.

Chemoselective O-acylation of hydroxyamino acids and amino alcohols under acidic reaction conditions: History, scope and applications

PubMed Central

2015-01-01

Summary Amino acids, whether natural, semisynthetic or synthetic, are among the most important and useful chiral building blocks available for organic chemical synthesis. In principle, they can function as inexpensive, chiral and densely functionalized starting materials. On the other hand, the use of amino acid starting materials routinely necessitates protective group chemistry, and in reality, large-scale preparations of even the simplest side-chain derivatives of many amino acids often become annoyingly strenuous due to the necessity of employing protecting groups, on one or more of the amino acid functionalities, during the synthetic sequence. However, in the case of hydroxyamino acids such as hydroxyproline, serine, threonine, tyrosine and 3,4-dihydroxyphenylalanine (DOPA), many O-acyl side-chain derivatives are directly accessible via a particularly expedient and scalable method not commonly applied until recently. Direct acylation of unprotected hydroxyamino acids with acyl halides or carboxylic anhydrides under appropriately acidic reaction conditions renders possible chemoselective O-acylation, furnishing the corresponding side-chain esters directly, on multigram-scale, in a single step, and without chromatographic purification. Assuming a certain degree of stability under acidic reaction conditions, the method is also applicable for a number of related compounds, such as various amino alcohols and the thiol-functional amino acid cysteine. While the basic methodology underlying this approach has been known for decades, it has evolved through recent developments connected to amino acid-derived chiral organocatalysts to become a more widely recognized procedure for large-scale preparation of many useful side-chain derivatives of hydroxyamino acids and related compounds. Such derivatives are useful in peptide chemistry and drug development, as amino acid amphiphiles for asymmetric catalysis, and as amino acid acrylic precursors for preparation of

Functionalization of Carbon Nanotubes via Electrophilic Substitution Reaction in Polyphosphoric Acid

DTIC Science & Technology

2006-07-26

1 Title of proposed research: Functionalization of Carbon Nanotubes via Electrophilic Substitution Reaction in Polyphosphoric Acid Proposer: Jong...Choi, J.-Y.; Tan, L.-S.; Baek, J.-B. “Functionalization of carbon nanotubes via electrophilic substitution reaction in polyphosphoric acid” AFOSR...2006 4. TITLE AND SUBTITLE Functionalization of carbon nanotubes via electrophilic substitution reaction in polyphosphoric acid 5a. CONTRACT

40 CFR 721.10211 - Octadecanoic acid, reaction products with diethylenetriamine and urea, acetates.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Octadecanoic acid, reaction products... SUBSTANCES Significant New Uses for Specific Chemical Substances § 721.10211 Octadecanoic acid, reaction... subject to reporting. (1) The chemical substance identified as octadecanoic acid, reaction products with...

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.

Gaseous diffusion system

DOEpatents

Garrett, George A.; Shacter, John

1978-01-01

1. A gaseous diffusion system comprising a plurality of diffusers connected in cascade to form a series of stages, each of said diffusers having a porous partition dividing it into a high pressure chamber and a low pressure chamber, and means for combining a portion of the enriched gas from a succeeding stage with a portion of the enriched gas from the low pressure chamber of each stage and feeding it into one extremity of the high pressure chamber thereof.

On Some Parabolic Type Problems from Thin Film Theory and Chemical Reaction-Diffusion Networks

NASA Astrophysics Data System (ADS)

Mohamed, Fatma Naser Ali

This dissertation considers some parabolic type problems from thin film theory and chemical reaction-diffusion networks. The dissertation consists of two parts: In the first part, we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove an existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that, in this case, the surface-tension energy dissipation is the mechanism responsible for the H1-norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type, are also successfully treated by the same means. [special characters omitted]. In the second part, we are concerned with the convergence of a certain space-discretization scheme -the so-called method of lines- for mass-action reaction-diffusion systems. First, we start with a toy model, namely. [special characters omitted]. and prove convergence of method of lines for this linear case. Here weak convergence in L2(0,1) is enough to prove convergence of the method of lines. Then we adopt the framework for convergence analysis introduced in [23] and concentrate on the proof-of-concept reaction. within 1D space, while at the same time noting that our techniques are readily generalizable to other reaction-diffusion networks and to more than one space dimension. Indeed, it will be obvious how to extend our proofs to the multi-dimensional case; we only note that the proof of the comparison principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream

Analysis of Classes of Singular Steady State Reaction Diffusion Equations

NASA Astrophysics Data System (ADS)

Son, Byungjae

We study positive radial solutions to classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We study both Laplacian as well as p-Laplacian problems with reaction terms that are p-sublinear at infinity. We consider both positone and semipositone reaction terms and establish existence, multiplicity and uniqueness results. Our existence and multiplicity results are achieved by a method of sub-supersolutions and uniqueness results via a combination of maximum principles, comparison principles, energy arguments and a-priori estimates. Our results significantly enhance the literature on p-sublinear positone and semipositone problems. Finally, we provide exact bifurcation curves for several one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and in the nonautonomous case, we employ shooting methods. We use numerical solvers in Mathematica to generate the bifurcation curves.

Modeling Studies of Inhomogeneity Effects during Laser Flash Photolysis Experiments: A Reaction-Diffusion Approach.

PubMed

Dóka, Éva; Lente, Gábor

2017-04-13

This work presents a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method. As an example, the aqueous reaction between the sulfate ion radical and iodide ion is used, for which sufficiently detailed experimental data are available from an earlier publication. The results showed that diffusion itself is in general too slow to influence the kinetic curves on the usual time scales of laser flash photolysis experiments. However, the use of the absorbances measured (e.g., to calculate the molar absorption coefficients of transient species) requires very detailed mathematical consideration and full knowledge of the geometrical shapes of the excitation laser beam and the separate detection light beam. It is also noted that the usual pseudo-first-order approach to evaluating the kinetic traces can be used successfully even if the usual large excess condition is not rigorously met in the reaction cell locally.

Temperature Dependence of Diffusion and Reaction at a Pd/SiC Contact

NASA Technical Reports Server (NTRS)

Shi, D.T.; Lu, W. J.; Bryant, E.; Elshot, K.; Lafate, K.; Chen, H.; Burger, A.; Collins, W. E.

1998-01-01

Schottky diodes of Palladium/SiC are good candidates for hydrogen and hydrocarbon gas sensors at elevated temperature. The detection sensibility of the diodes has been found heavily temperature dependent. In this work, emphasis has been put on the understanding of changes of physical and chemical properties of the Schottky diodes with variation of temperature. Schottky diodes were made by depositing ultra-thin palladium films onto silicon carbide substrates. The electrical and chemical properties of Pd/SiC Schottky contacts were studied by XPS and AES at different annealing temperatures. No significant change in the Schottky barrier height of the Pd/SiC contact was found in the temperature range of RT-400 C. However, both palladium diffused into SiC and silicon migrated into palladium thin film as well as onto surface were observed at room temperature. The formation of palladium compounds at the Pd/SiC interface was also observed. Both diffusion and reaction at the Pd/SiC interface became significant at 300 C and higher temperature. In addition, silicon oxide was found also at the interface of the Pd/SiC contact at high temperature. In this report, the mechanism of diffusion and reaction at the Pd/SiC interface will be discussed along with experimental approaches.

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.

Catalytical Conversion of Carbohydrates into Lactic Acid via Hydrothermal Reaction

NASA Astrophysics Data System (ADS)

Wei, Zhen; Jin, Fangming; Zhang, Guangyi; Zhang, Shiping; Yao, Guodong

2010-11-01

This paper focuses on catalytical conversion of carbohydrates into lactic acid, under the hydrothermal conditions, which may have a promising future for its high speediness and effectiveness. The catalysis of ZnO was investigated to improve the lactic acid yields. The results showed that the lactic acid yields increased immensely by the addition of ZnO. The effects of the reaction time and the addition amount of ZnO on the conversion of carbohydrates to lactic acid were studied. The highest lactic acid yields reached up to 28% starting from glucose after the reaction time of 60 s under the conditions of 0.2 mmol ZnO, 300° C, the filling rate of 35%, and over 30% starting from fructose at the same temperature and filling rate when the reaction time of 40 s and 2.0 mmol ZnO were employed. The collaborative effects of ZnO and NaOH used as the catalysts together at the same time were also studied. Furthermore, the catalytic mechanism of ZnO in the hydrothermal conversion of carbohydrates into lactic acid was discussed.

Atomistic modeling of water diffusion in hydrolytic biomaterials.

PubMed

Gautieri, Alfonso; Mezzanzanica, Andrea; Motta, Alberto; Redealli, Alberto; Vesentini, Simone

2012-04-01

One of the most promising applications of hydrolytically degrading biomaterials is their use as drug release carriers. These uses, however, require that the degradation and diffusion of drug are reliably predicted, which is complex to achieve through present experimental methods. Atomistic modeling can help in the knowledge-based design of degrading biomaterials with tuned drug delivery properties, giving insights on the small molecules diffusivity at intermediate states of the degradation process. We present here an atomistic-based approach to investigate the diffusion of water (through which hydrolytic degradation occurs) in degrading bulk models of poly(lactic acid) or PLA. We determine the water diffusion coefficient for different swelling states of the polymeric matrix (from almost dry to pure water) and for different degrees of degradation. We show that water diffusivity is highly influenced by the swelling degree, while little or not influenced by the degradation state. This approach, giving water diffusivity for different states of the matrix, can be combined with diffusion-reaction analytical methods in order to predict the degradation path on longer time scales. Furthermore, atomistic approach can be used to investigate diffusion of other relevant small molecules, eventually leading to the a priori knowledge of degradable biomaterials transport properties, helping the design of the drug delivery systems.

On the Maillard reaction of meteoritic amino acids

NASA Astrophysics Data System (ADS)

Kolb, Vera M.; Bajagic, Milica; Liesch, Patrick J.; Philip, Ajish; Cody, George D.

2006-08-01

We have performed the Maillard reaction of a series of meteoritic amino acids with sugar ribose under simulated prebiotic conditions, in the solid state at 65°C and at the room temperature. Many meteoritic amino acids are highly reactive with ribose, even at the room temperature. We have isolated high molecular weight products that are insoluble in water, and have studied their structure by the IR (infrared) and solid-state C-13 NMR (nuclear magnetic resonance) spectroscopic methods. The functional groups and their distribution were similar among these products, and were comparable to the previously isolated insoluble organic materials from the Maillard reaction of the common amino acids with ribose. In addition, there were some similarities with the insoluble organic material that is found on Murchison. Our results suggest that the Maillard products may contribute to the composition of the part of the insoluble organic material that is found on Murchison. We have also studied the reaction of sodium silicate solution with the Maillard mixtures, to elucidate the process by which the organic compounds are preserved under prebiotic conditions.

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.

In situ visualization of metallurgical reactions in nanoscale Cu/Sn diffusion couples

NASA Astrophysics Data System (ADS)

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

2015-03-01

The Cu-Sn metallurgical soldering reaction in two-segmented Cu-Sn nanowires is studied by in situ transmission electron microscopy. By varying the relative lengths of Cu and Sn segments, we show that the metallurgical reaction results in a Cu-Sn solid solution for small Sn/Cu length ratio while Cu-Sn intermetallic compounds (IMCs) for larger Sn/Cu length ratios. Upon heating the nanowires to ~500 °C, two phase transformation pathways occur, η-Cu6Sn5 --> ε-Cu3Sn --> δ-Cu41Sn11 for nanowires with a long Cu segment and η-Cu6Sn5 --> ε-Cu3Sn --> γ-Cu3Sn with a short Cu segment. The evolution of Kirkendall voids in the nanowires demonstrates that Cu diffuses faster than Sn in IMCs. Void growth results in the nanowire breakage that shuts off the inter-diffusion of Cu and Sn and thus leads to changes in the phase transformation pathway in the IMCs.

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 .

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.

Minoxidil Skin Delivery from Nanoemulsion Formulations Containing Eucalyptol or Oleic Acid: Enhanced Diffusivity and Follicular Targeting

PubMed Central

Abd, Eman; Benson, Heather A. E.; Roberts, Michael S.; Grice, Jeffrey E.

2018-01-01

In this work, we examined enhanced skin delivery of minoxidil applied in nanoemulsions incorporating skin penetration enhancers. Aliquots of fully characterized oil-in-water nanoemulsions (1 mL), containing minoxidil (2%) and the skin penetration enhancer oleic acid or eucalyptol as oil phases, were applied to full-thickness excised human skin in Franz diffusion cells, while aqueous solutions (1 mL) containing minoxidil were used as controls. Minoxidil in the stratum corneum (SC), hair follicles, deeper skin layers, and flux through the skin over 24 h was determined, as well as minoxidil solubility in the formulations and in the SC. The nanoemulsions significantly enhanced the permeation of minoxidil through skin compared with control solutions. The eucalyptol formulations (NE) promoted minoxidil retention in the SC and deeper skin layers more than did the oleic acid formulations, while the oleic acid formulations (NO) gave the greatest hair follicle penetration. Minoxidil maximum flux enhancement was associated with increases in both minoxidil SC solubility and skin diffusivity in both nanoemulsion systems. The mechanism of enhancement appeared to be driven largely by increased diffusivity, rather than increased partitioning into the stratum corneum, supporting the concept of enhanced fluidity and disruption of stratum corneum lipids. PMID:29370122

Wavefronts for a global reaction-diffusion population model with infinite distributed delay

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

We consider a global reaction-diffusion population model with infinite distributed delay which includes models of Nicholson's blowflies and hematopoiesis derived by Gurney, Mackey and Glass, respectively. The existence of monotone wavefronts is derived by using the abstract settings of functional differential equations and Schauder fixed point theory.

Weak Acid Ionization Constants and the Determination of Weak Acid-Weak Base Reaction Equilibrium Constants in the General Chemistry Laboratory

ERIC Educational Resources Information Center

Nyasulu, Frazier; McMills, Lauren; Barlag, Rebecca

2013-01-01

A laboratory to determine the equilibrium constants of weak acid negative weak base reactions is described. The equilibrium constants of component reactions when multiplied together equal the numerical value of the equilibrium constant of the summative reaction. The component reactions are weak acid ionization reactions, weak base hydrolysis…

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.

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.

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.

Quantitative modeling of the reaction/diffusion kinetics of two-chemistry photopolymers

NASA Astrophysics Data System (ADS)

Kowalski, Benjamin Andrew

Optically driven diffusion in photopolymers is an appealing material platform for a broad range of applications, in which the recorded refractive index patterns serve either as images (e.g. data storage, display holography) or as optical elements (e.g. custom GRIN components, integrated optical devices). A quantitative understanding of the reaction/diffusion kinetics is difficult to obtain directly, but is nevertheless necessary in order to fully exploit the wide array of design freedoms in these materials. A general strategy for characterizing these kinetics is proposed, in which key processes are decoupled and independently measured. This strategy enables prediction of a material's potential refractive index change, solely on the basis of its chemical components. The degree to which a material does not reach this potential reveals the fraction of monomer that has participated in unwanted reactions, reducing spatial resolution and dynamic range. This approach is demonstrated for a model material similar to commercial media, achieving quantitative predictions of index response over three orders of exposure dose (~1 to ~103 mJ cm-2) and three orders of feature size (0.35 to 500 microns). The resulting insights enable guided, rational design of new material formulations with demonstrated performance improvement.

Nucleic Acid Templated Reactions for Chemical Biology.

PubMed

Di Pisa, Margherita; Seitz, Oliver

2017-06-21

Nucleic acid directed bioorthogonal reactions offer the fascinating opportunity to unveil and redirect a plethora of intracellular mechanisms. Nano- to picomolar amounts of specific RNA molecules serve as templates and catalyze the selective formation of molecules that 1) exert biological effects, or 2) provide measurable signals for RNA detection. Turnover of reactants on the template is a valuable asset when concentrations of RNA templates are low. The idea is to use RNA-templated reactions to fully control the biodistribution of drugs and to push the detection limits of DNA or RNA analytes to extraordinary sensitivities. Herein we review recent and instructive examples of conditional synthesis or release of compounds for in cellulo protein interference and intracellular nucleic acid imaging. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Clustering mechanism of oxocarboxylic acids involving hydration reaction: Implications for the atmospheric models

NASA Astrophysics Data System (ADS)

Liu, Ling; Kupiainen-Määttä, Oona; Zhang, Haijie; Li, Hao; Zhong, Jie; Kurtén, Theo; Vehkamäki, Hanna; Zhang, Shaowen; Zhang, Yunhong; Ge, Maofa; Zhang, Xiuhui; Li, Zesheng

2018-06-01

The formation of atmospheric aerosol particles from condensable gases is a dominant source of particulate matter in the boundary layer, but the mechanism is still ambiguous. During the clustering process, precursors with different reactivities can induce various chemical reactions in addition to the formation of hydrogen bonds. However, the clustering mechanism involving chemical reactions is rarely considered in most of the nucleation process models. Oxocarboxylic acids are common compositions of secondary organic aerosol, but the role of oxocarboxylic acids in secondary organic aerosol formation is still not fully understood. In this paper, glyoxylic acid, the simplest and the most abundant atmospheric oxocarboxylic acid, has been selected as a representative example of oxocarboxylic acids in order to study the clustering mechanism involving hydration reactions using density functional theory combined with the Atmospheric Clusters Dynamic Code. The hydration reaction of glyoxylic acid can occur either in the gas phase or during the clustering process. Under atmospheric conditions, the total conversion ratio of glyoxylic acid to its hydration reaction product (2,2-dihydroxyacetic acid) in both gas phase and clusters can be up to 85%, and the product can further participate in the clustering process. The differences in cluster structures and properties induced by the hydration reaction lead to significant differences in cluster formation rates and pathways at relatively low temperatures.

Transport of Organic Compounds Through Porous Systems Containing Humic Acids.

PubMed

Smilek, Jiri; Sedlacek, Petr; Lastuvkova, Marcela; Kalina, Michal; Klucakova, Martina

2017-03-01

Soil pollution by the presence of different contaminants (e.g. heavy metal ions or pesticides) is one of the biggest problems worldwide. The positive affinity of natural humic acids towards these contaminants might contribute to the soil and ground water protection; therefore it is necessary to study the reactivity and barrier properties of humic acids. An original reactivity-mapping tool based on diffusion techniques designed to study the reactivity and barrier properties of polyelectrolytes was developed and tested on humic acids. The results of diffusion experiments demonstrate that the electrostatic interactions between humic acids functioning as a polyelectrolyte interpenetrated in a supporting hydrogel matrix (agarose) and cationic dye (methylene blue) as a model solute have a crucial impact on the rate of diffusion processes and on the barrier properties of hydrogels. The intensity of interactions was evaluated by fundamental diffusion parameters (effective diffusion coefficients and breakthrough time). The impact of modification of humic acids was also studied by means of diffusion experiments conducted on two types of standard humic acids (Leonardite 1S104H) and humic acids with selectively methylated carboxylic groups.

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

NASA Technical Reports Server (NTRS)

Plante, Ianik; Cucinotta, Francis A.

2011-01-01

Radiolytic species are formed approximately 1 ps after the passage of ionizing radiation through matter. After their formation, they diffuse and chemically react with other radiolytic species and neighboring biological molecules, leading to various oxidative damage. Therefore, the simulation of radiation chemistry is of considerable importance to understand how radiolytic species damage biological molecules [1]. The step-by-step simulation of chemical reactions is difficult, because the radiolytic species are distributed non-homogeneously in the medium. Consequently, computational approaches based on Green functions for diffusion-influenced reactions should be used [2]. Recently, Green functions for more complex type of reactions have been published [3-4]. We have developed exact random variate generators of these Green functions [5], which will allow us to use them in radiation chemistry codes. Moreover, simulating chemistry using the Green functions is which is computationally very demanding, because the probabilities of reactions between each pair of particles should be evaluated at each timestep [2]. This kind of problem is well adapted for General Purpose Graphic Processing Units (GPGPU), which can handle a large number of similar calculations simultaneously. These new developments will allow us to include more complex reactions in chemistry codes, and to improve the calculation time. This code should be of importance to link radiation track structure simulations and DNA damage models.

Continuous Flow Chemistry: Reaction of Diphenyldiazomethane with p-Nitrobenzoic Acid.

PubMed

Aw, Alex; Fritz, Marshall; Napoline, Jonathan W; Pollet, Pamela; Liotta, Charles L

2017-11-15

Continuous flow technology has been identified as instrumental for its environmental and economic advantages leveraging superior mixing, heat transfer and cost savings through the "scaling out" strategy as opposed to the traditional "scaling up". Herein, we report the reaction of diphenyldiazomethane with p-nitrobenzoic acid in both batch and flow modes. To effectively transfer the reaction from batch to flow mode, it is essential to first conduct the reaction in batch. As a consequence, the reaction of diphenyldiazomethane was first studied in batch as a function of temperature, reaction time, and concentration to obtain kinetic information and process parameters. The glass flow reactor set-up is described and combines two types of reaction modules with "mixing" and "linear" microstructures. Finally, the reaction of diphenyldiazomethane with p-nitrobenzoic acid was successfully conducted in the flow reactor, with up to 95% conversion of the diphenyldiazomethane in 11 min. This proof of concept reaction aims to provide insight for scientists to consider flow technology's competitiveness, sustainability, and versatility in their research.

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

40 CFR 721.9460 - Tall oil fatty acids, reaction products with polyamines, alkyl substituted.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Tall oil fatty acids, reaction... SUBSTANCES Significant New Uses for Specific Chemical Substances § 721.9460 Tall oil fatty acids, reaction... reporting. (1) The chemical substance identified generically as tall oil fatty acids, reaction products with...

40 CFR 721.9460 - Tall oil fatty acids, reaction products with polyamines, alkyl substituted.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Tall oil fatty acids, reaction... SUBSTANCES Significant New Uses for Specific Chemical Substances § 721.9460 Tall oil fatty acids, reaction... reporting. (1) The chemical substance identified generically as tall oil fatty acids, reaction products with...

40 CFR 721.10126 - Alkyl amino substituted triazine amino substituted benezenesulfonic acid reaction product with...

Code of Federal Regulations, 2010 CFR

2010-07-01

... substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo substituted phenyl azo... substituted triazine amino substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo... substituted triazine amino substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo...

40 CFR 721.10126 - Alkyl amino substituted triazine amino substituted benezenesulfonic acid reaction product with...

Code of Federal Regulations, 2011 CFR

2011-07-01

... substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo substituted phenyl azo... substituted triazine amino substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo... substituted triazine amino substituted benezenesulfonic acid reaction product with naphthalenesulfonato azo...

Students' Understanding of Acid, Base and Salt Reactions in Qualitative Analysis.

ERIC Educational Resources Information Center

Tan, Kim-Chwee Daniel; Goh, Ngoh-Khang; Chia, Lian-Sai; Treagust, David F.

2003-01-01

Uses a two-tier, multiple-choice diagnostic instrument to determine (n=915) grade 10 students' understanding of the acid, base, and salt reactions involved in basic qualitative analysis. Reports that many students did not understand the formation of precipitates and the complex salts, acid/salt-base reactions, and thermal decomposition involved in…

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.

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

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

NASA Astrophysics Data System (ADS)

Ivanov, Konstantin L.; Sadovsky, Vladimir M.; Lukzen, Nikita N.

2015-08-01

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting

Probe diffusion of labeled polymers inside polyacrylic acid solutions: A polyelectrolyte effect

NASA Astrophysics Data System (ADS)

Mishra, Banani; Mithra, K.; Khandai, Santripti; Jena, Sidhartha S.

2018-05-01

Probe diffusion of fluorescently labeled Dextran 40 inside polyelectrolyte solution of polyacrylic acid (PAA) was investigated using Fluorescence Recovery After Photobleaching technique. The crowding and interaction effects on probe diffusion were controlled by tuning background polymer and added external electrolyte concentration. For all the salt concentration, an overall decrease in diffusion coefficient is observed with rise in polymer concentration. The diffusion coefficient decreases with decrease in salt concentration whereas the solution viscosity increases, indicating a competition between viscous drag and electrostatic interaction. A large positive deviation from the ideal Stokes-Einstein relation is observed for high polymer and low salt concentration, which reduces markedly with addition of salt confirming polyelectrolyte effects, plays a major role in deciding the probe diffusion.

Flexible regulation of DNA displacement reaction through nucleic acid-recognition enzyme and its application in keypad lock system and biosensing.

PubMed

Li, Chao; Shi, Liu; Tao, Yaqin; Mao, Xiaoxia; Xiang, Yang; Li, Genxi

2017-08-30

Toehold-mediated DNA strand displacement reaction (SDR) plays pivotal roles for the construction of diverse dynamic DNA nanodevices. To date, many elements have been introduced into SDR system to achieve controllable activation and fine regulation. However, as the most relevant stimuli for nucleic acid involved reaction, nucleic acid-recognizing enzymes (NAEs) have received nearly no attention so far despite SDR often takes place in NAEs-enriched environment (i.e., biological fluids). Herein, we report a set of NAEs-controlled SDR strategies, which take full advantage of NAEs' properties. In this study, three different kinds of enzymes belonging to several classes (i.e., exonuclease, endonuclease and polymerase) have been used to activate or inhibit SDR, and more importantly, some mechanisms behind these strategies on how NAEs affect SDR have also been revealed. The exploration to use NAEs as possible cues to operate SDR will expand the available toolbox to build novel stimuli-fueled DNA nanodevices and could open the door to many applications including enzyme-triggered biocomputing and biosensing.

Transscleral diffusion of ethacrynic acid and sodium fluorescein

PubMed Central

Lin, Cheng-Wen; Wang, Yong; Challa, Pratap; Epstein, David L.

2007-01-01

Purpose One of the current limitations in developing novel glaucoma drugs that target the trabecular meshwork (TM) is the induced corneal toxicity from eyedrop formulations. To avoid the corneal toxicity, an alternative approach would be to deliver TM drugs through the sclera. To this end, we quantified ex vivo diffusion coefficient of a potential TM drug, ethacrynic acid (ECA), and investigated mechanisms of ECA transport in the sclera. Methods An Ussing-type diffusion apparatus was built to measure the apparent diffusion coefficient of ECA in fresh porcine sclera at 4 °C. To understand mechanisms of ECA transport, we quantified the transscleral transport of a fluorescent tracer, sodium fluorescein (NaF), that has a similar molecular weight but is more hydrophilic compared to ECA. Furthermore, we developed a mathematical model to simulate the transport processes and used it to analyze the experimental data. The model was also used to investigate the dependence of diffusion coefficients on volume fraction of viable cells and the binding of NaF and ECA to scleral tissues. Results The diffusion coefficients of ECA and NaF in the sclera were 48.5±15.1x10-7 cm2/s (n=9) and 5.23±1.93x10-7 cm2/s (n=8), respectively. Both diffusion coefficients were insensitive to cell shrinkage caused by ECA during the diffusion experiments and cell damage caused by the storage of tissues ex vivo before the experiments. Binding of ECA to scleral tissues could not be detected. The apparent maximum binding capacity and the apparent equilibrium dissociation constant for NaF were 80±5 mM and 2.5±0.5 mM (n=3), respectively. Conclusions These data demonstrated that ECA diffusion was minimally hindered by structures in the sclera, presumably due to the lack of cells and binding sites for ECA in the sclera. PMID:17356511

Geochemical modeling of reactions and partitioning of trace metals and radionuclides during titration of contaminated acidic sediments.

PubMed

Zhang, Fan; Luo, Wensui; Parker, Jack C; Spalding, Brian P; Brooks, Scott C; Watson, David B; Jardine, Philip M; Gu, Baohua

2008-11-01

Many geochemical reactions that control aqueous metal concentrations are directly affected by solution pH. However, changes in solution pH are strongly buffered by various aqueous phase and solid phase precipitation/dissolution and adsorption/desorption reactions. The ability to predict acid-base behavior of the soil-solution system is thus critical to predict metal transport under variable pH conditions. This studywas undertaken to develop a practical generic geochemical modeling approach to predict aqueous and solid phase concentrations of metals and anions during conditions of acid or base additions. The method of Spalding and Spalding was utilized to model soil buffer capacity and pH-dependent cation exchange capacity by treating aquifer solids as a polyprotic acid. To simulate the dynamic and pH-dependent anion exchange capacity, the aquifer solids were simultaneously treated as a polyprotic base controlled by mineral precipitation/ dissolution reactions. An equilibrium reaction model that describes aqueous complexation, precipitation, sorption and soil buffering with pH-dependent ion exchange was developed using HydroGeoChem v5.0 (HGC5). Comparison of model results with experimental titration data of pH, Al, Ca, Mg, Sr, Mn, Ni, Co, and SO4(2-) for contaminated sediments indicated close agreement suggesting that the model could potentially be used to predictthe acid-base behavior of the sediment-solution system under variable pH conditions.

Structure and reactions in some amphiphilic association systems

NASA Astrophysics Data System (ADS)

Guo, Rong

1999-06-01

surfactant CTAB system with various co-surfactants: n-pentanol, n-octanol, n-valeric acid, and n-caproic acid, but not in SDS or Triton X-100 systems. Presence of VC stabilizes both W/O and O/W microemulsions but destabilizes the lamellar liquid crystalline phase. Hence, the "phase transition" from the lamellar liquid crystalline phase to the isotropic phase of O/W, W/O and bicontinuous structure phase occurs with the addition of VC. The hydrotropic action of VC has been used in sunscreens to increase the solubility of sunscreen E 557. The UV absorption spectra of E557 in various media surprisingly had a dependence on the colloid structure. A new method, the preparation of water-soluble nanoparticles, has been found by employing the effect of the penetration of solvent from water layer to amphiphilic layer in lamellar liquid crystals on the solubility of inorganic salts. Water-insoluble nanoparticles have been synthesized by the reaction of two water-soluble inorganic salts in the lamellar liquid crystal. The particle size is less than 10nm and can be controlled by the thickness of the solvent layer in the lamellar liquid crystal. The lamellar liquid crystalline phase of the Triton X-100/decanol/water system has been chosen as a medium because of its large lamellar liquid crystal region and its stability when inorganic salts are added.

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.

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.

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

NASA Astrophysics Data System (ADS)

Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel

2017-05-01

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.

Diffusion of cis-5,8,11,14,17-eicosapentaenoic acid (1); carbon dioxide (2)

NASA Astrophysics Data System (ADS)

Winkelmann, J.

This document is part of Subvolume A `Gases in Gases, Liquids and their Mixtures' of Volume 15 `Diffusion in Gases, Liquids and Electrolytes' of Landolt-Börnstein Group IV `Physical Chemistry'. It is part of the chapter of the chapter `Diffusion in Pure Gases' and contains data on diffusion of (1) cis-5,8,11,14,17-eicosapentaenoic acid; (2) carbon dioxide

Diffuse charge and Faradaic reactions in porous electrodes

NASA Astrophysics Data System (ADS)

Biesheuvel, P. M.; Fu, Yeqing; Bazant, Martin Z.

2011-06-01

Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We

High School Forum: "Invitations to Enquiry": The Calcite/Acid Reaction.

ERIC Educational Resources Information Center

Herron, J. Dudley, Ed.; Driscoll, D. R.

1979-01-01

Describes a high school chemistry experiment which involves the reaction between calcite and hydrochloric and sulfuric acids. This reaction can be carried out as a projected demonstration and on an individual basis. (HM)

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

Predictions of diagenetic reactions in the presence of organic acids

NASA Astrophysics Data System (ADS)

Harrison, Wendy J.; Thyne, Geoffrey D.

1992-02-01

Stability constants have been estimated for cation complexes with anions of monofunctional and difunctional acids (combinations of Ca, Mg, Fe, Al, Sr, Mn, U, Th, Pb, Cu, Zn with formate, acetate, propionate, oxalate, malonate, succinate, and salicylate) between 0 and 200°C. Difunctional acid anions form much more stable complexes than monofunctional acid anions with aluminum; the importance of the aluminum-acetate complex is relatively minor in comparison to aluminum oxalate and malonate complexes. Divalent metal cations such as Mg, Ca, and Fe form more stable complexes with acetate than with difunctional acid anions. Aluminum-oxalate can dominate the species distribution of aluminum under acidic pH conditions, whereas the divalent cation-acetate and oxalate complexes rarely account for more than 60% of the total dissolved cation, and then only in more alkaline waters. Mineral thermodynamic affinities were calculated using the reaction path model EQ3/6 for waters having variable organic acid anion (OAA) contents under conditions representative of those found during normal burial diagenesis. The following scenarios are possible: 1) K-feldspar and albite are stable, anorthite dissolves 2) All feldpars are stable 3) Carbonates can be very unstable to slightly unstable, but never increase in stability. Organic acid anions are ineffective at neutral to alkaline pH in modifying stabilities of aluminosilicate minerals whereas the anions are variably effective under a wide range of pH in modifying carbonate mineral stabilities. Reaction path calculations demonstrate that the sequence of mineral reactions occurring in an arkosic sandstone-fluid system is only slightly modified by the presence of OAA. A spectrum of possible sandstone alteration mineralogies can be obtained depending on the selected boundary conditions: EQ3/6 predictions include quartz overgrowth, calcite replacement of plagioclase, albitization of plagioclase, and the formation of porosity-occluding calcite

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.

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

Mechanisms of proton transfer in Nafion: elementary reactions at the sulfonic acid groups.

PubMed

Sagarik, Kritsana; Phonyiem, Mayuree; Lao-ngam, Charoensak; Chaiwongwattana, Sermsiri

2008-04-21

Proton transfer reactions at the sulfonic acid groups in Nafion were theoretically studied, using complexes formed from triflic acid (CF3SO3H), H3O+ and H2O, as model systems. The investigations began with searching for potential precursors and transition states at low hydration levels, using the test-particle model (T-model), density functional theory (DFT) and ab initio calculations. They were employed as starting configurations in Born-Oppenheimer molecular dynamics (BOMD) simulations at 298 K, from which elementary reactions were analyzed and categorized. For the H3O+-H2O complexes, BOMD simulations suggested that a quasi-dynamic equilibrium could be established between the Eigen and Zundel complexes, and that was considered to be one of the most important elementary reactions in the proton transfer process. The average lifetime of H3O+ obtained from BOMD simulations is close to the lowest limit, estimated from low-frequency vibrational spectroscopy. It was demonstrated that proton transfer reactions at -SO3H are not concerted, due to the thermal energy fluctuation and the existence of various quasi-dynamic equilibria, and -SO3H could directly and indirectly mediate proton transfer reactions through the formation of proton defects, as well as the -SO3- and -SO3H2+ transition states.

Infrared Emission from Gas-Aerosol Reactions

DTIC Science & Technology

1982-09-01

Gaseous Amonia Infrared (IR) "Gas-aerosol Reactions Sulfuric Acid- amonia IR Luminescence Exothermic Reactions Octanoic Acid- amonia IR Laser Acid-base...of radiation observed from the reactions of chloro- sulfuric acid aerosol with gaseous amonia and water. Other systems which were screened including

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

PubMed

Allison, Stuart

2006-12-28

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

The chemical foundations of nitroalkene fatty acid signaling through addition reactions with thiols.

PubMed

Turell, Lucía; Steglich, Martina; Alvarez, Beatriz

2018-03-22

Nitroalkene fatty acids can be formed in vivo and administered exogenously. They exert pleiotropic signaling actions with cytoprotective and antiinflammatory effects. The presence of the potent electron withdrawing nitro group confers electrophilicity to the adjacent β-carbon. Thiols (precisely, thiolates) are strong nucleophiles and can react with nitroalkene fatty acids through reversible Michael addition reactions. In addition, nitroalkene fatty acids can undergo several other processes including metabolic oxidation, reduction, esterification, nitric oxide release and partition into hydrophobic compartments. The signaling actions of nitroalkenes are mainly mediated by reactions with critical thiols in regulatory proteins. Thus, the thio-Michael addition reaction provides a framework for understanding the molecular basis of the biological effects of nitroalkene fatty acids at the crossroads of thiol signaling and electrophilic lipid signaling. In this review, we describe the reactions of nitroalkene fatty acids in biological contexts. We focus on the Michael addition-elimination reaction with thiols and its mechanism, and extrapolate kinetic and thermodynamic considerations to in vivo settings. Copyright © 2018 Elsevier Inc. All rights reserved.

Reaction-diffusion-induced explosive crystallization in a metal-selenium nanometer film structure

NASA Astrophysics Data System (ADS)

Kogai, V. Ya.

2016-03-01

Experimental data for reaction-diffusion-induced explosive crystallization in a nanodimensional metal (Cu, Ag)/selenium structure are presented. It is found that after the metal layer has completely diffused into the amorphous Se film, the electrical potential rises from 0.14 to 1.21 V in the Cu(30 nm)/Se(140 nm) heterolayer and from 0.01 to 1.17 V in the Ag(30 nm)/Se(140 nm) heterolayer. The metals diffusing into the amorphous Se layer interact with Se, forming nuclei of a new phase (CuSe or Ag2Se). The intense growth of the CuSe and Ag2Se crystallization centers results in a considerable liberation of latent energy in the form of phase transformation heat and in explosive growth of CuSe and Ag2Se nanocrystalline particles. The mean size of CuSe and Ag2Se crystallites equals 25 and 50 nm, respectively.

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.

Antioxidant and chelating capacity of Maillard reaction products in amino acid-sugar model systems: applications for food processing.

PubMed

Mondaca-Navarro, Blanca A; Ávila-Villa, Luz A; González-Córdova, Aarón F; López-Cervantes, Jaime; Sánchez-Machado, Dalia I; Campas-Baypoli, Olga N; Rodríguez-Ramírez, Roberto

2017-08-01

Maillard reaction products (MRP) have gained increasing interest owing to their both positive and negative effects on human health. Aqueous amino acid-sugar model systems were studied in order to evaluate the antioxidant and chelating activity of MRP under conditions similar to those of food processing. Amino acids (cysteine, glycine, isoleucine and lysine) combined with different sugars (fructose or glucose) were heated to 100 and 130 °C for 30, 60 and 90 min. Antioxidant capacity was evaluated via ABTS and DPPH free radical scavenging assays, in addition to Fe 2+ and Cu 2+ ion chelating capacity. In the ABTS assay, the cysteine-fructose model system presented the highest antioxidant activity at 7.05 µmol mL -1 (130 °C, 60 min), expressed in Trolox equivalents. In the DPPH assay, the cysteine-glucose system presented the highest antioxidant activity at 3.79 µmol mL -1 (100 °C, 90 min). The maximum rate of chelation of Fe 2+ and Cu 2+ was 96.31 and 59.44% respectively in the lysine-fructose and cysteine-glucose systems (100 °C, 30 min). The model systems presented antioxidant and chelating activity under the analyzed temperatures and heating times, which are similar to the processing conditions of some foods. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

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

PubMed

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

2018-07-01

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

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.

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

NASA Astrophysics Data System (ADS)

Kittell, D. E.; Yarrington, C. D.; Hobbs, M. L.; Abere, M. J.; Adams, D. P.

2018-04-01

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Determination Hypoiodous Acid (HIO) By Peroxidase System Using Peroxidase Enzyme

NASA Astrophysics Data System (ADS)

Al-Baarri, A. N.; Legowo, A. M.; Widayat; Abduh, S. B. M.; Hadipernata, M.; Wisnubroto; Ardianti, D. K.; Susanto, M. N.; Yusuf, M.; Demasta, E. K.

2018-02-01

It has been understood that peroxidase enzyme including peroxidase serves as catalyzer to enzymatic reaction among hydrogen peroxide and halides, therefore this research was done for generating hypoiodous acid (HIO) from peroxidase system using peroxidase enzyme. Hydrogen peroxide, potassium iodide, and peroxidase enzyme were used to produce HIO. Determination the amount of formed HIO was done using 2,2'-azino-bis(3- ethylbenzothiazoline-6-sulphonic acid) or ABTS as substrate through the colorimetric measurement of hydrogen peroxide residue during reaction process using at 412 nm. The result indicated that residual hydrogen peroxide showed the minimum concentration after 60 minutes reaction time. Because the reaction started at the beginning time of mixing, hydrogen peroxide was unable to be eliminated totally to produce HIO. The reaction of peroxidase system was able to determine the beginning of mixing process but the reaction process could not eliminate the initial concentration of hydrogen peroxide indicating the maximum amount of production of HIO could be determined. In conclusion, the less of H2O2, higher HIO obtained and peroxidase enzymes can accelerate the formation of HIO.

Geochemical Modeling of Reactions and Partitioning of Trace Metals and Radionuclides during Titration of Contaminated Acidic Sediments

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

Zhang, Fan; Parker, Jack C.; Luo, Wensui

2008-01-01

Many geochemical reactions that control aqueous metal concentrations are directly affected by solution pH. However, changes in solution pH are strongly buffered by various aqueous phase and solid phase precipitation/dissolution and adsorption/desorption reactions. The ability to predict acid-base behavior of the soil-solution system is thus critical to predict metal transport under variable pH conditions. This study was undertaken to develop a practical generic geochemical modeling approach to predict aqueous and solid phase concentrations of metals and anions during conditions of acid or base additions. The method of Spalding and Spalding was utilized to model soil buffer capacity and pH-dependent cationmore » exchange capacity by treating aquifer solids as a polyprotic acid. To simulate the dynamic and pH-dependent anion exchange capacity, the aquifer solids were simultaneously treated as a polyprotic base controlled by mineral precipitation/dissolution reactions. An equilibrium reaction model that describes aqueous complexation, precipitation, sorption and soil buffering with pH-dependent ion exchange was developed using HydroGeoChem v5.0 (HGC5). Comparison of model results with experimental titration data of pH, Al, Ca, Mg, Sr, Mn, Ni, Co, and SO{sub 4}{sup 2-} for contaminated sediments indicated close agreement, suggesting that the model could potentially be used to predict the acid-base behavior of the sediment-solution system under variable pH conditions.« less

Total amino acid stabilization during cell-free protein synthesis reactions.

PubMed

Calhoun, Kara A; Swartz, James R

2006-05-17

Limitations in amino acid supply have been recognized as a substantial problem in cell-free protein synthesis reactions. Although enzymatic inhibitors and fed-batch techniques have been beneficial, the most robust way to stabilize amino acids is to remove the responsible enzymatic activities by genetically modifying the source strain used for cell extract preparation. Previous work showed this was possible for arginine, serine, and tryptophan, but cysteine degradation remained a major limitation in obtaining high protein synthesis yields. Through radiolabel techniques, we confirmed that cysteine degradation was caused by the activity of glutamate-cysteine ligase (gene gshA) in the cell extract. Next, we created Escherichia coli strain KC6 that combines a gshA deletion with previously described deletions for arginine, serine, and tryptophan stabilization. Strain KC6 grows well, and active cell extract can be produced from it for cell-free protein synthesis reactions. The extract from strain KC6 maintains stable amino acid concentrations of all 20 amino acids in a 3-h batch reaction. Yields for three different proteins improved 75-250% relative to cell-free expression using the control extract.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

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

Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N.; Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090

2015-08-28

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression formore » the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i

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.

Irreversible reactions and diffusive escape: Stationary properties

DOE PAGES

Krapivsky, Paul L.; Ben-Naim, Eli

2015-05-01

We study three basic diffusion-controlled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by particles, while the complementary half-line is empty. We show that the total number of particles that infiltrate the initially empty half-line is finite and has a stationary distribution. We determine the evolution of the average density from which we derive the average total number N of particles in the initially empty half-line; e.g. for annihilationmore » $$\\langle N\\rangle = \\frac{3}{16}+\\frac{1}{4\\π}$$ . For the coalescence process, we devise a procedure that in principle allows one to compute P(N), the probability to find exactly N particles in the initially empty half-line; we complete the calculations in the first non-trivial case (N = 1). As a by-product we derive the distance distribution between the two leading particles.« less

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

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

Study of stability of methotrexate in acidic solution spectrofluorimetric determination of methotrexate in pharmaceutical preparations through acid-catalyzed degradation reaction.

PubMed

Sabry, Suzy M; Abdel-Hady, M; Elsayed, M; Fahmy, Osama T; Maher, Hadir M

2003-07-14

Study of the degradation reaction of methotrexate (MTX) in acidic solution was carried out. Optimization of the experimental parameters of MTX acid hydrolysis was investigated. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (AMP), was developed. Stability of the standard solution of MTX prepared in sulfuric acid was discussed in the view of accelerated stability analysis. Two other comparative spectroflourimetric methods based on measuring the fluorescence intensities from either a condensation reaction with acetylacetone-formaldehyde (Hantzsch reaction) or a reaction with fluorescamine were also described. Beer's law validation, accuracy, precision, limits of detection, limits of quantification, and other aspects of analytical merit are presented in the text. The proposed methods were successfully applied for the analysis of MTX in pure drug and tablets dosage form. The sensitivity of the developed methods was favorable, so it was possible to be adopted for determination of MTX in plasma samples for routine use in high-dose MTX therapy.

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.

Roles of back diffusion and biodegradation reactions in sustaining MTBE/TBA plumes in alluvial media

NASA Astrophysics Data System (ADS)

Mackay, D. M.; Rasa, E.

2011-12-01

A plume of methyl tert-butyl ether (MTBE) and tert-butyl alcohol (TBA) originating from a gasoline spill in late 1994 at Vandenberg Air Force Base (VAFB) persisted above regulatory concentration goals for over 15 years within 200 feet of the original spill source. The plume persisted until 2010 despite excavation of the tanks and piping within months after the spill and excavations of additional contaminated sediments from the source area in 2007 and 2008. Two-dimensional reactive transport simulations of MTBE and TBA along the plume centerline were conducted for a 20-year period following the spill. As previously reported by Rasa et al. (2011), these analyses suggest that MTBE diffused from the thin anaerobic aquifer into the adjacent anaerobic silts and transformed to TBA in both aquifer and silt layers. After 2004, TBA was the dominant solute, diffusing back out of the silts into the aquifer and sustaining plume concentrations. Simulations also suggest that aerobic degradation of MTBE or TBA at the water table in the overlying silt layer significantly reduced the time for MTBE and TBA concentrations to reach regulatory goals by limiting the chemical mass available for back diffusion to the aquifer. We have extended that prior work; using the same reaction and diffusion parameters, we explored the sensitivity of the results to thicknesses of the alluvial layers in order to determine under what sets of conditions a reaction zone accessed only by vertical diffusion through a silt from an underlying contaminated aquifer can significantly affect time to achievement of compliance goals within the aquifer.

Relativistic collective diffusion in one-dimensional systems

NASA Astrophysics Data System (ADS)

Lin, Gui-Wu; Lam, Yu-Yiu; Zheng, Dong-Qin; Zhong, Wei-Rong

2018-05-01

The relativistic collective diffusion in one-dimensional molecular system is investigated through nonequilibrium molecular dynamics with Monte Carlo methods. We have proposed the relationship among the speed, the temperature, the density distribution and the collective diffusion coefficient of particles in a relativistic moving system. It is found that the relativistic speed of the system has no effect on the temperature, but the collective diffusion coefficient decreases to zero as the velocity of the system approaches to the speed of light. The collective diffusion coefficient is modified as D‧ = D(1 ‑w2 c2 )3 2 for satisfying the relativistic circumstances. The present results may contribute to the understanding of the behavior of the particles transport diffusion in a high speed system, as well as enlighten the study of biological metabolism at relativistic high speed situation.

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

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

NASA Astrophysics Data System (ADS)

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

2005-08-01

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

Reaction kinetics of free fatty acids esterification in palm fatty acid distillate using coconut shell biochar sulfonated catalyst

NASA Astrophysics Data System (ADS)

Hidayat, Arif; Rochmadi, Wijaya, Karna; Budiman, Arief

2015-12-01

Recently, a new strategy of preparing novel carbon-based solid acids has been developed. In this research, the esterification reactions of Palm Fatty Acid Distillate (PFAD) with methanol, using coconut shell biochar sulfonated catalyst from biomass wastes as catalyst, were studied. In this study, the coconut shell biochar sulfonated catalysts were synthesized by sulfonating the coconut shell biochar using concentrated H2SO4. The kinetics of free fatty acid (FFA) esterification in PFAD using a coconut shell biochar sulfonated catalyst was also studied. The effects of the mass ratio of catalyst to oil (1-10%), the molar ratio of methanol to oil (6:1-12:1), and the reaction temperature (40-60°C) were studied for the conversion of PFAD to optimize the reaction conditions. The results showed that the optimal conditions were an methanol to PFAD molar ratio of 12:1, the amount of catalyst of 10%w, and reaction temperature of 60°C. The proposed kinetic model shows a reversible second order reaction and represents all the experimental data satisfactorily, providing deeper insight into the kinetics of the reaction.

Sleeve reaction chamber system

DOEpatents

Northrup, M Allen [Berkeley, CA; Beeman, Barton V [San Mateo, CA; Benett, William J [Livermore, CA; Hadley, Dean R [Manteca, CA; Landre, Phoebe [Livermore, CA; Lehew, Stacy L [Livermore, CA; Krulevitch, Peter A [Pleasanton, CA

2009-08-25

A chemical reaction chamber system that combines devices such as doped polysilicon for heating, bulk silicon for convective cooling, and thermoelectric (TE) coolers to augment the heating and cooling rates of the reaction chamber or chambers. In addition the system includes non-silicon-based reaction chambers such as any high thermal conductivity material used in combination with a thermoelectric cooling mechanism (i.e., Peltier device). The heat contained in the thermally conductive part of the system can be used/reused to heat the device, thereby conserving energy and expediting the heating/cooling rates. The system combines a micromachined silicon reaction chamber, for example, with an additional module/device for augmented heating/cooling using the Peltier effect. This additional module is particularly useful in extreme environments (very hot or extremely cold) where augmented heating/cooling would be useful to speed up the thermal cycling rates. The chemical reaction chamber system has various applications for synthesis or processing of organic, inorganic, or biochemical reactions, including the polymerase chain reaction (PCR) and/or other DNA reactions, such as the ligase chain reaction.

Diffusion-controlled interface kinetics-inclusive system-theoretic propagation models for molecular communication systems

NASA Astrophysics Data System (ADS)

Chude-Okonkwo, Uche A. K.; Malekian, Reza; Maharaj, B. T.

2015-12-01

Inspired by biological systems, molecular communication has been proposed as a new communication paradigm that uses biochemical signals to transfer information from one nano device to another over a short distance. The biochemical nature of the information transfer process implies that for molecular communication purposes, the development of molecular channel models should take into consideration diffusion phenomenon as well as the physical/biochemical kinetic possibilities of the process. The physical and biochemical kinetics arise at the interfaces between the diffusion channel and the transmitter/receiver units. These interfaces are herein termed molecular antennas. In this paper, we present the deterministic propagation model of the molecular communication between an immobilized nanotransmitter and nanoreceiver, where the emission and reception kinetics are taken into consideration. Specifically, we derived closed-form system-theoretic models and expressions for configurations that represent different communication systems based on the type of molecular antennas used. The antennas considered are the nanopores at the transmitter and the surface receptor proteins/enzymes at the receiver. The developed models are simulated to show the influence of parameters such as the receiver radius, surface receptor protein/enzyme concentration, and various reaction rate constants. Results show that the effective receiver surface area and the rate constants are important to the system's output performance. Assuming high rate of catalysis, the analysis of the frequency behavior of the developed propagation channels in the form of transfer functions shows significant difference introduce by the inclusion of the molecular antennas into the diffusion-only model. It is also shown that for t > > 0 and with the information molecules' concentration greater than the Michaelis-Menten kinetic constant of the systems, the inclusion of surface receptors proteins and enzymes in the models

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

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

Kittell, David E.; Yarrington, Cole D.; Hobbs, M. L.

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quenchmore » limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Finally, possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. Finally, this higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.« less

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

DOE PAGES

Kittell, David E.; Yarrington, Cole D.; Hobbs, M. L.; ...

2018-04-14

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quenchmore » limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Finally, possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. Finally, this higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.« less

40 CFR 721.10189 - Fatty acids, tall-oil, reaction products with (butoxymethyl) oxirane formaldehyde-phenol polymer...

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Fatty acids, tall-oil, reaction... Substances § 721.10189 Fatty acids, tall-oil, reaction products with (butoxymethyl) oxirane formaldehyde... to reporting. (1) The chemical substance identified generically as fatty acids, tall-oil, reaction...

40 CFR 721.6181 - Fatty acid, reaction product with substituted oxirane, formaldehyde-phenol polymer glycidyl ether...

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Fatty acid, reaction product with... Specific Chemical Substances § 721.6181 Fatty acid, reaction product with substituted oxirane, formaldehyde... as fatty acid, reaction product with substituted oxirane, formaldehyde-phenol polymer glycidyl ether...

40 CFR 721.10189 - Fatty acids, tall-oil, reaction products with (butoxymethyl) oxirane formaldehyde-phenol polymer...

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Fatty acids, tall-oil, reaction... Substances § 721.10189 Fatty acids, tall-oil, reaction products with (butoxymethyl) oxirane formaldehyde... to reporting. (1) The chemical substance identified generically as fatty acids, tall-oil, reaction...

40 CFR 721.6181 - Fatty acid, reaction product with substituted oxirane, formaldehyde-phenol polymer glycidyl ether...

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Fatty acid, reaction product with... Specific Chemical Substances § 721.6181 Fatty acid, reaction product with substituted oxirane, formaldehyde... as fatty acid, reaction product with substituted oxirane, formaldehyde-phenol polymer glycidyl ether...

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.

Single-drop reactive extraction/extractive reaction with forced convective diffusion and interphase mass transfer

NASA Technical Reports Server (NTRS)

Kleinman, Leonid S.; Red, X. B., Jr.

1995-01-01

An algorithm has been developed for time-dependent forced convective diffusion-reaction having convection by a recirculating flow field within the drop that is hydrodynamically coupled at the interface with a convective external flow field that at infinity becomes a uniform free-streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet, or reactions can take place in both phases. The algorithm has been implemented, and for comparison results are shown here for the case of no reaction in either phase and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Single-drop reactive extraction/extractive reaction with forced convective diffusion and interphase mass transfer

NASA Technical Reports Server (NTRS)

Kleinman, Leonid S.; Reed, X. B., Jr.

1995-01-01

An algorithm has been developed for the forced convective diffusion-reaction problem for convection inside and outside a droplet by a recirculating flow field hydrodynamically coupled at the droplet interface with an external flow field that at infinity becomes a uniform streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet or reactions can take place in both phases. The algorithm has been implemented and results are shown here for the case of no reaction and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.