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.

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.

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

Aluminum/water reactions under extreme conditions

NASA Astrophysics Data System (ADS)

Hooper, Joseph

2013-03-01

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

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

PubMed Central

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

2011-01-01

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

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.

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

PubMed

Beaver, Matthew G; Woerpel, K A

2010-02-19

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

Conductive polymer layers to limit transfer of fuel reactants to catalysts of fuel cells to reduce reactant crossover

DOEpatents

Stanis, Ronald J.; Lambert, Timothy N.

2016-12-06

An apparatus of an aspect includes a fuel cell catalyst layer. The fuel cell catalyst layer is operable to catalyze a reaction involving a fuel reactant. A fuel cell gas diffusion layer is coupled with the fuel cell catalyst layer. The fuel cell gas diffusion layer includes a porous electrically conductive material. The porous electrically conductive material is operable to allow the fuel reactant to transfer through the fuel cell gas diffusion layer to reach the fuel cell catalyst layer. The porous electrically conductive material is also operable to conduct electrons associated with the reaction through the fuel cell gas diffusion layer. An electrically conductive polymer material is coupled with the fuel cell gas diffusion layer. The electrically conductive polymer material is operable to limit transfer of the fuel reactant to the fuel cell catalyst layer.

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.

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.

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

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

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

DOE PAGES

Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep; ...

2016-05-13

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases themore » equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.« less

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/

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

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

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

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

Rhenium-Oxygen Interactions at High Temperatures

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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

PubMed

Tholen, Danny; Zhu, Xin-Guang

2011-05-01

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

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

PubMed Central

Tholen, Danny; Zhu, Xin-Guang

2011-01-01

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

Scalar dissipation rates in non-conservative transport systems

PubMed Central

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

2014-01-01

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

Analysis of opposed jet hydrogen-air counter flow diffusion flame

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Materials outgassing rate decay in vacuum at isothermal conditions

NASA Astrophysics Data System (ADS)

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

2016-09-01

As a laboratory for scientific research, the International Space Station has been in Low Earth Orbit for over 17 years and is planned to be on-orbit for another 10 years. The ISS has been maintaining a relatively pristine contamination environment for science payloads. Materials outgassing induced contamination is currently the dominant source for sensitive surfaces on ISS and modelling the outgassing rate decay over a 20 to 30 year period is challenging. Using ASTM E 1559 rate data, materials outgassing is described herein as a diffusion-reaction process with the interface playing a key role. The observation of -1/2 (diffusion) or non-integers (reaction limited) as rate decay exponents for common ISS materials indicate classical reaction kinetics is unsatisfactory in modelling materials outgassing. Nonrandomness of reactant concentrations at the interface is the source of this deviation from classical reaction kinetics. A t-1/2 decay is adopted as the result of the correlation of the contaminant layer thicknesses and composition on returned ISS hardware, the existence of high outgassing silicone exhibiting near diffusion limited decay, the confirmation of nondepleted material after ten years in Low Earth Orbit, and a potential slowdown of long term materials outgassing kinetics due to silicone contaminants at the interface.

Plastoquinol diffusion in linear photosynthetic electron transport

PubMed Central

Mitchell, Rowan; Spillmann, Andreas; Haehnel, Wolfgang

1990-01-01

The diffusion of plastoquinol and its binding to the cytochrome bf complex, which occurs during linear photosynthetic electron transport and is analogous to reaction sequences found in most energy-converting membranes, has been studied in intact thylakoid membranes. The flash-induced electron transfer between the laterally separated photosystems II and photosystems I was measured by following the sigmoidal reduction kinetics of P-700+ after previous oxidation of the intersystem electron carriers. The amount of flash-induced plastoquinol produced at photosystem II was (a) reduced by inhibition with dichlorophenyl-dimethylurea and (b) increased by giving a second saturating flash. These signals were simulated by a new model which combines a deterministic simulation of reaction kinetics with a Monte Carlo approach to the diffusion of plastoquinol, taking into account the known structural features of the thylakoid membrane. The plastoquinol molecules were assumed to be oxidized by either a diffusion-limited or a nondiffusion-limited step in a collisional mechanism or after binding to the cytochrome bf complex. The model was able to account for the experimental observations with a nondiffusion-limited collisional mechanism or with a binding mechanism, giving minimum values for the diffusion coefficient of plastoquinol of 2 × 10-8 cm2s-1 and 3 × 10-7 cm2s-1, respectively. PMID:19431770

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.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Understanding Performance Limitations to Enable High Performance Magnesium-Ion Batteries

DOE PAGES

Kim, Sun Ung; Perdue, Brian; Apblett, Christopher A.; ...

2016-05-18

We developed a mathematical model in order to investigate the performance limiting factors of Mg-ion battery with a Chevrel phase (Mg xMo 6S 8) cathode and a Mg metal anode. Furthermore, the model was validated using experimental data from the literature [Cheng et al., Chem. Mater., 26, 4904 (2014)]. Two electrochemical reactions of the Chevrel phase with significantly different kinetics and solid diffusion were included in the porous electrode model, which captured the physics sufficiently well to generate charge curves of five rates (0.1C–2C) for two different particle sizes. Limitation analysis indicated that the solid diffusion and kinetics in themore » higher-voltage plateau limit the capacity and increase the overpotential in the Cheng et al.’s thin (20-μm) electrodes. The model reveals that the performance of the cells with reasonable thickness would also be subject to electrolyte-phase limitations. Finally, the simulation also suggested that the polarization losses on discharge will be lower than that on charge, because of the differences in the kinetics and solid diffusion between the two reactions of the Chevrel phase.« less

Computation of the unsteady facilitated transport of oxygen in hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1990-01-01

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

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.

Determination of the diffusion coefficient and phase-transfer rate parameter in LaNi{sub 5} and MmNi{sub 3.6}Co{sub 0.8}Mn{sub 0.4}Al{sub 0.3} using microelectrodes

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

Lundqvist, A.; Lindbergh, G.

1998-11-01

A potential-step method for determining the diffusion coefficient and phase-transfer parameter in metal hydrides by using microelectrodes was investigated. It was shown that a large potential step is not enough to ensure a completely diffusion-limited mass transfer if a surface-phase transfer reaction takes place at a finite rate. It was shown, using a kinetic expression for the surface phase-transfer reaction, that the slope of the logarithm of the current vs. time curve will be constant both in the case of the mass-transfer limited by diffusion or by diffusion and a surface-phase transfer. The diffusion coefficient and phase-transfer rate parameter weremore » accurately determined for MmNi{sub 3.6}Co{sub 0.8}Mn{sub 0.4}Al{sub 0.3} using a fit to the whole transient. The diffusion coefficient was found to be (1.3 {+-} 0.3) {times} 10{sup {minus}13} m{sup 2}/s. The fit was good and showed that a pure diffusion model was not enough to explain the observed transient. The diffusion coefficient and phase-transfer rate parameter were also estimated for pure LaNi{sub 5}. A fit of the whole curve showed that neither a pure diffusion model nor a model including phase transfer could explain the whole transient.« less

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

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

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

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

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

Liu, Yuanyuan; Liu, Chongxuan; Zhang, Changyong

2015-08-01

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

Consumption and diffusion of dissolved oxygen in sedimentary rocks.

PubMed

Manaka, M; Takeda, M

2016-10-01

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

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.

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.

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

PubMed

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

2011-07-01

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

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

PubMed Central

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

2011-01-01

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

Methylene migration and coupling on a non-reducible metal oxide: The reaction of dichloromethane on stoichiometric α-Cr 2O 3(0001)

DOE PAGES

Dong, Yujung; Brooks, John D.; Chen, Tsung-Liang; ...

2014-09-17

The reaction of CH 2Cl 2 over the nearly-stoichiometric α-Cr 2O 3(0001) surface produces gas phase ethylene, methane and surface chlorine adatoms. The reaction is initiated by the decomposition of CH 2Cl 2 into surface methylene and chlorine. Photoemission indicates that surface cations are the preferred binding sites for both methylene and chlorine adatoms. Two reaction channels are observed for methylene coupling to ethylene in temperature-programmed desorption (TPD). A desorption-limited, low-temperature route is attributed to two methylenes bound at a single site. The majority of ethylene is produced by a reaction-limited process involving surface migration (diffusion) of methylene as themore » rate-limiting step. DFT calculations indicate the surface diffusion mechanism is mediated by surface oxygen anions. The source of hydrogen for methane formation is adsorbed background water. Chlorine adatoms produced by the dissociation of CH 2Cl 2 deactivate the surface by simple site-blocking of surface Cr 3+ sites. Finally, a comparison of experiment and theory shows that DFT provides a better description of the surface chemistry of the carbene intermediate than DFT+U using reported parameters for a best representation of the bulk electronic properties of α-Cr 2O 3.« less

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model

NASA Astrophysics Data System (ADS)

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-08-01

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm’s shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

Simulation of Bacillus subtilis biofilm growth on agar plate by diffusion-reaction based continuum model.

PubMed

Zhang, Xianlong; Wang, Xiaoling; Nie, Kai; Li, Mingpeng; Sun, Qingping

2016-07-19

Various species of bacteria form highly organized spatially-structured aggregates known as biofilms. To understand how microenvironments impact biofilm growth dynamics, we propose a diffusion-reaction continuum model to simulate the formation of Bacillus subtilis biofilm on an agar plate. The extended finite element method combined with level set method are employed to perform the simulation, numerical results show the quantitative relationship between colony morphologies and nutrient depletion over time. Considering that the production of polysaccharide in wild-type cells may enhance biofilm spreading on the agar plate, we inoculate mutant colony incapable of producing polysaccharide to verify our results. Predictions of the glutamate source biofilm's shape parameters agree with the experimental mutant colony better than that of glycerol source biofilm, suggesting that glutamate is rate limiting nutrient for Bacillus subtilis biofilm growth on agar plate, and the diffusion-limited is a better description to the experiment. In addition, we find that the diffusion time scale is of the same magnitude as growth process, and the common-employed quasi-steady approximation is not applicable here.

High Temperature Degradation Mechanisms in Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.

1996-01-01

Polymer matrix composites are increasingly used in demanding structural applications in which they may be exposed to harsh environments. The durability of such materials is a major concern, potentially limiting both the integrity of the structures and their useful lifetimes. The goal of the current investigation is to develop a mechanism-based model of the chemical degradation which occurs, such that given the external chemical environment and temperatures throughout the laminate, laminate geometry, and ply and/or constituent material properties, we can calculate the concentration of diffusing substances and extent of chemical degradation as functions of time and position throughout the laminate. This objective is met through the development and use of analytical models, coupled to an analysis-driven experimental program which offers both quantitative and qualitative information on the degradation mechanism. Preliminary analyses using a coupled diffusion/reaction model are used to gain insight into the physics of the degradation mechanisms and to identify crucial material parameters. An experimental program is defined based on the results of the preliminary analysis which allows the determination of the necessary material coefficients. Thermogravimetric analyses are carried out in nitrogen, air, and oxygen to provide quantitative information on thermal and oxidative reactions. Powdered samples are used to eliminate diffusion effects. Tests in both inert and oxidative environments allow the separation of thermal and oxidative contributions to specimen mass loss. The concentration dependency of the oxidative reactions is determined from the tests in pure oxygen. Short term isothermal tests at different temperatures are carried out on neat resin and unidirectional macroscopic specimens to identify diffusion effects. Mass loss, specimen shrinkage, the formation of degraded surface layers and surface cracking are recorded as functions of exposure time. Geometry effects in the neat resin, and anisotropic diffusion effects in the composites, are identified through the use of specimens with different aspect ratios. The data is used with the model to determine reaction coefficients and effective diffusion coefficients. The empirical and analytical correlations confirm the preliminary model results which suggest that mass loss at lower temperatures is dominated by oxidative reactions and that these reaction are limited by diffusion of oxygen from the surface. The mechanism-based model is able to successfully capture the basic physics of the degradation phenomena under a wide range of test conditions. The analysis-based test design is successful in separating out oxidative, thermal, and diffusion effects to allow the determination of material coefficients. This success confirms the basic picture of the process; however, a more complete understanding of some aspects of the physics are required before truly predictive capability can be achieved.

Catalytic conversion in nanoporous materials: Concentration oscillations and spatial correlations due to inhibited transport and intermolecular interactions

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

Garcia, Andres; Evans, James W.

2016-11-03

We show that steady-state catalytic conversion in nanoporous materials can occur in a quasi-counter-diffusion mode with the reactant (product) concentration strongly decaying (growing) into the pore, but also with oscillations in the total concentration. These oscillations reflect the response of the fluid to the transition from an extended to a confined environment near the pore opening. We focus on the regime of strongly inhibited transport in narrow pores corresponding to single-file diffusion. Here, limited penetration of the reactant into the pores and the associated low reaction yield is impacted by strong spatial correlations induced by both reaction (non-equilibrium correlations) andmore » also by intermolecular interactions (thermodynamic correlations). We develop a generalized hydrodynamic formulation to effectively describe inhibited transport accounting for the effect of these correlations, and incorporate this description of transport into appropriate reaction-diffusion equations. These equations accurately describe both shorter-range concentration oscillations near the pore opening and the longer-range mesoscale variation of concentration profiles in the pore (and thus also describe reaction yield). Success of the analytic theory is validated by comparison with a precise kinetic Monte Carlo simulation of an appropriate molecular-level stochastic reaction-diffusion model. As a result, this work elucidates unconventional chemical kinetics in interacting confined systems.« less

Speeding up biomolecular interactions by molecular sledding

DOE PAGES

Turkin, Alexander; Zhang, Lei; Marcozzi, Alessio; ...

2015-10-07

In numerous biological processes associations involve a protein with its binding partner, an event that is preceded by a diffusion-mediated search bringing the two partners together. Often hindered by crowding in biologically relevant environments, three-dimensional diffusion can be slow and result in long bimolecular association times. Moreover, the initial association step between two binding partners often represents a rate-limiting step in biotechnologically relevant reactions. We also demonstrate the practical use of an 11-a.a. DNA-interacting peptide derived from adenovirus to reduce the dimensionality of diffusional search processes and speed up associations between biological macromolecules. We functionalize binding partners with the peptidemore » and demonstrate that the ability of the peptide to one-dimensionally diffuse along DNA results in a 20-fold reduction in reaction time. We also show that modifying PCR primers with the peptide sled enables significant acceleration of standard PCR reactions.« less

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.

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

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

PubMed

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

2012-05-10

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

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

PubMed

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

2010-06-22

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

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

An Investigation of Diffusion Rates in Wadsleyite at 21 GPa and 1500-1900 ° C

NASA Astrophysics Data System (ADS)

Murray, J.; Van Orman, J. A.; Fei, Y.

2002-05-01

Diffusion experiments on high-pressure solid phases provide important constraints on the viscosity of the mantle. We measured diffusion rates in wadsleyite, thought to be one of the most common minerals in the mantle transition zone, using a rim growth method. In each experiment a periclase (MgO) single crystal was surrounded by MgSiO3 glass and compressed in a multianvil device. The MgSiO3 glass rapidly transformed to ilmenite or majorite during heating, as confirmed by a "zero-time" experiment in which the sample was heated to the final run temperature at 100 K/min and then immediately quenched. Each sample was annealed at constant temperature for up to 47 hours to produce a reaction rim of polycrystalline wadsleyite (Mg2SiO4) with ~1 μ m grain size. Growth of the reaction rim was enabled by diffusion of chemical species across the wadsleyite layer, and the bulk diffusion coefficient of the rate-limiting species was calculated from the final rim width using the method described by Fisler and Mackwell (1994 Phys. Chem. Minerals 21:156-165). This method depends on knowledge of the change in chemical potential from the periclase/wadsleyite interface to the wadsleyite/ilmenite(majorite) interface, which we calculated using the internally consistent thermodynamic dataset of Fei et al. (1990 J. Geophys. Res. 95:6915-6928). In some of the experiments we coated the periclase crystal with a thin layer ( ~100 nm) of gold to mark the initial interface and indicate the relative fluxes of chemical species across the growing wadsleyite rim. In every case the gold remained adjacent to the periclase/wadsleyite interface, indicating that the flux of Mg and O across the reaction rim was much greater than the counterflux of Si, and that Mg and O were the more mobile species. For simplicity we assumed that Si was immobile and calculated Mg and O diffusivities assuming that each in turn was the rate-limiting species. The calculated Mg diffusivity is much slower than determined by Chakraborty et al. (1999 Science 283:362-364) and by Farber et al. (2000 J. Geophys. Res. 105:513-529). We therefore conclude that oxygen is the rate limiting species and that diffusion rates increase in the order DSi

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.

Substrate and metabolite diffusion within model medium for soft cheese in relation to growth of Penicillium camembertii.

PubMed

Aldarf, Mazen; Fourcade, Florence; Amrane, Abdeltif; Prigent, Yves

2006-08-01

Penicillium camembertii was cultivated on a jellified peptone-lactate based medium to simulate the composition of Camembert cheese. Diffusional limitations due to substrate consumption were not involved in the linear growth recorded during culture, while nitrogen (peptone) limitation accounted for growth cessation. Examination of gradients confirmed that medium neutralization was the consequence of lactate consumption and ammonium production. The diffusion of the lactate assimilated from the core to the rind and that of the ammonium produced from the rind to the core was described by means of a diffusion/reaction model involving a partial linking of consumption or production to growth. The model matched experimental data throughout growth.

A modelling approach for the heterogeneous oxidation of elastomers

NASA Astrophysics Data System (ADS)

Herzig, A.; Sekerakova, L.; Johlitz, M.; Lion, A.

2017-09-01

The influence of oxygen on elastomers, known as oxidation, is one of the most important ageing processes and becomes more and more important for nowadays applications. The interaction with thermal effects as well as antioxidants makes oxidation of polymers a complex process. Based on the polymer chosen and environmental conditions, the ageing processes may behave completely different. In a lot of cases the influence of oxygen is limited to the surface layer of the samples, commonly referred to as diffusion-limited oxidation. For the lifetime prediction of elastomer components, it is essential to have detailed knowledge about the absorption and diffusion behaviour of oxygen molecules during thermo-oxidative ageing and how they react with the elastomer. Experimental investigations on industrially used elastomeric materials are executed in order to develop and fit models, which shall be capable of predicting the permeation and consumption of oxygen as well as changes in the mechanical properties. The latter are of prime importance for technical applications of rubber components. Oxidation does not occur homogeneously over the entire elastomeric component. Hence, material models which include ageing effects have to be amplified in order to consider heterogeneous ageing, which highly depends on the ageing temperature. The influence of elevated temperatures upon accelerated ageing has to be critically analysed, and influences on the permeation and diffusion coefficient have to be taken into account. This work presents phenomenological models which describe the oxygen uptake and the diffusion into elastomers based on an improved understanding of ongoing chemical processes and diffusion limiting modifications. On the one side, oxygen uptake is modelled by means of Henry's law in which solubility is a function of the temperature as well as the ageing progress. The latter is an irreversible process and described by an inner differential evolution equation. On the other side, further diffusion of oxygen into the material is described by a model based on Fick's law, which is modified by a reaction term. The evolved diffusion-reaction equation depends on the ageing temperature as well as on the progress of ageing and is able to describe diffusion-limited oxidation.

Boundary-layer exchange by bubble: A novel method for generating transient nanofluidic layers

NASA Astrophysics Data System (ADS)

Jennissen, Herbert P.

2005-10-01

Unstirred layers (i.e., Nernst boundary layers) occur on every dynamic solid-liquid interface, constituting a diffusion barrier, since the velocity of a moving liquid approaches zero at the surface (no slip). If a macromolecule-surface reaction rate is higher than the diffusion rate, the Nernst layer is solute depleted and the reaction rate becomes mass-transport limited. The thickness of a Nernst boundary layer (δN) generally lies between 5 and 50μm. In an evanescent wave rheometer, measuring fibrinogen adsorption to fused silica, we made the fundamental observation that an air bubble preceding the sample through the flow cell abolishes the mass-transport limitation of the Nernst diffusion layer. Instead exponential kinetics are found. Experimental and simulation studies strongly indicate that these results are due to the elimination of the Nernst diffusion layer and its replacement by a dynamic nanofluidic layer (δν) maximally 200-300nm thick. It is suggested that the air bubble leads to a transient boundary-layer separation into a novel nanoboundary layer on the surface and the bulk fluid velocity profile separated by a vortex sheet with an estimated lifetime of 30-60s. A bubble-induced boundary-layer exchange from the Nernst to the nanoboundary layer and back is obtained, giving sufficient time for the measurement of unbiased exponential surface kinetics. Noteworthy is that the nanolayer can exist at all and displays properties such as (i) a long persistence and resistance to dissipation by the bulk liquid (boundary-layer-exchange-hysteresis) and (ii) a lack of solute depletion in spite of boundary-layer separation. The boundary-layer-exchange by bubble (BLEB) method therefore appears ideal for enhancing the rates of all types of diffusion-limited macromolecular reactions on surfaces with contact angles between 0° and 90° and only appears limited by slippage due to nanobubbles or an air gap beneath the nanofluidic layer on very hydrophobic surfaces. The possibility of producing nanoboundary layers without any nanostructuring or nanomachining should also be useful for fundamental physical studies in nanofluidics.

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

NASA Astrophysics Data System (ADS)

Papazian, John M.

1982-05-01

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

From conservative to reactive transport under diffusion-controlled conditions

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Diffusion Limited Supercritical Water Oxidation (SCWO) in Microgravity Environments

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

Connecting localized DNA strand displacement reactions

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

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

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

PubMed Central

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-01-01

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

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

PubMed Central

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

2015-01-01

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

Diffusion and binding analyzed with combined point FRAP and FCS.

PubMed

Im, Kang-Bin; Schmidt, Ute; Kang, Moon-Sik; Lee, Ji-Young; Bestvater, Felix; Wachsmuth, Malte

2013-09-01

To quantify more precisely and more reliably diffusion and reaction properties of biomolecules in living cells, a novel closed description in 3D of both the bleach and the post-bleach segment of fluorescence recovery after photobleaching (FRAP) data acquired at a point, i.e., a diffraction-limited observation area, termed point FRAP, is presented. It covers a complete coupled reaction-diffusion scheme for mobile molecules undergoing transient or long-term immobilization because of binding. We assess and confirm the feasibility with numerical solutions of the differential equations. By applying this model to free EYFP expressed in HeLa cells using a customized confocal laser scanning microscope that integrates point FRAP and fluorescence correlation spectroscopy (FCS), the applicability is validated by comparison with results from FCS. We show that by taking diffusion during bleaching into consideration and/or by employing a global analysis of series of bleach times, the results can be improved significantly. As the point FRAP approach allows to obtain data with diffraction-limited positioning accuracy, diffusion and binding properties of the exon-exon junction complex (EJC) components REF2-II and Magoh are obtained at different localizations in the nucleus of MCF7 cells and refine our view on the position-dependent association of the EJC factors with a maturating mRNP complex. Our findings corroborate the concept of combining point FRAP and FCS for a better understanding of the underlying diffusion and binding processes. Copyright © 2013 International Society for Advancement of Cytometry.

Mesophyll conductance and reaction-diffusion models for CO2 transport in C3 leaves; needs, opportunities and challenges.

PubMed

Berghuijs, Herman N C; Yin, Xinyou; Ho, Q Tri; Driever, Steven M; Retta, Moges A; Nicolaï, Bart M; Struik, Paul C

2016-11-01

One way to increase potential crop yield could be increasing mesophyll conductance g m . This variable determines the difference between the CO 2 partial pressure in the intercellular air spaces (C i ) and that near Rubisco (C c ). Various methods can determine g m from gas exchange measurements, often combined with measurements of chlorophyll fluorescence or carbon isotope discrimination. g m lumps all biochemical and physical factors that cause the difference between C c and C i . g m appears to vary with C i . This variability indicates that g m does not satisfy the physical definition of a conductance according to Fick's first law and is thus an apparent parameter. Uncertainty about the mechanisms that determine g m can be limited to some extent by using analytical models that partition g m into separate conductances. Such models are still only capable of describing the CO 2 diffusion pathway to a limited extent, as they make implicit assumptions about the position of mitochondria in the cells, which affect the re-assimilation of (photo)respired CO 2 . Alternatively, reaction-diffusion models may be used. Rather than quantifying g m , these models explicitly account for factors that affect the efficiency of CO 2 transport in the mesophyll. These models provide a better mechanistic description of the CO 2 diffusion pathways than mesophyll conductance models. Therefore, we argue that reaction-diffusion models should be used as an alternative to mesophyll conductance models, in case the aim of such a study is to identify traits that can be improved to increase g m . Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

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

PubMed

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

2014-03-26

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

Composite catalyst surfaces: Effect of inert and active heterogeneities on pattern formation

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

Baer, M.; Bangia, A.K.; Kevrekidis, I.G.

1996-12-05

Spatiotemporal dynamics in reaction-diffusion systems can be altered through the properties (reactivity, diffusivity) of the medium in which they occur. We construct active heterogeneous media (composite catalytic surfaces with inert as well as active illusions) using microelectronics fabrication techniques and study the spatiotemporal dynamics of heterogeneous catalytic reactions on these catalysts. In parallel, we perform simulations as well as numerical stability and bifurcation analysis of these patterns using mechanistic models. At the limit of large heterogeneity `grain size` (compared to the wavelength of spontaneously arising structures) the interaction patterns with inert or active boundaries dominates (e.g., pinning, transmission, and boundarymore » breakup of spirals, interaction of pulses with corners, `pacemaker` effects). At the opposite limit of very small or very finely distributed heterogeneity, effective behavior is observed (slight modulation of pulses, nearly uniform oscillations, effective spirals). Some representative studies of transitions between the two limits are presented. 48 refs., 11 figs.« less

Energy Distribution among Reaction Products. III: The Method of Measured Relaxation Applied to H + Cl2

NASA Technical Reports Server (NTRS)

Pacey, P. D.; Polyani, J. C.

1971-01-01

The method of measured relaxation is described for the determination of initial vibrational energy distribution in the products of exothermic reaction. Hydrogen atoms coming from an orifice were diffused into flowing chlorine gas. Measurements were made of the resultant ir chemiluminescence at successive points along the line of flow. The concurrent processes of reaction, diffusion, flow, radiation, and deactivation were analyzed in some detail on a computer. A variety of relaxation models were used in an attempt to place limits on k(nu prime), the rate constant for reaction to form HCl in specified vibrational energy levels: H+Cl2 yields (sup K(nu prime) HCl(sub nu prime) + Cl. The set of k(?) obtained from this work is in satisfactory agreement with those obtained by another experimental method (the method of arrested relaxation described in Parts IV and V of the present series.

Solution of non-steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Jana Ranjani, R.

2018-04-01

In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.

Fractal Aggregates in Tennis Ball Systems

ERIC Educational Resources Information Center

Sabin, J.; Bandin, M.; Prieto, G.; Sarmiento, F.

2009-01-01

We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the…

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.

Reaction Gradients Viewed Inside Single Photoactive Particles

NASA Astrophysics Data System (ADS)

Alpert, P.; Corral Arroyo, P.; Dou, J.; Kreiger, U.; Luo, B.; Peter, T.; Ammann, M.

2017-12-01

In terms of chemical selectivity and spatial resolution, a technique known as scanning transmission X-ray microscopy coupled to near-edge X-ray absorption fine structure spectroscopy (STXM/NEXAFS) is unmatched and will remain so for years into the future. We present a recent development coupling STXM/NEXAFS to a custom-built photochemical environmental reactor in which aerosol particles reside allowing for in situ chemical imaging. A laboratory investigation of metal-organic complex photochemistry was conducted. Transition metals are of great importance to atmospheric chemistry and aerosol photochemical aging due to their ability to catalyze oxidation reactions. Aerosol particles composed of mixtures of citric acid and iron citrate were probed for their organic carbon composition and iron oxidation state under atmospherically relevant conditions. At 40% relative humidity, oxygen diffusion and reaction was severely limited. Fe was reoxidized in the first 200 nm of the particle surface leaving reduced iron in the core. Similar gradients were observed at 60% RH, however waiting approximately 2 hours in the dark resulted in a recovery of the initial Fe(III) concentration. We draw two main conclusions from our findings. Frist, the oxidation gradients must have been the result of anoxic conditions at the interior of aerosol particles. This was predicted using a newly developed model for molecular diffusion through multiple layers with a reaction framework describing the photochemical processing of the metal organic matrix. Second, the lifetime of organic radicals in an anoxic diffusion limited organic matrix must be considerably long ( hours) to completely reoxidize iron as they wait for molecular oxygen. Long radical lifetimes in viscous organic aerosol in turn, could create high radical concentrations or favor radical-radical reactions in particles typically not considered when oxygen is plentiful. Our results impact predictions of aerosol physiochemical properties, e.g. aerosol toxicity, hygroscopicity, lifetime and light scattering properties over time which may be limited and evolve at different rates at the surface or core of particles.

Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes.

PubMed

Xu, Jingjie; Xie, Yan; Lu, Benzhuo; Zhang, Linbo

2016-08-25

The Debye-Hückel limiting law is used to study the binding kinetics of substrate-enzyme system as well as to estimate the reaction rate of a electrostatically steered diffusion-controlled reaction process. It is based on a linearized Poisson-Boltzmann model and known for its accurate predictions in dilute solutions. However, the substrate and product particles are in nonequilibrium states and are possibly charged, and their contributions to the total electrostatic field cannot be explicitly studied in the Poisson-Boltzmann model. Hence the influences of substrate and product on reaction rate coefficient were not known. In this work, we consider all the charged species, including the charged substrate, product, and mobile salt ions in a Poisson-Nernst-Planck model, and then compare the results with previous work. The results indicate that both the charged substrate and product can significantly influence the reaction rate coefficient with different behaviors under different setups of computational conditions. It is interesting to find that when substrate and product are both considered, under an overall neutral boundary condition for all the bulk charged species, the computed reaction rate kinetics recovers a similar Debye-Hückel limiting law again. This phenomenon implies that the charged product counteracts the influence of charged substrate on reaction rate coefficient. Our analysis discloses the fact that the total charge concentration of substrate and product, though in a nonequilibrium state individually, obeys an equilibrium Boltzmann distribution, and therefore contributes as a normal charged ion species to ionic strength. This explains why the Debye-Hückel limiting law still works in a considerable range of conditions even though the effects of charged substrate and product particles are not specifically and explicitly considered in the theory.

Nonlinear restrictions on dynamo action. [in magnetic fields of astrophysical objects

NASA Technical Reports Server (NTRS)

Vainshtein, Samuel I.; Cattaneo, Fausto

1992-01-01

Astrophysical dynamos operate in the limit of small magnetic diffusivity. In order for magnetic reconnection to occur, very small magnetic structures must form so that diffusion becomes effective. The formation of small-scale fields is accompanied by the stretching of the field lines and therefore by an amplification of the magnetic field strength. The back reaction of the magnetic field on the motions leads to the eventual saturation of the dynamo process, thus posing a constraint on the amount of magnetic flux that can be generated by dynamo action, It is argued that in the limit of small diffusivity only a small amount of flux, many orders of magnitude less than the observed fluxes, can be created by dynamo processes.

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.

Modification of the flow pass method as applied to problems of chemistry of planet atmospheres

NASA Technical Reports Server (NTRS)

Parshev, V. A.

1980-01-01

It was shown that the modified flow pass method possesses considerable effectiveness, both in the case when the coefficient of diffusion changes severely in the examined region and in the case when diffusion is the prevalent process, as compared with chemical reactions. The case when a regular pass proves inapplicable, or applicable in a limited interval of the decisive parameters, was examined.

Reactive nanolaminate pulsed-laser ignition mechanism: Modeling and experimental evidence of diffusion limited reactions

DOE PAGES

Yarrington, C. D.; Abere, M. J.; Adams, D. P.; ...

2017-04-03

We irradiated Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm 2 and 1189 W/cm 2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. While the shorter pulse shows uniform brightness, videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model themore » progress from reactants to products at both pulse widths. Finally, the model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.« less

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« 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.

Influence of cobalt and manganese content on the dehydrogenation capacity and kinetics of air-exposed LaNi 5+ x-type alloys in solid gas and electrochemical reactions

NASA Astrophysics Data System (ADS)

Raekelboom, E.; Cuevas, F.; Knosp, B.; Percheron-Guégan, A.

The effect of cobalt and manganese content on the dehydrogenation properties of air-exposed MmB 5+ x-type (Mm = mischmetal; B = Ni, Al, Co and Mn) alloys was investigated both in solid gas and electrochemical reactions. The cobalt and manganese content were varied separately while keeping constant the plateau pressure of the hydrides. The increase of the cobalt content leads to a decrease of the hydrogen capacity whereas the manganese content has no much effect. In solid gas reactions, the kinetics were found to be limited by the hydrogen diffusion through the surface oxidation layer. As for the electrochemistry, the kinetics are limited by a corrosion layer formed in alkaline medium. The desorption rates for both processes increase as the cobalt or manganese content decreases. This is thought to be due to an enhancement of the hydrogen diffusivity through the oxidation layer. As a result, a low cobalt or manganese content in MmB 5+ x alloys is found to be beneficial for the hydrogen desorption kinetics in both processes.

Isotachophoresis-Based Surface Immunoassay.

PubMed

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

2017-07-18

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

Rethinking pattern formation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Halatek, J.; Frey, E.

2018-05-01

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

Detox{sup SM} wet oxidation system studies for engineering scale up

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

Robertson, D.T.; Moslander, J.E.; Zigmond, J.A.

1995-12-31

Catalyzed wet oxidation utilizing iron(III) has been shown to have promise for treating many hazardous and mixed wastes. The reaction occurs at the surface of contact between an aqueous iron(III) solution and organic material. Studies with liquid- and vapor-phase organic waste surrogates have established reaction kinetics and the limits of reaction rate based on organic concentration and iron(III) diffusion. Continuing engineering studies have concentrated on reaction vessel agitator and solids feed configurations, an improved bench scale reflux condenser and reflux condenser calculations, sparging of organic compounds from the process condensate water, filtration of solids from the process solution, and flammabilitymore » limits for volatile organic compounds in the headspace of the reaction vessel under the reaction conditions. Detailed engineering design and fabrication of a demonstration unit for treatment of mixed waste is in progress.« less

Diffusional limits to the consumption of atmospheric methane by soils

USGS Publications Warehouse

Striegl, Robert G.

1993-01-01

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

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

Pore diffusion limits removal of monochloramine in treatment of swimming pool water using granular activated carbon.

PubMed

Skibinski, Bertram; Götze, Christoph; Worch, Eckhard; Uhl, Wolfgang

2018-04-01

Overall apparent reaction rates for the removal of monochloramine (MCA) in granular activated carbon (GAC) beds were determined using a fixed-bed reactor system and under conditions typical for swimming pool water treatment. Reaction rates dropped and quasi-stationary conditions were reached quickly. Diffusional mass transport in the pores was shown to be limiting the overall reaction rate. This was reflected consistently in the Thiele modulus, in the effect of temperature, pore size distribution and of grain size on the reaction rates. Pores <2.5 times the diameter of the monochloramine molecule were shown to be barely accessible for the monochloramine conversion reaction. GACs with a significant proportion of large mesopores were found to have the highest overall reactivity for monochloramine removal. Copyright © 2017 Elsevier Ltd. All rights reserved.

Direct simulations of chemically reacting turbulent mixing layers

NASA Technical Reports Server (NTRS)

Riley, J. J.; Metcalfe, R. W.

1984-01-01

The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

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

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

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

PubMed

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

2010-01-01

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

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

PubMed

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

2009-05-20

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

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads.

PubMed

Ha, Jiyeon; Engler, Cady R; Lee, Seung Jae

2008-07-01

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited. (c) 2007 Wiley Periodicals, Inc.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Nitric oxide diffusion to red blood cells limits extracellular, but not intraphagosomal, peroxynitrite formation by macrophages.

PubMed

Prolo, Carolina; Álvarez, María Noel; Ríos, Natalia; Peluffo, Gonzalo; Radi, Rafael; Romero, Natalia

2015-10-01

Macrophage-derived nitric oxide ((•)NO) participates in cytotoxic mechanisms against diverse microorganisms and tumor cells. These effects can be mediated by (•)NO itself or (•)NO-derived species such as peroxynitrite formed by its diffusion-controlled reaction with NADPH oxidase-derived superoxide radical anion (O(2)(•-)). In vivo, the facile extracellular diffusion of (•)NO as well as different competing consumption routes limit its bioavailability for the reaction with O(2)(•-) and, hence, peroxynitrite formation. In this work, we evaluated the extent by which (•)NO diffusion to red blood cells (RBC) can compete with activated macrophages-derived O(2)(•-) and affect peroxynitrite formation yields. Macrophage-dependent peroxynitrite production was determined by boron-based probes that react directly with peroxynitrite, namely, coumarin-7-boronic acid (CBA) and fluorescein-boronate (Fl-B). The influence of (•)NO diffusion to RBC on peroxynitrite formation was experimentally analyzed in co-incubations of (•)NO and O(2)(•-)-forming macrophages with erythrocytes. Additionally, we evaluated the permeation of (•)NO to RBC by measuring the intracellular oxidation of oxyhemoglobin to methemoglobin. Our results indicate that diluted RBC suspensions dose-dependently inhibit peroxynitrite formation, outcompeting the O(2)(•-) reaction. Computer-assisted kinetic studies evaluating peroxynitrite formation by its precursor radicals in the presence of RBC are in accordance with experimental results. Moreover, the presence of erythrocytes in the proximity of (•)NO and O(2)(•-)-forming macrophages prevented intracellular Fl-B oxidation pre-loaded in L1210 cells co-cultured with activated macrophages. On the other hand, Fl-B-coated latex beads incorporated in the macrophage phagocytic vacuole indicated that intraphagosomal probe oxidation by peroxynitrite was not affected by nearby RBC. Our data support that in the proximity of a blood vessel, (•)NO consumption by RBC will limit the extracellular formation (and subsequent cytotoxic effects) of peroxynitrite by activated macrophages, while the intraphagosomal yield of peroxynitrite will remain unaffected. Copyright © 2015. Published by Elsevier Inc.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

NASA Astrophysics Data System (ADS)

Hatakeyama, S.; Horiuchi, W.; Kohama, A.

2018-05-01

The nuclear surface provides useful information on nuclear radius, nuclear structure, as well as properties of nuclear matter. We discuss the relationship between the nuclear surface diffuseness and elastic scattering differential cross section at the first diffraction peak of high-energy nucleon-nucleus scattering as an efficient tool in order to extract the nuclear surface information from limited experimental data involving short-lived unstable nuclei. The high-energy reaction is described by a reliable microscopic reaction theory, the Glauber model. Extending the idea of the black sphere model, we find one-to-one correspondence between the nuclear bulk structure information and proton-nucleus elastic scattering diffraction peak. This implies that we can extract both the nuclear radius and diffuseness simultaneously, using the position of the first diffraction peak and its magnitude of the elastic scattering differential cross section. We confirm the reliability of this approach by using realistic density distributions obtained by a mean-field model.

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

Turbulent patterns in wall-bounded flows: A Turing instability?

NASA Astrophysics Data System (ADS)

Manneville, Paul

2012-06-01

In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the pipe flow transition involving reaction-diffusion concepts, we consider plane Couette flow in the same perspective and transform Waleffe's classical four-variable model of self-sustaining process into a reaction-diffusion model. We show that, upon fulfillment of a condition on the relative diffusivities of its variables, the featureless turbulent regime becomes unstable against patterning as the result of a Turing instability. A reduced two-variable model helps us to delineate the appropriate region of parameter space. An intrinsic status is therefore given to the pattern's wavelength for the first time. Virtues and limitations of the model are discussed, calling for a microscopic support of the phenomenological approach.

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

PubMed

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

2017-02-01

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

Nitrogen-doped carbonaceous catalysts for gas-diffusion cathodes for alkaline aluminum-air batteries

NASA Astrophysics Data System (ADS)

Davydova, E. S.; Atamanyuk, I. N.; Ilyukhin, A. S.; Shkolnikov, E. I.; Zhuk, A. Z.

2016-02-01

Cobalt tetramethoxyphenyl porphyrin and polyacrylonitrile - based catalysts for oxygen reduction reaction were synthesized and characterized by means of SEM, TEM, XPS, BET, limited evaporation method, rotating disc and rotating ring-disc electrode methods. Half-cell and Al-air cell tests were carried out to determine the characteristics of gas-diffusion cathodes. Effect of active layer thickness and its composition on the characteristics of the gas-diffusion cathodes was investigated. Power density of 300 mW cm-2 was achieved for alkaline Al-air cell with an air-breathing polyacrylonitrile-based cathode.

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

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

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 problem.

Solute-solvent complex switching dynamics of chloroform between acetone and dimethylsulfoxide-two-dimensional IR chemical exchange spectroscopy.

PubMed

Kwak, Kyungwon; Rosenfeld, Daniel E; Chung, Jean K; Fayer, Michael D

2008-11-06

Hydrogen bonds formed between C-H and various hydrogen bond acceptors play important roles in the structure of proteins and organic crystals, and the mechanisms of C-H bond cleavage reactions. Chloroform, a C-H hydrogen bond donor, can form weak hydrogen-bonded complexes with acetone and with dimethylsulfoxide (DMSO). When chloroform is dissolved in a mixed solvent consisting of acetone and DMSO, both types of hydrogen-bonded complexes exist. The two complexes, chloroform-acetone and chloroform-DMSO, are in equilibrium, and they rapidly interconvert by chloroform exchanging hydrogen bond acceptors. This fast hydrogen bond acceptor substitution reaction is probed using ultrafast two-dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy. Deuterated chloroform is used in the experiments, and the 2D-IR spectrum of the C-D stretching mode is measured. The chemical exchange of the chloroform hydrogen bonding partners is tracked by observing the time-dependent growth of off-diagonal peaks in the 2D-IR spectra. The measured substitution rate is 1/30 ps for an acetone molecule to replace a DMSO molecule in a chloroform-DMSO complex and 1/45 ps for a DMSO molecule to replace an acetone molecule in a chloroform-acetone complex. Free chloroform exists in the mixed solvent, and it acts as a reactive intermediate in the substitution reaction, analogous to a SN1 type reaction. From the measured rates and the equilibrium concentrations of acetone and DMSO, the dissociation rates for the chloroform-DMSO and chloroform-acetone complexes are found to be 1/24 ps and 1/5.5 ps, respectively. The difference between the measured rate for the complete substitution reaction and the rate for complex dissociation corresponds to the diffusion limited rate. The estimated diffusion limited rate agrees well with the result from a Smoluchowski treatment of diffusive reactions.

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.

Elementary reaction modeling of reversible CO/CO2 electrochemical conversion on patterned nickel electrodes

NASA Astrophysics Data System (ADS)

Luo, Yu; Shi, Yixiang; Li, Wenying; Cai, Ningsheng

2018-03-01

CO/CO2 are the major gas reactant/product in the fuel electrode of reversible solid oxide cells (RSOC). This study proposes a two-charge-transfer-step mechanism to describe the reaction and transfer processes of CO-CO2 electrochemical conversion on a patterned Ni electrode of RSOC. An elementary reaction model is developed to couple two charge transfer reactions, C(Ni)+O2-(YSZ) ↔ CO(Ni)+(YSZ) +2e- and CO(Ni)+O2-(YSZ) ↔ CO2(Ni)+(YSZ)+2e-, with adsorption/desorption, surface chemical reactions and surface diffusion. This model well validates in both solid oxide electrolysis cell (SOEC) and solid oxide fuel cell (SOFC) modes by the experimental data from a patterned Ni electrode with 10 μm stripe width at different pCO (0-0.25 atm), pCO2 (0-0.35 atm) and operating temperature (600-700 °C). This model indicates SOEC mode is dominated by charge transfer step C(Ni)+O2-(YSZ)↔CO(Ni)+(YSZ) +2e-, while SOFC mode by CO(Ni)+ O2-(YSZ)↔CO2(Ni)+(YSZ)+2e- on the patterned Ni electrode. The sensitivity analysis shows charge transfer step is the major rate-determining step for RSOC, besides, surface diffusion of CO and CO2 as well as CO2 adsorption also plays a significant role in the electrochemical reaction of SOEC while surface diffusion of CO and CO2 desorption could be co-limiting in SOFC.

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.

Temperature- and composition-dependent hydrogen diffusivity in palladium from statistically-averaged molecular dynamics

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

Zhou, Xiaowang; Heo, Tae Wook; Wood, Brandon C.

Solid-state hydrogen storage materials undergo complex phase transformations whose kinetics is often limited by hydrogen diffusion. Among metal hydrides, palladium hydride undergoes a diffusional phase transformation upon hydrogen uptake, during which the hydrogen diffusivity varies with hydrogen composition and temperature. Here we perform robust statistically-averaged molecular dynamics simulations to obtain a well-converged analytical expression for hydrogen diffusivity in bulk palladium that is valid throughout all stages of the reaction. Our studies confirm significant dependence of the diffusivity on composition and temperature that elucidate key trends in the available experimental measurements. Whereas at low hydrogen compositions, a single process dominates, atmore » high hydrogen compositions, diffusion is found to exhibit behavior consistent with multiple hopping barriers. Further analysis, supported by nudged elastic band computations, suggests that the multi-barrier diffusion can be interpreted as two distinct mechanisms corresponding to hydrogen-rich and hydrogen-poor local environments.« less

Temperature- and composition-dependent hydrogen diffusivity in palladium from statistically-averaged molecular dynamics

DOE PAGES

Zhou, Xiaowang; Heo, Tae Wook; Wood, Brandon C.; ...

2018-03-09

Solid-state hydrogen storage materials undergo complex phase transformations whose kinetics is often limited by hydrogen diffusion. Among metal hydrides, palladium hydride undergoes a diffusional phase transformation upon hydrogen uptake, during which the hydrogen diffusivity varies with hydrogen composition and temperature. Here we perform robust statistically-averaged molecular dynamics simulations to obtain a well-converged analytical expression for hydrogen diffusivity in bulk palladium that is valid throughout all stages of the reaction. Our studies confirm significant dependence of the diffusivity on composition and temperature that elucidate key trends in the available experimental measurements. Whereas at low hydrogen compositions, a single process dominates, atmore » high hydrogen compositions, diffusion is found to exhibit behavior consistent with multiple hopping barriers. Further analysis, supported by nudged elastic band computations, suggests that the multi-barrier diffusion can be interpreted as two distinct mechanisms corresponding to hydrogen-rich and hydrogen-poor local environments.« less

Single-image diffusion coefficient measurements of proteins in free solution.

PubMed

Zareh, Shannon Kian; DeSantis, Michael C; Kessler, Jonathan M; Li, Je-Luen; Wang, Y M

2012-04-04

Diffusion coefficient measurements are important for many biological and material investigations, such as studies of particle dynamics and kinetics, and size determinations. Among current measurement methods, single particle tracking (SPT) offers the unique ability to simultaneously obtain location and diffusion information about a molecule while using only femtomoles of sample. However, the temporal resolution of SPT is limited to seconds for single-color-labeled samples. By directly imaging three-dimensional diffusing fluorescent proteins and studying the widths of their intensity profiles, we were able to determine the proteins' diffusion coefficients using single protein images of submillisecond exposure times. This simple method improves the temporal resolution of diffusion coefficient measurements to submilliseconds, and can be readily applied to a range of particle sizes in SPT investigations and applications in which diffusion coefficient measurements are needed, such as reaction kinetics and particle size determinations. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

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.

An atmospheric pressure flow reactor: Gas phase kinetics and mechanism in tropospheric conditions without wall effects

NASA Technical Reports Server (NTRS)

Koontz, Steven L.; Davis, Dennis D.; Hansen, Merrill

1988-01-01

A new type of gas phase flow reactor, designed to permit the study of gas phase reactions near 1 atm of pressure, is described. A general solution to the flow/diffusion/reaction equations describing reactor performance under pseudo-first-order kinetic conditions is presented along with a discussion of critical reactor parameters and reactor limitations. The results of numerical simulations of the reactions of ozone with monomethylhydrazine and hydrazine are discussed, and performance data from a prototype flow reactor are presented.

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

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

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

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

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.

Kinetic effects of toluene blending on the extinction limit of n-decane diffusion flames

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

Won, Sang Hee; Sun, Wenting; Ju, Yiguang

The impact of toluene addition in n-decane on OH concentrations, maximum heat release rates, and extinction limits were studied experimentally and computationally by using counterflow diffusion flames with laser induced fluorescence imaging. Sensitivity analyses of kinetic path ways and species transport on flame extinction were also conducted. The results showed that the extinction strain rate of n-decane/toluene/nitrogen flames decreased significantly with an increase of toluene addition and depended linearly on the maximum OH concentration. It was revealed that the maximum OH concentration, which depends on the fuel H/C ratio, can be used as an index of the radical pool andmore » chemical heat release rate, since it plays a significant role on the heat production via the reaction with other species, such as CO, H{sub 2}, and HCO. Experimental results further demonstrated that toluene addition in n-decane dramatically reduced the peak OH concentration via H abstraction reactions and accelerated flame extinction via kinetic coupling between toluene and n-decane mechanisms. Comparisons between experiments and simulations revealed that the current toluene mechanism significantly over-predicts the radical destruction rate, leading to under-prediction of extinction limits and OH concentrations, especially caused by the uncertainty of the H abstraction reaction from toluene, which rate coefficient has a difference by a factor of 5 in the tested toluene models. In addition, sensitivity analysis of diffusive transport showed that in addition to n-decane and toluene, the transport of OH and H also considerably affects the extinction limit. A reduced linear correlation between the extinction limits of n-decane/toluene blended fuels and the H/C ratio as well as the mean fuel molecular weight was obtained. The results suggest that an explicit prediction of the extinction limits of aromatic and alkane blended fuels can be established by using H/C ratio (or radical index) and the mean fuel molecular weight which represent the rates of radical production and the fuel transport, respectively. (author)« less

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.

Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

NASA Technical Reports Server (NTRS)

Sutula, J. A.; Torero, J. L.; Ezekoye, O. A.

1999-01-01

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra(sub L) = (Beta)(g(sub 0))(L(exp 3) del T)/(alpha(v))) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

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.

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.

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

PubMed

Roques, L; Walker, E; Franck, P; Soubeyrand, S; Klein, E K

2016-08-01

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

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

NASA Astrophysics Data System (ADS)

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

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

THE SPATIO-TEMPORAL EVOLUTION OF SOLAR FLARES OBSERVED WITH AIA/SDO: FRACTAL DIFFUSION, SUB-DIFFUSION, OR LOGISTIC GROWTH?

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

Aschwanden, Markus J., E-mail: aschwanden@lmsal.com

2012-09-20

We explore the spatio-temporal evolution of solar flares by fitting a radial expansion model r(t) that consists of an exponentially growing acceleration phase, followed by a deceleration phase that is parameterized by the generalized diffusion function r(t){proportional_to}{kappa}(t - t{sub 1}){sup {beta}/2}, which includes the logistic growth limit ({beta} = 0), sub-diffusion ({beta} = 0-1), classical diffusion ({beta} = 1), super-diffusion ({beta} = 1-2), and the linear expansion limit ({beta} = 2). We analyze all M- and X-class flares observed with Geostationary Operational Environmental Satellite and Atmospheric Imaging Assembly/Solar Dynamics Observatory (SDO) during the first two years of the SDO mission,more » amounting to 155 events. We find that most flares operate in the sub-diffusive regime ({beta} = 0.53 {+-} 0.27), which we interpret in terms of anisotropic chain reactions of intermittent magnetic reconnection episodes in a low plasma-{beta} corona. We find a mean propagation speed of v = 15 {+-} 12 km s{sup -1}, with maximum speeds of v{sub max} = 80 {+-} 85 km s{sup -1} per flare, which is substantially slower than the sonic speeds expected for thermal diffusion of flare plasmas. The diffusive characteristics established here (for the first time for solar flares) is consistent with the fractal-diffusive self-organized criticality model, which predicted diffusive transport merely based on cellular automaton simulations.« less

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.

Cooperativity to increase Turing pattern space for synthetic biology.

PubMed

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

2015-02-20

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

Bootstrapping Least Squares Estimates in Biochemical Reaction Networks

PubMed Central

Linder, Daniel F.

2015-01-01

The paper proposes new computational methods of computing confidence bounds for the least squares estimates (LSEs) of rate constants in mass-action biochemical reaction network and stochastic epidemic models. Such LSEs are obtained by fitting the set of deterministic ordinary differential equations (ODEs), corresponding to the large volume limit of a reaction network, to network’s partially observed trajectory treated as a continuous-time, pure jump Markov process. In the large volume limit the LSEs are asymptotically Gaussian, but their limiting covariance structure is complicated since it is described by a set of nonlinear ODEs which are often ill-conditioned and numerically unstable. The current paper considers two bootstrap Monte-Carlo procedures, based on the diffusion and linear noise approximations for pure jump processes, which allow one to avoid solving the limiting covariance ODEs. The results are illustrated with both in-silico and real data examples from the LINE 1 gene retrotranscription model and compared with those obtained using other methods. PMID:25898769

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.

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

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

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

Understanding of interface structures and reaction mechanisms induced by Ge or GeO diffusion in Al{sub 2}O{sub 3}/Ge structure

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

Shibayama, Shigehisa; JSPS, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083; Kato, Kimihiko

2013-08-19

The reaction mechanisms at Al{sub 2}O{sub 3}/Ge interfaces with thermal oxidation through the Al{sub 2}O{sub 3} layer have been investigated. X-ray photoelectron spectroscopy reveals that an Al{sub 6}Ge{sub 2}O{sub 13} layer is formed near the interface, and a GeO{sub 2} layer is formed on the Al{sub 2}O{sub 3} surface, suggesting Ge or GeO diffusion from the Ge surface. It is also clarified that the Al{sub 6}Ge{sub 2}O{sub 13} layer is formed by the different mechanism with a small activation energy of 0.2 eV, compared with the GeO{sub 2} formation limited by oxygen diffusion. Formation of Al-O-Ge bonds due to themore » AlGeO formation could lead appropriate interface structures with high interface qualities.« less

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

PubMed

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

2017-02-01

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

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.

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.

Isotope fractionation by multicomponent diffusion (Invited)

NASA Astrophysics Data System (ADS)

Watkins, J. M.; Liang, Y.; Richter, F. M.; Ryerson, F. J.; DePaolo, D. J.

2013-12-01

Isotope fractionation by multicomponent diffusion The isotopic composition of mineral phases can be used to probe the temperatures and rates of mineral formation as well as the degree of post-mineralization alteration. The ability to interpret stable isotope variations is limited by our knowledge of three key parameters and their relative importance in determining the composition of a mineral grain and its surroundings: (1) thermodynamic (equilibrium) partitioning, (2) mass-dependent diffusivities, and (3) mass-dependent reaction rate coefficients. Understanding the mechanisms of diffusion and reaction in geological liquids, and how these mass transport processes discriminate between isotopes, represents an important problem that is receiving considerable attention in the geosciences. Our focus in this presentation will be isotope fractionation by chemical diffusion. Previous studies have documented that diffusive isotope effects vary depending on the cation as well as the liquid composition, but the ability to predict diffusive isotope effects from theory is limited; for example, it is unclear whether the magnitude of diffusive isotopic fractionations might also vary with the direction of diffusion in composition space. To test this hypothesis and to further guide the theoretical treatment of isotope diffusion, two chemical diffusion experiments and one self diffusion experiment were conducted at 1250°C and 0.7 GPa. In one experiment (A-B), CaO and Na2O counter-diffuse rapidly in the presence of a small SiO2 gradient. In the other experiment (D-E), CaO and SiO2 counter-diffuse more slowly in a small Na2O gradient. In both chemical diffusion experiments, Ca isotopes become fractionated by chemical diffusion but by different amounts, documenting for the first time that the magnitude of isotope fractionation by diffusion depends on the direction of diffusion in composition space. The magnitude of Ca isotope fractionation that develops is positively correlated with the rate of CaO diffusion; in A-B, the total variation is 2.5‰ whereas in D-E it is only 1.3‰. The diffusion of isotopes in a multicomponent system is modeled using a new expression for the isotope-specific diffusive flux that includes self diffusion terms in addition to the multicomponent chemical diffusion matrix. Kinetic theory predicts a mass dependence on isotopic mobility, i.e., self diffusivity, but it is unknown whether or how the mass dependence on self diffusivity translates into a mass dependence on chemical diffusion coefficients. The new experimental results allow us to assess several empirical expressions relating the self diffusivity and its mass dependence to the elements of the diffusion matrix and their mass dependence. Several plausible theoretical treatments can fit the data equally well. We are currently at the stage where experiments are guiding the theoretical treatment of the isotope fractionation by diffusion problem, underscoring the importance of experiments for aiding interpretations of isotopic variations in nature.

Particle-based modeling of heterogeneous chemical kinetics including mass transfer.

PubMed

Sengar, A; Kuipers, J A M; van Santen, Rutger A; Padding, J T

2017-08-01

Connecting the macroscopic world of continuous fields to the microscopic world of discrete molecular events is important for understanding several phenomena occurring at physical boundaries of systems. An important example is heterogeneous catalysis, where reactions take place at active surfaces, but the effective reaction rates are determined by transport limitations in the bulk fluid and reaction limitations on the catalyst surface. In this work we study the macro-micro connection in a model heterogeneous catalytic reactor by means of stochastic rotation dynamics. The model is able to resolve the convective and diffusive interplay between participating species, while including adsorption, desorption, and reaction processes on the catalytic surface. Here we apply the simulation methodology to a simple straight microchannel with a catalytic strip. Dimensionless Damkohler numbers are used to comment on the spatial concentration profiles of reactants and products near the catalyst strip and in the bulk. We end the discussion with an outlook on more complicated geometries and increasingly complex reactions.

Particle-based modeling of heterogeneous chemical kinetics including mass transfer

NASA Astrophysics Data System (ADS)

Sengar, A.; Kuipers, J. A. M.; van Santen, Rutger A.; Padding, J. T.

2017-08-01

Connecting the macroscopic world of continuous fields to the microscopic world of discrete molecular events is important for understanding several phenomena occurring at physical boundaries of systems. An important example is heterogeneous catalysis, where reactions take place at active surfaces, but the effective reaction rates are determined by transport limitations in the bulk fluid and reaction limitations on the catalyst surface. In this work we study the macro-micro connection in a model heterogeneous catalytic reactor by means of stochastic rotation dynamics. The model is able to resolve the convective and diffusive interplay between participating species, while including adsorption, desorption, and reaction processes on the catalytic surface. Here we apply the simulation methodology to a simple straight microchannel with a catalytic strip. Dimensionless Damkohler numbers are used to comment on the spatial concentration profiles of reactants and products near the catalyst strip and in the bulk. We end the discussion with an outlook on more complicated geometries and increasingly complex reactions.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

PubMed

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

2016-10-04

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

The Controversial Role of Inter-diffusion in Glass Alteration

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

Gin, Stephane; Neill, Lindsay; Fournier, M.

2016-11-15

Current kinetic models for nuclear waste glasses (e.g. GM2001, GRAAL) are based on a set of mechanisms that have been generally agreed upon within the international waste glass community. These mechanisms are: hydration of the glass, ion exchange reactions (the two processes are referred as inter-diffusion), hydrolysis of the silicate network, and condensation/precipitation of partly or completely hydrolyzed species that produces a porous and amorphous layer and crystalline phases on surface of the altered glass. Recently, a new idea with origins in the mineral dissolution community has been proposed that excludes inter-diffusion process as a potential rate-limiting mechanism. To understandmore » how the so-called interfacial dissolution/precipitation model can change the current understanding of glass behavior, a key experiment used to account for this model was replicated to further revisit the interpretation. This experiment was performed at 50°C, with SON68 glass, in static mode, deionized water and S/V ratio of 10 m-1 for 6 months. It turn out that glass alters in an intermediate kinetic regime between the forward and the residual rate. According to previous and new solid characterizations, it is concluded that neither a simple inter-diffusion model nor the interfacial dissolution precipitation model can account for the observed elemental profiles within the alteration layer. More generally, far and close-to-saturation conditions must be distinguished and literature provides evidences that inter-diffusion takes place in slightly acidic conditions and far from saturation. However, closer to saturation, when a sufficiently dense layer is formed, a new approach is proposed requiring a full description of chemical reactions taking place within the alteration layer and involving water molecules as it is thought that water accessibility to the pristine glass is the rate-limiting process.« less

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Understanding the initial irreversibility of metal sulfides for sodium-ion batteries via operando techniques

DOE PAGES

Wang, Liguang; Wang, Jiajun; Guo, Fangmin; ...

2018-11-13

Transition metal sulfides are promising high capacity anodes for sodium-ion batteries in terms of the conversion reaction with multiple alkali metal ions. Nonetheless, some inherent challenges such as sluggish sodium ion diffusion kinetics, large volume change, and poor cycle stability limit their implementation. Addressing these issues necessitates a comprehensive understanding the complex sodium ion storage mechanism particularly at the initial cycle. Here, taking nickel subsulfide as a model material, we reveal the complicated conversion reaction mechanism upon the first cycle by combining in operando 2D transmission X-ray microscopy with X-ray absorption spectroscopy, ex-situ 3D nano-tomography, high-energy X-ray diffraction and electrochemicalmore » impedance spectroscopy. This study demonstrates that the microstructure evolution, inherent slow sodium ions diffusion kinetics, and slow ion mobility at the two-phase interface contribute to the high irreversible capacity upon the first cycle. Finally, such understandings are critical for developing the conversion reaction materials with the desired electrochemical activity and stability.« less

Understanding the initial irreversibility of metal sulfides for sodium-ion batteries via operando techniques

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

Wang, Liguang; Wang, Jiajun; Guo, Fangmin

Transition metal sulfides are promising high capacity anodes for sodium-ion batteries in terms of the conversion reaction with multiple alkali metal ions. Nonetheless, some inherent challenges such as sluggish sodium ion diffusion kinetics, large volume change, and poor cycle stability limit their implementation. Addressing these issues necessitates a comprehensive understanding the complex sodium ion storage mechanism particularly at the initial cycle. Here, taking nickel subsulfide as a model material, we reveal the complicated conversion reaction mechanism upon the first cycle by combining in operando 2D transmission X-ray microscopy with X-ray absorption spectroscopy, ex-situ 3D nano-tomography, high-energy X-ray diffraction and electrochemicalmore » impedance spectroscopy. This study demonstrates that the microstructure evolution, inherent slow sodium ions diffusion kinetics, and slow ion mobility at the two-phase interface contribute to the high irreversible capacity upon the first cycle. Finally, such understandings are critical for developing the conversion reaction materials with the desired electrochemical activity and stability.« less

Zinc electrodeposition from flowing alkaline zincate solutions: Role of hydrogen evolution reaction

NASA Astrophysics Data System (ADS)

Dundálek, Jan; Šnajdr, Ivo; Libánský, Ondřej; Vrána, Jiří; Pocedič, Jaromír; Mazúr, Petr; Kosek, Juraj

2017-12-01

The hydrogen evolution reaction is known as a parasitic reaction during the zinc electrodeposition from alkaline zincate solutions and is thus responsible for current efficiency losses during the electrolysis. Besides that, the rising hydrogen bubbles may cause an extra convection within a diffusion layer, which leads to an enhanced mass transport of zincate ions to an electrode surface. In this work, the mentioned phenomena were studied experimentally in a flow through electrolyzer and the obtained data were subsequently evaluated by mathematical models. The results prove the indisputable influence of the rising hydrogen bubbles on the additional mixing of the diffusion layer, which partially compensates the drop of the current efficiency of the zinc deposition at higher current flows. Moreover, the results show that the current density ratio (i.e., the ratio of an overall current density to a zinc limiting current density) is not suitable for the description of the zinc deposition, because the hydrogen evolution current density is always involved in the overall current density.

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

Multistage adsorption of diffusing macromolecules and viruses

NASA Astrophysics Data System (ADS)

Chou, Tom; D'Orsogna, Maria R.

2007-09-01

We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein insertion, cell signaling, and the infection of cells by virus particles. For example, viral entry into healthy cells is possible only after a series of receptor and coreceptor binding events occurs at the cellular surface. We couple the diffusion of particles in the bulk phase with the multistage surface kinetics and derive an effective, integrodifferential boundary condition that contains a memory kernel embodying the delay induced by the surface reactions. This boundary condition takes the form of a singular perturbation problem in the limit where particle-surface interactions are short ranged. Moreover, depending on the surface kinetics, the delay kernel induces a nonmonotonic, transient replenishment of the bulk particle concentration near the interface. The approach generalizes that of Ward and Tordai [J. Chem. Phys. 14, 453 (1946)] and Diamant and Andelman [Colloids Surf. A 183-185, 259 (2001)] to include surface kinetics, giving rise to qualitatively new behaviors. Our analysis also suggests a simple scheme by which stochastic surface reactions may be coupled to deterministic bulk diffusion.

Fractal aggregates in tennis ball systems

NASA Astrophysics Data System (ADS)

Sabin, J.; Bandín, M.; Prieto, G.; Sarmiento, F.

2009-09-01

We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the images of the cluster of balls, following Forrest and Witten's pioneering studies on the aggregation of smoke particles, to estimate their fractal dimension.

Quantitative fluorescence imaging of protein diffusion and interaction in living cells.

PubMed

Capoulade, Jérémie; Wachsmuth, Malte; Hufnagel, Lars; Knop, Michael

2011-08-07

Diffusion processes and local dynamic equilibria inside cells lead to nonuniform spatial distributions of molecules, which are essential for processes such as nuclear organization and signaling in cell division, differentiation and migration. To understand these mechanisms, spatially resolved quantitative measurements of protein abundance, mobilities and interactions are needed, but current methods have limited capabilities to study dynamic parameters. Here we describe a microscope based on light-sheet illumination that allows massively parallel fluorescence correlation spectroscopy (FCS) measurements and use it to visualize the diffusion and interactions of proteins in mammalian cells and in isolated fly tissue. Imaging the mobility of heterochromatin protein HP1α (ref. 4) in cell nuclei we could provide high-resolution diffusion maps that reveal euchromatin areas with heterochromatin-like HP1α-chromatin interactions. We expect that FCS imaging will become a useful method for the precise characterization of cellular reaction-diffusion processes.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

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

A 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.

Point-particle method to compute diffusion-limited cellular uptake.

PubMed

Sozza, A; Piazza, F; Cencini, M; De Lillo, F; Boffetta, G

2018-02-01

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

CO2 diffusion into pore spaces limits weathering rate of an experimental basalt landscape

USGS Publications Warehouse

van Haren, Joost; Dontsova, Katerina; Barron-Gafford, Greg A.; Troch, Peter A.; Chorover, Jon; DeLong, Stephen B.; Breshears, David D.; Huxman, Travis E.; Pelletier, Jon D.; Saleska, Scott; Zeng, Xubin; Ruiz, Joaquin

2017-01-01

Basalt weathering is a key control over the global carbon cycle, though in situ measurements of carbon cycling are lacking. In an experimental, vegetation-free hillslope containing 330 m3 of ground basalt scoria, we measured real-time inorganic carbon dynamics within the porous media and seepage flow. The hillslope carbon flux (0.6–5.1 mg C m–2 h–1) matched weathering rates of natural basalt landscapes (0.4–8.8 mg C m–2 h–1) despite lacking the expected field-based impediments to weathering. After rainfall, a decrease in CO2 concentration ([CO2]) in pore spaces into solution suggested rapid carbon sequestration but slow reactant supply. Persistent low soil [CO2] implied that diffusion limited CO2 supply, while when sufficiently dry, reaction product concentrations limited further weathering. Strong influence of diffusion could cause spatial heterogeneity of weathering even in natural settings, implying that modeling studies need to include variable soil [CO2] to improve carbon cycling estimates associated with potential carbon sequestration methods.

Hydrogen diffusion in Zircon

NASA Astrophysics Data System (ADS)

Ingrin, Jannick; Zhang, Peipei

2016-04-01

Hydrogen mobility in gem quality zircon single crystals from Madagascar was investigated through H-D exchange experiments. Thin slices were annealed in a horizontal furnace flushed with a gas mixture of Ar/D2(10%) under ambient pressure between 900 ° C to 1150 ° C. FTIR analyses were performed on oriented slices before and after each annealing run. H diffusion along [100] and [010] follow the same diffusion law D = D0exp[-E /RT], with log D0 = 2.24 ± 1.57 (in m2/s) and E = 374 ± 39 kJ/mol. H diffusion along [001] follows a slightly more rapid diffusion law, with log D0 = 1.11 ± 0.22 (in m2/s) and E = 334 ± 49 kJ/mol. H diffusion in zircon has much higher activation energy and slower diffusivity than other NAMs below 1150 ° C even iron-poor garnets which are known to be among the slowest (Blanchard and Ingrin, 2004; Kurka et al. 2005). During H-D exchange zircon incorporates also deuterium. This hydration reaction involves uranium reduction as it is shown from the exchange of U5+ and U4+ characteristic bands in the near infrared region during annealing. It is the first time that a hydration reaction U5+ + OH- = U4+ + O2- + 1/2H2, is experimentally reported. The kinetics of deuterium incorporation is slightly slower than hydrogen diffusion, suggesting that the reaction is limited by hydrogen mobility. Hydrogen isotopic memory of zircon is higher than other NAMs. Zircons will be moderately retentive of H signatures at mid-crustal metamorphic temperatures. At 500 ° C, a zircon with a radius of 300 μm would retain its H isotopic signature over more than a million years. However, a zircon is unable to retain this information for geologically significant times under high-grade metamorphism unless the grain size is large enough. Refrences Blanchard, M. and Ingrin, J. (2004) Hydrogen diffusion in Dora Maira pyrope. Physics and Chemistry of Minerals, 31, 593-605. Kurka, A., Blanchard, M. and Ingrin, J. (2005) Kinetics of hydrogen extraction and deuteration in grossular. Mineralogical Magazine, 69, 359-371.

Investigation of the oxygen exchange mechanism on Pt|yttria stabilized zirconia at intermediate temperatures: Surface path versus bulk path

PubMed Central

Opitz, Alexander K.; Lutz, Alexander; Kubicek, Markus; Kubel, Frank; Hutter, Herbert; Fleig, Jürgen

2011-01-01

The oxygen exchange kinetics of platinum on yttria-stabilized zirconia (YSZ) was investigated by means of geometrically well-defined Pt microelectrodes. By variation of electrode size and temperature it was possible to separate two temperature regimes with different geometry dependencies of the polarization resistance. At higher temperatures (550–700 °C) an elementary step located close to the three phase boundary (TPB) with an activation energy of ∼1.6 eV was identified as rate limiting. At lower temperatures (300–400 °C) the rate limiting elementary step is related to the electrode area and exhibited a very low activation energy in the order of 0.2 eV. From these observations two parallel pathways for electrochemical oxygen exchange are concluded. The nature of these two elementary steps is discussed in terms of equivalent circuits. Two combinations of parallel rate limiting reaction steps are found to explain the observed geometry dependencies: (i) Diffusion through an impurity phase at the TPB in parallel to diffusion of oxygen through platinum – most likely along Pt grain boundaries – as area-related process. (ii) Co-limitation of oxygen diffusion along the Pt|YSZ interface and charge transfer at the interface with a short decay length of the corresponding transmission line (as TPB-related process) in parallel to oxygen diffusion through platinum. PMID:22210951

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

Flexible Hybrid Battery/Pseudocapacitor

NASA Technical Reports Server (NTRS)

Tucker, Dennis S.; Paley, Steven

2015-01-01

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

Fractional calculus and morphogen gradient formation

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Chlorine dioxide is a size-selective antimicrobial agent.

PubMed

Noszticzius, Zoltán; Wittmann, Maria; Kály-Kullai, Kristóf; Beregvári, Zoltán; Kiss, István; Rosivall, László; Szegedi, János

2013-01-01

ClO2, the so-called "ideal biocide", could also be applied as an antiseptic if it was understood why the solution killing microbes rapidly does not cause any harm to humans or to animals. Our aim was to find the source of that selectivity by studying its reaction-diffusion mechanism both theoretically and experimentally. ClO2 permeation measurements through protein membranes were performed and the time delay of ClO2 transport due to reaction and diffusion was determined. To calculate ClO2 penetration depths and estimate bacterial killing times, approximate solutions of the reaction-diffusion equation were derived. In these calculations evaporation rates of ClO2 were also measured and taken into account. The rate law of the reaction-diffusion model predicts that the killing time is proportional to the square of the characteristic size (e.g. diameter) of a body, thus, small ones will be killed extremely fast. For example, the killing time for a bacterium is on the order of milliseconds in a 300 ppm ClO2 solution. Thus, a few minutes of contact time (limited by the volatility of ClO2) is quite enough to kill all bacteria, but short enough to keep ClO2 penetration into the living tissues of a greater organism safely below 0.1 mm, minimizing cytotoxic effects when applying it as an antiseptic. Additional properties of ClO2, advantageous for an antiseptic, are also discussed. Most importantly, that bacteria are not able to develop resistance against ClO2 as it reacts with biological thiols which play a vital role in all living organisms. Selectivity of ClO2 between humans and bacteria is based not on their different biochemistry, but on their different size. We hope initiating clinical applications of this promising local antiseptic.

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

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

NASA Astrophysics Data System (ADS)

Shiraiwa, Manabu; Pfrang, Christian; Pöschl, Ulrich

2010-05-01

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

Reduction of production rate in Y-shaped microreactors in the presence of viscoelasticity.

PubMed

Helisaz, Hamed; Saidi, Mohammad Hassan; Sadeghi, Arman

2017-10-16

The viscoelasticity effects on the reaction-diffusion rates in a Y-shaped microreactor are studied utilizing the PTT rheological model. The flow is assumed to be fully developed and considered to be created under a combined action of electroosmotic and pressure forces. In general, finite-volume-based numerical simulations are conducted to handle the problem; however, analytical solutions based on the depthwise averaging approach are also obtained for the case for which there is no reaction between the inlet components. The analytical solutions are found to predict accurate results when the width to height ratio is at least 10 and acceptable results for lower aspect ratios. An investigation of the viscoelasticity effect reveals that it is accompanied by a significant reduction of the production rate and the production efficiency, defined as the ratio of the average product concentration to the inlet concentration of the limiting reactant. In addition, this effect gives rise to a more uniform transport with more symmetric concentration distributions. The pressure effects on the reaction-diffusion rates are also pronounced in the presence of viscoelasticity. Finally, the influences of the product diffusivity are investigated for the first time revealing that the lower it is the thinner the area of significant production becomes. Copyright © 2017 Elsevier B.V. All rights reserved.

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

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

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

2015-01-01

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

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

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

Reactive Radial Diffusion Model for the Aging/Sequestration Process

NASA Astrophysics Data System (ADS)

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

2001-12-01

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

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.

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

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

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

2012-05-30

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

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

PubMed

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

2012-06-01

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

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

Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Quenching

NASA Technical Reports Server (NTRS)

Fendell, Francis; Rungaldier, Harald; Gokoglu, Suleyman; Schultz, Donald

1997-01-01

For about a half century, the stabilization of a steady planar deflagration on a heat-sink-type flat-flame burner has been of extraordinary service for the theoretical modeling and diagnostic probing of combusting gaseous mixtures. However, most engineering devices and most unwanted fire involve the burning of initially unmixed reactants. The most vigorous burning of initially separated gaseous fuel and oxidizer is the diffusion flame. In this useful idealization (limiting case), the reactants are converted to product at a mathematically thin interface, so no interpenetration of fuel and oxidizer occurs. This limit is of practical importance because it often characterizes the condition of optimal performance (and sometimes environmentally objectionable operation) of a combustor. A steady planar diffusion flame is most closely approached in the laboratory in the counterflow apparatus. The utility of this simple-strain-rate flow for the modeling and probing of diffusion flames was noted by Pandya and Weinberg 35 years ago, though only in the last decade or so has its use become internationally common place. However, typically, as the strain rate a is reduced below about 20 cm(exp -1), and the diffusion-flame limit (reaction rate much faster than the flow rate) is approached, the burning is observed to become unstable in earth gravity. The advantageous steady planar flow is not available in the diffusion-flame limit in earth gravity. This is unfortunate because the typical spatial scale in a counterflow is (k/a)(sup 1/2), where k denotes a characteristic diffusion coefficient; thus, the length scale becomes large, and the reacting flow is particularly amenable to diagnostic probing, as the diffusion-flame limit is approached. The disruption of planar symmetry is owing the fact that, as the strain rate a decreases, the residence time (l/a) of the throughput in the counterflow burner increases. Observationally, when the residence time exceeds about 50 msec, the inevitably present convective (Rayleigh-Benard) instabilities, associated with hot-under-cold (flame-under-fresh-reactant) stratification of fluid in a gravitational field, have time to grow to finite amplitude during transit of the burner.

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

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-10-01

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

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.

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

NASA Astrophysics Data System (ADS)

Antoine, C.; Talbot, J.

2016-06-01

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

Adsorption and diffusion of fructose in zeolite HZSM-5: selection of models and methods for computational studies.

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

Cheng, L.; Curtiss, L. A.; Assary, R. S.

The adsorption and protonation of fructose in HZSM-5 have been studied for the assessment of models for accurate reaction energy calculations and the evaluation of molecular diffusivity. The adsorption and protonation were calculated using 2T, 5T, and 46T clusters as well as a periodic model. The results indicate that the reaction thermodynamics cannot be predicted correctly using small cluster models, such as 2T or 5T, because these small cluster models fail to represent the electrostatic effect of a zeolite cage, which provides additional stabilization to the ion pair formed upon the protonation of fructose. Structural parameters optimized using the 46Tmore » cluster model agree well with those of the full periodic model; however, the calculated reaction energies are in significant error due to the poor account of dispersion effects by density functional theory. The dispersion effects contribute -30.5 kcal/mol to the binding energy of fructose in the zeolite pore based on periodic model calculations that include dispersion interactions. The protonation of the fructose ternary carbon hydroxyl group was calculated to be exothermic by 5.5 kcal/mol with a reaction barrier of 2.9 kcal/mol using the periodic model with dispersion effects. Our results suggest that the internal diffusion of fructose in HZSM-5 is very likely to be energetically limited and only occurs at high temperature due to the large size of the molecule.« less

Adsorption and Diffusion of Fructose in Zeolite HZSM-5: Selection of Models and Methods for Computational Studies

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

Cheng, Lei; Curtiss, Larry A.; Assary, Rajeev S.

The adsorption and protonation of fructose inHZSM-5 have been studied for the assessment of models for accurate reaction energy calculations and the evaluation of molecular diffusivity. The adsorption and protonation were calculated using 2T, 5T, and 46T clusters as well as a periodic model. The results indicate that the reaction thermodynamics cannot be predicted correctly using small cluster models, such as 2T or 5T, because these small cluster models fail to represent the electrostatic effect of a zeolite cage, which provides additional stabilization to the ion pair formed upon the protonation of fructose. Structural parameters optimized using the 46T clustermore » model agree well with those of the full periodic model; however, the calculated reaction energies are in significant error due to the poor account of dispersion effects by density functional theory. The dispersion effects contribute -30.5 kcal/mol to the binding energy of fructose in the zeolite pore based on periodic model calculations that include dispersion interactions. The protonation of the fructose ternary carbon hydroxyl group was calculated to be exothermic by 5.5 kcal/mol with a reaction barrier of 2.9 kcal/mol using the periodic model with dispersion effects. Our results suggest that the internal diffusion of fructose in HZSM-5 is very likely to be energetically limited and only occurs at high temperature due to the large size of the molecule.« less

Gas uptake and chemical aging of semisolid organic aerosol particles

PubMed Central

Shiraiwa, Manabu; Ammann, Markus; Koop, Thomas; Pöschl, Ulrich

2011-01-01

Organic substances can adopt an amorphous solid or semisolid state, influencing the rate of heterogeneous reactions and multiphase processes in atmospheric aerosols. Here we demonstrate how molecular diffusion in the condensed phase affects the gas uptake and chemical transformation of semisolid organic particles. Flow tube experiments show that the ozone uptake and oxidative aging of amorphous protein is kinetically limited by bulk diffusion. The reactive gas uptake exhibits a pronounced increase with relative humidity, which can be explained by a decrease of viscosity and increase of diffusivity due to hygroscopic water uptake transforming the amorphous organic matrix from a glassy to a semisolid state (moisture-induced phase transition). The reaction rate depends on the condensed phase diffusion coefficients of both the oxidant and the organic reactant molecules, which can be described by a kinetic multilayer flux model but not by the traditional resistor model approach of multiphase chemistry. The chemical lifetime of reactive compounds in atmospheric particles can increase from seconds to days as the rate of diffusion in semisolid phases can decrease by multiple orders of magnitude in response to low temperature or low relative humidity. The findings demonstrate that the occurrence and properties of amorphous semisolid phases challenge traditional views and require advanced formalisms for the description of organic particle formation and transformation in atmospheric models of aerosol effects on air quality, public health, and climate. PMID:21690350

National treatment systems in global perspective.

PubMed

Klingemann, H

1999-09-01

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

Investigation of Fission Product Transport into Zeolite-A for Pyroprocessing Waste Minimization

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

James R. Allensworth; Michael F. Simpson; Man-Sung Yim

Methods to improve fission product salt sorption into zeolite-A have been investigated in an effort to reduce waste associated with the electrochemical treatment of spent nuclear fuel. It was demonstrated that individual fission product chloride salts were absorbed by zeolite-A in a solid-state process. As a result, recycling of LiCl-KCl appears feasible via adding a zone-freezing technique to the current treatment process. Ternary salt molten-state experiments showed the limiting kinetics of CsCl and SrCl2 sorption into the zeolite. CsCl sorption occurred rapidly relative to SrCl2 with no observed dependence on zeolite particle size, while SrCl2 sorption was highly dependent onmore » particle size. The application of experimental data to a developed reaction-diffusion-based sorption model yielded diffusivities of 8.04 × 10-6 and 4.04 × 10-7 cm2 /s for CsCl and SrCl2, respectively. Additionally, the chemical reaction term in the developed model was found to be insignificant compared to the diffusion term.« less

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

DOE PAGES

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

2017-10-30

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

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

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

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

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

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

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

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

2017-10-30

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

Inner clot diffusion and permeation during fibrinolysis.

PubMed Central

Diamond, S L; Anand, S

1993-01-01

A model of fibrinolysis was developed using multicomponent convection-diffusion equations with homogeneous reaction and heterogeneous adsorption and reaction. Fibrin is the dissolving stationary phase and plasminogen, tissue plasminogen activator (tPA), urokinase (uPA), and plasmin are the soluble mobile species. The model is based on an accurate molecular description of the fibrin fiber and protofibril structure and contains no adjustable parameters and one phenomenological parameter estimated from experiment. The model can predict lysis fronts moving across fibrin clots (fine or coarse fibers) of various densities under different administration regimes using uPA and tPA. We predict that pressure-driven permeation is the major mode of transport that allows for kinetically significant thrombolysis during clinical situations. Without permeation, clot lysis would be severely diffusion limited and would require hundreds of minutes. Adsorption of tPA to fibrin under conditions of permeation was a nonequilibrium process that tended to front load clots with tPA. Protein engineering efforts to design optimal thrombolytics will likely be affected by the permeation processes that occur during thrombolysis. PMID:8312497

Turing instability in reaction-diffusion systems with nonlinear diffusion

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

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

2013-10-15

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

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

PubMed

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

2017-03-14

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

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

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

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

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.

Silicon self-diffusion in single-crystal natural quartz and feldspar

NASA Astrophysics Data System (ADS)

Cherniak, D. J.

2003-09-01

Silicon diffusion was measured in natural quartz and anorthitic feldspar under dry, low-pressure (0.1 MPa) conditions using a 30Si tracer. Sources of diffusant consisted of 30Si-enriched silica powder for experiments on quartz and microcrystalline 30Si-doped synthetic feldspar of composition comparable to the feldspar specimens. Distributions of 30Si were measured with Rutherford backscattering spectrometry and nuclear reaction analysis, using the reaction 30Si (p,γ) 31P. The following Arrhenius relations were obtained for anneals at 1 atm in air. For quartz: transport normal to c: Dqtz,⊥c=7.97×10 -6 exp (-447±31 kJ mol -1/ RT) m 2 s -1; transport parallel to c: Dqtz,∥c=6.40×10 -6 exp (-443±22 kJ mol -1/ RT) m 2 s -1. For anorthitic feldspar (An 93): DAn=3.79×10 -7 exp (-465±50 kJ mol -1/ RT) m 2 s -1. The few successful experiments on diffusion in plagioclase of more albitic compositions (An 67 and An 23) reveal Si diffusivities a few orders of magnitude faster than that in the anorthite. The results for these feldspars bracket the determination of CaAl-NaSi interdiffusion under dry conditions by Grove et al. [Geochim. Cosmochim. Acta 48 (1984) 2113-2121], suggesting that the rate-limiting process is indeed Si diffusion. Si diffusion in quartz under more reducing conditions (NNO) is slightly slower (by about half an order of magnitude) than diffusion in samples annealed in air. This is consistent with observations made in studies of synthetic quartz [Béjina and Jaoul, Phys. Earth Planet. Inter. 50 (1988) 240-250].

Catalytic reaction processes revealed by scanning probe microscopy. [corrected].

PubMed

Jiang, Peng; Bao, Xinhe; Salmeron, Miquel

2015-05-19

Heterogeneous catalysis is of great importance for modern society. About 80% of the chemicals are produced by catalytic reactions. Green energy production and utilization as well as environmental protection also need efficient catalysts. Understanding the reaction mechanisms is crucial to improve the existing catalysts and develop new ones with better activity, selectivity, and stability. Three components are involved in one catalytic reaction: reactant, product, and catalyst. The catalytic reaction process consists of a series of elementary steps: adsorption, diffusion, reaction, and desorption. During reaction, the catalyst surface can change at the atomic level, with roughening, sintering, and segregation processes occurring dynamically in response to the reaction conditions. Therefore, it is imperative to obtain atomic-scale information for understanding catalytic reactions. Scanning probe microscopy (SPM) is a very appropriate tool for catalytic research at the atomic scale because of its unique atomic-resolution capability. A distinguishing feature of SPM, compared to other surface characterization techniques, such as X-ray photoelectron spectroscopy, is that there is no intrinsic limitation for SPM to work under realistic reaction conditions (usually high temperature and high pressure). Therefore, since it was introduced in 1981, scanning tunneling microscopy (STM) has been widely used to investigate the adsorption, diffusion, reaction, and desorption processes on solid catalyst surfaces at the atomic level. STM can also monitor dynamic changes of catalyst surfaces during reactions. These invaluable microscopic insights have not only deepened the understanding of catalytic processes, but also provided important guidance for the development of new catalysts. This Account will focus on elementary reaction processes revealed by SPM. First, we will demonstrate the power of SPM to investigate the adsorption and diffusion process of reactants on catalyst surfaces at the atomic level. Then the dynamic processes, including surface reconstruction, roughening, sintering, and phase separation, studied by SPM will be discussed. Furthermore, SPM provides valuable insights toward identifying the active sites and understanding the reaction mechanisms. We also illustrate here how both ultrahigh vacuum STM and high pressure STM provide valuable information, expanding the understanding provided by traditional surface science. We conclude with highlighting remarkable recent progress in noncontact atomic force microscopy (NC-AFM) and inelastic electron tunneling spectroscopy (IETS), and their impact on single-chemical-bond level characterization for catalytic reaction processes in the future.

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

NASA Astrophysics Data System (ADS)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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 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.

Theoretical and Numerical Investigation of Radiative Extinction of Diffusion Flames

NASA Technical Reports Server (NTRS)

Ray, Anjan

1996-01-01

The influence of soot radiation on diffusion flames was investigated using both analytical and numerical techniques. Soot generated in diffusion flames dominate the flame radiation over gaseous combustion products and can significantly lower the temperature of the flame. In low gravity situations there can be significant accumulation of soot and combustion products in the vicinity of the primary reaction zone owing to the absence of any convective buoyant flow. Such situations may result in substantial suppression of chemical activities in a flame, and the possibility of a radiative extinction may also be anticipated. The purpose of this work was to not only investigate the possibility of radiative extinction of a diffusion flame but also to qualitatively and quantitatively analyze the influence of soot radiation on a diffusion flame. In this study, first a hypothetical radiative loss profile of the form of a sech(sup 2) was assumed to influence a pure diffusion flame. It was observed that the reaction zone can, under certain circumstances, move through the radiative loss zone and locate itself on the fuel side of the loss zone contrary to our initial postulate. On increasing the intensity and/or width of the loss zone it was possible to extinguish the flame, and extinction plots were generated. In the presence of a convective flow, however, the movement of the temperature and reaction rate peaks indicated that the flame behavior is more complicated compared to a pure diffusional flame. A comprehensive model of soot formation, oxidation and radiation was used in a more involved analysis. The soot model of Syed, Stewart and Moss was used for soot nucleation and growth and the model of Nagle and Strickland-Constable was used for soot oxidation. The soot radiation was considered in the optically thin limit. An analysis of the flame structure revealed that the radiative loss term is countered both by the reaction term and the diffusion term. The essential balance for the soot volume fraction was found to be between the processes of soot convection and soot growth. Such a balance yielded to analytical treatment and the soot volume fraction could be expressed in the form of an integral. The integral was evaluated using two approximate methods and the results agreed very well with the numerical solutions for all cases examined.

Numerical quantification of habitability in serpentinizing systems

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

Multiple model approach to evaluation of accelerated carbonation for steelmaking slag in a slurry reactor.

PubMed

Pan, Shu-Yuan; Liu, Hsing-Lu; Chang, E-E; Kim, Hyunook; Chen, Yi-Hung; Chiang, Pen-Chi

2016-07-01

Basic oxygen furnace slag (BOFS) exhibits highly alkaline properties due to its high calcium content, which is beneficial to carbonation reaction. In this study, accelerated carbonation of BOFS was evaluated under different reaction times, temperatures, and liquid-to-solid (L/S) ratios in a slurry reactor. CO2 mass balance within the slurry reactor was carried out to validate the technical feasibility of fixing gaseous CO2 into solid precipitates. After that, a multiple model approach, i.e., theoretical kinetics and empirical surface model, for carbonation reaction was presented to determine the maximal carbonation conversion of BOFS in a slurry reactor. On one hand, the reaction kinetics of BOFS carbonation was evaluated by the shrinking core model (SCM). Calcite (CaCO3) was identified as a reaction product through the scanning electronic microscopy and X-ray diffraction analyses, which provided the rationale of applying the SCM in this study. The rate-limiting step of carbonation was found to be ash-diffusion controlled, and the effective diffusivity for carbonation of BOFS in a slurry reactor were determined accordingly. On the other hand, the carbonation conversion of BOFS was predicted by the response surface methodology (RSM) via a nonlinear mathematical programming. According to the experimental data, the highest carbonation conversion of BOFS achieved was 57% under an L/S ratio of 20 mL g(-1), a CO2 flow rate of 0.1 L min(-1), and a pressure of 101.3 kPa at 50 °C for 120 min. Furthermore, the applications and limitations of SCM and RSM were examined and exemplified by the carbonation of steelmaking slags. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Otto, Andereas; Wang, Jian; Radons, Günter

2017-11-01

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

Theoretical study of reactive and nonreactive turbulent coaxial jets

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Wakelyn, N. T.

1976-01-01

The hydrodynamic properties and the reaction kinetics of axisymmetric coaxial turbulent jets having steady mean quantities are investigated. From the analysis, limited to free turbulent boundary layer mixing of such jets, it is found that the two-equation model of turbulence is adequate for most nonreactive flows. For the reactive flows, where an allowance must be made for second order correlations of concentration fluctuations in the finite rate chemistry for initially inhomogeneous mixture, an equation similar to the concentration fluctuation equation of a related model is suggested. For diffusion limited reactions, the eddy breakup model based on concentration fluctuations is found satisfactory and simple to use. The theoretical results obtained from these various models are compared with some of the available experimental data.

Cookbook asymptotics for spiral and scroll waves in excitable media.

PubMed

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

Cookbook asymptotics for spiral and scroll waves in excitable media

NASA Astrophysics Data System (ADS)

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

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

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

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

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.

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.

Reactive solid surface morphology variation via ionic diffusion.

PubMed

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

2012-08-14

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

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

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

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

Cubic PdNP-based air-breathing cathodes integrated in glucose hybrid biofuel cells

NASA Astrophysics Data System (ADS)

Faggion Junior, D.; Haddad, R.; Giroud, F.; Holzinger, M.; Maduro de Campos, C. E.; Acuña, J. J. S.; Domingos, J. B.; Cosnier, S.

2016-05-01

Cubic Pd nanoparticles (PdNPs) were synthesized using ascorbic acid as a reducing agent and were evaluated for the catalytic oxygen reduction reaction. PdNPs were confined with multiwalled carbon nanotube (MWCNT) dispersions to form black suspensions and these inks were dropcast onto glassy carbon electrodes. Different nanoparticle sizes were synthesized and investigated upon oxygen reduction capacities (onset potential and electrocatalytic current densities) under O2 saturated conditions at varying pH values. Strong evidence of O2 diffusion limitation was demonstrated. In order to overcome oxygen concentration and diffusion limitations in solution, we used a gas diffusion layer to create a PdNP-based air-breathing cathode, which delivered -1.5 mA cm-2 at 0.0 V with an onset potential of 0.4 V. This air-breathing cathode was combined with a specially designed phenanthrolinequinone/glucose dehydrogenase-based anode to form a complete glucose/O2 hybrid bio-fuel cell providing an open circuit voltage of 0.554 V and delivering a maximal power output of 184 +/- 21 μW cm-2 at 0.19 V and pH 7.0.Cubic Pd nanoparticles (PdNPs) were synthesized using ascorbic acid as a reducing agent and were evaluated for the catalytic oxygen reduction reaction. PdNPs were confined with multiwalled carbon nanotube (MWCNT) dispersions to form black suspensions and these inks were dropcast onto glassy carbon electrodes. Different nanoparticle sizes were synthesized and investigated upon oxygen reduction capacities (onset potential and electrocatalytic current densities) under O2 saturated conditions at varying pH values. Strong evidence of O2 diffusion limitation was demonstrated. In order to overcome oxygen concentration and diffusion limitations in solution, we used a gas diffusion layer to create a PdNP-based air-breathing cathode, which delivered -1.5 mA cm-2 at 0.0 V with an onset potential of 0.4 V. This air-breathing cathode was combined with a specially designed phenanthrolinequinone/glucose dehydrogenase-based anode to form a complete glucose/O2 hybrid bio-fuel cell providing an open circuit voltage of 0.554 V and delivering a maximal power output of 184 +/- 21 μW cm-2 at 0.19 V and pH 7.0. Electronic supplementary information (ESI) available: Physical characterization, Fig. S1-S4 electrochemical experiments Fig. S5-S11. See DOI: 10.1039/c6nr01245k

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

PubMed

Mehala, N; Rajendran, L; Meena, V

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2015-12-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Yixi; Polinnaya, Rakesh; Vaddiraju, Sreeram

2018-05-01

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

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices

PubMed Central

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-01-01

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate Nα-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cm∕s, are generated around a small (∼1.2 mm) conductive ion exchange granule when ac electric fields (133 V∕cm) are applied across a miniature chamber smaller than 10 μl. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of ∼30 and ∼8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate. PMID:19693360

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices.

PubMed

Wang, Shau-Chun; Chen, Hsiao-Ping; Lai, Yi-Wen; Chau, Lai-Kwan; Chuang, Yu-Chun; Chen, Yi-Jie

2007-09-04

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate N(alpha)-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cms, are generated around a small ( approximately 1.2 mm) conductive ion exchange granule when ac electric fields (133 Vcm) are applied across a miniature chamber smaller than 10 mul. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of approximately 30 and approximately 8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate.

Predicting Upscaled Behavior of Aqueous Reactants in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

PubMed

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Zhang, XiaoLong; Zhong, Zheng

2017-08-01

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

Laser-induced desorption determinations of surface diffusion on Rh(111)

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

Seebauer, E.G.; Schmidt, L.D.

Surface diffusion of hydrogen, deuterium and CO on Rh(111) has been investigated by laser-induced thermal desorption (LITD) and compared with previous results for these species on Pt(111) and on other metals. For deuterium in the coverage range 0.02 < theta < 0.33, the pre-exponential factor D/sub 0/ - 8 x 10/sup -2/ cm/sup 2//s, with a diffusion activation energy 3.7 < E/sub diff/ < 4.3 kcal/mol. For CO, E/sub diff/ = 7 kcal/mol, but D/sub 0/ rises from 10/sup -3/ to 10/sup -2/ cm/sup 2//s between theta = 0.01 and 0.40. Values of E/sub diff/ on different surfaces appear tomore » correlate with differences in heats of adsorption in different binding states which form saddle point configurations in surface diffusion. In addition, oxidation reactions on Rh and on several other transition metal surfaces may be limited to CO or H surface diffusion. 30 refs., 3 figs., 1 tab.« less

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.

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

NASA Astrophysics Data System (ADS)

Schidlowski, Manfred

1985-12-01

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

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes.

PubMed

Hernandez-Perez, Ruth; García-Cordero, José L; Escobar, Juan V

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes

NASA Astrophysics Data System (ADS)

Hernandez-Perez, Ruth; García-Cordero, José L.; Escobar, Juan V.

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Diffusion and reaction within porous packing media: a phenomenological model.

PubMed

Jones, W L; Dockery, J D; Vogel, C R; Sturman, P J

1993-04-25

A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.

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

NASA Astrophysics Data System (ADS)

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

1999-06-01

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

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.

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

NASA Astrophysics Data System (ADS)

Rolih, Biljana; Ozolins, Vidvuds; Ozolins Team

2013-03-01

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

Interfacial characterization in carbon nanotube reinforced aluminum matrix composites

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

Housaer, F., E-mail: francois.housaer@ed.univ-lille1.fr; Beclin, F., E-mail: franck.beclin@univ-lille1.fr; Touzin, M., E-mail: matthieu.touzin@univ-lille1.fr

2015-12-15

In this work, the effects of the sintering parameters, such as temperature and the techniques used (HP and SPS), on CNT/Al composite interfaces are studied. The major role of the native aluminum oxide (Al{sub 2}O{sub 3}) layer covering the aluminum grains is highlighted. It is shown that, for a sintering temperature below 620 °C, the amorphous Al{sub 2}O{sub 3} layer prevents the reaction between aluminum and carbon. For greater sintering temperatures, the breaking of the oxide layer due to its crystallization leads to the formation of aluminum carbide (Al{sub 4}C{sub 3}) by reaction between aluminum and the CNT. The Al{submore » 4}C{sub 3} crystals grow perpendicularly to the matrix grain boundaries by thermally activated diffusion of the carbon atoms coming from the CNT. It is also demonstrated that, by limiting the sintering time, which is the case in SPS, it is possible to limit the growth of the Al{sub 4}C{sub 3} crystals and thus to preserve the CNT. - Highlights: • The high reactivity between CNT and Al matrix, resulting Al{sub 4}C{sub 3} formation during the sintering process is highlighted. • We demonstrate, thanks to in-situ TEM observations, that Al{sub 4}C{sub 3} crystals grow into aluminum grains by carbon diffusion. • The native aluminum oxide around the aluminum particles prevents the diffusion of carbon into the aluminum grains. • We show that the protective layer can be broken because of its crystallization, leading to the formation of Al{sub 4}C{sub 3}. • SPS, by limiting the sintering duration, is an interesting way for preparing CNT/Al composites without carbide formation.« less

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.

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

Revisiting point FRAP to quantitatively characterize anomalous diffusion in live cells.

PubMed

Daddysman, Matthew K; Fecko, Christopher J

2013-02-07

Fluorescence recovery after photobleaching (FRAP) is widely used to interrogate diffusion and binding of proteins in live cells. Herein, we apply two-photon excited FRAP with a diffraction limited bleaching and observation volume to study anomalous diffusion of unconjugated green fluorescence protein (GFP) in vitro and in cells. Experiments performed on dilute solutions of GFP reveal that reversible fluorophore bleaching can be mistakenly interpreted as anomalous diffusion. We derive a reaction-diffusion FRAP model that includes reversible photobleaching, and demonstrate that it properly accounts for these photophysics. We then apply this model to investigate the diffusion of GFP in HeLa cells and polytene cells of Drosophila larval salivary glands. GFP exhibits anomalous diffusion in the cytoplasm of both cell types and in HeLa nuclei. Polytene nuclei contain optically resolvable chromosomes, permitting FRAP experiments that focus separately on chromosomal or interchrosomal regions. We find that GFP exhibits anomalous diffusion in chromosomal regions but diffuses normally in regions devoid of chromatin. This observation indicates that obstructed transport through chromatin and not crowding by macromolecules is a source of anomalous diffusion in polytene nuclei. This behavior is likely true in other cells, so it will be important to account for this type of transport physics and for reversible photobleaching to properly interpret future FRAP experiments on DNA-binding proteins.

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

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

Liu, Fengshan; Guelder, OEmer L.

2005-11-01

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

Boundary-induced pattern formation from uniform temporal oscillation

NASA Astrophysics Data System (ADS)

Kohsokabe, Takahiro; Kaneko, Kunihiko

2018-04-01

Pattern dynamics triggered by fixing a boundary is investigated. By considering a reaction-diffusion equation that has a unique spatially uniform and limit cycle attractor under a periodic or Neumann boundary condition, and then by choosing a fixed boundary condition, we found three novel phases depending on the ratio of diffusion constants of activator to inhibitor: transformation of temporally periodic oscillation into a spatially periodic fixed pattern, travelling wave emitted from the boundary, and aperiodic spatiotemporal dynamics. The transformation into a fixed, periodic pattern is analyzed by crossing of local nullclines at each spatial point, shifted by diffusion terms, as is analyzed by using recursive equations, to obtain the spatial pattern as an attractor. The generality of the boundary-induced pattern formation as well as its relevance to biological morphogenesis is discussed.

The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak

PubMed Central

Li, Jing; Quan, Tingting; Zhang, Wei; Deng, Wei

2014-01-01

The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z 2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given. PMID:24892099

Role of Water Activity on Intergranular Transport at High Pressure

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

Kinetics of CO2 diffusion in human carbonic anhydrase: a study using molecular dynamics simulations and the Markov-state model.

PubMed

Chen, Gong; Kong, Xian; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

2017-05-10

Molecular dynamics (MD) simulations, in combination with the Markov-state model (MSM), were applied to probe CO 2 diffusion from an aqueous solution into the active site of human carbonic anhydrase II (hCA-II), an enzyme useful for enhanced CO 2 capture and utilization. The diffusion process in the hydrophobic pocket of hCA-II was illustrated in terms of a two-dimensional free-energy landscape. We found that CO 2 diffusion in hCA-II is a rate-limiting step in the CO 2 diffusion-binding-reaction process. The equilibrium distribution of CO 2 shows its preferential accumulation within a hydrophobic domain in the protein core region. An analysis of the committors and reactive fluxes indicates that the main pathway for CO 2 diffusion into the active site of hCA-II is through a binding pocket where residue Gln 136 contributes to the maximal flux. The simulation results offer a new perspective on the CO 2 hydration kinetics and useful insights toward the development of novel biochemical processes for more efficient CO 2 sequestration and utilization.

Domainal cleavage as an Anisotropic Reaction-diffusion Process

NASA Astrophysics Data System (ADS)

Mulchrone, Kieran; Meere, Patrick

2017-04-01

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

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

ERIC Educational Resources Information Center

Pojman, John A.

1990-01-01

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

Optical calorimetry in microfluidic droplets.

PubMed

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

2018-05-29

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

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

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

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

Near-limit flame structures at low Lewis number

NASA Technical Reports Server (NTRS)

Ronney, Paul D.

1990-01-01

The characteristics of premixed gas flames in mixtures with low Lewis numbers near flammability limits were studied experimentally using a low-gravity environment to reduce buoyant convection. The behavior of such flames was found to be dominated by diffusive-thermal instabilities. For sufficiently reactive mixtures, cellular structures resulting from these instabilities were observed and found to spawn new cells in regular patterns. For less reactive mixtures, cells formed shortly after ignition but did not spawn new cells; instead these cells evolved into a flame structure composed of stationary, apparently stable spherical flamelets. Experimental observations are found to be in qualitative agreement with elementary analytical models based on the interaction of heat release due to chemical reaction, differential diffusion of thermal energy and mass, flame front curvature, and volumetric heat losses due to gas and/or soot radiation.

Design requirements for ERD in diffusion-dominated media: how do injection interval, bioactive zones and reaction kinetics affect remediation performance?

NASA Astrophysics Data System (ADS)

Chambon, J.; Lemming, G.; Manoli, G.; Broholm, M. M.; Bjerg, P.; Binning, P. J.

2011-12-01

Enhanced Reductive Dechlorination (ERD) has been successfully used in high permeability media, such as sand aquifers, and is considered to be a promising technology for low permeability settings. Pilot and full-scale applications of ERD at several sites in Denmark have shown that the main challenge is to get contact between the injected bacteria and electron donor and the contaminants trapped in the low-permeability matrix. Sampling of intact cores from the low-permeability matrix has shown that the bioactive zones (where degradation occurs) are limited in the matrix, due to the slow diffusion transport processes, and this affects the timeframes for the remediation. Due to the limited ERD applications and the complex transport and reactive processes occurring in low-permeability media, design guidelines are currently not available for ERD in such settings, and remediation performance assessments are limited. The objective of this study is to combine existing knowledge from several sites with numerical modeling to assess the effect of the injection interval, development of bioactive zones and reaction kinetics on the remediation efficiency for ERD in diffusion-dominated media. A numerical model is developed to simulate ERD at a contaminated site, where the source area (mainly TCE) is located in a clayey till with fractures and interbedded sand lenses. Such contaminated sites are common in North America and Europe. Hydro-geological characterization provided information on geological heterogeneities and hydraulic parameters, which are relevant for clay till sites in general. The numerical model couples flow and transport in the fracture network and low-permeability matrix. Sequential degradation of TCE to ethene is modeled using Monod kinetics, and the kinetic parameters are obtained from laboratory experiments. The influence of the reaction kinetics on remediation efficiency is assessed by varying the biomass concentration of the specific degraders. The injected reactants (donor and bacteria) are assumed to spread in horizontal injection zones of various widths, depending on the development of bioactive zones. These injection zones are spaced at various intervals over depth, corresponding to the injection interval chosen. The results from the numerical model show that remediation timeframes can be reduced significantly by using closely spaced injection intervals and by ensuring the efficient spreading of the reactants into the clay till matrix. In contrast the reaction kinetics affect mass removal only up to a point where diffusive transport becomes limiting. Based on these results, guidelines on when ERD can be an effective remediation strategy in practice are provided. These take the form of dimensionless groupings (such as the Damkohler number), which combine site specific (physical and biogeochemical) and design parameters, and graphs showing how the main parameters affect remediation timeframes. Finally it is shown how model results can be used as input to other decision making tools such as life cycle assessment to guide remedial choices.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

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

PubMed

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

2017-11-01

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

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

PubMed Central

2014-01-01

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

Signal replication in a DNA nanostructure

NASA Astrophysics Data System (ADS)

Mendoza, Oscar; Houmadi, Said; Aimé, Jean-Pierre; Elezgaray, Juan

2017-01-01

Logic circuits based on DNA strand displacement reaction are the basic building blocks of future nanorobotic systems. The circuits tethered to DNA origami platforms present several advantages over solution-phase versions where couplings are always diffusion-limited. Here we consider a possible implementation of one of the basic operations needed in the design of these circuits, namely, signal replication. We show that with an appropriate preparation of the initial state, signal replication performs in a reproducible way. We also show the existence of side effects concomitant to the high effective concentrations in tethered circuits, such as slow leaky reactions and cross-activation.

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.

Deposition velocities and impact of physical properties on ozone removal for building materials

NASA Astrophysics Data System (ADS)

Lin, Chi-Chi; Hsu, Shu-Chen

2015-01-01

This study aims to estimate the ozone deposition velocities of eight commonly used building materials (BMs) which include calcium silicate board (CSB), green calcium silicate board (GCSB), mineral fiber ceiling (MFC), green mineral fiber ceiling (GMFC), gypsum board (GB), green gypsum board (GGB), wooden flooring (WF) and green wooden flooring (GWF). In addition, the impact of physical properties (specific surface area and total pore volume of BM) on ozone removal ability was also explored and discussed. Studies were conducted in a small-scale environmental stainless steel chamber. CSB and GCSB showed the highest ozone deposition velocities, while WF and GWF showed the lowest ozone deposition velocities among test BMs materials. All reaction probabilities were estimated to fall within the order of magnitude of 10-6. Green BMs showed lower reaction probabilities with ozone comparing with non-green BMs except for GGB. Consistent with the trends for deposition velocity, fleecy and porous materials exhibit higher reaction probabilities than smooth, non-porous surfaces. Specific surface area of BM is more closely related to ozone removal than total pore volume of BM with R2 of 0.93 vs. R2 of 0.84. Discussion of Thiele modulus for all test BMs indicates surface reactions are occurring quickly relative to internal diffusion and ozone removal is internal diffusion-limited.

A 2.5D Reactive Transport Model for Fracture Alteration Simulation

DOE PAGES

Deng, Hang; Molins, Sergi; Steefel, Carl; ...

2016-06-30

Understanding fracture alteration resulting from geochemical reactions is critical in predicting fluid migration in the subsurface and is relevant to multiple environmental challenges. Here in this paper, we present a novel 2.5D continuum reactive transport model that captures and predicts the spatial pattern of fracture aperture change and the development of an altered layer in the near-fracture region. The model considers permeability heterogeneity in the fracture plane and updates fracture apertures and flow fields based on local reactions. It tracks the reaction front of each mineral phase and calculates the thickness of the altered layer. Given this treatment, the modelmore » is able to account for the diffusion limitation on reaction rates associated with the altered layer. The model results are in good agreement with an experimental study in which a CO 2-acidified brine was injected into a fracture in the Duperow Dolomite, causing dissolution of calcite and dolomite that result in the formation of a preferential flow channel and an altered layer. Finally, with an effective diffusion coefficient consistent with the experimentally observed porosity of the altered layer, the model captures the progressive decrease in the dissolution rate of the fast-reacting mineral in the altered layer.« less

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-09-25

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

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

PubMed

Simpson, Matthew J

2015-01-01

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

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

Radiation-enhanced self- and boron diffusion in germanium

NASA Astrophysics Data System (ADS)

Schneider, S.; Bracht, H.; Klug, J. N.; Hansen, J. Lundsgaard; Larsen, A. Nylandsted; Bougeard, D.; Haller, E. E.

2013-03-01

We report experiments on proton radiation-enhanced self- and boron (B) diffusion in germanium (Ge) for temperatures between 515 ∘C and 720 ∘C. Modeling of the experimental diffusion profiles measured by means of secondary ion mass spectrometry is achieved on the basis of the Frenkel pair reaction and the interstitialcy and dissociative diffusion mechanisms. The numerical simulations ascertain concentrations of Ge interstitials and B-interstitial pairs that deviate by several orders of magnitude from their thermal equilibrium values. The dominance of self-interstitial related defects under irradiation leads to an enhanced self- and B diffusion in Ge. Analysis of the experimental profiles yields data for the diffusion of self-interstitials (I) and the thermal equilibrium concentration of BI pairs in Ge. The temperature dependence of these quantities provides the migration enthalpy of I and formation enthalpy of BI that are compared with recent results of atomistic calculations. The behavior of self- and B diffusion in Ge under concurrent annealing and irradiation is strongly affected by the property of the Ge surface to hinder the annihilation of self-interstitials. The limited annihilation efficiency of the Ge surface can be caused by donor-type surface states favored under vacuum annealing, but the physical origin remains unsolved.

Chlorine Dioxide Is a Size-Selective Antimicrobial Agent

PubMed Central

Noszticzius, Zoltán; Wittmann, Maria; Kály-Kullai, Kristóf; Beregvári, Zoltán; Kiss, István; Rosivall, László; Szegedi, János

2013-01-01

Background / Aims ClO2, the so-called “ideal biocide”, could also be applied as an antiseptic if it was understood why the solution killing microbes rapidly does not cause any harm to humans or to animals. Our aim was to find the source of that selectivity by studying its reaction-diffusion mechanism both theoretically and experimentally. Methods ClO2 permeation measurements through protein membranes were performed and the time delay of ClO2 transport due to reaction and diffusion was determined. To calculate ClO2 penetration depths and estimate bacterial killing times, approximate solutions of the reaction-diffusion equation were derived. In these calculations evaporation rates of ClO2 were also measured and taken into account. Results The rate law of the reaction-diffusion model predicts that the killing time is proportional to the square of the characteristic size (e.g. diameter) of a body, thus, small ones will be killed extremely fast. For example, the killing time for a bacterium is on the order of milliseconds in a 300 ppm ClO2 solution. Thus, a few minutes of contact time (limited by the volatility of ClO2) is quite enough to kill all bacteria, but short enough to keep ClO2 penetration into the living tissues of a greater organism safely below 0.1 mm, minimizing cytotoxic effects when applying it as an antiseptic. Additional properties of ClO2, advantageous for an antiseptic, are also discussed. Most importantly, that bacteria are not able to develop resistance against ClO2 as it reacts with biological thiols which play a vital role in all living organisms. Conclusion Selectivity of ClO2 between humans and bacteria is based not on their different biochemistry, but on their different size. We hope initiating clinical applications of this promising local antiseptic. PMID:24223899

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

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

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

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

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

Electrocatalytic performance of fuel cell reactions at low catalyst loading and high mass transport.

PubMed

Zalitis, Christopher M; Kramer, Denis; Kucernak, Anthony R

2013-03-28

An alternative approach to the rotating disk electrode (RDE) for characterising fuel cell electrocatalysts is presented. The approach combines high mass transport with a flat, uniform, and homogeneous catalyst deposition process, well suited for studying intrinsic catalyst properties at realistic operating conditions of a polymer electrolyte fuel cell (PEFC). Uniform catalyst layers were produced with loadings as low as 0.16 μgPt cm(-2) and thicknesses as low as 200 nm. Such ultra thin catalyst layers are considered advantageous to minimize internal resistances and mass transport limitations. Geometric current densities as high as 5.7 A cm(-2)Geo were experimentally achieved at a loading of 10.15 μgPt cm(-2) for the hydrogen oxidation reaction (HOR) at room temperature, which is three orders of magnitude higher than current densities achievable with the RDE. Modelling of the associated diffusion field suggests that such high performance is enabled by fast lateral diffusion within the electrode. The electrodes operate over a wide potential range with insignificant mass transport losses, allowing the study of the ORR at high overpotentials. Electrodes produced a specific current density of 31 ± 9 mA cm(-2)Spec at a potential of 0.65 V vs. RHE for the oxygen reduction reaction (ORR) and 600 ± 60 mA cm(-2)Spec for the peak potential of the HOR. The mass activity of a commercial 60 wt% Pt/C catalyst towards the ORR was found to exceed a range of literature PEFC mass activities across the entire potential range. The HOR also revealed fine structure in the limiting current range and an asymptotic current decay for potentials above 0.36 V. These characteristics are not visible with techniques limited by mass transport in aqueous media such as the RDE.

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

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

PubMed

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

2018-05-14

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

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.

Thickness engineering of atomic layer deposited Al2O3 films to suppress interfacial reaction and diffusion of Ni/Au gate metal in AlGaN/GaN HEMTs up to 600 °C in air

NASA Astrophysics Data System (ADS)

Suria, Ateeq J.; Yalamarthy, Ananth Saran; Heuser, Thomas A.; Bruefach, Alexandra; Chapin, Caitlin A.; So, Hongyun; Senesky, Debbie G.

2017-06-01

In this paper, we describe the use of 50 nm atomic layer deposited (ALD) Al2O3 to suppress the interfacial reaction and inter-diffusion between the gate metal and semiconductor interface, to extend the operation limit up to 600 °C in air. Suppression of diffusion is verified through Auger electron spectroscopy (AES) depth profiling and X-ray diffraction (XRD) and is further supported with electrical characterization. An ALD Al2O3 thin film (10 nm and 50 nm), which functions as a dielectric layer, was inserted between the gate metal (Ni/Au) and heterostructure-based semiconductor material (AlGaN/GaN) to form a metal-insulator-semiconductor high electron mobility transistor (MIS-HEMT). This extended the 50 nm ALD Al2O3 MIS-HEMT (50-MIS) current-voltage (Ids-Vds) and gate leakage (Ig,leakage) characteristics up to 600 °C. Both, the 10 nm ALD Al2O3 MIS-HEMT (10-MIS) and HEMT, failed above 350 °C, as evidenced by a sudden increase of approximately 50 times and 5.3 × 106 times in Ig,leakage, respectively. AES on the HEMT revealed the formation of a Ni-Au alloy and Ni present in the active region. Additionally, XRD showed existence of metal gallides in the HEMT. The 50-MIS enables the operation of AlGaN/GaN based electronics in oxidizing high-temperature environments, by suppressing interfacial reaction and inter-diffusion of the gate metal with the semiconductor.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2003-07-01

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

The effects of diffuse and distinct affect.

PubMed

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

2002-07-01

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

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

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

The effect of noise-induced variance on parameter recovery from reaction times.

PubMed

Vadillo, Miguel A; Garaizar, Pablo

2016-03-31

Technical noise can compromise the precision and accuracy of the reaction times collected in psychological experiments, especially in the case of Internet-based studies. Although this noise seems to have only a small impact on traditional statistical analyses, its effects on model fit to reaction-time distributions remains unexplored. Across four simulations we study the impact of technical noise on parameter recovery from data generated from an ex-Gaussian distribution and from a Ratcliff Diffusion Model. Our results suggest that the impact of noise-induced variance tends to be limited to specific parameters and conditions. Although we encourage researchers to adopt all measures to reduce the impact of noise on reaction-time experiments, we conclude that the typical amount of noise-induced variance found in these experiments does not pose substantial problems for statistical analyses based on model fitting.

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.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

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

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

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

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

2014-10-28

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

Electrocatalytic oxidation of hydrogen peroxide on a platinum electrode in the imitation of oxidative drug metabolism of lidocaine.

PubMed

Nouri-Nigjeh, Eslam; Bruins, Andries P; Bischoff, Rainer; Permentier, Hjalmar P

2012-10-21

Electrochemistry in combination with mass spectrometry has shown promise as a versatile technique not only in the analytical assessment of oxidative drug metabolism, but also for small-scale synthesis of drug metabolites. However, electrochemistry is generally limited to reactions initiated by direct electron transfer. In the case of substituted-aromatic compounds, oxidation proceeds through a Wheland-type intermediate where resonance stabilization of the positive charge determines the regioselectivity of the anodic substitution reaction, and hence limits the extent of generating drug metabolites in comparison with in vivo oxygen insertion reactions. In this study, we show that the electrocatalytic oxidation of hydrogen peroxide on a platinum electrode generates reactive oxygen species, presumably surface-bound platinum-oxo species, which are capable of oxygen insertion reactions in analogy to oxo-ferryl radical cations in the active site of Cytochrome P450. Electrochemical oxidation of lidocaine at constant potential in the presence of hydrogen peroxide produces both 3- and 4-hydroxylidocaine, suggesting reaction via an arene oxide rather than a Wheland-type intermediate. No benzylic hydroxylation was observed, thus freely diffusing radicals do not appear to be present. The results of the present study extend the possibilities of electrochemical imitation of oxidative drug metabolism to oxygen insertion reactions.

Pulsation-limited oxygen diffusion in the tumour microenvironment

NASA Astrophysics Data System (ADS)

Milotti, Edoardo; Stella, Sabrina; Chignola, Roberto

2017-01-01

Hypoxia is central to tumour evolution, growth, invasion and metastasis. Mathematical models of hypoxia based on reaction-diffusion equations provide seemingly incomplete descriptions as they fail to predict the measured oxygen concentrations in the tumour microenvironment. In an attempt to explain the discrepancies, we consider both the inhomogeneous distribution of oxygen-consuming cells in solid tumours and the dynamics of blood flow in the tumour microcirculation. We find that the low-frequency oscillations play an important role in the establishment of tumour hypoxia. The oscillations interact with consumption to inhibit oxygen diffusion in the microenvironment. This suggests that alpha-blockers-a class of drugs used to treat hypertension and stress disorders, and known to lower or even abolish low-frequency oscillations of arterial blood flow -may act as adjuvant drugs in the radiotherapy of solid tumours by enhancing the oxygen effect.

Pattern formation in superdiffusion Oregonator model

NASA Astrophysics Data System (ADS)

Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng

2016-10-01

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

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

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

Mechanochemical mechanism for reaction of aluminium nano- and micrometre-scale particles.

PubMed

Levitas, Valery I

2013-11-28

A recently suggested melt-dispersion mechanism (MDM) for fast reaction of aluminium (Al) nano- and a few micrometre-scale particles during fast heating is reviewed. Volume expansion of 6% during Al melting produces pressure of several GPa in a core and tensile hoop stresses of 10 GPa in an oxide shell. Such stresses cause dynamic fracture and spallation of the shell. After spallation, an unloading wave propagates to the centre of the particle and creates a tensile pressure of 3-8 GPa. Such a tensile pressure exceeds the cavitation strength of liquid Al and disperses the melt into small, bare clusters (fragments) that fly at a high velocity. Reaction of the clusters is not limited by diffusion through a pre-existing oxide shell. Some theoretical and experimental results related to the MDM are presented. Various theoretical predictions based on the MDM are in good qualitative and quantitative agreement with experiments, which resolves some basic puzzles in combustion of Al particles. Methods to control and improve reactivity of Al particles are formulated, which are exactly opposite to the current trends based on diffusion mechanism. Some of these suggestions have experimental confirmation.

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

PubMed

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

2012-11-01

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

Enhanced kinetics of Al{sub 0.97}Ga{sub 0.03}As wet oxidation through the use of hydrogenation

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

Le Du, M.; Sagnes, I.; Beaudoin, G.

2006-09-11

This letter reports on a different kinetic behavior of the wet thermal oxidation process resulting in Al{sub x}O{sub y} material depending on the AlAs material growth method, molecular beam epitaxy (MBE) or metal organic vapor phase epitaxy (MOVPE). A higher oxidation rate for MOVPE-grown materia is systemically found. Considering the major role of hydrogen in the wet oxidation reaction, it is believed this observation could be linked with the higher hydrogen residual concentration in MOVPE layers. Using a hydrogen plasma, MBE-grown Al{sub 0.97}Ga{sub 0.03}As layers were hydrogened prior to oxidation. This hydrogenated sample showed a ten times enhanced oxidation ratemore » as compared to the nonhydrogenated Al{sub 0.97}Ga{sub 0.03}As sample. This behavior is mainly attributed to a hydrogen induced modification of the diffusion limited regime, enhancing the diffusion length of oxidizing species and reaction products in the oxidized layers.« less

Chip-based ingroove microplasma with orthogonal signal collection: new approach for carbon-containing species detection through open air reaction for performance enhancement

PubMed Central

Meng, Fanying; Li, Xuemei; Duan, Yixiang

2014-01-01

A novel microplasma generator based on ceramic chips has been developed and coupled with optical emission spectrometry through orthogonal detection. Stable microplasma was generated between two electrodes in the ingroove discharge chamber and the optical fiber was set in perpendicular to the gas outlet to collect emitted light. The emission signal of CN is surprisingly enhanced by reacting carbon-containing species with back-diffusion nitrogen from open air, and the enhanced CN signal is successfully applied to sensitively detect organic compounds for the first time. This article focuses to study the structural characteristic and the signal enhancement mechanism through back-diffusion reaction. Several organic compounds were detected directly with the limits of detection down to ppb level. Besides, the advantages of low energy consumption and the chip-based discharge chamber show great potential to be applied in portable devices. This development may lead to a new way for the sensitive detection of organic compounds. PMID:24763181

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.

Analysis of operator splitting errors for near-limit flame simulations

NASA Astrophysics Data System (ADS)

Lu, Zhen; Zhou, Hua; Li, Shan; Ren, Zhuyin; Lu, Tianfeng; Law, Chung K.

2017-04-01

High-fidelity simulations of ignition, extinction and oscillatory combustion processes are of practical interest in a broad range of combustion applications. Splitting schemes, widely employed in reactive flow simulations, could fail for stiff reaction-diffusion systems exhibiting near-limit flame phenomena. The present work first employs a model perfectly stirred reactor (PSR) problem with an Arrhenius reaction term and a linear mixing term to study the effects of splitting errors on the near-limit combustion phenomena. Analysis shows that the errors induced by decoupling of the fractional steps may result in unphysical extinction or ignition. The analysis is then extended to the prediction of ignition, extinction and oscillatory combustion in unsteady PSRs of various fuel/air mixtures with a 9-species detailed mechanism for hydrogen oxidation and an 88-species skeletal mechanism for n-heptane oxidation, together with a Jacobian-based analysis for the time scales. The tested schemes include the Strang splitting, the balanced splitting, and a newly developed semi-implicit midpoint method. Results show that the semi-implicit midpoint method can accurately reproduce the dynamics of the near-limit flame phenomena and it is second-order accurate over a wide range of time step size. For the extinction and ignition processes, both the balanced splitting and midpoint method can yield accurate predictions, whereas the Strang splitting can lead to significant shifts on the ignition/extinction processes or even unphysical results. With an enriched H radical source in the inflow stream, a delay of the ignition process and the deviation on the equilibrium temperature are observed for the Strang splitting. On the contrary, the midpoint method that solves reaction and diffusion together matches the fully implicit accurate solution. The balanced splitting predicts the temperature rise correctly but with an over-predicted peak. For the sustainable and decaying oscillatory combustion from cool flames, both the Strang splitting and the midpoint method can successfully capture the dynamic behavior, whereas the balanced splitting scheme results in significant errors.

Random walk on a leash: a simple single-molecule diffusion model for surface-tethered redox molecules with flexible linkers.

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

We develop a random walk model to simulate the Brownian motion and the electrochemical response of a single molecule confined to an electrode surface via a flexible molecular tether. We use our simple model, which requires no prior knowledge of the physics of the molecular tether, to predict and better understand the voltammetric response of surface-confined redox molecules when motion of the redox molecule becomes important. The single molecule is confined to a hemispherical volume with a maximum radius determined by the flexible molecular tether (5-20 nm) and is allowed to undergo true three-dimensional diffusion. Distance- and potential-dependent electron transfer probabilities are evaluated throughout the simulations to generate cyclic voltammograms of the model system. We find that at sufficiently slow cyclic voltammetric scan rates the electrochemical reaction behaves like an adsorbed redox molecule with no mass transfer limitation; thus, the peak current is proportional to the scan rate. Conversely, at faster scan rates the diffusional motion of the molecule limits the simulated peak current, which exhibits a linear dependence on the square root of the scan rate. The switch between these two limiting regimes occurs when the diffusion layer thickness, (2Dt)(1/2), is ~10 times the tether length. Finally, we find that our model predicts the voltammetric behavior of a redox-active methylene blue tethered to an electrode surface via short flexible single-stranded, polythymine DNAs, allowing the estimation of diffusion coefficients for the end-tethered molecule.

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

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

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

Matching the reaction-diffusion simulation to dynamic [18F]FMISO PET measurements in tumors: extension to a flow-limited oxygen-dependent model.

PubMed

Shi, Kuangyu; Bayer, Christine; Gaertner, Florian C; Astner, Sabrina T; Wilkens, Jan J; Nüsslin, Fridtjof; Vaupel, Peter; Ziegler, Sibylle I

2017-02-01

Positron-emission tomography (PET) with hypoxia specific tracers provides a noninvasive method to assess the tumor oxygenation status. Reaction-diffusion models have advantages in revealing the quantitative relation between in vivo imaging and the tumor microenvironment. However, there is no quantitative comparison of the simulation results with the real PET measurements yet. The lack of experimental support hampers further applications of computational simulation models. This study aims to compare the simulation results with a preclinical [ 18 F]FMISO PET study and to optimize the reaction-diffusion model accordingly. Nude mice with xenografted human squamous cell carcinomas (CAL33) were investigated with a 2 h dynamic [ 18 F]FMISO PET followed by immunofluorescence staining using the hypoxia marker pimonidazole and the endothelium marker CD 31. A large data pool of tumor time-activity curves (TAC) was simulated for each mouse by feeding the arterial input function (AIF) extracted from experiments into the model with different configurations of the tumor microenvironment. A measured TAC was considered to match a simulated TAC when the difference metric was below a certain, noise-dependent threshold. As an extension to the well-established Kelly model, a flow-limited oxygen-dependent (FLOD) model was developed to improve the matching between measurements and simulations. The matching rate between the simulated TACs of the Kelly model and the mouse PET data ranged from 0 to 28.1% (on average 9.8%). By modifying the Kelly model to an FLOD model, the matching rate between the simulation and the PET measurements could be improved to 41.2-84.8% (on average 64.4%). Using a simulation data pool and a matching strategy, we were able to compare the simulated temporal course of dynamic PET with in vivo measurements. By modifying the Kelly model to a FLOD model, the computational simulation was able to approach the dynamic [ 18 F]FMISO measurements in the investigated tumors.

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

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1993-01-01

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

Ammonia Gas Transport and Reactions in Unsaturated Sediments: Implications for Use as an Amendment to Immobilize Inorganic Contaminants

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

Zhong, Lirong; Szecsody, James E.; Truex, Michael J.

Use of gas-phase amendments for in situ remediation of inorganic contaminants in unsaturated sediments of the vadose zone may be advantageous, but there has been limited development and testing of gas remediation technologies. Treatment with ammonia gas has been studied and has a potential for use in treating inorganic contaminants such as uranium because it induces a high pore-water pH causing mineral dissolution and subsequent formation of stable precipitates that decrease the mobility of some contaminants. For field application, knowledge of ammonia transport and the geochemical reactions induced by ammonia is needed. Laboratory studies were conducted to support calculations neededmore » for field treatment design, to quantify advective and diffusive ammonia transport in unsaturated sediments, to evaluate reactions among gas, sediment, and water, and to study reaction-induced pore-water chemistry changes as a function of ammonia delivery conditions. Ammonia gas quickly partitions into sediment pore water and increases pH up to 13.2. Injected ammonia gas front movement can be reasonably predicted by gas flow rate and equilibrium partitioning. The ammonia gas diffusion rate is a function of the water content in the sediment. Measured diffusion front movement was 0.05, 0.03, and 0.02 cm/hr. in sediments with 2.0%, 8.7%, and 13.0% water content, respectively. Sodium, aluminum, and silica pore-water concentrations increase on exposure to ammonia and then decline as aluminosilicates precipitate with declining pH. When uranium is present in the sediment and pore water, up to 85% of the water-leachable uranium was immobilized by ammonia treatment.« less

Physics of Fresh Produce Safety: Role of Diffusion and Tissue Reaction in Sanitization of Leafy Green Vegetables with Liquid and Gaseous Ozone-Based Sanitizers.

PubMed

Shynkaryk, Mykola V; Pyatkovskyy, Taras; Mohamed, Hussein M; Yousef, Ahmed E; Sastry, Sudhir K

2015-12-01

Produce safety has received much recent attention, with the emphasis being largely on discovery of how microbes invade produce. However, the sanitization operation deserves more attention than it has received. The ability of a sanitizer to reach the site of pathogens is a fundamental prerequisite for efficacy. This work addresses the transport processes of ozone (gaseous and liquid) sanitizer for decontamination of leafy greens. The liquid sanitizer was ineffective against Escherichia coli K-12 in situations where air bubbles may be trapped within cavities. A model was developed for diffusion of sanitizer into the interior of produce. The reaction rate of ozone with the surface of a lettuce leaf was determined experimentally and was used in a numerical simulation to evaluate ozone concentrations within the produce and to determine the time required to reach different locations. For aqueous ozone, the penetration depth was limited to several millimeters by ozone self-decomposition due to the significant time required for diffusion. In contrast, gaseous sanitizer was able to reach a depth of 100 mm in several minutes without depletion in the absence of reaction with surfaces. However, when the ozone gas reacted with the produce surface, gas concentration was significantly affected. Simulation data were validated experimentally by measuring ozone concentrations at the bottom of a cylinder made of lettuce leaf. The microbiological test confirmed the relationship between ozone transport, its self-decomposition, reaction with surrounding materials, and the degree of inactivation of E. coli K-12. Our study shows that decontamination of fresh produce, through direct contact with the sanitizer, is more feasible with gaseous than with aqueous sanitizers. Therefore, sanitization during a high-speed washing process is effective only for decontaminating the wash water.

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.

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.

Multi-scale continuum modeling of biological processes: from molecular electro-diffusion to sub-cellular signaling transduction

NASA Astrophysics Data System (ADS)

Cheng, Y.; Kekenes-Huskey, P.; Hake, J. E.; Holst, M. J.; McCammon, J. A.; Michailova, A. P.

2012-01-01

This paper presents a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales (http://mccammon.ucsd.edu/smol/, http://FETK.org) by numerical solution of the time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times, with increasing ionic strength, and demonstrate the role of an enzyme's electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a nonlinear, reaction-diffusion system describing Ca2+ ligand buffering and diffusion in experimentally derived rodent ventricular myocyte geometries. Results reveal the important role of mobile and stationary Ca2+ buffers, including Ca2+ indicator dye. We found that alterations in Ca2+-binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate sub-cellular Ca2+ signals. The model predicts that reduced off-rate in the whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca2+ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for the integration of molecular-scale information into simulations of cellular-scale systems.

Origins and implications of the ordering of oxygen vacancies and localized electrons on partially reduced CeO 2(111)

DOE PAGES

Sutton, Jonathan E.; Beste, Ariana; Steven H. Overbury

2015-10-12

In this study, we use density functional theory to explain the preferred structure of partially reduced CeO 2(111). Low-energy ordered structures are formed when the vacancies are isolated (maximized intervacancy separation) and the size of the Ce 3+ ions is minimized. Both conditions help minimize disruptions to the lattice around the vacancy. The stability of the ordered structures suggests that isolated vacancies are adequate for modeling more complex (e.g., catalytic) systems. Oxygen diffusion barriers are predicted to be low enough that O diffusion between vacancies is thermodynamically controlled at room temperature. The O-diffusion-reaction energies and barriers are decreased when onemore » Ce f electron hops from a nearest-neighbor Ce cation to a next-nearest-neighbor Ce cation, with a barrier that has been estimated to be slightly less than the barrier to O diffusion in the absence of polaron hopping. In conculsion, this indicates that polaron hopping plays a key role in facilitating the overall O diffusion process, and depending on the relative magnitudes of the polaron hopping and O diffusion barriers, polaron hopping may be the kinetically limiting process.« less

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2001-08-01

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

Composition and method for polymer moderated catalytic water formation

DOEpatents

Shepodd, Timothy Jon

1999-01-01

A composition suitable for safely removing hydrogen from gaseous mixtures containing hydrogen and oxygen, particularly those mixtures wherein the hydrogen concentration is within the explosive range. The composition comprises a hydrogenation catalyst, preferably Pd dispersed on carbon, wherein the concentration of Pd is from about 1-10 wt %, dispersed in a polymeric material matrix. As well as serving as a matrix to contain the hydrogenation catalyst, the polymeric material, which is substantially unreactive to hydrogen, provides both a diffusion restriction to hydrogen and oxygen, thereby limiting the rate at which the reactants (hydrogen and oxygen) can diffuse to the catalyst surface and thus, the production of heat from the recombination reaction and as a heat sink.

Isentropic phase changes in dissociating gases and the method of sound dispersion for the investigation of homogeneous gas reactions with very high speed : Conclusion

NASA Technical Reports Server (NTRS)

Damkohler, Gerhard

1950-01-01

The analytical results of Part I are also applied to sound dispersion by friction and heat conduction, An irreversible change of momentum, energy, and type of particle corresponding to friction, heat conduction, and diffusion effects can appear both in the direction of the sound field and traverse to it. Longitudinal damping, the coupling of longitudinal damping and that due to chemical and physical changes, and coupling of diffusion and compositional changes are treated for a plane sound wave of infinite extent. The same principles are also applied to sound effects in cylindrical tubes. The limitations of the method are discussed in some detail.

Size dependence of the propulsion velocity for catalytic Janus-sphere swimmers.

PubMed

Ebbens, Stephen; Tu, Mei-Hsien; Howse, Jonathan R; Golestanian, Ramin

2012-02-01

The propulsion velocity of active colloids that asymmetrically catalyze a chemical reaction is probed experimentally as a function of their sizes. It is found that over the experimentally accessible range, the velocity decays as a function of size, with a rate that is compatible with an inverse size dependence. A diffusion-reaction model for the concentrations of the fuel and waste molecules that takes into account a two-step process for the asymmetric catalytic activity on the surface of the colloid is shown to predict a similar behavior for colloids at the large size limit, with a saturation for smaller sizes. © 2012 American Physical Society

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

PubMed Central

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

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

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

PubMed Central

Simpson, Matthew J

2015-01-01

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

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.

Extreme high temperature redox kinetics in ceria: exploration of the transition from gas-phase to material-kinetic limitations

DOE PAGES

Ji, Ho-Il; Davenport, Timothy C.; Gopal, Chirranjeevi Balaji; ...

2016-07-18

The redox kinetics of undoped ceria (CeO 2-δ) are investigated by the electrical conductivity relaxation method in the oxygen partial pressure range of -4.3 ≤ log(pO 2/atm) ≤ -2.0 at 1400 °C. It is demonstrated that extremely large gas flow rates, relative to the mass of the oxide, are required in order to overcome gas phase limitations and access the material kinetic properties. Using these high flow rate conditions, the surface reaction rate constant k chem is found to obey the correlation log(k chem/cm s -1) = (0.84 ± 0.02) × log(pO 2/atm) - (0.99 ± 0.05) and increases withmore » oxygen partial pressure. This increase contrasts the known behavior of the dominant defect species, oxygen vacancies and free electrons, which decrease in concentration with increasing oxygen partial pressure. For the sample geometries employed, diffusion was too fast to be detected. At low gas flow rates, the relaxation process becomes limited by the capacity of the sweep gas to supply/remove oxygen to/from the oxide. An analytical expression is derived for the relaxation in the gas-phase limited regime, and the result reveals an exponential decay profile, identical in form to that known for a surface reaction limited process. Thus, measurements under varied gas flow rates are required to differentiate between surface reaction limited and gas flow limited behavior.« less

Extreme high temperature redox kinetics in ceria: exploration of the transition from gas-phase to material-kinetic limitations.

PubMed

Ji, Ho-Il; Davenport, Timothy C; Gopal, Chirranjeevi Balaji; Haile, Sossina M

2016-08-03

The redox kinetics of undoped ceria (CeO2-δ) are investigated by the electrical conductivity relaxation method in the oxygen partial pressure range of -4.3 ≤ log(pO2/atm) ≤ -2.0 at 1400 °C. It is demonstrated that extremely large gas flow rates, relative to the mass of the oxide, are required in order to overcome gas phase limitations and access the material kinetic properties. Using these high flow rate conditions, the surface reaction rate constant kchem is found to obey the correlation log(kchem/cm s(-1)) = (0.84 ± 0.02) × log(pO2/atm) - (0.99 ± 0.05) and increases with oxygen partial pressure. This increase contrasts the known behavior of the dominant defect species, oxygen vacancies and free electrons, which decrease in concentration with increasing oxygen partial pressure. For the sample geometries employed, diffusion was too fast to be detected. At low gas flow rates, the relaxation process becomes limited by the capacity of the sweep gas to supply/remove oxygen to/from the oxide. An analytical expression is derived for the relaxation in the gas-phase limited regime, and the result reveals an exponential decay profile, identical in form to that known for a surface reaction limited process. Thus, measurements under varied gas flow rates are required to differentiate between surface reaction limited and gas flow limited behavior.

Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations

NASA Astrophysics Data System (ADS)

Flegg, Mark B.; Hellander, Stefan; Erban, Radek

2015-05-01

In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a "ghost cell" in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step Δt (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: Δt → 0 and h is fixed; Δt → 0 and h → 0 such that √{ Δt } / h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model.

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

PubMed

Jensen, Frank B; Rohde, Sabina

2010-04-01

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

An electromechanical based deformable model for soft tissue simulation.

PubMed

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

2009-11-01

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

Reaction between aminoalkyl radicals and akyl halides: Dehalogenation by electron transfer?

NASA Astrophysics Data System (ADS)

Lalevée, J.; Fouassier, J. P.; Blanchard, N.; Ingold, K. U.

2011-07-01

Aminoalkyl radicals, such as Et2NCrad HCH3, have low oxidation potentials and are therefore powerful reducing agents. We have found that Et2NCrad HCH3 reacts with CCl4 and CBr4 in di-tert-butyl peroxide with bimolecular rate constants (measured by LFP) close, or equal, to the diffusion-controlled limit. For the less reactive halide, CH2Br2, the reaction rate is increased substantially by the addition of acetonitrile as a co-solvent. It is tentatively concluded that these reactions occur by electron-transfer from the aminoalkyl to the organohalide with formation of the iminium ion, Et2N+dbnd CHCH3 (NMR detection), halide ion and a halomethyl radical, e.g., rad CCl3 and rad CHCl2 (ESR, spin-trapping detection).

Osmotic propulsion: the osmotic motor.

PubMed

Córdova-Figueroa, Ubaldo M; Brady, John F

2008-04-18

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

Osmotic Propulsion: The Osmotic Motor

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor.

PubMed

Xiu, G H; Jiang, L; Li, P

2001-07-05

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor. Copyright 2001 John Wiley & Sons, Inc.

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

DOE PAGES

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

2015-09-30

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

Confinement regulates complex biochemical networks: initiation of blood clotting by "diffusion acting".

PubMed

Shen, Feng; Pompano, Rebecca R; Kastrup, Christian J; Ismagilov, Rustem F

2009-10-21

This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da(2), was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as "diffusion acting", which is distinct from "diffusion sensing". The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological "on" and "off" processes that are controlled by thresholds.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-09-30

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

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.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

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

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

PubMed

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

2014-10-01

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

Intercomparison of formaldehyde measurements in the tropical atmosphere

NASA Astrophysics Data System (ADS)

Trapp, Dorothea; De Serves, Claes

An intercomparison of formaldehyde measurements at low concentrations ( < 2.0 ppbv) was performed during the ASTROS '93 field campaign in Venezuela (Atmospheric Studies in the TROpical Savannah, September 1993). Formaldehyde was collected and measured by two different techniques: a porous membrane diffusion scrubber with fluorescent detection of the Hantzsch reaction product, and DNPH-traps (2,4-dinitrophenylhydrazine) followed by high performance liquid chromatography with a UV/VIS absorption detector. The time resolution for the diffusion scrubber instrument was 5 min while the DNPH-tr;ap samples were integrated over 30-60 min. The measured concentrations range from the detection limits (0.045 ppbv for the diffusion scrubber, 0.1 ppbv for the DNPH-traps) up to 2 ppbv. The correlation coefficient between the two techniques is r2 = 0.80 (n = 48) and the slope equals unity (1.02 ± 0.03). Both methods are found to be suitable for field experiments in the low ppbv range of formaldehyde.

The helical structure of DNA facilitates binding

NASA Astrophysics Data System (ADS)

Berg, Otto G.; Mahmutovic, Anel; Marklund, Emil; Elf, Johan

2016-09-01

The helical structure of DNA imposes constraints on the rate of diffusion-limited protein binding. Here we solve the reaction-diffusion equations for DNA-like geometries and extend with simulations when necessary. We find that the helical structure can make binding to the DNA more than twice as fast compared to a case where DNA would be reactive only along one side. We also find that this rate advantage remains when the contributions from steric constraints and rotational diffusion of the DNA-binding protein are included. Furthermore, we find that the association rate is insensitive to changes in the steric constraints on the DNA in the helix geometry, while it is much more dependent on the steric constraints on the DNA-binding protein. We conclude that the helical structure of DNA facilitates the nonspecific binding of transcription factors and structural DNA-binding proteins in general.

Two-dimensional enzyme diffusion in laterally confined DNA monolayers.

PubMed

Castronovo, Matteo; Lucesoli, Agnese; Parisse, Pietro; Kurnikova, Anastasia; Malhotra, Aseem; Grassi, Mario; Grassi, Gabriele; Scaggiante, Bruna; Casalis, Loredana; Scoles, Giacinto

2011-01-01

Addressing the effects of confinement and crowding on biomolecular function may provide insight into molecular mechanisms within living organisms, and may promote the development of novel biotechnology tools. Here, using molecular manipulation methods, we investigate restriction enzyme reactions with double-stranded (ds)DNA oligomers confined in relatively large (and flat) brushy matrices of monolayer patches of controlled, variable density. We show that enzymes from the contacting solution cannot access the dsDNAs from the top-matrix interface, and instead enter at the matrix sides to diffuse two-dimensionally in the gap between top- and bottom-matrix interfaces. This is achieved by limiting lateral access with a barrier made of high-density molecules that arrest enzyme diffusion. We put forward, as a possible explanation, a simple and general model that relates these data to the steric hindrance in the matrix, and we briefly discuss the implications and applications of this strikingly new phenomenon.

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.

Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (1 0 0) surfaces

NASA Astrophysics Data System (ADS)

Liu, Da-Jiang; Evans, James W.

2013-12-01

A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (1 0 0) or M(1 0 0) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(1 0 0) and O/M(1 0 0), as well as the interaction and reaction between different reactant species in mixed adlayers, such as (CO + O)/M(1 0 0). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(1 0 0) and O/M(1 0 0) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(1 0 0) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction-diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis.

Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (100) surfaces

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

Liu, Dajiang; Evans, James W.

2013-12-01

A realistic molecular-level description of catalytic reactions on single-crystal metal surfaces can be provided by stochastic multisite lattice-gas (msLG) models. This approach has general applicability, although in this report, we will focus on the example of CO-oxidation on the unreconstructed fcc metal (100) or M(100) surfaces of common catalyst metals M = Pd, Rh, Pt and Ir (i.e., avoiding regimes where Pt and Ir reconstruct). These models can capture the thermodynamics and kinetics of adsorbed layers for the individual reactants species, such as CO/M(100) and O/M(100), as well as the interaction and reaction between different reactant species in mixed adlayers,more » such as (CO + O)/M(100). The msLG models allow population of any of hollow, bridge, and top sites. This enables a more flexible and realistic description of adsorption and adlayer ordering, as well as of reaction configurations and configuration-dependent barriers. Adspecies adsorption and interaction energies, as well as barriers for various processes, constitute key model input. The choice of these energies is guided by experimental observations, as well as by extensive Density Functional Theory analysis. Model behavior is assessed via Kinetic Monte Carlo (KMC) simulation. We also address the simulation challenges and theoretical ramifications associated with very rapid diffusion and local equilibration of reactant adspecies such as CO. These msLG models are applied to describe adsorption, ordering, and temperature programmed desorption (TPD) for individual CO/M(100) and O/M(100) reactant adlayers. In addition, they are also applied to predict mixed (CO + O)/M(100) adlayer structure on the nanoscale, the complete bifurcation diagram for reactive steady-states under continuous flow conditions, temperature programmed reaction (TPR) spectra, and titration reactions for the CO-oxidation reaction. Extensive and reasonably successful comparison of model predictions is made with experimental data. Furthermore, we discuss the possible transition from traditional mean-field-type bistability and reaction kinetics for lower-pressure to multistability and enhanced fluctuation effects for moderate- or higher-pressure. Behavior in the latter regime reflects a stronger influence of adspecies interactions and also lower diffusivity in the higher-coverage mixed adlayer. We also analyze mesoscale spatiotemporal behavior including the propagation of reaction diffusion fronts between bistable reactive and inactive states, and associated nucleation-mediated transitions between these states. This behavior is controlled by complex surface mass transport processes, specifically chemical diffusion in mixed reactant adlayers for which we provide a precise theoretical formulation. The msLG models together with an appropriate treatment of chemical diffusivity enable equation-free heterogeneous coupled lattice-gas (HCLG) simulations of spatiotemporal behavior. In addition, msLG + HCLG modeling can describe coverage variations across polycrystalline catalysts surfaces, pressure variations across catalyst surfaces in microreactors, and could be incorporated into a multiphysics framework to describe mass and heat transfer limitations for high-pressure catalysis. (C) 2013 Elsevier Ltd. All rights reserved.« less

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

USGS Publications Warehouse

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

2016-01-01

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

Selective sweeps in growing microbial colonies

NASA Astrophysics Data System (ADS)

Korolev, Kirill S.; Müller, Melanie J. I.; Karahan, Nilay; Murray, Andrew W.; Hallatschek, Oskar; Nelson, David R.

2012-04-01

Evolutionary experiments with microbes are a powerful tool to study mutations and natural selection. These experiments, however, are often limited to the well-mixed environments of a test tube or a chemostat. Since spatial organization can significantly affect evolutionary dynamics, the need is growing for evolutionary experiments in spatially structured environments. The surface of a Petri dish provides such an environment, but a more detailed understanding of microbial growth on Petri dishes is necessary to interpret such experiments. We formulate a simple deterministic reaction-diffusion model, which successfully predicts the spatial patterns created by two competing species during colony expansion. We also derive the shape of these patterns analytically without relying on microscopic details of the model. In particular, we find that the relative fitness of two microbial strains can be estimated from the logarithmic spirals created by selective sweeps. The theory is tested with strains of the budding yeast Saccharomyces cerevisiae for spatial competitions with different initial conditions and for a range of relative fitnesses. The reaction-diffusion model also connects the microscopic parameters like growth rates and diffusion constants with macroscopic spatial patterns and predicts the relationship between fitness in liquid cultures and on Petri dishes, which we confirmed experimentally. Spatial sector patterns therefore provide an alternative fitness assay to the commonly used liquid culture fitness assays.

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

PubMed Central

2012-01-01

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

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.

Evidence of a kinetic isotope effect in nanoaluminum and water combustion.

PubMed

Tappan, Bryce C; Dirmyer, Matthew R; Risha, Grant A

2014-08-25

The normally innocuous combination of aluminum and water becomes violently reactive on the nanoscale. Research in the field of the combustion of nanoparticulate aluminum has important implications in the design of molecular aluminum clusters, hydrogen storage systems, as well as energetic formulations which could use extraterrestrial water for space propulsion. However, the mechanism that controls the reaction speed is poorly understood. While current models for micron-sized aluminum water combustion reactions place heavy emphasis on diffusional limitations, as reaction scales become commensurate with diffusion lengths (approaching the nanoscale) reaction rates have long been suspected to depend on chemical kinetics, but have never been definitely measured. The combustion analysis of nanoparticulate aluminum with H2O or D2O is presented. Different reaction rates resulting from the kinetic isotope effect are observed. The current study presents the first-ever observed kinetic isotope effect in a metal combustion reaction and verifies that chemical reaction kinetics play a major role in determining the global burning rate. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

PubMed

Chevalier, Michael W; El-Samad, Hana

2012-08-28

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

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

PubMed

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

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

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.

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.

Multi-Algorithm Particle Simulations with Spatiocyte.

PubMed

Arjunan, Satya N V; Takahashi, Koichi

2017-01-01

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

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

Tian, Huajun; Gao, Tao; Li, Xiaogang

Rechargeable magnesium batteries have attracted considerable attention because of their potential high energy density and low cost. However, their development has been severely hindered because of the lack of appropriate cathode materials. Here we report a rechargeable magnesium/iodine battery, in which the soluble iodine reacts with Mg 2+ to form a soluble intermediate and then an insoluble final product magnesium iodide. The liquid–solid two-phase reaction pathway circumvents solid-state Mg 2+ diffusion and ensures a large interfacial reaction area, leading to fast reaction kinetics and high reaction reversibility. As a result, the rechargeable magnesium/iodine battery shows a better rate capability (180more » mAh g –1 at 0.5 C and 140 mAh g –1 at 1 C) and a higher energy density (~400 Wh kg –1) than all other reported rechargeable magnesium batteries using intercalation cathodes. As a result, this study demonstrates that the liquid–solid two-phase reaction mechanism is promising in addressing the kinetic limitation of rechargeable magnesium batteries.« less

High power rechargeable magnesium/iodine battery chemistry

DOE PAGES

Tian, Huajun; Gao, Tao; Li, Xiaogang; ...

2017-01-10

Rechargeable magnesium batteries have attracted considerable attention because of their potential high energy density and low cost. However, their development has been severely hindered because of the lack of appropriate cathode materials. Here we report a rechargeable magnesium/iodine battery, in which the soluble iodine reacts with Mg 2+ to form a soluble intermediate and then an insoluble final product magnesium iodide. The liquid–solid two-phase reaction pathway circumvents solid-state Mg 2+ diffusion and ensures a large interfacial reaction area, leading to fast reaction kinetics and high reaction reversibility. As a result, the rechargeable magnesium/iodine battery shows a better rate capability (180more » mAh g –1 at 0.5 C and 140 mAh g –1 at 1 C) and a higher energy density (~400 Wh kg –1) than all other reported rechargeable magnesium batteries using intercalation cathodes. As a result, this study demonstrates that the liquid–solid two-phase reaction mechanism is promising in addressing the kinetic limitation of rechargeable magnesium batteries.« less

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

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Ilie, Silvana

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Modeling the rate-controlled sorption of hexavalent chromium

USGS Publications Warehouse

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

1985-01-01

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

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.

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.

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.

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)

On the Mass Distribution of Animal Species

NASA Astrophysics Data System (ADS)

Redner, Sidney; Clauset, Aaron; Schwab, David

2009-03-01

We develop a simple diffusion-reaction model to account for the broad and asymmetric distribution of adult body masses for species within related taxonomic groups. The model assumes three basic evolutionary features that control body mass: (i) a fixed lower limit that is set by metabolic constraints, (ii) a species extinction risk that is a weakly increasing function of body mass, and (iii) cladogenetic diffusion, in which daughter species have a slight tendency toward larger mass. The steady-state solution for the distribution of species masses in this model can be expressed in terms of the Airy function. This solution gives mass distributions that are in good agreement with data on 4002 terrestrial mammal species from the late Quaternary and 8617 extant bird species.

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

PubMed

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

2011-09-08

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

Anomalous Impact in Reaction-Diffusion Financial Models

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Convective instabilities in traveling fronts of addition polymerization

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Reaction-diffusion pattern in shoot apical meristem of plants.

PubMed

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

2011-03-29

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

Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants

PubMed Central

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

2011-01-01

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

Hyper-localized carbon mineralization in diffusion-limited basalt fractures

NASA Astrophysics Data System (ADS)

Menefee, A. H.; Giammar, D.; Ellis, B. R.

2017-12-01

Basalt formations could enable secure carbon sequestration through mineral trapping. CO2 injection acidifies formation brines and drives dissolution of the host rock, which releases divalent metal cations that combine with dissolved carbonate ions to form stable carbonate minerals. Here, a series of high-pressure flow-through experiments was conducted to evaluate how transport limitations and geochemical gradients drive microscale carbonation reactions in fractured basalts. To isolate advection- and diffusion-controlled zones, surfaces of saw-cut basalt cores were milled to create one primary flow channel adjoined by four dead-end fracture pathways. In the first experiment, a representative basalt brine (6.3 mM NaHCO3) equilibrated with CO2 (100ºC, 10 MPa) was injected at 1 mL/h under 20 MPa confining stress. The second experiment was conducted under the same physical conditions but [NaHCO3] was elevated to 640 mM, and in the third, temperature was also raised to 150ºC. Effluent chemistry was monitored via ICP-MS to infer dissolution trends and calibrate reactive transport models. Reacted cores were characterized using x-ray computed tomography (xCT), optical microscopy, scanning electron microscopy, and Raman spectroscopy. Carbonation occurred in all experiments but increased in experiments with higher alkalinity and higher temperature. At low [NaHCO3], secondary precipitate coatings formed distinct reaction fronts that varied with distance into dead-end fractures. Reactive transport modeling demonstrated that these reactions fronts were due to sharp gradients in pH and dissolved inorganic carbon. Carbonation was restricted to transport-limited vugs and pores between the confined core surfaces and was highly localized on reactive primary mineral grains (e.g. pyroxene) that contributed major divalent cations. Increasing [NaHCO3] by two orders of magnitude significantly enhanced carbonation and promoted Mg and Fe uptake into carbonates. While xCT scans revealed clays filling the advective path, no permeability changes were measured. Our coupled experiment-modeling approach further elucidates the geochemical conditions controlling carbonation reactions and extends unique microstructural observations to implications for long-term CO2 mineralization in basalt reservoirs.

The Effectiveness of Surface Coatings on Preventing Interfacial Reaction During Ultrasonic Welding of Aluminum to Magnesium

NASA Astrophysics Data System (ADS)

Panteli, Alexandria; Robson, Joseph D.; Chen, Ying-Chun; Prangnell, Philip B.

2013-12-01

High power ultrasonic spot welding (USW) is a solid-state joining process that is advantageous for welding difficult dissimilar material couples, like magnesium to aluminum. USW is also a useful technique for testing methods of controlling interfacial reaction in welding as the interface is not greatly displaced by the process. However, the high strain rate deformation in USW has been found to accelerate intermetallic compound (IMC) formation and a thick Al12Mg17 and Al3Mg2 reaction layer forms after relatively short welding times. In this work, we have investigated the potential of two approaches for reducing the IMC reaction rate in dissimilar Al-Mg ultrasonic welds, both involving coatings on the Mg sheet surface to (i) separate the join line from the weld interface, using a 100- μm-thick Al cold spray coating, and (ii) provide a diffusion barrier layer, using a thin manganese physical vapor deposition (PVD) coating. Both methods were found to reduce the level of reaction and increase the failure energy of the welds, but their effectiveness was limited due to issues with coating attachment and survivability during the welding cycle. The effect of the coatings on the joint's interface microstructure, and the fracture behavior have been investigated in detail. Kinetic modeling has been used to show that the benefit of the cold spray coating can be attributed to the reaction rate reverting to that expected under static conditions. This reduces the IMC growth rate by over 50 pct because at the weld line, the high strain rate dynamic deformation in USW normally enhances diffusion through the IMC layer. In comparison, the thin PVD barrier coating was found to rapidly break up early in USW and become dispersed throughout the deformation layer reducing its effectiveness.

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

NASA Technical Reports Server (NTRS)

Warrier, Sunil G.; Lin, Ray Y.

1993-01-01

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

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

PubMed

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

2012-01-07

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

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

PubMed

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

2017-08-01

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

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Predicting the drying properties of sludge based on hydrothermal treatment under subcritical conditions.

PubMed

Mäkelä, Mikko; Fraikin, Laurent; Léonard, Angélique; Benavente, Verónica; Fullana, Andrés

2016-03-15

The effects of hydrothermal treatment on the drying properties of sludge were determined. Sludge was hydrothermally treated at 180-260 °C for 0.5-5 h using NaOH and HCl as additives to influence reaction conditions. Untreated sludge and attained hydrochar samples were then dried under identical conditions with a laboratory microdryer and an X-ray microtomograph was used to follow changes in sample dimensions. The effective moisture diffusivities of sludge and hydrochar samples were determined and the effect of process conditions on respective mean diffusivities evaluated using multiple linear regression. Based on the results the drying time of untreated sludge decreased from approximately 80 min to 37-59 min for sludge hydrochar. Drying of untreated sludge was governed by the falling rate period where drying flux decreased continuously as a function of sludge moisture content due to heat and mass transfer limitations and sample shrinkage. Hydrothermal treatment increased the drying flux of sludge hydrochar and decreased the effect of internal heat and mass transfer limitations and sample shrinkage especially at higher treatment temperatures. The determined effective moisture diffusivities of sludge and hydrochar increased as a function of decreasing moisture content and the mean diffusivity of untreated sludge (8.56·10(-9) m(2) s(-1)) and sludge hydrochar (12.7-27.5·10(-9) m(2) s(-1)) were found statistically different. The attained regression model indicated that treatment temperature governed the mean diffusivity of hydrochar, as the effects of NaOH and HCl were statistically insignificant. The attained results enabled prediction of sludge drying properties through mean moisture diffusivity based on hydrothermal treatment conditions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Simultaneous measurement of pulmonary diffusing capacity for carbon monoxide and nitric oxide.

PubMed

Yamaguchi, Kazuhiro; Tsuji, Takao; Aoshiba, Kazutetsu; Nakamura, Hiroyuki

2018-03-01

In Europe and America, the newly-developed, simultaneous measurement of diffusing capacity for CO (D LCO ) and NO (D LNO ) has replaced the classic D LCO measurement for detecting the pathophysiological abnormalities in the acinar regions. However, simultaneous measurement of D LCO and D LNO is currently not used by Japanese physicians. To encourage the use of D LNO in Japan, the authors reviewed aspects of simultaneously-estimated D LCO and D LNO from previously published manuscripts. The simultaneous D LCO -D LNO technique identifies the alveolocapillary membrane-related diffusing capacity (membrane component, D M ) and the blood volume in pulmonary microcirculation (V C ); V C is the principal factor constituting the blood component of diffusing capacity (D B ,D B =θ·V C where θ is the specific gas conductance for CO or NO in the blood). As the association velocity of NO with hemoglobin (Hb) is fast and the affinity of NO with Hb is high in comparison with those of CO, θ NO can be taken as an invariable simply determined by diffusion limitation inside the erythrocyte. This means that θ NO is independent of the partial pressure of oxygen (PO 2 ). However, θ CO involves the limitations by diffusion and chemical reaction elicited by the erythrocyte, resulting in θ CO to be a PO 2 -dependent variable. Furthermore, D LCO is determined primarily by D B (∼77%), while D LNO is determined equally by D M (∼55%) and D B (∼45%). This suggests that D LCO is more sensitive for detecting microvascular diseases, while D LNO can equally identify alveolocapillary membrane and microcirculatory abnormalities. Copyright © 2017 The Japanese Respiratory Society. Published by Elsevier B.V. All rights reserved.

Crystallization kinetics of the borax decahydrate

NASA Astrophysics Data System (ADS)

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

2007-03-01

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

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.

Membrane Bioreactor With Pressure Cycle

NASA Technical Reports Server (NTRS)

Efthymiou, George S.; Shuler, Michael L.

1991-01-01

Improved class of multilayer membrane bioreactors uses convention forced by differences in pressure to overcome some of diffusional limitations of prior bioreactors. In reactor of new class, flow of nutrient solution reduces adverse gradients of concentration, keeps cells supplied with fresh nutrient, and sweeps away products faster than diffusion alone. As result, overall yield and rate of reaction increased. Pressures in sweeping gas and nutrient alternated to force nutrient liquid into and out of biocatalyst layer through hyrophilic membrane.

Structure and Dynamics of Solvent Landscapes in Charge-Transfer Reactions

NASA Astrophysics Data System (ADS)

Leite, Vitor B. Pereira

The dynamics of solvent polarization plays a major role in the control of charge transfer reactions. The success of Marcus theory describing the solvent influence via a single collective quadratic polarization coordinate has been remarkable. Onuchic and Wolynes have recently proposed (J. Chem Phys 98 (3) 2218, 1993) a simple model demonstrating how a many-dimensional-complex model composed by several dipole moments (representing solvent molecules or polar groups in proteins) can be reduced under the appropriate limits into the Marcus Model. This work presents a dynamical study of the same model, which is characterized by two parameters, an average dipole-dipole interaction as a term associated with the potential energy landscape roughness. It is shown why the effective potential, obtained using a thermodynamic approach, is appropriate for the dynamics of the system. At high temperatures, the system exhibits effective diffusive one-dimensional dynamics, where the Born-Marcus limit is recovered. At low temperatures, a glassy phase appears with a slow non-self-averaging dynamics. At intermediate temperatures, the concept of equivalent diffusion paths and polarization dependence effects are discussed. This approach is extended to treat more realistic solvent models. Real solvents are discussed in terms of simple parameters described above, and an analysis of how different regimes affect the rate of charge transfer is presented. Finally, these ideas are correlated to analogous problems in other areas.

Physical phenomena and the microgravity response

NASA Technical Reports Server (NTRS)

Todd, Paul

1989-01-01

The living biological cell is not a sack of Newtonian fluid containing systems of chemical reactions at equilibrium. It is a kinetically driven system, not a thermodynamically driven system. While the cell as a whole might be considered isothermal, at the scale of individual macromolecular events there is heat generated, and presumably sharp thermal gradients exist at the submicron level. Basic physical phenomena to be considered when exploring the cell's response to inertial acceleration include particle sedimentation, solutal convection, motility electrokinetics, cytoskeletal work, and hydrostatic pressure. Protein crystal growth experiments, for example, illustrate the profound effects of convection currents on macromolecular assembly. Reaction kinetics in the cell vary all the way from diffusion-limited to life-time limited. Transport processes vary from free diffusion, to facilitated and active transmembrane transport, to contractile-protein-driven motility, to crystalline immobilization. At least four physical states of matter exist in the cell: aqueous, non-aqueous, immiscible-aqueous, and solid. Levels of order vary from crystalline to free solution. The relative volumes of these states profoundly influence the cell's response to inertial acceleration. Such subcellular phenomena as stretch-receptor activation, microtubule re-assembly, synaptic junction formation, chemotactic receptor activation, and statolith sedimentation were studied recently with respect to both their basic mechanisms and their responsiveness to inertial acceleration. From such studies a widespread role of cytoskeletal organization is becoming apparent.

Geochemical impacts of waste disposal on the abyssal seafloor

NASA Astrophysics Data System (ADS)

Jahnke, Richard A.

1998-05-01

The response of pore water oxygen, nitrate, sulfate, sulfide, ammonium and methane and particulate organic carbon distributions to the input of 8.5 million m 3 (3.8×10 12 g) of organic-rich waste materials is simulated. The deposit is assumed to be conical with a maximum thickness of approximately 20 m. Remineralization reactions within the deposit rapidly deplete any initially available pore water oxidants such as oxygen, nitrate and sulfate, and are subsequently dominated by fermentation reactions. Diffusion downward of reduced metabolites, sulfide, ammonium and methane, depletes the available oxidants in the pore waters below the waste pile, increasing the thickness of the anoxic layer. While the impacted region is limited to essentially the deposition site, recovery of the pore waters is estimated to be >10 4 years. The overall computational results are corroborated by the pore water distributions observed at turbidite boundaries. Numerous uncertainties in the parameterizations limit the overall accuracy of the calculations presented. The most significant of these are: (1) A quantitatively accurate assessment of the remineralization rate of the deposited organic matter including its rate of inoculation by abyssal microorganisms; (2) a detailed assessment of potential non-diffusive pore water transport processes including advection due to compaction and buoyancy-driven flows and enhanced exchange due to macrobenthic irrigation activities and (3) an assessment of the potential alteration of pore space and methane reactivity due to gas hydrate formation.

Substitutional and Interstitial Diffusion in alpha2-Ti3Al(O)

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

Kinetic Monte Carlo Simulation of Oxygen Diffusion in Ytterbium Disilicate

NASA Technical Reports Server (NTRS)

Good, Brian S.

2015-01-01

Silicon-based ceramic components for next-generation jet turbine engines offer potential weight savings, as well as higher operating temperatures, both of which lead to increased efficiency and lower fuel costs. Silicon carbide (SiC), in particular, offers low density, good strength at high temperatures, and good oxidation resistance in dry air. However, reaction of SiC with high-temperature water vapor, as found in the hot section of jet turbine engines in operation, can cause rapid surface recession, which limits the lifetime of such components. Environmental Barrier Coatings (EBCs) are therefore needed if long component lifetime is to be achieved. Rare earth silicates such as Yb2Si2O7 and Yb2SiO5 have been proposed for such applications; in an effort to better understand diffusion in such materials, we have performed kinetic Monte Carlo (kMC) simulations of oxygen diffusion in Ytterbium disilicate, Yb2- Si2O7. The diffusive process is assumed to take place via the thermally activated hopping of oxygen atoms among oxygen vacancy sites or among interstitial sites. Migration barrier energies are computed using density functional theory (DFT).

Setting initial conditions for inflation with reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Bagchi, Partha; Das, Arpan; Dave, Shreyansh S.; Sengupta, Srikumar; Srivastava, Ajit M.

2018-03-01

We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction-diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a field domain changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).

The fractional diffusion limit of a kinetic model with biochemical pathway

NASA Astrophysics Data System (ADS)

Perthame, Benoît; Sun, Weiran; Tang, Min

2018-06-01

Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

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.

Finite Element Analysis Modeling of Chemical Vapor Deposition of Silicon Carbide

DTIC Science & Technology

2014-06-19

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

Parametric spatiotemporal oscillation in reaction-diffusion systems.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

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

Parametric spatiotemporal oscillation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Computation Of Facilitated Transport of O2 In Hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1991-01-01

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

Confinement Regulates Complex Biochemical Networks: Initiation of Blood Clotting by “Diffusion Acting”

PubMed Central

Shen, Feng; Pompano, Rebecca R.; Kastrup, Christian J.; Ismagilov, Rustem F.

2009-01-01

Abstract This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da2, was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as “diffusion acting”, which is distinct from “diffusion sensing”. The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological “on” and “off” processes that are controlled by thresholds. PMID:19843446

Biodegradation of sorbed chemicals in soil

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

Scow, K.M.; Fan, S.; Johnson, C.

Rates of biodegradation of sorbed chemicals are usually lower in soil than in aqueous systems, in part because sorption reduces the availability of the chemical to microorganisms. Biodegradation, sorption, and diffusion occur simultaneously and are tightly coupled. In soil, the rate of biodegradation is a function of a chemical`s diffusion coefficient, sorption partition coefficient, the distance it must diffuse from the site of sorption to microbial populations that can degrade it, and its biodegradation rate constant. A model (DSB model) was developed that describes biodegradation of chemicals limited in the availability by sorption and diffusion. Different kinetics expressions describe biodegradationmore » depending on whether the reaction is controlled by mass transfer (diffusion and sorption) or the intrinsic biodegradation rate, and whether biodegradation begins during or after the majority of sorption has occurred. We tested the hypothesis that there is a direct relationship between how strongly a chemical is sorbed and the chemical`s biodegradation rate. In six soils with different organic carbon contents, there was no relationship between the extent or rate of biodegradation and the sorption partition coefficient for phenanthrene. Aging of phenanthrene residues in soil led to a substantial reduction in the rate of biodegradation compared to biodegradation rates of recently added phenanthrene. Considerable research has focused on identification and development of techniques for enhancing in situ biodegradation of sorbed chemicals. Development of such techniques, especially those involving inoculation with microbial strains, should consider physical mass transfer limitations and potential decreases in bioavailability over time. 4 refs., 3 figs., 1 tab.« less

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

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Nagano, Seido

2012-02-01

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

Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

Incorporating Geochemical And Microbial Kinetics In Reactive Transport Models For Generation Of Acid Rock Drainage

NASA Astrophysics Data System (ADS)

Andre, B. J.; Rajaram, H.; Silverstein, J.

2010-12-01

Acid mine drainage, AMD, results from the oxidation of metal sulfide minerals (e.g. pyrite), producing ferrous iron and sulfuric acid. Acidophilic autotrophic bacteria such as Acidithiobacillus ferrooxidans and Leptospirillum ferrooxidans obtain energy by oxidizing ferrous iron back to ferric iron, using oxygen as the electron acceptor. Most existing models of AMD do not account for microbial kinetics or iron geochemistry rigorously. Instead they assume that oxygen limitation controls pyrite oxidation and thus focus on oxygen transport. These models have been successfully used for simulating conditions where oxygen availability is a limiting factor (e.g. source prevention by capping), but have not been shown to effectively model acid generation and effluent chemistry under a wider range of conditions. The key reactions, oxidation of pyrite and oxidation of ferrous iron, are both slow kinetic processes. Despite being extensively studied for the last thirty years, there is still not a consensus in the literature about the basic mechanisms, limiting factors or rate expressions for microbially enhanced oxidation of metal sulfides. An indirect leaching mechanism (chemical oxidation of pyrite by ferric iron to produce ferrous iron, with regeneration of ferric iron by microbial oxidation of ferrous iron) is used as the foundation of a conceptual model for microbially enhanced oxidation of pyrite. Using literature data, a rate expression for microbial consumption of ferrous iron is developed that accounts for oxygen, ferrous iron and pH limitation. Reaction rate expressions for oxidation of pyrite and chemical oxidation of ferrous iron are selected from the literature. A completely mixed stirred tank reactor (CSTR) model is implemented coupling the kinetic rate expressions, speciation calculations and flow. The model simulates generation of AMD and effluent chemistry that qualitatively agrees with column reactor and single rock experiments. A one dimensional reaction diffusion model at the scale of a single rock is developed incorporating the proposed kinetic rate expressions. Simulations of initiation, washout and AMD flows are discussed to gain a better understanding of the role of porosity, effective diffusivity and reactive surface area in generating AMD. Simulations indicate that flow boundary conditions control generation of acid rock drainage as porosity increases.

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

PubMed

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

1971-04-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method.

Kinetics of Heterogeneous Chemical Reactions: A Theoretical Model for the Accumulation of Pesticides in Soil

PubMed Central

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

1971-01-01

A theoretical model for the accumulation of pesticides in soil has been proposed and discussed from the viewpoint of heterogeneous reaction kinetics with a basic aim to understand the complex nature of soil processes relating to the environmental pollution. In the bulk of soil, the pesticide disappears by diffusion and a chemical reaction; the rate processes considered on the surface of soil are diffusion, chemical reaction, vaporization, and regular pesticide application. The differential equations involved have been solved analytically by the Laplace-transform method. PMID:5279519

Confirmation of monod model for biofiltration of styrene vapors from waste flue gas.

PubMed

Dehghanzadeh, Reza; Roshani, Babak; Asadi, Mahzar; Fahiminia, Mohammad; Aslhashemi, Ahmad

2012-01-01

The objective of this research was to investigate the kinetic behavior of the biofil¬tration process for the removal of styrene. A three stage compost based biofilter was inoculated with thickened activated sludge. The reaction order rate constants were obtained from continuous experiments and used as the specific growth rate for the Monod equation. The measured concentration profiles show a linear dependence on the bed height in the biofilter at higher loadings, such as 75 and 45 g m-3 h-1. This is the condition of reaction limitation for a reaction with zero-order kinetics. From the experimental data, maximum elimination capac¬ity (ECmax) was estimated to be 44, 40 and 26 g m-3 h-1 at empty bed retention times (EBRTs) of 120, 60 and 30 s, respectively. However, at lower loadings, the measured concentration profile of the biofilter is one of exponential increase, which is the condition of both reaction and diffusion limitations for a reaction with zero-order kinetics. Maximum elimination capacities found from the experimental results were the same as Monod model predictions. Both the experimental re¬sults and the model predictions showed the influence of EBRT on the removal rate of styrene, particularly for the highest loading rate. In terms of the practical applications of the proposed models have the advantage of being simpler than Monod kinetics and Monod kinetics requires a numerical solution.

Reaction limited aggregation in surfactant-mediated epitaxy

NASA Astrophysics Data System (ADS)

Wu, Jing; Liu, Bang-Gui; Zhang, Zhenyu; Wang, E. G.

2000-05-01

A theoretical model for reaction limited aggregation (RLA) is introduced to study the effect of a monolayer of surfactant on the formation of two-dimensional islands in heteroepitaxial and homoepitaxial growth. In this model the basic atomic processes are considered as follows. A stable island consists of the adatoms that have exchanged positions with the surfactant atoms beneath them. Movable active adatoms may (a) diffuse on the surfactant terrace, (b) exchange positions with the surfactant atoms beneath them and become island seeds (seed exchange), or (c) stick to stable islands and become stuck but still active adatoms. The rate-limiting step for the formation of a stable island is the seed exchange. Furthermore, a stuck but still active adatom must overcome a sizable potential-energy barrier to exchange positions with the surfactant atom beneath it and become a member of the stable island (aided exchange). The seed exchange process can occur with an adatom or collectively with an addimer. In the case of dimer exchange, the diffusing adatoms on the surfactant terrace can meet and (after exchanging) form stable dimers, which can then become island seeds. Systematic kinetic Monte Carlo simulations and rate-equation analysis of the model are carried out. The key finding of these simulations is that a counterintuitive fractal-to-compact island shape transition can be induced either by increasing deposition flux or by decreasing growth temperature. This major qualitative conclusion is valid for both the monomer and the dimer seed exchanges and for two different substrate lattices (square and triangular, respectively), although there are some quantitative differences in the flux and temperature dependence of the island density. The shape transition observed is contrary to the prediction of the classic diffusion-limited aggregation (DLA) theory, but in excellent qualitative agreement with recent experiments. In rationalizing the main finding, it is crucial to realize that the adatoms stuck to a stable island edge are still active and are surrounded by the surfactant atoms. Therefore, these stuck atoms cannot capture incoming adatoms before they join the island through aided exchange. As a result, an incoming adatom must on average hit the island many times before it finally finds a free edge site to stick to. This search is effectively equivalent to edge diffusion in DLA theory. The stuck adatoms thus act as shields which prevent other mobile adatoms from sticking to the stable islands. This shielding effect, determined by the aided exchange barrier and the density of the mobile adatoms, plays an essential role in inducing the above shape transition in surfactant-mediated epitaxial growth.

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

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

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

2013-04-02

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

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

Effects of Gas-Phase Radiation and Detailed Kinetics on the Burning and Extinction of a Solid Fuel

NASA Technical Reports Server (NTRS)

Rhatigan, Jennifer L.

2001-01-01

This is the first attempt to analyze both radiation and detailed kinetics on the burning and extinction of a solid fuel in a stagnation-point diffusion flame. We present a detailed and comparatively accurate computational model of a solid fuel flame along with a quantitative study of the kinetics mechanism, radiation interactions, and the extinction limits of the flame. A detailed kinetics model for the burning of solid trioxane (a trimer of formaldehyde) is coupled with a narrowband radiation model, with carbon dioxide, carbon monoxide, and water vapor as the gas-phase participating media. The solution of the solid trioxane diffusion flame over the flammable regime is presented in some detail, as this is the first solution of a heterogeneous trioxane flame. We identify high-temperature and low-temperature reaction paths for the heterogeneous trioxane flame. We then compare the adiabatic solution to solutions that include Surface radiation only and gas-phase and surface radiation using a black surface model. The analysis includes discussion of detailed flame chemistry over the flammable regime and, in particular, at the low stretch extinction limit. We emphasize the low stretch regime of the radiatively participating flame, since this is the region representative of microgravity flames. When only surface radiation is included, two extinction limits exist (the blow-off limit, and the low stretch radiative limit), and the burning rate and maximum flame temperatures are lower, as expected. With the inclusion of surface and gas-phase radiation, results show that, while flame temperatures are lower, the burning rate of the trioxane diffusion flame may actually increase at low stretch rate due to radiative feedback from the flame to the surface.

Multispecies diffusion models: A study of uranyl species diffusion

NASA Astrophysics Data System (ADS)

Liu, Chongxuan; Shang, Jianying; Zachara, John M.

2011-12-01

Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A, where intragranular diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that had been previously described using a semiempirical, multirate model. Compared with the multirate model, the diffusion models have the advantage to provide spatiotemporal speciation evolution within the diffusion domains.

Impact of physical properties on ozone removal by several porous materials.

PubMed

Gall, Elliott T; Corsi, Richard L; Siegel, Jeffrey A

2014-04-01

Models of reactive uptake of ozone in indoor environments generally describe materials through aerial (horizontal) projections of surface area, a potentially limiting assumption for porous materials. We investigated the effect of changing porosity/pore size, material thickness, and chamber fluid mechanic conditions on the reactive uptake of ozone to five materials: two cellulose filter papers, two cementitious materials, and an activated carbon cloth. Results include (1) material porosity and pore size distributions, (2) effective diffusion coefficients for ozone in materials, and (3) material-ozone deposition velocities and reaction probabilities. At small length scales (0.02-0.16 cm) increasing thickness caused increases in estimated reaction probabilities from 1 × 10(-6) to 5 × 10(-6) for one type of filter paper and from 1 × 10(-6) to 1 × 10(-5) for a second type of filter paper, an effect not observed for materials tested at larger thicknesses. For high porosity materials, increasing chamber transport-limited deposition velocities resulted in increases in reaction probabilities by factors of 1.4-2.0. The impact of physical properties and transport effects on values of the Thiele modulus, ranging across all materials from 0.03 to 13, is discussed in terms of the challenges in estimating reaction probabilities to porous materials in scenarios relevant to indoor environments.

Electrokinetic Microstrirring to Enhance Immunoassays

NASA Astrophysics Data System (ADS)

Feldman, Hope; Sigurdson, Marin; Meinhart, Carl

2006-11-01

Electrokinetic microstirring is used to improve the sensitivity of microfluidic heterogeneous immuno-sensors by enhancing the transport in diffusion-limited reactions. The AC electrokinetic force, Electrothermal Flow, is exploited to create a circular stirring fluid motion, thereby providing more binding opportunities between suspended and wall-immobilized molecules. This process can significantly reduce test times, important for both field-portable biosensors and for lab-based assays. A 2-D numerical simulation model is used to predict the effect of electrothermal flow on a heterogeneous immunoassay resulting from an AC potential applied to two parallel electrodes. The binding is increased by a factor of 7 for an applied voltage of 10 Vrms. The effect was investigated experimentally using a high affinity biotin-streptavidin reaction. Microstirred reaction rates were compared with passive reactions. The measurements show on average an order of magnitude increase in binding between immobilized biotin and fluorescently-labeled streptavidin after 5 minutes. Therefore, this technique shows significant promise for reducing incubation time and enhancing the sensitivity of immunoassays.

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

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Ray, Deb Shankar

2013-06-01

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

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

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

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

Hydrothermal corrosion of silicon carbide joints without radiation

DOE PAGES

Koyanagi, Takaaki; Katoh, Yutai; Terrani, Kurt A.; ...

2016-09-28

In this paper, hydrothermal corrosion of four types of the silicon carbide (SiC) to SiC plate joints were investigated under pressurized water reactor and boiling water reactor relevant chemical conditions without irradiation. The joints were formed by metal diffusion bonding using molybdenum or titanium interlayer, reaction sintering using Ti—Si—C system, and SiC nanopowder sintering. Most of the joints withstood the corrosion tests for five weeks. The recession of the SiC substrates was limited. Based on the recession of the bonding layers, it was concluded that all the joints except for the molybdenum diffusion bond are promising under the reducing environmentsmore » without radiation. Finally, the SiC nanopowder sintered joint was the most corrosion tolerant under the oxidizing environment among the four joints.« less

CAD/CAM-designed 3D-printed electroanalytical cell for the evaluation of nanostructured gas-diffusion electrodes

NASA Astrophysics Data System (ADS)

Chervin, Christopher N.; Parker, Joseph F.; Nelson, Eric S.; Rolison, Debra R.; Long, Jeffrey W.

2016-04-01

The ability to effectively screen and validate gas-diffusion electrodes is critical to the development of next-generation metal-air batteries and regenerative fuel cells. The limiting electrode in a classic two-terminal device such as a battery or fuel cell is difficult to discern without an internal reference electrode, but the flooded electrolyte characteristic of three-electrode electroanalytical cells negates the prime function of an air electrode—a void volume freely accessible to gases. The nanostructured catalysts that drive the energy-conversion reactions (e.g., oxygen reduction and evolution in the air electrode of metal-air batteries) are best evaluated in the electrode structure as-used in the practical device. We have designed, 3D-printed, and characterized an air-breathing, thermodynamically referenced electroanalytical cell that allows us to mimic the Janus arrangement of the gas-diffusion electrode in a metal-air cell: one face freely exposed to gases, the other wetted by electrolyte.

CAD/CAM-designed 3D-printed electroanalytical cell for the evaluation of nanostructured gas-diffusion electrodes.

PubMed

Chervin, Christopher N; Parker, Joseph F; Nelson, Eric S; Rolison, Debra R; Long, Jeffrey W

2016-04-29

The ability to effectively screen and validate gas-diffusion electrodes is critical to the development of next-generation metal-air batteries and regenerative fuel cells. The limiting electrode in a classic two-terminal device such as a battery or fuel cell is difficult to discern without an internal reference electrode, but the flooded electrolyte characteristic of three-electrode electroanalytical cells negates the prime function of an air electrode-a void volume freely accessible to gases. The nanostructured catalysts that drive the energy-conversion reactions (e.g., oxygen reduction and evolution in the air electrode of metal-air batteries) are best evaluated in the electrode structure as-used in the practical device. We have designed, 3D-printed, and characterized an air-breathing, thermodynamically referenced electroanalytical cell that allows us to mimic the Janus arrangement of the gas-diffusion electrode in a metal-air cell: one face freely exposed to gases, the other wetted by electrolyte.

Rotating disk electrode system for elevated pressures and temperatures.

PubMed

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

2015-06-01

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

Rotating disk electrode system for elevated pressures and temperatures

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Classical Molecular Dynamics with Mobile Protons.

PubMed

Lazaridis, Themis; Hummer, Gerhard

2017-11-27

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

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.

Reaction-diffusion basis of retroviral infectivity

NASA Astrophysics Data System (ADS)

Sadiq, S. Kashif

2016-11-01

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

Reactive diffusion in the presence of a diffusion barrier: Experiment and model

NASA Astrophysics Data System (ADS)

Mangelinck, D.; Luo, T.; Girardeaux, C.

2018-05-01

Reactions in thin films and diffusion barriers are important for applications such as protective coatings, electrical contact, and interconnections. In this work, the effect of a barrier on the kinetics of the formation for a single phase by reactive diffusion is investigated from both experimental and modeling point of views. Two types of diffusion barriers are studied: (i) a thin layer of W deposited between a Ni film and Si substrate and (ii) Ni alloy films, Ni(1%W) and Ni(5%Pt), that form a diffusion barrier during the reaction with the Si substrate. The effect of the barriers on the kinetics of δ-Ni2Si formation is determined by in situ X ray diffraction and compared to models that explain the kinetic slowdown induced by both types of barrier. A linear parabolic growth is found for the deposited barrier with an increasing linear contribution for increasing barrier thickness. On the contrary, the growth is mainly parabolic for the barrier formed by the reaction between an alloy film and the substrate. The permeability of the two types of barrier is determined and discussed. The developed models fit well with the dedicated model experiments, leading to a better understanding of the barrier effect on the reactive diffusion and allowing us to predict the barrier behaviour in various applications.

Enhanced reaction kinetics in biological cells

NASA Astrophysics Data System (ADS)

Loverdo, C.; Bénichou, O.; Moreau, M.; Voituriez, R.

2008-02-01

The cell cytoskeleton is a striking example of an `active' medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown to have a spectacular impact on the mechanical and rheological properties of the cellular medium, as well as on its transport properties: a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose an analytical model of transport-limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers such as vesicles. We derive analytically the average interaction time with motor proteins that optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures such as axons.

Convex Arrhenius plots and their interpretation

PubMed Central

Truhlar, Donald G.; Kohen, Amnon

2001-01-01

This paper draws attention to selected experiments on enzyme-catalyzed reactions that show convex Arrhenius plots, which are very rare, and points out that Tolman's interpretation of the activation energy places a fundamental model-independent constraint on any detailed explanation of these reactions. The analysis presented here shows that in such systems, the rate coefficient as a function of energy is not just increasing more slowly than expected, it is actually decreasing. This interpretation of the data provides a constraint on proposed microscopic models, i.e., it requires that any successful model of a reaction with a convex Arrhenius plot should be consistent with the microcanonical rate coefficient being a decreasing function of energy. The implications and limitations of this analysis to interpreting enzyme mechanisms are discussed. This model-independent conclusion has broad applicability to all fields of kinetics, and we also draw attention to an analogy with diffusion in metastable fluids and glasses. PMID:11158559

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

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

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

1993-03-01

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

Enantioselective Cyanation of Benzylic C–H Bonds via Copper-Catalyzed Radical Relay

PubMed Central

Zhang, Wen; Wang, Fei; McCann, Scott D.; Wang, Dinghai; Chen, Pinhong; Stahl, Shannon; Liu, Guosheng

2017-01-01

Direct methods for stereoselective functionalization of C(sp3)–H bonds in complex organic molecules could facilitate much more efficient preparation of therapeutics and agrochemicals. Here, we report a copper-catalyzed radical relay pathway for enantioselective conversion of benzylic C–H bonds into benzylic nitriles. Hydrogen-atom abstraction affords an achiral benzylic radical that undergoes asymmetric C(sp3)–CN bond upon reaction with a chiral copper catalyst. The reactions proceed efficiently at room temperature with the benzylic substrate as limiting reagent, exhibit broad substrate scope with high enantioselectivity (typically 90-99% enantiomeric excess), and afford products that are key precursors to important bioactive molecules. Mechanistic studies provide evidence for diffusible organic radicals and highlight the difference between these reactions and C–H oxidations mediated by enzymes and other catalysts that operate via radical rebound pathways. PMID:27701109

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Oxidative Uranium Release from Anoxic Sediments under Diffusion-Limited Conditions.

PubMed

Bone, Sharon E; Cahill, Melanie R; Jones, Morris E; Fendorf, Scott; Davis, James; Williams, Kenneth H; Bargar, John R

2017-10-03

Uranium (U) contamination occurs as a result of mining and ore processing; often in alluvial aquifers that contain organic-rich, reduced sediments that accumulate tetravalent U, U(IV). Uranium(IV) is sparingly soluble, but may be mobilized upon exposure to nitrate (NO 3 - ) and oxygen (O 2 ), which become elevated in groundwater due to seasonal fluctuations in the water table. The extent to which oxidative U mobilization can occur depends upon the transport properties of the sediments, the rate of U(IV) oxidation, and the availability of inorganic reductants and organic electron donors that consume oxidants. We investigated the processes governing U release upon exposure of reduced sediments to artificial groundwater containing O 2 or NO 3 - under diffusion-limited conditions. Little U was mobilized during the 85-day reaction, despite rapid diffusion of groundwater within the sediments and the presence of nonuraninite U(IV) species. The production of ferrous iron and sulfide in conjunction with rapid oxidant consumption suggested that the sediments harbored large concentrations of bioavailable organic carbon that fueled anaerobic microbial respiration and stabilized U(IV). Our results suggest that seasonal influxes of O 2 and NO 3 - may cause only localized mobilization of U without leading to export of U from the reducing sediments when ample organic carbon is present.

Eliminating Size-Associated Diffusion Constraints for Rapid On-Surface Bioassays with Nanoparticle Probes.

PubMed

Li, Junwei; Zrazhevskiy, Pavel; Gao, Xiaohu

2016-02-24

Nanoparticle probes enable implementation of advanced on-surface assay formats, but impose often underappreciated size-associated constraints, in particular on assay kinetics and sensitivity. The present study highlights substantially slower diffusion-limited assay kinetics due to the rapid development of a nanoprobe depletion layer next to the surface, which static incubation and mixing of bulk solution employed in conventional assay setups often fail to disrupt. In contrast, cyclic solution draining and replenishing yields reaction-limited assay kinetics irrespective of the probe size. Using common surface bioassays, enzyme-linked immunosorbent assays and immunofluorescence, this study shows that this conceptually distinct approach effectively "erases" size-dependent diffusion constraints, providing a straightforward route to rapid on-surface bioassays employing bulky probes and procedures involving multiple labeling cycles, such as multicycle single-cell molecular profiling. For proof-of-concept, the study demonstrates that the assay time can be shortened from hours to minutes with the same probe concentration and, at a typical incubation time, comparable target labeling can be achieved with up to eight times lower nanoprobe concentration. The findings are expected to enable realization of novel assay formats and stimulate development of rapid on-surface bioassays with nanoparticle probes. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

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

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

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

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

Interphase Transformations at Metal (Copper, Iron)-Polymer Gel-Electrolyte Interfaces

NASA Astrophysics Data System (ADS)

Lyamina, G. V.; Dubinina, O. V.; Vaitulevich, E. A.; Mokrousov, G. M.

2018-07-01

The results from studies of the interface boundaries between metals (copper and iron) and gel electrolyte based on methacrylic copolymers are organized systematically. In contrast to processes in liquid electrolytes, a number of key features of the reactions that occur at such interfaces are revealed: a diffusion limiting stage; a lack of reverse reactions; and the formation of coordination compounds of metal ions with the functional groups of polymers, the stabilities of which are several orders of magnitude greater than that of coordination with their low-molecular weight counterparts. It is shown that processes which employ polymeric organogels can be used for the careful cleaning of the metal surfaces, and for the formation of a desired phase composition on the latter.

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.; McManus, Hugh L.

1996-01-01

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

Reactions of silicon-based ceramics in mixed oxidation chlorination environments

NASA Technical Reports Server (NTRS)

Marra, John E.; Kreidler, Eric R.; Jacobson, Nathan S.; Fox, Dennis S.

1988-01-01

The reaction of silicon-based ceramics with 2 percent Cl2/Ar and 1 percent Cl2/1 percent to 20 percent O2/Ar at 950 C was studied with thermogravimetric analysis and high-pressure mass spectrometry. Pure Si, SiO2, several types of SiC, and Si3N4 were examined. The primary corrosion products were SiCl4(g) and SiO2(s) with smaller amounts of volatile silicon oxychlorides. The reactions appear to occur by chlorine penetration of the SiO2 layer, and gas-phase diffusion of the silicon chlorides away from the sample appears to be rate limiting. Pure SiO2 shows very little reaction with Cl2, SiC with excess Si is more reactive than the other materials with Cl2, whereas SiC with excess carbon is more reactive than the other materials with Cl2/O2. Si3N4 shows very little reaction with Cl2. These differences are explained on the basis of thermodynamic and microstructural factors.

Pyrolysis reaction models of waste tires: Application of Master-Plots method for energy conversion via devolatilization.

PubMed

Irmak Aslan, Dilan; Parthasarathy, Prakash; Goldfarb, Jillian L; Ceylan, Selim

2017-10-01

Land applied disposal of waste tires has far-reaching environmental, economic, and human health consequences. Pyrolysis represents a potential waste management solution, whereby the solid carbonaceous residue is heated in the absence of oxygen to produce liquid and gaseous fuels, and a solid char. The design of an efficient conversion unit requires information on the reaction kinetics of pyrolysis. This work is the first to probe the appropriate reaction model of waste tire pyrolysis. The average activation energy of pyrolysis was determined via iso-conversional methods over a mass fraction conversion range between 0.20 and 0.80 to be 162.8±23.2kJmol -1 . Using the Master Plots method, a reaction order of three was found to be the most suitable model to describe the pyrolytic decomposition. This suggests that the chemical reactions themselves (cracking, depolymerization, etc.), not diffusion or boundary layer interactions common with carbonaceous biomasses, are the rate-limiting steps in the pyrolytic decomposition of waste tires. Copyright © 2017 Elsevier Ltd. All rights reserved.

Hydrodynamic fingering instability induced by a precipitation reaction

NASA Astrophysics Data System (ADS)

De Wit, Anne; Nagatsu, Yuichiro

2014-05-01

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the build-up of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A+B → C type of reaction when a solution containing one of the reactant is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Finger-like precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice-versa. A mathematical modeling of the underlying mobility profile in the cell reconstructed on the basis of one-dimensional reaction-diffusion concentration profiles confirms that the instability originates from a local decrease in mobility driven by the precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

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.

Dispersal and spatial heterogeneity: Single species

USGS Publications Warehouse

DeAngelis, Donald L.; Ni, Wei-Ming; Zhang, Bo

2016-01-01

A recent result for a reaction-diffusion equation is that a population diffusing at any rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. This has so far been proven by Lou for the case in which the reaction term has only one parameter, m(x)">m(x)m(x), varying with spatial location x">xx, which serves as both the intrinsic growth rate coefficient and carrying capacity of the population. However, this striking result seems rather limited when applies to real populations. In order to make the model more relevant for ecologists, we consider a logistic reaction term, with two parameters, r(x)">r(x)r(x) for intrinsic growth rate, and K(x)">K(x)K(x) for carrying capacity. When r(x)">r(x)r(x) and K(x)">K(x)K(x) are proportional, the logistic equation takes a particularly simple form, and the earlier result still holds. In this paper we have established the result for the more general case of a positive correlation between r(x)">r(x)r(x) and K(x)">K(x)K(x) when dispersal rate is small. We review natural and laboratory systems to which these results are relevant and discuss the implications of the results to population theory and conservation ecology.

Synthesis, characterization and heterogeneous base catalysis of amino functionalized lanthanide metal-organic frameworks

NASA Astrophysics Data System (ADS)

Huang, Jinping; Li, Chunmei; Tao, Lingling; Zhu, Huilin; Hu, Gang

2017-10-01

Lanthanide metal-organic frameworks (Ln-MOFs) are featured by their tolerance to water and dense structure. In this work, an amine-functionalized Ln-MOF was facilely synthesized by coordination of terbium with 2-aminoterephthalic acid under the condition of microwave irradiation. The crystal structure was characterized by single crystal X-ray diffraction, FT-IR, Raman, TG-DTA and XPS analysis. The basic catalytic activity of the NH2-Tb-MOF was evaluated for Knoevenagel condensation and Henry reactions. Apart from the high activity and 100% selectivity to the condensation product, the NH2-Tb-MOF catalyst could be easily recycled and reused owing to the high stability of the MOF framework formed by coordination of Tb3+ with carboxylic groups. Remarkably, the NH2-Tb-MOF exhibited size-selective catalysis to substrates. For the small-sized reactants, it displayed comparable activity to the homogeneous catalyst of aniline owing to the high dispersion of NH2- active sites and the low diffusion limits. However, in the same reaction system, extremely poor activity in Knoevenagel condensation and Henry reaction for the bulky substrate 4-(tert-butyl) benzaldehyde was observed due to the both effects of substitute and inhibition of diffusion into the micropores. Crystal structure analysis provided a mechanistic evidence that the heterogeneous base catalysis arose from the amino groups densely distributed inside the micropores.

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

Vorotilin, V. P., E-mail: VPVorotilin@yandex.ru

A generalization of the theory of chemical transformation processes under turbulent mixing of reactants and arbitrary values of the rate of molecular reactions is presented that was previously developed for the variant of an instantaneous reaction [13]. The use of the features of instantaneous reactions when considering the general case, namely, the introduction of the concept of effective reaction for the reactant volumes and writing a closing conservation equation for these volumes, became possible due to the partition of the whole amount of reactants into “active” and “passive” classes; the reactants of the first class are not mixed and reactmore » by the mechanism of instantaneous reactions, while the reactants of the second class approach each other only through molecular diffusion, and therefore their contribution to the reaction process can be neglected. The physical mechanism of reaction for the limit regime of an ideal mixing reactor (IMR) is revealed and described. Although formally the reaction rate in this regime depends on the concentration of passive fractions of the reactants, according to the theory presented, the true (hidden) mechanism of the reaction is associated only with the reaction of the active fractions of the reactants with vanishingly small concentration in the volume of the reactor. It is shown that the rate constant of fast chemical reactions can be evaluated when the mixing intensity of reactants is much less than that needed to reach the mixing conditions in an IMR.« less

X-ray analysis of temperature induced defect structures in boron implanted silicon

NASA Astrophysics Data System (ADS)

Sztucki, M.; Metzger, T. H.; Kegel, I.; Tilke, A.; Rouvière, J. L.; Lübbert, D.; Arthur, J.; Patel, J. R.

2002-10-01

We demonstrate the application of surface sensitive diffuse x-ray scattering under the condition of grazing incidence and exit angles to investigate growth and dissolution of near-surface defects after boron implantation in silicon(001) and annealing. Silicon wafers were implanted with a boron dose of 6×1015 ions/cm2 at 32 keV and went through different annealing treatments. From the diffuse intensity close to the (220) surface Bragg peak we reveal the nature and kinetic behavior of the implantation induced defects. Analyzing the q dependence of the diffuse scattering, we are able to distinguish between point defect clusters and extrinsic stacking faults on {111} planes. Characteristic for stacking faults are diffuse x-ray intensity streaks along <111> directions, which allow for the determination of their growth and dissolution kinetics. For the annealing conditions of our crystals, we conclude that the kinetics of growth can be described by an Ostwald ripening model in which smaller faults shrink at the expense of the larger stacking faults. The growth is found to be limited by the self-diffusion of silicon interstitials. After longer rapid thermal annealing the stacking faults disappear almost completely without shrinking, most likely by transformation into perfect loops via a dislocation reaction. This model is confirmed by complementary cross-sectional transmission electron microscopy.

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.

Numerical Study of Pressure Influence on Methane-Oxygen Laminar Counterflow Diffusion Flames

NASA Astrophysics Data System (ADS)

Iino, Kimio; Akamatsu, Fumiteru; Katsuki, Masashi

We carried out numerical studies on methane/oxygen diffusion flames of counter-flow configuration to elucidate the influence of pressure on flame structure, heat release rate and reaction mechanisms. The chemistry in gas-phase was based on GRI-Mech 3.0 database. The thickness of diffusion flame became thinner with increasing strain rate a , with its characteristic flame thickness varying inversely with √a, especially its relation became significant with increasing pressure. Flame temperature increased with increasing pressure. Enhanced H2O production reactions, especially chain terminal reactions for H2O production, were found to be important in determining the flame temperature at high pressures. The small reduction in the flame temperature with increasing strain rate at high pressures, compared to the atmospheric pressure, is caused by the capacitor effect of product dissociation. From QRPDs, the third body dependent reactions were enhanced in high pressure conditions, hence C2 pathway was enhanced.

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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

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

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

2015-08-28

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

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.

Inward propagating chemical waves in Taylor vortices.

PubMed

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

Role of hydrogen bonds in the reaction mechanism of chalcone isomerase.

PubMed

Jez, Joseph M; Bowman, Marianne E; Noel, Joseph P

2002-04-23

In flavonoid, isoflavonoid, and anthocyanin biosynthesis, chalcone isomerase (CHI) catalyzes the intramolecular cyclization of chalcones into (S)-flavanones with a second-order rate constant that approaches the diffusion-controlled limit. The three-dimensional structures of alfalfa CHI complexed with different flavanones indicate that two sets of hydrogen bonds may possess critical roles in catalysis. The first set of interactions includes two conserved amino acids (Thr48 and Tyr106) that mediate a hydrogen bond network with two active site water molecules. The second set of hydrogen bonds occurs between the flavanone 7-hydroxyl group and two active site residues (Asn113 and Thr190). Comparison of the steady-state kinetic parameters of wild-type and mutant CHIs demonstrates that efficient cyclization of various chalcones into their respective flavanones requires both sets of contacts. For example, the T48A, T48S, Y106F, N113A, and T190A mutants exhibit 1550-, 3-, 30-, 7-, and 6-fold reductions in k(cat) and 2-3-fold changes in K(m) with 4,2',4'-trihydroxychalcone as a substrate. Kinetic comparisons of the pH-dependence of the reactions catalyzed by wild-type and mutant enzymes indicate that the active site hydrogen bonds contributed by these four residues do not significantly alter the pK(a) of the intramolecular cyclization reaction. Determinations of solvent kinetic isotope and solvent viscosity effects for wild-type and mutant enzymes reveal a change from a diffusion-controlled reaction to one limited by chemistry in the T48A and Y106F mutants. The X-ray crystal structures of the T48A and Y106F mutants support the assertion that the observed kinetic effects result from the loss of key hydrogen bonds at the CHI active site. Our results are consistent with a reaction mechanism for CHI in which Thr48 polarizes the ketone of the substrate and Tyr106 stabilizes a key catalytic water molecule. Hydrogen bonds contributed by Asn113 and Thr190 provide additional stabilization in the transition state. Conservation of these residues in CHIs from other plant species implies a common reaction mechanism for enzyme-catalyzed flavanone formation in all plants.

Multispecies reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Fatollahi, A. H.; Khorrami, M.; Shariati, A.

2000-10-01

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Compatibility of buffered uranium carbides with tungsten.

NASA Technical Reports Server (NTRS)

Phillips, W. M.

1971-01-01

Results of compatibility tests between tungsten and hyperstoichiometric uranium carbide alloys run at 1800 C for 1000 and 2500 hours. These tests compared tungsten-buffered uranium carbide with tungsten-buffered uranium-zirconium carbide. The zirconium carbide addition appeared to widen the homogeneity range of the uranium carbide, making additional carbon available for reaction. Reaction layers could be formed by either of two diffusion paths, one producing UWC2, while the second resulted in the formation of W2C. UWC2 acts as a diffusion barrier for carbon and slows the growth of the reaction layer with time, while carbon diffusion is relatively rapid in W2C, allowing equilibrium to be reached in less than 2500 hours at a temperature of 1800 C.

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.

General theory for integrated analysis of growth, gene, and protein expression in biofilms.

PubMed

Zhang, Tianyu; Pabst, Breana; Klapper, Isaac; Stewart, Philip S

2013-01-01

A theory for analysis and prediction of spatial and temporal patterns of gene and protein expression within microbial biofilms is derived. The theory integrates phenomena of solute reaction and diffusion, microbial growth, mRNA or protein synthesis, biomass advection, and gene transcript or protein turnover. Case studies illustrate the capacity of the theory to simulate heterogeneous spatial patterns and predict microbial activities in biofilms that are qualitatively different from those of planktonic cells. Specific scenarios analyzed include an inducible GFP or fluorescent protein reporter, a denitrification gene repressed by oxygen, an acid stress response gene, and a quorum sensing circuit. It is shown that the patterns of activity revealed by inducible stable fluorescent proteins or reporter unstable proteins overestimate the region of activity. This is due to advective spreading and finite protein turnover rates. In the cases of a gene induced by either limitation for a metabolic substrate or accumulation of a metabolic product, maximal expression is predicted in an internal stratum of the biofilm. A quorum sensing system that includes an oxygen-responsive negative regulator exhibits behavior that is distinct from any stage of a batch planktonic culture. Though here the analyses have been limited to simultaneous interactions of up to two substrates and two genes, the framework applies to arbitrarily large networks of genes and metabolites. Extension of reaction-diffusion modeling in biofilms to the analysis of individual genes and gene networks is an important advance that dovetails with the growing toolkit of molecular and genetic experimental techniques.

High power densities from high-temperature materials interactions. [thermionic energy conversion and metallic fluid heat pipes

NASA Technical Reports Server (NTRS)

Morris, J. F.

1981-01-01

Thermionic energy converters and metallic-fluid heat pipes are well suited to serve together synergistically. The two operating cycles appear as simple and isolated as their material problems seem forebodingly deceptive and complicated. Simplified equations verify material properties and interactions as primary influences on the operational effectiveness of both. Each experiences flow limitations in thermal emission and vaporization because of temperature restrictions redounding from thermophysicochemical stability considerations. Topics discussed include: (1) successful limitation of alkali-metal corrosion; (2) protection against external hot corrosive gases; (3) coping with external and internal vaporization; (4) controlling interfacial reactions and diffusion; and (5) meeting other thermophysical challenges; expansion matches and creep.

A novel (ex situ) method to quantify oxygen diffusion coefficient of polymer fuel cells backing and catalyst layers

NASA Astrophysics Data System (ADS)

Baricci, Andrea; Casalegno, Andrea

2016-09-01

Limiting current density of oxygen reduction reaction in polymer electrolyte fuel cells is determined by several mass transport resistances that lower the concentration of oxygen on the catalyst active site. Among them, diffusion across porous media plays a significant role. Despite the extensive experimental activity documented in PEMFC literature, only few efforts have been dedicated to the measurement of the effective transport properties in porous layers. In the present work, a methodology for ex situ measurement of the effective diffusion coefficient and Knudsen radius of porous layers for polymer electrolyte fuel cells (gas diffusion layer, micro porous layer and catalyst layer) is described and applied to high temperature polymer fuel cells State of Art materials. Regression of the measured quantities by means of a quasi 2D physical model is performed to quantify the Knudsen effect, which is reported to account, respectively, for 30% and 50% of the mass transport resistance in micro porous layer and catalyst layer. On the other side, the model reveals that pressure gradient consequent to permeation in porous layers of high temperature polymer fuel cells has a negligible effect on oxygen concentration in relevant operating conditions.

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

DOE PAGES

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

2017-02-07

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

An experimental design method leading to chemical Turing patterns.

PubMed

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

2009-05-08

Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

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

Microstructure evolution, thermal stability and fractal behavior of water vapor flow assisted in situ growth poly(vinylcarbazole)-titania quantum dots nanocomposites

NASA Astrophysics Data System (ADS)

Mombrú, Dominique; Romero, Mariano; Faccio, Ricardo; Mombrú, Alvaro W.

2017-12-01

Here, we report a novel strategy for the preparation of TiO2 quantum dots fillers prepared from alkoxide precursor via in situ water vapor flow diffusion into poly(N-vinylcarbazole) host. A detailed characterization by means of infrared and Raman spectroscopy, X-ray powder diffraction, small angle X-ray scattering and differential scanning calorimetry is reported. The growth mechanism of both crystallites and particles was mostly governed by the classical coarsening reaction limited growth and the polymer host showed no detectable chemical modifications at the interface or active participation in the growing process. The main relevance of our strategy respect to the typical sol-gel growth in solution is the possibility of the interruption of the reaction by simple stopping the water vapor flow diffusion into the polymer host thus achieving good control in the nanoparticles size. The thermal stability and fractal behavior of our nanocomposites were also studied by differential scanning calorimetry and in situ small angle X-ray scattering versus temperature. Strong correlations between modifications in the fractal behavior and glass transition or fusion processes were observed for these nanocomposites.

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

DOE PAGES

Hoffmann, Max J.; Bligaard, Thomas

2018-01-22

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

Accelerated Analyte Uptake on Single Beads in Microliter-scale Batch Separations using Acoustic Streaming: Plutonium Uptake by Anion Exchange for Analysis by Mass Spectrometry

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

Paxton, Walter F.; O'Hara, Matthew J.; Peper, Shane M.

2008-06-01

The use of acoustic streaming as a non-contact mixing platform to accelerate mass transport-limited diffusion processes in small volume heterogeneous reactions has been investigated. Single bead anion exchange of plutonium at nanomolar and sub-picomolar concentrations in 20 microliter liquid volumes was used to demonstrate the effect of acoustic mixing. Pu uptake rates on individual ~760 micrometer diameter AG 1x4 anion exchange resin beads were determined using acoustic mixing and compared with Pu uptake rates achieved by static diffusion alone. An 82 MHz surface acoustic wave (SAW) device was placed in contact with the underside of a 384-well microplate containing flat-bottomedmore » semiconical wells. Acoustic energy was coupled into the solution in the well, inducing acoustic streaming. Pu uptake rates were determined by the plutonium remaining in solution after specific elapsed time intervals, using liquid scintillation counting (LSC) for nanomolar concentrations and thermal ionization mass spectrometry (TIMS) analysis for the sub-picomolar concentration experiments. It was found that this small batch uptake reaction could be accelerated by a factor of about five-fold or more, depending on the acoustic power applied.« less

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

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

Hoffmann, Max J.; Bligaard, Thomas

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

Coupling between geochemical reactions and multicomponent gas and solute transport in unsaturated media: A reactive transport modeling study

USGS Publications Warehouse

Molins, S.; Mayer, K.U.

2007-01-01

The two‐way coupling that exists between biogeochemical reactions and vadose zone transport processes, in particular gas phase transport, determines the composition of soil gas. To explore these feedback processes quantitatively, multicomponent gas diffusion and advection are implemented into an existing reactive transport model that includes a full suite of geochemical reactions. Multicomponent gas diffusion is described on the basis of the dusty gas model, which accounts for all relevant gas diffusion mechanisms. The simulation of gas attenuation in partially saturated landfill soil covers, methane production, and oxidation in aquifers contaminated by organic compounds (e.g., an oil spill site) and pyrite oxidation in mine tailings demonstrate that both diffusive and advective gas transport can be affected by geochemical reactions. Methane oxidation in landfill covers reduces the existing upward pressure gradient, thereby decreasing the contribution of advective methane emissions to the atmosphere and enhancing the net flux of atmospheric oxygen into the soil column. At an oil spill site, methane oxidation causes a reversal in the direction of gas advection, which results in advective transport toward the zone of oxidation both from the ground surface and the deeper zone of methane production. Both diffusion and advection contribute to supply atmospheric oxygen into the subsurface, and methane emissions to the atmosphere are averted. During pyrite oxidation in mine tailings, pressure reduction in the reaction zone drives advective gas flow into the sediment column, enhancing the oxidation process. In carbonate‐rich mine tailings, calcite dissolution releases carbon dioxide, which partly offsets the pressure reduction caused by O2 consumption.

Ballistic Motion of Enzymes that Catalyze Highly Exothermic Reactions

NASA Astrophysics Data System (ADS)

Tsekouras, Konstantinos; Pressé, Steve

Recently we proposed that the experimentally observed enhanced diffusion of enzymes catalyzing highly exothermic reactions is a consequence of their mechanism for dissipating reaction energy. More specifically, we proposed that reaction energy spreads out from the reaction site in the form of an acoustic wave which causes the enzyme to asymmetrically deform into the solvent. The solvent reaction propels the enzyme. However, it has been noted that in water, high viscosity should reduce enzyme momentum to zero within a few ps, so any diffusion increase should not be observable. Here we provide a model explaining how small volumetric expansions of biomolecules inside water may cause fluid compression that in turn creates regions of low fluid density around the biomolecule. We then investigate the dynamics of the biomolecule in the presence of these perturbations.

Use of ion beams to simulate reaction of reactor fuels with their cladding

NASA Astrophysics Data System (ADS)

Birtcher, R. C.; Baldo, P.

2006-01-01

Processes occurring within reactor cores are not amenable to direct experimental observation. Among major concerns are damage, fission gas accumulation and reaction between the fuel and its cladding all of which lead to swelling. These questions can be investigated through simulation with ion beams. As an example, we discuss the irradiation driven interaction of uranium-molybdenum alloys, intended for use as low-enrichment reactor fuels, with aluminum, which is used as fuel cladding. Uranium-molybdenum coated with a 100 nm thin film of aluminum was irradiated with 3 MeV Kr ions to simulate fission fragment damage. Mixing and diffusion of aluminum was followed as a function of irradiation with RBS and nuclear reaction analysis using the 27Al(p,γ)28Si reaction which occurs at a proton energy of 991.9 keV. During irradiation at 150 °C, aluminum diffused into the uranium alloy at a irradiation driven diffusion rate of 30 nm2/dpa. At a dose of 90 dpa, uranium diffusion into the aluminum layer resulted in formation of an aluminide phase at the initial interface. The thickness of this phase grew until it consumed the aluminum layer. The rapid diffusion of Al into these reactor fuels may offer explanation of the observation that porosity is not observed in the fuel particles but on their periphery.

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

2009-06-01

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

Confirmation of Monod Model for Biofiltration of Styrene Vapors from Waste Flue Gas

PubMed Central

Dehghanzadeh, Reza; Roshani, Babak; Asadi, Mahzar; Fahiminia, Mohammad; AslHashemi, Ahmad

2012-01-01

Background: The objective of this research was to investigate the kinetic behavior of the biofil¬tration process for the removal of styrene. Methods: A three stage compost based biofilter was inoculated with thickened activated sludge. The reaction order rate constants were obtained from continuous experiments and used as the specific growth rate for the Monod equation. Results: The measured concentration profiles show a linear dependence on the bed height in the biofilter at higher loadings, such as 75 and 45 g m-3 h-1. This is the condition of reaction limitation for a reaction with zero-order kinetics. From the experimental data, maximum elimination capac¬ity (ECmax) was estimated to be 44, 40 and 26 g m-3 h-1 at empty bed retention times (EBRTs) of 120, 60 and 30 s, respectively. However, at lower loadings, the measured concentration profile of the biofilter is one of exponential increase, which is the condition of both reaction and diffusion limitations for a reaction with zero-order kinetics. Maximum elimination capacities found from the experimental results were the same as Monod model predictions. Both the experimental re¬sults and the model predictions showed the influence of EBRT on the removal rate of styrene, particularly for the highest loading rate. Conclusion: In terms of the practical applications of the proposed models have the advantage of being simpler than Monod kinetics and Monod kinetics requires a numerical solution. PMID:24688940

Transport coefficients and heat fluxes in non-equilibrium high-temperature flows with electronic excitation

NASA Astrophysics Data System (ADS)

Istomin, V. A.; Kustova, E. V.

2017-02-01

The influence of electronic excitation on transport processes in non-equilibrium high-temperature ionized mixture flows is studied. Two five-component mixtures, N 2 / N2 + / N / N + / e - and O 2 / O2 + / O / O + / e - , are considered taking into account the electronic degrees of freedom for atomic species as well as the rotational-vibrational-electronic degrees of freedom for molecular species, both neutral and ionized. Using the modified Chapman-Enskog method, the transport coefficients (thermal conductivity, shear viscosity and bulk viscosity, diffusion and thermal diffusion) are calculated in the temperature range 500-50 000 K. Thermal conductivity and bulk viscosity coefficients are strongly affected by electronic states, especially for neutral atomic species. Shear viscosity, diffusion, and thermal diffusion coefficients are not sensible to electronic excitation if the size of excited states is assumed to be constant. The limits of applicability for the Stokes relation are discussed; at high temperatures, this relation is violated not only for molecular species but also for electronically excited atomic gases. Two test cases of strongly non-equilibrium flows behind plane shock waves corresponding to the spacecraft re-entry (Hermes and Fire II) are simulated numerically. Fluid-dynamic variables and heat fluxes are evaluated in gases with electronic excitation. In inviscid flows without chemical-radiative coupling, the flow-field is weakly affected by electronic states; however, in viscous flows, their influence can be more important, in particular, on the convective heat flux. The contribution of different dissipative processes to the heat transfer is evaluated as well as the effect of reaction rate coefficients. The competition of diffusion and heat conduction processes reduces the overall effect of electronic excitation on the convective heating, especially for the Fire II test case. It is shown that reliable models of chemical reaction rates are of great importance for accurate predictions of the fluid dynamic variables and heat fluxes.

Patchy reaction-diffusion and population abundance: the relative importance of habitat amount and arrangement

Treesearch

Curtis H. Flather; Michael Bevers

2002-01-01

A discrete reaction-diffusion model was used to estimate long-term equilibrium populations of a hypothetical species inhabiting patchy landscapes to examine the relative importance of habitat amount and arrangement in explaining population size. When examined over a broad range of habitat amounts and arrangements, population size was largely determined by a pure amount...

M3FT-16OR020202112 - Report on viability of hydrothermal corrosion resistant SiC/SiC Joint development

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

Katoh, Yutai; Koyanagi, Takaaki; Kiggans Jr, James O.

2016-06-30

Hydrothermal corrosion of four types of the silicon carbide (SiC) to SiC plate joints were investigated under PWR and BWR relevant chemical conditions without irradiation. The joints were formed by metal diffusion bonding using molybdenum or titanium interlayer, reaction sintering using Ti-Si-C system, and SiC nanopowder sintering. Most of the formed joints withstood the corrosion tests for five weeks. The recession of the SiC substrates was limited. Based on the recession rate of the bonding layers, it was concluded that all the joints except for the molybdenum diffusion bond are promising under the reducing activity environments. The SiC nanopowder sinteredmore » joint was the most corrosion tolerant under the oxidizing activity environment among the four joints.« less

A study of the propagation, dynamics, and extinguishment of cellular flames using microgravity techniques

NASA Technical Reports Server (NTRS)

Ronney, Paul D.

1989-01-01

The characteristics of premixed gas flames in mixtures with low Lewis numbers, free of natural convection effects, were investigated and found to be dominated by diffusive-thermal instabilities. For sufficiently reactive mixtures, cellular structures resulting from these instabilities were observed and found to spawn new cells in regular patterns. For less reactive mixtures, cells formed shortly after ignition but did not spawn new cells; instead these cells evolved into a flame structure composed of stationary, apparently stable spherical flamelets. As a result of these phenomena, well-defined flammability limits were not observed. The experimental results are found to be in qualitative agreement with a simple analytical model based on the interaction of heat release due to chemical reaction, differential diffusion of thermal energy and mass, flame front curvature, and heat losses due to gas radiation.

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 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.

Electrochemistry in an acoustically levitated drop.

PubMed

Chainani, Edward T; Ngo, Khanh T; Scheeline, Alexander

2013-02-19

Levitated drops show potential as microreactors, especially when radicals are present as reactants or products. Solid/liquid interfaces are absent or minimized, avoiding adsorption and interfacial reaction of conventional microfluidics. We report amperometric detection in an acoustically levitated drop with simultaneous ballistic addition of reactant. A gold microelectrode sensor was fabricated with a lithographic process; active electrode area was defined by a photosensitive polyimide mask. The microdisk gold working electrode of radius 19 μm was characterized using ferrocenemethanol in aqueous buffer. Using cyclic voltammetry, the electrochemically active surface area was estimated by combining a recessed microdisk electrode model with the Randles-Sevcik equation. Computer-controlled ballistic introduction of reactant droplets into the levitated drop was developed. Chronoamperometric measurements of ferrocyanide added ballistically demonstrate electrochemical monitoring using the microfabricated electrode in a levitated drop. Although concentration increases with time due to drop evaporation, the extent of concentration is predictable with a linear evaporation model. Comparison of diffusion-limited currents in pendant and levitated drops show that convection arising from acoustic levitation causes an enhancement of diffusion-limited current on the order of 16%.

Electron transfer by excited benzoquinone anions: slow rates for two-electron transitions.

PubMed

Zamadar, Matibur; Cook, Andrew R; Lewandowska-Andralojc, Anna; Holroyd, Richard; Jiang, Yan; Bikalis, Jin; Miller, John R

2013-09-05

Electron transfer (ET) rate constants from the lowest excited state of the radical anion of benzoquinone, BQ(-•)*, were measured in THF solution. Rate constants for bimolecular electron transfer reactions typically reach the diffusion-controlled limit when the free-energy change, ΔG°, reaches -0.3 eV. The rate constants for ET from BQ(-•)* are one-to-two decades smaller at this energy and do not reach the diffusion-controlled limit until -ΔG° is 1.5-2.0 eV. The rates are so slow probably because a second electron must also undergo a transition to make use of the energy of the excited state. Similarly, ET, from solvated electrons to neutral BQ to form the lowest excited state, is slow, while fast ET is observed at a higher excited state, which can be populated in a transition involving only one electron. A simple picture based on perturbation theory can roughly account for the control of electron transfer by the need for transition of a second electron. The picture also explains how extra driving force (-ΔG°) can restore fast rates of electron transfer.

Variable order fractional Fokker-Planck equations derived from Continuous Time Random Walks

NASA Astrophysics Data System (ADS)

Straka, Peter

2018-08-01

Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent β(x) ∈(0 , 1) varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix varies throughout a cell. Scaling limits of CTRWs are known to have probability distributions which solve fractional Fokker-Planck type equations (FFPE). This correspondence between stochastic processes and FFPE solutions has many useful extensions e.g. to nonlinear particle interactions and reactions, but has not yet been sufficiently developed for FFPEs of the "variable order" type with non-constant β(x) . In this article, variable order FFPEs (VOFFPE) are derived from scaling limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW scaling limit to a bivariate Langevin process, which tracks the cumulative sum of jumps in one component and the cumulative sum of waiting times in the other. The spatially varying anomalous exponent is modelled by spatially varying β(x) -stable Lévy noise in the waiting time component. The VOFFPE displays a spatially heterogeneous temporal scaling behaviour, with generalized diffusivity and drift coefficients whose units are length2/timeβ(x) resp. length/timeβ(x). A global change of the time scale results in a spatially varying change in diffusivity and drift. A consequence of the mathematical derivation of a VOFFPE from CTRW limits in this article is that a solution of a VOFFPE can be approximated via Monte Carlo simulations. Based on such simulations, we are able to confirm that the VOFFPE is consistent under a change of the global time scale.

Rigorous results for the minimal speed of Kolmogorov-Petrovskii-Piscounov monotonic fronts with a cutoffa)

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Depassier, M. Cristina; Loss, Michael

2012-12-01

We study the effect of a cutoff on the speed of pulled fronts of the one-dimensional reaction diffusion equation. To accomplish this, we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles. This existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut-off parameter ɛ. From these bounds we estimate the range of validity of the Brunet-Derrida formula for a general class of reaction terms.

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.

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

PubMed

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

2014-04-17

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

(Bio)Sensing Using Nanoparticle Arrays: On the Effect of Analyte Transport on Sensitivity.

PubMed

Lynn, N Scott; Homola, Jiří

2016-12-20

There has recently been an extensive amount of work regarding the development of optical, electrical, and mechanical (bio)sensors employing planar arrays of surface-bound nanoparticles. The sensor output for these systems is dependent on the rate at which analyte is transported to, and interacts with, each nanoparticle in the array. There has so far been little discussion on the relationship between the design parameters of an array and the interplay of convection, diffusion, and reaction. Moreover, current methods providing such information require extensive computational simulation. Here we demonstrate that the rate of analyte transport to a nanoparticle array can be quantified analytically. We show that such rates are bound by both the rate to a single NP and that to a planar surface (having equivalent size as the array), with the specific rate determined by the fill fraction: the ratio between the total surface area used for biomolecular capture with respect to the entire sensing area. We characterize analyte transport to arrays with respect to changes in numerous parameters relevant to experiment, including variation of the nanoparticle shape and size, packing density, flow conditions, and analyte diffusivity. We also explore how analyte capture is dependent on the kinetic parameters related to an affinity-based biosensor, and furthermore, we classify the conditions under which the array might be diffusion- or reaction-limited. The results obtained herein are applicable toward the design and optimization of all (bio)sensors based on nanoparticle arrays.

Reduction Mechanisms of Cu2+-Doped Na2O-Al2O3-SiO2 Glasses during Heating in H2 Gas.

PubMed

Nogami, Masayuki; Quang, Vu Xuan; Ohki, Shinobu; Deguchi, Kenzo; Shimizu, Tadashi

2018-01-25

Controlling valence state of metal ions that are doped in materials has been widely applied for turning optical properties. Even though hydrogen has been proven effective to reduce metal ions because of its strong reducing capability, few comprehensive studies focus on practical applications because of the low diffusion rate of hydrogen in solids and the limited reaction near sample surfaces. Here, we investigated the reactions of hydrogen with Cu 2+ -doped Na 2 O-Al 2 O 3 -SiO 2 glass and found that a completely different reduction from results reported so far occurs, which is dominated by the Al/Na concentration ratio. For Al/Na < 1, Cu 2+ ions were reduced via hydrogen to metallic Cu, distributing in glass body. For Al/Na > 1, on the other hand, the reduction of Cu 2+ ions occurred simultaneously with the formation of OH bonds, whereas the reduced Cu metal moved outward and formed a metallic film on glass surface. The NMR and Fourier transform infrared results indicated that the Cu 2+ ions were surrounded by Al 3+ ions that formed AlO 4 , distorted AlO 4 , and AlO 5 units. The diffused H 2 gas reacted with the Al-O - ···Cu + units, forming Al-OH and metallic Cu, the latter of which moved freely toward glass surface and in return enhanced H 2 diffusion.

Laminar Soot Processes (LSP)

NASA Technical Reports Server (NTRS)

Dai, Z.; El-Leathy, A. M.; Kim, C. H.; Krishnan, S. S.; Lin, K.-C.; Xu, F.; Faeth, G. M.

2002-01-01

This is the final report of a research program considering the structure and the soot surface reaction properties of laminar nonpremixed (diffusion) flames. The study was limited to ground-based measurements of buoyant laminar jet diffusion flames at pressures of 0.1-1.0 atm. The motivation for the research is that soot formation in flames is a major unresolved problem of combustion science that influences the pollutant emissions, durability and performance of power and propulsion systems, as well as the potential for developing computational combustion. The investigation was divided into two phases considering the structure of laminar soot-containing diffusion flames and the soot surface reaction properties (soot surface growth and oxidation) of these flames, in turn. The first phase of the research addressed flame and soot structure properties of buoyant laminar jet diffusion flames at various pressures. The measurements showed that H, OH and O radical concentrations were generally in superequilibrium concentrations at atmospheric pressure but tended toward subequilibrium concentrations as pressures decreased. The measurements indicated that the original fuel decomposed into more robust compounds at elevated temperatures, such as acetylene (unless the original fuel was acetylene) and H, which are the major reactants for soot surface growth, and that the main effect of the parent fuel on soot surface growth involved its yield of acetylene and H for present test conditions. The second phase of the research addressed soot surface reaction properties, e.g., soot surface growth and surface oxidation. It was found that soot surface growth rates in both laminar premixed and diffusion flames were in good agreement, that these rates were relatively independent of fuel type, and that these rates could be correlated by the Hydrogen-Abstraction/Carbon-Addition (HACA) mechanisms of Colket and Hall (1994), Frenklach et al. (1990,1994), and Kazakov et al. (1995). It was also found that soot surface oxidation rates were relatively independent of fuel type, were not correlated with O2, CO2, H2O and O collision rates but were correlated with the collision rates of OH with a collision efficiency of 0.14, in agreement with the early measurements in premixed flames of Neoh et al. (1980), after allowing for oxidation by O2 via the classical rate expression of Nagle and Strickland-Constable (1962).

Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models.

PubMed

Drugowitsch, Jan

2016-02-11

We present a new, fast approach for drawing boundary crossing samples from Wiener diffusion models. Diffusion models are widely applied to model choices and reaction times in two-choice decisions. Samples from these models can be used to simulate the choices and reaction times they predict. These samples, in turn, can be utilized to adjust the models' parameters to match observed behavior from humans and other animals. Usually, such samples are drawn by simulating a stochastic differential equation in discrete time steps, which is slow and leads to biases in the reaction time estimates. Our method, instead, facilitates known expressions for first-passage time densities, which results in unbiased, exact samples and a hundred to thousand-fold speed increase in typical situations. In its most basic form it is restricted to diffusion models with symmetric boundaries and non-leaky accumulation, but our approach can be extended to also handle asymmetric boundaries or to approximate leaky accumulation.

Pattern formation in mass conserving reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Brauns, Fridtjof; Halatek, Jacob; Frey, Erwin

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