Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction rates for mesoscopic reaction-diffusion kinetics
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction rates for reaction-diffusion kinetics on unstructured meshes
Hellander, Stefan; Petzold, Linda
2017-02-01
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
Stochastic reaction-diffusion kinetics in the microscopic limit
Fange, David; Berg, Otto G.; Sjöberg, Paul; Elf, Johan
2010-01-01
Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system. PMID:21041672
Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry
Konkoli, Zoran
2009-01-01
In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging from systems biology approaches, through network analysis (motif identification) towards developing language and simulators for low level biochemical processes. Apart from simulation work, much of the efforts are directed to using mean field equations (equivalent to the equations of classical chemical kinetics) to address various problems (stability, robustness, sensitivity analysis, etc.). Rarely is the use of mean field equations questioned. This review will provide a brief overview of the situations when mean field equations fail and should not be used. These equations can be derived from the theory of diffusion controlled reactions, and emerge when assumption of perfect mixing is used.
1D to 3D diffusion-reaction kinetics of defects in crystals
Trinkaus, H.; Heinisch, H.L.; Barashev, A.V.
2002-01-01
Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce ...... and 3D limiting cases. The analytical result is fully confirmed by kinetic Monte Carlo simulations.......Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce...
A Note on the Kinetics of Diffusion-mediated Reactions
Naqvi, K Razi
2014-01-01
The prevalent scheme of a diffusion-mediated bimolecular reaction $A+B\\rightarrow P$ is an adaptation of that proposed by Briggs and Haldane for enzyme action [{\\em Biochem J.\\/}, 19:338--339, 1925]. The purpose of this Note is to explain, {\\em by using an argument involving no mathematics\\/}, why the breakup of the encounter complex cannot be described, except in special circumstances, in terms of a first-order process $\\{AB\\}\\rightarrow A+B$. Briefly, such a description neglects the occurrence of re-encounters, which lie at the heart of Noyes's theory of diffusion-mediated reactions. The relation $k=\\alpha k_{\\mbox{\\scriptsize e}}$ becomes valid only when $\\alpha$ (the reaction probability per encounter) is very much smaller than unity (activation-controlled reactions), or when $\\beta$ (the re-encounter probability) is negligible (as happens in a gas-phase reaction). References to some works (by the author and his collaborators) which propound the correct approach for finding $k$ are also supplied.
Control of DNA replication by anomalous reaction-diffusion kinetics
Bechhoefer, John; Gauthier, Michel
2010-03-01
DNA replication requires two distinct processes: the initiation of pre-licensed replication origins and the propagation of replication forks away from the fired origins. Experiments indicate that these origins are triggered over the whole genome at a rate I(t) (the number of initiations per unreplicated length per time) that increases throughout most of the synthesis (S) phase, before rapidly decreasing to zero at the end of the replication process. We propose a simple model for the control of DNA replication in which the rate of initiation of replication origins is controlled by protein-DNA interactions. Analyzing recent data from Xenopus frog embryos, we find that the initiation rate is reaction limited until nearly the end of replication, when it becomes diffusion limited. Initiation of origins is suppressed when the diffusion-limited search time dominates. To fit the experimental data, we find that the interaction between DNA and the rate-limiting protein must be subdiffusive.
Reaction diffusion and solid state chemical kinetics handbook
Dybkov, V I
2010-01-01
This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate
Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites
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.
Effect of mixing on reaction-diffusion kinetics for protein hydrogel-based microchips.
Zubtsov, D A; Ivanov, S M; Rubina, A Yu; Dementieva, E I; Chechetkin, V R; Zasedatelev, A S
2006-03-09
Protein hydrogel-based microchips are being developed for high-throughput evaluation of the concentrations and activities of various proteins. To shorten the time of analysis, the reaction-diffusion kinetics on gel microchips should be accelerated. Here we present the results of the experimental and theoretical analysis of the reaction-diffusion kinetics enforced by mixing with peristaltic pump. The experiments were carried out on gel-based protein microchips with immobilized antibodies under the conditions utilized for on-chip immunoassay. The dependence of fluorescence signals at saturation and corresponding saturation times on the concentrations of immobilized antibodies and antigen in solution proved to be in good agreement with theoretical predictions. It is shown that the enhancement of transport with peristaltic pump results in more than five-fold acceleration of binding kinetics. Our results suggest useful criteria for the optimal conditions for assays on gel microchips to balance high sensitivity and rapid fluorescence saturation kinetics.
Fedotov, Sergei
1998-10-01
An asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure, and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.
Meng-ge Liu; Wei Yu; Chi-xing Zhou
2006-01-01
The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N-1.5 (N is the length of chains), which is in consistent with de Gennes's result.
Heinisch, H.L.; Trinkaus, H.; Singh, Bachu Narain
2007-01-01
and confirmed by kinetic Monte Carlo (KMC) simulations. Here we report on KMC simulations investigating a different transition from 1D to 3D diffusion of 1D gliding loops for which their 1D migration is interrupted by occasional 2D migration due to conservative climb by dislocation core diffusion within a plane...... transverse to their 1D glide direction. Their transition from 1D to 3D kinetics is significantly different from that due to direction changes. The KMC results are compared to an analytical description of this diffusion mode in the form of a master curve relating the 1D normalized sink strength...
Wu, Zeng-Qiang; Li, Zhong-Qiu; Li, Jin-Yi; Gu, Jing; Xia, Xing-Hua
2016-05-25
The spatial positioning of enzymes and mass transport play crucial roles in the functionality and efficiency of enzyme cascade reactions. To fully understand the mass transport regulating kinetics of enzyme cascade reactions, we investigated the contribution of convective and diffusive transports to a cascade reaction of β-galactosidase (β-Gal)/glucose oxidase (GOx) confined in a microchannel. β-Gal and GOx are assembled on two separated gold films patterned in a polydimethylsiloxane (PDMS) microchannel with a controllable distance from 50 to 100 μm. Experimental results demonstrated that the reaction yield increases with decreasing distance between two enzymes and increasing substrate flow rate. Together with the simulation results, we extracted individual reaction kinetics of the enzyme cascade reaction and found that the reaction rate catalyzed by β-Gal occurred much faster than by GOx, and thus, the β-Gal catalytic reaction showed diffusion controll, whereas the GOx catalytic reaction showed kinetic controll. Since the decrease in the enzymes distance shortens the transport length of intermediate glucose to GOx, the amount of glucose reaching GOx will be increased in the unit time, and in turn, the enzyme cascade reaction yield will be increased with decreasing the gap distance. This phenomenon is similar to the intermediates pool of tricarboxylic acid (TCA) cycle in the metabolic system. This study promotes the understanding of the metabolic/signal transduction processes and active transport in biological systems and promises to design high performance biosensors and biofuel cells systems.
Kinetic pathways of diffusion and solid-state reactions in nanostructured thin films
Beke, D. L.; Langer, G. A.; Molnár, G.; Erdélyi, G.; Katona, G. L.; Lakatos, A.; Vad, K.
2013-06-01
Mass transport and solid-state reactions in nanocrystalline thin films are reviewed. It is illustrated that diffusion along different grain boundaries (GBs) can have important effects on the overall intermixing process between two pure films. These processes can be well characterized by a bimodal GB network, with different (fast and slow) diffusivities. First the atoms migrate along fast GBs and accumulate at the film surface. These accumulated atoms form a secondary diffusion source for back diffusion along slow boundaries. Thus the different GBs of the thin films can be gradually filled up with the diffusing atoms and composition depth profiles reflect the result of these processes. Similar processes can be observed in binary systems with intermetallic layers: instead of nucleation and growth of the reaction layer at the initial interface, the reaction takes place in the GBs and the amount of the product phase grows by the motion of its interfaces perpendicular to the GBs. Thus, the entire layer of the pure parent films can be consumed by this GB diffusion-induced solid-state reaction (GBDIREAC), and a fully homogeneous product layer can be obtained.
The DNA Binding Activity of p53 Displays Reaction-Diffusion Kinetics
Hinow, Peter; Rogers, Carl E.; Barbieri, Christopher E.; Pietenpol, Jennifer A.; Kenworthy, Anne K.; DiBenedetto, Emmanuele
2006-01-01
The tumor suppressor protein p53 plays a key role in maintaining the genomic stability of mammalian cells and preventing malignant transformation. In this study, we investigated the intracellular diffusion of a p53-GFP fusion protein using confocal fluorescence recovery after photobleaching. We show that the diffusion of p53-GFP within the nucleus is well described by a mathematical model for diffusion of particles that bind temporarily to a spatially homogeneous immobile structure with binding and release rates k1 and k2, respectively. The diffusion constant of p53-GFP was estimated to be Dp53-GFP = 15.4 μm2 s−1, significantly slower than that of GFP alone, DGFP = 41.6 μm2 s−1. The reaction rates of the binding and unbinding of p53-GFP were estimated as k1 = 0.3 s−1 and k2 = 0.4 s−1, respectively, values suggestive of nonspecific binding. Consistent with this finding, the diffusional mobilities of tumor-derived sequence-specific DNA binding mutants of p53 were indistinguishable from that of the wild-type protein. These data are consistent with a model in which, under steady-state conditions, p53 is latent and continuously scans DNA, requiring activation for sequence-specific DNA binding. PMID:16603489
Velikanov, M V; Velikanov, Mikhail V.; Kapral, Raymond
1998-01-01
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles on a lattice. The parameter \\gamma, the ratio of characteristic time scales of reaction and diffusion, is used to gauge the relative contributions of these two processes to the overall dynamics. For the case of relatively fast diffusion, i.e. \\gamma 0 these memory terms vanish and the mass-action law is recovered; b) the memory kernel is found to assume a simple exponential form. A comparison with numerical results from lattice gas automaton simulations is also carried out.
Villar-Cociña, E.
2005-06-01
Full Text Available A kinetic-diffusive model proposed by the authors in previous papers to describe pozzolanic reaction kinetics in sugar cane straw-clay ash (SCSCA/calcium hydroxide (CH systems is validated in this study. Two different methods (direct and indirect for determining pozzolanic activity were applied and their effect on pozzolanic reaction rate kinetic constants evaluated. Determined by fitting a model to the data, these constants are used to quantitatively characterize pozzolanic activity. The values of the kinetic constants calculated with the model were similar for the two methods. Classic kinetic models, such as the Jander, modified Jander and Zhuravlev models, were also applied to the system studied and the results were compared to the figures calculated with the model proposed. The kinetic-diffusive approach proposed was found to be valid regardless of the method for determining pozzolanic activity used, and to be the most suitable model for describing pozzolanic reaction kinetics in the SCSCA/lime system.
Se valida la aplicación de un modelo cinético-difusivo propuesto por los autores en trabajos anteriores para describir la cinética de reacción puzolánica en sistemas ceniza de paja de caña-arcilla (CPCAñúdróxido de calcio (CH. Se aplican 2 métodos diferentes de actividad puzolánica (directo e indirecto y se valora el efecto que pudieran tener los mismos sobre las constantes cinéticas de velocidad de reacción de la reacción puzolánica. Estas constantes cinéticas son determinadas en el proceso de ajuste del modelo y permiten caracterizar cuantitativamente la actividad puzolánica. Los resultados muestran la similitud de las constantes cinéticas de velocidad de reacción calculadas, aplicando el modelo a los resultados experimentales obtenidos por ambos métodos. Además, fueron aplicados al sistema estudiado modelos cinéticos el chicos como: modelo de Jander, modelo de Jander Modificado y el modelo de Zhuravlev y
Dellar, Paul
2016-11-01
We present discrete kinetic and lattice Boltzmann formulations for reaction cross-diffusion systems, as commonly used to model microbiological chemotaxis and macroscopic predator-prey interactions, and their hyperbolic extensions with fluid-like persistence terms. For example, the canonical Patlak-Keller-Segal model for chemotaxis involves a flux of cells up the gradient of a chemical secreted by the cells, in addition to the usual down-gradient diffusive fluxes. Existing lattice Boltzmann approaches for such systems use finite difference approximations to compute the flux of cells due to the chemical gradient. The resulting coupling between, and necessary synchronisation of the evolution of, adjacent grid points greatly complicates boundary conditions, and efficient implementation on graphical processing units (GPUs). We present a kinetic formulation using cross-collisions between bases of moments for the two sets of distribution functions to couple the fluxes of the two species, from which we construct lattice Boltzmann algorithms using second-order Strang splitting. We demonstrate an efficient GPU implementation, and verify second-order spatial convergence towards spectral solutions for benchmark problems such as the finite-time blow-up in the Patlak-Keller-Segal model.
La Rosa, Carmelo; Scalisi, Silvia; Lolicato, Fabio; Pannuzzo, Martina; Raudino, Antonio
2016-05-01
The protein transport inside a cell is a complex phenomenon that goes through several difficult steps. The facilitated transport requires sophisticated machineries involving protein assemblies. In this work, we developed a diffusion-reaction model to simulate co-transport kinetics of proteins and lipids. We assume the following: (a) there is always a small lipid concentration of order of the Critical Micellar Concentration (CMC) in equilibrium with the membrane; (b) the binding of lipids to proteins modulates the hydrophobicity of the complexes and, therefore, their ability to interact and merge with the bilayer; and (c) some lipids leave the bilayer to replenish those bound to proteins. The model leads to a pair of integral equations for the time-evolution of the adsorbed proteins in the lipid bilayer. Relationships between transport kinetics, CMC, and lipid-protein binding constants were found. Under particular conditions, a perturbation analysis suggests the onset of kinks in the protein adsorption kinetics. To validate our model, we performed leakage measurements of vesicles composed by either high or low CMC lipids interacting with Islet Amyloid PolyPeptide (IAPP) and Aβ (1-40) used as sample proteins. Since the lipid-protein complex stoichiometry is not easily accessible, molecular dynamics simulations were performed using monomeric IAPP interacting with an increasing number of phospholipids. Main results are the following: (a) 1:1 lipid-protein complexes generally show a faster insertion rate proportional to the complex hydrophobicity and inversely related to lipid CMC; (b) on increasing the number of bound lipids, the protein insertion rate decreases; and (c) at slow lipids desorption rate, the lipid-assisted proteins transport might exhibit a discontinuous behavior and does non-linearly depend on protein concentration.
Trinkaus, H.; Singh, Bachu Narain; Golubov, S.I.
In recent years, it has been shown that a number of striking features in the microstructural evolution occurring in metals under cascade damage generating irradiation (e.g. enhanced swelling near grain boundaries, decoration of dislocations with SIA loops, saturation of void growth and void lattice...... formation) can be rationalised in terms of intra-cascade clustering of vacancies and self-interstitial atoms (SIAs), differences in the thermal stability and mobility of the resulting clusters and one-dimensional (1D) glide diffusion of SIA clusters (“production bias model”). The 1D diffusion of SIA...... clusters is generally disturbed by changes between equivalent 1D diffusion paths and by transversal diffusion by self-climb, resulting in diffusion reaction kinetics between the 1D and 3D limiting cases. In this paper, a general treatment of such kinetics operating in systems containing random...
Parker, J.; Kim, U.; Widdowson, M.; Chappel, F.
2008-12-01
Explicit modeling of contaminant dissolution from heterogeneously distributed NAPL sources, microbial growth and reaction kinetics, and diffusion into or out of low permeability layers pose significant difficulties. These include the need to estimate a large number of parameters, which may subject to great uncertainty due to inverse problem ill-posedness given limited data, and to a lesser extent, the large computational effort that may be required to solve a rigorously formulated problem. An upscaled model for NAPL dissolution kinetics is utilized in the present study based on previous work, with extentions to consider concurrent effects of residual DNAPL and pools or lenses and to consider multi-component NAPL mixtures. An approach is presented to model microbially-mediated redox reactions subject to the assumption that microbial growth and reaction rates are primarily limited by transport processes rather than by microbial kinetics at time and space scales relevant for many remediation problems. The simplified model requires only stoichiometric coefficients for electron donor and electron acceptor half-reactions and the fraction of electron donor needed for cell synthesis. Contaminant diffusion into low permeability layers and subsequent back-diffusion is approximated as a first-order mass transfer problem with an effective mass transfer coefficient computed from aquifer-aquitard properties by equating second moments of diffusion and mass transfer solutions. Accuracy of the simplified model formulation is evaluated for a hypothetical problem involving a DNAPL source consisting of a mixture of TCE and Stoddard solvent with background dissolved organic carbon, oxygen and sulfate in groundwater for 40 years followed by injection of vegetable oil as a supplemental electron donor to enhance reductive dechlorination. The simplified solution is compared to numerical results that consider multi-species Monod kinetics with explicit treatment of back-diffusion.
Vass, József
2016-01-01
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables, which ensures the global stability of discretization. Convection-diffusion equations are notorious for their lack of stability, arising from the algebraic interaction of the convection and diffusion terms. Unexpectedly, our implemented numerical algorithm proves to be faster than computing exact solutions derived for a special case, while remaining reasonably accurate, as demonstrated in our runtime and error analysis.
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.
Chemical kinetics of gas reactions
Kondrat'Ev, V N
2013-01-01
Chemical Kinetics of Gas Reactions explores the advances in gas kinetics and thermal, photochemical, electrical discharge, and radiation chemical reactions. This book is composed of 10 chapters, and begins with the presentation of general kinetic rules for simple and complex chemical reactions. The next chapters deal with the experimental methods for evaluating chemical reaction mechanisms and some theories of elementary chemical processes. These topics are followed by discussions on certain class of chemical reactions, including unimolecular, bimolecular, and termolecular reactions. The rema
Saliba, Daniel; Al-Ghoul, Mazen
2016-11-01
We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Johannesson, Björn
2009-01-01
Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...... for the non-linear global matrix formulation. The developed model and its numerical solution procedure are checked by running test examples which results demonstrates robustness of the proposed approach....
2015-01-01
his chapter predicts the specific rates of reaction by means of a mathematical expression, the kinetics of the reaction. This expression can be derived through a mechanistic interpretation of an enzymatically catalyzed reaction, but it is essentially of empirical nature for cell reactions....... The models can be used in mass balances for design of processes under process conditions not yet studied experimentally. The value of the predictive kinetic model depends on the quality of the experimental data on which the model is based, and well-founded kinetic models for enzyme reactions have...... a considerable predictive power. This is also true for cell reaction models, when the model is used in its proper context. The chapter first discusses the kinetics for enzymatically catalyzed reactions (“enzyme reactions”). The kinetics can be derived from a mechanistic model. Then, the chapter derives empirical...
Resonance Reaction in Diffusion-Influenced Bimolecular Reactions
Kolb, Jakob J; Dzubiella, Joachim
2016-01-01
We investigate the influence of a stochastically fluctuating step-barrier potential on bimolecular reaction rates by exact analytical theory and stochastic simulations. We demonstrate that the system exhibits a new resonant reaction behavior with rate enhancement if an appropriately defined fluctuation decay length is of the order of the system size. Importantly, we find that in the proximity of resonance the standard reciprocal additivity law for diffusion and surface reaction rates is violated due to the dynamical coupling of multiple kinetic processes. Together, these findings may have important repercussions on the correct interpretation of various kinetic reaction problems in complex systems, as, e.g., in biomolecular association or catalysis.
Chambon, Julie Claire Claudia; Lemming, Gitte; Manoli, Gabriele
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...... 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...
Computer prediction system on solid/solid reaction kinetics
无
2001-01-01
A computer software system of kinetic predication of solid/solid reaction, KinPreSSR, was developed using Visual C++ and FoxPro. It includes two main modules, REACTION and DIFFUSION. KinPreSSR deals with the kinetics on the diffusion in solids as well as solid/solid reactions. The REACTION module in KinPreSSR was mainly described, which has organized the commonly recognized kinetic models, parameters, and employed both numerical and graphical methods for data analyses. The proper combination between the kinetic contents and the analytical methods enables users to use KinPreSSR for the evaluation and prediction of solid/solid reactions interested. As an example to show some of functions of KinPreSSR, the kinetics analysis for the reaction between SrCO3 and TiO2 powders to form SrTiO3 with a series of kinetic data from isothermal measurements was demonstrated.
Murcia, M D; Gómez, M; Bastida, J; Hidalgo, A M; Montiel, M C; Ortega, S
2014-08-01
A continuous tank reactor was used to remove 4-chlorophenol from aqueous solutions, using immobilized soybean peroxidase and hydrogen peroxide. The influence of operational variables (enzyme and substrate concentrations and spatial time) on the removal efficiency was studied. By using the kinetic law and the intrinsic kinetic parameters obtained in a previous work with a discontinuous tank reactor, the mass-balance differential equations of the transient state reactor model were solved and the theoretical conversion values were calculated. Several experimental series were used to obtain the values of the remaining model parameters by numerical calculation and using an error minimization algorithm. The model was checked by comparing the results obtained in some experiments (not used for the determination of the parameters) and the theoretical ones. The good concordance between the experimental and calculated conversion values confirmed that the design model can be used to predict the transient behaviour of the reactor.
Reaction kinetics of polybutylene terephthalate polycondensation reaction
Darda, P. J.; Hogendoorn, J. A.; Versteeg, G. F.; Souren, F.
2005-01-01
The kinetics of the forward polycondensation reaction of polybutylene terephthalate (PBT) has been investigated using thermogravimetric analysis (TGA). PBT - prepolymer with an initial degree of polymerization of 5.5 was used as starting material. The PBT prepolymer was prepared from dimethyl tereph
Reaction-diffusion pulses: a combustion model
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
Analysis of kinetic reaction mechanisms
Turányi, Tamás
2014-01-01
Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.
Combustion kinetics and reaction pathways
Klemm, R.B.; Sutherland, J.W. [Brookhaven National Laboratory, Upton, NY (United States)
1993-12-01
This project is focused on the fundamental chemistry of combustion. The overall objectives are to determine rate constants for elementary reactions and to elucidate the pathways of multichannel reactions. A multitechnique approach that features three independent experiments provides unique capabilities in performing reliable kinetic measurements over an exceptionally wide range in temperature, 300 to 2500 K. Recent kinetic work has focused on experimental studies and theoretical calculations of the methane dissociation system (CH{sub 4} + Ar {yields} CH{sub 3} + H + Ar and H + CH{sub 4} {yields} CH{sub 3} + H{sub 2}). Additionally, a discharge flow-photoionization mass spectrometer (DF-PIMS) experiment is used to determine branching fractions for multichannel reactions and to measure ionization thresholds of free radicals. Thus, these photoionization experiments generate data that are relevant to both reaction pathways studies (reaction dynamics) and fundamental thermochemical research. Two distinct advantages of performing PIMS with high intensity, tunable vacuum ultraviolet light at the National Synchrotron Light Source are high detection sensitivity and exceptional selectivity in monitoring radical species.
Reaction-diffusion basis of retroviral infectivity
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'.
Kinetics of heterogeneous catalytic reactions
Boudart, Michel
2014-01-01
This book is a critical account of the principles of the kinetics of heterogeneous catalytic reactions in the light of recent developments in surface science and catalysis science. Originally published in 1984. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase acc
Theory for Diffusion-Limited Oscillating Chemical Reactions
Bussemaker, H J
1997-01-01
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the theory gives an excellent quantitative prediction of the effect of slow diffusion on the periodic oscillations of the average concentrations in a spatially homogeneous state.
REACTION KINETICS OF CA-BASED SORBENTS WITH HC1
The kinetics of the reaction between CaO and HCl were investigated under conditions that minimize bulk mass transfer and pore diffusion limitations. Reactivity data from 0.2- to 1-s exposure to 5000 ppm HCl in a fixed bed reactor were analyzed by a shrinking core model of diffusi...
Chaudhury, Srabanti; Cherayil, Binny J
2007-09-14
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder--modeled by the anomalous diffusion of a particle in a harmonic well--are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme beta-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.
Walsh, S D C; Saar, M O
2010-12-01
This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.
Preventing Corrosion by Controlling Cathodic Reaction Kinetics
2016-03-25
Preventing corrosion by controlling cathodic reaction kinetics Progress Report for Period: 1 SEP 2015-31 MAR 2016 John Keith Department of...25 March 2016 Preventing corrosion by controlling cathodic reaction kinetics Annual Summary Report: FY16 PI: John Keith, 412-624-7016,jakeith...dominate the metal’s cathodic behavior. Within an alkaline environment, we expect the following reduction reactions to be catalyzed on the oxide
Mechanism and kinetics of hydrated electron diffusion
Tay, Kafui A; Boutin, Anne; 10.1063/1.2964101
2012-01-01
Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that of the solvent. As previously postulated by both experimental and theoretical works, the instantaneous response of the electron to the librational motions of surrounding water molecules constitutes the principal mode of motion. The diffusive mechanism can be understood within the traditional framework of transfer diffusion processes, where the diffusive step is akin to the exchange of an extramolecular electron between neighboring water molecules. This is a second-order process with a computed rate constant of 5.0 ps^{-1} at 298 K. In agreement with experiment the electron diffusion exhibits Arrhenius behavior over the temperature range of 298-400 K. We compute an activation energy of 8.9 kJ/mol. Through analysis of Arrhenius plots and the application of a simple random walk...
Kinetic studies of elementary chemical reactions
Durant, J.L. Jr. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
This program concerning kinetic studies of elementary chemical reactions is presently focussed on understanding reactions of NH{sub x} species. To reach this goal, the author is pursuing experimental studies of reaction rate coefficients and product branching fractions as well as using electronic structure calculations to calculate transition state properties and reaction rate calculations to relate these properties to predicted kinetic behavior. The synergy existing between the experimental and theoretical studies allow one to gain a deeper insight into more complex elementary reactions.
The speed of reaction-diffusion wavefronts in nonsteady media
Mendez, Vicenc [Departament de Medicina, Facultat de Ciencies de la Salut, Universitat Internacional de Catalunya. c/Gomera s/n, 08190-Sant Cugat del Valles (Barcelona) (Spain); Fort, Joaquim [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain); Pujol, Toni [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain)
2003-04-11
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
The speed of reaction-diffusion wavefronts in nonsteady media
Méndez, V; Pujol, T
2003-01-01
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
Kinetic theory of diffusion-limited nucleation
Philippe, T.; Bonvalet, M.; Blavette, D.
2016-05-01
We examine binary nucleation in the size and composition space {R,c} using the formalism of the multivariable theory [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)]. We show that the variable c drops out of consideration for very large curvature of the new phase Gibbs energy with composition. Consequently nuclei around the critical size have the critical composition, which is derived from the condition of criticality for the canonical variables and is found not to depend on surface tension. In this case, nucleation kinetics can be investigated in the size space only. Using macroscopic kinetics, we determine the general expression for the condensation rate when growth is limited by bulk diffusion, which accounts for both diffusion and capillarity and exhibits a different dependence with the critical size, as compared with the interface-limited regime. This new expression of the condensation rate for bulk diffusion-limited nucleation is the counterpart of the classical interface-limited result. We then extend our analysis to multicomponent solutions.
Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps.
Boninsegna, Lorenzo; Gobbo, Gianpaolo; Noé, Frank; Clementi, Cecilia
2015-12-08
Identification of the collective coordinates that describe rare events in complex molecular transitions such as protein folding has been a key challenge in the theoretical molecular sciences. In the Diffusion Map approach, one assumes that the molecular configurations sampled have been generated by a diffusion process, and one uses the eigenfunctions of the corresponding diffusion operator as reaction coordinates. While diffusion coordinates (DCs) appear to provide a good approximation to the true dynamical reaction coordinates, they are not parametrized using dynamical information. Thus, their approximation quality could not, as yet, be validated, nor could the diffusion map eigenvalues be used to compute relaxation rate constants of the system. Here we combine the Diffusion Map approach with the recently proposed Variational Approach for Conformation Dynamics (VAC). Diffusion Map coordinates are used as a basis set, and their optimal linear combination is sought using the VAC, which employs time-correlation information on the molecular dynamics (MD) trajectories. We have applied this approach to ultra-long MD simulations of the Fip35 WW domain and found that the first DCs are indeed a good approximation to the true reaction coordinates of the system, but they could be further improved using the VAC. Using the Diffusion Map basis, excellent approximations to the relaxation rates of the system are obtained. Finally, we evaluate the quality of different metric spaces and find that pairwise minimal root-mean-square deviation performs poorly, while operating in the recently introduced kinetic maps based on the time-lagged independent component analysis gives the best performance.
Chemical kinetics and reaction dynamics
Houston, Paul L
2006-01-01
This text teaches the principles underlying modern chemical kinetics in a clear, direct fashion, using several examples to enhance basic understanding. It features solutions to selected problems, with separate sections and appendices that cover more technical applications.Each chapter is self-contained and features an introduction that identifies its basic goals, their significance, and a general plan for their achievement. This text's important aims are to demonstrate that the basic kinetic principles are essential to the solution of modern chemical problems, and to show how the underlying qu
Turing instability in reaction-diffusion systems with nonlinear diffusion
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
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.
Reaction networks and kinetics of biochemical systems.
Arceo, Carlene Perpetua P; Jose, Editha C; Lao, Angelyn R; Mendoza, Eduardo R
2017-01-01
This paper further develops the connection between Chemical Reaction Network Theory (CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use algebraic properties of kinetic sets to study the set of complex factorizable kinetics CFK(N) on a CRN, which shares many characteristics with its subset of mass action kinetics. In particular, we extend the Theorem of Feinberg-Horn [9] on the coincidence of the kinetic and stoichiometric subsets of a mass action system to CF kinetics, using the concept of span surjectivity. We also introduce the branching type of a network, which determines the availability of kinetics on it and allows us to characterize the networks for which all kinetics are complex factorizable: A "Kinetics Landscape" provides an overview of kinetics sets, their algebraic properties and containment relationships. We then apply our results and those (of other CRNT researchers) reviewed in [1] to fifteen BST models of complex biological systems and discover novel network and kinetic properties that so far have not been widely studied in CRNT. In our view, these findings show an important benefit of connecting CRNT and BST modeling efforts. Copyright © 2016 Elsevier Inc. All rights reserved.
Connectionist and diffusion models of reaction time.
Ratcliff, R; Van Zandt, T; McKoon, G
1999-04-01
Two connectionist frameworks, GRAIN (J. L. McClelland, 1993) and brain-state-in-a-box (J. A. Anderson, 1991), and R. Ratcliff's (1978) diffusion model were evaluated using data from a signal detection task. Dependent variables included response probabilities, reaction times for correct and error responses, and shapes of reaction-time distributions. The diffusion model accounted for all aspects of the data, including error reaction times that had previously been a problem for all response-time models. The connectionist models accounted for many aspects of the data adequately, but each failed to a greater or lesser degree in important ways except for one model that was similar to the diffusion model. The findings advance the development of the diffusion model and show that the long tradition of reaction-time research and theory is a fertile domain for development and testing of connectionist assumptions about how decisions are generated over time.
Langevin Equations for Reaction-Diffusion Processes
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Reaction Kinetics of Nanostructured Silicon Carbide
Wallis, Kendra; Zerda, T. W.
2006-10-01
Nanostructured silicon carbide (SiC) is of interest particularly for use in nanocomposites that demonstrate high hardness as well as for use in semiconductor applications. Reaction kinetics studies of solid-solid reactions are relatively recent and present a method of determining the reaction mechanism and activation energy by measuring reaction rates. We have used induction heating to heat quickly, thus reducing the error in reaction time measurements. Data will be presented for reactions using silicon nanopowder (melting point of silicon. Using the well-known Avrami-Erofeev model, a two-parameter chi- square fit of the data provided a rate constant (k) and parameter (n), related to the reaction mechanism, for each temperature. From these data, an activation energy of 138 kJ/mol was calculated. In addition, the parameter n suggests the reaction mechanism, which will also be discussed. Experiments are continuing at higher temperatures to consider the liquid- solid reaction as well.
Diffusion and reaction in crowded environments
EcheverIa, Carlos [Laboratorio de Fisica Aplicada y Computacional, Departamento de Matematica y Fisica, Universidad Nacional Experimental del Tachira, San Cristobal 5001 (Venezuela); Tucci, Kay [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101 (Venezuela); Kapral, Raymond [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6 (Canada)
2007-02-14
The effects of molecular crowding on small molecule diffusion and chemical reaction rate coefficients are investigated. The systems considered comprise a random distribution of stationary spherical obstacles occupying a volume fraction {phi} of the system and a large number of small molecules whose dynamics are followed. Chemical reactions are studied in such crowded systems where, in addition to the obstacles, a large reactive sphere C is present that catalyses the reaction A+C {yields} B+C. Using a mesoscopic description of the dynamics employing multiparticle collisions among the small molecules, the {phi} dependence of the diffusion and reaction rate coefficients is computed. Both the diffusion and reaction rate coefficients decrease with increase of the obstacle volume fraction as expected but variations of these quantities with {phi} are not predicted by simple models of the dynamics.
The hydrothermal reaction kinetics of aspartic acid
Cox, Jenny S.; Seward, Terry M.
2007-02-01
Experimental data on the hydrothermal reaction kinetics of aspartic acid were acquired using a custom-built spectrophotometric reaction cell which permits in situ observation under hydrothermal conditions. The results of this study indicate that the reaction kinetics of dilute aspartic acid solutions are significantly different depending on the presence or absence of catalytic surfaces such as standard metal alloys. The spectroscopic data presented here represent the first direct observations, in situ and in real time, of an amino acid reacting in a hydrothermal solution. Quantitative kinetic information, including rate constants, concentration versus time profiles, and calculations of the individual component spectra, was obtained from the data using a chemometric approach based on factor analysis/principle component analysis which treats the rate expressions simultaneously as a system of differential algebraic equations (DAE) of index 1. Identification of the products was confirmed where possible by high pressure anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD). The reaction kinetics of aspartic acid under hydrothermal conditions was observed to be highly complex, in contrast to previous studies which indicated almost exclusively deamination. At lower temperatures (120-170 °C), several different reaction pathways were observed, including decarboxylation and polymerization, and the catalytic effects of reactor surfaces on the aspartic acid system were clearly demonstrated. At higher temperatures (above 170 °C), aspartic acid exhibited highly complex behaviour, with evidence indicating that it can simultaneously dimerize and cyclize, deaminate (by up to two pathways), and decarboxylate (by up to two pathways). These higher temperature kinetics were not fully resolvable in a quantitative manner due to the complexity of the system and the constraints of UV spectroscopy. The results of this study provide strong evidence that the reaction
Evaluation of true kinetic parameters for reversible immobilized enzyme reactions
Ishikawa, H.; Tanaka, T.; Kurose, K.; Hikita, H.
1987-06-01
For a reversible one-substrate reaction system that follows the Haldane reaction mechanism, a new and effective method has been proposed to extract true or intrinsic kinetic parameters of immobilized enzymes from diffusion limited rate data. The method utilizes the effectiveness factors correlated in terms of the general modulus defined by Aris and Bischoff, and a new modulus defined in the present study. It requires a trial-and-error calculation, but only a few data points. Furthermore, it provides a saving of materials such as substrates and enzymes, and takes less time for experiments compared to the initial rate methods. The usefulness of the method is demonstrated by determining the kinetic parameters for membrane bound fumarase which catalyzes the reaction of the conversion of fumarate to L-malate, for which the equilibrium constant is circa 4. (Refs. 20).
Kinetic modeling of reactions in Foods
Boekel, van M.A.J.S.
2008-01-01
The level of quality that food maintains as it travels down the production-to-consumption path is largely determined by the chemical, biochemical, physical, and microbiological changes that take place during its processing and storage. Kinetic Modeling of Reactions in Foods demonstrates how to effec
Reaction-diffusion master equation in the microscopic limit
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2012-04-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice reaction-diffusion master equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. Here we give a general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model and lets us quantify this limit in two and three dimensions. In this light we review and discuss recent work in which the RDME has been modified in different ways in order to better agree with the microscale model for very small voxel sizes.
On the Reaction Diffusion Master Equation in the Microscopic Limit
Hellander, Stefan; Petzold, Linda
2011-01-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice Reaction-Diffusion Master Equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. In this paper we give a new, general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model.
Reaction-Diffusion Automata Phenomenology, Localisations, Computation
Adamatzky, Andrew
2013-01-01
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments. This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...
Fluctuation in nonextensive reaction-diffusion systems
Wu Junlin; Chen Huaijun [Department of Physics, Shaanxi Normal University, Xian 710062 (China)
2007-05-15
The density fluctuation in a nonextensive reaction-diffusion system is investigated, where the nonequilibrium stationary-state distribution is described by the generalized Maxwell-Boltzmann distribution in the framework of Tsallis statistics (or nonextensive statistics). By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the system. As an example, we take the{sup 3}He reaction-diffusion model inside stars to analyse the nonextensive effect on the density fluctuation and we find that the nonextensive parameter q different from one plays a very important role in determining the characteristics of the fluctuation waves.
Diffusion and Surface Reaction in Heterogeneous Catalysis
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)
Approximating parameters in nonlinear reaction diffusion equations
Robert R. Ferdinand
2001-07-01
Full Text Available We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computationally generated data.
Reaction-Diffusion in the NEURON Simulator
Robert A. McDougal
2013-11-01
Full Text Available In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics on the dynamics of neuronal response in health and disease, NEURON has developed a Reaction-Diffusion (rxd module in Python which provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy’s sparse linear algebra library.
Reaction-diffusion in the NEURON simulator.
McDougal, Robert A; Hines, Michael L; Lytton, William W
2013-01-01
In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library.
Reaction kinetics of bond rotations in graphene
Skowron, Stephen T.
2016-04-12
The formation and healing processes of the fundamental topological defect in graphitic materials, the Stone-Wales (SW) defect, are brought into a chemical context by considering the rotation of a carbon-carbon bond as chemical reaction. We investigate the rates and mechanisms of these SW transformations in graphene at the atomic scale using transmission electron microscopy. We develop a statistical atomic kinetics formalism, using direct observations obtained under different conditions to determine key kinetic parameters of the reactions. Based on the obtained statistics we quantify thermally and irradiation induced routes, identifying a thermal process of healing with an activation energy consistent with predicted adatom catalysed mechanisms. We discover exceptionally high rates for irradiation induced SW healing, incompatible with the previously assumed mechanism of direct knock-on damage and indicating the presence of an efficient nonadiabatic coupling healing mechanism involving beam induced electronic excitations of the SW defect.
Kinetics of catalytic reactions solutions manual
Vannice, M Albert
2005-01-01
Including countless exercises and worked examples, this advanced reference work and textbook will be extremely useful for the work of many industrial scientists. It teaches readers to design kinetic experiments involving heterogeneous catalysts, to characterize these catalysts, to acquire rate data, to find heat and mass transfer limitations in these data, to select reaction models, to derive rate expressions based on these models, and to assess the consistency of these rate equations.
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Pozzolanic Reaction Kinetics of Coal Ashes
ZHENG Hongwei; WANG Zhijuan; QIAN Jueshi; SONG Yuanming; WANG Zhi
2009-01-01
The pozzolanic reactivity was determined by the hydration kinetics of pozzolanic reaction based on the fact that the hydration products of active SiO_2 and Al_2O_3 with lime were soluble in dilute hydrochloric acid.The results show that the pozzolanic reaction of active SiO_2 and Al2O3 of coal ashes follows apparent first-order kinetics.The reaction rate constant of FBC ashes is greater than that of PC ashes,while the activation energy of the former is lower than that of the latter.It is confirmed that the pozzolanic activity of fluidized bed combustion(FBC)ashes is significantly higher than that of PC ashes,and the reaction barrier of the former is lower than that of the latter,because the microstructures of FBC ashes,such as mineralogical composition,morphology and polymerization degree of [SiO_4]and[AlO_6]are more favorable to the pozzolanic activity development than those of PC ashes.
Enhanced Diffusion of Enzymes that Catalyze Exothermic Reactions
Golestanian, Ramin
2015-09-01
Enzymes have been recently found to exhibit enhanced diffusion due to their catalytic activities. A recent experiment [C. Riedel et al., Nature (London) 517, 227 (2015)] has found evidence that suggests this phenomenon might be controlled by the degree of exothermicity of the catalytic reaction involved. Four mechanisms that can lead to this effect, namely, self-thermophoresis, boost in kinetic energy, stochastic swimming, and collective heating are critically discussed, and it is shown that only the last two can be strong enough to account for the observations. The resulting quantitative description is used to examine the biological significance of the effect.
Reaction diffusion equations with boundary degeneracy
Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Rahbani, Janane
2012-01-01
We study the kinetics and mechanism of intercalation and de-intercalation of small anions during the formation of crystalline α-Co(OH) 2 and its transformation to β-Co(OH) 2 within a reaction-diffusion framework. We therein use fluorescence spectroscopy with Rhodamine 6G (Rh6G) as a probe as well as other spectroscopic and imaging techniques. The method is based on the reaction and diffusion of hydroxide ions into a gel matrix containing the Co(ii) ions, the conjugate anions to be intercalated and Rh6G. The advantage of this simple method is that it allows us to separate throughout space the various stages during the formation of α-Co(OH) 2 and its transformation to β-Co(OH) 2, thus enabling fluorescence measurements of the those stages by simply focusing on different areas of the tube. It also permits us to extract with ease the solids for characterization and image analysis. The macroscopic evolution of the system, which consists of a leading blue front designating the formation of α-Co(OH) 2 followed by a sharp blue/pink interface designating the transformation to the pink β-Co(OH) 2, exhibits different dynamics depending on the anion present in the gel. At a certain stage, the blue/pink interface stops its propagation and only the blue front continues. This represents clear evidence of the dependence of the kinetics of intercalation and de-intercalation on the nature of the anion. The coexisting polymorphs were collected and characterized using XRD, FTIR, Raman and UV-Vis. The fluorescence images of the α-Co(OH) 2 reveal clearly the presence of Rh6G between its layers, whereas images from the β polymorph indicate the opposite. Moreover, the fluorescence of Rh6G is monitored during the formation of α-Co(OH) 2 and its conversion to β-Co(OH) 2. During the formation, the fluorescence intensity and lifetime are significantly increased whereas the opposite happens during the transformation to the β phase. We are able to calculate the activation energies
De Oliveira Santos, F. [Grand Accelerateur National d' Ions Lourds, UMR 6415, 14 - Caen (France)
2007-07-01
Nuclear reactions can occur at low kinetic energy. Low-energy reactions are characterized by a strong dependence on the structure of the compound nucleus. It turns out that it is possible to study the nuclear structure by measuring these reactions. In this course, three types of reactions are treated: Resonant Elastic Scattering (such as N{sup 14}(p,p)N{sup 14}), Inelastic Scattering (such as N{sup 14}(p,p')N{sup 14*}) and Astrophysical reactions (such as N{sup 14}(p,{gamma})O{sup 15}). (author)
Determination of oxygen diffusion kinetics during thin film ruthenium oxidation
Coloma Ribera, R.; van de Kruijs, Robbert Wilhelmus Elisabeth; Yakshin, Andrey; Bijkerk, Frederik
2015-01-01
In situ X-ray reflectivity was used to reveal oxygen diffusion kinetics for thermal oxidation of polycrystalline ruthenium thin films and accurate determination of activation energies for this process. Diffusion rates in nanometer thin RuO2 films were found to show Arrhenius behaviour. However, a
Kinetic treatment of radiation reaction effects
Noble, Adam; Gratus, Jonathan; Burton, David; Ersfeld, Bernhard; Islam, M. Ranaul; Kravets, Yevgen; Raj, Gaurav; Jaroszynski, Dino
2011-05-01
Modern accelerators and light sources subject bunches of charged particles to quasiperiodic motion in extremely high electric fields, under which they may emit a substantial fraction of their energy. To properly describe the motion of these particle bunches, we require a kinetic theory of radiation reaction. We develop such a theory based on the notorious Lorentz-Dirac equation, and explore how it reduces to the usual Vlasov theory in the appropriate limit. As a simple illustration of the theory, we explore the radiative damping of Langmuir waves.
Reaction kinetic analysis of reactor surveillance data
Yoshiie, T.; Kinomura, A.; Nagai, Y.
2017-02-01
In the reactor pressure vessel surveillance data of a European-type pressurized water reactor (low-Cu steel), it was found that the concentration of matrix defects was very high, and a large number of precipitates existed. In this study, defect structure evolution obtained from surveillance data was simulated by reaction kinetic analysis using 15 rate equations. The saturation of precipitation and the growth of loops were simulated, but it was not possible to explain the increase in DBTT on the basis of the defect structures. The sub-grain boundary segregation of solutes was discussed for the origin of the DBTT increase.
Carbon Diffusion and Kinetics During the Lath Martensite Formation
Hsu (xu Zuyao), T.Y.
1995-01-01
Calculations verify that carbon diffusion may occur during the lath martensite formation. Accordingly, the diffusion of interstitial atoms or ions must be taken into account when martensitic transformation is defined as a diffusionless transformation. In derivation of the kinetics equation of the athermal martensitic transfomation, regarding the carbon diffusion, i .e. the enrichment of the austenite during the lath martensite formation, and ΔG(γ→α) being function of the temperature and the c...
Kinetics of Reaction Important in Oxygen Steelmaking
Coley, Kenneth S.; Chen, Elaine; Pomeroy, Michael
Recent work on modeling of BOF steelmaking is reviewed, highlighting the critical aspects of each approach. It is concluded that the most successful models should be based on a deep understanding of the mechanisms and kinetics of the critical reactions. The importance of the decarburization mechanism is discussed with particular reference to its role in droplet swelling or bloating which has a profound influence on the droplet residence time in the slag. Conditions which cause bloating are discussed and the rate determining step is proposed to be primarily nucleation of CO bubbles inside the metal droplet with some influence from growth by reaction at the bubble/metal interface. The discrepancy in the super-saturation ratio required for classical nucleation is discussed and an approach using a surface tension modifying parameter is illustrated. Finally, the role of CO nucleation in controlling the driving force for dephosphorization is discussed.
Single-molecule chemical reaction reveals molecular reaction kinetics and dynamics.
Zhang, Yuwei; Song, Ping; Fu, Qiang; Ruan, Mingbo; Xu, Weilin
2014-06-25
Understanding the microscopic elementary process of chemical reactions, especially in condensed phase, is highly desirable for improvement of efficiencies in industrial chemical processes. Here we show an approach to gaining new insights into elementary reactions in condensed phase by combining quantum chemical calculations with a single-molecule analysis. Elementary chemical reactions in liquid-phase, revealed from quantum chemical calculations, are studied by tracking the fluorescence of single dye molecules undergoing a reversible redox process. Statistical analyses of single-molecule trajectories reveal molecular reaction kinetics and dynamics of elementary reactions. The reactivity dynamic fluctuations of single molecules are evidenced and probably arise from either or both of the low-frequency approach of the molecule to the internal surface of the SiO2 nanosphere or the molecule diffusion-induced memory effect. This new approach could be applied to other chemical reactions in liquid phase to gain more insight into their molecular reaction kinetics and the dynamics of elementary steps.
Fractional Diffusion Limit for Collisional Kinetic Equations
Mellet, Antoine
2010-08-20
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
Kipriyanov, Alexander A; Kipriyanov, Alexey A; Doktorov, Alexander B
2010-11-07
The applicability of the Encounter Theory (ET) (the prototype of the Collision Theory) concepts for widely occurring diffusion assisted irreversible bulk reaction A+B→C (for example, radical reaction) in dilute solutions with arbitrary ratio of initial concentrations of reactants has been treated theoretically with modern many-particle method for the derivation of non-Markovian binary kinetic equations. The method shows that, just as in the reaction A+A→C considered earlier, the agreement with the Encounter Theory is observed when the familiar Integral Encounter Theory is used which is just a step in the derivation of kinetic equations in the framework of the method employed. It allows for two-particle correlations only, and fails to consider the correlation of reactant simultaneously with a partner and with a reactant in the bulk. However, the next step leading to the Modified Encounter Theory under reduction of equations to a regular form both extends the time applicability interval of ET homogeneous rate equation (as for reactions proceeding in excess of one of the reactants), and yields the inhomogeneous equation of the Generalized Encounter Theory (GET) that reveals macroscopic correlations induced by the encounters in a reservoir of free walks in full agreement with physical considerations. This means that the encounters of reactants in solution are correlated at rather large time interval of the reaction course. However, unlike the reaction A+A→C of identical reactants, the reaction A+B→C accumulation of the above macroscopic correlations (even with the initial concentrations of reactants being equal) proceeds much slower. Another distinction is that for the reaction A+A→C the long-term behavior of ET and GET kinetics is the same, while in the reaction A+B→C these kinetics behave differently. It is of interest that just taking account of the above macroscopic correlations in the reaction A+B→C (in GET) results in the universal character of the
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi
2009-12-28
A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.
Kinetics of Nitrogen Diffusion in Granular Manganese
ZHANG Jin-zhu; XU Chu-shao; ZHAO Yue-ping
2008-01-01
The kinetics and the influence of time on granular manganese nitriding were studied by means of a vacuum resistance furnace, X-ray diffraction technique, and LECO TC-436 oxygen/nitrogen determinator. The longer the nitriding time, the more the nitrogen pickup. Except for a trace of oxide MnO that developed, the metal manganese could thoroughly be nitrided to form Mn4N and a little ζ-phase (the stoichiometric components as Mn2N) with the nitriding time lasting. A kinetic model is developed to reveal the nitriding situation and agrees well with the experimental results.
Diffusion-limited reactions in crowded environments.
Dorsaz, N; De Michele, C; Piazza, F; De Los Rios, P; Foffi, G
2010-09-17
Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio R(s), the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing R(s), the encounter rate is substantially depressed and becomes even nonmonotonic for R(s)saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction.
Studies on the kinetics and intraparticle diffusivities of BOD, colour ...
EJIRO
1Department of Industrial Chemistry, Abia State University, P. M. B. 2000, Uturu, Abia State, Nigeria. ..... chemical reaction equation (Ho and Wang 2004; Majid et al., 1999). ... time and the reactor dimensions controlled by the system's kinetics.
Cumulative signal transmission in nonlinear reaction-diffusion networks.
Diego A Oyarzún
Full Text Available Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network's ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.
Chemical kinetic modeling of a methane opposed flow diffusion flame and comparison to experiments
Marinov, N.M., Pitz, W.J.; Westbrook, C.K. [Lawrence Livermore National Lab., CA (United States); Vincitore, A.M.; Senka, S.M. [Univ. of California, Los Angeles, CA (United States); Lutz, A.E. [Sandia National Labs., Livermore, CA (United States)
1998-01-01
The chemical structure of an opposed flow, methane diffusion flame is studied using a chemical kinetic model and the results are compared to experimental measurements. The chemical kinetic paths leading to aromatics and polycyclic aromatics hydrocarbons (PAHs) in the diffusion flame are identified. These paths all involve resonantly stabilized radicals which include propargyl, allyl, cyclopentadienyl, and benzyl radicals. The modeling results show reasonable agreement with the experimental measurements for the large hydrocarbon aliphatic compounds, aromatics, and PAHs. the benzene was predicted to be formed primarily by the reaction sequence of Allyl plus Propargyl equals Fulvene plus H plus H followed by fulvene isomerization to benzene. Naphthalene was modeled using the reaction of benzyl with propargyl, while the combination of cyclopentadienyl radicals were shown to be a minor contributor in the diffusion flame. The agreement between the model and experiment for the four-ring PAHs was poor.
Hamiltonian perspective on compartmental reaction-diffusion networks
Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M. A.
2014-01-01
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction diffusion system is a distri
Chemical computing with reaction-diffusion processes.
Gorecki, J; Gizynski, K; Guzowski, J; Gorecka, J N; Garstecki, P; Gruenert, G; Dittrich, P
2015-07-28
Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed.
Thermally activated reaction–diffusion-controlled chemical bulk reactions of gases and solids
S. Möller
2015-01-01
Full Text Available The chemical kinetics of the reaction of thin films with reactive gases is investigated. The removal of thin films using thermally activated solid–gas to gas reactions is a method to in-situ control deposition inventory in vacuum and plasma vessels. Significant scatter of experimental deposit removal rates at apparently similar conditions was observed in the past, highlighting the need for understanding the underlying processes. A model based on the presence of reactive gas in the films bulk and chemical kinetics is presented. The model describes the diffusion of reactive gas into the film and its chemical interaction with film constituents in the bulk using a stationary reaction–diffusion equation. This yields the reactive gas concentration and reaction rates. Diffusion and reaction rate limitations are depicted in parameter studies. Comparison with literature data on tokamak co-deposit removal results in good agreement of removal rates as a function of pressure, film thickness and temperature.
Voituriez, R.; Moreau, M.; Oshanin, G.
2004-01-01
The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \\textit{diffusion-limited} reactions (DLR), as exemplified here by association/dissociation $A+A \\rightleftharpoons B$ reactions. We consider a general model of long-ranged reactions, such that any pair of $A$ particles, separated by distance $\\mu$, may react with probability $\\omega_+(\\mu)$, and any $B$ may dissociate wit...
Galactic disks as reaction-diffusion systems
Smolin, L
1996-01-01
A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the development of inhomogeneities, leading to the development of spatial and temporal structure. At the linearized level a prediction for the length and time scales of the patterns is found. These instabilities arise for the same reason that pattern formation is seen in non-equilibrium chemical and biological systems, which is that the positive and negative feedback effects which govern the rates of the critical processes act over different distance scales, as in Turing's reaction-diffusion models. This shows that patterns would form in the disk even in the absence of gravitational effects, density waves, rotation, shear and external perturbations. These nonlinear effects may thus explain the spiral structure seen in the star forming regions of isolated flocculent galaxies.
Laser Spot Detection Based on Reaction Diffusion
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, Raquel; Duro, Natividad
2016-01-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations. PMID:26938537
Laser Spot Detection Based on Reaction Diffusion
Alejandro Vázquez-Otero
2016-03-01
Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Reaction and diffusion in turbulent combustion
Pope, S.B. [Mechanical and Aerospace Engineering, Ithaca, NY (United States)
1993-12-01
The motivation for this project is the need to obtain a better quantitative understanding of the technologically-important phenomenon of turbulent combustion. In nearly all applications in which fuel is burned-for example, fossil-fuel power plants, furnaces, gas-turbines and internal-combustion engines-the combustion takes place in a turbulent flow. Designers continually demand more quantitative information about this phenomenon-in the form of turbulent combustion models-so that they can design equipment with increased efficiency and decreased environmental impact. For some time the PI has been developing a class of turbulent combustion models known as PDF methods. These methods have the important virtue that both convection and reaction can be treated without turbulence-modelling assumptions. However, a mixing model is required to account for the effects of molecular diffusion. Currently, the available mixing models are known to have some significant defects. The major motivation of the project is to seek a better understanding of molecular diffusion in turbulent reactive flows, and hence to develop a better mixing model.
Modeling of Reaction Processes Controlled by Diffusion
Revelli, J
2003-01-01
Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider differe...
THE KINETICS OF FILM-DIFFUSION-LIMITED ION-EXCHANGE
KRAAIJEVELD, G; WESSELINGH, JA
1993-01-01
The film-diffusion-limited ion exchange kinetics for the HCl-NaCl and HCl-CaCl2 systems on a Lewatit S100 ion exchanger are investigated. The ion exchange processes are modelled using the Maxwell-Stefan transport equations. The model uses only one fitting parameter. the film thickness, the Maxwell-S
Generalized theory of diffusion based on kinetic theory
Schäfer, T.
2016-10-01
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high-temperature limit [Sommer et al., Nature (London) 472, 201 (2011), 10.1038/nature09989] is consistent with the diffusion constant predicted by kinetic theory.
A generalized Theory of Diffusion based on Kinetic Theory
Schaefer, Thomas
2016-01-01
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high temperature limit [Sommer et al., Nature 472, 201 (2011)] is consistent with the diffusion constant predicted by kinetic theory.
On the perturbation solution of interface-reaction controlled diffusion in solids
Zhi-Wei Cui; Feng Gao; Jian-Min Qu
2012-01-01
Insertion of species A into species B forms a product P through two kinetic processes,namely,(1) the chemical reaction between A and B that occurs at the B-P interface,and (2) the diffusion of species A in product P.These two processes are symbiotic in that the chemical reaction provides the driving force for the diffusion,while the diffusion sustains the chemical reaction by providing sufficient reactant to the reactive interface.In this paper,a mathematical framework is developed for the coupled reactiondiffusion processes.The resulting system of boundary and initial value problem is solved analytically for the case of interface-reaction controlled diffusion,i.e.,the rate of diffusion is much faster than the rate of chemical reaction at the interface so that the final kinetics are limited by the interface chemical reaction.Asymptotic expressions are given for the velocity of the reactive interface and the concentration of diffusing species under two different boundary conditions.
Mathematics analysis of polymerase chain reaction kinetic curves.
Sochivko, D G; Fedorov, A A; Varlamov, D A; Kurochkin, V E; Petrov, R V
2016-01-01
The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.
Doktorov, Alexander B.; Kipriyanov, Alexander A.; Kipriyanov, Alexey A.
2010-05-01
Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A +A→product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.
Doktorov, Alexander B; Kipriyanov, Alexander A; Kipriyanov, Alexey A
2010-05-28
Using an modern many-particle method for the derivation of non-Markovian binary kinetic equations, we have treated theoretically the applicability of the encounter theory (ET) (the prototype of the collision theory) concepts to the widely known diffusion assisted irreversible bulk reaction A+A-->product (for example, radical reaction) in dilute solutions. The method shows that the agreement with the ET is observed when the familiar integral ET is employed which in this method is just a step in the derivation of kinetic equations. It allows for two-particle correlations only, but fails to take account of correlation of reactant simultaneously with the partner of the encounter and the reactant in the bulk. However, the next step leading to the modified ET under transformation of equations to the regular form both extends the time range of the applicability of ET rate equation (as it was for reactions proceeding with one of the reactants in excess), and gives the equation of the generalized ET. In full agreement with physical considerations, this theory reveals macroscopic correlations induced by the encounters in the reservoir of free walks. This means that the encounters of reactants in solution are correlated on a rather large time interval of the reaction. Though any nonstationary (non-Markovian) effects manifest themselves rather weakly in the kinetics of the bimolecular reaction in question, just the existence of the revealed macroscopic correlations in the binary theory is of primary importance. In particular, it means that the well-known phenomena which are generally considered to be associated solely with correlation of particles on the encounter (for example, chemically induced dynamic nuclear polarization) may be induced by correlation in the reservoir of free random walks of radicals in solution.
Understanding Chemical Reaction Kinetics and Equilibrium with Interlocking Building Blocks
Cloonan, Carrie A.; Nichol, Carolyn A.; Hutchinson, John S.
2011-01-01
Chemical reaction kinetics and equilibrium are essential core concepts of chemistry but are challenging topics for many students, both at the high school and undergraduate university level. Visualization at the molecular level is valuable to aid understanding of reaction kinetics and equilibrium. This activity provides a discovery-based method to…
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida
2009-08-29
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
Kinetics of ozone-phenol reaction in aqueous solutions
Joshi, M.G.; Shambaugh, R.L.
1982-01-01
The kinetics of the reaction of ozone and phenol in aqueous medium was studied. The reaction was first order with respect to both ozone and phenol. The rate constant was found to increase with increase in the pH of the reaction mixture. Four different catalysts were examined for their effect on the rate of reaction. 30 refs.
Lopes, Fernanda Cristina Rezende; Tannous, Katia; Rueda-Ordóñez, Yesid Javier
2016-11-01
This work aims the study of decomposition kinetics of guarana seed residue using thermogravimetric analyzer under synthetic air atmosphere applying heating rates of 5, 10, and 15°C/min, from room temperature to 900°C. Three thermal decomposition stages were identified: dehydration (25.1-160°C), oxidative pyrolysis (240-370°C), and combustion (350-650°C). The activation energies, reaction model, and pre-exponential factor were determined through four isoconversional methods, master plots, and linearization of the conversion rate equation, respectively. A scheme of two-consecutive reactions was applied validating the kinetic parameters of first-order reaction and two-dimensional diffusion models for the oxidative pyrolysis stage (149.57kJ/mol, 6.97×10(10)1/s) and for combustion stage (77.98kJ/mol, 98.611/s), respectively. The comparison between theoretical and experimental conversion and conversion rate showed good agreement with average deviation lower than 2%, indicating that these results could be used for modeling of guarana seed residue. Copyright © 2016 Elsevier Ltd. All rights reserved.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
Diffusion kinetics of the ion exchange of benzocaine on sulfocationites
Al'tshuler, O. G.; Shkurenko, G. Yu.; Gorlov, A. A.; Al'tshuler, G. N.
2016-06-01
The theory of the ion exchange kinetics on strong acid cationites with the participation of weak electrolytes is discussed. The kinetics of desorption of benzocaine in the protonated and molecular forms from strong acid cationites, sulfonated polycalixarene, and KU-23 30/100 sulfocationite, is studied experimentally. It is shown that the flow of protonated benzocaine from cationite upon desorption proceeding by the ion-exchange mechanism is more intense than upon desorption of nonionized benzocaine molecules. It is established that the diffusion coefficient of benzocaine cations is (1.21 ± 0.23) × 10-12 m2/s in KU-23 30/100 sulfocation and (0.65 ± 0.06) × 10-13 m2/s in sulfonated polycalixarene, while the diffusion coefficient of benzocaine molecules is (0.65 ± 0.15) × 10-14 m2/s in sulfonated polycalixarene.
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Speed ot travelling waves in reaction-diffusion equations
Benguria, R D; Méndez, V
2002-01-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
Speed ot travelling waves in reaction-diffusion equations
Benguria, R.D.; Depassier, M.C. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Avda. Vicuna Mackenna 4860, Santiago (Chile); Mendez, V. [Facultat de Ciencies de la Salut, Universidad Internacional de Catalunya, Gomera s/n 08190 Sant Cugat del Valles, Barcelona (Spain)
2002-07-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
QUENCHING PROBLEMS OF DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION
无
2006-01-01
This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.
Kinetic Study of the Heck Reaction: An Interdisciplinary Experiment
Gozzi, Christel; Bouzidi, Naoual
2008-01-01
The aim of this experiment is to study and calculate the kinetic constant of a Heck reaction: the arylation of but-3-en-2-ol by iodobenzene catalyzed by palladium acetate in presence of triethylamine in DMF. The reaction leads to a mixture of two ketones. Students use GC analysis to quantify reagents and products of reaction. They control the…
Diffusion of Chloride Ions in Soils：Ⅱ.Kinetic and Ther—modynamic Characteristics
XUMINGGANG; ZHANGYIPING; 等
1997-01-01
The amounts of chloride ions diffused in four soils of different textures at the same water content under different temperature and at varied time were measured by the diffusion cell method using 36Cl-labelled CaCl2 solution,Five kinetic models were used to fit the dynamic process of the diffusion of chloride ions in the soils ,It was found that Elovich equation or power function equation was the best model to describe the process .The pseudothermodynamic parameters,i.e.the net reaction energy,the activation entropy, activation enthalpy and activation free energy of the diffusion,were dervied from the absolute reaction-rate theory.The results showed that these parameters decreased in the order of loessal soil>black lu soil> lou soil> yellow cinnamon soil,which indicated that the force an the heat-energy barrier to be overcome for diffusion decreased ,the diffusion rate increased and the disorder of the soil-solution-ion system due to diffusion decreased successively with the texture becoming heavier in the four soils.
Mix and Inject: Reaction Initiation by Diffusion for Time-Resolved Macromolecular Crystallography
Marius Schmidt
2013-01-01
Full Text Available Time-resolved macromolecular crystallography unifies structure determination with chemical kinetics, since the structures of transient states and chemical and kinetic mechanisms can be determined simultaneously from the same data. To start a reaction in an enzyme, typically, an initially inactive substrate present in the crystal is activated. This has particular disadvantages that are circumvented when active substrate is directly provided by diffusion. However, then it is prohibitive to use macroscopic crystals because diffusion times become too long. With small micro- and nanocrystals diffusion times are adequately short for most enzymes and the reaction can be swiftly initiated. We demonstrate here that a time-resolved crystallographic experiment becomes feasible by mixing substrate with enzyme nanocrystals which are subsequently injected into the X-ray beam of a pulsed X-ray source.
Diffusion-reaction compromise the polymorphs of precipitated calcium carbonate
Han Wang; Wenlai Huang; Yongsheng Han
2013-01-01
Diffusion is seldom considered by chemists and materialists in the preparation of materials while it plays an important role in the field of chemical engineering.If we look at crystallization at the atomic level,crystal growth in a solution starts from the diffusion of ions to the growing surface followed by the incorporation of ions into its lattice.Diffusion can be a rate determining step for the growth of crystals.In this paper,we take the crystallization of calcium carbonate as an example to illustrate the microscopic processes of diffusion and reaction and their compromising influence on the morphology of the crystals produced.The diffusion effect is studied in a specially designed three-cell reactor.Experiments show that a decrease of diffusion leads to retardation of supersaturation and the formation of a continuous concentration gradient in the reaction cell,thus promoting the formation of cubic calcite particles.The reaction rate is regulated by temperature.Increase of reaction rate favors the formation of needle-like aragonite particles.When diffusion and reaction play joint roles in the reaction system,their compromise dominates the formation of products,leading to a mixture of cubic and needle-like particles with a controllable ratio.Since diffusion and reaction are universal factors in the preparation of materials,the finding of this paper could be helpful in the controlled synthesis of other materials.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio J; Qian, Hong; Lin, Guang
2014-01-01
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. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems here are no closed 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. Our results show that current linear FCS theory could be adequate ...
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine ...
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine and Acidic Bromate : A Possible Cytoprotective Role against Hypobromous Acid. ... toxicity of bromine and hypobromous acid in the slightly basic physiological environments.
A relativistic correlationless kinetic equation with radiation reaction fully incorporated
Lai, H. M.
1984-06-01
The Landau-Lifshitz expression for the Lorentz-Dirac equation is used to derive a relativistic correlationless kinetic equation for a system of electrons with radiation reaction fully incorporated. Various situations and possible applications are discussed.
The thermodynamic natural path in chemical reaction kinetics
Moishe garfinkle
2000-01-01
Full Text Available The Natural Path approach to chemical reaction kinetics was developed to bridge the considerable gap between the Mass Action mechanistic approach and the non-mechanistic irreversible thermodynamic approach. The Natural Path approach can correlate empirical kinetic data with a high degree precision, as least equal to that achievable by the Mass-Action rate equations, but without recourse mechanistic considerations. The reaction velocities arising from the particular rate equation chosen by kineticists to best represent the kinetic behavior of a chemical reaction are the natural outcome of the Natural Path approach. Moreover, by virtue of its thermodynamic roots, equilibrium thermodynamic functions can be extracted from reaction kinetic data with considerable accuracy. These results support the intrinsic validity of the Natural Path approach.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Kinetics of Acid Reactions: Making Sense of Associated Concepts
Tan, Kim Chwee Daniel; Treagust, David F.; Chandrasegaran, A. L.; Mocerino, Mauro
2010-01-01
In chemical kinetics, in addition to the concepts related to kinetics, stoichiometry, chemical equilibrium and the characteristics of the reactants are often involved when comparing the rates of different reactions, making such comparisons very challenging for students at all levels, as well as for pre-service science teachers. Consequently, four…
Kinetics of the Exothermic Decomposition Reaction of s-Tripicryaminotrinitrobenzene
ZHAO Feng-qi; HU Rong-zu; GAO Hong-xu; LUO Yang; GAO Sheng-li; SONG Ji-rong; SHI Qi-zhen
2007-01-01
The kinetic parameters of the exothermic decomposition reaction of s-Tripicryaminotrinitrobenzene under linear temperature rise condition are studied by means of DSC. The results show that the empirical kinetic model function in difs-1, respectively. The critical temperature of thermal explosion of the compound is 267.36 ℃.
Exact solutions for a diffusion-reaction process in one dimension
Spouge, John L.
1988-03-01
This paper presents a new method for the solution of diffusion-reaction problems in one dimension. The method is used to derive some new exact results for the polymerization (cl-cl aggregation) and annihilation processes on openR and openZ. Through well-known dualities, these results have implications for the T=0 limit of the kinetic Ising model and for two interacting particle processes, the invasion and voter models. Prospectively, the method may be useful in providing one-dimensional verification for speculations in the theory of diffusion reaction.
XIONG diangTao; LI JingLong; ZHANG FuSheng; LIN Xin; HUANG WeiDong
2008-01-01
An irreversible thermodynamics model was constructed to study the combination reaction of two heterogeneous pure metals in diffusion bonding based on the theorem of minimum entropy production and the Curie principle. The correlation between the irreversible reaction and diffusion was discussed, which provided the kinetic inevitability of an incubation period of a primary phase. The analytical de-scriptions of the incubation period and the kinetically critical grain size of the pri-mary phase were deduced. Comparison of the experimental results of AI/Mo inter-facial reaction with the calculations indicated that the performed theoretical analy-sis was reliable.
Belousov-Zhabotinsky oscillatory reaction. Kinetics of malonic acid decomposition
LJILJANA KOLAR-ANIC
2000-10-01
Full Text Available The kinetics of the Belousov-Zhabotinsky (BZ oscillatory reaction was analyzed. With this aim, the time evolution of a reaction mixture composed of malonic acid, bromate, sulfuric acid and cerium(III was studied at 298 K. Pseudo-first order kinetics with respect to malonic acid as the species undergoing decomposition with a corresponding rate constant, k = 7.5×10-3 min-1, was found.
Physarum machines: encapsulating reaction-diffusion to compute spanning tree
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.
eduction for Michaelis-Menten-Henri kinetics in the presence of diffusion
Leonid V. Kalachev
2007-05-01
Full Text Available The Michaelis-Menten-Henri (MMH mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly with an enzyme, forming a complex which is transformed (irreversibly into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.
Kinetics of Model Reactions for Interfacial Polymerization
Henry Hall
2012-02-01
Full Text Available To model the rates of interfacial polycondensations, the rates of reaction of benzoyl chloride and methyl chloroformate with various aliphatic monoamines in acetonitrile were determined at 25 °C. Buffering with picric acid slowed these extremely fast reactions so the rate constants could be determined from the rate of disappearance of picrate ion. The rates of the amine reactions correlated linearly with their Swain-Scott nucleophilicities.
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Diffusion Reaction of Carbon Monoxide in the Human Lung
Kang, M.-Y.; Guénard, H.; Sapoval, B.
2017-08-01
The capture of CO, a standard lung function test, results from diffusion-reaction processes of CO with hemoglobin inside red blood cells (RBCs). In its current understanding, suggested by Roughton and Forster in 1957, the capture is represented by two independent resistances in series, one for diffusion from the gas to the RBC periphery, the second for internal diffusion reaction. Numerical studies in 3D model structures described here contradict the independence hypothesis. This results from two different theoretical reasons: (i) The RBC peripheries are not equi-concentrations; (ii) diffusion times in series are not additive.
Magnien, V
2005-12-15
The aim of this thesis is to understand better iron redox reactions and mechanisms in silicate glasses and melts. Particular interest has been paid to the influence of temperature and chemical composition. For this purpose, the influence of alkali element content, iron content and network formers on the kinetics of redox reactions has been determined through XANES and Raman spectroscopy experiments performed either near the glass transition or above the liquidus temperature. As a complement, electrical conductivity and RBS spectroscopy experiments have been made to characterize the diffusivity of the species that transport electrical charges and the reaction morphology, respectively. Temperature and composition variations can induce changes in the dominating redox mechanism. At a given temperature, the parameters that exert the strongest influence on redox mechanisms are the presence or lack of divalent cations and the existing decoupling between the mobility of network former and modifier elements. Near Tg, the diffusion of divalent cations, when present in the melt, controls the kinetics of iron redox reactions along with a flux of electron holes. Composition, through the degree of polymerization and the silicate network structure, influences the kinetics and the nature of the involved cations, but not the mechanisms of the reaction. Without alkaline earth elements, the kinetics of redox reactions are controlled by the diffusion of oxygen species. With increasing temperatures, the diffusivities of all ionic species tend to become similar. The decoupling between ionic fluxes then is reduced so that several mechanisms become kinetically equivalent and can thus coexist. (author)
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
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 closed 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.
Wang, Jing [Iowa State Univ., Ames, IA (United States)
2013-01-11
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. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. 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 (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates 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 gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Photocatalytic Water-Splitting Reaction from Catalytic and Kinetic Perspectives
Hisatomi, Takashi
2014-10-16
Abstract: Some particulate semiconductors loaded with nanoparticulate catalysts exhibit photocatalytic activity for the water-splitting reaction. The photocatalysis is distinct from the thermal catalysis because photocatalysis involves photophysical processes in particulate semiconductors. This review article presents a brief introduction to photocatalysis, followed by kinetic aspects of the photocatalytic water-splitting reaction.Graphical Abstract: [Figure not available: see fulltext.
Sample Duplication Method for Monte Carlo Simulation of Large Reaction-Diffusion System
张红东; 陆建明; 杨玉良
1994-01-01
The sample duplication method for the Monte Carlo simulation of large reaction-diffusion system is proposed in this paper. It is proved that the sample duplication method will effectively raise the efficiency and statistical precision of the simulation without changing the kinetic behaviour of the reaction-diffusion system and the critical condition for the bifurcation of the steady-states. The method has been applied to the simulation of spatial and time dissipative structure of Brusselator under the Dirichlet boundary condition. The results presented in this paper definitely show that the sample duplication method provides a very efficient way to sol-’e the master equation of large reaction-diffusion system. For the case of two-dimensional system, it is found that the computation time is reduced at least by a factor of two orders of magnitude compared to the algorithm reported in literature.
Kinetic Processes Crystal Growth, Diffusion, and Phase Transformations in Materials
Jackson, Kenneth A
2004-01-01
The formation of solids is governed by kinetic processes, which are closely related to the macroscopic behaviour of the resulting materials. With the main focus on ease of understanding, the author begins with the basic processes at the atomic level to illustrate their connections to material properties. Diffusion processes during crystal growth and phase transformations are examined in detail. Since the underlying mathematics are very complex, approximation methods typically used in practice are the prime choice of approach. Apart from metals and alloys, the book places special emphasis on th
Synchronous parallel kinetic Monte Carlo Diffusion in Heterogeneous Systems
Martinez Saez, Enrique [Los Alamos National Laboratory; Hetherly, Jeffery [Los Alamos National Laboratory; Caro, Jose A [Los Alamos National Laboratory
2010-12-06
A new hybrid Molecular Dynamics-kinetic Monte Carlo algorithm has been developed in order to study the basic mechanisms taking place in diffusion in concentrated alloys under the action of chemical and stress fields. Parallel implementation of the k-MC part based on a recently developed synchronous algorithm [1. Compo Phys. 227 (2008) 3804-3823] resorting on the introduction of a set of null events aiming at synchronizing the time for the different subdomains, added to the parallel efficiency of MD, provides the computer power required to evaluate jump rates 'on the flight', incorporating in this way the actual driving force emerging from chemical potential gradients, and the actual environment-dependent jump rates. The time gain has been analyzed and the parallel performance reported. The algorithm is tested on simple diffusion problems to verify its accuracy.
Effect of montmorillonite on kinetics of polyurethane preparation reaction
You Cao; Yu Jiang; Shu Lu Zhao; Xiao Jun Cai; Mei Long Hu; Bing Liao
2008-01-01
The prepolymerization and curing reaction kinetics of polyurethane/montmorillonite have been studied with end group analysisand FTIR respectively. It was found that the prepolymerization and curing reaction followed the 2nd-order kinetics. But theactivation energy of prepolymerization increased from 42.7 k J/mol to 56.5 k J/mol after the montmorillonite was added in thereaction system, and activation energy of curing reaction decreased from 64.4 kJ/mol to 17.5 k J/mol.
LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS
无
2006-01-01
This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Turing bifurcation in a reaction-diffusion system with density-dependent dispersal
Kumar, Niraj; Horsthemke, Werner
2010-05-01
Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction-diffusion system, where dispersal is described by simple Fickian diffusion. While activator-inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer-Meinhardt model.
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, B; Chatelain, P.; Koumoutsakos, P.
2008-01-01
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by ...
Reaction wheels for kinetic energy storage
Studer, P. A.
1984-01-01
In contrast to all existing reaction wheel implementations, an order of magnitude increase in speed can be obtained efficiently if power to the actuators can be recovered. This allows a combined attitude control-energy storage system to be developed with structure mounted reaction wheels. The feasibility of combining reaction wheels with energy storage wwheels is demonstrated. The power required for control torques is a function of wheel speed but this energy is not dissipated; it is stored in the wheel. The I(2)R loss resulting from a given torque is shown to be constant, independent of the design speed of the motor. What remains, in order to efficiently use high speed wheels (essential for energy storage) for control purposes, is to reduce rotational losses to acceptable levels. Progress was made in permanent magnet motor design for high speed operation. Variable field motors offer more control flexibility and efficiency over a broader speed range.
Target Patterns in Reaction-Diffusion Systems,
1981-01-01
new variable xd, the diffusion matrix in (1.1) is just DM and the velocities Vph and v,, in (4.20) and (4.21) are multiplied by C-I/2, Finally except...the (ksr)-’ / factors in (4.4), (4.19), (5.1), and (5.2) are absent in one dimension. However, the analysis for three dimensions hinges on whether (4.2
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2014-08-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables
A unifying kinetic framework for modeling oxidoreductase-catalyzed reactions
Chang, Ivan; Baldi, Pierre
2013-01-01
Motivation: Oxidoreductases are a fundamental class of enzymes responsible for the catalysis of oxidation–reduction reactions, crucial in most bioenergetic metabolic pathways. From their common root in the ancient prebiotic environment, oxidoreductases have evolved into diverse and elaborate protein structures with specific kinetic properties and mechanisms adapted to their individual functional roles and environmental conditions. While accurate kinetic modeling of oxidoreductases is thus imp...
Kinetic model for hydroisomerization reaction of C8-aromatics
Ouguan XU; Hongye SU; Xiaoming JIN; Jian CHU
2008-01-01
Based on the reported reaction networks, a novel six-component hydroisomerization reaction net-work with a new lumped species including C8-naphthenes and Cs-paraffins is proposed and a kinetic model for a commercial unit is also developed. An empirical catalyst deactivation function is incorporated into the model accounting for the loss in activity because of coke forma-tion on the catalyst surface during the long-term opera-tion. The Runge-Kutta method is used to solve the ordinary differential equations of the model. The reaction kinetic parameters are benchmarked with several sets of balanced plant data and estimated by the differential vari-able metric optimization method (BFGS). The kinetic model is validated by an industrial unit with sets of plant data under different operating conditions and simulation results show a good agreement between the model predic-tions and the plant observations.
The influence of gas-kinetic evolution on plasma reactions
Diver, D A; MacLachlan, C S; Potts, H E
2008-01-01
Plasmas in which there is a threshold for a dominant reaction to take place (such as recombination or attachment) will have particle distributions that evolve as the reaction progresses. The form of the Boltzmann collision term in such a context will cause the distribution to drift from its initial form, and so cause for example temperature fluctuations in the plasma if the distribution is originally Maxwellian. This behaviour will impact on the relevant reaction rates in a feedback loop that is missing from simple chemical kinetic descriptions since the plasma cannot be considered to be isothermal, as is the case in the latter approach. In this article we present a simple kinetic model that captures these essential features, showing how cumulative differences in the instantaneous species levels can arise over the purely chemical kinetic description, with implications for process yields and efficiencies.
Simple computation of reaction-diffusion processes on point clouds.
Macdonald, Colin B; Merriman, Barry; Ruuth, Steven J
2013-06-04
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
The bainite reaction kinetics in austempered ductile iron
Taran, Yu.N.; Uzlov, K.I.; Kutsov, A.Yu. [State Metall. Acad., Dnepropetrovsk (Ukraine). Phys. Metall. Dept.
1997-11-01
Bainitic reaction kinetics in ductile iron contained according to Ukrainian standard (weight%) 3.60-3.80 carbon, 2.60-2.80 Si, {proportional_to}0.12 Mn, {proportional_to}0.60 Cu and additionally alloyed by Mo (0.15-0.20) has been studied. It was found that the overall transformation kinetics becomes slower as transformation temperature increase. This is because more intensive redistribution of carbon into austenite at higher temperatures. Two austenites with different carbon content have been fixed and kinetics of their lattices parameters has been studied. (orig.). 6 refs.
Exact solutions for logistic reaction-diffusion equations in biology
Broadbridge, P.; Bradshaw-Hajek, B. H.
2016-08-01
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
Energy diffusion controlled reaction rate in dissipative Hamiltonian systems
Deng Mao-Lin; Zhu Wei-Qiu
2007-01-01
In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.
Diffusion and reaction in microbead agglomerates.
Nunes Kirchner, Carolina; Träuble, Markus; Wittstock, Gunther
2010-04-01
Scanning electrochemical microscopy has been used to analyze the flux of p-aminonophenol (PAP) produced by agglomerates of polymeric microbeads modified with galactosidase as a model system for the bead-based heterogeneous immunoassays. With the use of mixtures of enzyme-modified and bare beads in defined ratio, agglomerates with different saturation levels of the enzyme modification were produced. The PAP flux depends on the intrinsic kinetics of the galactosidase, the local availability of the substrate p-aminophenyl-beta-D-galactopyranoside (PAPG), and the external mass transport conditions in the surrounding of the agglomerate and the internal mass transport within the bead agglomerate. The internal mass transport is influenced by the diffusional shielding of the modified beads by unmodified beads. SECM in combination with optical microscopy was used to determine experimentally the external flux. These data are in quantitative agreement with boundary element simulation considering the SECM microelectrode as an interacting probe and treating the Michaelis-Menten kinetics of the enzyme as nonlinear boundary conditions with two independent concentration variables [PAP] and [PAPG]. The PAPG concentration at the surface of the bead agglomerate was taken as a boundary condition for the analysis of the internal mass transport condition as a function of the enzyme saturation in the bead agglomerate. The results of this analysis are represented as PAP flux per contributing modified bead and the flux from freely suspended galactosidase-modified beads. These numbers are compared to the same number from the SECM experiments. It is shown that depending on the enzyme saturation level a different situation can arise where either beads located at the outer surface of the agglomerate dominate the contribution to the measured external flux or where the contribution of buried beads cannot be neglected for explaining the measured external flux.
Restrictive liquid-phase diffusion and reaction in bidispersed catalysts
Lee, S.Y.; Seader, J.D. (Utah Univ., Salt Lake City, UT (United States). Dept. of Chemical Engineering); Tsai, C.H.; Massoth, F.E. (Utah Univ., Salt Lake City, UT (United States). Dept. of Fuels Engineering)
1991-08-01
In this paper, the effect of bidispersed pore-size distribution on liquid-phase diffusion and reaction in NiMo/Al{sub 2}O{sub 3} catalysts is investigated by applying two bidispersed-pore-structure models, the random-pore model and a globular-structure model, to extensive experimental data, which were obtained from sorptive diffusion measurements at ambient conditions and catalytic reaction rate measurements on nitrogen-containing compounds. Transport of the molecules in the catalysts was found to be controlled by micropore diffusion, in accordance with the random-pore model, rather than macropore diffusion as predicted by the globular-structure model. A qualitative criterion for micropore-diffusion control is proposed: relatively small macroporosity and high catalyst pellet density. Since most hydrotreating catalysts have high density, diffusion in these types of catalysts may be controlled by micropore diffusion. Accordingly, it is believed in this case that increasing the size of micropores may be more effective to reduce intraparticle diffusion resistance than incorporating macropores alone.
Reaction-diffusion models of decontamination
Hjorth, Poul G.
A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...... in the aqueous solution and then is oxidized by the decontaminant. The polymer is insoluble in water, and so builds up near the interface, where its presence can impede the transport of contaminant. In these circumstances, Dstl wish to have mathematical models that give an understanding of the process, and can...
Diagnostic Appraisal of Grade 12 Students' Understanding of Reaction Kinetics
Yan, Yaw Kai; Subramaniam, R.
2016-01-01
The study explored grade 12 students' understanding of reaction kinetics, a topic which has not been extensively explored in the chemistry education literature at this level. A 3-tier diagnostic instrument with 11 questions was developed--this format is of very recent origin and has been the subject of only a handful of studies. The findings…
Beltrán-Prieto Juan Carlos
2016-01-01
Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.
Reaction kinetics of fluorite in flow systems and surface chemistry
张荣华; 胡书敏
1996-01-01
The kinetic experiments of fluorite in water-HCl solution in an open-flow system at the temperatures ≤100℃ reveal that the variation of flow rate (U) can change the reaction rate orders from 0 to 2 or higher. In the far from equilibrium systems, the dissolution rates of fluorite in aqueous solutions have a zero order.The reaction rates are controlled by pH values of input solutions. In fact, the reaction rates are related to the concentrations of the active sites occupied by H+ on fluorite surface [SOH]. X-ray photospectroscopy observations on fluorite surface before and after reaction indicate that surface chemical processes control the reaction rates: Cl- cations attach on and enter into surface of fluorite besides H+ when fluorites react with HCl solutions, which affect the reaction rates.
Developing the reaction kinetics for a biodiesel reactor.
Slinn, Matthew; Kendall, Kevin
2009-04-01
The aim of this paper was to investigate the kinetics of the biodiesel reaction in order to find out how best to reach 96.5% methyl ester. The purity of the biodiesel product was examined using gas chromatography to the EN14214 FAME standard and real-time optical microscopy was used to observe the reaction. The problem was the reaction does not reach completion and the mechanism is not understood. It was observed that droplet size had a major influence on reaction end point and that the reaction was mass-transfer limited. This observation was confirmed by developing a mass-transfer based reaction model using the data from the batch reactor which agreed with results from other researchers. The model predicted better conversion with more mixing intensity. The results show that significant improvements could be made to the conventional FAME process.
Reaction-diffusion problems in the physics of hot plasmas
Wilhelmsson, H
2000-01-01
The physics of hot plasmas is of great importance for describing many phenomena in the universe and is fundamental for the prospect of future fusion energy production on Earth. Nontrivial results of nonlinear electromagnetic effects in plasmas include the self-organization and self-formation in the plasma of structures compact in time and space. These are the consequences of competing processes of nonlinear interactions and can be best described using reaction-diffusion equations. Reaction-Diffusion Problems in the Physics of Hot Plasmas is focused on paradigmatic problems of a reaction-diffusion type met in many branches of science, concerning in particular the nonlinear interaction of electromagnetic fields with plasmas.
Kinetics and equilibrium of solute diffusion into human hair.
Wang, Liming; Chen, Longjian; Han, Lujia; Lian, Guoping
2012-12-01
The uptake kinetics of five molecules by hair has been measured and the effects of pH and physical chemical properties of molecules were investigated. A theoretical model is proposed to analyze the experimental data. The results indicate that the binding affinity of solute to hair, as characterized by hair-water partition coefficient, scales to the hydrophobicity of the solute and decreases dramatically as the pH increases to the dissociation constant. The effective diffusion coefficient of solute depended not only on the molecular size as most previous studies suggested, but also on the binding affinity as well as solute dissociation. It appears that the uptake of molecules by hair is due to both hydrophobic interaction and ionic charge interaction. Based on theoretical considerations of the cellular structure, composition and physical chemical properties of hair, quantitative-structure-property-relationships (QSPR) have been proposed to predict the hair-water partition coefficient (PC) and the effective diffusion coefficient (D (e)) of solute. The proposed QSPR models fit well with the experimental data. This paper could be taken as a reference for investigating the adsorption properties for polymeric materials, fibres, and biomaterials.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R K; Haubold, H J
2011-01-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. [23,24], for the fundamental solution of the space-time fractional equation, including Haubold et al. [13] and Saxena et al. [38] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion...
Reaction-diffusion-branching models of stock price fluctuations
Tang, Lei-Han; Tian, Guang-Shan
Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ( H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
Chaotic advection, diffusion, and reactions in open flows
Tel, Tamas [Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, H-1518 Budapest, (Hungary); Karolyi, Gyoergy [Department of Civil Engineering Mechanics, Technical University of Budapest, Mueegyetem rpk. 3, H-1521 Budapest, (Hungary); Pentek, Aron [Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 (United States); Scheuring, Istvan [Department of Plant Taxonomy and Ecology, Research Group of Ecology and Theoretical Biology, Eoetvoes University, Ludovika ter 2, H-1083 Budapest, (Hungary); Toroczkai, Zoltan [Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States); Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435 (United States); Grebogi, Celso [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Kadtke, James [Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 (United States)
2000-03-01
We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.
Liquid Film Diffusion on Reaction Rate in Submerged Biofilters
Christiansen, Pia; Hollesen, Line; Harremoës, Poul
1995-01-01
Experiments were carried out in order to investigate the influence of liquid film diffusion on reaction rate in a submerged biofilter with denitrification and in order to compare with a theoretical study of the mass transfer coefficient. The experiments were carried out with varied flow, identified...... by the empty bed velocity of inflow and recirculation, respectively 1.3, 2.8, 5.6 and 10.9 m/h. The filter material consisted of 3 mm biostyren spheres. The results indicate that the influence of liquid film diffusion on reaction rate can be ignored....
Layer-adapted meshes for reaction-convection-diffusion problems
Linß, Torsten
2010-01-01
This book on numerical methods for singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. A classification and a survey of layer-adapted meshes for reaction-convection-diffusion problems are included. This structured and comprehensive account of current ideas in the numerical analysis for various methods on layer-adapted meshes is addressed to researchers in finite element theory and perturbation problems. Finite differences, finite elements and finite volumes are all covered.
Oscillatory enzyme reactions and Michaelis-Menten kinetics.
Goldbeter, Albert
2013-09-02
Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Reaction Mechanism Generator: Automatic construction of chemical kinetic mechanisms
Gao, Connie W.; Allen, Joshua W.; Green, William H.; West, Richard H.
2016-06-01
Reaction Mechanism Generator (RMG) constructs kinetic models composed of elementary chemical reaction steps using a general understanding of how molecules react. Species thermochemistry is estimated through Benson group additivity and reaction rate coefficients are estimated using a database of known rate rules and reaction templates. At its core, RMG relies on two fundamental data structures: graphs and trees. Graphs are used to represent chemical structures, and trees are used to represent thermodynamic and kinetic data. Models are generated using a rate-based algorithm which excludes species from the model based on reaction fluxes. RMG can generate reaction mechanisms for species involving carbon, hydrogen, oxygen, sulfur, and nitrogen. It also has capabilities for estimating transport and solvation properties, and it automatically computes pressure-dependent rate coefficients and identifies chemically-activated reaction paths. RMG is an object-oriented program written in Python, which provides a stable, robust programming architecture for developing an extensible and modular code base with a large suite of unit tests. Computationally intensive functions are cythonized for speed improvements.
Reaction kinetics of cellulose hydrolysis in subcritical and supercritical water
Olanrewaju, Kazeem Bode
The uncertainties in the continuous supply of fossil fuels from the crisis-ridden oil-rich region of the world is fast shifting focus on the need to utilize cellulosic biomass and develop more efficient technologies for its conversion to fuels and chemicals. One such technology is the rapid degradation of cellulose in supercritical water without the need for an enzyme or inorganic catalyst such as acid. This project focused on the study of reaction kinetics of cellulose hydrolysis in subcritical and supercritical water. Cellulose reactions at hydrothermal conditions can proceed via the homogeneous route involving dissolution and hydrolysis or the heterogeneous path of surface hydrolysis. The work is divided into three main parts. First, the detailed kinetic analysis of cellulose reactions in micro- and tubular reactors was conducted. Reaction kinetics models were applied, and kinetics parameters at both subcritical and supercritical conditions were evaluated. The second major task was the evaluation of yields of water soluble hydrolysates obtained from the hydrolysis of cellulose and starch in hydrothermal reactors. Lastly, changes in molecular weight distribution due to hydrothermolytic degradation of cellulose were investigated. These changes were also simulated based on different modes of scission, and the pattern generated from simulation was compared with the distribution pattern from experiments. For a better understanding of the reaction kinetics of cellulose in subcritical and supercritical water, a series of reactions was conducted in the microreactor. Hydrolysis of cellulose was performed at subcritical temperatures ranging from 270 to 340 °C (tau = 0.40--0.88 s). For the dissolution of cellulose, the reaction was conducted at supercritical temperatures ranging from 375 to 395 °C (tau = 0.27--0.44 s). The operating pressure for the reactions at both subcritical and supercritical conditions was 5000 psig. The results show that the rate-limiting step in
Chen, Longjian; Zhang, Haiyan; Li, Junbao; Lu, Minsheng; Guo, Xiaomiao; Han, Lujia
2015-02-01
Kinetic experiments on the dilute sulfuric acid pretreatment of corn stover were performed. A high xylan removal and a low inhibitor concentration were achieved by acid pretreatment. A novel diffusion-hydrolysis coupled kinetic model was proposed. The contribution to the xylose yield was analyzed by the kinetic model. Compared with the inhibitor furfural negatively affecting xylose yield, the fast and slow-hydrolyzing xylan significantly contributed to the xylose yield, however, their dominant roles were dependent on reaction temperature and time. The impact of particle size and acid concentration on the xylose yield were also investigated. The diffusion process may significantly influence the hydrolysis of large particles. Increasing the acid concentration from 0.15 M to 0.30 M significantly improved the xylose yield, whereas the extent of improvement decreased to near-quantitative when further increasing acid loading. These findings shed some light on the mechanism for dilute sulfuric acid hydrolysis of corn stover.
Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
Bernard Girau
2009-01-01
and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.
Internal Stabilization of a Mutualistic Reaction Diffusion System
Wang Yuan DONG
2007-01-01
We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use differ- ent internal controllers to stabilize different steady-state solutions. The controllers are provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Autocatalysis-driven clock reaction II: kinetics of the pentathionate-periodate reaction.
Xu, Li; Horváth, Attila K
2014-10-23
The pentathionate-periodate reaction has been investigated by spectrophotometrically monitoring the total amount of iodine evolved in the presence of phosphoric acid/dihydrogen phosphate buffer at 468 nm. The majority of the main characteristics of the title system is very reminiscent of that found recently in the pentathionate-iodate reaction, a system that led us to classify generally the clock reactions. Along with the pentathionate-iodate reaction the title system is proposed to belong to the autocatalysis-driven clock reactions as well. The kinetic model of the pentathionate-iodate system published recently was implemented by the necessary reactions of periodate to compose a 24-step kinetic model in which the mechanisms of the pentathionate-iodine, pentathionate-iodate, bisulfite-periodate, bisulfite-iodate, iodide-periodate, and the well-known Dushman reactions are combined. A thorough analysis revealed that the direct pentathionate-periodate reaction plays a role only to produce iodide ion via a finite sequence of reactions, and once its concentration reaches a certain level, the reaction is almost exclusively governed by the pentathionate-iodine, the iodide-periodate, and the Dushman reactions. As expected strong catalytic effect of the buffer composition is also found that can readily be explained by its well-known catalytic influence on the Dushman reaction.
A kinetic model for molecular diffusion through pores.
D'Agostino, Tommaso; Salis, Samuele; Ceccarelli, Matteo
2016-07-01
The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
Beijing ZHONG; Jun XI
2008-01-01
A reduced mechanism, which could couple with the multidimensional computational fluid dynamics code for quantitative description of a reacting flow, was developed for chemical kinetic modeling of polycyclic aro-matic hydrocarbon formation in an opposed-flow dif-fusion flame. The complete kinetic mechanism, which comprises 572 reactions and 108 species, was reduced to a simplified mechanism that includes only 83 reactions and 56 species through sensitivity analysis. The results computed via this reduced mechanism are nearly indistin-guishable from those via the detailed mechanism, which demonstrate that the model based on this reduced mech-anism can properly describe n-heptane oxidation chem-istry and quantitatively predict polycyclic aromatic hydrocarbon (such as benzene, naphthalene, phenan-threne and pyrene) formation in opposed-flow diffusion flames.
Reaction-diffusion pattern in shoot apical meristem of plants.
Hironori Fujita
Full Text Available 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.
Diffusion Kinetics of Carbonate Hydroxyapatite (CHAP) for Adsorbing F- Dissolved in Water
HUANG Zhiliang; ZHANG Lianmeng; LIU Yu; WANG Qilin; HE Qianjun; CHEN Wei
2006-01-01
A systematic research was performed about diffusion kinetics of adsorbing F- dissolved in water for carbonate hydroxyapatite (CHAP) from the natural hydroxyapatite which was modified by adulterating with CO32-. The result shows that the speed of F- adsorption is controlled by membrane diffusion when F- concentration is relatively low, which is expressed by the kinetic equation of diffusion Q=0.0005(Ci-C)(t-ti)+0.3967, or by vacancy diffusion when F- concentration is relatively high, which is expressed by the kinetic equation of diffusion In[C(o, t)]=8.4718-0.5048Int. Based on the feature of CHAP for adsorbing F- dissolved in water and its special channel of the structure of CO32-- modified hydroxyapatite, models of vacancy diffusion and membrane diffusion were established.
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Petr Stehlík
2015-01-01
Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
Parametric spatiotemporal oscillation in reaction-diffusion systems.
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.
Reaction diffusion equation with spatio-temporal delay
Zhao, Zhihong; Rong, Erhua
2014-07-01
We investigate reaction-diffusion equation with spatio-temporal delays, the global existence, uniqueness and asymptotic behavior of solutions for which in relation to constant steady-state solution, included in the region of attraction of a stable steady solution. It is shown that if the delay reaction function satisfies some conditions and the system possesses a pair of upper and lower solutions then there exists a unique global solution. In terms of the maximal and minimal constant solutions of the corresponding steady-state problem, we get the asymptotic stability of reaction-diffusion equation with spatio-temporal delay. Applying this theory to Lotka-Volterra model with spatio-temporal delay, we get the global solution asymptotically tend to the steady-state problem's steady-state solution.
Theory of diffusion-influenced reactions in complex geometries
Galanti, Marta; Fanelli, Duccio; Traytak, Sergey D.; Piazza, Francesco
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.
Theory of diffusion-influenced reactions in complex geometries
Galanti, Marta; Piazza, Francesco
2015-01-01
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical form...
STOCHASTIC CRACKING AND HEALING BEHAVIORS OF THIN FILMS DURING REACTION-DIFFUSION GROWTH
S.L. Zhu; S.L. Yang; Y.M. Xiong; M.S. Li; S.J. Geng; C.S. Hu; Fuhui Wang; W. T. Wu
2001-01-01
The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.
Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner
2017-01-01
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
Nanoconfinement effects: glucose oxidase reaction kinetics in nanofluidics.
Wang, Chen; Sheng, Zhen-Huan; Ouyang, Jun; Xu, Jing-Juan; Chen, Hong-Yuan; Xia, Xing-Hua
2012-02-01
Size-tunable nanofluidic devices coupled to an electrochemical detector have been designed and then used to study glucose oxidase (GOx) reaction kinetics confined in nanospaces. The devices are fabricated via a photochemical decomposition reaction, which forms nanochannels covered with carboxyl groups. The generated carboxyl groups enable us to chemically pattern biological molecules on the polymer surfaces via covalent bonding. With this approach, the activity of the immobilized biological molecules confined in nanospaces with different sizes has been investigated. GOx species are chemically immobilized on the surface of the nanochannels, catalyzing the oxidation of substrate glucose as it flows through the channels. The enzyme reaction product, hydrogen peroxide, passing through the nanochannels, reaches an electrochemical detector, giving rise to an increase in anodic current. This steady-state electrochemical current, which responds to various glucose concentrations, can be used to evaluate the GOx activity under confinement conditions. The results show significant nanoconfinement effects that are dependent on the channel size where the reaction occurs, demonstrating the importance of spatial confinement on the GOx reaction kinetics. The present approach provides an effective method for the study of enzyme activity and other bioassay systems, such as cell assays, drug discovery, and clinical diagnosis. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Kinetics of the reversible reaction of struvite crystallisation.
Crutchik, D; Garrido, J M
2016-07-01
The crystallisation of struvite could be a sustainable and economical alternative for recovering phosphorus from wastewater streams with high phosphate concentrations. Knowledge regarding the kinetics and thermodynamics that are involved in the crystallisation of struvite is the key to determine the optimal conditions for obtaining an efficient process. This study was conducted in a continuous stirred batch reactor. Different sets of experiments were performed in which struvite was either dissolved (undersaturated) or precipitated (oversaturated). These experiments were conducted at different temperatures (25, 30 and 35 °C) and pH values (8.2, 8.5 and 8.8) to determine the kinetics of struvite precipitation and dissolution. Struvite crystallisation was modelled as a reversible reaction. The kinetic rate parameters of struvite precipitation were 1.03·10(-4), 1.25·10(-4) and 1.54·10(-4) mol m(-2) min(-1) at 25, 30 and 35 °C, respectively. Similar kinetic rate parameters were determined for struvite dissolution. Struvite heterogeneous crystallisation can be represented by a first-order kinetic model that fitted well the experimental data.
Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
Kinetics of oxytetracycline reaction with a hydrous manganese oxide.
Rubert, Kennedy F; Pedersen, Joel A
2006-12-01
Tetracycline antibiotics comprise a class of broad spectrum antimicrobial agents finding application in human therapy, animal husbandry, aquaculture, and fruit crop production. To better understand the processes affecting these antibiotics in soils and sediments, the kinetics of oxytetracycline transformation by a hydrous manganese oxide (MnO2) were investigated as a function of reactant concentration, pH, and temperature. Oxytetracycline was rapidly degraded by MnO2. Initial reaction rates exhibited pronounced pH-dependence, increasing as pH decreased. Reaction of oxytetracycline with MnO2 was accompanied by generation of Mn(II) ions, suggesting oxidative transformation of the antibiotic. At pH 5.6, apparent reaction orders for oxytetracycline and MnO2 were 0.7 and 0.8. Reaction order with respect to H+ was 0.6 between pH 4 and 9. Initial reaction rates increased by a factor of approximately 2.4 for 10 degrees C temperature increases; the apparent activation energy (60 kJ x mol(-1)) was consistent with a surface-controlled reaction. Reactivity of tetracycline antibiotics toward MnO2 increased in the following order: rolitetracyline oxytetracycline manganese oxides in soils and sediments are likely to promote appreciable degradation of tetracycline antibiotics, and that reaction rates are strongly dependent on reaction time scale and solution conditions.
Kinetics and mechanism of the chlorine dioxide-trithionate reaction.
Cseko, György; Horváth, Attila K
2012-03-22
The trithionate-chlorine dioxide reaction has been studied spectrophotometrically in a slightly acidic medium at 25.0 ± 0.1 °C in acetate/acetic acid buffer monitoring the decay of chlorine dioxide at constant ionic strength (I = 0.5 M) adjusted by sodium perchlorate. We found that under our experimental conditions two limiting stoichiometries exist and the pH, the concentration of the reactants, and even the concentration of chloride ion affects the actual stoichiometry of the reaction that can be augmented by an appropriate linear combination of these limiting processes. It is also shown that although the formal kinetic order of trithionate is strictly one that of chlorine dioxide varies between 1 and 2, depending on the actual chlorine dioxide excess and the pH. Moreover, the otherwise sluggish chloride ion, which is also a product of the reaction, slightly accelerates the initial rate of chlorine dioxide consumption and may therefore act as an autocatalyst. In addition to that, overshoot-undershoot behavior is also observed in the [(·)ClO(2)]-time curves in the presence of chloride ion at chlorine dioxide excess. On the basis of the experiments, a 13-step kinetic model with 6 fitted kinetic parameter is proposed by nonlinear parameter estimation. © 2012 American Chemical Society
A robust methodology for kinetic model parameter estimation for biocatalytic reactions
Al-Haque, Naweed; Andrade Santacoloma, Paloma de Gracia; Lima Afonso Neto, Watson;
2012-01-01
Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme-catalyzed reactions generally include several...
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 were 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.
Reaction Path Optimization with Holonomic Constraints and Kinetic Energy Potentials.
Brokaw, Jason B; Haas, Kevin R; Chu, Jhih-Wei
2009-08-11
Two methods are developed to enhance the stability, efficiency, and robustness of reaction path optimization using a chain of replicas. First, distances between replicas are kept equal during path optimization via holonomic constraints. Finding a reaction path is, thus, transformed into a constrained optimization problem. This approach avoids force projections for finding minimum energy paths (MEPs), and fast-converging schemes such as quasi-Newton methods can be readily applied. Second, we define a new objective function - the total Hamiltonian - for reaction path optimization, by combining the kinetic energy potential of each replica with its potential energy function. Minimizing the total Hamiltonian of a chain determines a minimum Hamiltonian path (MHP). If the distances between replicas are kept equal and a consistent force constant is used, then the kinetic energy potentials of all replicas have the same value. The MHP in this case is the most probable isokinetic path. Our results indicate that low-temperature kinetic energy potentials (optimization and can significantly reduce the required steps of minimization by 2-3 times without causing noticeable differences between a MHP and MEP. These methods are applied to three test cases, the C7eq-to-Cax isomerization of an alanine dipeptide, the (4)C1-to-(1)C4 transition of an α-d-glucopyranose, and the helix-to-sheet transition of a GNNQQNY heptapeptide. By applying the methods developed in this work, convergence of reaction path optimization can be achieved for these complex transitions, involving full atomic details and a large number of replicas (>100). For the case of helix-to-sheet transition, we identify pathways whose energy barriers are consistent with experimental measurements. Further, we develop a method based on the work energy theorem to quantify the accuracy of reaction paths and to determine whether the atoms used to define a path are enough to provide quantitative estimation of energy barriers.
A Weak Comparison Principle for Reaction-Diffusion Systems
José Valero
2012-01-01
Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.
Exact solutions of certain nonlinear chemotaxis diffusion reaction equations
MISHRA AJAY; KAUSHAL R S; PRASAD AWADHESH
2016-05-01
Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.
A weak comparison principle for reaction-diffusion systems
Valero, José
2012-01-01
In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of fractional-order chemical autocatalysis with decay. Morever, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions $L^{\\infty}$ is proved for at least one solution of the problem.
Flow-Injection Responses of Diffusion Processes and Chemical Reactions
Andersen, Jens Enevold Thaulov
2000-01-01
The technique of Flow-injection Analysis (FIA), now aged 25 years, offers unique analytical methods that are fast, reliable and consuming an absolute minimum of chemicals. These advantages together with its inherent feasibility for automation warrant the future applications of FIA as an attractive...... be used in the resolution of FIA profiles to obtain information about the content of interference’s, in the study of chemical reaction kinetics and to measure absolute concentrations within the FIA-detector cell....
Kinetic study of CO2 reaction with CaO by a modified random pore model
Nouri S.M.M.
2016-03-01
Full Text Available In this work, a modified random pore model was developed to study the kinetics of the carbonation reaction of CaO. Pore size distributions of the CaO pellets were measured by nitrogen adsorption and mercury porosimetry methods. The experiments were carried out in a thermogravimeter at different isothermal temperatures and CO2 partial pressures. A fractional concentration dependency function showed the best accuracy for predicting the intrinsic rate of reaction. The activation energy was determined as 11 kcal/mole between 550–700°C. The effect of product layer formation was also taken into account by using the variable product layer diffusivity. Also, the model was successfully predicted the natural lime carbonation reaction data extracted from the literature.
Kinetic characteristics of continuous flow polymerase chain reaction chip: A numerical investigation
无
2010-01-01
Continuous flow PCR (polymerase chain reaction) chip holds impressive advantages compared to micro chamber PCR chip. In order to have better understanding of kinetic characteristics of continuous flow PCR chip, a comprehensive mathematical model is presented in this paper, including melting, annealing and extension phases of a typical PCR process which has the essence of a convection-diffusion-reaction system. Using this model, we can simulate the PCR process in series of reaction cycles. Numerical results show that the average sample velocity plays a significant role in affecting the amplification efficiency. Also, appropriate combination of the PCR mixture is important for high-quality DNA amplification. Giving a large initial DNA concentration range, the continuous flow PCR scheme holds excellent real-time detection ability theoretically. The present numerical model bridges the temperature distribution to the real DNA amplification, and thereby is able to successfully predict continuous flow PCR properties which are important for the chip design.
Kinetics and Mechanisms of Calcite Reactions with Saline Waters
Gorman, Brian P [Colorado School of Mines, Golden, CO (United States)
2015-09-02
Project Description: The general objective of the proposed research is to determine the kinetics and mechanisms of calcite reactions with saline waters over a wide range of saline water composition, pCO_{2}, and modest ranges in T and P. This will be accomplished by studying both reaction rates and solubility from changes in solution chemistry, and making nanoscale observations of calcite precipitate surface morphology and composition at the micro-to-nano-scale to provide an understanding of controlling reaction mechanisms and pathways. The specific objectives necessary to reach the general objective are: a) determination of how pCO_{2}, Ca^{2+}, ionic strength and “foreign” ions influence reaction rates; and b) investigate the influence of these parameters on apparent kinetic solubility from dissolution and precipitation reactions. This information will clearly be central to the construction of reliable reaction-transport models to predict reservoir and formation response to increased CO_{2} in saline waters. This program was initially collaborative with John Morse at Texas A&M, however his passing shortly after the beginning of this program resulted in abbreviated research time and effort. Summary of Results: Early studies using electron microscopy and spectroscopy indicated that carbonate precipitation from natural seawater (NSW) conditions onto aragonite substrates was mediated by a surface amorphous calcium carbonate layer. It was hypothesized that this ACC layer (observed after < 5days reaction time) was responsible for the abnormal reaction kinetics and also served as a metastable seed layer for growth of epitaxial aragonite. Further studies of the ACC formation mechanism indicated a strong dependence on the Mg concentration in solution. Subsequent studies at shorter times (10 hrs) on calcite substrates and in a wide range of supersaturation conditions did not indicate any ACC layer. Instead, an epitaxial layer by layer
Variation of kinetic isotope effect in multiple proton transfer reactions
B Saritha; M Durga Prasad
2012-01-01
Recently, we had suggested that the motion along the promoter mode in the first part of the IRC of proton transfer reaction enhances the delocalization of electrons on the acceptor atom into the * orbital of the donor-hydrogen covalent bond, and as a consequence weakens it. This leads to a reduction of the barrier to the proton transfer as well as the stretching frequency of donor-hydrogen bond. An extension of this to the concerted multiple proton transfer reactions implies that the kinetic isotope effect in such reaction depends exponentially on the number of protons that are being transferred. Computational evidence on three systems, (HF)3, formic acid dimer, and (H2O) clusters is provided to support this assertion.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Nitric oxide kinetics in the afterglow of a diffuse plasma filament
Burnette, D.; Montello, A.; Adamovich, I. V.; Lempert, W. R.
2014-08-01
A suite of laser diagnostics is used to study kinetics of vibrational energy transfer and plasma chemical reactions in a nanosecond pulse, diffuse filament electric discharge and afterglow in N2 and dry air at 100 Torr. Laser-induced fluorescence of NO and two-photon absorption laser-induced fluorescence of O and N atoms are used to measure absolute, time-resolved number densities of these species after the discharge pulse, and picosecond coherent anti-Stokes Raman spectroscopy is used to measure time-resolved rotational temperature and ground electronic state N2(v = 0-4) vibrational level populations. The plasma filament diameter, determined from plasma emission and NO planar laser-induced fluorescence images, remains nearly constant after the discharge pulse, over a few hundred microseconds, and does not exhibit expansion on microsecond time scale. Peak temperature in the discharge and the afterglow is low, T ≈ 370 K, in spite of significant vibrational nonequilibrium, with peak N2 vibrational temperature of Tv ≈ 2000 K. Significant vibrational temperature rise in the afterglow is likely caused by the downward N2-N2 vibration-vibration (V-V) energy transfer. Simple kinetic modeling of time-resolved N, O, and NO number densities in the afterglow, on the time scale longer compared to relaxation and quenching time of excited species generated in the plasma, is in good agreement with the data. In nitrogen, the N atom density after the discharge pulse is controlled by three-body recombination and radial diffusion. In air, N, NO and O concentrations are dominated by the reverse Zel'dovich reaction, N + NO → N2 + O, and ozone formation reaction, O + O2 + M → O3 + M, respectively. The effect of vibrationally excited nitrogen molecules and excited N atoms on NO formation kinetics is estimated to be negligible. The results suggest that NO formation in the nanosecond pulse discharge is dominated by reactions of excited electronic states of nitrogen, occurring on
Does reaction-diffusion support the duality of fragmentation effect?
Roques, Lionel
2009-01-01
There is a gap between single-species model predictions, and empirical studies, regarding the effect of habitat fragmentation per se, i.e., a process involving the breaking apart of habitat without loss of habitat. Empirical works indicate that fragmentation can have positive as well as negative effects, whereas, traditionally, single-species models predict a negative effect of fragmentation. Within the class of reaction-diffusion models, studies almost unanimously predict such a detrimental effect. In this paper, considering a single-species reaction-diffusion model with a removal -- or similarly harvesting -- term, in two dimensions, we find both positive and negative effects of fragmentation of the reserves, i.e. the protected regions where no removal occurs. Fragmented reserves lead to higher population sizes for time-constant removal terms. On the other hand, when the removal term is proportional to the population density, higher population sizes are obtained on aggregated reserves, but maximum yields ar...
Untangling knots via reaction-diffusion dynamics of vortex strings
Maucher, Fabian
2016-01-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2008-10-21
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle models of physical processes.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings
Maucher, Fabian; Sutcliffe, Paul
2016-04-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Controllability of Degenerating Reaction-Diffusion System in Electrocardiology
Bendahmane, Mostafa
2011-01-01
This paper is devoted to analyze the null controllability of a nonlinear reaction-diffusion system approximating a parabolic-elliptic system modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precisely estimate with respect to the degenerating parameter and it is done combining Carleman estimates and energy inequalities.
An Application of Equivalence Transformations to Reaction Diffusion Equations
Mariano Torrisi
2015-10-01
Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.
Resonant Phase Patterns in a Reaction-Diffusion System
Lin, Anna L.; Bertram, Matthias; Martinez, Karl; Swinney, Harry L.; Ardelea, Alexandre; Carey, Graham F.
2000-05-01
Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model. (c) 2000 The American Physical Society.
Kinetics of diamond-silicon reaction under high pressure-high temperature conditions
Pantea, Cristian
In this dissertation work, the kinetics of the reaction between diamond and silicon at high pressure-high temperature conditions was investigated. This study was motivated by the extremely limited amount of information related to the kinetics of the reaction in diamond-silicon carbide composites formation. It was found that the reaction between diamond and melted silicon and the subsequent silicon carbide formation is a two-stage process. The initial stage is a result of direct reaction of melted silicon with carbon atoms from the diamond surface, the phase boundary reaction. Further growth of SiC is much more complicated and when the outer surfaces of diamond crystals are covered with the silicon carbide layer it involves diffusion of carbon and silicon atoms through the SiC layer. The reaction takes place differently for the two regions of stability of carbon. In the graphite-stable region, the reaction between diamond and melted silicon is associated with the diamond-to-graphite phase transition, while in the diamond-stable region there is no intermediary step for the reaction. The data obtained at HPHT were fitted by the Avrami-Erofeev equation. It was found that the reaction is isotropic, the beta-SiC grown on different faces of the diamond crystals showing the same reaction rate, and that the controlling mechanism for the reaction is the diffusion. In the graphite-stable region the activation energy, 402 kJ/mol is slightly higher than in the diamond-stable region, 260 kJ/mol, as the reaction between diamond and melted silicon is associated with the diamond-to-graphite phase transition, which has higher activation energy. In the diamond-stable region, the calculated activation energy is higher for micron size diamond powders (≈260 kJ/mol), while for nanocrystalline diamond powders a lower value of 170 kJ/mol was obtained. This effect was attributed to nanocrystalline structure and strained bonds within grain boundaries in SiC formed from nanosize diamond
O'Hara, Kieran
2007-08-01
In the southern Appalachians, the Blue Ridge-Piedmont crystalline thrust sheet was emplaced onto low-grade Late Precambrian and Paleozoic sedimentary rocks in the footwall along a basal detachment consisting of phyllosilicate-rich mylonites (phyllonites). The phyllonites developed first by mechanical breakdown of feldspar followed by chemical breakdown to white mica in the presence of a pore fluid. Diffusion of solute in the pore fluid is the rate limiting step in controlling reaction rate and also the strain rate. Assuming solute diffusion follows the Stokes-Einstein equation, the shear strain rate is given by ⅆγ/ⅆt=2ωkT/5ηrx for shear stress ≥20 MPa, where n is a constant, ω is a geometric factor, k is Boltzmann's constant, T is absolute temperature, η is water viscosity, r is the atomic radius of the diffusing species, and x is the diffusion distance. A bulk diffusion coefficient in the range of ˜10 -10 to 10 -12 m 2/s over distances of 10-100 m results in strain rates of 10 -14 to 10 -13 s -1 in the temperature range 200-400 °C. It is concluded that greenschist grade crystalline thrust sheets develop on pre-existing basement faults that become weak during reaction softening and localize into high strain phyllonite zones in which pore fluid diffusion controls reaction rate and strain rate.
Thermodynamic criteria for estimating the kinetic parameters of catalytic reactions
Mitrichev, I. I.; Zhensa, A. V.; Kol'tsova, E. M.
2017-01-01
Kinetic parameters are estimated using two criteria in addition to the traditional criterion that considers the consistency between experimental and modeled conversion data: thermodynamic consistency and the consistency with entropy production (i.e., the absolute rate of the change in entropy due to exchange with the environment is consistent with the rate of entropy production in the steady state). A special procedure is developed and executed on a computer to achieve the thermodynamic consistency of a set of kinetic parameters with respect to both the standard entropy of a reaction and the standard enthalpy of a reaction. A problem of multi-criterion optimization, reduced to a single-criterion problem by summing weighted values of the three criteria listed above, is solved. Using the reaction of NO reduction with CO on a platinum catalyst as an example, it is shown that the set of parameters proposed by D.B. Mantri and P. Aghalayam gives much worse agreement with experimental values than the set obtained on the basis of three criteria: the sum of the squares of deviations for conversion, the thermodynamic consistency, and the consistency with entropy production.
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
Chemical Kinetic Modeling of Dimethyl Carbonate in an Opposed-Flow Diffusion Flame
Glaude, P A; Pitz, W J; Thomson, M J
2003-12-08
Dimethyl carbonate (DMC) has been of interest as an oxygenate additive to diesel fuel because of its high oxygen content. In this study, a chemical kinetic mechanism for DMC was developed for the first time and used to understand its combustion under conditions in an opposed flow diffusion flame. Computed results were compared to experimental results from an opposed flow diffusion flame. It was found that the decomposition rate DMC {yields} H{sub 3}COC(=O)O. + CH{sub 3} in the flame was much slower than originally thought because resonance stabilization in the H{sub 3}COC(=O)O. radical was less than expected. Also, a new molecular elimination path for DMC is proposed and its rate calculated by quantum chemical methods. In the simulations of DMC in the flame, it was determined that much of the oxygen in dimethyl carbonate goes directly to CO{sub 2}. This characteristic indicates that DMC would not be an effective oxygenate additive for reducing soot emissions from diesel engines. In an ideal oxygenate additive for diesel fuel, each oxygen atom stays bonded to one carbon atom in the products thereby preventing the formation of carbon-carbon bonds that can lead to soot. When CO2 is formed directly, two oxygen atoms are bonded to one carbon atom thereby wasting one oxygen atom in the oxygenate additive. To determine how much CO{sub 2} is formed directly, the branching ratio of the key reaction, CH{sub 3}OC.=O going to the products CH{sub 3} + CO{sub 2} or CH{sub 3}O + CO was determined by ab initio methods. The A-factors of the rate constant of this reaction were found to be about 20 times higher than previous factors estimates. The new reaction rate constants obtained can be used as reaction rate rules for all oxygenates that contain the ester moiety including biodiesel.
Kinetics and mechanisms of reactions involving small aromatic reactive intermediates
Lin, M.C. [Emory Univ., Atlanta, GA (United States)
1993-12-01
Small aromatic radicals such as C{sub 6}H{sub 5}, C{sub 6}H{sub 5}O and C{sub 6}H{sub 4} are key prototype species of their homologs. C{sub 6}H{sub 5} and its oxidation product, C{sub 6}H{sub 5}O are believed to be important intermediates which play a pivotal role in hydrocarbon combustion, particularly with regard to soot formation. Despite their fundamental importance, experimental data on the reaction mechanisms and reactivities of these species are very limited. For C{sub 6}H{sub 5}, most kinetic data except its reactions with NO and NO{sub 2}, were obtained by relative rate measurements. For C{sub 6}H{sub 5}O, the authors have earlier measured its fragmentation reaction producing C{sub 5}H{sub 5} + CO in shock waves. For C{sub 6}H{sub 4}, the only rate constant measured in the gas phase is its recombination rate at room temperature. The authors have proposed to investigate systematically the kinetics and mechanisms of this important class of molecules using two parallel laser diagnostic techniques--laser resonance absorption (LRA) and resonance enhanced multiphoton ionization mass spectrometry (REMPI/MS). In the past two years, study has been focused on the development of a new multipass adsorption technique--the {open_quotes}cavity-ring-down{close_quotes} technique for kinetic applications. The preliminary results of this study appear to be quite good and the sensitivity of the technique is at least comparable to that of the laser-induced fluorescence method.
Kinetic Study of the Austempering Reactions in Ductile Irons
Pérez, M. J.; Cisneros, M. M.; Almanza, E.; Haro, S.
2012-11-01
Kinetics of the reaction that occur during the austempering heat treatment in unalloyed and alloyed ductile irons with 1Cu-0.25Mo, 1Ni-0.25Mo, and 0.7Cu-1Ni-0.25Mo, was studied. The austenitization and austempering cycles were achieved by isothermal dilatometry in cylindrical samples of 2 mm in diameter and 12 mm in length. The specimens were austenitized at 870 °C for 120 min, followed by isothermal holding for 300 min at temperatures between 270 and 420 °C. Kinetic parameters such as the order of reaction " n" and the rate of reaction " k" were calculated using the Johnson-Mehl equation while the empirical activation energy was calculated by means of the Arrhenius equation. It was found that the values of " k" decreased with the addition of Cu, Ni, and Mo as well as with the reduction of the isothermal temperature. The activation energy changes with the austempering temperature, in the range 30,348-58,250 J/mol when the heat treatment was carried out between 370 and 420 °C and 10,336-26,683 J/mol when the temperature varied from 270 to 350 °C. The microstructures in samples austempered at 370 and 315 °C were observed by transmission electron microscopy. No carbides precipitation was observed on samples heat treated at 370 °C for less than 120 min, while at 315 °C carbides of hexagonal structure ɛ(Fe2.4C) were found from the beginning of the transformation. The smallest value of activation energy and a slower kinetic transformation seem to be related with the presence of a carbide phase. Additionally, the time results obtained for transformation fractions of 0.05 and 0.95 by the dilatometry analysis were used to build the temperature-time-transformation diagrams for the irons.
Ruzi, Mahmut; Anderson, David T
2015-12-17
Our group has been working to develop parahydrogen (pH2) matrix isolation spectroscopy as a method to study low-temperature condensed-phase reactions of atomic hydrogen with various reaction partners. Guided by the well-defined studies of cold atom chemistry in rare-gas solids, the special properties of quantum hosts such as solid pH2 afford new opportunities to study the analogous chemical reactions under quantum diffusion conditions in hopes of discovering new types of chemical reaction mechanisms. In this study, we present Fourier transform infrared spectroscopic studies of the 193 nm photoinduced chemistry of nitric oxide (NO) isolated in solid pH2 over the 1.8 to 4.3 K temperature range. Upon short-term in situ irradiation the NO readily undergoes photolysis to yield HNO, NOH, NH, NH3, H2O, and H atoms. We map the postphotolysis reactions of mobile H atoms with NO and document first-order growth in HNO and NOH reaction products for up to 5 h after photolysis. We perform three experiments at 4.3 K and one at 1.8 K to permit the temperature dependence of the reaction kinetics to be quantified. We observe Arrhenius-type behavior with a pre-exponential factor of A = 0.036(2) min(-1) and Ea = 2.39(1) cm(-1). This is in sharp contrast to previous H atom reactions we have studied in solid pH2 that display definitively non-Arrhenius behavior. The contrasting temperature dependence measured for the H + NO reaction is likely related to the details of H atom quantum diffusion in solid pH2 and deserves further study.
The reaction kinetics of amino radicals with sulfur dioxide
Gao, Yide; Glarborg, Peter; Marshall, Paul
2015-01-01
Application of the laser photolysis-laser-induced fluorescence method to the reaction NH2+SO2 in argon bath gas yields pressure-dependent, third-order kinetics which may be summarized as k = (1.49 ± 0.15) × 10-31 (T/298 K)-0.83cm6 molecule-2 s-1 over 292-555K, where the uncertainty is the 95...... yields a H2N-SO2 dissociation enthalpy of 73.5 kJ mol-1, and comparison with RRKM theory and the exponential down model for energy transfer yields down = 350 cm-1 for Ar at room temperature....
Kinetics of Reduction Reaction in Micro-Fluidized Bed
LINYin-he; GUOZhan—cheng; TANGHui—qing; REN Shan; LIJing—wei
2012-01-01
Micro-fluidized bed reactor is a new research method for the reduction of iron ore fines. The reactor is op- erated as a differential reactor to ensure a constant gas concentration and temperature within the reactor volume. In order to understand the dynamic process of the reduction reaction in micro-fluidized bed, a series of kinetic experi- ments were designed. In the micro fluidized bed, the use of shrinking core model describes the dynamic behavior of reduction of iron ore. And the apparent activation energy is calculated in the range of 700--850 ~C while the initial atmosphere is 100% content of CO.
KINETIC MODELS STUDY OF HYDRODESULPHURIZATION VACUUM DISTILLATE REACTION
AbdulMunem A. Karim
2013-05-01
Full Text Available This study deals with kinetics of hydrodesulphurization (HDS reaction of vacuum gas oil (611-833 K which was distillated from Kirkuk crude oil and which was obtained by blending the fractions, light vacuum gas oil (611 - 650 K, medium vacuum gas oil (650-690 K, heavy vacuum gas oil (690-727 K and very heavy vacuum gas oil (727-833 K. The vacuum gas oil was hydrotreated on a commercial cobalt-molybdenum alumina catalyst presulfied at specified conditions in a laboratory trickle bed reactor. The reaction temperature range (583-643 K,liquid hourly space velocity range (1.5-3.75 h-1 and hydrogen pressure was kept constant at 3.5 MPa with hydrogen to oil ratio about 250 lt/lt. The conversion results for desulphurization reaction appeared to obey the second order reaction. According to this model, the rate constants for desulphurization reaction were determined. Finally, the apparent activation energy (Ea, enthalpy of activation ( H* and entropy ( S* were calculated based on the values of rate constant (k2 and were equal 80.3792 KJ/mole, 75.2974 KJ/mole and 197.493 J/mole, respectively.
Python framework for kinetic modeling of electronically excited reaction pathways
Verboncoeur, John; Parsey, Guy; Guclu, Yaman; Christlieb, Andrew
2012-10-01
The use of plasma energy to enhance and control the chemical reactions during combustion, a technology referred to as ``plasma assisted combustion'' (PAC), can result in a variety of beneficial effects: e.g. stable lean operation, pollution reduction, and wider range of p-T operating conditions. While experimental evidence abounds, theoretical understanding of PAC is at best incomplete, and numerical tools still lack in reliable predictive capabilities. In the context of a joint experimental-numerical effort at Michigan State University, we present here an open-source modular Python framework dedicated to the dynamic optimization of non-equilibrium PAC systems. Multiple sources of experimental reaction data, e.g. reaction rates, cross-sections and oscillator strengths, are used in order to quantify the effect of data uncertainty and limiting assumptions. A collisional-radiative model (CRM) is implemented to organize reactions by importance and as a potential means of measuring a non-Maxwellian electron energy distribution function (EEDF), when coupled to optical emission spectroscopy data. Finally, we explore scaling laws in PAC parameter space using a kinetic global model (KGM) accelerated with CRM optimized reaction sequences and sparse stiff integrators.
Szalai, István; Cuiñas, Daniel; Takács, Nándor; Horváth, Judit; De Kepper, Patrick
2012-08-06
In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.
Kinetic Monte Carlo Simulation of Oxygen and Cation Diffusion in Yttria-Stabilized Zirconia
Good, Brian
2011-01-01
Yttria-stabilized zirconia (YSZ) is of interest to the aerospace community, notably for its application as a thermal barrier coating for turbine engine components. In such an application, diffusion of both oxygen ions and cations is of concern. Oxygen diffusion can lead to deterioration of a coated part, and often necessitates an environmental barrier coating. Cation diffusion in YSZ is much slower than oxygen diffusion. However, such diffusion is a mechanism by which creep takes place, potentially affecting the mechanical integrity and phase stability of the coating. In other applications, the high oxygen diffusivity of YSZ is useful, and makes the material of interest for use as a solid-state electrolyte in fuel cells. The kinetic Monte Carlo (kMC) method offers a number of advantages compared with the more widely known molecular dynamics simulation method. In particular, kMC is much more efficient for the study of processes, such as diffusion, that involve infrequent events. We describe the results of kinetic Monte Carlo computer simulations of oxygen and cation diffusion in YSZ. Using diffusive energy barriers from ab initio calculations and from the literature, we present results on the temperature dependence of oxygen and cation diffusivity, and on the dependence of the diffusivities on yttria concentration and oxygen sublattice vacancy concentration. We also present results of the effect on diffusivity of oxygen vacancies in the vicinity of the barrier cations that determine the oxygen diffusion energy barriers.
Enzymatic reactions in microfluidic devices: Michaelis-Menten kinetics.
Ristenpart, William D; Wan, Jiandi; Stone, Howard A
2008-05-01
Kinetic rate constants for enzymatic reactions are typically measured with a series of experiments at different substrate concentrations in a well-mixed container. Here we demonstrate a microfluidic technique for measuring Michaelis-Menten rate constants with only a single experiment. Enzyme and substrate are brought together in a coflow microfluidic device, and we establish analytically and numerically that the initial concentration of product scales with the distance x along the channel as x5/2. Measurements of the initial rate of product formation, combined with the quasi-steady rate of product formation further downstream, yield the rate constants. We corroborate the x5/2 scaling result experimentally using the bioluminescent reaction between ATP and luciferase/luciferin as a model system.
Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains
Crooks, E. C. M.; Hilhorst, D.
2016-08-01
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models of fast chemical reactions where either one or both reactant(s) is/are mobile. For appropriate initial data, solutions of four classes of problems each converge in the fast-reaction limit k → ∞ to a self-similar limit profile that has one of four forms, depending on how many components diffuse and whether the spatial domain is a half or whole line. For fixed k, long-time convergence to these same self-similar profiles is also established, thanks to a scaling argument of Kamin. Our results generalise earlier work of Hilhorst, van der Hout and Peletier to a much wider class of problems, and provide a quantitative description of the penetration of one substance into another in both the fast-reaction and long-time regimes.
Variational methods applied to problems of diffusion and reaction
Strieder, William
1973-01-01
This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free ...
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
Reaction route graphs. III. Non-minimal kinetic mechanisms.
Fishtik, Ilie; Callaghan, Caitlin A; Datta, Ravindra
2005-02-24
The concept of reaction route (RR) graphs introduced recently by us for kinetic mechanisms that produce minimal graphs is extended to the problem of non-minimal kinetic mechanisms for the case of a single overall reaction (OR). A RR graph is said to be minimal if all of the stoichiometric numbers in all direct RRs of the mechanism are equal to +/-1 and non-minimal if at least one stoichiometric number in a direct RR is non-unity, e.g., equal to +/-2. For a given mechanism, four unique topological characteristics of RR graphs are defined and enumerated, namely, direct full routes (FRs), empty routes (ERs), intermediate nodes (INs), and terminal nodes (TNs). These are further utilized to construct the RR graphs. One algorithm involves viewing each IN as a central node in a RR sub-graph. As a result, the construction and enumeration of RR graphs are reduced to the problem of balancing the peripheral nodes in the RR sub-graphs according to the list of FRs, ERs, INs, and TNs. An alternate method involves using an independent set of RRs to draw the RR graph while satisfying the INs and TNs. Three examples are presented to illustrate the application of non-minimal RR graph theory.
A global reaction route mapping-based kinetic Monte Carlo algorithm
Mitchell, Izaac; Irle, Stephan; Page, Alister J.
2016-07-01
We propose a new on-the-fly kinetic Monte Carlo (KMC) method that is based on exhaustive potential energy surface searching carried out with the global reaction route mapping (GRRM) algorithm. Starting from any given equilibrium state, this GRRM-KMC algorithm performs a one-step GRRM search to identify all surrounding transition states. Intrinsic reaction coordinate pathways are then calculated to identify potential subsequent equilibrium states. Harmonic transition state theory is used to calculate rate constants for all potential pathways, before a standard KMC accept/reject selection is performed. The selected pathway is then used to propagate the system forward in time, which is calculated on the basis of 1st order kinetics. The GRRM-KMC algorithm is validated here in two challenging contexts: intramolecular proton transfer in malonaldehyde and surface carbon diffusion on an iron nanoparticle. We demonstrate that in both cases the GRRM-KMC method is capable of reproducing the 1st order kinetics observed during independent quantum chemical molecular dynamics simulations using the density-functional tight-binding potential.
Kinetics and Mechanisms of the Acid-base Reaction Between NH3 and HCOOH in Interstellar Ice Analogs
Bergner, Jennifer B.; Öberg, Karin I.; Rajappan, Mahesh; Fayolle, Edith C.
2016-10-01
Interstellar complex organic molecules are commonly observed during star formation, and are proposed to form through radical chemistry in icy grain mantles. Reactions between ions and neutral molecules in ices may provide an alternative cold channel to complexity, as ion-neutral reactions are thought to have low or even no-energy barriers. Here we present a study of the kinetics and mechanisms of a potential ion-generating, acid-base reaction between NH3 and HCOOH to form the salt NH{}4+HCOO-. We observe salt growth at temperatures as low as 15 K, indicating that this reaction is feasible in cold environments. The kinetics of salt growth are best fit by a two-step model involving a slow “pre-reaction” step followed by a fast reaction step. The reaction energy barrier is determined to be 70 ± 30 K with a pre-exponential factor 1.4 ± 0.4 × 10-3 s-1. The pre-reaction rate varies under different experimental conditions and likely represents a combination of diffusion and orientation of reactant molecules. For a diffusion-limited case, the pre-reaction barrier is 770 ± 110 K with a pre-exponential factor of ˜7.6 × 10-3 s-1. Acid-base chemistry of common ice constituents is thus a potential cold pathway to generating ions in interstellar ices.
Liechty, Derek S.; Lewis, Mark J.
2010-01-01
Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction rate information) are extended to include reactions involving charged particles and electronic energy levels. The proposed extensions include ionization reactions, exothermic associative ionization reactions, endothermic and exothermic charge exchange reactions, and other exchange reactions involving ionized species. The extensions are shown to agree favorably with the measured Arrhenius rates for near-equilibrium conditions.
Mechanical reaction-diffusion model for bacterial population dynamics
Ngamsaad, Waipot
2015-01-01
The effect of mechanical interaction between cells on the spreading of bacterial population was investigated in one-dimensional space. A nonlinear reaction-diffusion equation has been formulated as a model for this dynamics. In this model, the bacterial cells are treated as the rod-like particles that interact, when contacting each other, through the hard-core repulsion. The repulsion introduces the exclusion process that causes the fast diffusion in bacterial population at high density. The propagation of the bacterial density as the traveling wave front in long time behavior has been analyzed. The analytical result reveals that the front speed is enhanced by the exclusion process---and its value depends on the packing fraction of cell. The numerical solutions of the model have been solved to confirm this prediction.
Turing instability in reaction-diffusion models on complex networks
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Kinetics of HCPB (bis-Hydroxycyclobutadiyne) diffusion in Sylgard
Renschler, C.L.; Gillen, K.T.; Keenan, M.R.
1987-01-01
Diffusion of HCPB away from a Pd catalyst results in loss of efficiency as a hydrogen getter. It is of interest to measure the diffusion rate of HCPB through Sylgard 1984 silicone rubber. This report describes the technique of density profiling to acquire this information. (JDH)
Diffusion kinetics of the glucose/glucose oxidase system in swift heavy ion track-based biosensors
Fink, Dietmar, E-mail: fink@xanum.uam.mx [Nuclear Physics Institute, 25068 Řež (Czech Republic); Departamento de Fisica, Universidad Autónoma Metropolitana-Iztapalapa, PO Box 55-534, 09340 México, DF (Mexico); Vacik, Jiri; Hnatowicz, V. [Nuclear Physics Institute, 25068 Řež (Czech Republic); Muñoz Hernandez, G. [Departamento de Fisica, Universidad Autónoma Metropolitana-Iztapalapa, PO Box 55-534, 09340 México, DF (Mexico); Garcia Arrelano, H. [Departamento de Ciencias Ambientales, División de Ciencias Biológicas y de la Salud, Universidad Autónoma Metropolitana-Lerma, Av. de las Garzas No. 10, Col. El Panteón, Lerma de Villada, Municipio de Lerma, Estado de México CP 52005 (Mexico); Alfonta, Lital [Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105 (Israel); Kiv, Arik [Department of Materials Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105 (Israel)
2017-05-01
Highlights: • Application of swift heavy ion tracks in biosensing. • Obtaining yet unknown diffusion coefficients of organic matter across etched ion tracks. • Obtaining diffusion coefficients of organics in etched ion tracks of biosensors. • Comparison with Renkin’s equation to predict the effective etched track diameter in the given experiments. - Abstract: For understanding of the diffusion kinetics and their optimization in swift heavy ion track-based biosensors, recently a diffusion simulation was performed. This simulation aimed at yielding the degree of enrichment of the enzymatic reaction products in the highly confined space of the etched ion tracks. A bunch of curves was obtained for the description of such sensors that depend only on the ratio of the diffusion coefficient of the products to that of the analyte within the tracks. As hitherto none of these two diffusion coefficients is accurately known, the present work was undertaken. The results of this paper allow one to quantify the previous simulation and hence yield realistic predictions of glucose-based biosensors. At this occasion, also the influence of the etched track radius on the diffusion coefficients was measured and compared with earlier prediction.
Statistical theory for the kinetics and dynamics of roaming reactions.
Klippenstein, Stephen J; Georgievskii, Yuri; Harding, Lawrence B
2011-12-22
We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.
Global dynamics of a reaction-diffusion system
Yuncheng You
2011-02-01
Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.
On the solutions of fractional reaction-diffusion equations
Jagdev Singh
2013-05-01
Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.
ENERGY ESTIMATES FOR DELAY DIFFUSION-REACTION EQUATIONS
J.A.Ferreira; P.M.da Silva
2008-01-01
In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions.The behaviour and the stability of the solution of such initial boundary value problems(IBVPs)are studied using the energy method.Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs.Using the discrete energy method we study the stability and convergence of the numerical approximations.Numerical experiments are carried out to illustrate our theoretical results.
Parametric pattern selection in a reaction-diffusion model.
Michael Stich
Full Text Available We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
Reaction Kinetic Equation for Char Combustion of Underground Coal Gasification
YU Hong-guan; YANG Lan-he; FENG Wei-min; LIU Shu-qin; SONG Zhen-qi
2006-01-01
Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined at 900℃ using a thermo-gravimetric (TG) analyzer connected to a flue gas analyzer and this equation. The equation was simplified for specific coals, including high ash content, low ash content, and low ash fusibility ones. The results show that 1) the apparent reaction rate constant increases with an increase in volatile matter value as dry ash-free basis, 2) the effective coefficient of diffusion decreases with an increase in ash as dry basis, and 3) the mass transfer coefficient is independent of coal quality on the whole. The apparent reaction rate constant, mass-transfer coefficient and effective coefficient of diffusion of six char samples range from 7.51×104 m/s to 8.98×104 m/s, 3.05×106 m/s to 3.23×106 m/s and 5.36×106 m2/s to 8.23×106 m2/s at 900℃, respectively.
Parabolic equations in biology growth, reaction, movement and diffusion
Perthame, Benoît
2015-01-01
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
Study on the reaction kinetics in pulsed RF discharges under RIE conditions
Baggerman, Jacobus Antonius Gijsbertus
1993-10-01
In the present-day electronics industry, reactive ion etching (RIE) is a technique widely used to etch thin films anisotropically. The subject of this thesis is the determination of (reaction) kinetics of rf discharges under RIE conditions. Special attention is given to determining quantitatively the rise and decay of densities and energy distributions of plasma particles. A production-type RIE reactor was used for all experiments. In chapter 2 the ion density is determined by LIF spectroscopy in a model (N2) discharge under RIE conditions. Chapter 3 concerns energy-flux density measurements on the various parts of the etch reactor in contact with a 30 Pa nitrogen rf discharge. Chapter 4 concerns the etch mechanism of various organic polymers in oxygen and argon of discharges under RIE conditions studied by performing energy-flux density and ion-flux density measurements on the powered electrode. The polymers of interest are a novolac-based photoresist, polyimide and polymethylmethacrylate (PMMA). The density and the reaction kinetics of ground-state methylidyne (CH radical) are determined by LIF in order to determine whether small molecules in addition to atoms are sputtered from the polymer surface. In chapter 5 a model is set up in which diffusion of CH from the substrate into the gas phase and chemical reactions in the gas phase are taken into account.
Kinetic Isotopic Fractionation During Diffusion of Ionic Speciesin Water
Richter, Frank M.; Mendybaev, Ruslan A.; Christensen, John; Hutcheon, Ian D.; Williams, Ross W.; Sturchio, Neil C.; Beloso Jr.,Abelardo D.
2005-06-09
Experiments specifically designed to measure the ratio of the diffusivities of ions dissolved in water were used to determine D{sub Li}/D{sub K}, D{sub 7{sub Li}}/D{sub 6{sub Li}}, D{sub 25{sub Mg}}/D{sub 24{sub Mg}}, D{sub 26{sub Mg}}/D{sub 25{sub Mg}}, and D{sub 37{sub Cl}}/D{sub 35{sub Cl}}. The measured ratio of the diffusion coefficients for Li and K in water (D{sub Li}/D{sub K} = 0.6) is in good agreement with published data, providing evidence that the experimental design being used resolves the relative mobility of ions with adequate precision to also be used for determining the fractionation of isotopes by diffusion in water. In the case of Li we found measurable isotopic fractionation associated with the diffusion of dissolved LiCl (D{sub 7{sub Li}}/D{sub 6{sub Li}} = 0.99772 {+-} 0.00026). This difference in the diffusion coefficient of {sup 7}Li compared to {sup 6}Li is significantly less than reported in an earlier study, a difference we attribute to the fact that in the earlier study Li diffused through a membrane separating the water reservoirs. Our experiments involving Mg diffusing in water found no measurable isotopic fractionation (D{sub 25{sub Mg}}/D{sub 24{sub Mg}} = 1.00003 {+-} 0.00006). Cl isotopes were fractionated during diffusion in water (D{sub 37{sub Cl}}/D{sub 35{sub Cl}} = 0.99857 {+-} 0.00080) whether or not the co-diffuser (Li or Mg) was isotopically fractionated. The isotopic fractionation associated with the diffusion of ions in water is much smaller than values we found previously for the isotopic fractionation of Li and Ca isotopes by diffusion in molten silicate liquids. A major distinction between water and silicate liquids is that water, being a polar liquid, surrounds dissolved ions with hydration shells, which very likely play an important but still poorly understood role in reducing isotopic fractionation associated with diffusion.
Salem Abdelmalek
2014-11-01
Full Text Available In this article we construct the invariant regions for m-component reaction-diffusion systems with a tridiagonal symmetric Toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. We establish the existence of global solutions, and use Lyapunov functional methods. The nonlinear reaction term is assumed to be of polynomial growth.
The Second Stokes Problem with Specular - Diffusive Boundary Conditions in Kinetic Theory
Akimova, V A; Yushkanov, A A
2012-01-01
The second Stokes problem with specular - diffusive boundary conditions of the kinetic theory is considered. The new method of the decision of the boundary problems of the kinetic theory is applied. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation of Fredholm type of the second kind. The decision is received in the form of Neumann's series.
Stepwise kinetic equilibrium models of quantitative polymerase chain reaction
Cobbs Gary
2012-08-01
Full Text Available Abstract Background Numerous models for use in interpreting quantitative PCR (qPCR data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. Results Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the
Thermochemistry, reaction paths, and kinetics on the tert-isooctane radical reaction with O2.
Snitsiriwat, Suarwee; Bozzelli, Joseph W
2014-07-03
Thermochemical properties of tert-isooctane hydroperoxide and its radicals are determined by computational chemistry. Enthalpies are determined using isodesmic reactions with B3LYP density function and CBS QB3 methods. Application of group additivity with comparison to calculated values is illustrated. Entropy and heat capacities are determined using geometric parameters and frequencies from the B3LYP/6-31G(d,p) calculations for the lowest energy conformer. Internal rotor potentials are determined for the tert-isooctane hydroperoxide and its radicals in order to identify isomer energies. Recommended values derived from the most stable conformers of tert-isooctane hydroperoxide of are -77.85 ± 0.44 kcal mol(-1). Isooctane is a highly branched molecule, and its structure has a significant effect on its thermochemistry and reaction barriers. Intramolecular interactions are shown to have a significant effect on the enthalpy of the isooctane parent and its radicals on peroxy/peroxide systems, the R• + O2 well depths and unimolecular reaction barriers. Bond dissociation energies and well depths, for tert-isooctane hydroperoxide → R• + O2 are 33.5 kcal mol(-1) compared to values of ∼38 to 40 kcal mol(-1) for the smaller tert-butyl-O2 → R• + O2. Transition states and kinetic parameters for intramolecular hydrogen atom transfer and molecular elimination channels are characterized to evaluate reaction paths and kinetics. Kinetic parameters are determined versus pressure and temperature for the chemically activated formation and unimolecular dissociation of the peroxide adducts. Multifrequency quantum RRK (QRRK) analysis is used for k(E) with master equation analysis for falloff. The major reaction paths at 1000 K are formation of isooctane plus HO2 followed by cyclic ether plus OH. Stabilization of the tert-isooctane hydroperoxy radical becomes important at lower temperatures.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Theory of diffusion-influenced reactions in complex geometries.
Galanti, Marta; Fanelli, Duccio; Traytak, Sergey D; Piazza, Francesco
2016-06-21
Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.
Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system
Abdusalam, H.A E-mail: hosny@operamail.com; Fahmy, E.S
2003-10-01
It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional.
Göppel, Tobias; Palyulin, Vladimir V; Gerland, Ulrich
2016-07-27
An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift-diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.
Atomic scale analysis of phase formation and diffusion kinetics in Ag/Al multilayer thin films
Aboulfadl, Hisham; Gallino, Isabella; Busch, Ralf; Mücklich, Frank
2016-11-01
Thin films generally exhibit unusual kinetics leading to chemical reactions far from equilibrium conditions. Binary metallic multilayer thin films with miscible elements show some similar behaviors with respect to interdiffusion and phase formation mechanisms. Interfacial density, lattice defects, internal stresses, layer morphologies and deposition conditions strongly control the mass transport between the individual layers. In the present work, Ag/Al multilayer thin films are used as a simple model system, in which the effects of the sputtering power and the bilayer period thickness on the interdiffusion and film reactions are investigated. Multilayers deposited by DC magnetron sputtering undergo calorimetric and microstructural analyses. In particular, atom probe tomography is extensively used to provide quantitative information on concentration gradients, grain boundary segregations, and reaction mechanisms. The magnitude of interdiffusion was found to be inversely proportional to the period thickness for the films deposited under the same conditions, and was reduced using low sputtering power. Both the local segregation at grain boundaries as well as pronounced non-equilibrium supersaturation effects play crucial roles during the early stages of the film reactions. For multilayers with small periods of 10 nm supersaturation of the Al layers with Ag precedes the polymorphic nucleation and growth of the hcp γ-Ag2Al phase. In larger periods the γ phase formation is triggered at junctions between grain boundaries and layers interfaces, where the pathway to heterogeneous nucleation is local supersaturation. Other Ag-rich phases also form as intermediate phases due to asymmetric diffusion rates of parent phases in the γ phase during annealing.
Database of atomistic reaction mechanisms with application to kinetic Monte Carlo.
Terrell, Rye; Welborn, Matthew; Chill, Samuel T; Henkelman, Graeme
2012-07-07
Kinetic Monte Carlo is a method used to model the state-to-state kinetics of atomic systems when all reaction mechanisms and rates are known a priori. Adaptive versions of this algorithm use saddle searches from each visited state so that unexpected and complex reaction mechanisms can also be included. Here, we describe how calculated reaction mechanisms can be stored concisely in a kinetic database and subsequently reused to reduce the computational cost of such simulations. As all accessible reaction mechanisms available in a system are contained in the database, the cost of the adaptive algorithm is reduced towards that of standard kinetic Monte Carlo.
CHEN LaiWen; WANG JingHua; LEE Chun-Hian
2009-01-01
When hyperthermal atomic oxygen collides with a silicon surface, an ultrathin oxidation regime characterized by fractional atomic-oxygen anions having low diffusive and reactive barriers, along with their enhanced diffusion due to both the electric field and image potential, will form on the surface. In accordance with these properties, an attempt was made in the present study to modify the AlmeidaGoncalves-Baumvol (AGB) model by setting the diffusivity and reaction rate constant to be diffusion-length dependence. According to the modified model, numerical parametric studies for oxidation thin growth were performed. The dependencies of the diffusion coefficient, the reaction rate constant,the attenuation length, and the adjustable parameter upon the translational kinetic energy, flux, temperature, and tangential flux of atomic oxygen were analyzed briefly via the fitting of the experimental data given by Tagawa et al. The numerical results confirmed the rationality of the modified diffusion-reaction model. The model together with the computer code developed in this study would be a useful tool for thickness evaluation of the protective film against the oxidation of atomic oxygen toward spacecraft surface materials in LEO environment.
A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics.
Saxton, Michael J
2008-02-01
Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.
RESEARCH OF KINETIC AND DIFFUSIVE MECHANISMS IN THE ADSORPTION OF Cu (II IN SUGAR CANE BAGASSE ASH
Julio Omar Prieto García
2016-10-01
Full Text Available In this paper a kinetic and diffusive study regarding adsorption of ions Cu (II on a sample of sugar cane bagasse ash is made. The results show that the second-order kinetic model better adjusts the experimental data than the Elovich and first-order kinetic model. The diffusive mechanism study shows that the diffusion in the liquid pellicle and in the micro-pores of the adsorbent prevail in the adsorption phenomenon.
Bandopadhyay, Aditya; Méheust, Yves; Dentz, Marco
2016-01-01
Mixing fronts, where fluids of different chemical compositions mix with each other, are typically subjected to velocity gradients, ranging from the pore scale to the catchment scale due to permeability variations and flow line geometries. A common trait of these processes is that the mixing interface is strained by shear. Depending on the P\\'eclet number $Pe$, which represents the ratio of the characteristic diffusion time to the characteristic advection time, and the Damk\\"ohler 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. This impact has been characterized mostly either in kinetics-limited or in mixing-limited conditions, that is, for either very low or very high $Da$. Here the coupling of shear flow and chemical reactivity is investigated for arbitrary Damk\\"ohler numbers, for a bimolecular reaction and an initial interface with separated reactants....
Interface diffusion kinetics and lifetime scaling in multilayer Bragg optics
van de Kruijs, Robbert Wilhelmus Elisabeth; Bruijn, S.; Yakshin, Andrey; Nedelcu, I.; Bijkerk, Frederik; van de Kruijs, R.W.E.
2011-01-01
The internal structure of Mo/Si multilayers is investigated during and after thermal annealing. Multilayer period compaction is shown to result from diffusion induced MoSi2 interlayer growth, reducing optical contrast and changing the reflected wavelength. We focus on early-stage interface growth
Ocampo-Perez, Raul; Leyva-Ramos, Roberto; Mendoza-Barron, Jovita; Guerrero-Coronado, Rosa M
2011-12-01
The concentration decay curves for the adsorption of phenol on organobentonite were obtained in an agitated tank batch adsorber. The experimental adsorption rate data were interpreted with diffusional models as well as first-order, second-order and Langmuir kinetic models. The surface diffusion model adjusted the data quite well, revealing that the overall rate of adsorption was controlled by surface diffusion. Furthermore, the surface diffusion coefficient increased raising the mass of phenol adsorbed at equilibrium and was independent of the particle diameter in the range 0.042-0.0126 cm. It was demonstrated that the overall rate of adsorption was essentially not affected by the external mass transfer. The second-order and the Langmuir kinetic models fitted the experimental data quite well; however, the kinetic constants of both models varied without any physical meaning while increasing the particle size and the mass of phenol adsorbed at equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.
ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.
Johannes Schöneberg
Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.
Chlorination of parabens: reaction kinetics and transformation product identification.
Mao, Qianhui; Ji, Feng; Wang, Wei; Wang, Qiquan; Hu, Zhenhu; Yuan, Shoujun
2016-11-01
The reactivity and fate of parabens during chlorination were investigated in this work. Chlorination kinetics of methylparaben (MeP), ethylparaben (EtP), propylparaben (PrP), and butylparaben (BuP) were studied in the pH range of 4.0 to 11.0 at 25 ± 1 °C. Apparent rate constants (k app) of 9.65 × 10(-3) M(-0.614)·s(-1), 1.77 × 10(-2) M(-1.019)·s(-1), 2.98 × 10(-2) M(-0.851)·s(-1), and 1.76 × 10(-2) M(-0.860)·s(-1) for MeP, EtP, PrP, and BuP, respectively, were obtained at pH 7.0. The rate constants depended on the solution pH, temperature, and NH4(+) concentration. The maximum k app was obtained at pH 8.0, and the minimum value was obtained at pH 11.0. The reaction rate constants increased with increasing temperature. When NH4(+) was added to the solution, the reaction of parabens was inhibited due to the rapid formation of chloramines. Two main transformation products, 3-chloro-parabens and 3,5-dichloro-parabens, were identified by GC-MS and LCMS-IT-TOF, and a reaction pathway was proposed. Dichlorinated parabens accumulated in solution, which is a threat to human health and the aqueous environment.
Non linear prompt neutron kinetics in multigroup diffusion theory
Ghatak, Ajoy Kumar
1963-06-15
It is shown that in the usual point kinetics formulation of the Fuch's model the assumption that the basic quantity is the ratio of prompt negative temperature coefficient to prompt neutron lifetime is correct in the limit that the higher mode effects can be neglected. The criticality calculation needed to calculate this coefficient is defined. The effect on the Fuch's model when the heat capacity and temperature coefficient vary linearly with temperature and delayed neutrons are taken into account is considered. The higher mode contributions in the presence of temperature feed-back effects are estimated. A method for calculating the space-dependent effects in non-linear kinetics is outlined. An analysis of the transient behavior of the TREAT reactor is also given. (C.E.S.)
Theory and application of stability for stochastic reaction diffusion systems
LUO Qi; DENG FeiQi; MAO XueRong; BAO JunDong; ZHANG YuTian
2008-01-01
So far, the Lyapunov direct method is still the moat effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding Ito formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the Ito stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, end exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob-tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Franz, Benjamin; Chapman, S Jonathan; Erban, Radek
2012-01-01
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface which partitions the domain and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.
Guiding brine shrimp through mazes by solving reaction diffusion equations
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
Reaction kinetics of solid fuels during entrained flow gasification
Tremel, Alexander
2012-10-24
Langmuir-Hinshelwood type equations. In the thermogravimetric analysis it is observed that the reactivity of char strongly depends on devolatilisation conditions. At higher temperature and longer time scales the char reactivity declines due to thermal deactivation. Standard char reactivity is measured in an atmospheric thermogravimetric analyser at 375 C to 400 C and in an oxygen containing atmosphere. The loss of reactivity can be described by a thermal deactivation model. As the influence of mass transport limitations on char conversion at high temperature cannot be measured directly, an effectiveness factor approach is derived to describe pore diffusion. A Sherwood Number correlation is used to account for boundary layer diffusion. The mass transport limitation models are combined with the submodels for devolatilisation, intrinsic reactivity, specific surface area evolution, and thermal char deactivation. The PiTER is modelled as a one-dimensional plug flow reactor, and a good correlation between experimental data and model predictions is achieved. The only adjustable parameter is the average pore diameter in the pore diffusion submodel. The model prediction is best for an average pore size of 47 Aa which is in the expected range as char conversion occurs in micro and mesopores. In order to transfer the data to technical applications, the model framework is used to design and optimise industrial scale entrained flow gasifiers. A 500 MW entrained flow gasifier operated at 2.5 MPa is modelled for the conversion of Rhenish lignite. The axial temperature profile and gas concentrations within the reaction zone are predicted, and the influence of gasifier volume and operation parameters on cold gas efficiency (CGE) and fuel conversion is analysed. The optimum oxygen to fuel stoichiometry leads to a cold gas efficiency of 79.7 %. However, a stoichiometry above the optimum might be required to achieve a higher fuel conversion and to adjust the gasifier outlet temperature to
SDDEs limits solutions to sublinear reaction-diffusion SPDEs
Hassan Allouba
2003-11-01
Full Text Available We start by introducing a new definition of solutions to heat-based SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations limits solutions. In contrast to the standard direct definition of SPDEs solutions; this new notion, which builds on and refines our SDDEs approach to SPDEs from earlier work, is entirely based on the approximating SDDEs. It is applicable to, and gives a multiscale view of, a variety of SPDEs. We extend this approach in related work to other heat-based SPDEs (Burgers, Allen-Cahn, and others and to the difficult case of SPDEs with multi-dimensional spacial variable. We focus here on one-spacial-dimensional reaction-diffusion SPDEs; and we prove the existence of a SDDEs limit solution to these equations under less-than-Lipschitz conditions on the drift and the diffusion coefficients, thus extending our earlier SDDEs work to the nonzero drift case. The regularity of this solution is obtained as a by-product of the existence estimates. The uniqueness in law of our SPDEs follows, for a large class of such drifts/diffusions, as a simple extension of our recent Allen-Cahn uniqueness result. We also examine briefly, through order parameters $epsilon_1$ and $epsilon_2$ multiplied by the Laplacian and the noise, the effect of letting $epsilon_1,epsilon_2o 0$ at different speeds. More precisely, it is shown that the ratio $epsilon_2/epsilon_1^{1/4}$ determines the behavior as $epsilon_1,epsilon_2o 0$.
Characterization of Cocycle Attractors for Nonautonomous Reaction-Diffusion Equations
Cardoso, C. A.; Langa, J. A.; Obaya, R.
In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction-diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li-Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee-Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability. PMID:25474327
Diffusion kinetics of nitrogen in tantalum during plasma-nitriding
张德元; 林勤; 曾卫军; 李放; 许兰萍; 付青峰
2001-01-01
The activation energies of nitrogen in tantalum on plasma nitriding conditions were calculated according to the experimental data of hardness of plasma-nitriding of tantalum vs time and temperature. The activation energy calculated is 148.873±0.390 kJ/mol. The depth increasing of nitriding layer with time follows square root relation. The nitriding process of tantalum is controlled by diffusion of nitrogen atoms in tantalum solid solution.
Bergner, Jennifer B; Rajappan, Mahesh; Fayolle, Edith C
2016-01-01
Interstellar complex organic molecules (COMs) are commonly observed during star formation, and are proposed to form through radical chemistry in icy grain mantles. Reactions between ions and neutral molecules in ices may provide an alternative cold channel to complexity, as ion-neutral reactions are thought to have low or even no energy barriers. Here we present a study of a the kinetics and mechanisms of a potential ion-generating acid-base reaction between NH$_{3}$ and HCOOH to form the salt NH$_{4}^{+}$HCOO$^{-}$. We observe salt growth at temperatures as low as 15K, indicating that this reaction is feasible in cold environments. The kinetics of salt growth are best fit by a two-step model involving a slow "pre-reaction" step followed by a fast reaction step. The reaction energy barrier is determined to be 70 $\\pm$ 30K with a pre-exponential factor 1.4 $\\pm$ 0.4 x 10$^{-3}$ s$^{-1}$. The pre-reaction rate varies under different experimental conditions and likely represents a combination of diffusion and or...
Kinetic structure of the electron diffusion region in antiparallel magnetic reconnection.
Ng, J; Egedal, J; Le, A; Daughton, W; Chen, L-J
2011-02-11
Strong electron pressure anisotropy has been observed upstream of electron diffusion regions during reconnection in Earth's magnetotail and kinetic simulations. For collisionless antiparallel reconnection, we find that the anisotropy drives the electron current in the electron diffusion region, and that this current is insensitive to the reconnection electric field. Reconstruction of the electron distribution function within this region at enhanced resolutions reveals its highly structured nature and the mechanism by which the pressure anisotropy sets the structure of the region.
Interior Controllability of a 2×2 Reaction-Diffusion System with Cross-Diffusion Matrix
Hugo Leiva
2009-01-01
Full Text Available We prove the interior approximate controllability for the following 2×2 reaction-diffusion system with cross-diffusion matrix ut=aΔu−β(−Δ1/2u+bΔv+1ωf1(t,x in (0,τ×Ω, vt=cΔu−dΔv−β(−Δ1/2v+1ωf2(t,x in (0,τ×Ω, u=v=0, on (0,T×∂Ω, u(0,x=u0(x, v(0,x=v0(x, x∈Ω, where Ω is a bounded domain in ℝN (N≥1, u0,v0∈L2(Ω, the 2×2 diffusion matrix D=[abcd] has semisimple and positive eigenvalues 0<ρ1≤ρ2, β is an arbitrary constant, ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, and the distributed controls f1,f2∈L2([0,τ];L2(Ω. Specifically, we prove the following statement: if λ11/2ρ1+β>0 (where λ1 is the first eigenvalue of −Δ, then for all τ>0 and all open nonempty subset ω of Ω the system is approximately controllable on [0,τ].
Yan NIU; F. Gesmundo
2003-01-01
The phase diagrams of ternary systems involving two metal components and one oxidant are considered first, the limitations to their use is discussed in relation to the high temperature oxidation of binary alloys. Kinetic diagrams,which are useful to predict the conditions for the stability of the two mutually insoluble oxides as the external scale, are then calculated on the basis of thermodynamic and kinetic data concerning both the alloys and the oxides, assuming the validity of the parabolic rate law. A combination of the two types of diagrams provides a more detail information about the oxidation behavior of binary alloys. The calculation of the diffusion paths, which relate the oxidant pressure to the composition of the system in terms of the alloy components both in the alloy and in the scale during an initial stage of the reaction in the presence of the parabolic rate law, is finally developed.
Gargano, Immacolata; Olivieri, Giuseppe; Spasiano, Danilo; Andreozzi, Roberto; Pollio, Antonino; Marotta, Raffaele; Ambrosio, D' Nicola; Marzocchella, Antonio
2015-01-01
The kinetic characterization of the photosynthetic activity in autotrophic microalgae plays a key role in the design of optimized photobioreactors. This paper presents a procedure to assess kinetic parameters of a three-state photosynthetic reaction centres model. Four kinetic parameters of the
Zhang, Yongfeng; Jiang, Chao; Bai, Xianming
2017-01-01
This report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along is found to be slightly higher than that along , with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins. PMID:28106154
Zhang, Yongfeng; Jiang, Chao; Bai, Xianming
2017-01-01
This report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along is found to be slightly higher than that along , with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-22
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-01
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Borisenko, Alexander
2016-05-01
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface, and, therefore, the entire nucleation-growth kinetics is altered. Unless quite obvious, this effect has been ignored in classical nucleation theory. To illustrate the results of this approach, for the case of homogeneous nucleation, we calculate the total solubility and the nucleation rate as functions of two parameters of the model (the reduced interface energy and the inverse second Damköhler number), and we compare these results to the classical ones. One can conclude that discrepancies with classical nucleation theory are great in the diffusion-limited regime, when the rate of bulk diffusion is small compared to the rate of interface reactions, while in the opposite interface-limited case they vanish.
Study of the diffusion of points defects in crystalline silicon using the kinetic ART method
Trochet, Mickael; Brommer, Peter; Beland, Laurent-Karim; Joly, Jean-Francois; Mousseau, Normand
2013-03-01
Because of the long-time scale involved, the activated diffusion of point defects is often studied in standard molecular dynamics at high temperatures only, making it more difficult to characterize complex diffusion mechanisms. Here, we turn to the study of point defect diffusion in crystalline silicon using kinetic ART (kART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building based on the activation-relaxation technique (ART nouveau). By generating catalogs of diffusion mechanisms and fully incorporating elastic and off-lattice effects, kART is a unique tool for characterizing this problem. More precisely, using kART with the standard Stillinger-Weber potential we consider the evolution of crystalline cells with 1 to 4 vacancies and 1 to 4 interstitials at various temperatures and to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics in addition to identifying special configurations such as a 2-interstitial super-diffuser.
Reply to Comment on "Enhanced diffusion of enzymes that catalyze exothermic reactions"
Golestanian, Ramin
2016-01-01
Catalytically active enzymes have recently been observed to exhibit enhanced diffusion. In a recent work [C. Riedel et al., Nature 517, 227 (2015)], it has been suggested that this phenomenon is correlated with the degree of exothermicity of the reaction, and a mechanism was proposed to explain the phenomenon based on channeling the released heat into the center of mass kinetic energy of the enzyme. I addressed this question by comparing four different mechanisms, and concluded that collective heating is the strongest candidate out of those four to explain the phenomenon, and in particular, several orders of magnitude stronger than the mechanism proposed by Riedel et al. In a recent preprint (arXiv:1608.05433), K. Tsekouras, C. Riedel, R. Gabizon, S. Marqusee, S. Presse, and C. Bustamante present a comment on my paper [R. Golestanian, Phys. Rev. Lett. 115, 108102 (2015); arXiv:1508.03219], which I address here in this reply.
Park, Soohyung; Agmon, Noam
2008-05-15
We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.
Kinetics of the Reaction of CO2 with Aqueous Potassium Salt of Taurine and Glycine
Kumar, P.S.; Hogendoorn, J.A.; Versteeg, G.F.; Feron, P.H.M.
2003-01-01
The kinetics of the reaction between CO2 and aqueous potassium salts of taurine and glycine was measured at 295 K in a stirred-cell reactor with a flat gas–liquid interface. For aqueous potassium taurate solutions, the temperature effect on the reaction kinetics was measured at 285 and 305 K. Unlike
Reaction Kinetics in cw Rare-Gas Halogen Lamps
Salvermoser, M.; Murnick, D. E.; Ulrich, A.; Wieser, J.
1999-10-01
Pumping with a continuous low energy (excimer gas mixtures, the reaction kinetics leading to efficient vuv emission from ArF and F2 at 193nm and 157nm respectively has been studied. The scaling of the pumping power density with energy to the inverse 2.5 power and cube of the pressure allows a wide range of pumping rates to be considered. And, by studying the spectrum and yield as a function of pressure and gas mixture, optimum conditions for vuv emission can be determined and specific formation and quenching channels can be isolated. Energy transfer efficiency near 10% has been obtained at 193nm for neon-argon-fluorine (1:0.008:0.0004) mixtures and at 157nm for neon-fluorine (1:0.002) at two to three bar pressure. Lamps emitting tens of milliwatts light output from a 0.8mm diameter point have been stable for tens of hours. Scaling to at least 10W/cm^2str continuous output is possible.
Aquilanti, Vincenzo; Coutinho, Nayara Dantas; Carvalho-Silva, Valter Henrique
2017-03-01
This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.
Accelerated stochastic and hybrid methods for spatial simulations of reaction-diffusion systems
Rossinelli, D; Bayati, B; Koumoutsakos, P.
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial т-Leaping (Sт -Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid т-Leaping (Hт-Leaping), combining a deterministic diffusion approximation with a т-Leaping acceleration of the stochastic reactions. The algorithms are v...
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.
A practical guide to stochastic simulations of reaction-diffusion processes
Erban, Radek; Chapman, Jonathan; Maini, Philip
2007-01-01
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given. Finally, basic stochastic reaction-diffusion methods are presented. The connections between stochastic simul...
2005-01-01
International audience; This article, the second in the series, presents kinetic and photochemical data evaluated by the IUPAC Subcommittee on Gas Kinetic Data Evaluation for Atmospheric Chemistry. It covers the gas phase and photochemical reactions of Organic species, which were last published in 1999, and were updated on the IUPAC website in late 2002. The article consists of a summary sheet, containing the recommended kinetic parameters for the evaluated reactions, and eight appendices con...
A reaction diffusion model of pattern formation in clustering of adatoms on silicon surfaces
Trilochan Bagarti
2012-12-01
Full Text Available We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically.
Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry.
Hansen, Lee D; Transtrum, Mark K; Quinn, Colette; Demarse, Neil
2016-05-01
Isothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data. This article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions. A complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error. Methods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. Copyright © 2015 Elsevier B.V. All rights reserved.
Kinetic Monte Carlo Simulation of Cation Diffusion in Low-K Ceramics
Good, Brian
2013-01-01
Low thermal conductivity (low-K) ceramic materials are of interest to the aerospace community for use as the thermal barrier component of coating systems for turbine engine components. In particular, zirconia-based materials exhibit both low thermal conductivity and structural stability at high temperature, making them suitable for such applications. Because creep is one of the potential failure modes, and because diffusion is a mechanism by which creep takes place, we have performed computer simulations of cation diffusion in a variety of zirconia-based low-K materials. The kinetic Monte Carlo simulation method is an alternative to the more widely known molecular dynamics (MD) method. It is designed to study "infrequent-event" processes, such as diffusion, for which MD simulation can be highly inefficient. We describe the results of kinetic Monte Carlo computer simulations of cation diffusion in several zirconia-based materials, specifically, zirconia doped with Y, Gd, Nb and Yb. Diffusion paths are identified, and migration energy barriers are obtained from density functional calculations and from the literature. We present results on the temperature dependence of the diffusivity, and on the effects of the presence of oxygen vacancies in cation diffusion barrier complexes as well.
Wang, Shangping; Oldenhof, Harriëtte; Dai, Xiaolei; Haverich, Axel; Hilfiker, Andres; Harder, Michael; Wolkers, Willem F
2014-02-01
Decellularized tissues can be used as matrix implants. The aims of this study were to investigate protein stability and solvent accessibility in decellularized pulmonary heart valve tissues. Protein denaturation profiles of tissues were studied by differential scanning calorimetry. Protein solvent accessibility of tissue exposed to D2O, and diffusion kinetics of various protective molecules were studied by Fourier transform infrared spectroscopy. Little changes were observed in the protein denaturation temperature during storage, at either 5 or 40°C. Glycerol was found to stabilize proteins; it increased the protein denaturation temperature. The stabilizing effect of glycerol disappeared after washing the sample with saline solution. Hydrogen-to-deuterium exchange rates of protein amide groups were fastest in leaflet tissue, followed by artery and muscle tissue. Diffusion of glycerol was found to be fastest in muscle tissue, followed by artery and leaflet tissue. Diffusion coefficients were derived and used to estimate the time needed to reach saturation. Fixation of tissue with glutaraldehyde had little effects on exchange and diffusion rates. Diffusion rates decreased with increasing molecular size. Proteins in decellularized heart valve tissue are stable during storage. Glycerol increases protein stability in a reversible manner. Solvent accessibility studies of protein amide groups provide an additional tool to study proteins in tissues. Diffusion coefficients can be derived to simulate diffusion kinetics of protective molecules in tissues. This study provides novel tools to evaluate protein stability and solvent accessibility in tissues, which can be used to develop biopreservation strategies.
Kinetic theory of self-diffusion in a moderately dense one-component plasma
Suttorp, L.G.
1980-01-01
A microscopic description of self-diffusion in a moderately dense classical one-component plasma is given on the basis of renormalized kinetic theory. The effects of close binary collisions and of collective interactions in the plasma are taken into account through the use of a composite memory kern
Trochet, Mickaël; Béland, Laurent Karim; Joly, Jean-François; Brommer, Peter; Mousseau, Normand
2015-06-01
We study point-defect diffusion in crystalline silicon using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities based on the activation-relaxation technique (ART nouveau), coupled to the standard Stillinger-Weber potential. We focus more particularly on the evolution of crystalline cells with one to four vacancies and one to four interstitials in order to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics. We show formation energies, activation barriers for the ground state of all eight systems, and migration barriers for those systems that diffuse. Additionally, we characterize diffusion paths and special configurations such as dumbbell complex, di-interstitial (IV-pair+2I) superdiffuser, tetrahedral vacancy complex, and more. This study points to an unsuspected dynamical richness even for this apparently simple system that can only be uncovered by exhaustive and systematic approaches such as the kinetic activation-relaxation technique.
Xu, Yanhui; Wu, Jun; Li, Decheng; Zheng, Junwei [The Institute of Chemical Power Sources, Soochow (Suzhou) University, Suzhou 215006 (China); Chen, Ying [Max-Planck-Institut fuer Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Duesseldorf (Germany); Ju, Hua [School of Urban Rail Transportation, Soochow (Suzhou) University, Ganjiang East Road 178, Suzhou 215021 (China)
2010-06-15
The derivation and proposal of major electrochemical techniques used to determine and calculate the electrochemical kinetic parameters is basically based on the electrochemical reaction taking place at liquid/solid or liquid/liquid interface in which all the reactants and products are soluble in liquid aqueous solution or liquid mercury electrode, or are volatile gas. Such electrochemical reaction system is classical and traditional (ERS1). Recently, the electrochemical behavior of some materials used as the active electrode materials in chemical power sources has attracted much attention. In chemical power source systems, either reactant or product, or both are insoluble. This kind of electrochemical reaction system (ERS2) is slightly different from ERS1. The application of these electrochemical techniques/equations to chemical power sources' system requires carefulness. The misuse of these electrochemical techniques can be easily found in the literatures and some of them even lead to a wrong conclusion. In this review, almost all the electrochemical techniques to measure the exchange current and diffusion coefficient were compiled for reference to the readers, including pulse step, electrochemical impedance, alternating cyclic voltammetry, etc. The necessary requirements/conditions to apply these techniques have been briefly discussed and some simple examples were also discussed for a better understanding. (author)
Pontes, P. C.; Naveira-Cotta, C. P.
2016-09-01
The theoretical analysis for the design of microreactors in biodiesel production is a complicated task due to the complex liquid-liquid flow and mass transfer processes, and the transesterification reaction that takes place within these microsystems. Thus, computational simulation is an important tool that aids in understanding the physical-chemical phenomenon and, consequently, in determining the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. A diffusive-convective-reactive coupled nonlinear mathematical model, that governs the mass transfer process during the transesterification reaction in parallel plates microreactors, under isothermal conditions, is here described. A hybrid numerical-analytical solution via the Generalized Integral Transform Technique (GITT) for this partial differential system is developed and the eigenfunction expansions convergence rates are extensively analyzed and illustrated. The heuristic method of Particle Swarm Optimization (PSO) is applied in the inverse analysis of the proposed direct problem, to estimate the reaction kinetics constants, which is a critical step in the design of such microsystems. The results present a good agreement with the limited experimental data in the literature, but indicate that the GITT methodology combined with the PSO approach provide a reliable computational algorithm for direct-inverse analysis in such reactive mass transfer problems.
Chemical Reactions and Kinetics of the Carbon Monoxide Coupling in the Presence of Hydrogen
Fandong Meng; Genhui Xu; Zhenhua Li; Pa Du
2002-01-01
The chemical reactions and kinetics of the catalytic coupling reaction of carbon monoxide to diethyl oxalate were studied in the presence of hydrogen over a supported palladium catalyst in the gaseous phase at the typical coupling reaction conditions. The experiments were performed in a continuous flow fixed-bed reactor. The results indicated that hydrogen only reacts with ethyl nitrite to form ethanol, and kinetic studies revealed that the rate-determining step is the surface reaction of adsorbed hydrogen and the ethoxy radical (EtO-). A kinetic model is proposed and a comparison of the observed and calculated conversions showed that the rate expressions are of rather high confidence.
Complex kinetics of a Landolt-type reaction: the later phase of the thiosulfate-iodate reaction.
Varga, Dénes; Nagypál, István; Horváth, Attila K
2010-05-13
The thiosulfate-iodate reaction has been studied spectrophotometrically in slightly acidic medium at 25.0 +/- 0.1 degrees C in acetate/acetic acid buffer by monitoring the absorbance at 468 nm at the isosbestic point of iodine-triiodide ion system. The formation of iodine after the Landolt time follows a rather complex kinetic behavior depending on the pH and on the concentration of the reactants as well. It is shown that the key intermediate of the reaction is I(2)O(2), its equilibrium formation from the well-known Dushman reaction along with their further reactions followed by subsequent reactions of HOI, HIO(2), S(2)O(3)OH(-), and S(2)O(3)I(-) adequately accounts for all the experimentally measured characteristics of the kinetic curves. A 19-step kinetic model is proposed and discussed with 13 fitted and 7 fixed parameters in detail.
The First Integral Method to Study a Class of Reaction-Diffusion Equations
KE Yun-Quan; YU Jun
2005-01-01
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
Wang, Li; Yan, Bokai
2016-05-01
We present a new asymptotic-preserving scheme for the linear Boltzmann equation which, under appropriate scaling, leads to a fractional diffusion limit. Our scheme rests on novel micro-macro decomposition to the distribution function, which splits the original kinetic equation following a reshuffled Hilbert expansion. As opposed to classical diffusion limit, a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter. Our idea is, while solving the macro-micro part in a truncated velocity domain (truncation only depends on numerical accuracy), to incorporate an integrated tail over the velocity space that is beyond the truncation, and its major component can be precomputed once with any accuracy. Such an addition is essential to drive the solution to the correct asymptotic limit. Numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes.
Zhang, Fan [ORNL; Yeh, Gour-Tsyh [University of Central Florida, Orlando; Parker, Jack C [ORNL; Brooks, Scott C [ORNL; Pace, Molly [ORNL; Kim, Young Jin [ORNL; Jardine, Philip M [ORNL; Watson, David B [ORNL
2007-01-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C.; Brooks, Scott C.; Pace, Molly N.; Kim, Young-Jin; Jardine, Philip M.; Watson, David B.
2007-06-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M- NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
Kinetic modelling of GlmU reactions - prioritization of reaction for therapeutic application.
Vivek K Singh
Full Text Available Mycobacterium tuberculosis(Mtu, a successful pathogen, has developed resistance against the existing anti-tubercular drugs necessitating discovery of drugs with novel action. Enzymes involved in peptidoglycan biosynthesis are attractive targets for antibacterial drug discovery. The bifunctional enzyme mycobacterial GlmU (Glucosamine 1-phosphate N-acetyltransferase/ N-acetylglucosamine-1-phosphate uridyltransferase has been a target enzyme for drug discovery. Its C- and N- terminal domains catalyze acetyltransferase (rxn-1 and uridyltransferase (rxn-2 activities respectively and the final product is involved in peptidoglycan synthesis. However, the bifunctional nature of GlmU poses difficulty in deciding which function to be intervened for therapeutic advantage. Genetic analysis showed this as an essential gene but it is still unclear whether any one or both of the activities are critical for cell survival. Often enzymatic activity with suitable high-throughput assay is chosen for random screening, which may not be the appropriate biological function inhibited for maximal effect. Prediction of rate-limiting function by dynamic network analysis of reactions could be an option to identify the appropriate function. With a view to provide insights into biochemical assays with appropriate activity for inhibitor screening, kinetic modelling studies on GlmU were undertaken. Kinetic model of Mtu GlmU-catalyzed reactions was built based on the available kinetic data on Mtu and deduction from Escherichia coli data. Several model variants were constructed including coupled/decoupled, varying metabolite concentrations and presence/absence of product inhibitions. This study demonstrates that in coupled model at low metabolite concentrations, inhibition of either of the GlmU reactions cause significant decrement in the overall GlmU rate. However at higher metabolite concentrations, rxn-2 showed higher decrement. Moreover, with available intracellular
Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.
Dhillon, Daljit Singh J; Milinkovitch, Michel C; Zwicker, Matthias
2017-04-01
In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.
Stochastic flows, reaction-diffusion processes, and morphogenesis
Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.
1983-02-01
Recently, an exact procedure has been introduced (C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)) for calculating the expected walk length
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics
Biderman, N. J.; Sundaramoorthy, R.; Haldar, Pradeep; Lloyd, J. R.
2016-05-01
Two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) were conducted to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se2 (CIGS) and Cu2ZnSn(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 the 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. 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.
Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics
N. J. Biderman
2016-05-01
Full Text Available Two sets of diffusion-reaction numerical simulations using a finite difference method (FDM were conducted to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,GaSe2 (CIGS and Cu2ZnSn(S, Se4 (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 the 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. 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.
Diffusion Kinetics of Chromium in a Novel Super304H Stainless Steel
Ping, Shao Bo; Xie, Fei; Wang, Rui Kun; Zheng, Zhi Jun; Gao, Yan
2017-02-01
Diffusion behavior and diffusion kinetics of chromium (Cr) from the pure chromium coating in the matrix of Super304H and TP304H steels were investigated in a temperature range of 600-900 ℃ by using energy-dispersive spectrum (EDS) quantitative line scanning and Fick's second law of diffusion. Pure Cr coating was obtained by electroplating. Experimental results show that the diffusion depth and diffusivity of Cr increase gradually with the increase in temperature. The diffusion activation energy of Cr is found to be lower and the diffusion coefficient of Cr to be higher in the Super304H steel than those in the TP304H steel at the same temperature. Furthermore, the diffusion equation of Cr in the Super304H and TP304H steels is D_{Cr/Super304H} = 1.08 × 10^-15{exp(-6.08 × 10^4/RT) and D_{Cr/TP304H} = 2.29 × 10^-15{exp (-7.44 × 10^4/RT), respectively.
An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene
Kehua Zhong
2017-07-01
Full Text Available The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex.
Some kinetics aspects of chlorine-solids reactions
Kanari, N.
2010-02-01
Full Text Available The present paper describes detailed kinetics investigations on some selected chlorine-solid reactions through thermogravimetric measurements. The solids studied in this article include chemical pure oxides and sulfides as well as their natural bearing materials. The chlorinating agents employed are gaseous mixtures of Cl_{2}+N_{2} (chlorination, Cl_{2}+O_{2} (oxychlorination, and Cl_{2}+CO (carbochlorination. Results are presented as effects of various parameters on the reaction rate of these solids with these chlorinating agents. It was observed that the reactivity of these solids towards different chlorinating agents varied widely. Sulfides could be chlorinated at room temperature, while carbochlorination of chromium (III oxide was possible only above 500 °C. The variation of the chlorination rate of these complex materials with respect to gas velocity, composition and temperature enabled us to focus some light on the plausible reaction mechanisms and stoichiometries. The obtained results were used for selective removal of iron from chromite concentrates, extraction of valuable metals from sulfide materials, purification of MgO samples, etc.
Este trabajo describe detalladas investigaciones cinéticas en algunas reacciones seleccionadas de cloro-sólido a través de medidas termogravimétricas. Los sólidos estudiados en este artículo incluyen óxidos químicos puros y sulfuros, así como sus materiales naturales de soporte. Los agentes de cloración empleados son mezclas de gases de Cl_{2}+N_{2} (cloración, Cl_{2}+O_{2} (oxicloración y Cl_{2}+O_{2} (carbocloración. Los resultados se presentan como efecto de varios parámetros en el porcentaje de reacción de estos sólidos con los agentes de cloración. Se ha observado que la reactividad de estos sólidos a través de diferentes agentes de cloración varía ampliamente. Los sulfuros se pudieron
Estimation and prediction of convection-diffusion-reaction systems from point measurement
Vries, D.
2008-01-01
Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the propos
LEE; Chun-Hian
2009-01-01
When hyperthermal atomic oxygen collides with a silicon surface, an ultrathin oxidation regime characterized by fractional atomic-oxygen anions having low diffusive and reactive barriers, along with their enhanced diffusion due to both the electric field and image potential, will form on the surface. In ac- cordance with these properties, an attempt was made in the present study to modify the Almeida- Goncalves-Baumvol (AGB) model by setting the diffusivity and reaction rate constant to be diffu- sion-length dependence. According to the modified model, numerical parametric studies for oxidation thin growth were performed. The dependencies of the diffusion coefficient, the reaction rate constant, the attenuation length, and the adjustable parameter upon the translational kinetic energy, flux, tem- perature, and tangential flux of atomic oxygen were analyzed briefly via the fitting of the experimental data given by Tagawa et al. The numerical results confirmed the rationality of the modified diffu- sion-reaction model. The model together with the computer code developed in this study would be a useful tool for thickness evaluation of the protective film against the oxidation of atomic oxygen toward spacecraft surface materials in LEO environment.
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.
QIN Yan; LIU Haihua; HUANG Zhixiong; MEI Qilin
2007-01-01
Several kinetic models for unsaturated polyester cure reaction and some existing parameter estimation techniques of these models were introduced. Correlated kinetic parameters and kinetic equations of the autocatalytic empirical kinetic model of LPSMC system were determined by using isothermal DSC to scan the system which was thickened by crystalline polymer (PEG-MAH). Through using a serial curing degree of the system to validate the model, the experimental results were basically identical with the predictions of the autocatalytic empirical kinetic model. This model could provide a theoretical reference to the determination of molding techniques of low pressure SMC.
A reaction-diffusion model of human brain development.
Julien Lefèvre
2010-04-01
Full Text Available Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds and gyri (top of folds. We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to initial conditions in our model. Last but not least, the parameters of our model are able to produce different kinds of patterns that can be linked to developmental pathologies such as polymicrogyria and lissencephaly. The main significance of our model is that it proposes a first approach to the issue of reproducibility and variability of the cortical folding.
Model for reaction kinetics in pyrolysis of wood
Ahuja, P.; Singh, P.C.; Upadhyay, S.N.; Kumar, S. [Banaras Hindu Univ., Varanasi (India)
1996-12-31
A reaction model for the pyrolysis of small and large particles of wood Is developed. The chemical reactions that take place when biomass is pyrolyzed are the devolatilization reactions (primary) and due to the vapour-solid interactions (secondary). In the case of small particles, when the volatiles are immediately removed by the purge gas, only primary reactions occur and the reaction model is described by weight loss and char forming reactions. The of heterogeneous secondary reactions occur in the case of large particles due to the interaction between the volatiles and the hot nascent primary char. A chain reaction mechanism of secondary char formation is proposed. The model takes both the volatiles retention time and cracking and repolymerization reactions of the vapours with the decomposing solid as well as autocatalysis into consideration. 7 refs., 3 figs., 2 tabs.
Model for reaction kinetics in pyrolysis of wood
Ahuja, P.; Singh, P.C.; Upadhyay, S.N.; Kuma, S. [Banaras Hindu Univ., Varanasi (India)
1996-12-31
A reaction model for the pyrolysis of small and large particles of wood is developed. The chemical reactions that take place when biomass is pyrolyzed are the devolatilization reactions (primary) and due to the vapour-solid interactions (secondary). In the case of small particles, when the volatiles are immediately removed by the purge gas, only primary reactions occur and the reaction model is described by weight loss and char forming reactions. The heterogeneous secondary reactions occur in the case of large particles due to the interaction between the volatiles and the hot nascent primary char. A chain reaction mechanism of secondary char formation is proposed. The model takes both the volatiles retention time and cracking and repolymerization reactions of the vapours with the decomposing solid as well as autocatalysis into consideration. 6 refs., 3 figs., 2 tabs.
Alexander P. Mathews; ishora K. Panda
2012-01-01
A novel electrode design for the in situ generation of ozone in the reaction zone of a tubular reactor is described in this work. The ozone generator uses a porous inner electrode tube in the corona discharge assembly, and the ozone generated around the outer periphery of the porous tube diffuses into the tubular reactor and reacts with the contaminants in the fluid that is being treated. A mathematical model that includes absorption and second order reaction in the film is developed to describe ozonation kinetics of a contaminant dye in the tubular reactor. The model describes the experimental data for dye decolorization, oxidation byproducts, dissolved ozone, and ozone gas concentrations well. Model analysis indicates that the fast dye decolorization reaction occurs partly in the liquid film and partly in the bulk fluid. The model can be used in the selection of appropriate gas-liquid contactors for efficient oxidation of contaminants in effluents.
Almagrbi Abdualnaser Muftah
2014-01-01
Full Text Available This article presents a methodology for kinetic parameter estimation which is based on standard optimization methods. The parameter estimation procedure is applied to the example of modelling of non-catalytic transesterification reaction, based on laboratory experiments performed under elevated pressure. The kinetic model employed in this study consists of three consecutive and parallel reversible reactions of the second order, with six kinetic constants. The influence of the mass transfer effects was considered as well. The best results were obtained by Genetic Algorithm method. The application of this method resulted in kinetic parameters with improved accuracy in predicting concentrations of important reaction intermediates, i.e. diglycerides and monoglycerides. Activation energies of kinetic parameters obtained by the Genetic Algorithm method are in very good agreement with theoretical values determined by molecular orbital calculations. [Projekat Ministarstva nauke Republike Srbije, br. III-45019
Li, Jianhua; Peng, Jianbiao; Zhang, Ya; Ji, Yuefei; Shi, Huanhuan; Mao, Liang; Gao, Shixiang
2016-06-05
This study investigated and compared reaction kinetics, product characterization, and toxicity variation of triclosan (TCS) removal mediated by soybean peroxidase (SBP), a recognized potential peroxidase for removing phenolic pollutants, and the commonly used horseradish peroxidase (HRP) with the goal of assessing the technical feasibility of SBP-catalyzed removal of TCS. Reaction conditions such as pH, H2O2 concentration and enzyme dosage were found to have a strong influence on the removal efficiency of TCS. SBP can retain its catalytic ability to remove TCS over broad ranges of pH and H2O2 concentration, while the optimal pH and H2O2 concentration were 7.0 and 8μM, respectively. 98% TCS was removed with only 0.1UmL(-1) SBP in 30min reaction time, while an HRP dose of 0.3UmL(-1) was required to achieve the similar conversion. The catalytic performance of SBP towards TCS was more efficient than that of HRP, which can be explained by catalytic rate constant (KCAT) and catalytic efficiency (KCAT/KM) for the two enzymes. MS analysis in combination with quantum chemistry computation showed that the polymerization products were generated via CC and CO coupling pathways. The polymers were proved to be nontoxic through growth inhibition of green alga (Scenedesmus obliquus). Taking into consideration of the enzymatic treatment cost, SBP may be a better alternative to HRP upon the removal and detoxification of TCS in water/wastewater treatment.
Gaskins, Delora K.; Pruc, Emily E.; Epstein, Irving R.; Dolnik, Milos
2016-07-01
Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation.
Complex Kinetics in the Reaction of Taurine with Aqueous Bromine ...
The reaction of chlorite and thiourea,4 for example, had shown complex ..... From an analysis of the combination of the slow reaction R4 and the very rapid reaction ..... 22 B.S. Martincigh, C. Mundoma and R. H. Simoyi, J. Phys. Chem. A, 1998,.
Gabrieli, Andrea; Demontis, Pierfranco; Pazzona, Federico G; Suffritti, Giuseppe B
2011-05-01
Understanding the behaviors of molecules in tight confinement is a challenging task. Standard simulation tools like kinetic Monte Carlo have proven to be very effective in the study of adsorption and diffusion phenomena in microporous materials, but they turn out to be very inefficient when simulation time and length scales are extended. In this paper we have explored the possibility of application of a discrete version of the synchronous parallel kinetic Monte Carlo algorithm introduced by Martínez et al. [J. Comput. Phys. 227, 3804 (2008)] to the study of aromatic hydrocarbons diffusion in zeolites. The efficiency of this algorithm is investigated as a function of the number of processors and domain size. We show that with an accurate choice of domains size it is possible to achieve very good efficiencies thus permitting us to effectively extend space and time scales of the simulated system. © 2011 American Physical Society
The influence of state-to-state kinetics on diffusion and heat transfer behind shock waves
Kunova, O.; Kustova, E.; Mekhonoshina, M.; Nagnibeda, E. [Saint Petersburg State University, 198504, Universitetskiy pr., 28, Saint Petersburg (Russian Federation)
2014-12-09
In the paper, the influence of vibrational and chemical kinetics on heat transfer and diffusion in hypersonic flows of N{sub 2}/N mixture in the relaxation zone behind shock waves is studied on the basis of the state-to-state kinetic theory approach. The results of calculations of vibrational level populations ni, gas temperature T, total energy flux q, diffusion velocities of molecules at different vibrational states V{sub i} and atoms V{sub a} in the relaxation zone behind a shock front are presented for the free stream Mach number M = 10, 15. The contribution of different dissipative processes to the total energy flux is estimated for various flow conditions. The impact of non-equilibrium vibrational distributions in the free stream on molecular level populations and transport properties in the relaxation zone is shown.
Kinetics and thermodynamics of chemical reactions in Li/SOCl2 cells
Hansen, Lee D.; Frank, Harvey
1987-01-01
Work is described that was designed to determine the kinetic constants necessary to extrapolate kinetic data on Li/SOCl2 cells over the temperature range from 25 to 75 C. A second objective was to characterize as far as possible the chemical reactions that occur in the cells since these reactions may be important in understanding the potential hazards of these cells. The kinetics of the corrosion processes in undischarged Li/SOCl2 cells were determined and separated according to their occurrence at the anode and cathode; the effects that switching the current on and off has on the corrosion reactions was determined; and the effects of discharge state on the kinetics of the corrosion process were found. A thermodynamic analysis of the current-producing reactions in the cell was done and is included.
Kinetics and thermodynamics of chemical reactions in Li/SOCl2 cells
Hansen, Lee D.; Frank, Harvey
1987-01-01
Work is described that was designed to determine the kinetic constants necessary to extrapolate kinetic data on Li/SOCl2 cells over the temperature range from 25 to 75 C. A second objective was to characterize as far as possible the chemical reactions that occur in the cells since these reactions may be important in understanding the potential hazards of these cells. The kinetics of the corrosion processes in undischarged Li/SOCl2 cells were determined and separated according to their occurrence at the anode and cathode; the effects that switching the current on and off has on the corrosion reactions was determined; and the effects of discharge state on the kinetics of the corrosion process were found. A thermodynamic analysis of the current-producing reactions in the cell was done and is included.
Cybulskis, Viktor J.; Smeltz, Andrew D.; Zvinevich, Yury; Gounder, Rajamani; Delgass, W. Nicholas; Ribeiro, Fabio H.
2016-01-01
Understanding catalytic chemistry, collecting and interpreting kinetic data, and operating chemical reactors are critical skills for chemical engineers. This laboratory experiment provides students with a hands-on supplement to a course in chemical kinetics and reaction engineering. The oxidation of methane with a palladium catalyst supported on…
A kinetic model for the glucose/glycine Maillard reaction pathways
Martins, S.I.F.S.; Boekel, van M.A.J.S.
2005-01-01
A comprehensive kinetic model for the glucose/glycine Maillard reaction is proposed based on an approach called multiresponse kinetic modelling. Special attention was paid to reactants, intermediates and end products: -fructose, N-(1-deoxy--fructos-1-yl)-glycine (DFG), 1-deoxy-2,3-hexodiulose and
Koga, Nobuyoshi; Goshi, Yuri; Yoshikawa, Masahiro; Tatsuoka, Tomoyuki
2014-01-01
An undergraduate kinetic experiment of the thermal decomposition of solids by microscopic observation and thermal analysis was developed by investigating a suitable reaction, applicable techniques of thermal analysis and microscopic observation, and a reliable kinetic calculation method. The thermal decomposition of sodium hydrogen carbonate is…
Koga, Nobuyoshi; Goshi, Yuri; Yoshikawa, Masahiro; Tatsuoka, Tomoyuki
2014-01-01
An undergraduate kinetic experiment of the thermal decomposition of solids by microscopic observation and thermal analysis was developed by investigating a suitable reaction, applicable techniques of thermal analysis and microscopic observation, and a reliable kinetic calculation method. The thermal decomposition of sodium hydrogen carbonate is…
Utilization of the Recycle Reactor in Determining Kinetics of Gas-Solid Catalytic Reactions.
Paspek, Stephen C.; And Others
1980-01-01
Describes a laboratory scale reactor that determines the kinetics of a gas-solid catalytic reaction. The external recycle reactor construction is detailed with accompanying diagrams. Experimental details, application of the reactor to CO oxidation kinetics, interphase gradients, and intraphase gradients are discussed. (CS)
Kinetics and Mechanism of Interfacial Reaction in a SiCf/Ti Composite
Guoxing ZHANG; Qiang KANG; Nanlin SHI; Geping LI; Dong LI
2003-01-01
In order to evaluate the interfacial reaction, a SiCf/Ti (TA1) composite was fabricated by a vacuum hot pressingmethod and then heat-treated in vacuum at 800℃ for up to 100 h. The elemental distributions of C, Si and Ti at theinterfacial reaction zone were investigated. It was found that the reaction zone occurs during the fabrication processand continuously grows at high temperature because the Si and C atoms diffuse from SiC fibers to the matrix and Tiatoms diffuse in the opposite direction. The growth of the reaction zone is diffusion controlled and the mechanismof the reaction can be described by a reactive diffusion model of solid-state growth of an AmBn layer between twoelementary substances A and B.
An algorithm for multi-group two-dimensional neutron diffusion kinetics in nuclear reactor cores
Marcelo Schramm
2016-01-01
The objective of this thesis is to introduce a new methodology for two{dimensional multi{ group neutron diffusion kinetics in a reactor core. The presented methodology uses a polyno- mial approximation in a rectangular homogeneous domain with non{homogeneous boundary conditions. As it consists on a truncated Taylor series, its error estimates varies with the size of the rectangle. The coefficients are obtained mainly by their relations with the independent term, which is determined by the dif...
A kinetic study on non-catalytic reactions in hydroprocessing Boscan crude oil
A. Marafi; E. Kam; A. Stanislaus [Kuwait Institute for Scientific Research, Safat (Kuwait). Petroleum Refining Department, Petroleum Research and Studies Center
2008-08-15
Non-catalytic hydrothermal cracking reactions are known to associate with catalytic hydrocracking reactions. In a recent study on hydroprocessing of Boscan crude over a specific catalyst system containing three distinct catalysts, it was found that hydrodesulfurization (HDS) and hydrodemetallation (HDM) reactions continued even when the catalyst is severely deactivated. Since the reactor was packed with considerable amount of inert material besides the three catalysts, it will be advantage to determine if the inert materials can also facilitate hydroprocessing reactions. A series of kinetic experiments for the inert particles was undertaken under different space velocity and temperature conditions. The extent of catalytic and non-catalytic hydroprocessing reactions was assessed. Through statistical analysis, the initial reaction rate constant, reaction order and activation energy for various hydroprocessing reactions were then determined. The absolute average deviations (AAD) of the kinetics values obtained for inert materials are less than 10%. 25 refs., 7 figs., 4 tabs.
Otero, Toribio F
2017-01-18
In this perspective the empirical kinetics of conducting polymers exchanging anions and solvent during electrochemical reactions to get dense reactive gels is reviewed. The reaction drives conformational movements of the chains (molecular motors), exchange of ions and solvent with the electrolyte and structural (relaxation, swelling, shrinking and compaction) gel changes. Reaction-driven structural changes are identified and quantified from electrochemical responses. The empirical reaction activation energy (Ea), the reaction coefficient (k) and the reaction orders (α and β) change as a function of the conformational energy variation during the reaction. This conformational energy becomes an empirical magnitude. Ea, k, α and β include and provide quantitative conformational and structural information. The chemical kinetics becomes structural chemical kinetics (SCK) for reactions driving conformational movements of the reactants. The electrochemically stimulated conformational relaxation model describes empirical results and some results from the literature for biochemical reactions. In parallel the development of an emerging technological world of soft, wet, multifunctional and biomimetic tools and anthropomorphic robots driven by reactions of the constitutive material, as in biological organs, can be now envisaged being theoretically supported by the kinetic model.
Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction
Manish Agrawal; S B Santra; Rajat Anand; Rajaram Swaminathan
2008-08-01
The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with increase in macromolecular crowding. Moreover, many cellular processes are dependent on molecular diffusion in the cell cytosol. The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model qualitatively explains some of the experimental observations.
Apparent Rate Constant for Diffusion-Controlled Three molecular (catalytic) reaction
Burlatsky, S. F.; Moreau, M
1996-01-01
We present simple explicit estimates for the apparent reaction rate constant for three molecular reactions, which are important in catalysis. For small concentrations and $d> 1$, the apparent reaction rate constant depends only on the diffusion coefficients and sizes of the particles. For small concentrations and $d\\le 1$, it is also time -- dependent. For large concentrations, it gains the dependence on concentrations.
Kinetics for the reaction of hydrogen with uranium powder
Stakebake, J.L.
1979-01-01
The reaction of hydrogen with uranium powder was investigated at 13.3 and 26.6 kPa between 50 and 250/sup 0/C. The reaction order was independent of temperature but varied from 2/3-order at 13.3 kPa to 1st-order at 26.6 kPa. Increasing temperatures resulted in decreasing reaction rates over the temperature range studied. A reaction mechanism with adsorption as the rate controlling step is proposed to explain the temperature behavior. Decomposition of the hydride was found to follow a zero-order rate process.
Reaction-Diffusion Systems: Front Propagation and Spatial Structures
Cencini, Massimo; Lopez, Cristobal; Vergni, Davide
After the pioneering works of Kolmogorov, Petrovskii and Piskunov [1] and Fisher [2] in 1937 on the nonlinear diffusion equation and its traveling wave solutions, scientists from many different disciplines have been captivated by questions about structure, formation and dynamics of patterns in reactive media. Combustion, spreading of epidemics, diffusive transport of chemicals in cells and population dynamics are just a few examples bearing witness of the influence of those works in different areas of modern science.
The kinetic resolution of enantiomers by means of enzymatic reactions
Otto, P.P.H.L.
1990-01-01
For conversions involving a single enzyme, and under certain limiting conditions, the process of kinetic resolution can be described with five variables, which can be determined experimentally. Their quantitative relations have been derived. If any three of these variables are known the other two ca
Effect of Temperature and Phase Constitution on Kinetics of La Diffusion
阎牧夫; SunY; 等
2002-01-01
The diffusion of La inε－Fe2-3N(ε)andν′-Fe4N(ν′)phases produced by plasma nitriding was studied.It is found that with increasing nitriding time,theεphase continuously decomposes into ν′one under employed experimental condition and compared with ν′phase orε+ν′ones,the mono oneεhas an impedient effect on depth of La diffusion,The growth of La layer in dual phases and mono one follows an approximate exponential law and a parabolic one ,respectively,and this kinetics law does not change with increasing temperature,The effect of increasing temperature in the range of 520to560℃on La diffusion depth is less than that of phase constitution change such as the decompostition ofεphase intoν′one.
Validity conditions for stochastic chemical kinetics in diffusion-limited systems
Gillespie, Daniel T.; Petzold, Linda R.; Seitaridou, Effrosyni
2014-02-01
The chemical master equation (CME) and the mathematically equivalent stochastic simulation algorithm (SSA) assume that the reactant molecules in a chemically reacting system are "dilute" and "well-mixed" throughout the containing volume. Here we clarify what those two conditions mean, and we show why their satisfaction is necessary in order for bimolecular reactions to physically occur in the manner assumed by the CME and the SSA. We prove that these conditions are closely connected, in that a system will stay well-mixed if and only if it is dilute. We explore the implications of these validity conditions for the reaction-diffusion (or spatially inhomogeneous) extensions of the CME and the SSA to systems whose containing volumes are not necessarily well-mixed, but can be partitioned into cubical subvolumes (voxels) that are. We show that the validity conditions, together with an additional condition that is needed to ensure the physical validity of the diffusion-induced jump probability rates of molecules between voxels, require the voxel edge length to have a strictly positive lower bound. We prove that if the voxel edge length is steadily decreased in a way that respects that lower bound, the average rate at which bimolecular reactions occur in the reaction-diffusion CME and SSA will remain constant, while the average rate of diffusive transfer reactions will increase as the inverse square of the voxel edge length. We conclude that even though the reaction-diffusion CME and SSA are inherently approximate, and cannot be made exact by shrinking the voxel size to zero, they should nevertheless be useful in many practical situations.
Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms
Tokar, M. Z.
2016-12-01
Hydrogen isotope atoms, generated by charge-exchange (c-x) of neutral particles recycling from the first wall of a fusion reactor, are described either kinetically or in a diffusion approximation. In a one-dimensional (1-D) geometry, kinetic calculations are accelerated enormously by applying an approximate pass method for the assessment of integrals in the velocity space. This permits to perform an exhaustive comparison of calculations done with both approaches. The diffusion approximation is deduced directly from the velocity distribution function of c-x atoms in the limit of charge-exchanges with ions occurring much more frequently than ionization by electrons. The profiles across the flux surfaces of the plasma parameters averaged along the main part of the scrape-off layer (SOL), beyond the X-point and divertor regions, are calculated from the one-dimensional equations where parallel flows of charged particles and energy towards the divertor are taken into account as additional loss terms. It is demonstrated that the heat losses can be firmly estimated from the SOL averaged parameters only; for the particle loss the conditions in the divertor are of importance and the sensitivity of the results to the so-called "divertor impact factor" is investigated. The coupled 1-D models for neutral and charged species, with c-x atoms described either kinetically or in the diffusion approximation, are applied to assess the SOL conditions in a fusion reactor, with the input parameters from the European DEMO project. It is shown that the diffusion approximation provides practically the same profiles across the flux surfaces for the plasma density, electron, and ion temperatures, as those obtained with the kinetic description for c-x atoms. The main difference between the two approaches is observed in the characteristics of these species themselves. In particular, their energy flux onto the wall is underestimated in calculations with the diffusion approximation by 20 %-30
Bahr, J.M.
1990-01-01
This paper extends a four-step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation-dissolution reaction are used to demonstrate the nature of departures from equilibrium-controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes. -from Author
Rebo, Hans Petter
1999-07-01
In Norway, the limited offshore oil resources, the abundance of natural gas and the need to recover associated gas from the crude oil production have made the utilisation of natural gas the focus of increased attention. Most products from refineries and chemical industry are formed by gas phase reactions over solid materials like metals, metal oxides and zeolites. Heterogeneous catalysts are in addition frequently used for environmental purposes and energy production. In the work described in this thesis, an experimental set-up was built and used to study some typical processes in heterogeneous catalysis. The set-up included a tapered element oscillating microbalance (TEOM) for measuring mass changes. The following properties of the TEOM were found particularly useful: (1) Frequent frequency counting makes the TEOM suitable for recording transient uptake curves, (2) High sensitivity of the microbalance makes it possible to work with low catalyst loading and still obtain high signal to noise ratio, and (3) Reliable kinetic data are obtained due to the fixed bed characteristics of the TEOM. Adsorption and diffusion of o-xylene and toluene in a commercial HZSM-5 zeolite were studied at 30, 100 and 200 {sup o}C and at partial pressures in the range of 0.002-0.1 bar. The effect of coke on the adsorption and diffusion properties were studied by adsorption experiments at 30 {sup o}C of ethane, toluene and n-hexane before and after coke formation during ethene oligomerisation at 475 {sup o}C and at P(ethene)=0.8 bar. The oligomerisation of ethene over HZSM-5 was used as a model reaction for comparing coke formation in a gravimetric microbalance and in the TEOM. The work also includes a study of coke formation and the effect of coke on the kinetics of propene dehydrogenation over Pt-Sn/Al{sub 2}O{sub 3} catalysts at 500-580 {sup o}C.
Gao, Feng; Walter, Eric D.; Karp, Eric M.; Luo, Jin-Yong; Tonkyn, Russell G.; Kwak, Ja Hun; Szanyi, Janos; Peden, Charles HF
2013-04-01
Cu-SSZ-13 catalysts with various Cu loadings were prepared via solution ion exchange. The hydrated samples were studied with Electron Paramagnetic Resonance (EPR). Cu2+ ion coordination numbers were obtained by analyzing the hyperfine structures while Cu-Cu distances were estimated from line broadening of the EPR features. By coupling EPR and temperature-programmed reduction (TPR) results, two Cu2+ ion locations were suggested. Standard and fast NH3-SCR, as well as non-selective NH3 oxidation reactions were carried out over these catalysts at high space velocities. For the SCR reaction, intra-particle diffusion limitation was found throughout the reaction temperatures investigated. Although clear structure-activity relationships cannot be derived, the reaction results allow for reactant diffusivities and Cu2+ ion locations to be estimated. The slower NH3 oxidation reaction, on the other hand, is kinetically limited at low temperatures, and, therefore, allows for a correlation between Cu2+ ion location and reaction kinetics to be made. Furthermore, the dynamic Cu2+ ion motion as a function of temperature could also be derived from the NH3 oxidation kinetics.
One-Dimensional Reaction-Diffusion Simulation of Cu Migration in Polycrystalline CdTe Solar Cells
Guo, Da [Arizona State University; Akis, Richard [Arizona State University; Brinkman, Daniel [Arizona State University; Sankin, Igor [First Solar; Fang, Tian [First Solar; Vasileska, Dragica [Arizona State University; Ringhofer, Christain [Arizona State University
2014-06-13
In this work, we report on developing 1D reaction-diffusion solver to understand the kinetics of p-type doping formation in CdTe absorbers and to shine some light on underlying causes of metastabilities observed in CdTe PV devices. Evolution of intrinsic and Cu-related defects in CdTe solar cell has been studied in time-space domain self-consistently with free carrier transport and Poisson equation. Resulting device performance was simulated as a function of Cu diffusion anneal time showing pronounced effect the evolution of associated acceptor and donor states can cause on device characteristics. Although 1D simulation has intrinsic limitations when applied to poly-crystalline films, the results suggest strong potential of the approach in better understanding of the performance and metastabilities of CdTe photovoltaic device.
Li, Jianhua; Peng, Jianbiao [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China); Zhang, Ya [Nanjing Institute of Environmental Sciences, Ministry of Environmental Protection of the People’s Republic of China, Nanjing 210042 (China); Ji, Yuefei [College of Resources and Environmental Science, Nanjing Agricultural University, Nanjing 210095 (China); Shi, Huanhuan; Mao, Liang [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China); Gao, Shixiang, E-mail: ecsxg@nju.edu.cn [State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing 210023 (China)
2016-06-05
Highlights: • Enzymatic treatment of triclosan in water by soybean and horseradish peroxidases. • pH, H{sub 2}O{sub 2} concentration and enzyme dosage affected the removal efficiency of TCS. • The removal of TCS by SBP was more efficient than that of HRP. • K{sub CAT} and K{sub CAT}/K{sub M} values for SBP toward TCS were much higher than those for HRP. • Polymers formed via radical coupling mechanism were nontoxic to the growth of alga. - Abstract: This study investigated and compared reaction kinetics, product characterization, and toxicity variation of triclosan (TCS) removal mediated by soybean peroxidase (SBP), a recognized potential peroxidase for removing phenolic pollutants, and the commonly used horseradish peroxidase (HRP) with the goal of assessing the technical feasibility of SBP-catalyzed removal of TCS. Reaction conditions such as pH, H{sub 2}O{sub 2} concentration and enzyme dosage were found to have a strong influence on the removal efficiency of TCS. SBP can retain its catalytic ability to remove TCS over broad ranges of pH and H{sub 2}O{sub 2} concentration, while the optimal pH and H{sub 2}O{sub 2} concentration were 7.0 and 8 μM, respectively. 98% TCS was removed with only 0.1 U mL{sup −1} SBP in 30 min reaction time, while an HRP dose of 0.3 U mL{sup −1} was required to achieve the similar conversion. The catalytic performance of SBP towards TCS was more efficient than that of HRP, which can be explained by catalytic rate constant (K{sub CAT}) and catalytic efficiency (K{sub CAT}/K{sub M}) for the two enzymes. MS analysis in combination with quantum chemistry computation showed that the polymerization products were generated via C−C and C−O coupling pathways. The polymers were proved to be nontoxic through growth inhibition of green alga (Scenedesmus obliquus). Taking into consideration of the enzymatic treatment cost, SBP may be a better alternative to HRP upon the removal and detoxification of TCS in water
The Study of Kinetics of Diffusion and Phase Formation in the Layered Iron-Beryllium System
Kuterbekov, K. A.; Nurkenov, S. A.; Kislitsin, S. B.; Kuketayev, T. A.; Nurakhmetov, T. N.
2017-02-01
The methods of Mössbauer spectroscopy with X-ray phase analysis and Rutherford backscattering of protons were used to study the kinetics of diffusion and phase transformations in the layered iron-beryllium system. For the first time, the authors suggested and implemented a method for retardation of diffusion and phase formation processes in the layered iron-beryllium system using the barrier layer. It was established that the barrier layer limits the zone of beryllium dissolution in the area of implanted layer. The impact of the barrier layer on kinetics of thermally induced processes of diffusion and phase transformations in the layered Fe-Be system was determined using the example of Fe (10 μm): O+ - Be (0.7 μm) - 57Fe (0.1 μm). The authors suggested and implemented a method for recovery of the distribution function of the admixture atom concentration in the solid matrix-admixture solution on the basis of the X-ray diffraction data. The kinetics of mutual diffusion was determined for Fe and Be atoms in the α-Fe(Be) solution for both sides of the layered systems with a barrier layer and without it using the suggested method for recovery of the distribution function of the Be atom concentration. It was established that for the system without a barrier layer, the share of iron atoms ends at tann 5 h on the coating side and at tann 7.5 h on the iron side, while for the barrier layer case - at tann 20 h on the coating side and at tann 40 h on the iron side.
The Spectroscopy and Reaction Kinetics of Coordinated Unsaturated Metal Carbonyls.
1985-10-20
liquid disso- ciation. I. Martyn Poliakoff and Eric Weitz, to be published in "Advances in Organo- metallic Chemistry" (1985). 2. A. J. Ouderkirk, P... Poliakoff and Eric Weitz, to be published in Annual Review of Organometallic Chemistry, 1985. c) Gas Phase Infrared Spectroscopy and Recombination Kinetics...support of this work by the 7.. 7 donors of the Petroleum Research Fund, administered by the American Chemical * -Society. We thank Dr. Martyn Poliakoff
Simulation of reaction-diffusion processes in three dimensions using CUDA
Molnar, Ferenc; Meszaros, Robert; Lagzi, Istvan
2010-01-01
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves t...
Magnetic Resonance Determinations of Structure and Reaction Kinetics of Epoxy/Amine Systems.
1981-12-31
bisphenol A ( DGEBA ), and two model compounds, a secondary amine nitroxide and a tertiary amine nitroxide. The rate constants for both reactions (kl, k2...EPR EXPERIMENTS ON EPOXY RESINS ....................................... 4 2.1 Nitroxide- DGEBA Kinetics ......................................... 4 2.2...dependence of the rate constants for METAMIN and DIMETAMIN reactions with DGEBA ...................................... 14 11. EPR spectra observed at 299
Kinetic calculations and mechanism definition for reactions in an ammonium perchlorate flame
Ermolin, N.E.; Fomin, V.M.; Korobeinichev, O.P.; Tereshchenko, A.G.
1982-09-01
This article reports on detailed calculations on the reaction kinetics in APC flames on the basis of a wide set of possible reactions and experimental data on the initial composition of the gas mixture (gasification products from APC). The purpose is to select the most important reactions in this system by comparing the calculations on the kinetics with experimental data on the concentration profiles in APC flames. Discusses kinetic equations; rate constants as the reaction mechanism; results from kinetic calculations; and identification of major stages. A laminar flame such as that provided by ammonium perchlorate is described in general form by a system of differential equations that incorporate the transport of heat and matter in the presence of chemical reactions. APC is a system consisting of 4 elements (N,H,Cl and O). Points out that the scheme enables one to determine which reactions are responsible for producing the final products. Suggests that in the future one will be able to analyze experimental data on the reaction-rate profiles for stable components in order to determine either the atom and radical concentrations or the rate constants of the reactions involving them.
Reaction diffusion in Ni–Al diffusion couples in steady magnetic fields
Li, Chuanjun, E-mail: cjli21@shu.edu.cn [School of Materials Science and Engineering, Shanghai University, Shanghai 200072 (China); Yuan, Zhaojing; Guo, Rui; Xuan, Weidong; Ren, Zhongming; Zhong, Yunbo; Li, Xi [School of Materials Science and Engineering, Shanghai University, Shanghai 200072 (China); Wang, Hui; Wang, Qiuliang [Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190 (China)
2015-08-25
Highlights: • The Ni–Al diffusion couples were prepared by the electrodeposition technique. • The magnetic field reduced the growth rates of product layers in diffusion couples. • The effect of the magnetic field on diffusion depends on its intensity and direction. • The spiral motion of an atom in the magnetic field reduces diffusivity. - Abstract: The effect of a steady magnetic field on reactive diffusion in Ni–Al diffusion couples was investigated. The diffusion couples prepared by the electrodeposition technique were annealed in the temperature range of 530–590 °C with and without the magnetic field of 6 T. Regardless of the magnetic field, two intermetallic compounds, i.e., Ni{sub 2}Al{sub 3} and NiAl{sub 3}, were present in the product layers of diffusion couples. NiAl{sub 3} phase shows island-like structures at relatively lower temperatures while the Ni{sub 2}Al{sub 3} phase forms a typical layered structure. The growth of Ni{sub 2}Al{sub 3} layer was found to be parabolic. When the diffusion direction was perpendicular to the direction of the magnetic field, the external magnetic field reduced the growth rate of the Ni{sub 2}Al{sub 3} phase. Whereas the magnetic field had no obvious effect on the growth rate of Ni{sub 2}Al{sub 3} layers in the diffusion configuration of mutually parallel directions. The magnetic field intensity and direction dependence of growth rate of Ni{sub 2}Al{sub 3} intermetallic layers can be attributed to the change in number of collision of an atom with neighbors during diffusion due to spiral motion under the action of the Lorentz force, which leads to change the frequency factor, not activation energy, for layer growth.
Kinetic Studies of Reactions in Solution Using Fast Mass Spectrometry
2013-08-13
REPORT Directorate of Chemistry and Materials Research NUMBER(S) AFOSR/RSA, 875 Randolph St., Suite 325, Rm 3112, Arlington, VA 222C 3 12...Mass Spectrometry to detect transient intermediates and decomposition products of catalyzed organometallic reactions Identifying intermediates is...in organometallic catalysis. HV N2 45o 5 mm 2 mm Reagent A Reagent B MS Secondary microdroplets Surface ~2-5 ms reaction time
Graphene liquid marbles as photothermal miniature reactors for reaction kinetics modulation.
Gao, Wei; Lee, Hiang Kwee; Hobley, Jonathan; Liu, Tianxi; Phang, In Yee; Ling, Xing Yi
2015-03-23
We demonstrate the fabrication of graphene liquid marbles as photothermal miniature reactors with precise temperature control for reaction kinetics modulation. Graphene liquid marbles show rapid and highly reproducible photothermal behavior while maintaining their excellent mechanical robustness. By tuning the applied laser power, swift regulation of graphene liquid marble's surface temperature between 21-135 °C and its encapsulated water temperature between 21-74 °C are demonstrated. The temperature regulation modulates the reaction kinetics in our graphene liquid marble, achieving a 12-fold superior reaction rate constant for methylene blue degradation than at room temperature.
Zhidkov, A.B.; Smirnov, E.P.
1989-02-01
This work is devoted to the study of the kinetics of the reaction of titanium tetrachloride with the hydride functional groups of diamond. The research was performed on submicron powders of ASM 0.7/0.3 grade synthetic diamond with a specific surface area of 8.0 m/sup 2//g as measured from the adsorption of nitrogen. The reaction was carried out in a flow-through quartz reactor in a flow of dry He. The content of the titanium in the samples was determined by a photocolorimetric method. A kinetic equation for the reaction of diamond with titanium tetrachloride was found on the basis of a statistical approach.
Kinetics of the Bray-Liebhafsky oscillatory reaction perturbed by polymer supported cobalt catalyst
Maksimović J.P.
2011-01-01
Full Text Available The Bray-Liebhafsky (BL oscillatory reaction generated in the batch reactor at 62- 68 oC was perturbed by cobalt(II-nitrate, supported on the macroreticular copolymer of poly-4-vinylpyridine with divinylbenzene (Co-PVPDVB. The kinetic data was analyzed of the complex pathways of the hydrogen peroxide decomposition in the examined BL reaction. The obtained results confirm that the kinetics of the BL reaction in the presence Co-PVPDVB comes partially from the Co-catalyst and partially from the macroreticular copolymer support.
Reaction Kinetics for Heterogeneous Oxidation of Mn（Ⅲ）—Toluene
张彰; 朱宪
2002-01-01
The reaction kinetics of the heterogeneous oxidation oftoluene with Mn3+ was studied by considering the effects of disproportionation of Mn3+ in reaction system,a “parallel”modulus was set up.And then the concentration of Mn3+ in disproportionation and the concentration of benzaldehyde in oxidation were respectively determined in turn.the rate constant,order and pseudo-activation energy of the heterogeneous oxidation were obtained by mathematical deduction and the kinetic equation was concluded.In addition,the reaction mechanism was analyzed.It shows that the results are completely consistent with modulus.
Accelerated stochastic and hybrid methods for spatial simulations of reaction diffusion systems
Rossinelli, Diego; Bayati, Basil; Koumoutsakos, Petros
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial τ-Leaping ( Sτ-Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid τ-Leaping ( Hτ-Leaping), combining a deterministic diffusion approximation with a τ-Leaping acceleration of the stochastic reactions. The algorithms are validated by solving Fisher's equation and used to explore the role of the number of particles in pattern formation. The results indicate that the present algorithms have a nearly constant time complexity with respect to the number of events (reaction and diffusion), unlike the exact stochastic simulation algorithm which scales linearly.
A Lagrangian particle method for reaction-diffusion systems on deforming surfaces.
Bergdorf, Michael; Sbalzarini, Ivo F; Koumoutsakos, Petros
2010-11-01
Reaction-diffusion processes on complex deforming surfaces are fundamental to a number of biological processes ranging from embryonic development to cancer tumor growth and angiogenesis. The simulation of these processes using continuum reaction-diffusion models requires computational methods capable of accurately tracking the geometric deformations and discretizing on them the governing equations. We employ a Lagrangian level-set formulation to capture the deformation of the geometry and use an embedding formulation and an adaptive particle method to discretize both the level-set equations and the corresponding reaction-diffusion. We validate the proposed method and discuss its advantages and drawbacks through simulations of reaction-diffusion equations on complex and deforming geometries.
A CLASS OF REACTION-DIFFUSION EQUATIONS WITH HYSTERESIS DIFFERENTIAL OPERATOR
XuLongfeng
2002-01-01
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems.
Chiu, Chichia; Yu, Jui-Ling
2007-04-01
Reaction-diffusion-chemotaxis systems have proven to be fairly accurate mathematical models for many pattern formation problems in chemistry and biology. These systems are important for computer simulations of patterns, parameter estimations as well as analysis of the biological systems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. In this paper, a general reaction-diffusion-chemotaxis system is considered for specific numerical issues of pattern simulations. We propose a fully explicit discretization combined with a variable optimal time step strategy for solving the reaction-diffusion-chemotaxis system. Theorems about stability and convergence of the algorithm are given to show that the algorithm is highly stable and efficient. Numerical experiment results on a model problem are given for comparison with other numerical methods. Simulations on two real biological experiments will also be shown.
THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION
无
2012-01-01
A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.
A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION
Xie Feng
2003-01-01
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.
Kinetic and mechanistic studies of free-radical reactions in combustion
Tully, F.P. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
Combustion is driven by energy-releasing chemical reactions. Free radicals that participate in chain reactions carry the combustion process from reactants to products. Research in chemical kinetics enables us to understand the microscopic mechanisms involved in individual chemical reactions as well as to determine the rates at which they proceed. Both types of information are required for an understanding of how flames burn, why engines knock, how to minimize the production of pollutants, and many other important questions in combustion. In this program the authors emphasize accurate measurements over wide temperature ranges of the rates at which ubiquitous free radicals react with stable molecules. The authors investigate a variety of OH, CN, and CH + stable molecule reactions important to fuel conversion, emphasizing application of the extraordinarily precise technique of laser photolysis/continuous-wave laser-induced fluorescence (LP/cwLIF). This precision enables kinetic measurements to serve as mechanistic probes. Since considerable effort is required to study each individual reaction, prudent selection is critical. Two factors encourage selection of a specific reaction: (1) the rates and mechanisms of the subject reaction are required input to a combustion model; and (2) the reaction is a chemical prototype which, upon characterization, will provide fundamental insight into chemical reactivity, facilitate estimation of kinetic parameters for similar reactions, and constrain and test the computational limits of reaction-rate theory. Most studies performed in this project satisfy both conditions.
张焕军; 朱国才
2004-01-01
The carbonization of magnesium oxide particles by CO2 was investigated using a stirring mill reactor.The effects of the system temperature, stirring rotation speed, influx rate of CO2 and initial diameter of the magnesium oxide particles on the carbonization process were determined. The results show that the system temperature and the stirring rotation speed are the most significant influencing factors on the carbonization rate. The determination of critical decomposition temperature (CDT) gives the maximum carbonization rate with other conditions fixed. A theoretical model involving mass transfer and reaction kinetics was presented for the carbonization process.The apparent activation energy was calculated to be 32.8kJ·mo1-1. The carbonization process is co-controlled by diffusive mass transfer and chemical reaction. The model fits well with the experimental results.
Center of mass velocity during diffusion: Comparisons of fluid and kinetic models
Vold, Erik; Yin, Lin; Taitano, William; Molvig, Kim; Albright, B. J.
2016-11-01
We examine the diffusion process between two ideal gases mixing across an initial discontinuity by comparing fluid and kinetic model results and find several similarities between ideal gases and plasma transport. Binary diffusion requires a net zero species mass flux in the Lagrange frame to assure momentum conservation in collisions. Diffusion between ideal gases is often assumed to be isobaric and isothermal which requires constant molar density. We show this condition exists only in the lab frame at late times (many collision times) after a pressure transient relaxes. The sum of molar flux across an initial discontinuity is non-zero for species of differing atomic masses resulting in a pressure perturbation. The results show three phases of mixing: a pressure discontinuity forms across the initial interface (times of a few collisions), pressure perturbations propagate away from the mix region (time scales of an acoustic transit) and at late times characteristic of the diffusion process, the pressure relaxes leaving a non-zero center of mass flow velocity. The center of mass velocity associated with the outward propagating pressure waves is required to conserve momentum in the rest frame. Implications are considered in multi-species diffusion numerics and in applications. Work performed under the auspices of the U.S. DOE by the LANS, LLC, Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. Funding provided by the Advanced Simulation and Computing (ASC) Program.
A COMPUTERIZED SYSTEM ON KINETIC ANALYSIS AND EVALUATION OF GAS/SOLID REACTIONS
J.H. Liu; J. Y. Zhang; S.K. Wei
2003-01-01
The present paper presents the structure, features and functions of a computerized system on kinetic analysis and evaluation of gas/solid reactions, KinPreGSR. KinPreGSR is a menu driven system, can be operated with MS Windows as workbench in a PC computer. It has been developed using visual C++ with FoxPro hybrid coding technique.KinPreGSR combines the characteristics of gas/solid reactions with the kinetic models as well as mass and heat transfer equations. The database files were established for the apparent activation energies of some reduction and decomposition reactions to allow the prediction of the reaction kinetics to some extents. Outputs can be displayed using graphical or numerical forms. Examples regarding the oxide reduction and carbonate decomposition under isothermal conditions are given to show those functions.
Saunders, John E; Chen, Hao; Brauer, Chris; Clayton, McGregor; Chen, Weijian; Barnes, Jack A; Loock, Hans-Peter
2015-12-07
The uptake and release of sorbates into films and coatings is typically accompanied by changes of the films' refractive index and thickness. We provide a comprehensive model to calculate the concentration of the sorbate from the average refractive index and the film thickness, and validate the model experimentally. The mass fraction of the analyte partitioned into a film is described quantitatively by the Lorentz-Lorenz equation and the Clausius-Mosotti equation. To validate the model, the uptake kinetics of water and other solvents into SU-8 films (d = 40-45 μm) were explored. Large-angle interferometric refractometry measurements can be used to characterize films that are between 15 μm to 150 μm thick and, Fourier analysis, is used to determine independently the thickness, the average refractive index and the refractive index at the film-substrate interface at one-second time intervals. From these values the mass fraction of water in SU-8 was calculated. The kinetics were best described by two independent uptake processes having different rates. Each process followed one-dimensional Fickian diffusion kinetics with diffusion coefficients for water into SU-8 photoresist film of 5.67 × 10(-9) cm(2) s(-1) and 61.2 × 10(-9) cm(2) s(-1).
L.R.B. Gonçalves
1997-12-01
Full Text Available In this work the effects of diffusion on the hydrolysis of maltose using glucoamylase immobilized on macroporous silica at 30o C are studied. Two different kinds of experimental assays are carried out: one using free enzyme and the other using an enzyme covalently linked to macroporous silica, preactivated with glutaraldehyde. Free enzyme assays are used to estimate the kinetic parameters for hydrolysis of maltose at 30ºC, according to a Michaelis-Menten equation, with inhibition by the product. Runs with the immobilized enzyme enable us to estimate dextrin diffusivities in silica, assuming that the inherent kinetic parameters are equal to the intrinsic ones. The values of kinetic and mass transfer parameters are: K3 = 0.90x10-5 g/U.s, Km = 0.61x10-3 g/ml, Ki = 1.23x10-1 g/ml, DMs = 0.50x10-6 cm2 /s and DGs = 0.55x10-6 cm2 /s
Simulating Some Complex Phenomena in Hydrothermal Ore-Forming Processes by Reaction-Diffusion CNN
Xu Deyi; Yu Chongwen; Bao Zhengyu
2003-01-01
Complexity phenomena like dynamic and static patterns, order from disorder, chaos and catastrophe were simulated by the application of 2-D reaction-diffusion CNN of two state variables and two diffusion coefficients transformed from Zhabotinksii model. They revealed somehow the mechanism of hydrothermal ore-forming processes, and answered several questions about the onset of ore forming.
熊岳山; 韦永康
2001-01-01
The sediment reaction and diffusion equation with generalized initial and boundary condition is studied. By using Laplace transform and Jordan lemma , an analytical solution is got, which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng ). Some problems arisen in the computation of analytical solution formula are also analysed.
Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems
Wang, Haiyan
2010-01-01
Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction-diffusion systems. In this paper, we shall establish the spreading speed for a large class of non-cooperative reaction-diffusion systems and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. As an application, our results are applied to a partially cooperative system describing interactions between ungulates and grass.
Abstracts of International Conference on Diffusion and Reactions: From Basis to Applications
NONE
1994-12-31
The conference has been devoted to diffusion of corrosion agents and chemical reactions (sulfidation and oxidation) in metals, alloys and composite materials from the view point of their corrosion mechanism and material resistance in different conditions.The three main topics have been broadly represented at the conference sessions: heterogeneous reactions; high temperature diffusion and corrosion mechanism and current problems and trends in development and characterization of materials.
AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL
闫振亚; 张鸿庆
2001-01-01
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.
Kelath Murali Manoj
Full Text Available Many heme enzymes show remarkable versatility and atypical kinetics. The fungal extracellular enzyme chloroperoxidase (CPO characterizes a variety of one and two electron redox reactions in the presence of hydroperoxides. A structural counterpart, found in mammalian microsomal cytochrome P450 (CYP, uses molecular oxygen plus NADPH for the oxidative metabolism (predominantly hydroxylation of substrate in conjunction with a redox partner enzyme, cytochrome P450 reductase. In this study, we employ the two above-mentioned heme-thiolate proteins to probe the reaction kinetics and mechanism of heme enzymes. Hitherto, a substrate inhibition model based upon non-productive binding of substrate (two-site model was used to account for the inhibition of reaction at higher substrate concentrations for the CYP reaction systems. Herein, the observation of substrate inhibition is shown for both peroxide and final substrate in CPO catalyzed peroxidations. Further, analogy is drawn in the "steady state kinetics" of CPO and CYP reaction systems. New experimental observations and analyses indicate that a scheme of competing reactions (involving primary product with enzyme or other reaction components/intermediates is relevant in such complex reaction mixtures. The presence of non-selective reactive intermediate(s affords alternate reaction routes at various substrate/product concentrations, thereby leading to a lowered detectable concentration of "the product of interest" in the reaction milieu. Occam's razor favors the new hypothesis. With the new hypothesis as foundation, a new biphasic treatment to analyze the kinetics is put forth. We also introduce a key concept of "substrate concentration at maximum observed rate". The new treatment affords a more acceptable fit for observable experimental kinetic data of heme redox enzymes.
Solutions of fractional reaction-diffusion equations in terms of the H-function
Haubold, H. J.; Mathai, A. M.; Saxena, R. K.
2007-12-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction-diffusion equations. The advantage of using Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation containing this derivative includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of neutral fractional diffusion, space-fractional diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-functions in compact form.
Kinetic studies of the infrared-induced reaction between atomic chlorine and solid parahydrogen
Raston, Paul L.; Kettwich, Sharon C.; Anderson, David T.
2015-04-01
We present Fourier-transform infrared (FTIR) spectroscopic studies of the IR-induced Cl + H2(v = 1) → HCl + H reaction in a parahydrogen (pH2) matrix aimed at distinguishing between two proposed reactions mechanisms; direct-IR and vibron-mediated. The Cl atom reactants are produced via 355 nm in situ photolysis of a Cl2 doped pH2 matrix. After photolysis is complete, a long-pass IR filter in the FTIR beam is removed and we measure the ensuing IR-induced reaction kinetics using rapid scan FTIR spectroscopy. We follow both the decay of the Cl atom reactant and growth of the HCl product using the Cl spin-orbit (SO) + Q1(0) and HCl R1(0) transitions, respectively. We show the IR-induced reaction mechanism depends on the spectral profile of the IR radiation; for IR spectral profiles that have significant IR intensities between 4000 and 5000 cm-1 we observe first-order kinetics that are assigned to a vibron-mediated mechanism and for spectral profiles that have significant IR intensities that include the Cl SO + Q1(0) transition near 5094 cm-1 we observe bi-exponential kinetics that are dominated by the direct-IR mechanism at early reaction times. We can distinguish between the two mechanisms using the observed kinetics. We investigate the reaction kinetics for different FTIR optical setups, for a range of sample conditions, and start and stop the IR-induced reaction to investigate the importance of secondary H atom reactions. We also study the IR-induced reaction in Br/Cl co-doped pH2 samples and show the presence of the Br atom quenches the vibron-mediated reaction kinetics presumably because the Br-atoms serve as efficient vibron traps. This paper indicates that in a highly enriched pH2 matrix the H atoms that are produced by the IR-induced Cl atom reaction likely do not play a significant role in the measured reaction kinetics which implies these secondary H atom reactions are highly selective.
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Woolley, Thomas E.
2012-05-22
Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
Defect reactions in gallium antimonide studied by zinc and self-diffusion
Sunder, Kirsten; Bracht, Hartmut
2007-12-01
Extrinsic diffusion of zinc (Zn) in gallium antimonide (GaSb) under Ga-rich conditions was analyzed on the basis of the kick-out and the dissociative diffusion mechanism. It is concluded that the changeover of interstitial Zn to substitutional gallium (Ga) sites is mainly mediated by Ga interstitials ( IGa). Fitting of the Zn profiles provides the relative contributions of IGa to Ga diffusion. This contribution is lower than the directly measured Ga diffusion coefficient indicating that Ga diffusion in GaSb is rather mediated by Ga vacancies than by Ga interstitials even under Ga-rich conditions. This finding supports transformation reactions between native point defects that are confirmed by first-principles total-energy calculations. In addition Ga and Sb diffusion experiments under H22 atmosphere were performed to reconcile the controversial data on self-diffusion in GaSb published by Weiler et al. and Bracht et al.
Verhamme, Ingrid M; Bock, Paul E
2008-09-19
Binding of the fibrinolytic proteinase plasmin (Pm) to streptokinase (SK) in a tight stoichiometric complex transforms Pm into a potent proteolytic activator of plasminogen. SK binding to the catalytic domain of Pm, with a dissociation constant of 12 pm, is assisted by SK Lys(414) binding to a Pm kringle, which accounts for a 11-20-fold affinity decrease when Pm lysine binding sites are blocked by 6-aminohexanoic acid (6-AHA) or benzamidine. The pathway of SK.Pm catalytic complex formation was characterized by stopped-flow kinetics of SK and the Lys(414) deletion mutant (SKDeltaK414) binding to Pm labeled at the active site with 5-fluorescein ([5F]FFR-Pm) and the reverse reactions by competitive displacement of [5F]FFR-Pm with active site-blocked Pm. The rate constants for the biexponential fluorescence quenching caused by SK and SKDeltaK414 binding to [5F]FFR-Pm were saturable as a function of SK concentration, reporting encounter complex affinities of 62-110 nm in the absence of lysine analogs and 4900-6500 and 1430-2200 nm in the presence of 6-AHA and benzamidine, respectively. The encounter complex with SKDeltaK414 was approximately 10-fold weaker in the absence of lysine analogs but indistinguishable from that of native SK in the presence of 6-AHA and benzamidine. The studies delineate for the first time the sequence of molecular events in the formation of the SK.Pm catalytic complex and its regulation by kringle ligands. Analysis of the forward and reverse reactions supports a binding mechanism in which SK Lys(414) binding to a Pm kringle accompanies near-diffusion-limited encounter complex formation followed by two slower, tightening conformational changes.
Wu, Zeng-Qiang; Du, Wen-Bin; Li, Jin-Yi; Xia, Xing-Hua; Fang, Qun
2015-08-01
Numerical simulation can provide valuable insights for complex microfluidic phenomena coupling mixing and diffusion processes. Herein, a novel finite element model (FEM) has been established to extract chemical reaction kinetics in a microfluidic flow injection analysis (micro-FIA) system using high throughput sample introduction. To reduce the computation burden, the finite element mesh generation is performed with different scales based on the different geometric sizes of micro-FIA. In order to study the contribution of chemical reaction kinetics under non-equilibrium condition, a pseudo-first-order chemical kinetics equation is adopted in the numerical simulations. The effect of reactants diffusion on reaction products is evaluated, and the results demonstrate that the Taylor dispersion plays a determining role in the micro-FIA system. In addition, the effects of flow velocity and injection volume on the reaction product are also simulated. The simulated results agree well with the ones from experiments. Although gravity driven flow is used to the numerical model in the present study, the FEM model also can be applied into the systems with other driving forces such as pressure. Therefore, the established FEM model will facilitate the understanding of reaction mechanism in micro-FIA systems and help us to optimize the manifold of micro-FIA systems.
Stimulating kinetic of aerobic reactions skilled athlete in sport dance
Lee Bo
2010-10-01
Full Text Available Changes speed of development of reaction of frequency of heart-throbs are appraised under act of the program of trainings facilities. Directions stimulation of the cardiorespiratory system of sportsmen are rotined. In research took part 2 homogeneous groups of sportsmen for 12 sportsmen (6 pair. It is set that the high-rate of development of reactions of aerobic power providing reflects reactive properties of the cardiorespiratory system and influences on efficiency of functional preparation on the whole. Possibilities of estimation of reactive properties of the cardiorespiratory system are rotined in the natural terms of training process.
Xu, Li; Horváth, Attila K
2014-08-14
The pentathionate-iodate reaction has been investigated by spectrophotometrically monitoring the formation of the total amount of iodine at 468 nm in the presence of phosphoric acid/dihydrogen phosphate buffer. We noticed that iodine forms only after a fairly long time lag, and the inverse of time necessary to produce a certain amount of iodine is linearly proportional to the initial concentration of iodate ion and the square of the hydrogen ion concentration, while depending complexly on the concentration of substrate pentathionate. This reaction can therefore be treated as a clock reaction but differs from the original Landolt reaction in the sense that substrate pentathionate and the clock species iodine coexist for a relatively long time--due to their relatively slow direct reaction--depending on the experimental circumstances. Furthermore, we also provided experimental evidence that iodide ion acts as an autocatalyst of the system. A 14-step kinetic model is proposed in which the mechanisms of the pentathionate-iodine, bisulfite-iodate, and the well-known Dushman reactions are combined. A thorough analysis revealed that the direct pentathionate-iodate reaction plays a role only to produce iodide ions via a finite sequence of reactions, and once its concentration reaches a certain level, the reaction is almost exclusively governed by the pentathionate-iodine and the Dushman reactions. As expected, a strong catalytic effect of the buffer composition is also found that can readily be explained by its well-known catalytic influence on the original Dushman reaction.
Kinetics of the decomposition reaction of phosphorite concentrate
Huang Run
2014-01-01
Full Text Available Apatite is the raw material, which is mainly used in phosphate fertilizer, and part are used in yellow phosphorus, red phosphorus, and phosphoric acid in the industry. With the decrease of the high grade phosphorite lump, the agglomeration process is necessary for the phosphorite concentrate after beneficiation process. The decomposition behavior and the phase transformation are of vital importance for the agglomeration process of phosphorite. In this study, the thermal kinetic analysis method was used to study the kinetics of the decomposition of phosphorite concentrate. The phosphorite concentrate was heated under various heating rate, and the phases in the sample heated were examined by the X-ray diffraction method. It was found that the main phases in the phosphorite are fluorapatiteCa5(PO43F, quartz SiO2,and dolomite CaMg(CO32.The endothermic DSC peak corresponding to the mass loss caused by the decomposition of dolomite covers from 600°C to 850°C. The activation energy of the decomposition of dolomite, which increases with the increase in the extent of conversion, is about 71.6~123.6kJ/mol. The mechanism equation for the decomposition of dolomite agrees with the Valensi equation and G-B equation.
Describing diffusion, reaction and convection on porous medium
D'Ajello, P C T; Nunes, G L
2013-01-01
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic medium diffuses until they react to the electrode surface and become part thereof. Our model consists in formulating convenient boundary conditions for the transport equation, that somewhat resembles the real system but is nevertheless simple enough to be solved, and then solve it. Similar approach was taken by Nicholson [1, 2], except that, to avoid the difficulties regarding the boundary conditions, he considered none whatsoever, and proposed a modified diffusion coefficient for the porous medium instead. Apropos, our model, with moving boundary condition pertain to the class of problems know as The Stefan problem [3].
von Kameke, A.; Huhn, F.; Muñuzuri, A. P.; Pérez-Muñuzuri, V.
2013-02-01
In the absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present that can be parametrized in terms of effective or turbulent diffusion D*, these patterns should be attainable on a much greater, boosted length scale. However, so far, experimental evidence of these boosted patterns in a turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi-two-dimensional turbulent flow. The wave patterns observed are ˜50 times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient D* of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov equation, vf∝D*, for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with D* as expected from molecular diffusion, since the wave fronts turn out to be highly filamentous.
Spiral and Antispiral Waves in Reaction-Diffusion Systems
LIUYu-Fang; WUYan-Ning; XUHou-Ju; SUNJin-Feng
2004-01-01
Spiral waves are ubiquitous phenomena in nonlinear chemical, physical, and biological systems. But antispiral waves are infrequent to date. The transition between spiral and antispiral waves has been rarely explored. We have analyzed the extended Brusselator model and the extended Oregonator model by linear stability analysis. We have demonstrated that it is possible and plausible to realize the transition between them by control of diffusion coefficient of inactivator from theoretical analysis and numerical simulations.
nonlinear kinetics and mechanism of nile blue reaction
Prof. S.B. Jonnalagadda
under varied oxidative and reducing media is pivotal in their applications as ... communication, we report the complex mechanism of the reaction between nile blue ... Both the instruments were interfaced for data storage and have ..... The authors acknowledge the financial support received from the University of Durban-.
Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.
2014-10-01
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.
Using Chemical Reaction Kinetics to Predict Optimal Antibiotic Treatment Strategies
Abel zur Wiesch, Pia; Cohen, Ted
2017-01-01
Identifying optimal dosing of antibiotics has proven challenging—some antibiotics are most effective when they are administered periodically at high doses, while others work best when minimizing concentration fluctuations. Mechanistic explanations for why antibiotics differ in their optimal dosing are lacking, limiting our ability to predict optimal therapy and leading to long and costly experiments. We use mathematical models that describe both bacterial growth and intracellular antibiotic-target binding to investigate the effects of fluctuating antibiotic concentrations on individual bacterial cells and bacterial populations. We show that physicochemical parameters, e.g. the rate of drug transmembrane diffusion and the antibiotic-target complex half-life are sufficient to explain which treatment strategy is most effective. If the drug-target complex dissociates rapidly, the antibiotic must be kept constantly at a concentration that prevents bacterial replication. If antibiotics cross bacterial cell envelopes slowly to reach their target, there is a delay in the onset of action that may be reduced by increasing initial antibiotic concentration. Finally, slow drug-target dissociation and slow diffusion out of cells act to prolong antibiotic effects, thereby allowing for less frequent dosing. Our model can be used as a tool in the rational design of treatment for bacterial infections. It is easily adaptable to other biological systems, e.g. HIV, malaria and cancer, where the effects of physiological fluctuations of drug concentration are also poorly understood. PMID:28060813
Using Chemical Reaction Kinetics to Predict Optimal Antibiotic Treatment Strategies.
Abel Zur Wiesch, Pia; Clarelli, Fabrizio; Cohen, Ted
2017-01-01
Identifying optimal dosing of antibiotics has proven challenging-some antibiotics are most effective when they are administered periodically at high doses, while others work best when minimizing concentration fluctuations. Mechanistic explanations for why antibiotics differ in their optimal dosing are lacking, limiting our ability to predict optimal therapy and leading to long and costly experiments. We use mathematical models that describe both bacterial growth and intracellular antibiotic-target binding to investigate the effects of fluctuating antibiotic concentrations on individual bacterial cells and bacterial populations. We show that physicochemical parameters, e.g. the rate of drug transmembrane diffusion and the antibiotic-target complex half-life are sufficient to explain which treatment strategy is most effective. If the drug-target complex dissociates rapidly, the antibiotic must be kept constantly at a concentration that prevents bacterial replication. If antibiotics cross bacterial cell envelopes slowly to reach their target, there is a delay in the onset of action that may be reduced by increasing initial antibiotic concentration. Finally, slow drug-target dissociation and slow diffusion out of cells act to prolong antibiotic effects, thereby allowing for less frequent dosing. Our model can be used as a tool in the rational design of treatment for bacterial infections. It is easily adaptable to other biological systems, e.g. HIV, malaria and cancer, where the effects of physiological fluctuations of drug concentration are also poorly understood.
A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.
Amadei, A; de Groot, B L; Ceruso, M A; Paci, M; Di Nola, A; Berendsen, H J
1999-05-15
The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.
Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N. [International Tomography Center, Siberian Branch, Russian Academy of Sciences, Institutskaya St. 3a, Novosibirsk 630090 (Russian Federation); Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090 (Russian Federation); Sadovsky, Vladimir M. [Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk 660036 (Russian Federation)
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 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
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
Ping Chen
2012-01-01
Full Text Available The kinetics of photosensitizer 2-devinyl-2-(1-methoxylethyl chlorin f (CPD4 uptake in MCF-7 human breast cancer cells is described by a diffusion kinetics model and experimentally investigated using laser scanning confocal microscopy (LSCM. CPD4 permeated into MCF-7 cells with increasing incubation time, which was followed by its binding to cell organelles. Subcellular distribution study revealed that CPD4 was primarily localized on the mitochondria and membranes, supporting that the mode of transmembrane transport was diffusion. A kinetics model describing CPD4 passing through the plasma membrane of MCF-7 cells was proposed based on Fick's first law of diffusion. The kinetics of cellular uptake of CPD4 was studied by three-dimensional LSCM. By fitting the experimental data using the above model, important cellular uptake and distribution parameters were obtained, which are of clinical significance in photodynamic therapy.
Reaction kinetics, molecular action, and mechanisms of cellulolytic proteins.
Mosier, N S; Hall, P; Ladisch, C M; Ladisch, M R
1999-01-01
Cellulolytic proteins form a complex of enzymes that work together to depolymerize cellulose to the soluble products cellobiose and glucose. Fundamental studies on their molecular mechanisms have been facilitated by advances in molecular biology. These studies have shown homology between cellulases from different microorganisms, and common mechanisms between enzymes whose modes of action have sometimes been viewed as being different, as suggested by the distribution of soluble products. A more complete picture of the cellulolytic action of these proteins has emerged and combines the physical and chemical characteristics of solid cellulose substrates with the specialized structure and function of the cellulases that break it down. This chapter combines the fundamentals of cellulose structure with enzyme function in a manner that relates the cellulose binding and biochemical kinetics at the catalytic site of the proteins to the macroscopic behavior of cellulase enzyme systems.
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
Atkinson, R.; Baulch, D. L.; Cox, R A; J. N. Crowley; Hampson, R. F.; Hynes, R. G.; Jenkin, M. E.; M. J. Rossi; Troe, J.
2007-01-01
International audience; This article, the third in the series, presents kinetic and photochemical data evaluated by the IUPAC Subcommittee on Gas Kinetic Data Evaluation for Atmospheric Chemistry. It covers the gas phase and photochemical reactions of inorganic halogen species, which were last published in J. Phys. Chem. Ref. Data, in 2000 (Atkinson et al., 2000), were updated on the IUPAC website in 2003 and are updated again in the present evaluation. The article consists of a summary sheet...
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
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 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.
Medien, H. A. A.
1998-02-01
A spectrophotometric method is described for the determination of amino acids. The method is based on the reaction between amino acids and syringaldehyde at pH 9.0, by which a color is developed with maximum absorption at 420 nm in aqueous methyl alcohol. The absorption of the product obeys Beer's law within the concentration range of 0.025-0.5 mM of original amino acid. The kinetics of the reaction follows overall second order kinetics, first order in each of the reactants. The rates of the reaction were investigated as a function of pH of the reaction medium and structure of the amino compounds. Logarithms of the second-order rate constants increased with amino acid anion concentration as the pH was increased. The mechanisms of the reaction have been discussed.
Realistic boundary conditions for stochastic simulations of reaction-diffusion processes
Erban, R; Erban, Radek
2006-01-01
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecul...
Complex Cure Kinetics of the Hydroxyl-Epoxide Reaction in DGEBA Epoxy Hardened with Diethanolamine
Ancipink, Windy; McCoy, John; Kropka, Jamie; Celina, Mathias
The curing of a diglycidyl ether of bisphenol-A Epoxy (Epon 828) with diethanolamine (DEA) involves a fast amine-epoxide reaction followed by a slower hydroxyl-epoxide reaction. At curing temperatures below 100°C, the time scales of these two reactions are well separated, and the hydroxyl addition can be studied as an ''isolated'' reaction. The hydroxyl-epoxide reaction is of great interest due to the complex kinetics involved, which are brought about by competing reactions. The reaction kinetics are believed to be tertiary amine catalyzed and are well fit to a modified form of the Kamal-type equation. Here we study the complex long term reaction kinetics at various temperatures, by using isothermal modulated differential scanning calorimetry, micro calorimetry, and infrared spectroscopy. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Self-learning kinetic Monte Carlo simulations of Al diffusion in Mg
Nandipati, Giridhar; Govind, Niranjan; Andersen, Amity; Rohatgi, Aashish
2016-03-16
Atomistic on-lattice self-learning kinetic Monte Carlo (SLKMC) method was used to examine the vacancy-mediated diffusion of an Al atom in pure hcp Mg. Local atomic environment dependent activation barriers for vacancy-atom exchange processes were calculated on-the-fly using climbing image nudged-elastic band method (CI-NEB) and using a Mg-Al binary modified embedded-atom method (MEAM) interatomic potential. Diffusivities of vacancy and Al atom in pure Mg were obtained from SLKMC simulations and are compared with values available in the literature that are obtained from experiments and first-principle calculations. Al Diffusivities obtained from SLKMC simulations are lower, due to larger activation barriers and lower diffusivity prefactors, than those available in the literature but have same order of magnitude. We present all vacancy-Mg and vacancy-Al atom exchange processes and their activation barriers that were identified in SLKMC simulations. We will describe a simple mapping scheme to map a hcp lattice on to a simple cubic lattice that would enable hcp lattices to be simulated in an on-lattice KMC framework. We also present the pattern recognition scheme used in SLKMC simulations.
Equilibration Kinetics and Chemical Diffusion of Indium-Doped TiO2.
Nowotny, Janusz; Alim, Mohammad A
2015-04-30
The present work reports the gas/solid equilibration kinetics for In-doped TiO2 (0.4 atom % In) at elevated temperatures (1023-1273 K) in the gas phase of controlled oxygen activity [10(-13) Pa TiO2, the chemical diffusion coefficient for In-doped TiO2 exhibits a maximum at the n-p transition point. The activation energy of the chemical diffusion exhibits a decrease with temperature from 200 kJ/mol at 1023 K to an insignificant value at 1273 K. This effect is reflective of a segregation-induced electrical potential barrier blocking the transport of defects. The absolute value of the chemical diffusion coefficient for In-doped TiO2 is larger from that of pure TiO2 by a factor of approximately 10. The effect of indium on the diffusion rate is considered in terms of the associated concentration of oxygen vacancies, which are formed in order to satisfy the charge neutrality for In-doped TiO2.
Use of Competition Kinetics with Fast Reactions of Grignard Reagents
Holm, Torkil
2000-01-01
may account for almost all the product even when present as only 1 part in 100 parts of the competing agent. In this way allylmagnesium bromide is estimated to react with acetone, benzophenone, benzaldehyde, and diethylacetaldehyde ca. 1.5 x 105 times faster than does butylmagnesium bromide. The rates...... or effects of polar substituents with isotopically or otherwise substituted benzophenones. A recently reported a-deuterium secondary KIE for the reaction of benzaldehyde with allylmagnesium bromide was observed at -78 °C , but was absent at room temperature. It is suggested that the reaction of benzophenone...... and benzaldehyde with allylmagnesium bromide has a radical-concerted mechanism since no radical type products are produced and since no colour from an intermediate ketyl is observed even at -78 °C....
Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function
HUANG Ye-hui; WENG Pei-xuan
2012-01-01
A reaction-diffusion model for a single spccies with age structure and nonlocal reaction for periodic time t is derived.Some results about the model with monotone birth function are firstly introduced,and then by constructing two auxiliary equations and squeezing method,the spreading speed for the system with nonmonotone birth function is obtained.
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gra
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
Assessing Effects of Oxidizer Characteristics on Composite Reaction Kinetics
2013-12-01
these 2 reactants react to form the products shown. For a complete reaction it was necessary to have two oxygen molecules for each methane molecule. A...properties such as high density (13.31 g cm-3) and large neutron capture cross section such that Hf and HfH2 are widely used for nuclear reactor and...volume can be calculated. In this case, plastic work per volume is = = 2 (−) , where Y is the yield strength of the plate
Chlorination of tramadol: Reaction kinetics, mechanism and genotoxicity evaluation.
Cheng, Hanyang; Song, Dean; Chang, Yangyang; Liu, Huijuan; Qu, Jiuhui
2015-12-01
Tramadol (TRA) is one of the most detected analgesics in environmental matrices, and it is of high significance to study the reactivity of TRA during chlorination considering its potential toxicity to the environment. The chlorine/TRA reaction is first order with respect to the TRA concentration, and a combination of first-order and second-order with respect to chlorine concentration. The pH dependence of the observed rate constants (kobs) showed that the TRA oxidation reactivity increased with increasing pH. kobs can be quantitatively described by considering all active species including Cl2, Cl2O and HOCl, and the individual rate constants of HOCl/TRA(0), HOCl/TRAH(+), Cl2/TRA and Cl2O/TRA reactions were calculated to be (2.61±0.29)×10(3)M(-1)s(-1), 14.73±4.17M(-1)s(-1), (3.93±0.34)×10(5)M(-1)s(-1) and (5.66±1.83)×10(6)M(-1)s(-1), respectively. Eleven degradation products were detected with UPLC-Q-TOF-MS, and the corresponding structures of eight products found under various pH conditions were proposed. The amine group was proposed to be the initial attack site under alkaline pH conditions, where reaction of the deprotonated amine group with HOCl is favorable. Under acidic and neutral pH conditions, however, two possible reaction pathways were proposed. One is an electrophilic substitution on the aromatic ring, and another is an electrophilic substitution on the nitrogen, leading to an N-chlorinated intermediate, which can be further oxidized. Finally, the SOS/umu test showed that the genotoxicity of TRA chlorination products increased with increasing dosage of chlorine, which was mostly attributed to the formation of some chlorine substitution products.
Reaction kinetics of resveratrol with tert-butoxyl radicals
Džeba, Iva; Pedzinski, Tomasz; Mihaljević, Branka
2012-09-01
The rate constant for the reaction of t-butoxyl radicals with resveratrol was studied under pseudo-first order conditions. The rate constant was determined by measuring the phenoxyl radical formation rate at 390 nm as function of resveratrol concentration in acetonitrile. The rate constant was determined to be 6.5×108 M-1s-1. This high value indicates the high reactivity consistent with the strong antioxidant activity of resveratrol.
Reaction Kinetic Parameters and Surface Thermodynamic Properties of Cu2O Nanocubes
Xingxing Li
2015-07-01
Full Text Available Cuprous oxide (Cu2O nanocubes were synthesized by reducing Cu(OH2 in the presence of sodium citrate at room temperature. The samples were characterized in detail by field-emission scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, X-ray powder diffraction, and N2 absorption (BET specific surface area. The equations for acquiring reaction kinetic parameters and surface thermodynamic properties of Cu2O nanocubes were deduced by establishment of the relations between thermodynamic functions of Cu2O nanocubes and these of the bulk Cu2O. Combined with thermochemical cycle, transition state theory, basic theory of chemical thermodynamics, and in situ microcalorimetry, reaction kinetic parameters, specific surface enthalpy, specific surface Gibbs free energy, and specific surface entropy of Cu2O nanocubes were successfully determined. We also introduced a universal route for gaining reaction kinetic parameters and surface thermodynamic properties of nanomaterials.
Chen, Hongsheng; Zheng, Zhong; Chen, Zhiwei; Yu, Wenzhou; Yue, Junrong
2017-04-01
The reduction kinetics of Brazilian hematite by CO is investigated in a Micro Fluidized Bed Reaction Analyzer (MFBRA) using an analyzing method based on Johnson-Mehl-Avrami (JMA) model at temperatures of 973 K (700 °C), 1023 K (750 °C), 1073 K (800 °C), and 1123 K (850 °C). The solid products at different reduction stages are evaluated by SEM/EDS and XRD technologies. Results indicate that the reduction process is better to be discussed in terms of a parallel reaction model that consists of the reactions of hematite to wüstite and wüstite to iron, rather than a stepwise route. Meanwhile, the controlling mechanism of the reduction process is found to vary with temperature and the degree of conversion. The overall process is controlled by the gas-solid reaction occurring at the iron/wüstite interface in the initial stages, and then is limited by the nucleation of wüstite, and finally shifts to diffusion control. Moreover, the reactions of hematite to wüstite and wüstite to iron take place simultaneously but with different time dependences, and the apparent activation energies of hematite to wüstite and wüstite to iron are determined as 83.61 and 80.40 KJ/mol, respectively.
Chen, Hongsheng; Zheng, Zhong; Chen, Zhiwei; Yu, Wenzhou; Yue, Junrong
2017-01-01
The reduction kinetics of Brazilian hematite by CO is investigated in a Micro Fluidized Bed Reaction Analyzer (MFBRA) using an analyzing method based on Johnson-Mehl-Avrami (JMA) model at temperatures of 973 K (700 °C), 1023 K (750 °C), 1073 K (800 °C), and 1123 K (850 °C). The solid products at different reduction stages are evaluated by SEM/EDS and XRD technologies. Results indicate that the reduction process is better to be discussed in terms of a parallel reaction model that consists of the reactions of hematite to wüstite and wüstite to iron, rather than a stepwise route. Meanwhile, the controlling mechanism of the reduction process is found to vary with temperature and the degree of conversion. The overall process is controlled by the gas-solid reaction occurring at the iron/wüstite interface in the initial stages, and then is limited by the nucleation of wüstite, and finally shifts to diffusion control. Moreover, the reactions of hematite to wüstite and wüstite to iron take place simultaneously but with different time dependences, and the apparent activation energies of hematite to wüstite and wüstite to iron are determined as 83.61 and 80.40 KJ/mol, respectively.
Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
Xiaoqin Wang
2013-01-01
Full Text Available We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
Electrochemical kinetics theoretical aspects
Vetter, Klaus J
1967-01-01
Electrochemical Kinetics: Theoretical Aspects focuses on the processes, methodologies, reactions, and transformations in electrochemical kinetics. The book first offers information on electrochemical thermodynamics and the theory of overvoltage. Topics include equilibrium potentials, concepts and definitions, electrical double layer and electrocapillarity, and charge-transfer, diffusion, and reaction overvoltage. Crystallization overvoltage, total overvoltage, and resistance polarization are also discussed. The text then examines the methods of determining electrochemical reaction mechanisms
Reaction kinetics and mechanism of magnetic field effects in cryptochrome
Solov'yov, Ilia; Schulten, Klaus
2012-01-01
Creatures as varied as mammals, fish, insects, reptiles, and birds have an intriguing sixth sense that allows them to orient themselves in the Earth's magnetic field. Despite decades of study, the physical basis of this magnetic sense remains elusive. A likely mechanism is furnished by magnetically...... sensitive radical pair reactions occurring in the retina, the light-sensitive part of animal eyes. A photoreceptor, cryptochrome, has been suggested to endow birds with magnetoreceptive abilities as the protein has been shown to exhibit the biophysical properties required for an animal magnetoreceptor...
Saeed, Rehana; Nadeem, Syed Muhammad Saqib
2016-06-01
The kinetics of the electron transfer reaction of methylene green and titanium trichloride was investigated in different solvents by spectrophotometry at different temperatures. The the reaction rate was determined by monitoring the absorbance as a function of time at λmax 655 nm. The reaction is pseudo-first order, dependent only on the concentration of titanium trichloride at a fixed concentration of methylene green. The effect of an aqueous alcoholic solvent was studied in the acidic range of pH from 4 to 7. It was observed that the reaction rate increased with an increase in polarity of the reaction medium. The the reaction rate was high in acidic conditions and decreased with a further increase in acidity. The increase in temperature increased the rate of the electron transfer reaction of methylene green and titanium trichloride. The activation energy ( E a) was calculated by the Arrhenius relation. The absence of any reaction intermediate was confirmed by spectroscopic and kinetic investigations. A plausible mechanism for the reaction in line with outer-sphere reaction pathway has been proposed. Thermodynamic parameters such as the activation energy ( E a), enthalpy change (Δ H), free energy change (Δ G), and entropy change (Δ S) were also evaluated
Ogasawara, Haruka; Koga, Nobuyoshi
2014-04-03
In this study, ferrous oxalate dihydrate polymorph particles, α- and β-phases, with square bipyramidal and quadratic prismatic shapes, respectively, were synthesized. Thermal dehydration of the samples was subjected to kinetic study as a typical reaction that indicates a significant induction period and a sigmoidal mass-loss behavior. On the basis of the formal kinetic analysis of the mass-loss traces recorded under isothermal, nonisothermal, and constant transformation rate conditions and the morphological observations of the surface textures of the partially reacted sample particles, a combined kinetic model for the induction period-surface reaction-phase boundary reaction was developed. The sigmoidal mass-loss behavior after the significant induction period under isothermal conditions was satisfactorily simulated by the combined kinetic model. The kinetic parameters for the component processes of induction period, surface reaction, and phase boundary reaction were separately determined from the kinetic simulation. The differences in the kinetic behaviors of the induction period and the phase boundary reaction between α- and β-phase samples were well described by the kinetic parameters. The applicability of the combined kinetic model to practical systems was demonstrated through characterizing the physicogeometrical kinetics of the thermal dehydration of ferrous oxalate dihydrate polymorphs.
KINETICS: A computer program to analyze chemical reaction data. Revision 2
Braun, R.L.; Burnham, A.K.
1994-09-01
KINETICS (Version 3.2) is a copyrighted, user-friendly kinetics analysis computer program designed for reactions such-as kerogen or polymer decomposition. It can fit rate parameters to chemical reaction data (rate or cumulative reacted) measured at a series of constant temperatures, constant heating rates, or arbitrary thermal histories. The program uses two models with conversion-dependent Azrhenius parameters and two models with activation energy distributions. The discrete distribution model fits an average frequency factor and relative fractions and activation energies for up to 25 parallel, fast-order reactions. The Gaussian distribution model fits a frequency factor, activation energy, Gaussian distribution parameter, and reaction order for up to 3 parallel reactions. For both distribution models, if the experiments are at a series of constant heating rates, the program uses a very fast approximate fitting procedure to determine possible initial parameter-estimates for the subsequent nonlinear regression analysis. This increases the probability that the regression analysis will properly. converge with a minimum of computer time. Once convergence is reached by the discrete model, the parameter space is further systematically searched to achieve global convergence. With the Gaussian model, the calculated rates or integrals can be convoluted with an experimental tracer signal during the nonlinear regression to account for dispersion effects often found in real chemical reaction data. KINETICS can also be used in an application mode to calculate reaction rates and integrals for previously determined Gaussian or discrete, parameters, using an arbitrary thermal history. Four additional models have been incorporated for the kinetics analysis of polymers and other materials, including some kerogens, which have a reaction-rate profile that is narrower than that for a single first-order reaction.
Self-triggering reaction kinetics between nitrates and aluminium powder
Demichela, Micaela [SAfeR-Centro Studi su Sicurezza Affidabilita e Rischi, Dipartimento di Scienza dei Materiali e Ingegneria Chimica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, I 10129 Torino (Italy)], E-mail: micaela.demichela@polito.it
2007-09-05
During the night between the 19 and 20 September 2003, a loud explosion occurred at about 3 km from the town of Carignano that was clearly heard at a distance of some tens of kilometres. The explosion almost completely destroyed most of the laboratories of the Panzera Company that were used for the production of fireworks. The results of the research activities that were carried out using a differential scanning calorimeter (DSC) on the same raw materials that made up the pyrotechnical mixture that exploded are reported in this paper. This activity was carried out to identify the dynamics of the accident. It proved possible to verify how the event was produced because of a slow exothermic reaction which, after about 8 h, caused the self-triggering of 120 kg of finished product. The detonation can therefore be put down to a runaway reaction in the solid phase, whose primogenial causes can be attributed to a still craftsman type production system, not conformed to the rigorous controls and inspections as those required by a safety management system for major risk plants, as the Panzera Company was.
Kinetics of pozzolanic reaction for preparation of flue gas desulfurizer from fly ash and Ca(OH)2
WANG Jingang; HU Jinbang; WANG Daobin; DUAN Zhenya
2007-01-01
A kinetic model of the pozzolanic reaction for the preparation of flue gas desulfurizers from fly ash and Ca(OH)2 was deduced on the basis of solid phase reaction kinetic theory.Kinetic expressions and parameters were obtained and verified by experiment.A comparison of calculated results with experimental results showed that precision in kinetic expressions was good.The apparent reaction rate constants of the pozzolanic reaction could be raised by increasing the specific surface area of fly ash and the hydration temperature,and by using a suitable additive.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)
2015-06-15
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.
Contribution to an effective design method for stationary reaction-diffusion patterns
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.
Contribution to an effective design method for stationary reaction-diffusion patterns.
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.
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar
2017-03-01
We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two
Traveling wave solutions for reaction-diffusion systems
Pedersen, Michael; Lin, Zhigui; Tian, Canrong
2010-01-01
This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions......, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model....
Yang Qi; Zhenmin Cheng; Zhiming Zhou
2015-01-01
Ni/Mg–Al catalysts derived from hydrotalcite-type precursors were prepared by a co-precipitation technique and applied to steam reforming of methane. By comparison with Ni/γ-Al2O3 and Ni/α-Al2O3 catalysts prepared by in-cipient wetness impregnation, the Ni/Mg–Al catalyst presented much higher activity as a result of higher specific surface area and better Ni dispersion. The Ni/Mg–Al catalyst with a Ni/Mg/Al molar ratio of 0.5:2.5:1 exhibited the highest activity for steam methane reforming and was selected for kinetic investigation. With external and inter-nal diffusion limitations eliminated, kinetic experiments were carried out at atmospheric pressure and over a temperature range of 823–973 K. The results demonstrated that the overal conversion of CH4 and the conversion of CH4 to CO2 were strongly influenced by reaction temperature, residence time of reactants as wel as molar ratio of steam to methane. A classical Langmuir–Hinshelwood kinetic model proposed by Xu and Froment (1989) fitted the experimental data with excellent agreement. The estimated adsorption parameters were consistent thermodynamical y.
Thermo-Kinetic Investigation of Comparative Ligand Effect on Cysteine Iron Redox Reaction
Masood Ahmad Rizvi
2015-03-01
Full Text Available Transition metal ions in their free state bring unwanted biological oxidations generating oxidative stress. The ligand modulated redox potential can be indispensable in prevention of such oxidative stress by blocking the redundant bio-redox reactions. In this study we investigated the comparative ligand effect on the thermo-kinetic aspects of biologically important cysteine iron (III redox reaction using spectrophotometric and potentiometric methods. The results were corroborated with the complexation effect on redox potential of iron(III-iron(II redox couple. The selected ligands were found to increase the rate of cysteine iron (III redox reaction in proportion to their stability of iron (II complex (EDTA < terpy < bipy < phen. A kinetic profile and the catalytic role of copper (II ions by means of redox shuttle mechanism for the cysteine iron (III redox reaction in presence of 1,10-phenanthroline (phen ligand is also reported.
Mechanism and kinetics of the NOCO reaction on Rh
Zhdanov, V. P.; Kasemo, B.
During the past 15 years, the NOCO reaction on Rh has attracted considerable attention of the researchers working in academic and applied surface science. The practical importance of this reaction is connected with its relevance for environmental chemistry. From the point of view of academic studies, the NOCO reaction on Rh is of interest because it represents one of the simplest examples from the class of catalytic reactions occurring via decomposition of adsorbed species. At present, the detailed kinetic data for this reaction are available both for single-crystal and supported Rh, at ultrahigh vacuum (UHV) conditions and also at realistic pressures. For this reason, the NOCO reaction on Rh has become one of the major testing platforms for a microscopic, surface-science based approach to heterogeneous catalysis. The present review shows how far the progress in this field has come. In particular, the review describes in detail the evolution of the ideas for the mechanism of the reaction and also presents the data for the elementary reaction steps, obtained primarily on Rh(1 1 1) at UHV conditions. Then, the possibility of using these data for simulation of the reaction kinetics at moderate pressures, P NO ⋍ P CO ⋍ 0.01 bar, is discussed. The technological aspects of application of Rh in the automotive exhaust systems are surveyed as well, but only briefly.
Baup, S; Wolbert, D; Laplanche, A
2002-10-01
Three pesticides (atrazine, bromoxynil and diuron) and two granular activated carbons are involved in equilibrium and kinetic adsorption experiments. Equilibrium is represented by Freundlich isotherm law and kinetic is described by the Homogeneous Surface Diffusion Model, based on external mass transfer and intraparticle surface diffusion. Equilibrium and long-term experiments are conducted to compare Powdered Activated Carbon and Granular Activated Carbon. These first investigations show that crushing GAC into PAC improves the accessibility of the adsorption sites without increasing the number of these sites. In a second part, kinetics experiments are carried out using a Differential Column Batch Reactor. Thanks to this experimental device, the external mass transfer coefficient k(f) is calculated from empirical correlation and the effect of external mass transfer on adsorption is likely to be minimized. In order to obtain the intraparticle surface diffusion coefficient D. for these pesticides, comparisons between experimental kinetic data and simulations are conducted and the best agreement leads to the Ds coefficient. This procedure appears to be an efficient way to acquire surface diffusion coefficients for the adsorption of pesticides onto GAC. Finally it points out the role of surface diffusivity in the adsorption rate. As a matter of fact, even if the amount of the target-compound that could be potentially adsorbed is really important, its surface diffusion coefficient may be small, so that its adsorption may not have enough contact time to be totally achieved.
Zhang, Yi; Tong, Yujin; Lu, Leilei; Osawa, Masatoshi; Ye, Shen
2010-01-01
The kinetics of electrocatalytic dissociation reaction of dimethyl ether (DME) on a platinum (Pt) polycrystalline electrode in an acidic solution yielding carbon monoxide (CO) has been quantitatively analyzed by in situ IR spectroscopy in the potential region between 100 and 500 mV (vs reversible hydrogen electrode). A two-step consecutive reaction model, an initial dehydrogenation step followed by a CO formation step, is proposed for the dissociation process of the DME molecule. The mechanis...
Studies of Reaction Kinetics of Methane Hydrate Dissocation in Porous Media
Moridis, George J.; Seol, Yongkoo; Kneafsey, Timothy J.
2005-03-10
The objective of this study is the description of the kinetic dissociation of CH4-hydrates in porous media, and the determination of the corresponding kinetic parameters. Knowledge of the kinetic dissociation behavior of hydrates can play a critical role in the evaluation of gas production potential of gas hydrate accumulations in geologic media. We analyzed data from a sequence of tests of CH4-hydrate dissociation by means of thermal stimulation. These tests had been conducted on sand cores partially saturated with water, hydrate and CH4 gas, and contained in an x-ray-transparent aluminum pressure vessel. The pressure, volume of released gas, and temperature (at several locations within the cores) were measured. To avoid misinterpreting local changes as global processes, x-ray computed tomography scans provided accurate images of the location and movement of the reaction interface during the course of the experiments. Analysis of the data by means of inverse modeling (history matching ) provided estimates of the thermal properties and of the kinetic parameters of the hydration reaction in porous media. Comparison of the results from the hydrate-bearing porous media cores to those from pure CH4-hydrate samples provided a measure of the effect of the porous medium on the kinetic reaction. A tentative model of composite thermal conductivity of hydrate-bearing media was also developed.
Kinetic modeling and fitting software for interconnected reaction schemes: VisKin.
Zhang, Xuan; Andrews, Jared N; Pedersen, Steen E
2007-02-15
Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.
Materer, Nicholas F.; Apblett, Allen; Kadossov, Evgueni B.; Khan, Kashif Rashid; Casper, Walter; Hays, Kevin; Shams, Eman F.
2016-06-01
Microcrystalline tungsten bronze thin films were prepared using wet chemical techniques to reduce a tungsten oxide thin film that was prepared by thermal oxidation of a sputter deposited tungsten metal film on a quartz substrate. The crystallinity of these films was determined by X-ray diffraction and the surface was characterized by X-ray and Ultra-Violet Photoelectron spectroscopy. The total amount of hydrogen incorporated in the film was monitored using absorbance spectroscopy at 900 nm. The oxidation kinetics of the film and the hydrogenation of nitrobenzene in hexane were measured as a function of film thickness. A satisfactory fit of the resulting kinetics was obtained using a model that involves two simultaneous processes. The first one is the proton diffusion from the bulk of the film to the surface, and the second is a reaction of the surface protons with the oxidants. Finally, the dependence of the reaction rates on the presence of catalytic amounts of first row transition metals on the surface of the film was explored.
Kinetic studies on the reaction between dicyanocobinamide and hypochlorous acid.
Dhiman Maitra
Full Text Available Hypochlorous acid (HOCl is a potent oxidant generated by myeloperoxidase (MPO, which is an abundant enzyme used for defense against microbes. We examined the potential role of HOCl in corrin ring destruction and subsequent formation of cyanogen chloride (CNCl from dicyanocobinamide ((CN2-Cbi. Stopped-flow analysis revealed that the reaction consists of at least three observable steps, including at least two sequential transient intermediates prior to corrin ring destruction. The first two steps were attributed to sequential replacement of the two cyanide ligands with hypochlorite, while the third step was the destruction of the corrin ring. The formation of (OCl(CN-Cbi and its conversion to (OCl2-Cbi was fitted to a first order rate equation with second order rate constants of 0.002 and 0.0002 µM(-1 s(-1, respectively. The significantly lower rate of the second step compared to the first suggests that the replacement of the first cyanide molecule by hypochlorite causes an alteration in the ligand trans effects changing the affinity and/or accessibility of Co toward hypochlorite. Plots of the apparent rate constants as a function of HOCl concentration for all the three steps were linear with Y-intercepts close to zero, indicating that HOCl binds in an irreversible one-step mechanism. Collectively, these results illustrate functional differences in the corrin ring environments toward binding of diatomic ligands.
Politowicz, P.A.; Kozak, J.J.
1987-12-01
The authors study surface-mediated, diffusion-controlled reactive processes on particles whose overall geometry is homeomorphic to a sphere. Rather than assuming that a coreactant can diffuse freely over the surface of the particle to a target site (reaction center), they consider the case where the coreactant can migrate only among N-1 satellite sites that are networked to the reaction site by means of a number of pathways or reaction channels. Five distinct lattice topologies are considered and they study the reaction efficiency both for the case where the satellite sites are passive and for the case where reaction may occur with finite probability at these sites. The results obtained for this class of surface problems are compared with those obtained by assuming that the reaction-diffusion process takes place on a planar, two-dimensional surface (lattice). The applicability of their results to surface-mediated processes on organizates (cells, vesicles, micelles) and on colloidally dispersed catalyst particles is brought out in the Introduction, and the correspondence between the lattice-based, Markovian approach developed here and Fickian models of surface diffusion, particularly with regard to the exponentiality of the decay, is discussed in the concluding section.
Modelling the impact of an invasive insect via reaction-diffusion.
Roques, Lionel; Auger-Rozenberg, Marie-Anne; Roques, Alain
2008-11-01
An exotic, specialist seed chalcid, Megastigmus schimitscheki, has been introduced along with its cedar host seeds from Turkey to southeastern France during the early 1990s. It is now expanding in plantations of Atlas Cedar (Cedrus atlantica). We propose a model to predict the expansion and impact of this insect. This model couples a time-discrete equation for the ovo-larval stage with a two-dimensional reaction-diffusion equation for the adult stage, through a formula linking the solution of the reaction-diffusion equation to a seed attack rate. Two main diffusion operators, of Fokker-Planck and Fickian types, are tested. We show that taking account of the dependence of the insect mobility with respect to spatial heterogeneity, and choosing the appropriate diffusion operator, are critical factors for obtaining good predictions.
Scaling of morphogenetic patterns in reaction-diffusion systems.
Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier
2016-09-07
Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.
Kinetics of self-interstitials reactions in p-type silicon irradiated with alpha particles
Makarenko, L.F., E-mail: makarenko@bsu.by [Department of Applied Mathematics and Computer Science, Belarusian State University, Independence Ave. 4, 220030 Minsk (Belarus); Moll, M. [CERN, Geneva (Switzerland); Evans-Freeman, J.H. [University of Canterbury, Christchurch (New Zealand); Lastovski, S.B.; Murin, L.I.; Korshunov, F.P. [Scientific-Practical Materials Research Centre of NAS of Belarus, Minsk (Belarus)
2012-08-01
New findings on the self-interstitial migration in p-type silicon are presented. They are based on experimental studies of the formation kinetics of defects related to interstitial carbon after irradiation with alpha particles. The main parameters characterizing the interaction rate of silicon self-interstitials with substitutional carbon atoms have been determined. A preliminary interpretation of the experimental data is given. The interpretation takes into account different diffusivities of self-interstitials in their singly and doubly ionized states.
Asymmetric hydrogenation with highly active IndolPhos-Rh catalysts: kinetics and reaction mechanism
Wassenaar, J.; Kuil, M.; Lutz, M.; Spek, A.L.; Reek, J.N.H.
2010-01-01
The mechanism of the IndolPhos-Rh-catalyzed asymmetric hydrogenation of prochiral olefins has been investigated by means of X-ray crystal structure determination, kinetic measurements, high-pressure NMR spectroscopy, and DFT calculations. The mechanistic study indicates that the reaction follows an
Battaglia, Francine [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Agblevor, Foster [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Klein, Michael [Univ. of Delaware, Newark, DE (United States); Sheikhi, Reza [Northeastern Univ., Boston, MA (United States)
2015-12-31
A collaborative effort involving experiments, kinetic modeling, and computational fluid dynamics (CFD) was used to understand co-gasification of coal-biomass mixtures. The overall goal of the work was to determine the key reactive properties for coal-biomass mixed fuels. Sub-bituminous coal was mixed with biomass feedstocks to determine the fluidization and gasification characteristics of hybrid poplar wood, switchgrass and corn stover. It was found that corn stover and poplar wood were the best feedstocks to use with coal. The novel approach of this project was the use of a red mud catalyst to improve gasification and lower gasification temperatures. An important results was the reduction of agglomeration of the biomass using the catalyst. An outcome of this work was the characterization of the chemical kinetics and reaction mechanisms of the co-gasification fuels, and the development of a set of models that can be integrated into other modeling environments. The multiphase flow code, MFIX, was used to simulate and predict the hydrodynamics and co-gasification, and results were validated with the experiments. The reaction kinetics modeling was used to develop a smaller set of reactions for tractable CFD calculations that represented the experiments. Finally, an efficient tool was developed, MCHARS, and coupled with MFIX to efficiently simulate the complex reaction kinetics.
Interfacial reaction kinetics of coated SiC fibers with various titanium alloys
Gundel, D. B.; Wawner, F. E.
1991-01-01
The kinetics of the reaction between the silicon carbide fibers and the titanium-based alloy matrix was investigated at temperatures from 800 to 1000 C for several titanium-based alloys (including Ti-1100 alloy and BETA 21S) and unalloyed Ti, reinforced with coated silicon carbide fiber SCS-6. The reaction zone growth kinetics was studied by exposing vacuum encapsulated samples to temperatures from 700 to 1000 C for times up to 150 hrs, followed by SAM observations of samples which were polished perpendicular to the fiber axis and etched. It was found that the reaction zone growth kinetics of the alpha (hcp) and beta (bcc) phases of unalloyed titanium reacting with SCS-6 fibers exhibited different values of the apparent activation energy and of the preexponential factor. Additions of other metals to Ti was found to slow down the reaction kinetics. Among the alloys studied, the Ti-1100 was the slowest reacting conventional alloy and the Ti-14Al-21Nb (in wt pct) was the slowest overall.
Atmospheric chemistry of CF3COOH. Kinetics of the reaction with OH radicals
Møgelberg, T.E.; Nielsen, O.J.; Sehested, J.;
1994-01-01
Two different experimental techniques were used to study the kinetics of the reaction of OH radicals with trifluoroacetic acid, CF3COOH. Using a pulse radiolysis absolute rate technique, rate constants at 315 and 348 K were determined to be (1.6 +/- 0.4) x 10(-13) and (1.5 +/- 0.2) x 10(-13) cm3...
Employing Magnetic Levitation to Monitor Reaction Kinetics and Measure Activation Energy
Benz, Lauren; Cesafsky, Karen E.; Le, Tran; Park, Aileen; Malicky, David
2012-01-01
This article describes a simple and inexpensive undergraduate-level kinetics experiment that uses magnetic levitation to monitor the progress and determine the activation energy of a condensation reaction on a polymeric solid support. The method employs a cuvette filled with a paramagnetic solution positioned between two strong magnets. The…
Battaglia, Francine [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Agblevor, Foster [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Klein, Michael [Univ. of Delaware, Newark, DE (United States); Sheikhi, Reza [Northeastern Univ., Boston, MA (United States)
2015-09-30
A collaborative effort involving experiments, kinetic modeling, and computational fluid dynamics (CFD) was used to understand co-gasification of coal-biomass mixtures. The overall goal of the work was to determine the key reactive properties for coal-biomass mixed fuels. Sub-bituminous coal was mixed with biomass feedstocks to determine the fluidization and gasification characteristics of hybrid poplar wood, switchgrass and corn stover. It was found that corn stover and poplar wood were the best feedstocks to use with coal. The novel approach of this project was the use of a red mud catalyst to improve gasification and lower gasification temperatures. An important results was the reduction of agglomeration of the biomass using the catalyst. An outcome of this work was the characterization of the chemical kinetics and reaction mechanisms of the co-gasification fuels, and the development of a set of models that can be integrated into other modeling environments. The multiphase flow code, MFIX, was used to simulate and predict the hydrodynamics and co-gasification, and results were validated with the experiments. The reaction kinetics modeling was used to develop a smaller set of reactions for tractable CFD calculations that represented the experiments. Finally, an efficient tool was developed, MCHARS, and coupled with MFIX to efficiently simulate the complex reaction kinetics.
Pedersen, Torben Møller; Jensen, Jakob Feldthusen; Humble, Rikke Eva
2000-01-01
A racemic aldehyde can undergo parallel kinetic resolution (PKR) by simultaneous reaction with two different chiral phosphonates, differing either in the structure of the chiral auxiliary or in the structure of the phosphoryl group (i.e., one (E)- and one (Z)-selective reagent). This strategy all...
An Inexpensive Kinetic Study: The Reaction of FD&C Red #3 (Erythrosin B) with Hypochlorite
Henary, Maher M.; Russell, Arlene A.
2007-01-01
Kinetics constitutes a core topic in both the lecture and laboratory components of lower- level chemistry courses. While textbook examples can ignore issues of time, temperature and safety, the laboratory can not. Reactions must occur slowly enough to be detected by students, occur rapidly enough for data collection in the few hours assigned to a…
Employing Magnetic Levitation to Monitor Reaction Kinetics and Measure Activation Energy
Benz, Lauren; Cesafsky, Karen E.; Le, Tran; Park, Aileen; Malicky, David
2012-01-01
This article describes a simple and inexpensive undergraduate-level kinetics experiment that uses magnetic levitation to monitor the progress and determine the activation energy of a condensation reaction on a polymeric solid support. The method employs a cuvette filled with a paramagnetic solution positioned between two strong magnets. The…
Marcus Theory: Thermodynamics CAN Control the Kinetics of Electron Transfer Reactions
Silverstein, Todd P.
2012-01-01
Although it is generally true that thermodynamics do not influence kinetics, this is NOT the case for electron transfer reactions in solution. Marcus Theory explains why this is so, using straightforward physical chemical principles such as transition state theory, Arrhenius' Law, and the Franck-Condon Principle. Here the background and…
Estimating kinetic parameters of complex catalytic reactions using a curve resolution based method
Cruz, S.C.; Rothenberg, G.; Westerhuis, J.A.; Smilde, A.K.
2008-01-01
A Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) based algorithm is used to extract kinetic parameters from on-line FT - NIR data of a series of Heck reactions between iodobenzene and n-butyl acrylate (NBA), measured at different temperatures with different catalysts. Four
On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics
Rao, Shodhan; Jayawardhana, Bayu; Schaft, Arjan van der
2012-01-01
Motivated by the recent progresses on the interplay between the graph theory and systems theory, we revisit the analysis of reversible chemical reaction networks described by mass action kinetics by reformulating it using the graph knowledge of the underlying networks. Based on this formulation, we
Toward a Kinetic Model for Acrylamide Formation in a Glucose-Asparagine Reaction System
Knol, J.J.; Loon, W.A.M.; Linssen, J.P.H.; Ruck, A.L.; Boekel, van M.A.J.S.
2005-01-01
A kinetic model for the formation of acrylamide in a glucose-asparagine reaction system is pro-posed. Equimolar solutions (0.2 M) of glucose and asparagine were heated at different tempera-tures (120-200 C) at pH 6.8. Besides the reactants, acrylamide, fructose, and melanoidins were quantified after
A novel reactor for determination of kinetics for solid catalyzed gas reactions
Borman, P.C.; Borman, P.C.; Bos, A.N.R.; Bos, A.N.R.; Westerterp, K.R.
1994-01-01
A novel perfectly mixed laboratory reactor for determining kinetics of heterogeneously catalyzed gas-phase reactions has been developed. Perfect mixing is achieved by circulating the gas in the reactor using an axial flow impeller in a well streamlined enclosure. Pellets are fixed in a rectangular
Variable elimination in chemical reaction networks with mass-action kinetics
Feliu, Elisenda; Wiuf, C.
2012-01-01
We consider chemical reaction networks taken with mass-action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop an algebraic framework and procedure for linear elimination...
The renneting of milk : a kinetic study of the enzymic and aggregation reactions
Hooydonk, van A.C.M.
1987-01-01
The rennet-induced clotting of milk was studied under various conditions. The kinetics of the enzymic and aggregation reactions was analysed separately and, where possible, related to the physico-chemical properties of the casein micelle and its environment.
The effects of important
Abdel-Kader, M. H.; Steiner, U.
1983-01-01
Three experiments using merocyanine M suitable as an integrated laboratory experience for undergraduates are described. Experiments demonstrate: complete molecular cycle composed of photochemical, thermal, and protolytic reaction steps; kinetics of cis-trans isomerization of the dye; and mechanism of base catalysis for thermal isomerization of the…
Asymmetric hydrogenation with highly active IndolPhos-Rh catalysts: kinetics and reaction mechanism
Wassenaar, J.; Kuil, M.; Lutz, M.; Spek, A.L.; Reek, J.N.H.
2010-01-01
The mechanism of the Indol- Phos–Rh-catalyzed asymmetric hydrogenation of prochiral olefins has been investigated by means of X-ray crystal structure determination, kinetic measurements, high-pressure NMR spectroscopy, and DFT calculations. The mechanistic study indicates that the reaction follows a
Asymmetric hydrogenation with highly active IndolPhos-Rh catalysts: kinetics and reaction mechanism
Wassenaar, J.; Kuil, M.; Lutz, M.; Spek, A.L.; Reek, J.N.H.
2010-01-01
The mechanism of the IndolPhos-Rh-catalyzed asymmetric hydrogenation of prochiral olefins has been investigated by means of X-ray crystal structure determination, kinetic measurements, high-pressure NMR spectroscopy, and DFT calculations. The mechanistic study indicates that the reaction follows an
Kinetic Study of the Reaction between Tert-butyl Hydrazine and Nitrous Acid
2001-01-01
The kinetic study of the reaction between tert-butyl hydrazine(TBH)and nitrous acid in nitric acid system is performed by spectrophotometry. The effect of some factors such as the concentration of TBH, the concentration of nitric acid, ionic strength, temperature and the
Sayar, N.A.; Chen, B.H.; Lye, G.J.
2009-01-01
In this paper we have used a proposed mathematical model, describing the carbon-carbon bond format ion reaction between beta-hydroxypyruvate and glycolaldehyde to synthesise L-erythrulose, catalysed by the enzyme transketolase, for the analysis of the sensitivity of the process to its kinetic par....... (C) 2009 Elsevier B.V. All rights reserved....
A novel reactor for determination of kinetics for solid catalyzed gas reactions
Borman, P.C.; Bos, A.N.R.; Westerterp, K.R.
1994-01-01
A novel perfectly mixed laboratory reactor for determining kinetics of heterogeneously catalyzed gas-phase reactions has been developed. Perfect mixing is achieved by circulating the gas in the reactor using an axial flow impeller in a well streamlined enclosure. Pellets are fixed in a rectangular o
A Gas-Kinetic Scheme for Multimaterial Flows and Its Application in Chemical Reaction
Lian, Yongsheng; Xu, Kun
1999-01-01
This paper concerns the extension of the multicomponent gas-kinetic BGK-type scheme to multidimensional chemical reactive flow calculations. In the kinetic model, each component satisfies its individual gas-kinetic BGK equation and the equilibrium states of both components are coupled in space and time due to the momentum and energy exchange in the course of particle collisions. At the same time, according to the chemical reaction rule one component can be changed into another component with the release of energy, where the reactant and product could have different gamma. Many numerical test cases are included in this paper, which show the robustness and accuracy of kinetic approach in the description of multicomponent reactive flows.
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
Prediction of Reaction Kinetic of Al- Doura Heavy Naphtha Reforming Process Using Genetic Algorithm
Ramzy H. Saihod
2015-07-01
Full Text Available In this study, genetic algorithm was used to predict the reaction kinetics of Iraqi heavy naphtha catalytic reforming process located in Al-Doura refinery in Baghdad. One-dimensional steady state model was derived to describe commercial catalytic reforming unit consisting of four catalytic reforming reactors in series process. The experimental information (Reformate composition and output temperature for each four reactors collected at different operating conditions was used to predict the parameters of the proposed kinetic model. The kinetic model involving 24 components, 1 to 11 carbon atoms for paraffins and 6 to 11 carbon atom for naphthenes and aromatics with 71 reactions. The pre-exponential Arrhenius constants and activation energies were determined after fine tuning of the model results with experimental data. The input to the optimization is the compositions for 21 components and the temperature for the effluent stream for each one of the four reactors within the reforming process while the output of optimization is 142 predicted kinetic parameters for 71 reactions within reforming process. The differential optimization technique using genetic algorithm to predict the parameters of the kinetic model. To validate the kinetic model, the simulation results of the model based on proposed kinetic model was compared with the experimental results. The comparison between the predicted and commercially results shows a good agreement, while the percentage of absolute error for aromatics compositions are (7.5, 2, 8.3, and 6.1% and the temperature absolute percentage error are (0.49, 0.5, 0.01, and 0.3% for four reactors respectively.
Cox process representation and inference for stochastic reaction-diffusion processes
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.
A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation
Chunye Gong
2014-01-01
Full Text Available The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M compared with O(NM for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
Dynamical Behavior of Core 3 He Nuclear Reaction-Diffusion Systems and Sun's Gravitational Field
DU Jiulin; SHEN Hong
2005-01-01
The coupling of the sun's gravitational field with processes of diffusion and convection exerts a significant influence on the dynamical behavior of the core 3He nuclear reaction-diffusion system. Stability analyses of the system are made in this paper by using the theory of nonequilibrium dynamics. It is showed that, in the nuclear reaction regions extending from the center to about 0.38 times of the radius of the sun, the gravitational field enables the core 3He nuclear reaction-diffusion system to become unstable and, after the instability, new states to appear in the system have characteristic of time oscillation. This may change the production rates of both 7Be and 8B neutrinos.
Finite volume element method for analysis of unsteady reaction-diffusion problems
Sutthisak Phongthanapanich; Pramote Dechaumphai
2009-01-01
A finite volume element method is developed for analyzing unsteady scalar reaction--diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction--diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the highgradient boundary layers.
Chen, Weiliang
2016-01-01
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any serial implementation. This led to development of parallel solutions that benefit from the boost in performance of modern large-scale supercomputers. In this paper, we describe an MPI-based, parallel Operator-Splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its usage in real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecul...
L.I. Gladka
2012-10-01
Full Text Available The analysis of basic and combined models for calculation of effective kinetic coefficients required to describe diffusion processes in two-phase heterogeneous environments is conducted. For a transition zone that grows between two interacting diffusion phases was built a new model of effective medium. In this model the effective kinetic coefficient depends on the kinetic coefficients in each of the phases, volumetric particle phases and additional free parameter, which generally characterizes the type of structure of a bi-phase zone. It is shown that the combined model is constructed to describe the percolation behavior of effective medium. The phenomenological approach describes the formation and development of bi-phase zones in ternary systems which including streams through both phases and the analysis of the impact of the model on the resulting effective medium diffusion zone.
Bonnardot, J.
1998-11-19
Hydro-treatment of petroleum shortcuts permits elimination of unwanted components in order to increase combustion in engine and to decrease atmospheric pollution. Hydro-desulfurization (HDS), Hydro-denitrogenation (HDN) and Hydrogenation of aromatics (HDA) of a LCO (Light Cycle Oil)-Type gas oil have been studied using a new pilot at a fixed temperature with a NiMo/Al{sub 2}O{sub 3} catalyst. A hydrodynamic study showed that reactions occurring in the up-flow fixed bed reactor that has been used during the experiments, were governed exclusively by chemical reaction rates and not by diffusion. Through detailed chemical analysis, height chemical groups have been considered: three aromatics groups, one sulfided group, one nitrogenized and NH{sub 3}, H{sub 2}S, H{sub 2}. Two Langmuir-Hinshelwood-type kinetic models with either one or two types of sites have been established. The model with two types of site - one site of hydrogenation and one site of hydrogenolysis - showed a better fit in the modeling of the experimental results. This model enables to forecast the influence of partial pressure of H{sub 2}S and partial pressure of H{sub 2} on hydro-treatment reactions of a LCO-type gas oil. (author) 119 refs.
Bench-scale Kinetics Study of Mercury Reactions in FGD Liquors
Gary Blythe; John Currie; David DeBerry
2008-03-31
This document is the final report for Cooperative Agreement DE-FC26-04NT42314, 'Kinetics Study of Mercury Reactions in FGD Liquors'. The project was co-funded by the U.S. DOE National Energy Technology Laboratory and EPRI. The objective of the project has been to determine the mechanisms and kinetics of the aqueous reactions of mercury absorbed by wet flue gas desulfurization (FGD) systems, and develop a kinetics model to predict mercury reactions in wet FGD systems. The model may be used to determine optimum wet FGD design and operating conditions to maximize mercury capture in wet FGD systems. Initially, a series of bench-top, liquid-phase reactor tests were conducted and mercury species concentrations were measured by UV/visible light spectroscopy to determine reactant and byproduct concentrations over time. Other measurement methods, such as atomic absorption, were used to measure concentrations of vapor-phase elemental mercury, that cannot be measured by UV/visible light spectroscopy. Next, a series of bench-scale wet FGD simulation tests were conducted. Because of the significant effects of sulfite concentration on mercury re-emission rates, new methods were developed for operating and controlling the bench-scale FGD experiments. Approximately 140 bench-scale wet FGD tests were conducted and several unusual and pertinent effects of process chemistry on mercury re-emissions were identified and characterized. These data have been used to develop an empirically adjusted, theoretically based kinetics model to predict mercury species reactions in wet FGD systems. The model has been verified in tests conducted with the bench-scale wet FGD system, where both gas-phase and liquid-phase mercury concentrations were measured to determine if the model accurately predicts the tendency for mercury re-emissions. This report presents and discusses results from the initial laboratory kinetics measurements, the bench-scale wet FGD tests, and the kinetics modeling
Nadeem, Syed Muhammad Saqib; Saeed, Rehana
2017-08-01
The photo-kinetics of photoinduced transformation reaction of methylene green and titanium trichloride was investigated in water and different aqueous-alcoholic solvents. The reaction is pseudo-first order, dependent only on the concentration of titanium trichloride at fixed concentration of methylene green. The effect of water and aqueous-alcoholic solvents was studied in the acidic range from 4 to 7. It was observed that the quantum yield (φ) of reaction increased with increase in polarity of the solvent. The quantum yield (φ) was high in acidic condition and decreased with further increase in acidity. The quantum yield (φ) increased sharply with increase in concentration of titanium trichloride while it almost remained unaffected by change in concentration of methylene green. The addition of ions increased the quantum yield (φ) of reaction. The increase in temperature decreased the rate and quantum yield (φ) of reaction. An electron transfer mechanism for the reaction has been proposed in accordance with the kinetics of reaction. The absence of any reaction intermediate was confirmed by spectroscopic investigations. Activation energy ( E a) was calculated by Arrhenius relation. Thermodynamic parameters such as activation energy ( E a), enthalpy change (Δ H), free energy change (Δ G) and entropy change (Δ S) were also evaluated.
SurfKin: an ab initio kinetic code for modeling surface reactions.
Le, Thong Nguyen-Minh; Liu, Bin; Huynh, Lam K
2014-10-05
In this article, we describe a C/C++ program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas-surface reactions. Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics. Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory. Methane decomposition and water-gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations. The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions. SurfKin also opens a possibility for designing nanoscale model catalysts.