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

PubMed

Gan, Qintao; Lv, Tianshi; Fu, Zhenhua

2016-04-01

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

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

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

PubMed

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

1971-04-01

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

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

PubMed Central

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

1971-01-01

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

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

PubMed

Ovchinnikov, Victor; Nam, Kwangho; Karplus, Martin

2016-08-25

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

Mesoscopic Modeling of Blood Clotting: Coagulation Cascade and Platelets Adhesion

NASA Astrophysics Data System (ADS)

Yazdani, Alireza; Li, Zhen; Karniadakis, George

2015-11-01

The process of clot formation and growth at a site on a blood vessel wall involve a number of multi-scale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and flow. To model these processes we have incorporated advection-diffusion-reaction (ADR) of multiple species into an extended version of Dissipative Particle Dynamics (DPD) method which is considered as a coarse-grained Molecular Dynamics method. At the continuum level this is equivalent to the Navier-Stokes equation plus one advection-diffusion equation for each specie. The chemistry of clot formation is now understood to be determined by mechanisms involving reactions among many species in dilute solution, where reaction rate constants and species diffusion coefficients in plasma are known. The role of blood particulates, i.e. red cells and platelets, in the clotting process is studied by including them separately and together in the simulations. An agonist-induced platelet activation mechanism is presented, while platelets adhesive dynamics based on a stochastic bond formation/dissociation process is included in the model.

An electromechanical based deformable model for soft tissue simulation.

PubMed

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

2009-11-01

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

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

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

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

2016-03-15

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

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

NASA Astrophysics Data System (ADS)

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

2007-10-01

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

Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models.

PubMed

Drugowitsch, Jan

2016-02-11

We present a new, fast approach for drawing boundary crossing samples from Wiener diffusion models. Diffusion models are widely applied to model choices and reaction times in two-choice decisions. Samples from these models can be used to simulate the choices and reaction times they predict. These samples, in turn, can be utilized to adjust the models' parameters to match observed behavior from humans and other animals. Usually, such samples are drawn by simulating a stochastic differential equation in discrete time steps, which is slow and leads to biases in the reaction time estimates. Our method, instead, facilitates known expressions for first-passage time densities, which results in unbiased, exact samples and a hundred to thousand-fold speed increase in typical situations. In its most basic form it is restricted to diffusion models with symmetric boundaries and non-leaky accumulation, but our approach can be extended to also handle asymmetric boundaries or to approximate leaky accumulation.

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

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2015-09-01

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

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

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

2002-01-01

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

Strain-based diffusion solver for realistic representation of diffusion front in physical reactions

PubMed Central

2017-01-01

When simulating fluids, such as water or fire, interacting with solids, it is a challenging problem to represent details of diffusion front in physical reaction. Previous approaches commonly use isotropic or anisotropic diffusion to model the transport of a quantity through a medium or long interface. We have identified unrealistic monotonous patterns with previous approaches and therefore, propose to extend these approaches by integrating the deformation of the material with the diffusion process. Specifically, stretching deformation represented by strain is incorporated in a divergence-constrained diffusion model. A novel diffusion model is introduced to increase the global rate at which the solid acquires relevant quantities, such as heat or saturation. This ensures that the equations describing fluid flow are linked to the change of solid geometry, and also satisfy the divergence-free condition. Experiments show that our method produces convincing results. PMID:28448591

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics

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

Ryan, Emily M.; Tartakovsky, Alexandre M.; Amon, Cristina

2010-08-26

In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries.more » The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.« less

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

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

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

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

PubMed

Simpson, Matthew J

2015-01-01

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

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

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

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

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

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

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

NASA Astrophysics Data System (ADS)

Plante, Ianik; Devroye, Luc

2017-10-01

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

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

PubMed

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

2006-09-01

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

Effective Stochastic Model for Reactive Transport

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

PubMed

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

1976-11-01

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

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

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

PubMed Central

Simpson, Matthew J

2015-01-01

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

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

PubMed

MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

2016-03-15

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Computation of the unsteady facilitated transport of oxygen in hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1990-01-01

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

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

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

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Theoretical modeling of PEB procedure on EUV resist using FDM formulation

NASA Astrophysics Data System (ADS)

Kim, Muyoung; Moon, Junghwan; Choi, Joonmyung; Lee, Byunghoon; Jeong, Changyoung; Kim, Heebom; Cho, Maenghyo

2018-03-01

Semiconductor manufacturing industry has reduced the size of wafer for enhanced productivity and performance, and Extreme Ultraviolet (EUV) light source is considered as a promising solution for downsizing. A series of EUV lithography procedures contain complex photo-chemical reaction on photoresist, and it causes technical difficulties on constructing theoretical framework which facilitates rigorous investigation of underlying mechanism. Thus, we formulated finite difference method (FDM) model of post exposure bake (PEB) process on positive chemically amplified resist (CAR), and it involved acid diffusion coupled-deprotection reaction. The model is based on Fick's second law and first-order chemical reaction rate law for diffusion and deprotection, respectively. Two kinetic parameters, diffusion coefficient of acid and rate constant of deprotection, which were obtained by experiment and atomic scale simulation were applied to the model. As a result, we obtained time evolutional protecting ratio of each functional group in resist monomer which can be used to predict resulting polymer morphology after overall chemical reactions. This achievement will be the cornerstone of multiscale modeling which provides fundamental understanding on important factors for EUV performance and rational design of the next-generation photoresist.

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

PubMed Central

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

2012-01-01

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

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

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

NASA Astrophysics Data System (ADS)

Konkoli, Zoran

2004-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

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

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

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

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

PubMed

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

2017-02-01

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

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

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

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

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

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Ilie, Silvana

2017-12-01

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

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

PubMed

Sheng, Yin; Zeng, Zhigang

2018-07-01

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

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

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

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

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

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

2011-08-23

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

Dynamical spike solutions in a nonlocal model of pattern formation

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

PubMed

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

2017-05-17

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

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

PubMed Central

Akan, Ozgur B.

2018-01-01

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

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

PubMed

Kuscu, Murat; Akan, Ozgur B

2018-01-01

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

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

PubMed Central

2014-01-01

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

A reaction-diffusion model of CO2 influx into an oocyte

PubMed Central

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

2012-01-01

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

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

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

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Wen, Zijuan; Fu, Shengmao

2009-08-01

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

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

PubMed

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

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

Multiscale Modeling of Diffusion in a Crowded Environment.

PubMed

Meinecke, Lina

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

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

PubMed

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

2016-07-19

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

A "desperation-reaction" model of medical diffusion.

PubMed Central

Warner, K E

1975-01-01

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

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation.

PubMed

Arjunan, Satya Nanda Vel; Tomita, Masaru

2010-03-01

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally. The online version of this article (doi:10.1007/s11693-009-9047-2) contains supplementary material, which is available to authorized users.

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

PubMed

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

2010-02-21

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

Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems

PubMed Central

Hummer, Gerhard

2015-01-01

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions. PMID:26005592

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

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Jana Ranjani, R.

2018-04-01

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

Coupling Schemes for Multiphysics Reactor Simulation

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

Vijay Mahadeven; Jean Ragusa

2007-11-01

This report documents the progress of the student Vijay S. Mahadevan from the Nuclear Engineering Department of Texas A&M University over the summer of 2007 during his visit to the INL. The purpose of his visit was to investigate the physics-based preconditioned Jacobian-free Newton-Krylov method applied to physics relevant to nuclear reactor simulation. To this end he studied two test problems that represented reaction-diffusion and advection-reaction. These two test problems will provide the basis for future work in which neutron diffusion, nonlinear heat conduction, and a twophase flow model will be tightly coupled to provide an accurate model of amore » BWR core.« less

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Eun, Changsun

2017-11-01

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

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

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

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

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

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

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

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

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

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

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

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

PubMed

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

2016-11-01

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

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

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

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

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

PubMed

Dóka, Éva; Lente, Gábor

2017-04-13

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

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

PubMed

Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich

2013-05-17

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

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

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

PubMed

Endeward, Volker

2012-05-01

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

Reaction-diffusion systems in natural sciences and new technology transfer

NASA Astrophysics Data System (ADS)

Keller, André A.

2012-12-01

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

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

PubMed

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

2013-08-01

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

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

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

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

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries

PubMed Central

Secomb, Timothy W.

2016-01-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10–30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. PMID:26443811

Time scale of random sequential adsorption.

PubMed

Erban, Radek; Chapman, S Jonathan

2007-04-01

A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) The kinetics of the chemical reaction between adsorbing molecules and the surface and (ii) geometrical constraints on the surface made by molecules which are already adsorbed. The process (i) is modeled in a diffusion-driven context, i.e., the conditional probability of adsorbing a molecule provided that the molecule hits the surface is related to the macroscopic surface reaction rate. The geometrical constraint (ii) is modeled using random sequential adsorption (RSA), which is the sequential addition of molecules at random positions on a surface; one attempt to attach a molecule is made per one RSA simulation time step. By coupling RSA with the diffusion of molecules in the solution above the surface the RSA simulation time step is related to the real physical time. The method is illustrated on a model of chemisorption of reactive polymers to a virus surface.

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

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

Lundqvist, A.; Lindbergh, G.

1998-11-01

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

Quantitative correlations between collision induced dissociation mass spectrometry coupled with electrospray ionization or atmospheric pressure chemical ionization mass spectrometry - Experiment and theory

NASA Astrophysics Data System (ADS)

Ivanova, Bojidarka; Spiteller, Michael

2018-04-01

The problematic that we consider in this paper treats the quantitative correlation model equations between experimental kinetic and thermodynamic parameters of coupled electrospray ionization (ESI) mass spectrometry (MS) or atmospheric pressure chemical ionization (APCI) mass spectrometry with collision induced dissociation mass spectrometry, accounting for the fact that the physical phenomena and mechanisms of ESI- and APCI-ion formation are completely different. There are described forty two fragment reactions of three analytes under independent ESI- and APCI-measurements. The developed new quantitative models allow us to study correlatively the reaction kinetics and thermodynamics using the methods of mass spectrometry, which complementary application with the methods of the quantum chemistry provide 3D structural information of the analytes. Both static and dynamic quantum chemical computations are carried out. The object of analyses are [2,3-dimethyl-4-(4-methyl-benzoyl)-2,3-di-p-tolyl-cyclobutyl]-p-tolyl-methanone (1) and the polycyclic aromatic hydrocarbons derivatives of dibenzoperylen (2) and tetrabenzo [a,c,fg,op]naphthacene (3), respectively. As far as (1) is known to be a product of [2π+2π] cycloaddition reactions of chalcone (1,3-di-p-tolyl-propenone), however producing cyclic derivatives with different stereo selectivity, so that the study provide crucial data about the capability of mass spectrometry to provide determine the stereo selectivity of the analytes. This work also first provides quantitative treatment of the relations '3D molecular/electronic structures'-'quantum chemical diffusion coefficient'-'mass spectrometric diffusion coefficient', thus extending the capability of the mass spectrometry for determination of the exact 3D structure of the analytes using independent measurements and computations of the diffusion coefficients. The determination of the experimental diffusion parameters is carried out within the 'current monitoring method' evaluating the translation diffusion of charged analytes, while the theoretical modelling of MS ions and computations of theoretical diffusion coefficients are based on the Arrhenius type behavior of the charged species under ESI- and APCI-conditions. Although the study provide certain sound considerations for the quantitative relations between the reaction kinetic-thermodynamics and 3D structure of the analytes together with correlations between 3D molecular/electronic structures-quantum chemical diffusion coefficient-mass spectrometric diffusion coefficient, which contribute significantly to the structural analytical chemistry, the results have importance to other areas such as organic synthesis and catalysis as well.

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

PubMed

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

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

1997-09-01

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

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

NASA Astrophysics Data System (ADS)

Schwarz, Karsten; Rieger, Heiko

2013-03-01

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

A simple reaction-rate model for turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Bangert, L. H.

1975-01-01

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

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

NASA Astrophysics Data System (ADS)

Alford, John G.

2015-05-01

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

Direct simulations of chemically reacting turbulent mixing layers

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Anomalous Impact in Reaction-Diffusion Financial Models

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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

PubMed Central

2012-01-01

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

Modelling wildland fire propagation by tracking random fronts

NASA Astrophysics Data System (ADS)

Pagnini, G.; Mentrelli, A.

2013-11-01

Wildland fire propagation is studied in literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternative each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay and an infinite support, while the level-set method, which is a front tracking technique, generates a sharp function with a finite support. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random character that are extremely important in wildland fire propagation. As a consequence the fire front gets a random character, too. Hence a tracking method for random fronts is needed. In particular, the level-set contourn is here randomized accordingly to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterizing role proper to the level-set approach. The resulting model emerges to be suitable to simulate effects due to turbulent convection as fire flank and backing fire, the faster fire spread because of the actions by hot air pre-heating and by ember landing, and also the fire overcoming a firebreak zone that is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation it follows a correction for the rate of spread formula due to the mean jump-length of firebrands in the downwind direction for the leeward sector of the fireline contour.

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

DOE PAGES

Xu, X.; Sumption, M. D.

2016-01-12

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

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

Adaptive two-regime method: Application to front propagation

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

Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Flegg, Mark, E-mail: mark.flegg@monash.edu

2014-03-28

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in termsmore » of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.« less

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

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

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

PubMed Central

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

2015-01-01

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

Turing instability in reaction-diffusion systems with nonlinear diffusion

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

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

2013-10-15

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

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

NASA Astrophysics Data System (ADS)

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

2002-06-01

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

Diffusion and saponification inside porous cellulose triacetate fibers.

PubMed

Braun, Jennifer L; Kadla, John F

2005-01-01

Cellulose triacetate (CTA) fibers were partially hydrolyzed in 0.054 N solutions of NaOH/H(2)O and NaOMe/MeOH. The surface concentration of acetyl groups was determined using ATR-FTIR. Total acetyl content was determined by the alkaline hydrolysis method. Fiber cross-sections were stained with Congo red in order to examine the interface between reacted and unreacted material; these data were used to estimate the rate constant k and effective diffusivity D(B) for each reagent during the early stages of reaction by means of a volume-based unreacted core model. For NaOH/H(2)O, k = 0.37 L mol(-1) min(-1) and D(B) = 6.2 x 10(-7) cm(2)/sec; for NaOMe/MeOH, k = 4.0 L mol(-1) min(-1) and D(B) = 5.7 x 10(-6) cm(2)/sec. The NaOMe/MeOH reaction has a larger rate constant due to solvent effects and the greater nucleophilicity of MeO(-) as compared to OH(-); the reaction has a larger effective diffusivity because CTA swells more in MeOH than it does in water. Similarities between calculated concentration profiles for each case indicate that the relatively diffuse interface seen in fibers from the NaOMe/MeOH reaction results from factors not considered in the model; shrinkage of stained fiber cross-sections suggests that increased disruption of intermolecular forces may be the cause.

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

PubMed Central

Lu, Benzhuo; Zhou, Y.C.

2011-01-01

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

Atomistic modeling of water diffusion in hydrolytic biomaterials.

PubMed

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

2012-04-01

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

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

PubMed

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

2011-03-15

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

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

PubMed

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

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

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries.

PubMed

Secomb, Timothy W

2016-12-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

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

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

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

2016-01-15

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

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

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

Liu, Fengshan; Guelder, OEmer L.

2005-11-01

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

To Model Chemical Reactivity in Heterogeneous Emulsions, Think Homogeneous Microemulsions.

PubMed

Bravo-Díaz, Carlos; Romsted, Laurence Stuart; Liu, Changyao; Losada-Barreiro, Sonia; Pastoriza-Gallego, Maria José; Gao, Xiang; Gu, Qing; Krishnan, Gunaseelan; Sánchez-Paz, Verónica; Zhang, Yongliang; Dar, Aijaz Ahmad

2015-08-25

Two important and unsolved problems in the food industry and also fundamental questions in colloid chemistry are how to measure molecular distributions, especially antioxidants (AOs), and how to model chemical reactivity, including AO efficiency in opaque emulsions. The key to understanding reactivity in organized surfactant media is that reaction mechanisms are consistent with a discrete structures-separate continuous regions duality. Aggregate structures in emulsions are determined by highly cooperative but weak organizing forces that allow reactants to diffuse at rates approaching their diffusion-controlled limit. Reactant distributions for slow thermal bimolecular reactions are in dynamic equilibrium, and their distributions are proportional to their relative solubilities in the oil, interfacial, and aqueous regions. Our chemical kinetic method is grounded in thermodynamics and combines a pseudophase model with methods for monitoring the reactions of AOs with a hydrophobic arenediazonium ion probe in opaque emulsions. We introduce (a) the logic and basic assumptions of the pseudophase model used to define the distributions of AOs among the oil, interfacial, and aqueous regions in microemulsions and emulsions and (b) the dye derivatization and linear sweep voltammetry methods for monitoring the rates of reaction in opaque emulsions. Our results show that this approach provides a unique, versatile, and robust method for obtaining quantitative estimates of AO partition coefficients or partition constants and distributions and interfacial rate constants in emulsions. The examples provided illustrate the effects of various emulsion properties on AO distributions such as oil hydrophobicity, emulsifier structure and HLB, temperature, droplet size, surfactant charge, and acidity on reactant distributions. Finally, we show that the chemical kinetic method provides a natural explanation for the cut-off effect, a maximum followed by a sharp reduction in AO efficiency with increasing alkyl chain length of a particular AO. We conclude with perspectives and prospects.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Comprehensive Model of Single Particle Pulverized Coal Combustion Extended to Oxy-Coal Conditions

DOE PAGES

Holland, Troy; Fletcher, Thomas H.

2017-02-22

Oxy-fired coal combustion is a promising potential carbon capture technology. Predictive CFD simulations are valuable tools in evaluating and deploying oxy-fuel and other carbon capture technologies either as retrofit technologies or for new construction. But, accurate predictive simulations require physically realistic submodels with low computational requirements. In particular, comprehensive char oxidation and gasification models have been developed that describe multiple reaction and diffusion processes. Our work extends a comprehensive char conversion code (CCK), which treats surface oxidation and gasification reactions as well as processes such as film diffusion, pore diffusion, ash encapsulation, and annealing. In this work several submodels inmore » the CCK code were updated with more realistic physics or otherwise extended to function in oxy-coal conditions. Improved submodels include the annealing model, the swelling model, the mode of burning parameter, and the kinetic model, as well as the addition of the chemical percolation devolatilization (CPD) model. We compare our results of the char combustion model to oxy-coal data, and further compared to parallel data sets near conventional conditions. A potential method to apply the detailed code in CFD work is given.« less

Comprehensive Model of Single Particle Pulverized Coal Combustion Extended to Oxy-Coal Conditions

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

Holland, Troy; Fletcher, Thomas H.

Oxy-fired coal combustion is a promising potential carbon capture technology. Predictive CFD simulations are valuable tools in evaluating and deploying oxy-fuel and other carbon capture technologies either as retrofit technologies or for new construction. But, accurate predictive simulations require physically realistic submodels with low computational requirements. In particular, comprehensive char oxidation and gasification models have been developed that describe multiple reaction and diffusion processes. Our work extends a comprehensive char conversion code (CCK), which treats surface oxidation and gasification reactions as well as processes such as film diffusion, pore diffusion, ash encapsulation, and annealing. In this work several submodels inmore » the CCK code were updated with more realistic physics or otherwise extended to function in oxy-coal conditions. Improved submodels include the annealing model, the swelling model, the mode of burning parameter, and the kinetic model, as well as the addition of the chemical percolation devolatilization (CPD) model. We compare our results of the char combustion model to oxy-coal data, and further compared to parallel data sets near conventional conditions. A potential method to apply the detailed code in CFD work is given.« less

Numerical study of chemical reactions in a surface microdischarge tube with mist flow based on experiment

NASA Astrophysics Data System (ADS)

Shibata, T.; Nishiyama, H.

2014-03-01

Recently, a water treatment method of spraying solution into a discharge region has been developed and shows high energy efficiency. In this study, a simulation model of a water treatment method using a surface microdischarge (SMD) tube with mist flow is proposed for further understanding the detailed chemical reactions. Our model has three phases (plasma, gas and liquid) and three simulation steps. The carrier gas is humid air including 2% or 3% water vapour. The chemical species diffusion characteristics in the SMD tube and the concentrations in a droplet are clarified in a wide pH interval. The simulation results show that the chemical species generated on the SMD tube inner wall are diffused to the central axis and dissolved into fine droplets. Especially, OH radicals dissolve into droplets a few mm away from the SMD tube wall because of acidification of the droplets. Furthermore, the hydrogen peroxide density, which is the most important indicator of a radical reaction in water, is influenced by the initial solution pH. This pH dependence results from ozone self-decomposition in water.

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

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

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

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

PubMed

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

2011-01-15

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

Reaction-diffusion pattern in shoot apical meristem of plants.

PubMed

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

2011-03-29

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

Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants

PubMed Central

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

2011-01-01

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

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

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

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

2014-05-30

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

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

PubMed

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

2011-03-21

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

Ligand diffusion in proteins via enhanced sampling in molecular dynamics.

PubMed

Rydzewski, J; Nowak, W

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

DOE PAGES

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

2016-05-20

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

Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Efficient Conservative Reformulation Schemes for Lithium Intercalation

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

Urisanga, PC; Rife, D; De, S

Porous electrode theory coupled with transport and reaction mechanisms is a widely used technique to model Li-ion batteries employing an appropriate discretization or approximation for solid phase diffusion with electrode particles. One of the major difficulties in simulating Li-ion battery models is the need to account for solid phase diffusion in a second radial dimension r, which increases the computation time/cost to a great extent. Various methods that reduce the computational cost have been introduced to treat this phenomenon, but most of them do not guarantee mass conservation. The aim of this paper is to introduce an inherently mass conservingmore » yet computationally efficient method for solid phase diffusion based on Lobatto III A quadrature. This paper also presents coupling of the new solid phase reformulation scheme with a macro-homogeneous porous electrode theory based pseudo 20 model for Li-ion battery. (C) The Author(s) 2015. Published by ECS. All rights reserved.« less

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

A note on stress-driven anisotropic diffusion and its role in active deformable media.

PubMed

Cherubini, Christian; Filippi, Simonetta; Gizzi, Alessio; Ruiz-Baier, Ricardo

2017-10-07

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue. Copyright © 2017. Published by Elsevier Ltd.

Neurocomputation by Reaction Diffusion

NASA Astrophysics Data System (ADS)

Liang, Ping

1995-08-01

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

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

PubMed

Mehala, N; Rajendran, L; Meena, V

2017-02-01

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

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

PubMed

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

2012-04-28

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

Pyrolysis reaction models of waste tires: Application of Master-Plots method for energy conversion via devolatilization.

PubMed

Irmak Aslan, Dilan; Parthasarathy, Prakash; Goldfarb, Jillian L; Ceylan, Selim

2017-10-01

Land applied disposal of waste tires has far-reaching environmental, economic, and human health consequences. Pyrolysis represents a potential waste management solution, whereby the solid carbonaceous residue is heated in the absence of oxygen to produce liquid and gaseous fuels, and a solid char. The design of an efficient conversion unit requires information on the reaction kinetics of pyrolysis. This work is the first to probe the appropriate reaction model of waste tire pyrolysis. The average activation energy of pyrolysis was determined via iso-conversional methods over a mass fraction conversion range between 0.20 and 0.80 to be 162.8±23.2kJmol -1 . Using the Master Plots method, a reaction order of three was found to be the most suitable model to describe the pyrolytic decomposition. This suggests that the chemical reactions themselves (cracking, depolymerization, etc.), not diffusion or boundary layer interactions common with carbonaceous biomasses, are the rate-limiting steps in the pyrolytic decomposition of waste tires. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

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

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

2015-07-07

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

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.; McManus, Hugh L.

1996-01-01

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Reaction rates for mesoscopic reaction-diffusion kinetics

DOE PAGES

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2015-02-23

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In thismore » paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. Finally, we show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.« less

Reaction rates for mesoscopic reaction-diffusion kinetics

PubMed Central

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2016-01-01

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results. PMID:25768640

Scaling behavior in corrosion and growth of a passive film.

PubMed

Aarão Reis, F D A; Stafiej, Janusz

2007-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

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

An investigation on the modelling of kinetics of thermal decomposition of hazardous mercury wastes.

PubMed

Busto, Yailen; M G Tack, Filip; Peralta, Luis M; Cabrera, Xiomara; Arteaga-Pérez, Luis E

2013-09-15

The kinetics of mercury removal from solid wastes generated by chlor-alkali plants were studied. The reaction order and model-free method with an isoconversional approach were used to estimate the kinetic parameters and reaction mechanism that apply to the thermal decomposition of hazardous mercury wastes. As a first approach to the understanding of thermal decomposition for this type of systems (poly-disperse and multi-component), a novel scheme of six reactions was proposed to represent the behaviour of mercury compounds in the solid matrix during the treatment. An integration-optimization algorithm was used in the screening of nine mechanistic models to develop kinetic expressions that best describe the process. The kinetic parameters were calculated by fitting each of these models to the experimental data. It was demonstrated that the D₁-diffusion mechanism appeared to govern the process at 250°C and high residence times, whereas at 450°C a combination of the diffusion mechanism (D₁) and the third order reaction mechanism (F3) fitted the kinetics of the conversions. The developed models can be applied in engineering calculations to dimension the installations and determine the optimal conditions to treat a mercury containing sludge. Copyright © 2013 Elsevier B.V. All rights reserved.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

Lu, Benzhuo; Zhou, Y C; Huber, Gary A; Bond, Stephen D; Holst, Michael J; McCammon, J Andrew

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

The influence of fuel-air swirl intensity on flame structures of syngas swirl-stabilized diffusion flame

NASA Astrophysics Data System (ADS)

Shao, Weiwei; Xiong, Yan; Mu, Kejin; Zhang, Zhedian; Wang, Yue; Xiao, Yunhan

2010-06-01

Flame structures of a syngas swirl-stabilized diffusion flame in a model combustor were measured using the OH-PLIF method under different fuel and air swirl intensity. The flame operated under atmospheric pressure with air and a typical low heating-value syngas with a composition of 28.5% CO, 22.5% H2 and 49% N2 at a thermal power of 34 kW. Results indicate that increasing the air swirl intensity with the same fuel, swirl intensity flame structures showed little difference except a small reduction of flame length; but also, with the same air swirl intensity, fuel swirl intensity showed great influence on flame shape, length and reaction zone distribution. Therefore, compared with air swirl intensity, fuel swirl intensity appeared a key effect on the flame structure for the model combustor. Instantaneous OH-PLIF images showed that three distinct typical structures with an obvious difference of reaction zone distribution were found at low swirl intensity, while a much compacter flame structure with a single, stable and uniform reaction zone distribution was found at large fuel-air swirl intensity. It means that larger swirl intensity leads to efficient, stable combustion of the syngas diffusion flame.

An experimental design method leading to chemical Turing patterns.

PubMed

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

2009-05-08

Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

Numerical study of influence of molecular diffusion in the Mild combustion regime

NASA Astrophysics Data System (ADS)

Mardani, Amir; Tabejamaat, Sadegh; Ghamari, Mohsen

2010-09-01

In this paper, the importance of molecular diffusion versus turbulent transport in the moderate or intense low-oxygen dilution (Mild) combustion mode has been numerically studied. The experimental conditions of Dally et al. [Proc. Combust. Inst. 29 (2002) 1147-1154] were used for modelling. The EDC model was used to describe the turbulence-chemistry interaction. The DRM-22 reduced mechanism and the GRI 2.11 full mechanism were used to represent the chemical reactions of an H2/methane jet flame. The importance of molecular diffusion for various O2 levels, jet Reynolds numbers and H2 fuel contents was investigated. Results show that the molecular diffusion in Mild combustion cannot be ignored in comparison with the turbulent transport. Also, the method of inclusion of molecular diffusion in combustion modelling has a considerable effect on the accuracy of numerical modelling of Mild combustion. By decreasing the jet Reynolds number, decreasing the oxygen concentration in the airflow or increasing H2 in the fuel mixture, the influence of molecular diffusion on Mild combustion increases.

Synthesis of Biofluidic Microsystems (SYNBIOSYS)

DTIC Science & Technology

2007-10-01

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

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

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

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

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

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach.

PubMed

Zhou, Y C; Lu, Benzhuo; Huber, Gary A; Holst, Michael J; McCammon, J Andrew

2008-01-17

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

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

NASA Astrophysics Data System (ADS)

Nagano, Seido

2012-02-01

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

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

NASA Astrophysics Data System (ADS)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and the scheme's stability and convergence properties are discussed. While evaluating different methods for discretizing the coupled flux boundary condition, we discover a thresholding behaviour in the adaptive time stepper, and perform additional tests to investigate it. Finally, a method based on ghost points is chosen for its favorable numerical properties compared to the alternatives. With this method, we are able to run simulations with a large range of parameters, including any value of the nondimensionalized Debye length epsilon. The numerical code is first used to run simulations to explore the effects of polarization, surface coverage, and temperature. The code is also used to perform frequency sweeps of input signals in order to mimic impedance spectroscopy experiments. Finally, in Chapter 5, we use our model to apply ramped voltages to electrochemical systems, and show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking (polarized) electrodes, and electrolytes with background charge. Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. No general theory of linear-sweep voltammetry is available, however, for unsupported electrolytes and for other situations where diffuse charge effects play a role. We show theoretical and simulated current-voltage curves for liquid and solid thin films, cells with blocking electrodes, and membranes with fixed background charge. The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, but capacitive charging of the double layers is also studied, for early time transients at reactive electrodes and for non-reactive blocking electrodes. The final chapter highlights the role of diffuse charge in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows

NASA Technical Reports Server (NTRS)

Norris, Andrew T.; Hsu, Andrew T.

1994-01-01

In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

Modelling wildland fire propagation by tracking random fronts

NASA Astrophysics Data System (ADS)

Pagnini, G.; Mentrelli, A.

2014-08-01

Wildland fire propagation is studied in the literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternatives to each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay, and it is not zero in an infinite domain, while the level-set method, which is a front tracking technique, generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random nature and they are extremely important in wildland fire propagation. Consequently, the fire front gets a random character, too; hence, a tracking method for random fronts is needed. In particular, the level-set contour is randomised here according to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical of the level-set approach. The resulting model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation, a correction follows for the formula of the rate of spread which is due to the mean jump length of firebrands in the downwind direction for the leeward sector of the fireline contour. The presented study constitutes a proof of concept, and it needs to be subjected to a future validation.

Predicting Upscaled Behavior of Aqueous Reactants in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment.

PubMed

Yurk, Brian P

2016-10-01

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection-diffusion-reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.

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

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

Liu, Yuanyuan; Liu, Chongxuan; Zhang, Changyong

2015-08-01

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

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2001-08-01

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

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

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

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

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

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

PubMed

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

2015-10-15

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

Lagrangian numerical methods for ocean biogeochemical simulations

NASA Astrophysics Data System (ADS)

Paparella, Francesco; Popolizio, Marina

2018-05-01

We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

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

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

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

1993-10-01

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

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

Laser-Induced Fluorescence Measurements and Modeling of Nitric Oxide in Counterflow Diffusion Flames

NASA Technical Reports Server (NTRS)

Ravikrishna, Rayavarapu V.

2000-01-01

The feasibility of making quantitative nonintrusive NO concentration ([NO]) measurements in nonpremixed flames has been assessed by obtaining laser-induced fluorescence (LIF) measurements of [NO] in counterflow diffusion flames at atmospheric and higher pressures. Comparisons at atmospheric pressure between laser-saturated fluorescence (LSF) and linear LIF measurements in four diluted ethane-air counterflow diffusion flames with strain rates from 5 to 48/s yielded excellent agreement from fuel-lean to moderately fuel-rich conditions, thus indicating the utility of a model-based quenching correction technique, which was then extended to higher pressures. Quantitative LIF measurements of [NO] in three diluted methane-air counterflow diffusion flames with strain rates from 5 to 35/s were compared with OPPDIF model predictions using the GRI (version 2.11) chemical kinetic mechanism. The comparisons revealed that the GRI mechanism underpredicts prompt-NO by 30-50% at atmospheric pressure. Based on these measurements, a modified reaction rate coefficient for the prompt-NO initiation reaction was proposed which causes the predictions to match experimental data. Temperature measurements using thin filament pyrometry (TFP) in conjunction with a new calibration method utilizing a near-adiabatic H2-air Hencken burner gave very good comparisons with model predictions in these counterflow diffusion flames. Quantitative LIF measurements of [NO] were also obtained in four methane-air counterflow partially-premixed flames with fuel-side equivalence ratios (phi(sub B)) of 1.45, 1.6, 1.8 and 2.0. The measurements were in excellent agreement with model predictions when accounting for radiative heat loss. Spatial separation between regions dominated by the prompt and thermal NO mechanisms was observed in the phi(sub B) = 1.45 flame. The modified rate coefficient proposed earlier for the prompt-NO initiation reaction improved agreement between code predictions and measurements in the region where prompt-NO dominates. Finally, LIF measurements of NO were obtained in counterflow diffusion flames at 2 to 5 atm. Comparisons between [NO] measurements and predictions show that the GRI mechanism underpredicts prompt-NO by a factor of two to three at all pressures. In general, the results indicate a need for refinement of the CH chemistry, especially the pressure-dependent CH formation and destruction reactions.

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

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

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

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2011-01-01

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

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

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

2011-01-01

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

Materials Outgassing Rate Decay in Vacuum at Isothermal Conditions

NASA Technical Reports Server (NTRS)

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Gouni, Sreeja Reddy

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

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

PubMed Central

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

2011-01-01

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

A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

NASA Astrophysics Data System (ADS)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

NASA Technical Reports Server (NTRS)

VanOverbeke, Thomas J.

1998-01-01

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

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

PubMed

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

2014-06-01

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

Stability and Hopf Bifurcation in a Reaction-Diffusion Model with Chemotaxis and Nonlocal Delay Effect

NASA Astrophysics Data System (ADS)

Li, Dong; Guo, Shangjiang

Chemotaxis is an observed phenomenon in which a biological individual moves preferentially toward a relatively high concentration, which is contrary to the process of natural diffusion. In this paper, we study a reaction-diffusion model with chemotaxis and nonlocal delay effect under Dirichlet boundary condition by using Lyapunov-Schmidt reduction and the implicit function theorem. The existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady state solutions are investigated. Moreover, our results are illustrated by an application to the model with a logistic source, homogeneous kernel and one-dimensional spatial domain.

Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation.

PubMed

Glimm, Tilmann; Zhang, Jianying; Shen, Yun-Qiu; Newman, Stuart A

2012-03-01

We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.

Parametric spatiotemporal oscillation in reaction-diffusion systems.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

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

Parametric spatiotemporal oscillation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

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

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

PubMed

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

2018-02-01

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

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units

PubMed Central

Vigelius, Matthias; Meyer, Bernd

2012-01-01

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. PMID:22506001

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

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

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

2013-04-02

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

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

PubMed

Everaers, Ralf; Rosa, Angelo

2012-01-07

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

Modeling transport kinetics in clinoptilolite-phosphate rock systems

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

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

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

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

Dynamic coupling between coordinates in a model for biomolecular isomerization

NASA Astrophysics Data System (ADS)

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

2006-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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

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

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

2015-08-28

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

Hybrid method for numerical modelling of LWR coolant chemistry

NASA Astrophysics Data System (ADS)

Swiatla-Wojcik, Dorota

2016-10-01

A comprehensive approach is proposed to model radiation chemistry of the cooling water under exposure to neutron and gamma radiation at 300 °C. It covers diffusion-kinetic processes in radiation tracks and secondary reactions in the bulk coolant. Steady-state concentrations of the radiolytic products have been assessed based on the simulated time dependent concentration profiles. The principal reactions contributing to the formation of H2, O2 and H2O2 were indicated. Simulation was carried out depending on the amount of extra hydrogen dissolved in the coolant to reduce concentration of corrosive agents. High sensitivity to the rate of reaction H+H2O=OH+H2 is shown and discussed.

Guiding brine shrimp through mazes by solving reaction diffusion equations

NASA Astrophysics Data System (ADS)

Singal, Krishma; Fenton, Flavio

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

Numerical modeling of the dynamic response of a bioluminescent bacterial biosensor.

PubMed

Affi, Mahmoud; Solliec, Camille; Legentilhomme, Patrick; Comiti, Jacques; Legrand, Jack; Jouanneau, Sulivan; Thouand, Gérald

2016-12-01

Water quality and water management are worldwide issues. The analysis of pollutants and in particular, heavy metals, is generally conducted by sensitive but expensive physicochemical methods. Other alternative methods of analysis, such as microbial biosensors, have been developed for their potential simplicity and expected moderate cost. Using a biosensor for a long time generates many changes in the growth of the immobilized bacteria and consequently alters the robustness of the detection. This work simulated the operation of a biosensor for the long-term detection of cadmium and improved our understanding of the bioluminescence reaction dynamics of bioreporter bacteria inside an agarose matrix. The choice of the numerical tools is justified by the difficulty to measure experimentally in every condition the biosensor functioning during a long time (several days). The numerical simulation of a biomass profile is made by coupling the diffusion equation and the consumption/reaction of the nutrients by the bacteria. The numerical results show very good agreement with the experimental profiles. The growth model verified that the bacterial growth is conditioned by both the diffusion and the consumption of the nutrients. Thus, there is a high bacterial density in the first millimeter of the immobilization matrix. The growth model has been very useful for the development of the bioluminescence model inside the gel and shows that a concentration of oxygen greater than or equal to 22 % of saturation is required to maintain a significant level of bioluminescence. A continuous feeding of nutrients during the process of detection of cadmium leads to a biofilm which reduces the diffusion of nutrients and restricts the presence of oxygen from the first layer of the agarose (1 mm) and affects the intensity of the bioluminescent reaction. The main advantage of this work is to link experimental works with numerical models of growth and bioluminescence in order to provide a general purpose model to understand, anticipate, or predict the dysfunction of a biosensor using immobilized bioluminescent bioreporter in a matrix.

Theoretical and Numerical Investigation of Radiative Extinction of Diffusion Flames

NASA Technical Reports Server (NTRS)

Ray, Anjan

1996-01-01

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

Restoration of rhythmicity in diffusively coupled dynamical networks.

PubMed

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

2015-07-15

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

A Self-Contained Mapping Closure Approximation for Scalar Mixing

NASA Technical Reports Server (NTRS)

He, Guo-Wei; Zhang, Zi-Fan

2003-01-01

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

Turing instability in reaction-diffusion models on complex networks

NASA Astrophysics Data System (ADS)

Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya

2016-09-01

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

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

PubMed Central

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

2012-01-01

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

A diffusion modelling approach to understanding contextual cueing effects in children with ADHD

PubMed Central

Weigard, Alexander; Huang-Pollock, Cynthia

2014-01-01

Background Strong theoretical models suggest implicit learning deficits may exist among children with Attention Deficit Hyperactivity Disorder (ADHD). Method We examine implicit contextual cueing (CC) effects among children with ADHD (n=72) and non-ADHD Controls (n=36). Results Using Ratcliff’s drift diffusion model, we found that among Controls, the CC effect is due to improvements in attentional guidance and to reductions in response threshold. Children with ADHD did not show a CC effect; although they were able to use implicitly acquired information to deploy attentional focus, they had more difficulty adjusting their response thresholds. Conclusions Improvements in attentional guidance and reductions in response threshold together underlie the CC effect. Results are consistent with neurocognitive models of ADHD that posit sub-cortical dysfunction but intact spatial attention, and encourage the use of alternative data analytic methods when dealing with reaction time data. PMID:24798140

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

PubMed Central

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

2017-01-01

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

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2003-07-01

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

Monte Carlo PDF method for turbulent reacting flow in a jet-stirred reactor

NASA Astrophysics Data System (ADS)

Roekaerts, D.

1992-01-01

A stochastic algorithm for the solution of the modeled scalar probability density function (PDF) transport equation for single-phase turbulent reacting flow is described. Cylindrical symmetry is assumed. The PDF is represented by ensembles of N representative values of the thermochemical variables in each cell of a nonuniform finite-difference grid and operations on these elements representing convection, diffusion, mixing and reaction are derived. A simplified model and solution algorithm which neglects the influence of turbulent fluctuations on mean reaction rates is also described. Both algorithms are applied to a selectivity problem in a real reactor.

Diffusion-controlled reactions modeling in Geant4-DNA

NASA Astrophysics Data System (ADS)

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

2014-10-01

Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k-d tree data structure for quickly locating, for a given molecule, its closest reactants. The performance advantage is presented in terms of complexity, and the accuracy of the new algorithm is demonstrated by simulating radiation chemistry in the context of the Geant4-DNA project. Application The time-dependent radiolytic yields of the main chemical species formed after irradiation are computed for incident protons at different energies (from 50 MeV to 500 keV). Both the time-evolution and energy dependency of the yields are discussed. The evolution, at one microsecond, of the yields of hydroxyls and solvated electrons with respect to the linear energy transfer is compared to theoretical and experimental data. According to our results, at high linear energy transfer, modeling radiation chemistry in the trading compartment representation might be adopted.

Reaction-diffusion processes and metapopulation models on duplex networks

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Application of reaction-diffusion models to cell patterning in Xenopus retina. Initiation of patterns and their biological stability.

PubMed

Shoaf, S A; Conway, K; Hunt, R K

1984-08-07

We have examined the behavior of two reaction-diffusion models, originally proposed by Gierer & Meinhardt (1972) and by Kauffman, Shymko & Trabert (1978), for biological pattern formation. Calculations are presented for pattern formation on a disc (approximating the geometry of a number of embryonic anlagen including the frog eye rudiment), emphasizing the sensitivity of patterns to changes in initial conditions and to perturbations in the geometry of the morphogen-producing space. Analysis of the linearized equations from the models enabled us to select appropriate parameters and disc size for pattern growth. A computer-implemented finite element method was used to solve the non-linear model equations reiteratively. For the Gierer-Meinhardt model, initial activation (varying in size over two orders of magnitude) of one point on the disc's edge was sufficient to generate the primary gradient. Various parts of the disc were removed (remaining only as diffusible space) from the morphogen-producing cycle to investigate the effects of cells dropping out of the cycle due to cell death or malfunction (single point removed) or differentiation (center removed), as occur in the Xenopus eye rudiment. The resulting patterns had the same general shape and amplitude as normal gradients. Nor did a two-fold increase in disc size affect the pattern-generating ability of the model. Disc fragments bearing their primary gradient patterns were fused (with gradients in opposite directions, but each parallel to the fusion line). The resulting patterns generated by the model showed many similarities to results of "compound eye" experiments in Xenopus. Similar patterns were obtained with the model of Kauffman's group (1978), but we found less stability of the pattern subject to simulations of central differentiation. However, removal of a single point from the morphogen cycle (cell death) did not result in any change. The sensitivity of the Kauffman et al. model to shape perturbations is not surprising since the model was originally designed to use shape and increasing size during growth to generate a sequence of transient patterns. However, the Gierer-Meinhardt model is remarkably stable even when subjected to a wide range of perturbations in the diffusible space, thus allowing it to cope with normal biological variability, and offering an exciting range of possibilities for reaction-diffusion models as mechanisms underlying the spatial patterns of tissue structures.

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

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

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

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

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

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

2015-05-01

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

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

PubMed

Ochoa, F L

1984-01-01

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

Reactive solid surface morphology variation via ionic diffusion.

PubMed

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

2012-08-14

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

Synthesis of Refractory Compounds with Gasless Combustion Reactions.

DTIC Science & Technology

1983-09-01

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

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

PubMed Central

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

2015-01-01

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

A reaction-diffusion model for market fluctuations - A relation between price change and traded volumes

NASA Astrophysics Data System (ADS)

Yuvan, Steven; Bier, Martin

2018-02-01

Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

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

High Temperature Degradation Mechanisms in Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Cunningham, Ronan A.

1996-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Modeling of turbulent chemical reaction

NASA Technical Reports Server (NTRS)

Chen, J.-Y.

1995-01-01

Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.

Reaction-diffusion basis of retroviral infectivity

NASA Astrophysics Data System (ADS)

Sadiq, S. Kashif

2016-11-01

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

Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics.

PubMed

Marquez-Lago, Tatiana T; Burrage, Kevin

2007-09-14

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.

A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics

PubMed Central

Vuong, A.-T.; Rauch, A. D.

2017-01-01

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection–diffusion–reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics. PMID:28413347

PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC

USGS Publications Warehouse

Parkhurst, David L.; Wissmeier, Laurin

2015-01-01

PhreeqcRM is a geochemical reaction module designed specifically to perform equilibrium and kinetic reaction calculations for reactive transport simulators that use an operator-splitting approach. The basic function of the reaction module is to take component concentrations from the model cells of the transport simulator, run geochemical reactions, and return updated component concentrations to the transport simulator. If multicomponent diffusion is modeled (e.g., Nernst–Planck equation), then aqueous species concentrations can be used instead of component concentrations. The reaction capabilities are a complete implementation of the reaction capabilities of PHREEQC. In each cell, the reaction module maintains the composition of all of the reactants, which may include minerals, exchangers, surface complexers, gas phases, solid solutions, and user-defined kinetic reactants.PhreeqcRM assigns initial and boundary conditions for model cells based on standard PHREEQC input definitions (files or strings) of chemical compositions of solutions and reactants. Additional PhreeqcRM capabilities include methods to eliminate reaction calculations for inactive parts of a model domain, transfer concentrations and other model properties, and retrieve selected results. The module demonstrates good scalability for parallel processing by using multiprocessing with MPI (message passing interface) on distributed memory systems, and limited scalability using multithreading with OpenMP on shared memory systems. PhreeqcRM is written in C++, but interfaces allow methods to be called from C or Fortran. By using the PhreeqcRM reaction module, an existing multicomponent transport simulator can be extended to simulate a wide range of geochemical reactions. Results of the implementation of PhreeqcRM as the reaction engine for transport simulators PHAST and FEFLOW are shown by using an analytical solution and the reactive transport benchmark of MoMaS.

Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment.

PubMed

Appelo, C A J; Vinsot, A; Mettler, S; Wechner, S

2008-10-23

A borehole in the Callovo-Oxfordian clay rock in ANDRA's underground research facility was sampled during 1 year and chemically analyzed. Diffusion between porewater and the borehole solution resulted in concentration changes which were modeled with PHREEQC's multicomponent diffusion module. In the model, the clay rock's pore space is divided in free porewater (electrically neutral) and diffuse double layer water (devoid of anions). Diffusion is calculated separately for the two domains, and individually for all the solute species while a zero-charge flux is maintained. We explain how the finite difference formulas for radial diffusion can be translated into mixing factors for solutions. Operator splitting is used to calculate advective flow and chemical reactions such as ion exchange and calcite dissolution and precipitation. The ion exchange reaction is formulated in the form of surface complexation, which allows distributing charge over the fixed sites and the diffuse double layer. The charge distribution affects pH when calcite dissolves, and modeling of the experimental data shows that about 7% of the cation exchange capacity resides in the diffuse double layer. The model calculates the observed concentration changes very well and provides an estimate of the pristine porewater composition in the clay rock.

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

NASA Astrophysics Data System (ADS)

Zhang, XiaoLong; Zhong, Zheng

2017-08-01

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

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

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

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

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

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

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

Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

NASA Astrophysics Data System (ADS)

Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.

2017-03-01

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.

Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

PubMed Central

Angiolini, Juan; Plachta, Nicolas; Mocskos, Esteban; Levi, Valeria

2015-01-01

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments. PMID:26039162

The Fisher-KPP problem with doubly nonlinear diffusion

NASA Astrophysics Data System (ADS)

Audrito, Alessandro; Vázquez, Juan Luis

2017-12-01

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space.

PubMed

Wickman, Jonas; Diehl, Sebastian; Blasius, Bernd; Klausmeier, Christopher A; Ryabov, Alexey B; Brännström, Åke

2017-04-01

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

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

NASA Astrophysics Data System (ADS)

Ginn, T. R.

2018-01-01

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

Hydrodynamic fingering instability induced by a precipitation reaction

NASA Astrophysics Data System (ADS)

De Wit, Anne; Nagatsu, Yuichiro

2014-05-01

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the build-up of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A+B → C type of reaction when a solution containing one of the reactant is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Finger-like precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice-versa. A mathematical modeling of the underlying mobility profile in the cell reconstructed on the basis of one-dimensional reaction-diffusion concentration profiles confirms that the instability originates from a local decrease in mobility driven by the precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns.

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

2009-06-01

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

Multigrid methods for numerical simulation of laminar diffusion flames

NASA Technical Reports Server (NTRS)

Liu, C.; Liu, Z.; Mccormick, S.

1993-01-01

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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

NASA Astrophysics Data System (ADS)

Paster, Amir; Bolster, Diogo; Aquino, Tomas

2015-04-01

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

Modeling the rate-controlled sorption of hexavalent chromium

USGS Publications Warehouse

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

1985-01-01

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

Spatiotemporal pattern in somitogenesis: a non-Turing scenario with wave propagation.

PubMed

Nagahara, Hiroki; Ma, Yue; Takenaka, Yoshiko; Kageyama, Ryoichiro; Yoshikawa, Kenichi

2009-08-01

Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatiotemporal structures in a self-organized manner, such as temporal rhythms, switching phenomena, and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field. Based on the present model, we discuss the underlying physical principles that are independent of the details of biomolecular reactions. We also discuss the framework of spatial discreteness based on the reaction-diffusion model in relation to a cellular array, by comparison with an actual experimental observation.

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

PubMed

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

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

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

PubMed

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

2011-07-01

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

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

PubMed Central

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

2011-01-01

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

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

PubMed

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

2017-02-01

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

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advectivemore » dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.« less

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

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

Devincent, Sandra M.; Michal, Gary M.

1993-01-01

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

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Highly Viscous States Affect the Browning of Atmospheric Organic Particulate Matter

PubMed Central

2018-01-01

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

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

PubMed

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

2018-02-28

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

A new necessary condition for Turing instabilities.

PubMed

Elragig, Aiman; Townley, Stuart

2012-09-01

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community. Copyright © 2012 Elsevier Inc. All rights reserved.

Coupling between geochemical reactions and multicomponent gas and solute transport in unsaturated media: A reactive transport modeling study

USGS Publications Warehouse

Molins, S.; Mayer, K.U.

2007-01-01

The two‐way coupling that exists between biogeochemical reactions and vadose zone transport processes, in particular gas phase transport, determines the composition of soil gas. To explore these feedback processes quantitatively, multicomponent gas diffusion and advection are implemented into an existing reactive transport model that includes a full suite of geochemical reactions. Multicomponent gas diffusion is described on the basis of the dusty gas model, which accounts for all relevant gas diffusion mechanisms. The simulation of gas attenuation in partially saturated landfill soil covers, methane production, and oxidation in aquifers contaminated by organic compounds (e.g., an oil spill site) and pyrite oxidation in mine tailings demonstrate that both diffusive and advective gas transport can be affected by geochemical reactions. Methane oxidation in landfill covers reduces the existing upward pressure gradient, thereby decreasing the contribution of advective methane emissions to the atmosphere and enhancing the net flux of atmospheric oxygen into the soil column. At an oil spill site, methane oxidation causes a reversal in the direction of gas advection, which results in advective transport toward the zone of oxidation both from the ground surface and the deeper zone of methane production. Both diffusion and advection contribute to supply atmospheric oxygen into the subsurface, and methane emissions to the atmosphere are averted. During pyrite oxidation in mine tailings, pressure reduction in the reaction zone drives advective gas flow into the sediment column, enhancing the oxidation process. In carbonate‐rich mine tailings, calcite dissolution releases carbon dioxide, which partly offsets the pressure reduction caused by O2 consumption.

From conservative to reactive transport under diffusion-controlled conditions

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

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

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

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

Osmotic propulsion: the osmotic motor.

PubMed

Córdova-Figueroa, Ubaldo M; Brady, John F

2008-04-18

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

Osmotic Propulsion: The Osmotic Motor

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

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

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

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

NASA Technical Reports Server (NTRS)

Takahashi, Fumiaki; Katta, Viswanath R.

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

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

Wavenumber distribution in Hopf-wave instability: the reversible Selkov model of glycolytic oscillation.

PubMed

Dutt, Arun K

2005-09-22

We have investigated the short-wave instability due to Hopf bifurcation in a reaction-diffusion model of glycolytic oscillations. Very low values of the ratio d of the diffusion coefficient of the inhibitor (ATP) and that of the activator (ADP) do help to create short waves, whereas high values of the ratio d and the complexing reaction of the activator ADP reduces drastically the wave-instability domain, generating much longer wavelengths.

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

PubMed

Dematté, Lorenzo

2012-01-01

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

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

PubMed

Li, Shaobai; Dasmahapatra, Srinandan; Maharatna, Koushik

2015-12-01

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

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

Progress toward bridging from atomistic to continuum modeling to predict nuclear waste glass dissolution.

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

Zapol, Peter; Bourg, Ian; Criscenti, Louise Jacqueline

2011-10-01

This report summarizes research performed for the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Subcontinuum and Upscaling Task. The work conducted focused on developing a roadmap to include molecular scale, mechanistic information in continuum-scale models of nuclear waste glass dissolution. This information is derived from molecular-scale modeling efforts that are validated through comparison with experimental data. In addition to developing a master plan to incorporate a subcontinuum mechanistic understanding of glass dissolution into continuum models, methods were developed to generate constitutive dissolution rate expressions from quantum calculations, force field models were selected to generate multicomponent glass structures and gel layers,more » classical molecular modeling was used to study diffusion through nanopores analogous to those in the interfacial gel layer, and a micro-continuum model (K{mu}C) was developed to study coupled diffusion and reaction at the glass-gel-solution interface.« less

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

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

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

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

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

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

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

1999-08-01

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

Effect of electron Monte Carlo collisions on a hybrid simulation of a low-pressure capacitively coupled plasma

NASA Astrophysics Data System (ADS)

Hwang, Seok Won; Lee, Ho-Jun; Lee, Hae June

2014-12-01

Fluid models have been widely used and conducted successfully in high pressure plasma simulations where the drift-diffusion and the local-field approximation are valid. However, fluid models are not able to demonstrate non-local effects related to large electron energy relaxation mean free path in low pressure plasmas. To overcome this weakness, a hybrid model coupling electron Monte Carlo collision (EMCC) method with the fluid model is introduced to obtain precise electron energy distribution functions using pseudo-particles. Steady state simulation results by a one-dimensional hybrid model which includes EMCC method for the collisional reactions but uses drift-diffusion approximation for electron transport in a fluid model are compared with those of a conventional particle-in-cell (PIC) and a fluid model for low pressure capacitively coupled plasmas. At a wide range of pressure, the hybrid model agrees well with the PIC simulation with a reduced calculation time while the fluid model shows discrepancy in the results of the plasma density and the electron temperature.

Vortex-scalar element calculations of a diffusion flame stabilized on a plane mixing layer

NASA Technical Reports Server (NTRS)

Ghoniem, Ahmed F.; Givi, Peyman

1987-01-01

The vortex-scalar element method, a scheme which utilizes vortex elements to discretize the region of high vorticity and scalar elements to represent species or temperature fields, is utilized in the numerical simulations of a two-dimensional reacting mixing layer. Computations are performed for a diffusion flame at high Reynolds and Peclet numbers without resorting to turbulence models. In the nonreacting flow, the mean and fluctuation profiles of a conserved scalar show good agreement with experimental measurements. Results for the reacting flow indicate that for temperature independent kinetics, the chemical reaction begins immediately downstream of the splitter plate where mixing starts. Results for the reacting flow with Arrhenius kinetics show an ignition delay, which depends on reactant temperature, before significant chemical reaction occurs. Harmonic forcing changes the structure of the layer, and concomitantly the rates of mixing and reaction, in accordance with experimental results. Strong stretch within the braids in the nonequilibrium kinetics case causes local flame quenching due to the temperature drop associated with the large convective fluxes.

Localization of (photo)respiration and CO2 re-assimilation in tomato leaves investigated with a reaction-diffusion model

PubMed Central

Berghuijs, Herman N. C.; Yin, Xinyou; Ho, Q. Tri; Verboven, Pieter; Nicolaï, Bart M.

2017-01-01

The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro) leaves, if (photo)respiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photo)respiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photo)respired CO2 is affected by environmental conditions and physiological parameters. PMID:28880924

Localization of (photo)respiration and CO2 re-assimilation in tomato leaves investigated with a reaction-diffusion model.

PubMed

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

2017-01-01

The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro) leaves, if (photo)respiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photo)respiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photo)respired CO2 is affected by environmental conditions and physiological parameters.

The use of solid-state reactions with volume loss to engineer stress and porosity into the fiber-matrix interface of a ceramic composite

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

Hay, R.S.

The effect of the 11 vol% losing during reaction of yttrium-aluminas garnet (YAG) and zirconia was observed in zirconia coated single-crystal alumina fiber-YAG matrix composites. The reaction caused plastic deformation in the alumina fibers, and possibly a minor amount of porosity at fiber-matrix interfaces that was usually indistinguishable from matrix porosity. The results were analyzed by models for diffusive cavitation modified to use reaction self-stress. Crack-healing, tensile stress states along the reaction front that approach plane stress, and the small volume of self-stressed material make crack-like pores unlikely at the high temperatures required for reaction. Smaller matrix grains might promotemore » formation of smaller cavities but are also incompatible with high temperature. Both modeling and experiment suggest that sufficient porosity for crack deflection and fiber pullout cannot form unless processing methods that form dense composites at lower temperatures are used.« less

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

DOE PAGES

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

2017-02-07

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

Diffusion-controlled reactions modeling in Geant4-DNA

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

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

2014-10-01

Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing allmore » the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The performance advantage is presented in terms of complexity, and the accuracy of the new algorithm is demonstrated by simulating radiation chemistry in the context of the Geant4-DNA project. Application The time-dependent radiolytic yields of the main chemical species formed after irradiation are computed for incident protons at different energies (from 50 MeV to 500 keV). Both the time-evolution and energy dependency of the yields are discussed. The evolution, at one microsecond, of the yields of hydroxyls and solvated electrons with respect to the linear energy transfer is compared to theoretical and experimental data. According to our results, at high linear energy transfer, modeling radiation chemistry in the trading compartment representation might be adopted.« less

Fluctuation correlation models for receptor immobilization

NASA Astrophysics Data System (ADS)

Fourcade, B.

2017-12-01

Nanoscale dynamics with cycles of receptor diffusion and immobilization by cell-external-or-internal factors is a key process in living cell adhesion phenomena at the origin of a plethora of signal transduction pathways. Motivated by modern correlation microscopy approaches, the receptor correlation functions in physical models based on diffusion-influenced reaction is studied. Using analytical and stochastic modeling, this paper focuses on the hybrid regime where diffusion and reaction are not truly separable. The time receptor autocorrelation functions are shown to be indexed by different time scales and their asymptotic expansions are given. Stochastic simulations show that this analysis can be extended to situations with a small number of molecules. It is also demonstrated that this analysis applies when receptor immobilization is coupled to environmental noise.

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

NASA Astrophysics Data System (ADS)

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

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

Finite Element Analysis Modeling of Chemical Vapor Deposition of Silicon Carbide

DTIC Science & Technology

2014-06-19

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

Control of transversal instabilities in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

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

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

2014-10-01

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

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

DOE PAGES

Hoffmann, Max J.; Bligaard, Thomas

2018-01-22

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

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

Hoffmann, Max J.; Bligaard, Thomas

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

A fractional reaction-diffusion description of supply and demand

NASA Astrophysics Data System (ADS)

Benzaquen, Michael; Bouchaud, Jean-Philippe

2018-02-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

Mohamed, Fatma Naser Ali

This dissertation considers some parabolic type problems from thin film theory and chemical reaction-diffusion networks. The dissertation consists of two parts: In the first part, we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove an existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that, in this case, the surface-tension energy dissipation is the mechanism responsible for the H1-norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type, are also successfully treated by the same means. [special characters omitted]. In the second part, we are concerned with the convergence of a certain space-discretization scheme -the so-called method of lines- for mass-action reaction-diffusion systems. First, we start with a toy model, namely. [special characters omitted]. and prove convergence of method of lines for this linear case. Here weak convergence in L2(0,1) is enough to prove convergence of the method of lines. Then we adopt the framework for convergence analysis introduced in [23] and concentrate on the proof-of-concept reaction. within 1D space, while at the same time noting that our techniques are readily generalizable to other reaction-diffusion networks and to more than one space dimension. Indeed, it will be obvious how to extend our proofs to the multi-dimensional case; we only note that the proof of the comparison principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream numerical tool and the specialized literature is rather scarce. The method amounts to discretizing evolutionary PDE's in space only, so it produces a semi-discrete numerical scheme which consists of a system of ODE's (in the time variable). To prove convergence of the semi-discrete MOL scheme to the original PDE one needs to perform some more or less traditional analysis: it is necessary to show that the scheme is consistent with the continuous problem and that the discretized version of the spatial differential operator retains sufficient dissipative properties in order to allow an application of Gronwall's Lemma to the error term. As shown in [23], a uniform (in time) consistency estimate is sufficient to obtain convergence; however, the consistency estimate we proved is not uniform for a small time, so we cannot directly employ the results in [23] to prove convergence in our case. Instead, we prove all the required estimates "from the scratch", then we use their exact quantitative form in order to conclude convergence.

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

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

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

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

PubMed

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

2010-06-07

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

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

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

Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions

NASA Astrophysics Data System (ADS)

Yeh, Gour-Tsyh (George); Siegel, Malcolm D.; Li, Ming-Hsu

2001-02-01

The couplings among chemical reaction rates, advective and diffusive transport in fractured media or soils, and changes in hydraulic properties due to precipitation and dissolution within fractures and in rock matrix are important for both nuclear waste disposal and remediation of contaminated sites. This paper describes the development and application of LEHGC2.0, a mechanistically based numerical model for simulation of coupled fluid flow and reactive chemical transport, including both fast and slow reactions in variably saturated media. Theoretical bases and numerical implementations are summarized, and two example problems are demonstrated. The first example deals with the effect of precipitation/dissolution on fluid flow and matrix diffusion in a two-dimensional fractured media. Because of the precipitation and decreased diffusion of solute from the fracture into the matrix, retardation in the fractured medium is not as large as the case wherein interactions between chemical reactions and transport are not considered. The second example focuses on a complicated but realistic advective-dispersive-reactive transport problem. This example exemplifies the need for innovative numerical algorithms to solve problems involving stiff geochemical reactions.

Multi-Algorithm Particle Simulations with Spatiocyte.

PubMed

Arjunan, Satya N V; Takahashi, Koichi

2017-01-01

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

Study on Kinetic Mechanism of Bastnaesite Concentrates Decomposition Using Calcium Hydroxide

NASA Astrophysics Data System (ADS)

Cen, Peng; Wu, Wenyuan; Bian, Xue

2018-06-01

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

On the Chemistry of Hydrides of N Atoms and O+ Ions

NASA Astrophysics Data System (ADS)

Awad, Zainab; Viti, Serena; Williams, David A.

2016-08-01

Previous work by various authors has suggested that the detection by Herschel/HIFI of nitrogen hydrides along the low-density lines of sight toward G10.6-0.4 (W31C) cannot be accounted for by gas-phase chemical models. In this paper we investigate the role of surface reactions on dust grains in diffuse regions, and we find that formation of the hydrides by surface reactions on dust grains with efficiency comparable to that for H2 formation reconciles models with observations of nitrogen hydrides. However, similar surface reactions do not contribute significantly to the hydrides of O+ ions detected by Herschel/HIFI that are present along many sight lines in the Galaxy. The O+ hydrides can be accounted for by conventional gas-phase chemistry either in diffuse clouds of very low density with normal cosmic-ray fluxes or in somewhat denser diffuse clouds with high cosmic-ray fluxes. Hydride chemistry in dense dark clouds appears to be dominated by gas-phase ion-molecule reactions.

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

PubMed

Allison, Stuart

2006-12-28

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Patchy reaction-diffusion and population abundance: the relative importance of habitat amount and arrangement

Treesearch

Curtis H. Flather; Michael Bevers

2002-01-01

A discrete reaction-diffusion model was used to estimate long-term equilibrium populations of a hypothetical species inhabiting patchy landscapes to examine the relative importance of habitat amount and arrangement in explaining population size. When examined over a broad range of habitat amounts and arrangements, population size was largely determined by a pure amount...

Gas and grain chemical composition in cold cores as predicted by the Nautilus three-phase model

NASA Astrophysics Data System (ADS)

Ruaud, Maxime; Wakelam, Valentine; Hersant, Franck

2016-07-01

We present an extended version of the two-phase gas-grain code NAUTILUS to the three-phase modelling of gas and grain chemistry of cold cores. In this model, both the mantle and the surface are considered as chemically active. We also take into account the competition among reaction, diffusion and evaporation. The model predictions are confronted to ice observations in the envelope of low-mass and massive young stellar objects as well as towards background stars. Modelled gas-phase abundances are compared to species observed towards TMC-1 (CP) and L134N dark clouds. We find that our model successfully reproduces the observed ice species. It is found that the reaction-diffusion competition strongly enhances reactions with barriers and more specifically reactions with H2, which is abundant on grains. This finding highlights the importance having a good approach to determine the abundance of H2 on grains. Consequently, it is found that the major N-bearing species on grains go from NH3 to N2 and HCN when the reaction-diffusion competition is taken into account. In the gas phase and before a few 105 yr, we find that the three-phase model does not have a strong impact on the observed species compared to the two-phase model. After this time, the computed abundances dramatically decrease due to the strong accretion on dust, which is not counterbalanced by the desorption less efficient than in the two-phase model. This strongly constrains the chemical age of cold cores to be of the order of few 105 yr.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

NASA Astrophysics Data System (ADS)

Vidal-Henriquez, Estefania; Zykov, Vladimir; Bodenschatz, Eberhard; Gholami, Azam

2017-10-01

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

Individual Differences in Components of Reaction Time Distributions and Their Relations to Working Memory and Intelligence

ERIC Educational Resources Information Center

Schmiedek, Florian; Oberauer, Klaus; Wilhelm, Oliver; Suss, Heinz-Martin; Wittmann, Werner W.

2007-01-01

The authors bring together approaches from cognitive and individual differences psychology to model characteristics of reaction time distributions beyond measures of central tendency. Ex-Gaussian distributions and a diffusion model approach are used to describe individuals' reaction time data. The authors identified common latent factors for each…

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

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

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

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

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

PubMed

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

2016-08-01

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

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

NASA Astrophysics Data System (ADS)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

Inward propagating chemical waves in Taylor vortices.

PubMed

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

Intra-particle migration of mercury in granular polysulfide-rubber-coated activated carbon (PSR-AC)

PubMed Central

Kim, Eun-Ah; Masue-Slowey, Yoko; Fendorf, Scott; Luthy, Richard G.

2011-01-01

The depth profile of mercuric ion after the reaction with polysulfide-rubber-coated activated carbon (PSR-AC) was investigated using micro-x-ray fluorescence (μ-XRF) imaging techniques and mathematical modeling. The μ-XRF results revealed that mercury was concentrated at 0~100 μm from the exterior of the particle after three months of treatment with PSR-AC in 10 ppm HgCl2 aqueous solution. The μ-X-ray absorption near edge spectroscopic (μ-XANES) analyses indicated HgS as a major mercury species, and suggested that the intra-particle mercury transport involved a chemical reaction with PSR polymer. An intra-particle mass transfer model was developed based on either a Langmuir sorption isotherm with liquid phase diffusion (Langmuir model) or a kinetic sorption with surface diffusion (kinetic sorption model). The Langmuir model predicted the general trend of mercury diffusion, although at a slower rate than observed from the μ-XRF map. A kinetic sorption model suggested faster mercury transport, which overestimated the movement of mercuric ions through an exchange reaction between the fast and slow reaction sites. Both μ-XRF and mathematical modeling results suggest mercury removal occurs not only at the outer surface of the PSR-AC particle but also at some interior regions due to a large PSR surface area within an AC particle. PMID:22133913

Analysis of Classes of Singular Steady State Reaction Diffusion Equations

NASA Astrophysics Data System (ADS)

Son, Byungjae

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Spatial modeling of cell signaling networks.

PubMed

Cowan, Ann E; Moraru, Ion I; Schaff, James C; Slepchenko, Boris M; Loew, Leslie M

2012-01-01

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling. Copyright © 2012 Elsevier Inc. All rights reserved.

Influencing factors and kinetics analysis on the leaching of iron from boron carbide waste-scrap with ultrasound-assisted method.

PubMed

Li, Xin; Xing, Pengfei; Du, Xinghong; Gao, Shuaibo; Chen, Chen

2017-09-01

In this paper, the ultrasound-assisted leaching of iron from boron carbide waste-scrap was investigated and the optimization of different influencing factors had also been performed. The factors investigated were acid concentration, liquid-solid ratio, leaching temperature, ultrasonic power and frequency. The leaching of iron with conventional method at various temperatures was also performed. The results show the maximum iron leaching ratios are 87.4%, 94.5% for 80min-leaching with conventional method and 50min-leaching with ultrasound assistance, respectively. The leaching of waste-scrap with conventional method fits the chemical reaction-controlled model. The leaching with ultrasound assistance fits chemical reaction-controlled model, diffusion-controlled model for the first stage and second stage, respectively. The assistance of ultrasound can greatly improve the iron leaching ratio, accelerate the leaching rate, shorten leaching time and lower the residual iron, comparing with conventional method. The advantages of ultrasound-assisted leaching were also confirmed by the SEM-EDS analysis and elemental analysis of the raw material and leached solid samples. Copyright © 2017 Elsevier B.V. All rights reserved.

A transport equation for the scalar dissipation in reacting flows with variable density: First results

NASA Technical Reports Server (NTRS)

Mantel, T.

1993-01-01

Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Role of Water Activity on Intergranular Transport at High Pressure

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Domainal cleavage as an Anisotropic Reaction-diffusion Process

NASA Astrophysics Data System (ADS)

Mulchrone, Kieran; Meere, Patrick

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Bootstrapping Least Squares Estimates in Biochemical Reaction Networks

PubMed Central

Linder, Daniel F.

2015-01-01

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

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

PubMed

Chevalier, Michael W; El-Samad, Hana

2012-08-28

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

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

NASA Astrophysics Data System (ADS)

Nec, Yana

2018-01-01

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

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

PubMed

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

2015-05-14

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

Polymeric hydrogen diffusion barrier, high-pressure storage tank so equipped, method of fabricating a storage tank and method of preventing hydrogen diffusion

DOEpatents

Lessing, Paul A [Idaho Falls, ID

2008-07-22

An electrochemically active hydrogen diffusion barrier which comprises an anode layer, a cathode layer, and an intermediate electrolyte layer, which is conductive to protons and substantially impermeable to hydrogen. A catalytic metal present in or adjacent to the anode layer catalyzes an electrochemical reaction that converts any hydrogen that diffuses through the electrolyte layer to protons and electrons. The protons and electrons are transported to the cathode layer and reacted to form hydrogen. The hydrogen diffusion barrier is applied to a polymeric substrate used in a storage tank to store hydrogen under high pressure. A storage tank equipped with the electrochemically active hydrogen diffusion barrier, a method of fabricating the storage tank, and a method of preventing hydrogen from diffusing out of a storage tank are also disclosed.

Polymeric hydrogen diffusion barrier, high-pressure storage tank so equipped, method of fabricating a storage tank and method of preventing hydrogen diffusion

DOEpatents

Lessing, Paul A.

2004-09-07

An electrochemically active hydrogen diffusion barrier which comprises an anode layer, a cathode layer, and an intermediate electrolyte layer, which is conductive to protons and substantially impermeable to hydrogen. A catalytic metal present in or adjacent to the anode layer catalyzes an electrochemical reaction that converts any hydrogen that diffuses through the electrolyte layer to protons and electrons. The protons and electrons are transported to the cathode layer and reacted to form hydrogen. The hydrogen diffusion barrier is applied to a polymeric substrate used in a storage tank to store hydrogen under high pressure. A storage tank equipped with the electrochemically active hydrogen diffusion barrier, a method of fabricating the storage tank, and a method of preventing hydrogen from diffusing out of a storage tank are also disclosed.

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

NASA Astrophysics Data System (ADS)

Radszuweit, M.; Engel, H.; Bär, M.

2010-12-01

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

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

NASA Astrophysics Data System (ADS)

Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi

2017-11-01

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.

Modeling CO2 mass transfer in amine mixtures: PZ-AMP and PZ-MDEA.

PubMed

Puxty, Graeme; Rowland, Robert

2011-03-15

The most common method of carbon dioxide (CO(2)) capture is the absorption of CO(2) into a falling thin film of an aqueous amine solution. Modeling of mass transfer during CO(2) absorption is an important way to gain insight and understanding about the underlying processes that are occurring. In this work a new software tool has been used to model CO(2) absorption into aqueous piperazine (PZ) and binary mixtures of PZ with 2-amino-2-methyl-1-propanol (AMP) or methyldiethanolamine (MDEA). The tool solves partial differential and simultaneous equations describing diffusion and chemical reaction automatically derived from reactions written using chemical notation. It has been demonstrated that by using reactions that are chemically plausible the mass transfer in binary mixtures can be fully described by combining the chemical reactions and their associated parameters determined for single amines. The observed enhanced mass transfer in binary mixtures can be explained through chemical interactions occurring in the mixture without need to resort to using additional reactions or unusual transport phenomena such as the "shuttle mechanism".

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

PubMed Central

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Peltier-based cloud chamber

NASA Astrophysics Data System (ADS)

Nar, Sevda Yeliz; Cakir, Altan

2018-02-01

Particles produced by nuclear decay, cosmic radiation and reactions can be identified through various methods. One of these methods that has been effective in the last century is the cloud chamber. The chamber makes visible cosmic particles that we are exposed to radiation per second. Diffusion cloud chamber is a kind of cloud chamber that is cooled by dry ice. This traditional model has some application difficulties. In this work, Peltier-based cloud chamber cooled by thermoelectric modules is studied. The new model provided uniformly cooled base of the chamber, moreover, it has longer lifetime than the traditional chamber in terms of observation time. This gain has reduced the costs which spent each time for cosmic particle observation. The chamber is an easy-to-use system according to traditional diffusion cloud chamber. The new model is portable, easier to make, and can be used in the nuclear physics experiments. In addition, it would be very useful to observe Muons which are the direct evidence for Lorentz contraction and time expansion predicted by Einsteins special relativity principle.

MODELING DIFFUSION AND REACTION IN SOILS: X. A UNIFYING MODEL FOR SOLUTE AND GAS DIFFUSIVITY IN UNSATURATED SOIL. (R825433)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Variational fine-grained data assimilation schemes for atmospheric chemistry transport and transformation models

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir; Tsvetova, Elena

2015-04-01

The paper concerns data assimilation problem for an atmospheric chemistry transport and transformation models. Data assimilation is carried out within variation approach on a single time step of the approximated model. A control function is introduced into the model source term (emission rate) to provide flexibility to adjust to data. This function is evaluated as the minimum of the target functional combining control function norm to a misfit between measured and model-simulated analog of data. This provides a flow-dependent and physically-plausible structure of the resulting analysis and reduces the need to calculate model error covariance matrices that are sought within conventional approach to data assimilation. Extension of the atmospheric transport model with a chemical transformations module influences data assimilation algorithms performance. This influence is investigated with numerical experiments for different meteorological conditions altering convection-diffusion processes characteristics, namely strong, medium and low wind conditions. To study the impact of transformation and data assimilation, we compare results for a convection-diffusion model (without data assimilation), convection-diffusion with assimilation, convection-diffusion-reaction (without data assimilation) and convection-diffusion-reaction-assimilation models. Both high dimensionalities of the atmospheric chemistry models and a real-time mode of operation demand for computational efficiency of the algorithms. Computational issues with complicated models can be solved by using a splitting technique. As the result a model is presented as a set of relatively independent simple models equipped with a kind of coupling procedure. With regard to data assimilation two approaches can be identified. In a fine-grained approach data assimilation is carried out on the separate splitting stages [1,2] independently on shared measurement data. The same situation arises when constructing a hybrid model out of two models each having its own assimilation scheme. In integrated schemes data assimilation is carried out with respect to the split model as a whole. First approach is more efficient from computational point of view, for in some important cases it can be implemented without iterations [2]. Its shortcoming is that control functions in different part of the model are adjusted independently thus having less evident physical sense. With the aid of numerical experiments we compare the two approaches. Work has been partially supported by COST Action ES1004 STSM Grants #16817 and #21654, RFBR 14-01-31482 mol a and 14-01-00125, Programmes # 4 Presidium RAS and # 3 MSD RAS, integration projects SB RAS #8 and #35. References: [1] V. V. Penenko Variational methods of data assimilation and inverse problems for studying the atmosphere, ocean, and environment Num. Anal. and Appl., 2009 V 2 No 4, 341-351. [2] A.V. Penenko and V.V. Penenko. Direct data assimilation method for convection-diffusion models based on splitting scheme. Computational technologies, 19(4):69-83, 2014.

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

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

Analysis of opposed jet hydrogen-air counter flow diffusion flame

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Exact PDF equations and closure approximations for advective-reactive transport

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

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

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

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

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

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

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

DOE PAGES

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

2018-04-14

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

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

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

NASA Astrophysics Data System (ADS)

Manneville, Paul

2012-06-01

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

Lateral uniformity in chemical composition along a buried reaction front in polymers using off-specular reflectivity.

PubMed

Lavery, Kristopher A; Prabhu, Vivek M; Satija, Sushil; Wu, Wen-Li

2010-12-01

Off-specular neutron reflectometry was applied to characterize the form and amplitude of lateral compositional variations at a buried reaction-diffusion front. In this work, off-specular neutron measurements were first calibrated using off-specular x-ray reflectivity and atomic force microscopy via a roughened glass surface, both as a free surface and as a buried interface that was prepared by spin coating thin polymer films upon the glass surface. All three methods provided consistent roughness values despite the difference in their detection mechanism. Our neutron results demonstrated, for the first time, that the compositional heterogeneity at a buried reaction front can be measured; the model system used in this study mimics the deprotection reaction that occurs during the photolithographic process necessary for manufacturing integrated circuits.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

NASA Astrophysics Data System (ADS)

Dibak, Manuel; del Razo, Mauricio J.; De Sancho, David; Schütte, Christof; Noé, Frank

2018-06-01

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

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

PubMed Central

Johnson, Margaret E.; Hummer, Gerhard

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

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

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

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

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

Monte Carlo simulations of coupled diffusion and surface reactions during the aqueous corrosion of borosilicate glasses

DOE PAGES

Kerisit, Sebastien; Pierce, Eric M.; Ryan, Joseph V.

2014-09-19

Borosilicate nuclear waste glasses develop complex altered layers as a result of coupled processes such as hydrolysis of network species, condensation of Si species, and diffusion. However, diffusion has often been overlooked in Monte Carlo models of the aqueous corrosion of borosilicate glasses. Therefore, in this paper three different models for dissolved Si diffusion in the altered layer were implemented in a Monte Carlo model and evaluated for glasses in the compositional range (75 - x) mol% SiO 2 (12.5 + x/2) mol% B 2O 3 and (12.5 + x/2) mol% Na 2O, where 0 ≤ x ≤ 20%, andmore » corroded in static conditions at a surface-area-to-volume ratio of 1000 m -1. The three models considered instantaneous homogenization (M1), linear concentration gradients (M2), and concentration profiles determined by solving Fick's 2nd law using a finite difference method (M3). Model M3 revealed that concentration profiles in the altered layer are not linear and show changes in shape and magnitude as corrosion progresses, unlike those assumed in model M2. Furthermore, model M3 showed that, for borosilicate glasses with a high forward dissolution rate compared to the diffusion rate, the gradual polymerization and densification of the altered layer is significantly delayed compared to models M1 and M2. Finally, models M1 and M2 were found to be appropriate models only for glasses with high release rates such as simple borosilicate glasses with low ZrO 2 content.« less

Modeling Biogeochemical Cycling of Heavy Metals in Lake Coeur d'Alene Sediments

NASA Astrophysics Data System (ADS)

Sengor, S. S.; Spycher, N.; Belding, E.; Curthoys, K.; Ginn, T. R.

2005-12-01

Mining of precious metals since the late 1800's have left Lake Coeur d'Alene (LCdA) sediments heavily enriched with toxic metals, including Cd, Cu, Pb, and Zn. Indigenous microbes however are capable of catalyzing reactions that detoxify the benthic and aqueous lake environments, and thus constitute an important driving component in the biogeochemical cycles of these metals. Here we report on the development of a quantitative model of transport, fate, exposure and effects of toxic compounds on benthic microbial communities at LCdA. First, chemical data from the LCdA area have been compiled from multiple sources to investigate trends in chemical occurrence, as well as to define model boundary conditions. The model is structured as 1-D diffusive reactive transport model to simulate spatial and temporal distribution of metals through the benthic sediments. Inorganic reaction processes included in the model are aqueous speciation, surface complexation, mineral precipitation/dissolution and abiotic redox reactions. Simulations with and without surface complexation are carried out to evaluate the effect of sorption and the conservative behaviour of metals within the benthic sediments under abiotic and purely diffusive transport. The 1-D inorganic diffusive transport model is then coupled to a biotic reaction network including consortium biodegradation kinetics with multiple electron acceptors, product toxicity, and energy partitioning. Multiyear simulations are performed, with water column chemistry established as a boundary condition from extant data, to explore the role of biogeochemical dynamics on benthic fluxes of metals in the long term.

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

NASA Astrophysics Data System (ADS)

Pilli, Siva P.

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

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

NASA Technical Reports Server (NTRS)

Ramos, J. I.

1986-01-01

Results from a one-dimensional combustion model employing a constant eddy diffusivity and a one-step chemical reaction are compared with those of one-zone and two-zone thermodynamic models to study the flame propagation in a spark-ignition engine. One-dimensional model predictions are found to be very sensitive to the eddy diffusivity and reaction rate data. The average mixing temperature found using the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, and that of the one-dimensional model is higher than those predicted by both thermodynamic models during the expansion stroke. The one-dimensional model is shown to predict an accelerating flame even when the front approaches the cold cylinder wall.

Isotachophoresis-Based Surface Immunoassay.

PubMed

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

2017-07-18

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

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

PubMed

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

2016-04-08

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

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

PubMed Central

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

2016-01-01

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

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

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

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

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

NASA Astrophysics Data System (ADS)

Liu, Da-Jiang; Evans, James W.

2013-12-01

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

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

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

Liu, Dajiang; Evans, James W.

2013-12-01

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

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

PubMed Central

Wils, Stefan; Schutter, Erik De

2008-01-01

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

EUPDF: Eulerian Monte Carlo Probability Density Function Solver for Applications With Parallel Computing, Unstructured Grids, and Sprays

NASA Technical Reports Server (NTRS)

Raju, M. S.

1998-01-01

The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic-diffusion flames and spray flames. The EUPDF source code will be available with the National Combustion Code (NCC) as a complete package.

Ozone-surface interactions: Investigations of mechanisms, kinetics, mass transport, and implications for indoor air quality

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

Morrison, Glenn Charles

1999-12-01

In this dissertation, results are presented of laboratory investigations and mathematical modeling efforts designed to better understand the interactions of ozone with surfaces. In the laboratory, carpet and duct materials were exposed to ozone and measured ozone uptake kinetics and the ozone induced emissions of volatile organic compounds. To understand the results of the experiments, mathematical methods were developed to describe dynamic indoor aldehyde concentrations, mass transport of reactive species to smooth surfaces, the equivalent reaction probability of whole carpet due to the surface reactivity of fibers and carpet backing, and ozone aging of surfaces. Carpets, separated carpet fibers, andmore » separated carpet backing all tended to release aldehydes when exposed to ozone. Secondary emissions were mostly n-nonanal and several other smaller aldehydes. The pattern of emissions suggested that vegetable oils may be precursors for these oxidized emissions. Several possible precursors and experiments in which linseed and tung oils were tested for their secondary emission potential were discussed. Dynamic emission rates of 2-nonenal from a residential carpet may indicate that intermediate species in the oxidation of conjugated olefins can significantly delay aldehyde emissions and act as reservoir for these compounds. The ozone induced emission rate of 2-nonenal, a very odorous compound, can result in odorous indoor concentrations for several years. Surface ozone reactivity is a key parameter in determining the flux of ozone to a surface, is parameterized by the reaction probability, which is simply the probability that an ozone molecule will be irreversibly consumed when it strikes a surface. In laboratory studies of two residential and two commercial carpets, the ozone reaction probability for carpet fibers, carpet backing and the equivalent reaction probability for whole carpet were determined. Typically reaction probability values for these materials were 10 -7, 10 -5, and 10 -5 respectively. To understand how internal surface area influences the equivalent reaction probability of whole carpet, a model of ozone diffusion into and reaction with internal carpet components was developed. This was then used to predict apparent reaction probabilities for carpet. He combines this with a modified model of turbulent mass transfer developed by Liu, et al. to predict deposition rates and indoor ozone concentrations. The model predicts that carpet should have an equivalent reaction probability of about 10 -5, matching laboratory measurements of the reaction probability. For both carpet and duct materials, surfaces become progressively quenched (aging), losing the ability to react or otherwise take up ozone. He evaluated the functional form of aging and find that the reaction probability follows a power function with respect to the cumulative uptake of ozone. To understand ozone aging of surfaces, he developed several mathematical descriptions of aging based on two different mechanisms. The observed functional form of aging is mimicked by a model which describes ozone diffusion with internal reaction in a solid. He shows that the fleecy nature of carpet materials in combination with the model of ozone diffusion below a fiber surface and internal reaction may explain the functional form and the magnitude of power function parameters observed due to ozone interactions with carpet. The ozone induced aldehyde emissions, measured from duct materials, were combined with an indoor air quality model to show that concentrations of aldehydes indoors may approach odorous levels. He shows that ducts are unlikely to be a significant sink for ozone due to the low reaction probability in combination with the short residence time of air in ducts.« less

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents.

PubMed

Bürger, Raimund; Chowell, Gerardo; Gavilán, Elvis; Mulet, Pep; Villada, Luis M

2018-02-01

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.

ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments

PubMed Central

Schöneberg, Johannes; Noé, Frank

2013-01-01

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. PMID:24040218

Multiscale model of light harvesting by photosystem II in plants

DOE PAGES

Amarnath, Kapil; Bennett, Doran I. G.; Schneider, Anna R.; ...

2016-01-19

The first step of photosynthesis in plants is the absorption of sunlight by pigments in the antenna complexes of photosystem II (PSII), followed by transfer of the nascent excitation energy to the reaction centers, where long-term storage as chemical energy is initiated. Quantum mechanical mechanisms must be invoked to explain the transport of excitation within individual antenna. However, it is unclear how these mechanisms influence transfer across assemblies of antenna and thus the photochemical yield at reaction centers in the functional thylakoid membrane. In this paper, we model light harvesting at the several-hundred-nanometer scale of the PSII membrane, while preservingmore » the dominant quantum effects previously observed in individual complexes. We show that excitation moves diffusively through the antenna with a diffusion length of 50 nm until it reaches a reaction center, where charge separation serves as an energetic trap. The diffusion length is a single parameter that incorporates the enhancing effect of excited state delocalization on individual rates of energy transfer as well as the complex kinetics that arise due to energy transfer and loss by decay to the ground state. The diffusion length determines PSII’s high quantum efficiency in ideal conditions, as well as how it is altered by the membrane morphology and the closure of reaction centers. Finally, we anticipate that the model will be useful in resolving the nonphotochemical quenching mechanisms that PSII employs in conditions of high light stress.« less

Nonlinear Chemical Dynamics and Synchronization

NASA Astrophysics Data System (ADS)

Li, Ning

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

Explicit spatiotemporal simulation of receptor-G protein coupling in rod cell disk membranes.

PubMed

Schöneberg, Johannes; Heck, Martin; Hofmann, Klaus Peter; Noé, Frank

2014-09-02

Dim-light vision is mediated by retinal rod cells. Rhodopsin (R), a G-protein-coupled receptor, switches to its active form (R(∗)) in response to absorbing a single photon and activates multiple copies of the G-protein transducin (G) that trigger further downstream reactions of the phototransduction cascade. The classical assumption is that R and G are uniformly distributed and freely diffusing on disk membranes. Recent experimental findings have challenged this view by showing specific R architectures, including RG precomplexes, nonuniform R density, specific R arrangements, and immobile fractions of R. Here, we derive a physical model that describes the first steps of the photoactivation cascade in spatiotemporal detail and single-molecule resolution. The model was implemented in the ReaDDy software for particle-based reaction-diffusion simulations. Detailed kinetic in vitro experiments are used to parametrize the reaction rates and diffusion constants of R and G. Particle diffusion and G activation are then studied under different conditions of R-R interaction. It is found that the classical free-diffusion model is consistent with the available kinetic data. The existence of precomplexes between inactive R and G is only consistent with the data if these precomplexes are weak, with much larger dissociation rates than suggested elsewhere. Microarchitectures of R, such as dimer racks, would effectively immobilize R but have little impact on the diffusivity of G and on the overall amplification of the cascade at the level of the G protein. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

PubMed

Jensen, Frank B; Rohde, Sabina

2010-04-01

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

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

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

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

The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion.

PubMed

Yates, Christian A; Flegg, Mark B

2015-05-06

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of the first, it is derived in the continuum limit over the PDE region alone. We test our hybrid methods for functionality and accuracy in a variety of different scenarios by comparing the averaged simulations with analytical solutions of PDEs for mean concentrations. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

An Investigation of a Hybrid Mixing Model for PDF Simulations of Turbulent Premixed Flames

NASA Astrophysics Data System (ADS)

Zhou, Hua; Li, Shan; Wang, Hu; Ren, Zhuyin

2015-11-01

Predictive simulations of turbulent premixed flames over a wide range of Damköhler numbers in the framework of Probability Density Function (PDF) method still remain challenging due to the deficiency in current micro-mixing models. In this work, a hybrid micro-mixing model, valid in both the flamelet regime and broken reaction zone regime, is proposed. A priori testing of this model is first performed by examining the conditional scalar dissipation rate and conditional scalar diffusion in a 3-D direct numerical simulation dataset of a temporally evolving turbulent slot jet flame of lean premixed H2-air in the thin reaction zone regime. Then, this new model is applied to PDF simulations of the Piloted Premixed Jet Burner (PPJB) flames, which are a set of highly shear turbulent premixed flames and feature strong turbulence-chemistry interaction at high Reynolds and Karlovitz numbers. Supported by NSFC 51476087 and NSFC 91441202.

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

NASA Astrophysics Data System (ADS)

Windus, Alastair; Jensen, Henrik J.

2008-11-01

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

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

PubMed

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

2015-01-01

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

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Synthesis and materialization of a reaction-diffusion French flag pattern

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

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

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

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

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

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

NASA Astrophysics Data System (ADS)

Shiraiwa, Manabu; Pfrang, Christian; Pöschl, Ulrich

2010-05-01

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

Ballistic Motion of Enzymes that Catalyze Highly Exothermic Reactions

NASA Astrophysics Data System (ADS)

Tsekouras, Konstantinos; Pressé, Steve

Recently we proposed that the experimentally observed enhanced diffusion of enzymes catalyzing highly exothermic reactions is a consequence of their mechanism for dissipating reaction energy. More specifically, we proposed that reaction energy spreads out from the reaction site in the form of an acoustic wave which causes the enzyme to asymmetrically deform into the solvent. The solvent reaction propels the enzyme. However, it has been noted that in water, high viscosity should reduce enzyme momentum to zero within a few ps, so any diffusion increase should not be observable. Here we provide a model explaining how small volumetric expansions of biomolecules inside water may cause fluid compression that in turn creates regions of low fluid density around the biomolecule. We then investigate the dynamics of the biomolecule in the presence of these perturbations.

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

PubMed

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

2018-07-01

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

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

NASA Technical Reports Server (NTRS)

Vogel, Bernhard; Vogel, Heike; Fiedler, Franz

1994-01-01

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

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Bolhuis, Peter

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Numerically exploring habitat fragmentation effects on populations using cell-based coupled map lattices

Treesearch

Michael Bevers; Curtis H. Flather

1999-01-01

We examine habitat size, shape, and arrangement effects on populations using a discrete reaction-diffusion model. Diffusion is modeled passively and applied to a cellular grid of territories forming a coupled map lattice. Dispersal mortality is proportional to the amount of nonhabitat and fully occupied habitat surrounding a given cell, with distance decay. After...

Finite element modeling of contaminant transport in soils including the effect of chemical reactions.

PubMed

Javadi, A A; Al-Najjar, M M

2007-05-17

The movement of chemicals through soils to the groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. Recent studies have shown that the current models and methods are not able to adequately describe the leaching of nutrients through soils, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. Furthermore, the effect of chemical reactions on the fate and transport of contaminants is not included in many of the existing numerical models for contaminant transport. In this paper a numerical model is presented for simulation of the flow of water and air and contaminant transport through unsaturated soils with the main focus being on the effects of chemical reactions. The governing equations of miscible contaminant transport including advection, dispersion-diffusion and adsorption effects together with the effect of chemical reactions are presented. The mathematical framework and the numerical implementation of the model are described in detail. The model is validated by application to a number of test cases from the literature and is then applied to the simulation of a physical model test involving transport of contaminants in a block of soil with particular reference to the effects of chemical reactions. Comparison of the results of the numerical model with the experimental results shows that the model is capable of predicting the effects of chemical reactions with very high accuracy. The importance of consideration of the effects of chemical reactions is highlighted.

Analysis of a diffuse interface model of multispecies tumor growth

NASA Astrophysics Data System (ADS)

Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

2017-04-01

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.

Modeling of FMISO [F18] nanoparticle PET tracer in normal-cancerous tissue based on real clinical image.

PubMed

Asgari, Hanie; Soltani, M; Sefidgar, Mostafa

2018-07-01

Hypoxia as one of the principal properties of tumor cells is a reaction to the deprivation of oxygen. The location of tumor cells could be identified by assessment of oxygen and nutrient level in human body. Positron emission tomography (PET) is a well-known non-invasive method that is able to measure hypoxia based on the FMISO (Fluoromisonidazole) tracer dynamic. This paper aims to study the PET tracer concentration through convection-diffusion-reaction equations in a real human capillary-like network. A non-uniform oxygen pressure along the capillary path and convection mechanism for FMISO transport are taken into account to accurately model the characteristics of the tracer. To this end, a multi-scale model consists of laminar blood flow through the capillary network, interstitial pressure, oxygen pressure, FMISO diffusion and FMISO convection transport in the extravascular region is developed. The present model considers both normal and tumor tissue regions in computational domain. The accuracy of numerical model is verified with the experimental results available in the literature. The convection and diffusion types of transport mechanism are employed in order to calculate the concentration of FMISO in the normal and tumor sub-domain. The influences of intravascular oxygen pressure, FMISO transport mechanisms, capillary density and different types of tissue on the FMISO concentration have been investigated. According to result (Table 4) the convection mechanism of FMISO molecules transportation is negligible, but it causes more accuracy of the proposed model. The approach of present study can be employed in order to investigate the effects of various parameters, such as tumor shape, on the dynamic behavior of different PET tracers, such as FDG, can be extended to different case study problems, such as drug delivery. Copyright © 2018 Elsevier Inc. All rights reserved.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

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

The chemistry and diffusion of aircraft exhausts in the lower stratosphere during the first few hours after fly-by. [with attention to ozone depletion by SST exhaust plumes

NASA Technical Reports Server (NTRS)

Hilst, G. R.

1974-01-01

An analysis of the hydrogen-nitrogen-oxygen reaction systems in the lower stratosphere as they are initially perturbed by individual aircraft engine exhaust plumes was conducted in order to determine whether any significant chemical reactions occur, either among exhaust chemical species, or between these species and the environmental ozone, while the exhaust products are confined to intact plume segments at relatively high concentrations. The joint effects of diffusive mixing and chemical kinetics on the reactions were also studied, using the techniques of second-order closure diffusion/chemistry models. The focus of the study was on the larger problem of the potential depletion of ozone by supersonic transport aircraft exhaust materials emitted into the lower stratosphere.

Development of a second order closure model for computation of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Varma, A. K.; Donaldson, C. D.

1974-01-01

A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions.

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

PubMed

Chen, Juan; Cui, Baotong; Chen, YangQuan

2018-06-11

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

Unprecedented homotopy perturbation method for solving nonlinear equations in the enzymatic reaction of glucose in a spherical matrix.

PubMed

Saranya, K; Mohan, V; Kizek, R; Fernandez, C; Rajendran, L

2018-02-01

The theory of glucose-responsive composite membranes for the planar diffusion and reaction process is extended to a microsphere membrane. The theoretical model of glucose oxidation and hydrogen peroxide production in the chitosan-aliginate microsphere has been discussed in this manuscript for the first time. We have successfully reported an analytical derived methodology utilizing homotopy perturbation to perform the numerical simulation. The influence and sensitive analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide are also discussed. The theoretical results enable to predict and optimize the performance of enzyme kinetics.

A 2D model of axial symmetry for proximal tubule of an average human nephron: indicative results of diffusion, convection and absorption processes

NASA Astrophysics Data System (ADS)

Insfrán, J. F.; Ubal, S.; Di Paolo, y. J.

2016-04-01

A simplified model of a proximal convoluted tubule of an average human nephron is presented. The model considers the 2D axisymmetric flow of the luminal solution exchanging matter with the tubule walls and the peritubular fluid by means of 0D models for the epithelial cells. The tubule radius is considered to vary along the conduit due to the trans-epithelial pressure difference. The fate of more than ten typical solutes is tracked down by the model. The Navier-Stokes and Reaction-Diffusion-Advection equations (considering the electro-neutrality principle) are solved in the lumen, giving a detailed picture of the velocity, pressure and concentration fields, along with trans-membrane fluxes and tubule deformation, via coupling with the 0D model for the tubule wall. The calculations are carried out numerically by means of the finite element method. The results obtained show good agreement with those published by other authors using models that ignore the diffusive transport and disregard a detailed calculation of velocity, pressure and concentrations. This work should be seen as a first approach towards the development of a more comprehensive model of the filtration process taking place in the kidneys, which ultimately helps in devising a device that can mimic/complement the renal function.

Pyrolysis of Musa balbisiana flower petal using thermogravimetric studies.

PubMed

Sriram, Aswin; Swaminathan, Ganapathiraman

2018-05-11

In the present study, thermogravimetric analysis of Musa balbisiana flower petal was carried out to study the degradation behaviour and the kinetics in the pyrolytic reaction. The pyrolysis was carried out in the temperature range of 35-900 °C at different heating rates of 5, 10 and 20 °C/min. The kinetics was investigated using different models like Kissinger-Akahira-Sunose (KAS), Flynn-Ozawa-Wall (FOW), Friedman and Broido's plot. The average E a values determined by KAS, FOW and Friedman methods were 137.94, 136.76 and 133.36 kJ/mol respectively. Coats-Redfern method was utilized to determine the pre-exponential factors and the reaction order of the pyrolysis. For the conversion rates 0.1 and 0.2, both Valensi and Ginstling diffusion models were found out to be appropriate for the solid state reaction mechanism. The HHV of Musa balbisiana flower petal was 16.35 MJ/kg, suggested as a potential bio-feedstock energy source from agro-waste. Copyright © 2018. Published by Elsevier Ltd.

Unified path integral approach to theories of diffusion-influenced reactions

NASA Astrophysics Data System (ADS)

Prüstel, Thorsten; Meier-Schellersheim, Martin

2017-08-01

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

Hydrodynamic Fingering Instability Induced by a Precipitation Reaction

NASA Astrophysics Data System (ADS)

Nagatsu, Y.; Ishii, Y.; Tada, Y.; De Wit, A.

2014-07-01

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the buildup of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A +B→C type of reaction when a solution containing one of the reactants is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Fingerlike precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice versa. A mathematical modeling of the underlying mobility profile confirms that the instability originates from a local decrease in mobility driven by the localized precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns.

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

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

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

1998-12-01

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

What Can the Diffusion Model Tell Us About Prospective Memory?

PubMed Central

Horn, Sebastian S.; Bayen, Ute J.; Smith, Rebekah E.

2011-01-01

Cognitive process models, such as Ratcliff’s (1978) diffusion model, are useful tools for examining cost- or interference effects in event-based prospective memory (PM). The diffusion model includes several parameters that provide insight into how and why ongoing-task performance may be affected by a PM task and is ideally suited to analyze performance because both reaction time and accuracy are taken into account. Separate analyses of these measures can easily yield misleading interpretations in cases of speed-accuracy tradeoffs. The diffusion model allows us to measure possible criterion shifts and is thus an important methodological improvement over standard analyses. Performance in an ongoing lexical decision task (Smith, 2003) was analyzed with the diffusion model. The results suggest that criterion shifts play an important role when a PM task is added, but do not fully explain the cost effect on RT. PMID:21443332

Mechanisms underlying anomalous diffusion in the plasma membrane.

PubMed

Krapf, Diego

2015-01-01

The plasma membrane is a complex fluid where lipids and proteins undergo diffusive motion critical to biochemical reactions. Through quantitative imaging analyses such as single-particle tracking, it is observed that diffusion in the cell membrane is usually anomalous in the sense that the mean squared displacement is not linear with time. This chapter describes the different models that are employed to describe anomalous diffusion, paying special attention to the experimental evidence that supports these models in the plasma membrane. We review models based on anticorrelated displacements, such as fractional Brownian motion and obstructed diffusion, and nonstationary models such as continuous time random walks. We also emphasize evidence for the formation of distinct compartments that transiently form on the cell surface. Finally, we overview heterogeneous diffusion processes in the plasma membrane, which have recently attracted considerable interest. Copyright © 2015. Published by Elsevier Inc.

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Crystal plasticity modeling of irradiation growth in Zircaloy-2

NASA Astrophysics Data System (ADS)

Patra, Anirban; Tomé, Carlos N.; Golubov, Stanislav I.

2017-08-01

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.

A kinetic study of the replacement of calcite marble by fluorite

NASA Astrophysics Data System (ADS)

Trindade Pedrosa, Elisabete; Boeck, Lena; Putnis, Christine V.; Putnis, Andrew

2016-04-01

Replacement reactions are relevant in any situation that involves the reequilibration between a solid and an aqueous fluid phase and are commonly controlled by an interface-coupled dissolution-precipitation mechanism (Putnis and Putnis, 2007). These reactions control many large-scale Earth processes whenever aqueous fluids are available, such as during metamorphism, metasomatism, and weathering. An important consequence of coupled dissolution-precipitation is the generation of porosity in the product phase that then allows the infiltration of the fluid within the mineral being replaced. Understanding the mechanism and kinetics of the replacement of carbonates by fluorite has application in earth sciences and engineering. Fluorite (CaF2) occurs in all kinds of rocks (igneous, sedimentary, and metamorphic) and its origin is commonly associated with hydrothermal fluids. Moreover, calcium carbonate has been suggested as a successful seed material for the sequestration of fluoride from contaminated waters (Waghmare and Arfin, 2015). The aim of the present work is to investigate aspects of the replacement of calcium carbonate by fluorite to better understand the mechanism and kinetics of this reaction. Small cubes (˜ 3 × 3 × 3 mm) of Carrara marble (CaCO3 > 99 %) were cut and reacted with a 4 M ammonium fluoride (NH4F) solution for different times (1 to 48 hours) and temperatures (60, 80, 100, and 140 ° C). The microstructure of the product phases was analysed using SEM. The kinetics of replacement was monitored from the Rietveld analysis of X-ray powder diffraction patterns of the products as a function of temperature and reaction time. After reaction, all samples preserved their size and external morphology (a pseudomorphic replacement) and the product phase (fluorite) was highly porous. The activation energy Ea (kJ/mol) of the replacement reaction was empirically determined by both model-fitting and model-free methods. The isoconversional method yielded an empirical activation energy of 41 kJ/mol, and a statistical approach applied to the model-fitting method revealed that the replacement of Carrara marble by fluorite is better fitted to a diffusion-controlled process. This is consistent with ion diffusion through the fluid phase. These results suggest that the replacement reaction is dependent on the fluid migration rate through the newly formed porosity. Putnis, A., Putnis C.V., 2007. The mechanism of reequilibration of solids in the presence of a fluid phase. Journal of Solid State Chemistry, 180, 1783-1786. Waghmare, S.S., Arfin, T. (2015). Fluoride removal from water by calcium materials: A state-of-the-art review. Int. J. Innov. Res. Sci. Eng. Technol. 4, 8090-8102.

Lithium diffusion in polyether ether ketone and polyimide stimulated by in situ electron irradiation and studied by the neutron depth profiling method

NASA Astrophysics Data System (ADS)

Vacik, J.; Hnatowicz, V.; Attar, F. M. D.; Mathakari, N. L.; Dahiwale, S. S.; Dhole, S. D.; Bhoraskar, V. N.

2014-10-01

Diffusion of lithium from a LiCl aqueous solution into polyether ether ketone (PEEK) and polyimide (PI) assisted by in situ irradiation with 6.5 MeV electrons was studied by the neutron depth profiling method. The number of the Li atoms was found to be roughly proportional to the diffusion time. Regardless of the diffusion time, the measured depth profiles in PEEK exhibit a nearly exponential form, indicating achievement of a steady-state phase of a diffusion-reaction process specified in the text. The form of the profiles in PI is more complex and it depends strongly on the diffusion time. For the longer diffusion time, the profile consists of near-surface bell-shaped part due to Fickian-like diffusion and deeper exponential part.

Silver release from nanocomposite Ag/alginate hydrogels in the presence of chloride ions: experimental results and mathematical modeling

NASA Astrophysics Data System (ADS)

Kostic, Danijela; Vidovic, Srđan; Obradovic, Bojana

2016-03-01

A stepwise experimental and mathematical modeling approach was used to assess silver release from nanocomposite Ag/alginate microbeads in wet and dried forms into water and into normal saline solution chosen as a simplified model for certain biological fluids (e.g., blood plasma, wound exudates, sweat, etc). Three phenomena were connected and mathematically described: diffusion of silver nanoparticles (AgNPs) within the alginate hydrogel, AgNP oxidation/dissolution and reaction with chloride ions, and diffusion of the resultant silver-chloride species. Mathematical modeling results agreed well with the experimental data with the AgNP diffusion coefficient estimated as 1.3 × 10-18 m2 s-1, while the first-order kinetic rate constant of AgNP oxidation/dissolution and diffusivity of silver-chloride species were shown to be inversely related. In specific, rapid rehydration and swelling of dry Ag/alginate microbeads induced fast AgNP oxidation/dissolution reaction with Cl- and AgCl precipitation within the microbeads with the lowest diffusivity of silver-chloride species compared to wet microbeads in normal saline. The proposed mathematical model provided an insight into the phenomena related to silver release from nanocomposite Ca-alginate hydrogels relevant for use of antimicrobial devices and established, at the same time, a basis for further in-depth studies of AgNP interactions in hydrogels in the presence of chloride ions.

Materials outgassing rate decay in vacuum at isothermal conditions

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

PubMed Central

Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

2016-01-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell. PMID:27959915

Multiscale Simulations of Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, D. M.; Bakarji, J.

2014-12-01

Discrete, particle-based simulations offer distinct advantages when modeling solute transport and chemical reactions. For example, Brownian motion is often used to model diffusion in complex pore networks, and Gillespie-type algorithms allow one to handle multicomponent chemical reactions with uncertain reaction pathways. Yet such models can be computationally more intensive than their continuum-scale counterparts, e.g., advection-dispersion-reaction equations. Combining the discrete and continuum models has a potential to resolve the quantity of interest with a required degree of physicochemical granularity at acceptable computational cost. We present computational examples of such "hybrid models" and discuss the challenges associated with coupling these two levels of description.

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

PubMed

Tanaka, Yoshitaro; Yamamoto, Hiroko; Ninomiya, Hirokazu

2017-06-01

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

A stochastic model of solid state thin film deposition: Application to chalcopyrite growth

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

Lovelett, Robert J.; Pang, Xueqi; Roberts, Tyler M.

Developing high fidelity quantitative models of solid state reaction systems can be challenging, especially in deposition systems where, in addition to the multiple competing processes occurring simultaneously, the solid interacts with its atmosphere. In this work, we develop a model for the growth of a thin solid film where species from the atmosphere adsorb, diffuse, and react with the film. The model is mesoscale and describes an entire film with thickness on the order of microns. Because it is stochastic, the model allows us to examine inhomogeneities and agglomerations that would be impossible to characterize with deterministic methods. We demonstratemore » the modeling approach with the example of chalcopyrite Cu(InGa)(SeS){sub 2} thin film growth via precursor reaction, which is a common industrial method for fabricating thin film photovoltaic modules. The model is used to understand how and why through-film variation in the composition of Cu(InGa)(SeS){sub 2} thin films arises and persists. We believe that the model will be valuable as an effective quantitative description of many other materials systems used in semiconductors, energy storage, and other fast-growing industries.« less

A stochastic model of solid state thin film deposition: Application to chalcopyrite growth

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

Lovelett, Robert J.; Pang, Xueqi; Roberts, Tyler M.

Developing high fidelity quantitative models of solid state reaction systems can be challenging, especially in deposition systems where, in addition to the multiple competing processes occurring simultaneously, the solid interacts with its atmosphere. Here, we develop a model for the growth of a thin solid film where species from the atmosphere adsorb, diffuse, and react with the film. The model is mesoscale and describes an entire film with thickness on the order of microns. Because it is stochastic, the model allows us to examine inhomogeneities and agglomerations that would be impossible to characterize with deterministic methods. We also demonstrate themore » modeling approach with the example of chalcopyrite Cu(InGa)(SeS) 2 thin film growth via precursor reaction, which is a common industrial method for fabricating thin film photovoltaic modules. The model is used to understand how and why through-film variation in the composition of Cu(InGa)(SeS) 2 thin films arises and persists. Finally, we believe that the model will be valuable as an effective quantitative description of many other materials systems used in semiconductors, energy storage, and other fast-growing industries.« less

A stochastic model of solid state thin film deposition: Application to chalcopyrite growth

DOE PAGES

Lovelett, Robert J.; Pang, Xueqi; Roberts, Tyler M.; ...

2016-04-01

Developing high fidelity quantitative models of solid state reaction systems can be challenging, especially in deposition systems where, in addition to the multiple competing processes occurring simultaneously, the solid interacts with its atmosphere. Here, we develop a model for the growth of a thin solid film where species from the atmosphere adsorb, diffuse, and react with the film. The model is mesoscale and describes an entire film with thickness on the order of microns. Because it is stochastic, the model allows us to examine inhomogeneities and agglomerations that would be impossible to characterize with deterministic methods. We also demonstrate themore » modeling approach with the example of chalcopyrite Cu(InGa)(SeS) 2 thin film growth via precursor reaction, which is a common industrial method for fabricating thin film photovoltaic modules. The model is used to understand how and why through-film variation in the composition of Cu(InGa)(SeS) 2 thin films arises and persists. Finally, we believe that the model will be valuable as an effective quantitative description of many other materials systems used in semiconductors, energy storage, and other fast-growing industries.« less

Determination of Diffusion Profiles in Altered Wellbore Cement Using X-ray Computed Tomography Methods

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

Mason, Harris E.; Walsh, Stuart D. C.; DuFrane, Wyatt L.

2014-06-17

The development of accurate, predictive models for use in determining wellbore integrity requires detailed information about the chemical and mechanical changes occurring in hardened Portland cements. X-ray computed tomography (XRCT) provides a method that can nondestructively probe these changes in three dimensions. Here, we describe a method for extracting subvoxel mineralogical and chemical information from synchrotron XRCT images by combining advanced image segmentation with geochemical models of cement alteration. The method relies on determining “effective linear activity coefficients” (ELAC) for the white light source to generate calibration curves that relate the image grayscales to material composition. The resulting data setmore » supports the modeling of cement alteration by CO 2-rich brine with discrete increases in calcium concentration at reaction boundaries. The results of these XRCT analyses can be used to further improve coupled geochemical and mechanical models of cement alteration in the wellbore environment.« less

Nonlinear Systems.

ERIC Educational Resources Information Center

Seider, Warren D.; Ungar, Lyle H.

1987-01-01

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

A computational model of amoeboid cell swimming

NASA Astrophysics Data System (ADS)

Campbell, Eric J.; Bagchi, Prosenjit

2017-10-01

Amoeboid cells propel by generating pseudopods that are finger-like protrusions of the cell body that continually grow, bifurcate, and retract. Pseudopod-driven motility of amoeboid cells represents a complex and multiscale process that involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Here we present a 3D model of pseudopod-driven swimming of an amoeba suspended in a fluid without any adhesion and in the absence of any chemoattractant. Our model is based on front-tracking/immersed-boundary methods, and it combines large deformation of the cell, a coarse-grain model for molecular reactions, and cytoplasmic and extracellular fluid flow. The predicted shapes of the swimming cell from our model show similarity with experimental observations. We predict that the swimming behavior changes from random-like to persistent unidirectional motion, and that the swimming speed increases, with increasing cell deformability and protein diffusivity. The unidirectionality in cell swimming is observed without any external cues and as a direct result of a change in pseudopod dynamics. We find that pseudopods become preferentially focused near the front of the cell and appear in greater numbers with increasing cell deformability and protein diffusivity, thereby increasing the swimming speed and making the cell shape more elongated. We find that the swimming speed is minimum when the cytoplasm viscosity is close to the extracellular fluid viscosity. We further find that the speed increases significantly as the cytoplasm becomes less viscous compared with the extracellular fluid, resembling the viscous fingering phenomenon observed in interfacial flows. While these results support the notion that softer cells migrate more aggressively, they also suggest a strong coupling between membrane elasticity, membrane protein diffusivity, and fluid viscosity.

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

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

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

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

NASA Astrophysics Data System (ADS)

Yuguchi, Takashi; Nishiyama, Tadao

2008-12-01

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

Modeling solute clustering in the diffusion layer around a growing crystal.

PubMed

Shiau, Lie-Ding; Lu, Yung-Fang

2009-03-07

The mechanism of crystal growth from solution is often thought to consist of a mass transfer diffusion step followed by a surface reaction step. Solute molecules might form clusters in the diffusion step before incorporating into the crystal lattice. A model is proposed in this work to simulate the evolution of the cluster size distribution due to the simultaneous aggregation and breakage of solute molecules in the diffusion layer around a growing crystal in the stirred solution. The crystallization of KAl(SO(4))(2)12H(2)O from aqueous solution is studied to illustrate the effect of supersaturation and diffusion layer thickness on the number-average degree of clustering and the size distribution of solute clusters in the diffusion layer.

Pattern formation in mass conserving reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Brauns, Fridtjof; Halatek, Jacob; Frey, Erwin

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

Methodes d'optimisation des parametres 2D du reflecteur dans un reacteur a eau pressurisee

NASA Astrophysics Data System (ADS)

Clerc, Thomas

With a third of the reactors in activity, the Pressurized Water Reactor (PWR) is today the most used reactor design in the world. This technology equips all the 19 EDF power plants. PWRs fit into the category of thermal reactors, because it is mainly the thermal neutrons that contribute to the fission reaction. The pressurized light water is both used as the moderator of the reaction and as the coolant. The active part of the core is composed of uranium, slightly enriched in uranium 235. The reflector is a region surrounding the active core, and containing mostly water and stainless steel. The purpose of the reflector is to protect the vessel from radiations, and also to slow down the neutrons and reflect them into the core. Given that the neutrons participate to the reaction of fission, the study of their behavior within the core is capital to understand the general functioning of how the reactor works. The neutrons behavior is ruled by the transport equation, which is very complex to solve numerically, and requires very long calculation. This is the reason why the core codes that will be used in this study solve simplified equations to approach the neutrons behavior in the core, in an acceptable calculation time. In particular, we will focus our study on the diffusion equation and approximated transport equations, such as SPN or S N equations. The physical properties of the reflector are radically different from those of the fissile core, and this structural change causes important tilt in the neutron flux at the core/reflector interface. This is why it is very important to accurately design the reflector, in order to precisely recover the neutrons behavior over the whole core. Existing reflector calculation techniques are based on the Lefebvre-Lebigot method. This method is only valid if the energy continuum of the neutrons is discretized in two energy groups, and if the diffusion equation is used. The method leads to the calculation of a homogeneous reflector. The aim of this study is to create a computational scheme able to compute the parameters of heterogeneous, multi-group reflectors, with both diffusion and SPN/SN operators. For this purpose, two computational schemes are designed to perform such a reflector calculation. The strategy used in both schemes is to minimize the discrepancies between a power distribution computed with a core code and a reference distribution, which will be obtained with an APOLLO2 calculation based on the method Method Of Characteristics (MOC). In both computational schemes, the optimization parameters, also called control variables, are the diffusion coefficients in each zone of the reflector, for diffusion calculations, and the P-1 corrected macroscopic total cross-sections in each zone of the reflector, for SPN/SN calculations (or correction factors on these parameters). After a first validation of our computational schemes, the results are computed, always by optimizing the fast diffusion coefficient for each zone of the reflector. All the tools of the data assimilation have been used to reflect the different behavior of the solvers in the different parts of the core. Moreover, the reflector is refined in six separated zones, corresponding to the physical structure of the reflector. There will be then six control variables for the optimization algorithms. [special characters omitted]. Our computational schemes are then able to compute heterogeneous, 2-group or multi-group reflectors, using diffusion or SPN/SN operators. The optimization performed reduces the discrepancies distribution between the power computed with the core codes and the reference power. However, there are two main limitations to this study: first the homogeneous modeling of the reflector assemblies doesn't allow to properly describe its physical structure near the core/reflector interface. Moreover, the fissile assemblies are modeled in infinite medium, and this model reaches its limit at the core/reflector interface. These two problems should be tackled in future studies. (Abstract shortened by UMI.).

Study of rare encounters in a membrane using quenching of cascade reaction between triplet and photochrome probes with nitroxide radicals.

PubMed

Medvedeva, Nataly; Papper, Vladislav; Likhtenshtein, Gertz I

2005-09-21

Measurements of active encounters between molecules in native membranes containing ingredients, including proteins, are of prime importance. To estimate rare encounters in a high range of rate constants (rate coefficients) and distances between interacting molecules in membranes, a cascade of photochemical reactions for molecules diffusing in multilamellar liposomes was investigated. The sensitised cascade triplet cis-trans photoisomerisation of the excited stilbene involves the use of a triplet sensitiser (Erythrosin B), a photochrome stilbene-derivative probe (4-dimethylamino-4'-aminostilbene) exhibiting the phenomenon of trans-cis photoisomerisation, and nitroxide radicals (5-doxyl stearic acid) to quench the excited triplet state of the sensitiser. Measurement of the phosphorescence lifetime of Erythrosin B and the fluorescence enhancement of the stilbene-derivative photochrome probe, at various concentrations of the nitroxide probe, made it possible to calculate the quenching rate constant k(q)= 1.1 x 10(15) cm2 M(-1) s(-1) and the rate constant of the triplet-triplet energy transfer between the sensitiser and stilbene probe k(T)= 1.0 x 10(12) cm2 M(-1) s(-1). These values, together with the data on diffusion rate constant, obtained by methods utilising various theoretical characteristic times of about seven orders of magnitude and the experimental rate constants of about five orders of magnitude, were found to be in good agreement with the advanced theory of diffusion-controlled reactions in two dimensions. Because the characteristic time of the proposed cascade method is relatively large (0.1 s), it is possible to follow rare collisions between molecules and free radicals in model and biological membranes with a very sensitive fluorescence spectroscopy technique, using a relatively low concentration of probes.

Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions.

PubMed Central

Zhou, H X; Szabo, A

1996-01-01

A general formalism is developed for calculating the time-dependent rate coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), including rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long times k(t) is shown to have the asymptotic expansion k(infinity)[1 + k(infinity) (pie Dt)-1/2 /4 pie D + ...], where D is the relative translational diffusion constant. An approximate analytical method for calculating k(t) is presented. This is based on the approximation that the probability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate coefficient then is determined by the Green function in the absence of chemical reaction. Within the framework of this approximation, two general relations are obtained. The first relation allows the rate coefficient for an arbitrary amplitude of the reactivity to be found if the rate coefficient for one amplitude of the reactivity is known. The second relation allows the rate coefficient in the presence of conformational gating to be found from that in the absence of conformational gating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamics simulations. Two simulation procedures involving the propagation of nonreactive trajectories initiated only from the reactive region are described and illustrated on a model system. Both analytical and simulation results demonstrate the accuracy of the equilibrium-distribution approximation method. PMID:8913584

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

PubMed

Maybank, Philip J; Whiteley, Jonathan P

2014-02-01

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

Hydrodynamics of bacterial colonies: A model

NASA Astrophysics Data System (ADS)

Lega, J.; Passot, T.

2003-03-01

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis. As shown in numerical simulations, our model reproduces both usual colony shapes and typical hydrodynamic motions, such as the whirls and jets recently observed in wet colonies of Bacillus subtilis. The approach presented here could be extended to different experimental situations and provides a general framework for the use of advection-reaction-diffusion equations in modeling bacterial colonies.

Temperature-dependent structure and phase variation of nickel silicide nanowire arrays prepared by in situ silicidation

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

Liu, Hailong; She, Guangwei, E-mail: shegw@mail.ipc.ac.cn; Mu, Lixuan

Graphical abstract: Display Omitted Highlight: ► Nickel silicides nanowire arrays prepared by a simple in situ silicidation method. ► Phases of nickel silicides could be varied by tuning the reaction temperature. ► A growth model was proposed for the nickel silicides nanowires. ► Diffusion rates of Ni and Si play a critical role for the phase variation. -- Abstract: In this paper, we report an in situ silicidizing method to prepare nickel silicide nanowire arrays with varied structures and phases. The in situ reaction (silicidation) between Si and NiCl{sub 2} led to conversion of Si nanowires to nickel silicide nanowires.more » Structures and phases of the obtained nickel silicides could be varied by changing the reaction temperature. At a relatively lower temperature of 700 °C, the products are Si/NiSi core/shell nanowires or NiSi nanowires, depending on the concentration of NiCl{sub 2} solution. At a higher temperature (800 °C and 900 °C), other phases of the nickel silicides, including Ni{sub 2}Si, Ni{sub 31}Si{sub 12}, and NiSi{sub 2}, were obtained. It is proposed that the different diffusion rates of Ni and Si atoms at different temperatures played a critical role in the formation of nickel silicide nanowires with different phases.« less

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Kinetics of Cation and Oxyanion Adsorption and Desorption on Ferrihydrite: Roles of Ferrihydrite Binding Sites and a Unified Model

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

Tian, Lei; Shi, Zhenqing; Lu, Yang

Understanding the kinetics of toxic ion reactions with ferrihydrite is crucial for predicting the dynamic behavior of contaminants in soil environments. In this study, the kinetics of As(V), Cr(VI), Cu, and Pb adsorption and desorption on ferrihydrite were investigated with a combination of laboratory macroscopic experiments, microscopic investigation and mechanistic modeling. The rates of As(V), Cr(VI), Cu, and Pb adsorption and desorption on ferrihydrite, as systematically studied using a stirred-flow method, was highly dependent on the reaction pH and metal concentrations and varied significantly among four metals. Spherical aberration-corrected scanning transmission electron microscopy (Cs-STEM) showed, at sub-nano scales, all fourmore » metals were distributed within the ferrihydrite particle aggregates homogeneously after adsorption reactions, with no evidence of surface diffusion-controlled processes. Based on experimental results, we developed a unifying kinetics model for both cation and oxyanion adsorption/desorption on ferrihydrite based on the mechanistic-based equilibrium model CD-MUSIC. Overall, the model described the kinetic results well, and we quantitatively demonstrated how the equilibrium properties of the cation and oxyanion binding to various ferrihydrite sites affected the adsorption and desorption rates. Our results provided a unifying quantitative modeling method for the kinetics of both cation and oxyanion adsorption/desorption on iron minerals.« less

Multispecies diffusion models: A study of uranyl species diffusion

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

A novel (ex situ) method to quantify oxygen diffusion coefficient of polymer fuel cells backing and catalyst layers

NASA Astrophysics Data System (ADS)

Baricci, Andrea; Casalegno, Andrea

2016-09-01

Limiting current density of oxygen reduction reaction in polymer electrolyte fuel cells is determined by several mass transport resistances that lower the concentration of oxygen on the catalyst active site. Among them, diffusion across porous media plays a significant role. Despite the extensive experimental activity documented in PEMFC literature, only few efforts have been dedicated to the measurement of the effective transport properties in porous layers. In the present work, a methodology for ex situ measurement of the effective diffusion coefficient and Knudsen radius of porous layers for polymer electrolyte fuel cells (gas diffusion layer, micro porous layer and catalyst layer) is described and applied to high temperature polymer fuel cells State of Art materials. Regression of the measured quantities by means of a quasi 2D physical model is performed to quantify the Knudsen effect, which is reported to account, respectively, for 30% and 50% of the mass transport resistance in micro porous layer and catalyst layer. On the other side, the model reveals that pressure gradient consequent to permeation in porous layers of high temperature polymer fuel cells has a negligible effect on oxygen concentration in relevant operating conditions.

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

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

Garcia, Andres; Evans, James W.

2016-11-03

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

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases.

PubMed

Roniotis, Alexandros; Manikis, Georgios C; Sakkalis, Vangelis; Zervakis, Michalis E; Karatzanis, Ioannis; Marias, Kostas

2012-03-01

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved. © 2012 IEEE

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

NASA Astrophysics Data System (ADS)

Amaya-Ventura, Gilberto; Rodríguez-Romo, Suemi

2011-09-01

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

Nonlinear diffusion and viral spread through the leaf of a plant

NASA Astrophysics Data System (ADS)

Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.

2016-10-01

The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.

Surface diffusion of cyclic hydrocarbons on nickel

NASA Astrophysics Data System (ADS)

Silverwood, I. P.; Armstrong, J.

2018-08-01

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

Reactive Radial Diffusion Model for the Aging/Sequestration Process

NASA Astrophysics Data System (ADS)

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

2001-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Considering the reversibility of passive and reactive transport problems: Are forward-in-time and backward-in-time models ever equivalent?

NASA Astrophysics Data System (ADS)

Engdahl, N.

2017-12-01

Backward in time (BIT) simulations of passive tracers are often used for capture zone analysis, source area identification, and generation of travel time and age distributions. The BIT approach has the potential to become an immensely powerful tool for direct inverse modeling but the necessary relationships between the processes modeled in the forward and backward models have yet to be formally established. This study explores the time reversibility of passive and reactive transport models in a variety of 2D heterogeneous domains using particle-based random walk methods for the transport and nonlinear reaction steps. Distributed forward models are used to generate synthetic observations that form the initial conditions for the backward in time models and we consider both linear-flood and point injections. The results for passive travel time distributions show that forward and backward models are not exactly equivalent but that the linear-flood BIT models are reasonable approximations. Point based BIT models fall within the travel time range of the forward models, though their distributions can be distinctive in some cases. The BIT approximation is not as robust when nonlinear reactive transport is considered and we find that this reaction system is only exactly reversible under uniform flow conditions. We use a series of simplified, longitudinally symmetric, but heterogeneous, domains to illustrate the causes of these discrepancies between the two model types. Many of the discrepancies arise because diffusion is a "self-adjoint" operator, which causes mass to spread in the forward and backward models. This allows particles to enter low velocity regions in the both models, which has opposite effects in the forward and reverse models. It may be possible to circumvent some of these limitations using an anti-diffusion model to undo mixing when time is reversed, but this is beyond the capabilities of the existing Lagrangian methods.

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

NASA Astrophysics Data System (ADS)

Chen, Yixi; Polinnaya, Rakesh; Vaddiraju, Sreeram

2018-05-01

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

A diffusion modeling approach to understanding contextual cueing effects in children with ADHD.

PubMed

Weigard, Alexander; Huang-Pollock, Cynthia

2014-12-01

Strong theoretical models suggest implicit learning deficits may exist among children with Attention Deficit Hyperactivity Disorder (ADHD). We examine implicit contextual cueing (CC) effects among children with ADHD (n = 72) and non-ADHD Controls (n = 36). Using Ratcliff's drift diffusion model, we found that among Controls, the CC effect is due to improvements in attentional guidance and to reductions in response threshold. Children with ADHD did not show a CC effect; although they were able to use implicitly acquired information to deploy attentional focus, they had more difficulty adjusting their response thresholds. Improvements in attentional guidance and reductions in response threshold together underlie the CC effect. Results are consistent with neurocognitive models of ADHD that posit subcortical dysfunction but intact spatial attention, and encourage the use of alternative data analytic methods when dealing with reaction time data. © 2014 The Authors. Journal of Child Psychology and Psychiatry. © 2014 Association for Child and Adolescent Mental Health.

Study on the isospin equilibration phenomenon in nuclear reactions 40Ca + 40Ca , 40Ca + 46Ti , 40Ca + 48Ca , 48Ca + 48Ca at 25 MeV/nucleon by using the CHIMERA multidetector

NASA Astrophysics Data System (ADS)

Martorana, N. S.; Auditore, L.; Berceanu, I.; Cardella, G.; Chatterjee, M. B.; De Luca, S.; De Filippo, E.; Dell'Aquila, D.; Gnoffo, B.; Lanzalone, G.; Lombardo, I.; Maiolino, C.; Norella, S.; Pagano, A.; Pagano, E. V.; Papa, M.; Pirrone, S.; Politi, G.; Porto, F.; Quattrocchi, L.; Rizzo, F.; Russotto, P.; Trifirò, A.; Trimarchi, M.; Verde, G.; Vigilante, M.

2017-11-01

We report on the results obtained by studying nuclear reactions between isotopes of Ca and Ti at 25 MeV/nucleon. We used the multidetector CHIMERA to detect charged reaction products. In particular, we studied two main effects: the isospin diffusion and the isospin drift. In order to study these processes we performed a moving-source analysis on kinetic energy spectra of the isobar nuclei ^{3H} and ^{3He} . This method allows to isolate the emission from the typical sources produced in reactions at Fermi energy: projectile like fragment (PLF), target like fragment (TLF), and mid-velocity (MV) emission. The obtained results are compared to previous experimental investigations and to simulations obtained with CoMD-II model.

Drosophila segmentation: supercomputer simulation of prepattern hierarchy.

PubMed

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

1990-08-09

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

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

PubMed

Peng, Rui; Zhao, Xiao-Qiang

2016-02-01

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

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Electron-stimulated reactions in layered CO/H2O films: Hydrogen atom diffusion and the sequential hydrogenation of CO to methanol

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

Petrik, Nikolay G.; Monckton, Rhiannon J.; Koehler, Sven

Low-energy (100 eV) electron-stimulated reactions in layered H2O/CO/H2O ices are investigated. For CO trapped within approximately 50 ML of the vacuum interface in the amorphous solid water (ASW) films, both oxidation and reduction reactions are observed. However for CO buried more deeply in the film, only the reduction of CO to methanol is observed. Experiments with layered films of H2O and D2O show that the hydrogen atoms participating in the reduction of the buried CO originate in region from ~10 – 40 ML below the surface of the ASW films and subsequently diffuse through the film. For deeply buried COmore » layers, the CO reduction reactions quickly increase with temperature above ~60 K. We present a simple chemical kinetic model that treats the diffusion of hydrogen atoms in the ASW and sequential hydrogenation of the CO to methanol that accounts for the observations.« less

A Reaction-Diffusion Model of Vector-Borne Disease with Periodic Delays

NASA Astrophysics Data System (ADS)

Wu, Ruiwen; Zhao, Xiao-Qiang

2018-06-01

A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction-diffusion model of vector-borne disease with periodic delays. We introduce the basic reproduction number R_0 for this model and then establish a threshold-type result on its global dynamics in terms of R_0 . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when R_0>1 . Numerically, we study the malaria transmission in Maputo Province, Mozambique.

Two-dimensional enzyme diffusion in laterally confined DNA monolayers.

PubMed

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

2011-01-01

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

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

DOE PAGES

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

2017-03-08

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

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

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

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

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

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

PubMed

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

2016-03-15

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

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

PubMed

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

2015-01-01

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

Novel developments and applications of the classical adiabatic dynamics technique

NASA Astrophysics Data System (ADS)

Rosso, Lula

The present work aims to apply and develop modern molecular dynamics techniques based on a novel analysis of the classical adiabatic dynamics approach. In the first part of this thesis, Car-Parrinello ab-initio molecular dynamics, a successful technique based on adiabatic dynamics, is used to study the charge transport mechanism in solid ammonium perchlorate (AP) crystal exposed to an ammonia-rich environment. AP is a solid-state proton conductor composed of NH+4 and ClO-4 units that can undergo a decomposition process at high temperature, leading to its use such as rocket fuel. After computing IR spectra and carefully analysing the dynamics at different temperatures, we found that the charge transport mechanism in the pure crystal is dominated by diffusion of the ammonium ions and that the translational diffusion is strongly coupled to rotational diffusion of the two types of ions present. When the pure ammonium-perchlorate crystal is doped with neutral ammonia, another mechanism comes into play, namely, the Grotthuss proton hopping mechanism via short-lived N2H+7 complexes. In the second part of this thesis, adiabatic dynamics will be used to develop an alternative approach to the calculation of free energy profiles along reaction paths. The new method (AFED) is based on the creation of an adiabatic separation between the reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass. These conditions allow the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profile is obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, no postprocessing of the output data is required. The new method is applied to a variety of model problems and extended to calculate conformational surfaces of small peptides and the chemical potential of a Lennard-Jones liquid. The comparison with established methods shows that the new approach calculates free energy profiles with greater ease and efficiency.

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

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

Wampler, William R., E-mail: wrwampl@sandia.gov; Myers, Samuel M.

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers,more » and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.« less

Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

PubMed

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

2017-07-01

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

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

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

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

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

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

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

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

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

NASA Technical Reports Server (NTRS)

Parshev, V. A.

1980-01-01

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

A preliminary sensitivity analysis of the coupled diffusion and chemistry model. [effect of SST operations on ambient ozone in lower stratosphere

NASA Technical Reports Server (NTRS)

Hilst, G. R.; Contiliano, R. M.

1973-01-01

The sensitivity of the coupled chemistry/diffusion model's outputs to a wide range of variation of the model's independent variables has been investigated. It is shown that the efficiency with which the now catalytic cycle destroys ambient O3 is extremely sensitive to the amount of NO emitted and to the relative rates of turbulent diffusion and chemical reactions. For representative conditions in the stratosphere, a tenfold variation of either the turbulence intensity or the reaction rate constant or the source strength can vary the efficiency from 1% to 50%. If the duration of Phase 3 is a significant fraction of the total residence time of the plume, then these efficiency variations can alter O3 depletion rates by more than a factor of two. These results, therefore, point toward those variables which must be accurately defined or measured if one is to adequately predict the effect of SST operations on the ambient inventory of O3 in the lower stratosphere.

Influence of Wind Pressure on the Carbonation of Concrete

PubMed Central

Zou, Dujian; Liu, Tiejun; Du, Chengcheng; Teng, Jun

2015-01-01

Carbonation is one of the major deteriorations that accelerate steel corrosion in reinforced concrete structures. Many mathematical/numerical models of the carbonation process, primarily diffusion-reaction models, have been established to predict the carbonation depth. However, the mass transfer of carbon dioxide in porous concrete includes molecular diffusion and convection mass transfer. In particular, the convection mass transfer induced by pressure difference is called penetration mass transfer. This paper presents the influence of penetration mass transfer on the carbonation. A penetration-reaction carbonation model was constructed and validated by accelerated test results under high pressure. Then the characteristics of wind pressure on the carbonation were investigated through finite element analysis considering steady and fluctuating wind flows. The results indicate that the wind pressure on the surface of concrete buildings results in deeper carbonation depth than that just considering the diffusion of carbon dioxide. In addition, the influence of wind pressure on carbonation tends to increase significantly with carbonation depth. PMID:28793462

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Influence of Wind Pressure on the Carbonation of Concrete.

PubMed

Zou, Dujian; Liu, Tiejun; Du, Chengcheng; Teng, Jun

2015-07-24

Carbonation is one of the major deteriorations that accelerate steel corrosion in reinforced concrete structures. Many mathematical/numerical models of the carbonation process, primarily diffusion-reaction models, have been established to predict the carbonation depth. However, the mass transfer of carbon dioxide in porous concrete includes molecular diffusion and convection mass transfer. In particular, the convection mass transfer induced by pressure difference is called penetration mass transfer. This paper presents the influence of penetration mass transfer on the carbonation. A penetration-reaction carbonation model was constructed and validated by accelerated test results under high pressure. Then the characteristics of wind pressure on the carbonation were investigated through finite element analysis considering steady and fluctuating wind flows. The results indicate that the wind pressure on the surface of concrete buildings results in deeper carbonation depth than that just considering the diffusion of carbon dioxide. In addition, the influence of wind pressure on carbonation tends to increase significantly with carbonation depth.

How the contagion at links influences epidemic spreading

NASA Astrophysics Data System (ADS)

Ruan, Zhongyuan; Tang, Ming; Liu, Zonghua

2013-04-01

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

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Chlorine Dioxide Is a Size-Selective Antimicrobial Agent

PubMed Central

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

2013-01-01

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

Modeling growth kinetics of thin films made by atomic layer deposition in lateral high-aspect-ratio structures

NASA Astrophysics Data System (ADS)

Ylilammi, Markku; Ylivaara, Oili M. E.; Puurunen, Riikka L.

2018-05-01

The conformality of thin films grown by atomic layer deposition (ALD) is studied using all-silicon test structures with long narrow lateral channels. A diffusion model, developed in this work, is used for studying the propagation of ALD growth in narrow channels. The diffusion model takes into account the gas transportation at low pressures, the dynamic Langmuir adsorption model for the film growth and the effect of channel narrowing due to film growth. The film growth is calculated by solving the diffusion equation with surface reactions. An efficient analytic approximate solution of the diffusion equation is developed for fitting the model to the measured thickness profile. The fitting gives the equilibrium constant of adsorption and the sticking coefficient. This model and Gordon's plug flow model are compared. The simulations predict the experimental measurement results quite well for Al2O3 and TiO2 ALD processes.

A method for modeling oxygen diffusion in an agent-based model with application to host-pathogen infection

DOE PAGES

Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.

2015-01-01

This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figuremore » 1 is the evolution of the diffusion profiles of a containment granuloma over time.« less

Improved brain tumor segmentation by utilizing tumor growth model in longitudinal brain MRI

NASA Astrophysics Data System (ADS)

Pei, Linmin; Reza, Syed M. S.; Li, Wei; Davatzikos, Christos; Iftekharuddin, Khan M.

2017-03-01

In this work, we propose a novel method to improve texture based tumor segmentation by fusing cell density patterns that are generated from tumor growth modeling. To model tumor growth, we solve the reaction-diffusion equation by using Lattice-Boltzmann method (LBM). Computational tumor growth modeling obtains the cell density distribution that potentially indicates the predicted tissue locations in the brain over time. The density patterns is then considered as novel features along with other texture (such as fractal, and multifractal Brownian motion (mBm)), and intensity features in MRI for improved brain tumor segmentation. We evaluate the proposed method with about one hundred longitudinal MRI scans from five patients obtained from public BRATS 2015 data set, validated by the ground truth. The result shows significant improvement of complete tumor segmentation using ANOVA analysis for five patients in longitudinal MR images.

Improved brain tumor segmentation by utilizing tumor growth model in longitudinal brain MRI.

PubMed

Pei, Linmin; Reza, Syed M S; Li, Wei; Davatzikos, Christos; Iftekharuddin, Khan M

2017-02-11

In this work, we propose a novel method to improve texture based tumor segmentation by fusing cell density patterns that are generated from tumor growth modeling. In order to model tumor growth, we solve the reaction-diffusion equation by using Lattice-Boltzmann method (LBM). Computational tumor growth modeling obtains the cell density distribution that potentially indicates the predicted tissue locations in the brain over time. The density patterns is then considered as novel features along with other texture (such as fractal, and multifractal Brownian motion (mBm)), and intensity features in MRI for improved brain tumor segmentation. We evaluate the proposed method with about one hundred longitudinal MRI scans from five patients obtained from public BRATS 2015 data set, validated by the ground truth. The result shows significant improvement of complete tumor segmentation using ANOVA analysis for five patients in longitudinal MR images.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Pattern formation in three-dimensional reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Callahan, T. K.; Knobloch, E.

1999-08-01

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

Chemistry with spatial control using particles and streams†

PubMed Central

Kalinin, Yevgeniy V.; Murali, Adithya

2012-01-01

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

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

PubMed

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

2011-10-14

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

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Predictive Finite Rate Model for Oxygen-Carbon Interactions at High Temperature

NASA Astrophysics Data System (ADS)

Poovathingal, Savio

An oxidation model for carbon surfaces is developed to predict ablation rates for carbon heat shields used in hypersonic vehicles. Unlike existing empirical models, the approach used here was to probe gas-surface interactions individually and then based on an understanding of the relevant fundamental processes, build a predictive model that would be accurate over a wide range of pressures and temperatures, and even microstructures. Initially, molecular dynamics was used to understand the oxidation processes on the surface. The molecular dynamics simulations were compared to molecular beam experiments and good qualitative agreement was observed. The simulations reproduced cylindrical pitting observed in the experiments where oxidation was rapid and primarily occurred around a defect. However, the studies were limited to small systems at low temperatures and could simulate time scales only of the order of nanoseconds. Molecular beam experiments at high surface temperature indicated that a majority of surface reaction products were produced through thermal mechanisms. Since the reactions were thermal, they occurred over long time scales which were computationally prohibitive for molecular dynamics to simulate. The experiments provided detailed dynamical data on the scattering of O, O2, CO, and CO2 and it was found that the data from molecular beam experiments could be used directly to build a model. The data was initially used to deduce surface reaction probabilities at 800 K. The reaction probabilities were then incorporated into the direct simulation Monte Carlo (DSMC) method. Simulations were performed where the microstructure was resolved and dissociated oxygen convected and diffused towards it. For a gas-surface temperature of 800 K, it was found that despite CO being the dominant surface reaction product, a gas-phase reaction forms significant CO2 within the microstructure region. It was also found that surface area did not play any role in concentration of reaction products because the reaction probabilities were in the diffusion dominant regime. The molecular beam data at different surface temperatures was then used to build a finite rate model. Each reaction mechanism and all rate parameters of the new model were determined individually based on the molecular beam data. Despite the experiments being performed at near vacuum conditions, the finite rate model developed using the data could be used at pressures and temperatures relevant to hypersonic conditions. The new model was implemented in a computational fluid dynamics (CFD) solver and flow over a hypersonic vehicle was simulated. The new model predicted similar overall mass loss rates compared to existing models, however, the individual species production rates were completely different. The most notable difference was that the new model (based on molecular beam data) predicts CO as the oxidation reaction product with virtually no CO2 production, whereas existing models predict the exact opposite trend. CO being the dominant oxidation product is consistent with recent high enthalpy wind tunnel experiments. The discovery that measurements taken in molecular beam facilities are able to determine individual reaction mechanisms, including dependence on surface coverage, opens up an entirely new way of constructing ablation models.

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

NASA Astrophysics Data System (ADS)

de Waal, H.; Pretorius, R.

1999-10-01

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

Collision cascades enhanced hydrogen redistribution in cobalt implanted hydrogenated diamond-like carbon films

NASA Astrophysics Data System (ADS)

Gupta, P.; Becker, H.-W.; Williams, G. V. M.; Hübner, R.; Heinig, K.-H.; Markwitz, A.

2017-03-01

Hydrogenated diamond-like carbon films produced by C3H6 deposition at 5 kV and implanted at room temperature with 30 keV Co atoms to 12 at.% show not only a bimodal distribution of Co atoms but also a massive redistribution of hydrogen in the films. Resonant nuclear reaction analysis was used to measure the hydrogen depth profiles (15N-method). Depletion of hydrogen near the surface was measured to be as low as 7 at.% followed by hydrogen accumulation from 27 to 35 at.%. A model is proposed considering the thermal energy deposited by collision cascade for thermal insulators. In this model, sufficient energy is provided for dissociated hydrogen to diffuse out of the sample from the surface and diffuse into the sample towards the interface which is however limited by the range of the incoming Co ions. At a hydrogen concentration of ∼35 at.%, the concentration gradient of the mobile unbounded hydrogen atoms is neutralised effectively stopping diffusion towards the interface. The results point towards new routes of controlling the composition and distribution of elements at the nanoscale within a base matrix without using any heat treatment methods. Exploring these opportunities can lead to a new horizon of materials and device engineering needed for enabling advanced technologies and applications.