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

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

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

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

PubMed

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

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

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions. A review and a perspective

NASA Astrophysics Data System (ADS)

Cartes, C.; Descalzi, O.; Brand, H. R.

2014-10-01

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.

A Model for Selection of Eyespots on Butterfly Wings.

PubMed

Sekimura, Toshio; Venkataraman, Chandrasekhar; Madzvamuse, Anotida

2015-01-01

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

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

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.

A variable turbulent Prandtl and Schmidt number model study for scramjet applications

NASA Astrophysics Data System (ADS)

Keistler, Patrick

A turbulence model that allows for the calculation of the variable turbulent Prandtl (Prt) and Schmidt (Sct) numbers as part of the solution is presented. The model also accounts for the interactions between turbulence and chemistry by modeling the corresponding terms. Four equations are added to the baseline k-zeta turbulence model: two equations for enthalpy variance and its dissipation rate to calculate the turbulent diffusivity, and two equations for the concentrations variance and its dissipation rate to calculate the turbulent diffusion coefficient. The underlying turbulence model already accounts for compressibility effects. The variable Prt /Sct turbulence model is validated and tuned by simulating a wide variety of experiments. Included in the experiments are two-dimensional, axisymmetric, and three-dimensional mixing and combustion cases. The combustion cases involved either hydrogen and air, or hydrogen, ethylene, and air. Two chemical kinetic models are employed for each of these situations. For the hydrogen and air cases, a seven species/seven reaction model where the reaction rates are temperature dependent and a nine species/nineteen reaction model where the reaction rates are dependent on both pressure and temperature are used. For the cases involving ethylene, a 15 species/44 reaction reduced model that is both pressure and temperature dependent is used, along with a 22 species/18 global reaction reduced model that makes use of the quasi-steady-state approximation. In general, fair to good agreement is indicated for all simulated experiments. The turbulence/chemistry interaction terms are found to have a significant impact on flame location for the two-dimensional combustion case, with excellent experimental agreement when the terms are included. In most cases, the hydrogen chemical mechanisms behave nearly identically, but for one case, the pressure dependent model would not auto-ignite at the same conditions as the experiment and the other chemical model. The model was artificially ignited in that case. For the cases involving ethylene combustion, the chemical model has a profound impact on the flame size, shape, and ignition location. However, without quantitative experimental data, it is difficult to determine which one is more suitable for this particular application.

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

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

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.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

Modelling Tethered Enzymatic Reactions

NASA Astrophysics Data System (ADS)

Solis Salas, Citlali; Goyette, Jesse; Coker-Gordon, Nicola; Bridge, Marcus; Isaacson, Samuel; Allard, Jun; Maini, Philip; Dushek, Omer

Enzymatic reactions are key to cell functioning, and whilst much work has been done in protein interaction in cases where diffusion is possible, interactions of tethered proteins are poorly understood. Yet, because of the large role cell membranes play in enzymatic reactions, several reactions may take place where one of the proteins is bound to a fixed point in space. We develop a model to characterize tethered signalling between the phosphatase SHP-1 interacting with a tethered, phosphorylated protein. We compare our model to experimental data obtained using surface plasmon resonance (SPR). We show that a single SPR experiment recovers 5 independent biophysical/biochemical constants. We also compare the results between a three dimensional model and a two dimensional model. The work gives the opportunity to use known techniques to learn more about signalling processes, and new insights into how enzyme tethering alters cellular signalling. With support from the Mexican Council for Science and Technology (CONACyT), the Public Education Secretariat (SEP), and the Mexican National Autonomous University's Foundation (Fundacion UNAM).

Speeding up biomolecular interactions by molecular sledding

DOE PAGES

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

2015-10-07

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

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

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

Development of morphogen gradient: The role of dimension and discreteness

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

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

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

Patterns and Oscillations in Reaction-Diffusion Systems with Intrinsic Fluctuations

NASA Astrophysics Data System (ADS)

Giver, Michael; Goldstein, Daniel; Chakraborty, Bulbul

2013-03-01

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

Numerical simulation of two-dimensional flow over a heated carbon surface with coupled heterogeneous and homogeneous reactions

NASA Astrophysics Data System (ADS)

Johnson, Ryan Federick; Chelliah, Harsha Kumar

2017-01-01

For a range of flow and chemical timescales, numerical simulations of two-dimensional laminar flow over a reacting carbon surface were performed to understand further the complex coupling between heterogeneous and homogeneous reactions. An open-source computational package (OpenFOAM®) was used with previously developed lumped heterogeneous reaction models for carbon surfaces and a detailed homogeneous reaction model for CO oxidation. The influence of finite-rate chemical kinetics was explored by varying the surface temperatures from 1800 to 2600 K, while flow residence time effects were explored by varying the free-stream velocity up to 50 m/s. The reacting boundary layer structure dependence on the residence time was analysed by extracting the ratio of chemical source and species diffusion terms. The important contributions of radical species reactions on overall carbon removal rate, which is often neglected in multi-dimensional simulations, are highlighted. The results provide a framework for future development and validation of lumped heterogeneous reaction models based on multi-dimensional reacting flow configurations.

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.

Intracellular signal propagation in a two-dimensional autocatalytic reaction model.

PubMed

Castiglione, F; Bernaschi, M; Succi, S; Heinrich, R; Kirschner, M W

2002-09-01

We study a simple reaction scheme in a two-dimensional lattice of particles or molecules with a refractory state. We analyze the dynamics of the propagating front as a function of physical-chemical properties of the host medium. The anisotropy of the medium significantly affects the smoothness of the wave front. Similarly, if particles or molecules may diffuse slowly to neighboring sites, then the front wave is more likely to be irregular. Both situations affect the ability of the whole system to relax to the original state, which is a required feature in the biological cells. Attempts to map this simple reaction scheme to reactions involved in the intracellular pathways suggest that, in some cases, signal transduction might take both connotation of a random walk and a propagating wave, depending on the local density of the medium. In particular, a sufficient condition for the appearance of waves in high-density regions of the media, is the existence of at least one autocatalytic reaction in the chain of reactions characterizing the pathway.

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.

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.

Wave Phenomena in Reaction-Diffusion Systems

NASA Astrophysics Data System (ADS)

Steinbock, Oliver; Engel, Harald

2013-12-01

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

Regulation of a Viral Proteinase by a Peptide and DNA in One-dimensional Space

PubMed Central

Blainey, Paul C.; Graziano, Vito; Pérez-Berná, Ana J.; McGrath, William J.; Flint, S. Jane; San Martín, Carmen; Xie, X. Sunney; Mangel, Walter F.

2013-01-01

Precursor proteins used in the assembly of adenovirus virions must be processed by the virally encoded adenovirus proteinase (AVP) before the virus particle becomes infectious. An activated adenovirus proteinase, the AVP-pVIc complex, was shown to slide along viral DNA with an extremely fast one-dimensional diffusion constant, 21.0 ± 1.9 × 106 bp2/s. In principle, one-dimensional diffusion can provide a means for DNA-bound proteinases to locate and process DNA-bound substrates. Here, we show that this is correct. In vitro, AVP-pVIc complexes processed a purified virion precursor protein in a DNA-dependent reaction; in a quasi in vivo environment, heat-disrupted ts-1 virions, AVP-pVIc complexes processed five different precursor proteins in DNA-dependent reactions. Sliding of AVP-pVIc complexes along DNA illustrates a new biochemical mechanism by which a proteinase can locate its substrates, represents a new paradigm for virion maturation, and reveals a new way of exploiting the surface of DNA. PMID:23043138

Laser range profile of cones

NASA Astrophysics Data System (ADS)

Zhou, Wenzhen; Gong, Yanjun; Wang, Mingjun; Gong, Lei

2016-10-01

technology. Laser one-dimensional range profile can reflect the characteristics of the target shape and surface material. These techniques were motivated by applications of laser radar to target discrimination in ballistic missile defense. The radar equation of pulse laser about cone is given in this paper. This paper demonstrates the analytical model of laser one-dimensional range profile of cone based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cones are given. Laser one-dimensional range profiles of cone, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser one-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. Laser one-dimensional range profiles of different pulse width of cone is given in this paper. The influences of surface material, pulse width, attitude on the one-dimensional range are analyzed. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. The two-dimensional range profile of roughness target can provide range resolved information. An analytical model of two-dimensional laser range profile of cone is proposed. The simulations of two-dimensional laser range profiles of some cones are given. Laser two-dimensional range profiles of cone, whose surface mater with diffuse lambertian reflectance, is given in this paper. Laser two-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. The influence of pulse width, surface material on laser two-dimensional range profile is analyzed. Laser one-dimensional range profile and laser two-dimensional range profile are called as laser range profile (LRP).

Computational Analyses of Complex Flows with Chemical Reactions

NASA Astrophysics Data System (ADS)

Bae, Kang-Sik

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

Single-Molecule Test for Markovianity of the Dynamics along a Reaction Coordinate.

PubMed

Berezhkovskii, Alexander M; Makarov, Dmitrii E

2018-05-03

In an effort to answer the much-debated question of whether the time evolution of common experimental observables can be described as one-dimensional diffusion in the potential of mean force, we propose a simple criterion that allows one to test whether the Markov assumption is applicable to a single-molecule trajectory x( t). This test does not involve fitting of the data to any presupposed model and can be applied to experimental data with relatively low temporal resolution.

Ab initio quantum mechanical calculation of the reaction probability for the Cl-+PH2Cl→ClPH2+Cl- reaction

NASA Astrophysics Data System (ADS)

Farahani, Pooria; Lundberg, Marcus; Karlsson, Hans O.

2013-11-01

The SN2 substitution reactions at phosphorus play a key role in organic and biological processes. Quantum molecular dynamics simulations have been performed to study the prototype reaction Cl-+PH2Cl→ClPH2+Cl-, using one and two-dimensional models. A potential energy surface, showing an energy well for a transition complex, was generated using ab initio electronic structure calculations. The one-dimensional model is essentially reflection free, whereas the more realistic two-dimensional model displays involved resonance structures in the reaction probability. The reaction rate is almost two orders of magnitude smaller for the two-dimensional compared to the one-dimensional model. Energetic errors in the potential energy surface is estimated to affect the rate by only a factor of two. This shows that for these types of reactions it is more important to increase the dimensionality of the modeling than to increase the accuracy of the electronic structure calculation.

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

PubMed

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

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

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.

A stochastic multi-scale method for turbulent premixed combustion

NASA Astrophysics Data System (ADS)

Cha, Chong M.

2002-11-01

The stochastic chemistry algorithm of Bunker et al. and Gillespie is used to perform the chemical reactions in a transported probability density function (PDF) modeling approach of turbulent combustion. Recently, Kraft & Wagner have demonstrated a 100-fold gain in computational speed (for a 100 species mechanism) using the stochastic approach over the conventional, direct integration method of solving for the chemistry. Here, the stochastic chemistry algorithm is applied to develop a new transported PDF model of turbulent premixed combustion. The methodology relies on representing the relevant spatially dependent physical processes as queuing events. The canonical problem of a one-dimensional premixed flame is used for validation. For the laminar case, molecular diffusion is described by a random walk. For the turbulent case, one of two different material transport submodels can provide the necessary closure: Taylor dispersion or Kerstein's one-dimensional turbulence approach. The former exploits ``eddy diffusivity'' and hence would be much more computationally tractable for practical applications. Various validation studies are performed. Results from the Monte Carlo simulations compare well to asymptotic solutions of laminar premixed flames, both with and without high activation temperatures. The correct scaling of the turbulent burning velocity is predicted in both Damköhler's small- and large-scale turbulence limits. The effect of applying the eddy diffusivity concept in the various regimes is discussed.

Users manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

Schoellhamer, D.H.; Jobson, H.E.

1986-01-01

A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)

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.

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.

Structure and Dynamics of Solvent Landscapes in Charge-Transfer Reactions

NASA Astrophysics Data System (ADS)

Leite, Vitor B. Pereira

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

Rigorous results for the minimal speed of Kolmogorov-Petrovskii-Piscounov monotonic fronts with a cutoffa)

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Depassier, M. Cristina; Loss, Michael

2012-12-01

We study the effect of a cutoff on the speed of pulled fronts of the one-dimensional reaction diffusion equation. To accomplish this, we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles. This existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut-off parameter ɛ. From these bounds we estimate the range of validity of the Brunet-Derrida formula for a general class of reaction terms.

User's guide to PHREEQC (Version 2) : a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations

USGS Publications Warehouse

Parkhurst, David L.; Appelo, C.A.J.

1999-01-01

PHREEQC version 2 is a computer program written in the C programming language that is designed to perform a wide variety of low-temperature aqueous geochemical calculations. PHREEQC is based on an ion-association aqueous model and has capabilities for (1) speciation and saturation-index calculations; (2) batch-reaction and one-dimensional (1D) transport calculations involving reversible reactions, which include aqueous, mineral, gas, solid-solution, surface-complexation, and ion-exchange equilibria, and irreversible reactions, which include specified mole transfers of reactants, kinetically controlled reactions, mixing of solutions, and temperature changes; and (3) inverse modeling, which finds sets of mineral and gas mole transfers that account for differences in composition between waters, within specified compositional uncertainty limits.New features in PHREEQC version 2 relative to version 1 include capabilities to simulate dispersion (or diffusion) and stagnant zones in 1D-transport calculations, to model kinetic reactions with user-defined rate expressions, to model the formation or dissolution of ideal, multicomponent or nonideal, binary solid solutions, to model fixed-volume gas phases in addition to fixed-pressure gas phases, to allow the number of surface or exchange sites to vary with the dissolution or precipitation of minerals or kinetic reactants, to include isotope mole balances in inverse modeling calculations, to automatically use multiple sets of convergence parameters, to print user-defined quantities to the primary output file and (or) to a file suitable for importation into a spreadsheet, and to define solution compositions in a format more compatible with spreadsheet programs. This report presents the equations that are the basis for chemical equilibrium, kinetic, transport, and inverse-modeling calculations in PHREEQC; describes the input for the program; and presents examples that demonstrate most of the program's capabilities.

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.

An idealised study of the effects of small scales on chemistry in a two-dimensional turbulent flow.

NASA Astrophysics Data System (ADS)

Chaalal, F. Ait; Bartello, P.; Bourqui, M.

2009-04-01

The non-linear nature of stratospheric chemical reactions makes them sensitive to mixing and diffusion. Most stratospheric Climate-Chemistry Models neglect the effects of sub-grid flow structures on chemistry. Several previous studies have pointed out that such unresolved small scales could significantly affect the chemistry. However this problem has not been thoroughly studied from a theoretical point of view. To fulfill this gap, we investigate the interactions between advection, diffusion and chemistry for a simple bimolecular reaction between two initially unmixed reactants, within the framework of two-dimensional isotropic and homogenous turbulence. This is a highly simplified representation of quasi-isentropic mixing in the stratosphere. Our goal here is to describe and understand how the production rate of the product species is affected by the size of the smallest scales of the tracer field, as determined by the tracer diffusion coefficient ΰ. The spatial average of the prognostic equation for the product's concentration involves the covariance of the reactants. The time evolution of this covariance depends in turn on a dissipative term, and on second and third order chemical terms. The set of equations is not closed and any finite resolution model would need a parameterization of the dissipation and a closure hypothesis on the chemical terms. To study these terms, we perform ensembles of direct numerical simulations using a pseudo-spectral two-dimensional periodic model. The ensembles span different initial conditions of the flow and different tracer diffusion coefficients ΰ. Our results show a strong dependence of the total production on the diffusion coefficient. This production scales like ΰp(t) , where p(t) is a positive decreasing function of time. This scaling is very similar to the one found by Tan et al. (1998) for atmospheric flows on the deactivation of chlorine by nitrogen oxide at the southern edge of the winter time polar vortex. Furthermore, the time derivative of the reactants' covariance is found to be only very weakly dependent on the chemical reaction rate, for both slow and fast chemistries compared to the advection. The variations of the dissipation and of the chemical terms with the reaction speed compensate each other. As a consequence, the calculation of the product's concentration using the covariance of the dissipation without chemistry is a good approximation of the effect of diffusion with chemistry. Reference Tan, DGH; Haynes, PH; MacKenzie, AR; et al., Effects of fluid-dynamical stirring and mixing on the deactivation of stratospheric chlorine, Journal of Geophysical Research-Atmospheres, Volume: 103 Issue: D1 Pages: 1585-1605 (1998).

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

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.

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

PubMed Central

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

2015-01-01

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

Laminar flamelet modeling of turbulent diffusion flames

NASA Technical Reports Server (NTRS)

Mell, W. E.; Kosaly, G.; Planche, O.; Poinsot, T.; Ferziger, J. H.

1990-01-01

In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.

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

NASA Astrophysics Data System (ADS)

Konishi, Keiji; Hara, Naoyuki

2018-05-01

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

Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies

NASA Astrophysics Data System (ADS)

Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration

Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.

The calculation of a turbulent diffusion flame in a free shear flow with a statistical turbulence model

NASA Astrophysics Data System (ADS)

Bywater, R. J.

1980-01-01

Solutions are presented for the turbulent diffusion flame in a two-dimensional shear layer based upon a kinetic theory of turbulence (KTT). The fuel and oxidizer comprising the two streams are considered to react infinitely fast according to a one-step, irreversible kinetic mechanism. The solutions are obtained by direct numerical calculation of the transverse velocity probability density function (PDF) and the associated species distributions. The mean reactant profiles calculated from the solutions display the characteristic thick, turbulent flame zone. The phenomena result from the fact that in the context of the KTT, species react only when in the same velocity cell. This coincides with the known physical requirement that molecular mixing precedes reaction. The solutions demonstrate this behavior by showing how reactants can coexist in the mean, even when infinite reaction rates are enforced at each point (t,x,u) of velocity space.

4D Biofabrication of Branching Multicellular Structures: A Morphogenesis Simulation Based on Turing’s Reaction-Diffusion Dynamics

NASA Astrophysics Data System (ADS)

Zhu, Xiaolu; Yang, Hao

2017-12-01

The recently emerged four-dimensional (4D) biofabrication technique aims to create dynamic three-dimensional (3D) biological structures that can transform their shapes or functionalities with time when an external stimulus is imposed or when cell postprinting self-assembly occurs. The evolution of 3D pattern of branching geometry via self-assembly of cells is critical for 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear that how the formation and evolution of these branching pattern are biologically encoded. We study the 4D fabrication of lung branching structures utilizing a simulation model on the reaction-diffusion mechanism, which is established using partial differential equations of four variables, describing the reaction and diffusion process of morphogens with time during the development process of lung branching. The simulation results present the forming process of 3D branching pattern, and also interpret the behaviors of side branching and tip splitting as the stalk growing, through 3D visualization of numerical simulation.

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

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

DOE PAGES

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

2017-10-30

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

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

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

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

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

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

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

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

2017-10-30

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

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Dynamic colloidal assembly pathways via low dimensional models

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

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

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.

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

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

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

A 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

Studies in premixed combustion. [Benjamin Levich Inst. for Physico-Chemical Hydrodynamics, City College of CUNY, New York, New York

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

Sivashinsky, G.I.

1993-01-01

During the period under review, significant progress was been made in studying the intrinsic dynamics of premixed flames and the problems of flame-flow interaction. (1) A weakly nonlinear model for Bunsen burner stabilized flames was proposed and employed for the simulation of three-dimensional polyhedral flames -- one of the most graphic manifestations of thermal-diffusive instability in premixed combustion. (2) A high-precision large-scale numerical simulation of Bunsen burner tip structure was conducted. The results obtained supported the earlier conjecture that the tip opening observed in low Lewis number systems is a purely optical effect not involving either flame extinction or leakagemore » of unburned fuel. (3) A one-dimensional model describing a reaction wave moving through a unidirectional periodic flow field is proposed and studied numerically. For long-wavelength fields the system exhibits a peculiar non-uniqueness of possible propagation regimes. The transition from one regime to another occurs in a manner of hysteresis.« less

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

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

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

NASA Astrophysics Data System (ADS)

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-01

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (˜5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

PubMed

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-21

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (∼5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Dynamics of A + B --> C reaction fronts in the presence of buoyancy-driven convection.

PubMed

Rongy, L; Trevelyan, P M J; De Wit, A

2008-08-22

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.

Pair and triple correlations in the A+B-->B diffusion-controlled reaction

NASA Astrophysics Data System (ADS)

Kuzovkov, Vladimir; Kotomin, Eugene

1994-03-01

An exact solution for the one-dimensional kinetics of the diffusion-controlled reaction A+B-->B is obtained by means of the three-particle correlation functions. Because of a lattice discreteness each site could be occupied by a single particle only which leads to the so-called ``bus effect'': Recombination of any particle A is defined by a spatial configuration of two nearest particles B only surrounding A from its left and right. This results in the unusual algebraic decay law, n(t)~t-1, which asymptotically (as t-->∞) does not depend on the trap B concentration.

Characteristic power spectrum of diffusive interface dynamics in the two-dimensional Ising model

NASA Astrophysics Data System (ADS)

Masumoto, Yusuke; Takesue, Shinji

2018-05-01

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

NASA Astrophysics Data System (ADS)

Schlup, Jason; Blanquart, Guillaume

2018-03-01

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.

Control of scroll wave turbulence in a three-dimensional reaction-diffusion system with gradient.

PubMed

Qiao, Chun; Wu, Yabi; Lu, Xiaochuan; Wang, Chunyan; Ouyang, Qi; Wang, Hongli

2008-06-01

In this paper, we summarize our recent experimental and theoretical works on observation and control of scroll wave (SW) turbulence. The experiments were conducted in a three-dimensional Belousov-Zhabotinsky reaction-diffusion system with chemical concentration gradients in one dimension. A spatially homogeneous external forcing was used in the experiments as a control; it was realized by illuminating white light on the light sensitive reaction medium. We observed that, in the oscillatory regime of the system, SW can appear automatically in the gradient system, which will be led to spatiotemporal chaos under certain conditions. A suitable periodic forcing may stabilize inherent turbulence of SW. The mechanism of the transition to SW turbulence is due to the phase twist of SW in the presence of chemical gradients, while modulating the phase twist with a proper periodic forcing can delay this transition. Using the FitzHugh-Nagumo model with an external periodic forcing, we confirmed the control mechanism with numerical simulation. Moreover, we also show in the simulation that adding temporal external noise to the system may have the same control effect. During this process, we observed a new state called "intermittent turbulence," which may undergo a transition into a new type of SW collapse when the noise intensity is further increased. The intermittent state and the collapse could be explained by a random process.

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.

Transport of volatile organic compounds across the capillary fringe

USGS Publications Warehouse

McCarthy, Kathleen A.; Johnson, Richard L.

1993-01-01

Physical experiments were conducted to investigate the transport of a dissolved volatile organic compound (trichloroethylene, TCE) from shallow groundwater to the unsaturated zone under a variety of conditions including changes in the soil moisture profile and water table position. Experimental data indicated that at moderate groundwater velocities (0.1 m/d), vertical mechanical dispersion was negligible and molecular diffusion was the dominant vertical transport mechanism. Under these conditions, TCE concentrations decreased nearly 3 orders of magnitude across the capillary fringe and soil gas concentrations remained low relative to those of underlying groundwater. Data collected during a water table drop showed a short-term increase in concentrations throughout most of the unsaturated zone, but these concentrations quickly declined and approached initial values after the water table was returned to its original level. In the deep part of the unsaturated zone, the water table drop resulted in a long-term decrease in concentrations, illustrating the effects of hysteresis in the soil moisture profile. A two-dimensional random walk advection-diffusion model was developed to simulate the experimental conditions, and numerical simulations agreed well with experimental data. A simpler, one-dimensional finite-difference diffusion-dispersion model was also developed. One-dimensional simulations based on molecular diffusion also agreed well with experimental data. Simulations which incorporated mechanical dispersion tended to overestimate flux across the capillary fringe. Good agreement between the one- and two-dimensional models suggested that a simple, one-dimensional approximation of vertical transport across the capillary fringe can be useful when conditions are appropriate.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Existence and non-existence of transition fronts in mixed ignition-monostable media

NASA Astrophysics Data System (ADS)

Graham, Cole; Shean Lim, Tau; Ma, Andrew; Weber, David

2018-02-01

We study transition fronts for one-dimensional reaction-diffusion equations with compactly-perturbed ignition-monostable reactions. We establish an almost sharp condition on reactions which characterizes the existence and non-existence of fronts. In particular, we prove that a strong inhomogeneity in the reaction prevents formation of transition fronts, while a weak inhomogeneity gives rise to a front. Our work extends the results and methods introduced in Nolen et al 2012 (Arch. Ration. Mech. Anal. 203 217-46), which studied the same question in inhomogeneous KPP media.

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.

Pattern formation for NO+N H3 on Pt(100): Two-dimensional numerical results

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2005-01-01

The Lombardo-Fink-Imbihl model of the NO+NH3 reaction on a Pt(100) surface consists of seven coupled ordinary differential equations (ODE) and shows stable relaxation oscillations with sharp transitions in the relevant temperature range. Here we study numerically the effect of coupling of these oscillators by surface diffusion in two dimensions. We find different types of patterns, in particular phase clusters and standing waves. In models of related surface reactions such clustered solutions are known to exist only under a global coupling through the gas phase. This global coupling is replaced here by relatively fast diffusion of two variables which are kinetically slaved in the ODE. We also compare our simulations with experimental results and discuss some shortcomings of the model.

A multiphysics microstructure-resolved model for silicon anode lithium-ion batteries

NASA Astrophysics Data System (ADS)

Wang, Miao; Xiao, Xinran; Huang, Xiaosong

2017-04-01

Silicon (Si) is one of the most promising next generation anode materials for lithium-ion batteries (LIBs), but the use of Si in LIBs has been rather limited. The main challenge is its large volume change (up to 300%) during battery cycling. This can lead to the fracture of Si, failure at the interfaces between electrode components, and large dimensional change on the cell level. To optimize the Si electrode/battery design, a model that considers the interactions of different cell components is needed. This paper presents the development of a multiphysics microstructure-resolved model (MRM) for LIB cells with a-Si anode. The model considered the electrochemical reactions, Li transports in electrolyte and electrodes, dimensional changes and stresses, property evolution with the structure, and the coupling relationships. Important model parameters, such as the diffusivity, reaction rate constant, and apparent transfer coefficient, were determined by correlating the simulation results to experiments. The model was validated with experimental results in the literature. The use of this model was demonstrated in a parameter study of Si nanowall|Li cells. The specific and volumetric capacities of the cell as a function of the size, length/size ratio, spacing of the nanostructure, and Li+ concentration in electrolyte were investigated.

Numerical investigations of hybrid rocket engines

NASA Astrophysics Data System (ADS)

Betelin, V. B.; Kushnirenko, A. G.; Smirnov, N. N.; Nikitin, V. F.; Tyurenkova, V. V.; Stamov, L. I.

2018-03-01

Paper presents the results of numerical studies of hybrid rocket engines operating cycle including unsteady-state transition stage. A mathematical model is developed accounting for the peculiarities of diffusion combustion of fuel in the flow of oxidant, which is composed of oxygen-nitrogen mixture. Three dimensional unsteady-state simulations of chemically reacting gas mixture above thermochemically destructing surface are performed. The results show that the diffusion combustion brings to strongly non-uniform fuel mass regression rate in the flow direction. Diffusive deceleration of chemical reaction brings to the decrease of fuel regression rate in the longitudinal direction.

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

DTIC Science & Technology

2013-05-09

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

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed

Berry, Hugues

2002-10-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed Central

Berry, Hugues

2002-01-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes. PMID:12324410

Fractional Steps methods for transient problems on commodity computer architectures

NASA Astrophysics Data System (ADS)

Krotkiewski, M.; Dabrowski, M.; Podladchikov, Y. Y.

2008-12-01

Fractional Steps methods are suitable for modeling transient processes that are central to many geological applications. Low memory requirements and modest computational complexity facilitates calculations on high-resolution three-dimensional models. An efficient implementation of Alternating Direction Implicit/Locally One-Dimensional schemes for an Opteron-based shared memory system is presented. The memory bandwidth usage, the main bottleneck on modern computer architectures, is specially addressed. High efficiency of above 2 GFlops per CPU is sustained for problems of 1 billion degrees of freedom. The optimized sequential implementation of all 1D sweeps is comparable in execution time to copying the used data in the memory. Scalability of the parallel implementation on up to 8 CPUs is close to perfect. Performing one timestep of the Locally One-Dimensional scheme on a system of 1000 3 unknowns on 8 CPUs takes only 11 s. We validate the LOD scheme using a computational model of an isolated inclusion subject to a constant far field flux. Next, we study numerically the evolution of a diffusion front and the effective thermal conductivity of composites consisting of multiple inclusions and compare the results with predictions based on the differential effective medium approach. Finally, application of the developed parabolic solver is suggested for a real-world problem of fluid transport and reactions inside a reservoir.

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

NASA Astrophysics Data System (ADS)

Jahani, Fereidoun

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

Diffusion in higher dimensional SYK model with complex fermions

NASA Astrophysics Data System (ADS)

Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

2018-01-01

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

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.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

Limit Properties of One Dimensional Periodic Hopping Model

NASA Astrophysics Data System (ADS)

Zhang, Yun-xin

2010-02-01

One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expressions of the limits of mean velocity and diffusion constant of this model as the number of internal mechanochemical sates tend to infinity are obtained. These results will be helpful to understand the limit of the one dimensional hopping model. At the same time, the work can be used to get more useful results in continuous form from the corresponding ones obtained by discrete models.

Molybdate transport in a chemically complex aquifer: Field measurements compared with solute-transport model predictions

USGS Publications Warehouse

Stollenwerk, Kenneth G.

1998-01-01

A natural-gradient tracer test was conducted in an unconfined sand and gravel aquifer on Cape Cod, Massachusetts. Molybdate was included in the injectate to study the effects of variable groundwater chemistry on its aqueous distribution and to evaluate the reliability of laboratory experiments for identifying and quantifying reactions that control the transport of reactive solutes in groundwater. Transport of molybdate in this aquifer was controlled by adsorption. The amount adsorbed varied with aqueous chemistry that changed with depth as freshwater recharge mixed with a plume of sewage-contaminated groundwater. Molybdate adsorption was strongest near the water table where pH (5.7) and the concentration of the competing solutes phosphate (2.3 micromolar) and sulfate (86 micromolar) were low. Adsorption of molybdate decreased with depth as pH increased to 6.5, phosphate increased to 40 micromolar, and sulfate increased to 340 micromolar. A one-site diffuse-layer surface-complexation model and a two-site diffuse-layer surface-complexation model were used to simulate adsorption. Reactions and equilibrium constants for both models were determined in laboratory experiments and used in the reactive-transport model PHAST to simulate the two-dimensional transport of molybdate during the tracer test. No geochemical parameters were adjusted in the simulation to improve the fit between model and field data. Both models simulated the travel distance of the molybdate cloud to within 10% during the 2-year tracer test; however, the two-site diffuse-layer model more accurately simulated the molybdate concentration distribution within the cloud.

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.

Spintronics: spin accumulation in mesoscopic systems.

PubMed

Johnson, Mark

2002-04-25

In spintronics, in which use is made of the spin degree of freedom of the electron, issues concerning electrical spin injection and detection of electron spin diffusion are fundamentally important. Jedema et al. describe a magneto-resistance study in which they claim to have observed spin accumulation in a mesoscopic copper wire, but their one-dimensional model ignores two-dimensional spin-diffusion effects, which casts doubt on their analysis. A two-dimensional vector formalism of spin transport is called for to model spin-injection experiments, and the identification of spurious background resistance effects is crucial.

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.

Comparison of analytical and experimental performance of a wind-tunnel diffuser section

NASA Technical Reports Server (NTRS)

Shyne, R. J.; Moore, R. D.; Boldman, D. R.

1986-01-01

Wind tunnel diffuser performance is evaluated by comparing experimental data with analytical results predicted by an one-dimensional integration procedure with skin friction coefficient, a two-dimensional interactive boundary layer procedure for analyzing conical diffusers, and a two-dimensional, integral, compressible laminar and turbulent boundary layer code. Pressure, temperature, and velocity data for a 3.25 deg equivalent cone half-angle diffuser (37.3 in., 94.742 cm outlet diameter) was obtained from the one-tenth scale Altitude Wind Tunnel modeling program at the NASA Lewis Research Center. The comparison is performed at Mach numbers of 0.162 (Re = 3.097x19(6)), 0.326 (Re = 6.2737x19(6)), and 0.363 (Re = 7.0129x10(6)). The Reynolds numbers are all based on an inlet diffuser diameter of 32.4 in., 82.296 cm, and reasonable quantitative agreement was obtained between the experimental data and computational codes.

Three-Dimensional Transport Modeling for Proton Exchange Membrane(PEM) Fuel Cell with Micro Parallel Flow Field

PubMed Central

Lee, Pil Hyong; Han, Sang Seok; Hwang, Sang Soon

2008-01-01

Modeling and simulation for heat and mass transport in micro channel are being used extensively in researches and industrial applications to gain better understanding of the fundamental processes and to optimize fuel cell designs before building a prototype for engineering application. In this study, we used a single-phase, fully three dimensional simulation model for PEMFC that can deal with both anode and cathode flow field for examining the micro flow channel with electrochemical reaction. The results show that hydrogen and oxygen were solely supplied to the membrane by diffusion mechanism rather than convection transport, and the higher pressure drop at cathode side is thought to be caused by higher flow rate of oxygen at cathode. And it is found that the amount of water in cathode channel was determined by water formation due to electrochemical reaction plus electro-osmotic mass flux directing toward the cathode side. And it is very important to model the back diffusion and electro-osmotic mass flux accurately since the two flux was closely correlated each other and greatly influenced for determination of ionic conductivity of the membrane which directly affects the performance of fuel cell. PMID:27879774

Simulation of the effects of sub-breakdown electric fields on the chemical kinetics in nonpremixed counterflow methane/air flames

NASA Astrophysics Data System (ADS)

Belhi, Memdouh; Im, Hong; Computational Reacting Flows Laboratory, Clean Combustion Research Center Team

2017-11-01

The effects of an electric field on the combustion kinetics in nonpremixed counterflow methane/air flames were investigated via one-dimensional numerical simulations. A classical fluid model coupling Poison's equation with transport equations for combustion species and electric field-induced particles was used. A methane-air reaction mechanism accounting for the natural ionization in flames was combined with a set of reactions that describe the formation of active particles induced by the electric field. Kinetic parameters for electron-impact reactions and transport coefficients of electrons were modeled as functions of reduced electric field via solutions to the Boltzmann kinetic equation using the BOLSIG code. Mobility of ions was computed based on the (n,6,4) and coulomb interaction potentials, while the diffusion coefficient was approximated from the mobility using Einstein relation. Contributions of electron dissociation, excitation and ionization processes were characterized quantitatively. An analysis to identify the plasma regime where the electric field can alter the combustion kinetic was proposed.

Modeling variably saturated multispecies reactive groundwater solute transport with MODFLOW-UZF and RT3D

USGS Publications Warehouse

Bailey, Ryan T.; Morway, Eric D.; Niswonger, Richard G.; Gates, Timothy K.

2013-01-01

A numerical model was developed that is capable of simulating multispecies reactive solute transport in variably saturated porous media. This model consists of a modified version of the reactive transport model RT3D (Reactive Transport in 3 Dimensions) that is linked to the Unsaturated-Zone Flow (UZF1) package and MODFLOW. Referred to as UZF-RT3D, the model is tested against published analytical benchmarks as well as other published contaminant transport models, including HYDRUS-1D, VS2DT, and SUTRA, and the coupled flow and transport modeling system of CATHY and TRAN3D. Comparisons in one-dimensional, two-dimensional, and three-dimensional variably saturated systems are explored. While several test cases are included to verify the correct implementation of variably saturated transport in UZF-RT3D, other cases are included to demonstrate the usefulness of the code in terms of model run-time and handling the reaction kinetics of multiple interacting species in variably saturated subsurface systems. As UZF1 relies on a kinematic-wave approximation for unsaturated flow that neglects the diffusive terms in Richards equation, UZF-RT3D can be used for large-scale aquifer systems for which the UZF1 formulation is reasonable, that is, capillary-pressure gradients can be neglected and soil parameters can be treated as homogeneous. Decreased model run-time and the ability to include site-specific chemical species and chemical reactions make UZF-RT3D an attractive model for efficient simulation of multispecies reactive transport in variably saturated large-scale subsurface systems.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Investigating axial diffusion in cylindrical pores using confocal single-particle fluorescence correlation spectroscopy.

PubMed

Chen, Fang; Neupane, Bhanu; Li, Peiyuan; Su, Wei; Wang, Gufeng

2016-08-01

We explored the feasibility of using confocal fluorescence correlation spectroscopy to study small nanoparticle diffusion in hundred-nanometer-sized cylindrical pores. By modeling single particle diffusion in tube-like confined three-dimensional space aligned parallel to the confocal optical axis, we showed that two diffusion dynamics can be observed in both original intensity traces and the autocorrelation functions (ACFs): the confined two-dimensional lateral diffusion and the unconfined one-dimensional (1D) axial diffusion. The separation of the axial and confined lateral diffusion dynamics provides an opportunity to study diffusions in different dimensions separately. We further experimentally studied 45 nm carboxylated polystyrene particles diffusing in 300 nm alumina pores. The experimental data showed consistency with the simulation. To extract the accurate axial diffusion coefficient, we found that a 1D diffusion model with a Lorentzian axial collection profile needs to be used to analyze the experimental ACFs. The diffusion of the 45 nm nanoparticles in polyethyleneglycol-passivated 300 nm pores slowed down by a factor of ∼2, which can be satisfactorily explained by hydrodynamic frictions. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Oxidative Attack of Carbon/Carbon Substrates through Coating Pinholes

NASA Technical Reports Server (NTRS)

Jacobson, Nathan S.; Leonhardt, Todd; Curry, Donald; Rapp, Robert A.

1998-01-01

A critical issue with oxidation protected carbon/carbon composites used for spacecraft thermal protection is the formation of coating pinholes. In laboratory experiments, artificial pinholes were drilled through SiC-coatings on a carbon/carbon material and the material was oxidized at 600, 1000, and 1400 C at reduced pressures of air. The attack of the carbon/carbon was quantified by both weight loss and a novel cross-sectioning technique. A two-zone, one dimensional diffusion control model was adapted to analyze this problem. Agreement of the model with experiment was reasonable at 1000 and 1400 C; however results at lower temperatures show clear deviations from the theory suggesting that surface reaction control plays a role.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers.

PubMed

Rongy, L; Goyal, N; Meiburg, E; De Wit, A

2007-09-21

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].

The structure of mass-loading shocks. [interaction of solar wind with cometary coma or local interstellar medium using two-fluid model

NASA Technical Reports Server (NTRS)

Zank, G. P.; Khabibrakhmanov, I. KH.; Story, T.

1993-01-01

A new two-fluid model which describes mass loading in the solar wind (e.g., the interaction of the solar wind with a cometary coma or the local interstellar medium) is presented. The self-consistent back-reaction of the mass-loaded ions is included through their effective scattering in low-frequency MHD turbulence and the invocation of a diffusive approximation. Such an approximation has the advantage of introducing self-consistent dissipation coefficients into the governing equations, thereby facilitating the investigation of the internal structure of shocks in mass-loading environments. To illustrate the utility of the new model, we consider the structure of cometary shocks in the hypersonic one-dimensional limit, finding that the incoming solar wind is slowed by both mass loading and the development of a large cometary ion pressure gradient. The shock is broadened and smoothed by the cometary ions with a thickness of the order of the cometary ion diffusion scale.

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

PubMed

Manz, Niklas; Steinbock, Oliver

2006-09-01

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

A 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.

Multiplexed immunosensing and kinetics monitoring in nanofluidic devices with highly enhanced target capture efficiency

PubMed Central

Lin, Yii-Lih; Huang, Yen-Jun; Teerapanich, Pattamon; Leïchlé, Thierry

2016-01-01

Nanofluidic devices promise high reaction efficiency and fast kinetic responses due to the spatial constriction of transported biomolecules with confined molecular diffusion. However, parallel detection of multiple biomolecules, particularly proteins, in highly confined space remains challenging. This study integrates extended nanofluidics with embedded protein microarray to achieve multiplexed real-time biosensing and kinetics monitoring. Implementation of embedded standard-sized antibody microarray is attained by epoxy-silane surface modification and a room-temperature low-aspect-ratio bonding technique. An effective sample transport is achieved by electrokinetic pumping via electroosmotic flow. Through the nanoslit-based spatial confinement, the antigen-antibody binding reaction is enhanced with ∼100% efficiency and may be directly observed with fluorescence microscopy without the requirement of intermediate washing steps. The image-based data provide numerous spatially distributed reaction kinetic curves and are collectively modeled using a simple one-dimensional convection-reaction model. This study represents an integrated nanofluidic solution for real-time multiplexed immunosensing and kinetics monitoring, starting from device fabrication, protein immobilization, device bonding, sample transport, to data analysis at Péclet number less than 1. PMID:27375819

Mixing Regimes in a Spatially Confined, Two-Dimensional, Supersonic Shear Layer

DTIC Science & Technology

1992-07-31

MODEL ................................... 3 THE MODEL PROBLEMS .............................................. 6 THE ONE-DIMENSIONAL PROBLEM...the effects of the numerical diffusion on the spectrum. Guirguis et al.ś and Farouk et al."’ have studied spatially evolving mixing layers for equal...approximations. Physical and Numerical Model General Formulation We solve the time-dependent, two-dimensional, compressible, Navier-Stokes equations for a

A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles

NASA Astrophysics Data System (ADS)

Hauser, Andreas W.; Schnedlitz, Martin; Ernst, Wolfgang E.

2017-06-01

A kinetic Monte Carlo approach on a coarse-grained lattice is developed for the simulation of surface diffusion processes of Ni, Pd and Au structures with diameters in the range of a few nanometers. Intensity information obtained via standard two-dimensional transmission electron microscopy imaging techniques is used to create three-dimensional structure models as input for a cellular automaton. A series of update rules based on reaction kinetics is defined to allow for a stepwise evolution in time with the aim to simulate surface diffusion phenomena such as Rayleigh breakup and surface wetting. The material flow, in our case represented by the hopping of discrete portions of metal on a given grid, is driven by the attempt to minimize the surface energy, which can be achieved by maximizing the number of filled neighbor cells.

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.

Three-dimensional modelling of trace species in the Arctic lower stratosphere

NASA Technical Reports Server (NTRS)

Chipperfield, Martyn; Cariolle, Daniel; Simon, Pascal; Ramaroson, Richard

1994-01-01

A three-dimensional radiative-dynamical-chemical model has been developed and used to study some aspects of modeling the polar lower stratosphere. The model includes a comprehensive gas-phase chemistry scheme as well as a treatment of heterogeneous reactions occurring on the surface of polar stratospheric clouds. Tracer transport is treated by an accurate, nondispersive scheme with little diffusion suited to the representation of strong gradients. Results from a model simulation of early February 1990 are presented and used to illustrate the importance of the model transport scheme. The model simulation is also used to examine the potential for Arctic ozone destruction and the relative contributions of the chemical cycles responsible.

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

NASA Astrophysics Data System (ADS)

L'Heureux, Ivan

2018-02-01

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

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

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

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

Measuring and Overcoming Limits of the Saffman-Delbrück Model for Soap Film Viscosities

PubMed Central

Vivek, Skanda; Weeks, Eric R.

2015-01-01

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness. PMID:25822262

Measuring and overcoming limits of the Saffman-Delbrück model for soap film viscosities.

PubMed

Vivek, Skanda; Weeks, Eric R

2015-01-01

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

A model-based understanding of solid-oxide electrolysis cells (SOECs) for syngas production by H2O/CO2 co-electrolysis

NASA Astrophysics Data System (ADS)

Menon, Vikram; Fu, Qingxi; Janardhanan, Vinod M.; Deutschmann, Olaf

2015-01-01

High temperature co-electrolysis of H2O and CO2 offers a promising route for syngas (H2, CO) production via efficient use of heat and electricity. The performance of a SOEC during co-electrolysis is investigated by focusing on the interactions between transport processes and electrochemical parameters. Electrochemistry at the three-phase boundary is modeled by a modified Butler-Volmer approach that considers H2O electrolysis and CO2 electrolysis, individually, as electrochemically active charge transfer pathways. The model is independent of the geometrical structure. A 42-step elementary heterogeneous reaction mechanism for the thermo-catalytic chemistry in the fuel electrode, the dusty gas model (DGM) to account for multi-component diffusion through porous media, and a plug flow model for flow through the channels are used in the model. Two sets of experimental data are reproduced by the simulations, in order to deduce parameters of the electrochemical model. The influence of micro-structural properties, inlet cathode gas velocity, and temperature are discussed. Reaction flow analysis is performed, at OCV, to study methane production characteristics and kinetics during co-electrolysis. Simulations are carried out for configurations ranging from simple one-dimensional electrochemical button cells to quasi-two-dimensional co-flow planar cells, to demonstrate the effectiveness of the computational tool for performance and design optimization.

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.

Numerical investigations of passive scalar transport in Taylor-Couette flows: Counter-rotation effect

NASA Astrophysics Data System (ADS)

Ouazib, Nabila; Salhi, Yacine; Si-Ahmed, El-Khider; Legrand, Jack; Degrez, G.

2017-07-01

Numerical methods for solving convection-diffusion-reaction (CDR) scalar transport equation in three-dimensional flow are used in the present investigation. The flow is confined between two concentric cylinders both the inner cylinder and the outer one are allowed to rotate. Direct numerical simulations (DNS) have been achieved to study the effects of the gravitational and the centrifugal potentials on the stability of incompressible Taylor-Couette flow. The Navier-Stokes equations and the uncoupled convection-diffusion-reaction equation are solved using a spectral development in one direction combined together with a finite element discretization in the two remaining directions. The complexity of the patterns is highlighted. Since, it increases as the rotation rates of the cylinders increase. In addition, the effect of the counter-rotation of the cylinders on the mass transfer is pointed out.

Water-Rock Interaction Simulations of Iron Oxide Mobilization and Precipitation: Implications of Cross-diffusion Reactions for Terrestrial and Mars 'Blueberry' Hematite Concretions

NASA Astrophysics Data System (ADS)

Park, A. J.; Chan, M. A.; Parry, W. T.

2005-12-01

Modeling of how terrestrial concretions form can provide valuable insights into understanding water-rock interactions that led to the formation of hematite concretions at Meridiani Planum, Mars. Numerical simulations of iron oxide concretions in the Jurassic Navajo Sandstone of southern Utah provide physical and chemical input parameters for emulating conditions that may have prevailed on Mars. In the terrestrial example, iron oxide coatings on eolian sand grains are reduced and mobilized by methane or petroleum. Precipitation of goethite or hematite occurs as Fe interacts with oxygen. Conditions that produced Navajo Sandstone concretions can range from a regional scale that is strongly affected by advection of large pore volumes of water, to small sub-meter scale features that are dominantly controlled by diffusive processes. Hematite concretions are results of a small-scale cross-diffusional process, where Fe and oxygen are supplied from two opposite sides from the 'middle' zone of mixing where concretions precipitate. This is an ideal natural system where Liesegang banding and other self-organized patterns can evolve. A complicating variable here is the sedimentologic (both mineralogic and textural) heterogeneity that, in reality, may be the key factor controlling the nucleation and precipitation habits (including possible competitive growth) of hematite concretions. Sym.8 water-rock interaction simulator program was used for the Navajo Sandstone concretions. Sym.8 is a water-rock simulator that accounts for advective and diffusive mass-transfer, and equilibrium and kinetic reactions. The program uses a dynamic composite media texture model to address changing sediment composition and texture to be consistent with the reaction progress. Initial one-dimensional simulation results indicate precipitation heterogeneity in the range of sub-meters, e.g., possible banding and distribution of iron oxide nodules may be centimeters apart for published diffusivities and water chemistries of the solutes involved. This modeling effort underscores the importance of coupled reactions and mass-transfer in formation of iron oxide concretions in both terrestrial and Mars sediments. Methane is interpreted to be the reactive agent that mobilizes iron in Navajo Sandstone. On Mars volatile volcanic gases may be the reactive agents that mobilize iron from volcanic sediments. In both cases, subsequent diffusive and advective mass-transfer coupled to nonlinear chemical reactions produces localized precipitates.

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

NASA Astrophysics Data System (ADS)

Saliba, Daniel; Al-Ghoul, Mazen

2016-11-01

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

A one-dimensional diffusion analogy model for estimation of tide heights in selected tidal marshes in Connecticut

USGS Publications Warehouse

Bjerklie, David M.; O’Brien, Kevin; Rozsa, Ron

2013-01-01

A one-dimensional diffusion analogy model for estimating tide heights in coastal marshes was developed and calibrated by using data from previous tidal-marsh studies. The method is simpler to use than other one- and two-dimensional hydrodynamic models because it does not require marsh depth and tidal prism information; however, the one-dimensional diffusion analogy model cannot be used to estimate tide heights, flow velocities, and tide arrival times for tide conditions other than the highest tide for which it is calibrated. Limited validation of the method indicates that it has an accuracy within 0.3 feet. The method can be applied with limited calibration information that is based entirely on remote sensing or geographic information system data layers. The method can be used to estimate high-tide heights in tidal wetlands drained by tide gates where tide levels cannot be observed directly by opening the gates without risk of flooding properties and structures. A geographic information system application of the method is demonstrated for Sybil Creek marsh in Branford, Connecticut. The tidal flux into this marsh is controlled by two tide gates that prevent full tidal inundation of the marsh. The method application shows reasonable tide heights for the gates-closed condition (the normal condition) and the one-gate-open condition on the basis of comparison with observed heights. The condition with all tide gates open (two gates) was simulated with the model; results indicate where several structures would be flooded if the gates were removed as part of restoration efforts or if the tide gates were to fail.

Prediction of oxygen distribution in aortic valve leaflet considering diffusion and convection.

PubMed

Wang, Ling; Korossis, Sotirios; Fisher, John; Ingham, Eileen; Jin, Zhongmin

2011-07-01

Oxygen supply and transport is an important consideration in the development of tissue engineered constructs. Previous studies from our group have focused on the effect of tissue thickness on the oxygen diffusion within a three-dimensional aortic valve leaflet model, and highlighted the necessity for additional transport mechanisms such as oxygen convection. The aims of this study were to investigate the effect of interstitial fluid flow within the aortic valve leaflet, induced by the cyclic loading of the leaflet, on oxygen transport. Indentation testing and finite element modelings were employed to derive the biphasic properties of the leaflet tissue. The biphasic properties were subsequently used in the computational modeling of oxygen convection in the leaflet, which was based on the effective interstitial fluid velocity and the tissue deformation. Subsequently, the oxygen profile was predicted within the valve leaflet model by solving the diffusion and convection equation simultaneously utilizing the finite difference method. The compression modulus (E) and hydraulic permeability were determined by adapting a finite element model to the experimental indentation test on valvular tissue, E = 0.05MPa, and k =2.0 mm4/Ns. Finite element model of oxygen convection in valvular tissue incorporating the predicted biphasic properties was developed and the interstitial fluid flow rate was calculated falling in range of 0.025-0.25 mm/s depending on the tissue depth. Oxygen distribution within valvular tissue was predicted using one-dimensional oxygen diffusion model taking into consider the interstitial fluid effect. It was found that convection did enhance the oxygen transport in valvular tissue by up to 68% increase in the minimum oxygen tension within the tissue, depending on the strain level of the tissue as reaction of the magnitude and frequencies of the cardiac loading. The effective interstitial fluid velocity was found to play an important role in enhancing the oxygen transport within the valve leaflet. Such an understanding is important in the development of valvular tissue engineered constructs.

Time-dependent computational studies of flames in microgravity

NASA Technical Reports Server (NTRS)

Oran, Elaine S.; Kailasanath, K.

1989-01-01

The research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of the NASA Microgravity Science and Applications Program is described. The primary focus was on investigating fundamental questions concerning the propagation and extinction of premixed flames in Earth gravity and in microgravity environments. The approach was to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. A combination of one-dimensional and two-dimensional simulations was used to investigate the effects of curvature and dilution on ignition and propagation of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the mechanism leading to cellular instability, and to study the effects of gravity on the transition to cellular structure. A flame in a microgravity environment can be extinguished without external losses, and the mechanism leading to cellular structure is not preferential diffusion but a thermo-diffusive instability. The simulations have also lead to a better understanding of the interactions between buoyancy forces and the processes leading to thermo-diffusive instability.

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.

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.

Incorporating convection into one-dimensional solute redistribution during crystal growth from the melt I. The steady-state solution

NASA Astrophysics Data System (ADS)

Yen, C. T.; Tiller, W. A.

1992-03-01

A one-dimensional mathematical analysis is made of the redistribution of solute which occurs during crystal growth from a convected melt. In this analysis, the important contribution from lateral melt convection to one-dimensional solute redistribution analysis is taken into consideration via an annihilation/creation term in the one-dimensional solute transport equation. Calculations of solute redistribution under steady-state conditions have been carried out analytically. It is found that this new solute redistribution model overcomes several weaknesses that occur when applying the Burton, Prim and Slichter solute segregation equation (1953) in real melt growth situations. It is also found that, with this correction, the diffusion coefficients for solute's in liquid silicon are now found to be in the same range as other liquid metal diffusion coefficients.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

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.

Diffusion in random networks

DOE PAGES

Zhang, Duan Z.; Padrino, Juan C.

2017-06-01

The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem,more » we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt $-$1/4 rather than xt $-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.« less

Catalytic ignition model in a monolithic reactor with in-depth reaction

NASA Technical Reports Server (NTRS)

Tien, Ta-Ching; Tien, James S.

1990-01-01

Two transient models have been developed to study the catalytic ignition in a monolithic catalytic reactor. The special feature in these models is the inclusion of thermal and species structures in the porous catalytic layer. There are many time scales involved in the catalytic ignition problem, and these two models are developed with different time scales. In the full transient model, the equations are non-dimensionalized by the shortest time scale (mass diffusion across the catalytic layer). It is therefore accurate but is computationally costly. In the energy-integral model, only the slowest process (solid heat-up) is taken as nonsteady. It is approximate but computationally efficient. In the computations performed, the catalyst is platinum and the reactants are rich mixtures of hydrogen and oxygen. One-step global chemical reaction rates are used for both gas-phase homogeneous reaction and catalytic heterogeneous reaction. The computed results reveal the transient ignition processes in detail, including the structure variation with time in the reactive catalytic layer. An ignition map using reactor length and catalyst loading is constructed. The comparison of computed results between the two transient models verifies the applicability of the energy-integral model when the time is greater than the second largest time scale of the system. It also suggests that a proper combined use of the two models can catch all the transient phenomena while minimizing the computational cost.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2017-11-01

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

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.

An algorithm for variational data assimilation of contact concentration measurements for atmospheric chemistry models

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir

2014-05-01

Contact concentration measurement data assimilation problem is considered for convection-diffusion-reaction models originating from the atmospheric chemistry study. High dimensionality of models imposes strict requirements on the computational efficiency of the algorithms. Data assimilation is carried out within the variation approach on a single time step of the approximated model. A control function is introduced into the source term of the model to provide flexibility for data assimilation. This function is evaluated as the minimum of the target functional that connects its norm to a misfit between measured and model-simulated data. In the case mathematical model acts as a natural Tikhonov regularizer for the ill-posed measurement data inversion problem. This provides flow-dependent and physically-plausible structure of the resulting analysis and reduces a need to calculate model error covariance matrices that are sought within conventional approach to data assimilation. The advantage comes at the cost of the adjoint problem solution. This issue is solved within the frameworks of splitting-based realization of the basic convection-diffusion-reaction model. The model is split with respect to physical processes and spatial variables. A contact measurement data is assimilated on each one-dimensional convection-diffusion splitting stage. In this case a computationally-efficient direct scheme for both direct and adjoint problem solution can be constructed based on the matrix sweep method. Data assimilation (or regularization) parameter that regulates ratio between model and data in the resulting analysis is obtained with Morozov discrepancy principle. For the proper performance the algorithm takes measurement noise estimation. In the case of Gaussian errors the probability that the used Chi-squared-based estimate is the upper one acts as the assimilation parameter. A solution obtained can be used as the initial guess for data assimilation algorithms that assimilate outside the splitting stages and involve iterations. Splitting method stage that is responsible for chemical transformation processes is realized with the explicit discrete-analytical scheme with respect to time. The scheme is based on analytical extraction of the exponential terms from the solution. This provides unconditional positive sign for the evaluated concentrations. Splitting-based structure of the algorithm provides means for efficient parallel realization. The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004.

A parallel reaction-transport model applied to cement hydration and microstructure development

NASA Astrophysics Data System (ADS)

Bullard, Jeffrey W.; Enjolras, Edith; George, William L.; Satterfield, Steven G.; Terrill, Judith E.

2010-03-01

A recently described stochastic reaction-transport model on three-dimensional lattices is parallelized and is used to simulate the time-dependent structural and chemical evolution in multicomponent reactive systems. The model, called HydratiCA, uses probabilistic rules to simulate the kinetics of diffusion, homogeneous reactions and heterogeneous phenomena such as solid nucleation, growth and dissolution in complex three-dimensional systems. The algorithms require information only from each lattice site and its immediate neighbors, and this localization enables the parallelized model to exhibit near-linear scaling up to several hundred processors. Although applicable to a wide range of material systems, including sedimentary rock beds, reacting colloids and biochemical systems, validation is performed here on two minerals that are commonly found in Portland cement paste, calcium hydroxide and ettringite, by comparing their simulated dissolution or precipitation rates far from equilibrium to standard rate equations, and also by comparing simulated equilibrium states to thermodynamic calculations, as a function of temperature and pH. Finally, we demonstrate how HydratiCA can be used to investigate microstructure characteristics, such as spatial correlations between different condensed phases, in more complex microstructures.

Computation and visualization of spreading depression based on reaction-diffusion equation with recovery

NASA Astrophysics Data System (ADS)

Ding, Hongxia; Chen, Shangbin; Zeng, Shuai; Zeng, Shaoqun; Liu, Qian; Luo, Qingming

2008-12-01

Spreading depression (SD) shows as propagating suppression of electrical activity, which relates with migraine and focal cerebral ischaemia. The putative mechanism of SD is the reaction-diffusion hypothesis involving potassium ions. In part inspired by optical imaging of two SD waves collision, we aimed to show the merged and large wavefront but not annihilation during collision by experimental and computational study. This paper modified Reggia et al established bistable equation with recovery to compute and visualize SD. Firstly, the media tissue of SD was assumed as one-dimensional continuum. The Crank-Nicholson method was used to solve the modified equations with recovery term. Then, the computation results were extended to two-dimensional space by symmetry. One individual SD was visualized as a concentric wave initiating from the stimulation point. The mergence but not annihilation of two colliding waves of SD was demonstrated. In addition, the dynamics of SD depending on the parameters was studied and presented. The results allied SD with the emerging concepts of volume transmission. This work not only supplied a paradigm to compute and visualize SD but also became a tool to explore the mechanisms of SD.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Butyrophenone on O-TiO2(110): one-dimensional motion in a weakly confined potential well.

PubMed

Jensen, Stephen C; Shank, Alex; Madix, Robert J; Friend, Cynthia M

2012-04-24

We demonstrate the one-dimensional confinement of weakly bound butyrophenone molecules between strongly bound complexes formed via reaction with oxygen on TiO(2)(110). Butyrophenone weakly bound to Ti rows through the carbonyl oxygen diffuses freely in one dimension along the rows even at 55 K, persisting for many minutes before hopping out of the 1-D well. Quantitative analysis yields an estimate of the migration barrier of 0.11 eV and a frequency factor of 6.5 × 10(9) Hz. These studies demonstrate that weakly bound organic molecules can be confined on a surface by creating molecular barriers, potentially altering their assembly.

Experimental and Numerical Study of Ammonium Perchlorate Counterflow Diffusion Flames

NASA Technical Reports Server (NTRS)

Smooke, M. D.; Yetter, R. A.; Parr, T. P.; Hanson-Parr, D. M.; Tanoff, M. A.

1999-01-01

Many solid rocket propellants are based on a composite mixture of ammonium perchlorate (AP) oxidizer and polymeric binder fuels. In these propellants, complex three-dimensional diffusion flame structures between the AP and binder decomposition products, dependent upon the length scales of the heterogeneous mixture, drive the combustion via heat transfer back to the surface. Changing the AP crystal size changes the burn rate of such propellants. Large AP crystals are governed by the cooler AP self-deflagration flame and burn slowly, while small AP crystals are governed more by the hot diffusion flame with the binder and burn faster. This allows control of composite propellant ballistic properties via particle size variation. Previous measurements on these diffusion flames in the planar two-dimensional sandwich configuration yielded insight into controlling flame structure, but there are several drawbacks that make comparison with modeling difficult. First, the flames are two-dimensional and this makes modeling much more complex computationally than with one-dimensional problems, such as RDX self- and laser-supported deflagration. In addition, little is known about the nature, concentration, and evolution rates of the gaseous chemical species produced by the various binders as they decompose. This makes comparison with models quite difficult. Alternatively, counterflow flames provide an excellent geometric configuration within which AP/binder diffusion flames can be studied both experimentally and computationally.

Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

PubMed

Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

2012-04-01

This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

Modeling enzymatic hydrolysis of lignocellulosic substrates using confocal fluorescence microscopy I: filter paper cellulose.

PubMed

Luterbacher, Jeremy S; Moran-Mirabal, Jose M; Burkholder, Eric W; Walker, Larry P

2015-01-01

Enzymatic hydrolysis is one of the critical steps in depolymerizing lignocellulosic biomass into fermentable sugars for further upgrading into fuels and/or chemicals. However, many studies still rely on empirical trends to optimize enzymatic reactions. An improved understanding of enzymatic hydrolysis could allow research efforts to follow a rational design guided by an appropriate theoretical framework. In this study, we present a method to image cellulosic substrates with complex three-dimensional structure, such as filter paper, undergoing hydrolysis under conditions relevant to industrial saccharification processes (i.e., temperature of 50°C, using commercial cellulolytic cocktails). Fluorescence intensities resulting from confocal images were used to estimate parameters for a diffusion and reaction model. Furthermore, the observation of a relatively constant bound enzyme fluorescence signal throughout hydrolysis supported our modeling assumption regarding the structure of biomass during hydrolysis. The observed behavior suggests that pore evolution can be modeled as widening of infinitely long slits. The resulting model accurately predicts the concentrations of soluble carbohydrates obtained from independent saccharification experiments conducted in bulk, demonstrating its relevance to biomass conversion work. © 2014 Wiley Periodicals, Inc.

Numerical Simulation of Hydrogen Air Supersonic Coaxial Jet

NASA Astrophysics Data System (ADS)

Dharavath, Malsur; Manna, Pulinbehari; Chakraborty, Debasis

2017-10-01

In the present study, the turbulent structure of coaxial supersonic H2-air jet is explored numerically by solving three dimensional RANS equations along with two equation k-ɛ turbulence model. Grid independence of the solution is demonstrated by estimating the error distribution using Grid Convergence Index. Distributions of flow parameters in different planes are analyzed to explain the mixing and combustion characteristics of high speed coaxial jets. The flow field is seen mostly diffusive in nature and hydrogen diffusion is confined to core region of the jet. Both single step laminar finite rate chemistry and turbulent reacting calculation employing EDM combustion model are performed to find the effect of turbulence-chemistry interaction in the flow field. Laminar reaction predicts higher H2 mol fraction compared to turbulent reaction because of lower reaction rate caused by turbulence chemistry interaction. Profiles of major species and temperature match well with experimental data at different axial locations; although, the computed profiles show a narrower shape in the far field region. These results demonstrate that standard two equation class turbulence model with single step kinetics based turbulence chemistry interaction can describe H2-air reaction adequately in high speed flows.

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

PubMed Central

2014-01-01

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

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

PubMed

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

2014-04-11

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

APOLLO: a general code for transport, slowing-down and thermalization calculations in heterogeneous media

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

Kavenoky, A.

1973-01-01

From national topical meeting on mathematical models and computational techniques for analysis of nuclear systems; Ann Arbor, Michigan, USA (8 Apr 1973). In mathematical models and computational techniques for analysis of nuclear systems. APOLLO calculates the space-and-energy-dependent flux for a one dimensional medium, in the multigroup approximation of the transport equation. For a one dimensional medium, refined collision probabilities have been developed for the resolution of the integral form of the transport equation; these collision probabilities increase accuracy and save computing time. The interaction between a few cells can also be treated by the multicell option of APOLLO. The diffusionmore » coefficient and the material buckling can be computed in the various B and P approximations with a linearly anisotropic scattering law, even in the thermal range of the spectrum. Eventually this coefficient is corrected for streaming by use of Benoist's theory. The self-shielding of the heavy isotopes is treated by a new and accurate technique which preserves the reaction rates of the fundamental fine structure flux. APOLLO can perform a depletion calculation for one cell, a group of cells or a complete reactor. The results of an APOLLO calculation are the space-and-energy-dependent flux, the material buckling or any reaction rate; these results can also be macroscopic cross sections used as input data for a 2D or 3D depletion and diffusion code in reactor geometry. 10 references. (auth)« less

Zero dimensional model of atmospheric SMD discharge and afterglow in humid air

NASA Astrophysics Data System (ADS)

Smith, Ryan; Kemaneci, Efe; Offerhaus, Bjoern; Stapelmann, Katharina; Peter Brinkmann, Ralph

2016-09-01

A novel mesh-like Surface Micro Discharge (SMD) device designed for surface wound treatment is simulated by multiple time-scaled zero-dimensional models. The chemical dynamics of the discharge are resolved in time at atmospheric pressure in humid conditions. Simulated are the particle densities of electrons, 26 ionic species, and 26 reactive neutral species including: O3, NO, and HNO3. The total of 53 described species are constrained by 624 reactions within the simulated plasma discharge volume. The neutral species are allowed to diffuse into a diffusive gas regime which is of primary interest. Two interdependent zero-dimensional models separated by nine orders of magnitude in temporal resolution are used to accomplish this; thereby reducing the computational load. Through variation of control parameters such as: ignition frequency, deposited power density, duty cycle, humidity level, and N2 content, the ideal operation conditions for the SMD device can be predicted. The described model has been verified by matching simulation parameters and comparing results to that of previous works. Current operating conditions of the experimental mesh-like SMD were matched and results are compared to the simulations. Work supported by SFB TR 87.

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

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

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

2014-10-28

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

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

PubMed Central

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

2007-01-01

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

A new methodology to determine kinetic parameters for one- and two-step chemical models

NASA Technical Reports Server (NTRS)

Mantel, T.; Egolfopoulos, F. N.; Bowman, C. T.

1996-01-01

In this paper, a new methodology to determine kinetic parameters for simple chemical models and simple transport properties classically used in DNS of premixed combustion is presented. First, a one-dimensional code is utilized to performed steady unstrained laminar methane-air flame in order to verify intrinsic features of laminar flames such as burning velocity and temperature and concentration profiles. Second, the flame response to steady and unsteady strain in the opposed jet configuration is numerically investigated. It appears that for a well determined set of parameters, one- and two-step mechanisms reproduce the extinction limit of a laminar flame submitted to a steady strain. Computations with the GRI-mech mechanism (177 reactions, 39 species) and multicomponent transport properties are used to validate these simplified models. A sensitivity analysis of the preferential diffusion of heat and reactants when the Lewis number is close to unity indicates that the response of the flame to an oscillating strain is very sensitive to this number. As an application of this methodology, the interaction between a two-dimensional vortex pair and a premixed laminar flame is performed by Direct Numerical Simulation (DNS) using the one- and two-step mechanisms. Comparison with the experimental results of Samaniego et al. (1994) shows a significant improvement in the description of the interaction when the two-step model is used.

Moments of action provide insight into critical times for advection-diffusion-reaction processes.

PubMed

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

2012-09-01

Berezhkovskii and co-workers introduced the concept of local accumulation time as a finite measure of the time required for the transient solution of a reaction-diffusion equation to effectively reach steady state [Biophys J. 99, L59 (2010); Phys. Rev. E 83, 051906 (2011)]. Berezhkovskii's approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb [IMA J. Appl. Math. 47, 193 (1991)]. Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time, the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one-dimensional linear advection-diffusion-reaction partial differential equation (PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random-walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.

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

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

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

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

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

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.

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.

A one-dimensional Fickian model to predict the Ga depth profiles in three-stage Cu(In,Ga)Se{sub 2}

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

Rodriguez-Alvarez, H., E-mail: humberto.rodriguez@helmholtz-berlin.de; Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin; Mainz, R.

2014-05-28

We present a one-dimensional Fickian model that predicts the formation of a double Ga gradient during the fabrication of Cu(In,Ga)Se{sub 2} thin films by three-stage thermal co-evaporation. The model is based on chemical reaction equations, structural data, and effective Ga diffusivities. In the model, the Cu(In,Ga)Se{sub 2} surface is depleted from Ga during the deposition of Cu-Se in the second deposition stage, leading to an accumulation of Ga near the back contact. During the third deposition stage, where In-Ga-Se is deposited at the surface, the atomic fluxes within the growing layer are inverted. This results in the formation of amore » double Ga gradient within the Cu(In,Ga)Se{sub 2} layer and reproduces experimentally observed Ga distributions. The final shape of the Ga depth profile strongly depends on the temperatures, times and deposition rates used. The model is used to evaluate possible paths to flatten the marked Ga depth profile that is obtained when depositing at low substrate temperatures. We conclude that inserting Ga during the second deposition stage is an effective way to achieve this.« less

Using spatially detailed water-quality data and solute-transport modeling to improve support total maximum daily load development

USGS Publications Warehouse

Walton-Day, Katherine; Runkel, Robert L.; Kimball, Briant A.

2012-01-01

Spatially detailed mass-loading studies and solute-transport modeling using OTIS (One-dimensional Transport with Inflow and Storage) demonstrate how natural attenuation and loading from distinct and diffuse sources control stream water quality and affect load reductions predicted in total maximum daily loads (TMDLs). Mass-loading data collected during low-flow from Cement Creek (a low-pH, metal-rich stream because of natural and mining sources, and subject to TMDL requirements) were used to calibrate OTIS and showed spatially variable effects of natural attenuation (instream reactions) and loading from diffuse (groundwater) and distinct sources. OTIS simulations of the possible effects of TMDL-recommended remediation of mine sites showed less improvement to dissolved zinc load and concentration (14% decrease) than did the TMDL (53-63% decrease). The TMDL (1) assumed conservative transport, (2) accounted for loads removed by remediation by subtracting them from total load at the stream mouth, and (3) did not include diffuse-source loads. In OTIS, loads were reduced near their source; the resulting concentration was decreased by natural attenuation and increased by diffuse-source loads during downstream transport. Thus, by not including natural attenuation and loading from diffuse sources, the TMDL overestimated remediation effects at low flow. Use of the techniques presented herein could improve TMDLs by incorporating these processes during TMDL development.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Estimation of diffusion coefficients from voltammetric signals by support vector and gaussian process regression

PubMed Central

2014-01-01

Background Support vector regression (SVR) and Gaussian process regression (GPR) were used for the analysis of electroanalytical experimental data to estimate diffusion coefficients. Results For simulated cyclic voltammograms based on the EC, Eqr, and EqrC mechanisms these regression algorithms in combination with nonlinear kernel/covariance functions yielded diffusion coefficients with higher accuracy as compared to the standard approach of calculating diffusion coefficients relying on the Nicholson-Shain equation. The level of accuracy achieved by SVR and GPR is virtually independent of the rate constants governing the respective reaction steps. Further, the reduction of high-dimensional voltammetric signals by manual selection of typical voltammetric peak features decreased the performance of both regression algorithms compared to a reduction by downsampling or principal component analysis. After training on simulated data sets, diffusion coefficients were estimated by the regression algorithms for experimental data comprising voltammetric signals for three organometallic complexes. Conclusions Estimated diffusion coefficients closely matched the values determined by the parameter fitting method, but reduced the required computational time considerably for one of the reaction mechanisms. The automated processing of voltammograms according to the regression algorithms yields better results than the conventional analysis of peak-related data. PMID:24987463

An analysis of the effect of defect structures on catalytic surfaces by the boundary element technique

NASA Astrophysics Data System (ADS)

Peirce, Anthony P.; Rabitz, Herschel

1988-08-01

The boundary element (BE) technique is used to analyze the effect of defects on one-dimensional chemically active surfaces. The standard BE algorithm for diffusion is modified to include the effects of bulk desorption by making use of an asymptotic expansion technique to evaluate influences near boundaries and defect sites. An explicit time evolution scheme is proposed to treat the non-linear equations associated with defect sites. The proposed BE algorithm is shown to provide an efficient and convergent algorithm for modelling localized non-linear behavior. Since it exploits the actual Green's function of the linear diffusion-desorption process that takes place on the surface, the BE algorithm is extremely stable. The BE algorithm is applied to a number of interesting physical problems in which non-linear reactions occur at localized defects. The Lotka-Volterra system is considered in which the source, sink and predator-prey interaction terms are distributed at different defect sites in the domain and in which the defects are coupled by diffusion. This example provides a stringent test of the stability of the numerical algorithm. Marginal stability oscillations are analyzed for the Prigogine-Lefever reaction that occurs on a lattice of defects. Dissipative effects are observed for large perturbations to the marginal stability state, and rapid spatial reorganization of uniformly distributed initial perturbations is seen to take place. In another series of examples the effect of defect locations on the balance between desorptive processes on chemically active surfaces is considered. The effect of dynamic pulsing at various time-scales is considered for a one species reactive trapping model. Similar competitive behavior between neighboring defects previously observed for static adsorption levels is shown to persist for dynamic loading of the surface. The analysis of a more complex three species reaction process also provides evidence of competitive behavior between neighboring defect sites. The proposed BE algorithm is shown to provide a useful technique for analyzing the effect of defect sites on chemically active surfaces.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Fast pyrolysis kinetics of alkali lignin: Evaluation of apparent rate parameters and product time evolution.

PubMed

Ojha, Deepak Kumar; Viju, Daniel; Vinu, R

2017-10-01

In this study, the apparent kinetics of fast pyrolysis of alkali lignin was evaluated by obtaining isothermal mass loss data in the timescale of 2-30s at 400-700°C in an analytical pyrolyzer. The data were analyzed using different reaction models to determine the rate constants and apparent rate parameters. First order and one dimensional diffusion models resulted in good fits with experimental data with apparent activation energy of 23kJmol -1 . Kinetic compensation effect was established using a large number of kinetic parameters reported in the literature for pyrolysis of different lignins. The time evolution of the major functional groups in the pyrolysate was analyzed using in situ Fourier transform infrared spectroscopy. Maximum production of the volatiles occurred around 10-12s. A clear transformation of guaiacols to phenol, catechol and their derivatives, and aromatic hydrocarbons was observed with increasing temperature. The plausible reaction steps involved in various transformations are discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

One-Dimension Diffusion Preparation of Concentration-Gradient Fe₂O₃/SiO₂ Aerogel.

PubMed

Zhang, Ting; Wang, Haoran; Zhou, Bin; Ji, Xiujie; Wang, Hongqiang; Du, Ai

2018-06-21

Concentration-gradient Fe₂O₃/SiO₂ aerogels were prepared by placing an MTMS (methyltrimethoxysilane)-derived SiO₂ aerogel on an iron gauze with an HCl atmosphere via one-dimensional diffusion, ammonia-atmosphere fixing, supercritical fluid drying and thermal treatment. The energy dispersive spectra show that the Fe/Si molar ratios change gradually from 2.14% to 18.48% with a height of 40 mm. Pore-size distribution results show that the average pore size of the sample decreases from 15.8 nm to 3.1 nm after diffusion. This corresponds well with TEM results, indicating a pore-filling effect of the Fe compound. In order to precisely control the gradient, diffusion kinetics are further studied by analyzing the influence of time and position on the concentration of the wet gel. At last, it is found that the diffusion process could be fitted well with the one-dimensional model of Fick’s second law, demonstrating the feasibility of the precise design and control of the concentration gradient.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain.

PubMed

d'Errico, Michele; Sammarco, Paolo; Vairo, Giuseppe

2015-09-01

Pharmacokinetics induced by drug eluting stents (DES) in coronary walls is modeled by means of a one-dimensional multi-layered model, accounting for vessel curvature and non-homogeneous properties of the arterial tissues. The model includes diffusion mechanisms, advection effects related to plasma filtration through the walls, and bio-chemical drug reactions. A non-classical Sturm-Liouville problem with discontinuous coefficients is derived, whose closed-form analytical solution is obtained via an eigenfunction expansion. Soundness and consistency of the proposed approach are shown by numerical computations based on possible clinical treatments involving both hydrophilic and hydrophobic drugs. The influence of the main model parameters on drug delivery mechanisms is analyzed, highlighting the effects induced by vessel curvature and yielding comparative indications and useful insights into the concurring mechanisms governing the pharmacokinetics. Copyright © 2015. Published by Elsevier Inc.

Effect of finite-rate chemistry and unequal Schmidt numbers on turbulent non-premixed flames modeled with single-step chemistry

NASA Technical Reports Server (NTRS)

Chen, J. H.; Mahalingam, S.; Puri, I. K.; Vervisch, L.

1992-01-01

The interaction between a quasi-laminar flame and a turbulent flowfield is investigated through direct numerical simulations (DNS) of reacting flow in two- and three-dimensional domains. Effects due to finite-rate chemistry are studied using a single step global reaction A (fuel) + B (oxidizer) yields P (product), and by varying a global Damkoehler number, as a result of which the turbulence-chemistry interaction in the flame is found to generate a wide variety of conditions, ranging from near-equilibrium to near-extinction. Differential diffusion effects are studied by changing the Schmidt number of one reactive species to one-half. It is observed that laminar flamelet response is followed within the turbulent flowfield, except in regions where transient effects seem to dominate.

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

PubMed

Tholen, Danny; Zhu, Xin-Guang

2011-05-01

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

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

PubMed Central

Tholen, Danny; Zhu, Xin-Guang

2011-01-01

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

The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak

PubMed Central

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

2014-01-01

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

Monitoring equilibrium reaction dynamics of a nearly barrierless molecular rotor using ultrafast vibrational echoes

NASA Astrophysics Data System (ADS)

Nilsen, Ian A.; Osborne, Derek G.; White, Aaron M.; Anna, Jessica M.; Kubarych, Kevin J.

2014-10-01

Using rapidly acquired spectral diffusion, a recently developed variation of heterodyne detected infrared photon echo spectroscopy, we observe ˜3 ps solvent independent spectral diffusion of benzene chromium tricarbonyl (C6H6Cr(CO)3, BCT) in a series of nonpolar linear alkane solvents. The spectral dynamics is attributed to low-barrier internal torsional motion. This tripod complex has two stable minima corresponding to staggered and eclipsed conformations, which differ in energy by roughly half of kBT. The solvent independence is due to the relative size of the rotor compared with the solvent molecules, which create a solvent cage in which torsional motion occurs largely free from solvent damping. Since the one-dimensional transition state is computed to be only 0.03 kBT above the higher energy eclipsed conformation, this model system offers an unusual, nearly barrierless reaction, which nevertheless is characterized by torsional coordinate dependent vibrational frequencies. Hence, by studying the spectral diffusion of the tripod carbonyls, it is possible to gain insight into the fundamental dynamics of internal rotational motion, and we find some evidence for the importance of non-diffusive ballistic motion even in the room-temperature liquid environment. Using several different approaches to describe equilibrium kinetics, as well as the influence of reactive dynamics on spectroscopic observables, we provide evidence that the low-barrier torsional motion of BCT provides an excellent test case for detailed studies of the links between chemical exchange and linear and nonlinear vibrational spectroscopy.

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.

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.

A bio-inspired N-doped porous carbon electrocatalyst with hierarchical superstructure for efficient oxygen reduction reaction

NASA Astrophysics Data System (ADS)

Miao, Yue-E.; Yan, Jiajie; Ouyang, Yue; Lu, Hengyi; Lai, Feili; Wu, Yue; Liu, Tianxi

2018-06-01

The bio-inspired hierarchical "grape cluster" superstructure provides an effective integration of one-dimensional carbon nanofibers (CNF) with isolated carbonaceous nanoparticles into three-dimensional (3D) conductive frameworks for efficient electron and mass transfer. Herein, a 3D N-doped porous carbon electrocatalyst consisting of carbon nanofibers with grape-like N-doped hollow carbon particles (CNF@NC) has been prepared through a simple electrospinning strategy combined with in-situ growth and carbonization processes. Such a bio-inspired hierarchically organized conductive network largely facilitates both the mass diffusion and electron transfer during the oxygen reduction reactions (ORR). Therefore, the metal-free CNF@NC catalyst demonstrates superior catalytic activity with an absolute four-electron transfer mechanism, strong methanol tolerance and good long-term stability towards ORR in alkaline media.

BLT-EC (Breach, Leach and Transport-Equilibrium Chemistry) data input guide. A computer model for simulating release and coupled geochemical transport of contaminants from a subsurface disposal facility

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

MacKinnon, R.J.; Sullivan, T.M.; Kinsey, R.R.

1997-05-01

The BLT-EC computer code has been developed, implemented, and tested. BLT-EC is a two-dimensional finite element computer code capable of simulating the time-dependent release and reactive transport of aqueous phase species in a subsurface soil system. BLT-EC contains models to simulate the processes (container degradation, waste-form performance, transport, chemical reactions, and radioactive production and decay) most relevant to estimating the release and transport of contaminants from a subsurface disposal system. Water flow is provided through tabular input or auxiliary files. Container degradation considers localized failure due to pitting corrosion and general failure due to uniform surface degradation processes. Waste-form performancemore » considers release to be limited by one of four mechanisms: rinse with partitioning, diffusion, uniform surface degradation, and solubility. Transport considers the processes of advection, dispersion, diffusion, chemical reaction, radioactive production and decay, and sources (waste form releases). Chemical reactions accounted for include complexation, sorption, dissolution-precipitation, oxidation-reduction, and ion exchange. Radioactive production and decay in the waste form is simulated. To improve the usefulness of BLT-EC, a pre-processor, ECIN, which assists in the creation of chemistry input files, and a post-processor, BLTPLOT, which provides a visual display of the data have been developed. BLT-EC also includes an extensive database of thermodynamic data that is also accessible to ECIN. This document reviews the models implemented in BLT-EC and serves as a guide to creating input files and applying BLT-EC.« less

Feasibility of High Energy Lasers for Interdiction Activities

DTIC Science & Technology

2017-12-01

2.3.2 Power in the Bucket Another parameter we will use in this study is the power-in-the-bucket. The “bucket” is defined as the area on the target we...the heat diffusion equation for a one -dimensional case (where the x-direction is into the target) and assuming a semi-infinite slab of material. The... studied and modeled. One of the approaches to describe these interactions is by making a one -dimensional mathematical model assuming [8]: 1. A semi

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

Rottschäfer, Vivi; Doelman, Arjen

1998-07-01

The Ginzburg-Landau (GL) equation ‘generically’ describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains. In this paper we consider the transition from this generic situation to a degenerate (co-dimension 2) case in which the GL approach is no longer valid. Instead of studying a general underlying model problem, we consider a two-dimensional system of coupled reaction-diffusion equations in one spatial dimension. We show that near the degeneration the behaviour of small perturbations is governed by the extended Fisher-Kolmogorov (eFK) equation (at leading order). The relation between the GL-equation and the eFK-equation is quite subtle, but can be analysed in detail. The main goal of this paper is to study this relation, which we do asymptotically. The asymptotic analysis is compared to numerical simulations of the full reaction-diffusion system. As one approaches the co-dimension 2 point, we observe that the stable stationary periodic patterns predicted by the GL-equation evolve towards various different families of stable, stationary (but not necessarily periodic) so-called ‘multi-bump’ solutions. In the literature, these multi-bump patterns are shown to exist as solutions of the eFK-equation, but there is no proof of the asymptotic stability of these solutions. Our results suggest that these multi-bump patterns can also be asymptotically stable in large classes of model problems.

Inverse design of centrifugal compressor vaned diffusers in inlet shear flows

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

Zangeneh, M.

1996-04-01

A three-dimensional inverse design method in which the blade (or vane) geometry is designed for specified distributions of circulation and blade thickness is applied to the design of centrifugal compressor vaned diffusers. Two generic diffusers are designed, one with uniform inlet flow (equivalent to a conventional design) and the other with a sheared inlet flow. The inlet shear flow effects are modeled in the design method by using the so-called ``Secondary Flow Approximation`` in which the Bernoulli surfaces are convected by the tangentially mean inviscid flow field. The difference between the vane geometry of the uniform inlet flow and nonuniformmore » inlet flow diffusers is found to be most significant from 50 percent chord to the trailing edge region. The flows through both diffusers are computed by using Denton`s three-dimensional inviscid Euler solver and Dawes` three-dimensional Navier-Stokes solver under sheared in-flow conditions. The predictions indicate improved pressure recovery and internal flow field for the diffuser designed for shear inlet flow conditions.« less

Spatial variation of a short-lived intermediate chemical species in a Couette reactor

NASA Astrophysics Data System (ADS)

Vigil, R. Dennis; Ouyang, Q.; Swinney, Harry L.

1992-04-01

We have conducted experiments and simulations of the spatial variation of a short-lived intermediate species (triiodide) in the autocatalytic oxidation of arsenite by iodate in a reactor that is essentially one dimensional—the Couette reactor. (This reactor consists of two concentric cylinders with the inner one rotating and the outer one at rest; reagents are continuously fed and removed at each end in such a way that there is no net axial flux and there are opposing arsenite and iodate gradients.) The predictions of a one-dimensional reaction-diffusion model, which has no adjustable parameters, are in good qualitative (and, in some cases, quantitative) agreement with experiments. Thus, the Couette reactor, which is used to deliberately create spatial inhomogeneities, can be exploited to enhance the recovery of short-lived intermediate species relative to that which can be obtained with either a batch or continuous-flow stirred-tank reactor.

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism.

PubMed

Di Patti, Francesca; Lavacchi, Laura; Arbel-Goren, Rinat; Schein-Lubomirsky, Leora; Fanelli, Duccio; Stavans, Joel

2018-05-01

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

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%.

Assessing the inherent uncertainty of one-dimensional diffusions

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2013-01-01

In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.

Deposition on disordered substrates with precursor layer diffusion

NASA Astrophysics Data System (ADS)

Filipe, J. A. N.; Rodgers, G. J.; Tavassoli, Z.

1998-09-01

Recently we introduced a one-dimensional accelerated random sequential adsorption process as a model for chemisorption with precursor layer diffusion. In this paper we consider this deposition process on disordered or impure substrates. The problem is solved exactly on both the lattice and continuum and for various impurity distributions. The results are compared with those from the standard random sequential adsorption model.

Computer model of one-dimensional equilibrium controlled sorption processes

USGS Publications Warehouse

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

1984-01-01

A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)

Reaction Kernel Structure of a Slot Jet Diffusion Flame in Microgravity

NASA Technical Reports Server (NTRS)

Takahashi, F.; Katta, V. R.

2001-01-01

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

Pattern formation in superdiffusion Oregonator model

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Characterization of single-file diffusion in one-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Theisen, W. L.; Sheridan, T. E.

2010-11-01

Single-file diffusion occurs in one-dimensional systems when particles cannot pass each other and the mean-squared displacement (msd) of these particles increases with time t. Diffusive processes that follow Ficks law predict that the msd increases as t, however, single-file diffusion is sub-Fickean meaning that the msd is predicted to increase as t^1/2. One-dimensional dusty plasma rings have been created under strongly coupled, over-damped conditions. Particle position data from these rings will be analyzed to determine the scaling of the msd with time. Results will be compared with predictions of single-file diffusion theory.

Catalytic oxidation of toluene: comparative study over powder and monolithic manganese-nickel mixed oxide catalysts.

PubMed

Duplančić, Marina; Tomašić, Vesna; Gomzi, Zoran

2017-07-05

This paper is focused on development of the metal monolithic structure for total oxidation of toluene at low temperature. The well-adhered catalyst, based on the mixed oxides of manganese and nickel, is washcoated on the Al/Al 2 O 3 plates as metallic support. For the comparison purposes, results observed for the manganese-nickel mixed oxide supported on the metallic monolith are compared with those obtained using powder type of the same catalyst. Prepared manganese-nickel mixed oxides in both configurations show remarkable low-temperature activity for the toluene oxidation. The reaction temperature T 50 corresponding to 50% of the toluene conversion is observed at temperatures of ca. 400-430 K for the powder catalyst and at ca. 450-490 K for the monolith configuration. The appropriate mathematical models, such as one-dimensional (1D) pseudo-homogeneous model of the fixed bed reactor and the 1D heterogeneous model of the metal monolith reactor, are applied to describe and compare catalytic performances of both reactors. Validation of the applied models is performed by comparing experimental data with theoretical predictions. The obtained results confirmed that the reaction over the monolithic structure is kinetically controlled, while in the case of the powder catalyst the reaction rate is influenced by the intraphase diffusion.

A genetically optimized kinetic model for ethanol electro-oxidation on Pt-based binary catalysts used in direct ethanol fuel cells

NASA Astrophysics Data System (ADS)

Sánchez-Monreal, Juan; García-Salaberri, Pablo A.; Vera, Marcos

2017-09-01

A one-dimensional model is proposed for the anode of a liquid-feed direct ethanol fuel cell. The complex kinetics of the ethanol electro-oxidation reaction is described using a multi-step reaction mechanism that considers free and adsorbed intermediate species on Pt-based binary catalysts. The adsorbed species are modeled using coverage factors to account for the blockage of the active reaction sites on the catalyst surface. The reaction rates are described by Butler-Volmer equations that are coupled to a one-dimensional mass transport model, which incorporates the effect of ethanol and acetaldehyde crossover. The proposed kinetic model circumvents the acetaldehyde bottleneck effect observed in previous studies by incorporating CH3CHOHads among the adsorbed intermediates. A multi-objetive genetic algorithm is used to determine the reaction constants using anode polarization and product selectivity data obtained from the literature. By adjusting the reaction constants using the methodology developed here, different catalyst layers could be modeled and their selectivities could be successfully reproduced.

Effects of 3 dimensional crystal geometry and orientation on 1D and 2D time-scale determinations of magmatic processes using olivine and orthopyroxene

NASA Astrophysics Data System (ADS)

Shea, Thomas; Krimer, Daniel; Costa, Fidel; Hammer, Julia

2014-05-01

One of the achievements in recent years in volcanology is the determination of time-scales of magmatic processes via diffusion in minerals and its addition to the petrologists' and volcanologists' toolbox. The method typically requires one-dimensional modeling of randomly cut crystals from two-dimensional thin sections. Here we address the question whether using 1D (traverse) or 2D (surface) datasets exploited from randomly cut 3D crystals introduces a bias or dispersion in the time-scales estimated, and how this error can be improved or eliminated. Computational simulations were performed using a concentration-dependent, finite-difference solution to the diffusion equation in 3D. The starting numerical models involved simple geometries (spheres, parallelepipeds), Mg/Fe zoning patterns (either normal or reverse), and isotropic diffusion coefficients. Subsequent models progressively incorporated more complexity, 3D olivines possessing representative polyhedral morphologies, diffusion anisotropy along the different crystallographic axes, and more intricate core-rim zoning patterns. Sections and profiles used to compare 1, 2 and 3D diffusion models were selected to be (1) parallel to the crystal axes, (2) randomly oriented but passing through the olivine center, or (3) randomly oriented and sectioned. Results show that time-scales estimated on randomly cut traverses (1D) or surfaces (2D) can be widely distributed around the actual durations of 3D diffusion (~0.2 to 10 times the true diffusion time). The magnitude over- or underestimations of duration are a complex combination of the geometry of the crystal, the zoning pattern, the orientation of the cuts with respect to the crystallographic axes, and the degree of diffusion anisotropy. Errors on estimated time-scales retrieved from such models may thus be significant. Drastic reductions in the uncertainty of calculated diffusion times can be obtained by following some simple guidelines during the course of data collection (i.e. selection of crystals and concentration profiles, acquisition of crystallographic orientation data), thus allowing derivation of robust time-scales.

Spontaneous Symmetry Breaking Turing-Type Pattern Formation in a Confined Dictyostelium Cell Mass

NASA Astrophysics Data System (ADS)

Sawai, Satoshi; Maeda, Yasuo; Sawada, Yasuji

2000-09-01

We have discovered a new type of patterning which occurs in a two-dimensionally confined cell mass of the cellular slime mold Dictyostelium discoideum. Besides the longitudinal structure reported earlier, we observed a spontaneous symmetry breaking spot pattern whose wavelength shows similar strain dependency to that of the longitudinal pattern. We propose that these structures are due to a reaction-diffusion Turing instability similar to the one which has been exemplified by CIMA (chlorite-iodide-malonic acid) reaction. The present finding may exhibit the first biochemical Turing structure in a developmental system with a controllable boundary condition.

Three-dimensional modeling of metabolic species transport in the cornea with a hydrogel intrastromal inlay.

PubMed

Pinsky, Peter M

2014-05-15

Intrastromal inlays for refractive correction of presbyopia are being adopted into clinical practice. An important concern is the effect of the inlay on the long-term health of the cornea due to disturbances in the concentration profiles of metabolic species. A three-dimensional metabolic model for the cornea is employed to investigate oxygen, glucose, and lactate ion transport in the cornea and to estimate changes in species concentrations induced by the introduction of a hydrogel inlay. A reaction-diffusion metabolic model, appropriate for highly oxygen-permeable hydrogel inlays, is used to describe cellular consumption of oxygen and glucose and production of lactic acid. A three-layer corneal geometry (epithelium, stroma, endothelium) is employed with a hydrogel inlay placed under a lamellar flap. The model is solved numerically by the finite element method. For a commercially available hydrogel material with a relative inlay diffusivity of 43.5%, maximum glucose depletion and lactate ion accumulation occur anterior to the inlay and both are less than 3%. Below 20% relative diffusivity, glucose depletion and lactate ion accumulation increase exponentially. Glucose depletion increases slightly with increasing depth of inlay placement. The flux of metabolic species is modified by an inlay, depending on the inlay relative diffusivity. For commercially available hydrogel materials and a typical inlay design, predicted changes in species concentrations are small when compared to the variation of concentrations across the normal cornea. In general, glucose depletion and lactate ion accumulation are highly sensitive to inlay diffusivity and somewhat insensitive to inlay depth. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Interplay between inhibited transport and reaction in nanoporous materials

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

Ackerman, David Michael

2013-01-01

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

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

PubMed

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

2017-05-10

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

Progress in MOSFET double-layer metalization

NASA Technical Reports Server (NTRS)

Gassaway, J. D.; Trotter, J. D.; Wade, T. E.

1980-01-01

Report describes one-year research effort in VLSL fabrication. Four activities are described: theoretical study of two-dimensional diffusion in SOS (silicon-on-sapphire); setup of sputtering system, furnaces, and photolithography equipment; experiments on double layer metal; and investigation of two-dimensional modeling of MOSFET's (metal-oxide-semiconductor field-effect transistors).

Transverse liquid fuel jet breakup, burning, and ignition

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

Li, Hsi-shang

1990-01-01

An analytical/numerical study of the breakup, burning, and ignition of liquid fuels injected transversely into a hot air stream is conducted. The non-reacting liquid jet breakup location is determined by the local sonic point criterion first proposed by Schetz, et al. (1980). Two models, one employing analysis of an elliptical jet cross-section and the other employing a two-dimensional blunt body to represent the transverse jet, have been used for sonic point calculations. An auxiliary criterion based on surface tension stability is used as a separate means of determining the breakup location. For the reacting liquid jet problem, a diffusion flamemore » supported by a one-step chemical reaction within the gaseous boundary layer is solved along the ellipse surface in subsonic crossflow. Typical flame structures and concentration profiles have been calculated for various locations along the jet cross-section as a function of upstream Mach numbers. The integrated reaction rate along the jet cross-section is used to predict ignition position, which is found to be situated near the stagnation point. While a multi-step reaction is needed to represent the ignition process more accurately, the present calculation does yield reasonable predictions concerning ignition along a curved surface.« less

Transverse liquid fuel jet breakup, burning, and ignition. M.S. Thesis

NASA Technical Reports Server (NTRS)

Li, Hsi-Shang

1990-01-01

An analytical study of the breakup, burning, and ignition of liquid fuels injected transversely into a hot air stream is conducted. The non-reacting liquid jet breakup location is determined by the local sonic point criterion. Two models, one employing analysis of an elliptical jet cross-section and the other employing a two-dimensional blunt body to represent the transverse jet, were used for sonic point calculations. An auxiliary criterion based on surface tension stability is used as a separate means of determining the breakup location. For the reacting liquid jet problem, a diffusion flame supported by a one-step chemical reaction within the gaseous boundary layer is solved along the ellipse surface in subsonic cross flow. Typical flame structures and concentration profiles were calculated for various locations along the jet cross-section as a function of upstream Mach numbers. The integration reaction rate along the jet cross-section is used to predict ignition position, which is found to be situated near the stagnation point. While a multi-step reaction is needed to represent the ignition process more accurately, the present calculation does yield reasonable predictions concerning ignition along a curved surface.

A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling

NASA Astrophysics Data System (ADS)

Eibern, Hendrik; Schmidt, Hauke

1999-08-01

The inverse problem of data assimilation of tropospheric trace gas observations into an Eulerian chemistry transport model has been solved by the four-dimensional variational technique including chemical reactions, transport, and diffusion. The University of Cologne European Air Pollution Dispersion Chemistry Transport Model 2 with the Regional Acid Deposition Model 2 gas phase mechanism is taken as the basis for developing a full four-dimensional variational data assimilation package, on the basis of the adjoint model version, which includes the adjoint operators of horizontal and vertical advection, implicit vertical diffusion, and the adjoint gas phase mechanism. To assess the potential and limitations of the technique without degrading the impact of nonperfect meteorological analyses and statistically not established error covariance estimates, artificial meteorological data and observations are used. The results are presented on the basis of a suite of experiments, where reduced records of artificial "observations" are provided to the assimilation procedure, while other "data" is retained for performance control of the analysis. The paper demonstrates that the four-dimensional variational technique is applicable for a comprehensive chemistry transport model in terms of computational and storage requirements on advanced parallel platforms. It is further shown that observed species can generally be analyzed, even if the "measurements" have unbiased random errors. More challenging experiments are presented, aiming to tax the skill of the method (1) by restricting available observations mostly to surface ozone observations for a limited assimilation interval of 6 hours and (2) by starting with poorly chosen first guess values. In this first such application to a three-dimensional chemistry transport model, success was also achieved in analyzing not only observed but also chemically closely related unobserved constituents.

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.

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

PubMed

Zhang, Jinzhong; Zhou, Luqun; Ouyang, Qi

2007-02-15

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

Reaction 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.

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

PubMed

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

2014-07-01

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

Electrochemical kinetic and mass transfer model for direct ethanol alkaline fuel cell (DEAFC)

NASA Astrophysics Data System (ADS)

Abdullah, S.; Kamarudin, S. K.; Hasran, U. A.; Masdar, M. S.; Daud, W. R. W.

2016-07-01

A mathematical model is developed for a liquid-feed DEAFC incorporating an alkaline anion-exchange membrane. The one-dimensional mass transport of chemical species is modelled using isothermal, single-phase and steady-state assumptions. The anode and cathode electrochemical reactions use the Tafel kinetics approach, with two limiting cases, for the reaction order. The model fully accounts for the mixed potential effects of ethanol oxidation at the cathode due to ethanol crossover via an alkaline anion-exchange membrane. In contrast to a polymer electrolyte membrane model, the current model considers the flux of ethanol at the membrane as the difference between diffusive and electroosmotic effects. The model is used to investigate the effects of the ethanol and alkali inlet feed concentrations at the anode. The model predicts that the cell performance is almost identical for different ethanol concentrations at a low current density. Moreover, the model results show that feeding the DEAFC with 5 M NaOH and 3 M ethanol at specific operating conditions yields a better performance at a higher current density. Furthermore, the model indicates that crossover effects on the DEAFC performance are significant. The cell performance decrease from its theoretical value when a parasitic current is enabled in the model.

Multidimensional MnO2 nanohair-decorated hybrid multichannel carbon nanofiber as an electrode material for high-performance supercapacitors

NASA Astrophysics Data System (ADS)

Jun, Jaemoon; Lee, Jun Seop; Shin, Dong Hoon; Kim, Sung Gun; Jang, Jyongsik

2015-09-01

One-dimensional (1D)-structured nanomaterials represent one of the most attractive candidates for energy-storage systems due to their contribution to design simplicity, fast charge-transportation network, and their allowance for more accessible ion diffusion. In particular, 1D-structured nanomaterials with a highly complex inner-pore configuration enhance functionality by taking advantage of both the hollow and 1D structures. In this study, we report a MnO2 nanohair-decorated, hybrid multichannel carbon nanofiber (Mn_MCNF) fabricated via single-nozzle co-electrospinning of two immiscible polymer solutions, followed by carbonization and redox reactions. With improved ion accessibility, the optimized Mn_MCNF sample (Mn_MCNF_60 corresponding to a reaction duration time of 60 min for optimal MnO2 nanohair growth) exhibited a high specific capacitance of 855 F g-1 and excellent cycling performance with ~87.3% capacitance retention over 5000 cycles.One-dimensional (1D)-structured nanomaterials represent one of the most attractive candidates for energy-storage systems due to their contribution to design simplicity, fast charge-transportation network, and their allowance for more accessible ion diffusion. In particular, 1D-structured nanomaterials with a highly complex inner-pore configuration enhance functionality by taking advantage of both the hollow and 1D structures. In this study, we report a MnO2 nanohair-decorated, hybrid multichannel carbon nanofiber (Mn_MCNF) fabricated via single-nozzle co-electrospinning of two immiscible polymer solutions, followed by carbonization and redox reactions. With improved ion accessibility, the optimized Mn_MCNF sample (Mn_MCNF_60 corresponding to a reaction duration time of 60 min for optimal MnO2 nanohair growth) exhibited a high specific capacitance of 855 F g-1 and excellent cycling performance with ~87.3% capacitance retention over 5000 cycles. Electronic supplementary information (ESI) available: Experimental data includes optical images, TGA, magnified pore distribution curves and supercapacitor device of the MCNF and Mn_MCNF. See DOI: 10.1039/C5NR03616J

Diffusion of interacting particles in discrete geometries: Equilibrium and dynamical properties

NASA Astrophysics Data System (ADS)

Becker, T.; Nelissen, K.; Cleuren, B.; Partoens, B.; Van den Broeck, C.

2014-11-01

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013), 10.1103/PhysRevLett.111.110601]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a 1 /L dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.

The effects of noise on binocular rivalry waves: a stochastic neural field model

NASA Astrophysics Data System (ADS)

Webber, Matthew A.; Bressloff, Paul C.

2013-03-01

We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave.

Insights into the role of wettability in cathode catalyst layer of proton exchange membrane fuel cell; pore scale immiscible flow and transport processes

NASA Astrophysics Data System (ADS)

Fathi, H.; Raoof, A.; Mansouri, S. H.

2017-05-01

The production of liquid water in cathode catalyst layer, CCL, is a significant barrier to increase the efficiency of proton exchange membrane fuel cell. Here we present, for the first time, a direct three-dimensional pore-scale modelling to look at the complex immiscible two-phase flow in CCL. After production of the liquid water at the surface of CCL agglomerates due to the electrochemical reactions, water spatial distribution affects transport of oxygen through the CCL as well as the rate of reaction at the agglomerate surfaces. To explore the wettability effects, we apply hydrophilic and hydrophobic properties using different surface contact angles. Effective diffusivity is calculated under several water saturation levels. Results indicate larger diffusive transport values for hydrophilic domain compared to the hydrophobic media where the liquid water preferentially floods the larger pores. However, hydrophobic domain showed more available surface area and higher oxygen consumption rate at the reaction sites under various saturation levels, which is explained by the effect of wettability on pore-scale distribution of water. Hydrophobic domain, with a contact angle of 150, reveals efficient water removal where only 28% of the pore space stays saturated. This condition contributes to the enhanced available reaction surface area and oxygen diffusivity.

One-dimensional Turbulence Models of Type I X-ray Bursts

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

Hou, Chen

Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection.more » Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more 12C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.« less

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.

Escarpment evolution on high-elevation rifted margins: Insights derived from a surface processes model that combines diffusion, advection and reaction

NASA Technical Reports Server (NTRS)

Kooi, Henk; Beaumont, Christopher

1994-01-01

Experiments with a surface processes model of large-scale (1-1000 km) long-term (1-100 m.y.) erosional denudation are used to establish the controls on the evolution of a model escarpment that is related to the rifting of a continent. The mdoel describes changes in topographic form as a result of sumultaneous short- and long-range mass transport representing hillslope (diffusive) processes and fluvial transport (advection), repsectively. Fluvial entrainment is modeled as a first-order kinetic reaction which reflects the erodibility of the substrate, and therefore the fluvial system is not necessarily carrying at capacity. One dimensional and planform models demonstrate that the principal controls on the evolution of an initially steep model escarpment are (1) antecedent topography/drainage; (2) the timesale (or equivalently a length scale) in the fluvial entrainment reaction; (3) the flexural response of the lithosphere to denudation; and (4) the relative efficiencies of the short- and long-range transport processes. When rainfall and substrate lithology are uniform, a significant amount of discharge draining over the escarpment top causes it to degrade. Only when the top of the model escarpment coincides with a drainage divide can escarpment retreat occur for these conditions. An additional requirement for retreat of a model escarpment without decline is a long reaction time scale for fluvial entrainment. This corresponds to a substrate that is hard to detach by flucial erosion, and therefore to fluvial erosion that is not transport limited. Coninuous backtilting of an escarpment due ot flexural isostatic uplift in response to denudational unloading helps maintain the scarp top as a divide. It is essntial if the escarpment gradient is to be preserved during retreat in a uniform lithology. Low flexural rigidieties propote steep and slowly retreating escarpments. For given rainfall and substrate conditions, the morphology of a retraeating model escarpment is determined by the ratio of hte short-range diffusive and long range advective transport efficiencies. A low ration (which is interpreted to correspond to a more humid, temperate climate) produces a convex upper slope, and concave lower slope morphology and only major escarpments are predicted to preserve a high scarp gradient. Lithological contrasts in hte model produce more complex morphologies and predict the formation of scarps crowned by an erosionaly resistant caprock. However, resistant caprocks are not an essential requirement for model scarps to retreat. We conclude that the inferred controls and model behavior are both consistent with the present-day morphology of rifted continental margins and with modern conceptual models of landscape evolution.

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

NASA Astrophysics Data System (ADS)

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

2006-12-01

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

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

PubMed Central

Song, Hongjun; Wang, Yi; Pant, Kapil

2011-01-01

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection–diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability. PMID:22247719

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model.

PubMed

Song, Hongjun; Wang, Yi; Pant, Kapil

2012-01-01

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.

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.

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.

Modeling and 3D-simulation of hydrogen production via methanol steam reforming in copper-coated channels of a mini reformer

NASA Astrophysics Data System (ADS)

Sari, Ataallah; Sabziani, Javad

2017-06-01

Modeling and CFD simulation of a three-dimensional microreactor includes thirteen structured parallel channels is performed to study the hydrogen production via methanol steam reforming reaction over a Cu/ZnO/Al2O3 catalyst. The well-known Langmuir-Hinshelwood macro kinetic rate expressions reported by Peppley and coworkers [49] are considered to model the methanol steam reforming reactions. The effects of inlet steam to methanol ratio, pre-heat temperature, channels geometry and size, and the level of external heat flux on the hydrogen quality and quantity (i.e., hydrogen flow rate and CO concentration) are investigated. Moreover, the possibility of reducing the CO concentration by passing the reactor effluent through a water gas shift channel placed in series with the methanol reformer is studied. Afterwards, the simulation results are compared with the experimental data reported in the literature considering two different approaches of mixture-averaged and Maxwell-Stefan formulations to evaluate the diffusive flux of mass. The results indicate that the predictions of the Maxwell-Stefan model is in better agreement with experimental data than mixture-averaged one, especially at the lower feed flow rates.

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.

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).

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.

A Computational Approach to Increase Time Scales in Brownian Dynamics–Based Reaction-Diffusion Modeling

PubMed Central

Frazier, Zachary

2012-01-01

Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237

Spatiotemporal Patterns in a Predator-Prey Model with Cross-Diffusion Effect

NASA Astrophysics Data System (ADS)

Sambath, M.; Balachandran, K.; Guin, L. N.

The present research deals with the emergence of spatiotemporal patterns of a two-dimensional (2D) continuous predator-prey system with cross-diffusion effect. First, we work out the critical lines of Hopf and Turing bifurcations of the current model system in a 2D spatial domain by means of bifurcation theory. More specifically, the exact Turing region is specified in a two-parameter space. In effect, by choosing the cross-diffusion coefficient as one of the momentous parameter, we demonstrate that the model system undergoes a sequence of spatiotemporal patterns in a homogeneous environment through diffusion-driven instability. Our results via numerical simulation authenticate that cross-diffusion be able to create stationary patterns which enrich the findings of pattern formation in an ecosystem.

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.

The origin of life is a spatially localized stochastic transition

PubMed Central

2012-01-01

Background Life depends on biopolymer sequences as catalysts and as genetic material. A key step in the Origin of Life is the emergence of an autocatalytic system of biopolymers. Here we study computational models that address the way a living autocatalytic system could have emerged from a non-living chemical system, as envisaged in the RNA World hypothesis. Results We consider (i) a chemical reaction system describing RNA polymerization, and (ii) a simple model of catalytic replicators that we call the Two’s Company model. Both systems have two stable states: a non-living state, characterized by a slow spontaneous rate of RNA synthesis, and a living state, characterized by rapid autocatalytic RNA synthesis. The origin of life is a transition between these two stable states. The transition is driven by stochastic concentration fluctuations involving relatively small numbers of molecules in a localized region of space. These models are simulated on a two-dimensional lattice in which reactions occur locally on single sites and diffusion occurs by hopping of molecules to neighbouring sites. Conclusions If diffusion is very rapid, the system is well-mixed. The transition to life becomes increasingly difficult as the lattice size is increased because the concentration fluctuations that drive the transition become relatively smaller when larger numbers of molecules are involved. In contrast, when diffusion occurs at a finite rate, concentration fluctuations are local. The transition to life occurs in one local region and then spreads across the rest of the surface. The transition becomes easier with larger lattice sizes because there are more independent regions in which it could occur. The key observations that apply to our models and to the real world are that the origin of life is a rare stochastic event that is localized in one region of space due to the limited rate of diffusion of the molecules involved and that the subsequent spread across the surface is deterministic. It is likely that the time required for the deterministic spread is much shorter than the waiting time for the origin, in which case life evolves only once on a planet, and then rapidly occupies the whole surface. Reviewers Reviewed by Omer Markovitch (nominated by Doron Lancet), Claus Wilke, and Nobuto Takeuchi (nominated by Eugene Koonin). PMID:23176307

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

Nanostructured carbon-metal oxide composite electrodes for supercapacitors: a review

NASA Astrophysics Data System (ADS)

Zhi, Mingjia; Xiang, Chengcheng; Li, Jiangtian; Li, Ming; Wu, Nianqiang

2012-12-01

This paper presents a review of the research progress in the carbon-metal oxide composites for supercapacitor electrodes. In the past decade, various carbon-metal oxide composite electrodes have been developed by integrating metal oxides into different carbon nanostructures including zero-dimensional carbon nanoparticles, one-dimensional nanostructures (carbon nanotubes and carbon nanofibers), two-dimensional nanosheets (graphene and reduced graphene oxides) as well as three-dimensional porous carbon nano-architectures. This paper has described the constituent, the structure and the properties of the carbon-metal oxide composites. An emphasis is placed on the synergistic effects of the composite on the performance of supercapacitors in terms of specific capacitance, energy density, power density, rate capability and cyclic stability. This paper has also discussed the physico-chemical processes such as charge transport, ion diffusion and redox reactions involved in supercapacitors.

Nanostructured carbon-metal oxide composite electrodes for supercapacitors: a review.

PubMed

Zhi, Mingjia; Xiang, Chengcheng; Li, Jiangtian; Li, Ming; Wu, Nianqiang

2013-01-07

This paper presents a review of the research progress in the carbon-metal oxide composites for supercapacitor electrodes. In the past decade, various carbon-metal oxide composite electrodes have been developed by integrating metal oxides into different carbon nanostructures including zero-dimensional carbon nanoparticles, one-dimensional nanostructures (carbon nanotubes and carbon nanofibers), two-dimensional nanosheets (graphene and reduced graphene oxides) as well as three-dimensional porous carbon nano-architectures. This paper has described the constituent, the structure and the properties of the carbon-metal oxide composites. An emphasis is placed on the synergistic effects of the composite on the performance of supercapacitors in terms of specific capacitance, energy density, power density, rate capability and cyclic stability. This paper has also discussed the physico-chemical processes such as charge transport, ion diffusion and redox reactions involved in supercapacitors.

Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES

NASA Astrophysics Data System (ADS)

Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

High resolution approach to the native state ensemble kinetics and thermodynamics.

PubMed

Wu, Sangwook; Zhuravlev, Pavel I; Papoian, Garegin A

2008-12-15

Many biologically interesting functions such as allosteric switching or protein-ligand binding are determined by the kinetics and mechanisms of transitions between various conformational substates of the native basin of globular proteins. To advance our understanding of these processes, we constructed a two-dimensional free energy surface (FES) of the native basin of a small globular protein, Trp-cage. The corresponding order parameters were defined using two native substructures of Trp-cage. These calculations were based on extensive explicit water all-atom molecular dynamics simulations. Using the obtained two-dimensional FES, we studied the transition kinetics between two Trp-cage conformations, finding that switching process shows a borderline behavior between diffusive and weakly-activated dynamics. The transition is well-characterized kinetically as a biexponential process. We also introduced a new one-dimensional reaction coordinate for the conformational transition, finding reasonable qualitative agreement with the two-dimensional kinetics results. We investigated the distribution of all the 38 native nuclear magnetic resonance structures on the obtained FES, analyzing interactions that stabilize specific low-energy conformations. Finally, we constructed a FES for the same system but with simple dielectric model of water instead of explicit water, finding that the results were surprisingly similar in a small region centered on the native conformations. The dissimilarities between the explicit and implicit model on the larger-scale point to the important role of water in mediating interactions between amino acid residues.

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

NASA Technical Reports Server (NTRS)

Williams, Powtawche N.

1998-01-01

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

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.

Topics in Diffusion Limited Reaction Processes

NASA Astrophysics Data System (ADS)

Lin, Jian-Cheng

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

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.

Illumination in diverse codimensions

NASA Technical Reports Server (NTRS)

Banks, David C.

1994-01-01

This paper derives a model of diffuse and specular illumination in arbitrarily large dimensions, based on a few characteristics of material and light in three-space. It then describes how to adjust for the anomaly of excess brightness in large codimensions. If a surface is grooved or furry, it can be illuminated with a hybrid model that incorporates both the one dimensional geometry (the grooves or fur) and the two dimensional geometry (the surface).

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.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Photodynamic therapy: computer modeling of diffusion and reaction phenomena

NASA Astrophysics Data System (ADS)

Hampton, James A.; Mahama, Patricia A.; Fournier, Ronald L.; Henning, Jeffery P.

1996-04-01

We have developed a transient, one-dimensional mathematical model for the reaction and diffusion phenomena that occurs during photodynamic therapy (PDT). This model is referred to as the PDTmodem program. The model is solved by the Crank-Nicholson finite difference technique and can be used to predict the fates of important molecular species within the intercapillary tissue undergoing PDT. The following factors govern molecular oxygen consumption and singlet oxygen generation within a tumor: (1) photosensitizer concentration; (2) fluence rate; and (3) intercapillary spacing. In an effort to maximize direct tumor cell killing, the model allows educated decisions to be made to insure the uniform generation and exposure of singlet oxygen to tumor cells across the intercapillary space. Based on predictions made by the model, we have determined that the singlet oxygen concentration profile within the intercapillary space is controlled by the product of the drug concentration, and light fluence rate. The model predicts that at high levels of this product, within seconds singlet oxygen generation is limited to a small core of cells immediately surrounding the capillary. The remainder of the tumor tissue in the intercapillary space is anoxic and protected from the generation and toxic effects of singlet oxygen. However, at lower values of this product, the PDT-induced anoxic regions are not observed. An important finding is that an optimal value of this product can be defined that maintains the singlet oxygen concentration throughout the intercapillary space at a near constant level. Direct tumor cell killing is therefore postulated to depend on the singlet oxygen exposure, defined as the product of the uniform singlet oxygen concentration and the time of exposure, and not on the total light dose.

Efficient reactive Brownian dynamics

DOE PAGES

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-21

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Efficient reactive Brownian dynamics

NASA Astrophysics Data System (ADS)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-01

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.

Efficient reactive Brownian dynamics

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

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

Large-scale one-dimensional Bi x O y I z nanostructures: synthesis, characterization, and photocatalytic applications

NASA Astrophysics Data System (ADS)

Liu, Chaohong; Zhang, Dun

2015-03-01

The performances of Bi x O y I z photofunctional materials are very sensitive to their composition and microstructures; however, the morphology evolution and crystallization process of one-dimensional Bi x O y I z nanostructures, the roles of experimental factors, and related reaction mechanisms remain poorly understood. In this work, large-scale one-dimensional Bi x O y I z nanostructures were fabricated using simple inorganic iodine source. By combing the results of X-ray diffraction and scanning electron microscope, the effect of volume ratios of water and ethanol, concentration of NaOH, and reaction time on the morphologies and crystal phases of Bi x O y I z were elaborated. On the basis of characterizations, a possible process for the growth of Bi5O7I nanobelts was proposed. The optical performances of Bi x O y I z nanostructures were evaluated by ultraviolet-visible-near infrared diffuse reflectance spectra as well as photocatalytic degradation of organic dye and corrosive bacteria. The as-prepared Bi5O7I/Bi2O2CO3/BiOI composite showed excellent photocatalytic activity over malachite green under visible light irradiation, which was deduced closely related to its heterojunction structures.

A Two Species Bump-On-Tail Model With Relaxation for Energetic Particle Driven Modes

NASA Astrophysics Data System (ADS)

Aslanyan, V.; Porkolab, M.; Sharapov, S. E.; Spong, D. A.

2017-10-01

Energetic particle driven Alfvén Eigenmodes (AEs) observed in present day experiments exhibit various nonlinear behaviours varying from steady state amplitude at a fixed frequency to bursting amplitudes and sweeping frequency. Using the appropriate action-angle variables, the problem of resonant wave-particle interaction becomes effectively one-dimensional. Previously, a simple one-dimensional Bump-On-Tail (BOT) model has proven to be one of the most effective in describing characteristic nonlinear near-threshold wave evolution scenarios. In particular, dynamical friction causes bursting mode evolution, while diffusive relaxation may give steady-state, periodic or chaotic mode evolution. BOT has now been extended to include two populations of fast particles, with one dominated by dynamical friction at the resonance and the other by diffusion; the relative size of the populations determines the temporal evolution of the resulting wave. This suggests an explanation for recent observations on the TJ-II stellarator, where a transition between steady state and bursting occured as the magnetic configuration varied. The two species model is then applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions. This work was supported by the US DoE and the RCUK Energy Programme [Grant Number EP/P012450/1].

Simulating contaminant attenuation, double-porosity exchange, and water age in aquifers using MOC3D

USGS Publications Warehouse

Goode, Daniel J.

1999-01-01

MOC3D is a general-purpose computer model developed by the U.S. Geological Survey (USGS) for simulation of three-dimensional solute transport in ground water (Konikow and others, 1996). The model is an update to the widely used USGS two-dimensional solute-transport model (MOC) and is implemented as an optional “package” for the ground-water flow model MODFLOW (Harbaugh and McDonald, 1996). Directly coupling the time-tested MOC transport algorithms with the widely used MODFLOW program makes MOC3D a powerful tool for simulation of solute transport in ground water in many hydrogeologic settings. The model simulates transport processes that include:Advection - Transport of dissolved solutes at the same rate as the average ground-water flow velocity.Diffusion - Spreading of solute from areas of high concentration to areas of low concentration, caused by “random” molecular motionDispersion - Diffusion-like spreading of solute that is caused primarily by spatial variability in aquifer properties, which results in spatial variability in transport velocity.Retardation - Reduction in the apparent solute velocity, compared to the ground-water velocity, caused by linear equilibrium sorption on aquifer materials.Decay - Disappearance of solute caused by reactions such as radioactive decay or biodegradation that are proportional to concentration.Growth - Creation (or disappearance) of solute mass caused by reactions that proceed independent of the solute concentration, such as some cases of biodegradationDouble-porosity exchange - rate-limited exchange of solute mass between mobile and immobile zones; for example, between fractures and the rock matrix.

The Effects of Intrinsic Noise on an Inhomogeneous Lattice of Chemical Oscillators

NASA Astrophysics Data System (ADS)

Giver, Michael; Jabeen, Zahera; Chakraborty, Bulbul

2012-02-01

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including biochemical reactions within cells, predator-prey populations, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional system to the case of a non-uniform one dimensional lattice using a combination of analytical techniques and Monte Carlo simulations.

Sub-Fickean Diffusion in a One-Dimensional Plasma Ring

NASA Astrophysics Data System (ADS)

Theisen, W. L.

2013-12-01

A one-dimensional dusty plasma ring is formed in a strongly-coupled complex plasma. The dust particles in the ring can be characterized as a one-dimensional system where the particles cannot pass each other. The particles perform random walks due to thermal motions. This single-file self diffusion is characterized by the mean-squared displacement (msd) of the individual particles which increases with time t. Diffusive processes that follow Ficks law predict that the msd increases as t, however, single-file diffusion is sub-Fickean meaning that the msd is predicted to increase as t^(1/2). Particle position data from the dusty plasma ring is analyzed to determine the scaling of the msd with time. Results are compared with predictions of single-file diffusion theory.

Continuous versus discontinuous albedo representations in a simple diffusive climate model

NASA Astrophysics Data System (ADS)

Simmons, P. A.; Griffel, D. H.

1988-07-01

A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

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

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-09-15

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delaymore » time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.« less

Optical measurement of transverse molecular diffusion in a microchannel.

PubMed Central

Kamholz, A E; Schilling, E A; Yager, P

2001-01-01

Quantitative analysis of molecular diffusion is a necessity for the efficient design of most microfluidic devices as well as an important biophysical method in its own right. This study demonstrates the rapid measurement of diffusion coefficients of large and small molecules in a microfluidic device, the T-sensor, by means of conventional epifluorescence microscopy. Data were collected by monitoring the transverse flux of analyte from a sample stream into a second stream flowing alongside it. As indicated by the low Reynolds numbers of the system (< 1), flow is laminar, and molecular transport between streams occurs only by diffusion. Quantitative determinations were made by fitting data with predictions of a one-dimensional model. Analysis was made of the flow development and its effect on the distribution of diffusing analyte using a three-dimensional modeling software package. Diffusion coefficients were measured for four fluorescently labeled molecules: fluorescein-biotin, insulin, ovalbumin, and streptavidin. The resulting values differed from accepted results by an average of 2.4%. Microfluidic system parameters can be selected to achieve accurate diffusion coefficient measurements and to optimize other microfluidic devices that rely on precise transverse transport of molecules. PMID:11259309

Evaluation of Finite-Rate Gas/Surface Interaction Models for a Carbon Based Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Goekcen, Tahir

2015-01-01

Two sets of finite-rate gas-surface interaction model between air and the carbon surface are studied. The first set is an engineering model with one-way chemical reactions, and the second set is a more detailed model with two-way chemical reactions. These two proposed models intend to cover the carbon surface ablation conditions including the low temperature rate-controlled oxidation, the mid-temperature diffusion-controlled oxidation, and the high temperature sublimation. The prediction of carbon surface recession is achieved by coupling a material thermal response code and a Navier-Stokes flow code. The material thermal response code used in this study is the Two-dimensional Implicit Thermal-response and Ablation Program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting full Navier-Stokes equations using Data Parallel Line Relaxation method. Recession analyses of stagnation tests conducted in NASA Ames Research Center arc-jet facilities with heat fluxes ranging from 45 to 1100 wcm2 are performed and compared with data for model validation. The ablating material used in these arc-jet tests is Phenolic Impregnated Carbon Ablator. Additionally, computational predictions of surface recession and shape change are in good agreement with measurement for arc-jet conditions of Small Probe Reentry Investigation for Thermal Protection System Engineering.

Venus climate stability and volcanic resurfacing rates

NASA Technical Reports Server (NTRS)

Bullock, M. A.; Grinspoon, D. H.; Pollack, J. B.

1994-01-01

The climate of Venus is to a large degree controlled by the radiative properties of its massive atmosphere. In addition, outgassing due to volcanic activity, exospheric escape processes, and surface/atmosphere interactions may all be important in moderating the abundances of atmospheric CO2 and other volatiles. We have developed an evolutionary climate model for Venus using a systems approach that emphasizes feedbacks between elements in the climate system. Modules for atmospheric radiative transfer, surface/atmosphere interactions, tropospheric chemistry, and exospheric escape processes have so far been developed. Climate feedback loops result from interconnections between modules, in the form of the environmental parameters pressure, temperature, and atmospheric mixing ratios. The radiative transfer module has been implemented by using Rosseland mean opacities in a one dimensional grey radiative-convective model. The model has been solved for the static (time independent) case to determine climate equilibrium points. The dynamics of the model have also been explored by employing reaction/diffusion kinetics for possible surface atmosphere heterogeneous reactions over geologic timescales. It was found that under current conditions, the model predicts that the climate of Venus is at or near an unstable equilibrium point. The effects of constant rate volcanism and corresponding exsolution of volatiles on the stability of the climate model were also explored.

The stability and slow dynamics of spot patterns in the 2D Brusselator model: The effect of open systems and heterogeneities

NASA Astrophysics Data System (ADS)

Tzou, J. C.; Ward, M. J.

2018-06-01

Spot patterns, whereby the activator field becomes spatially localized near certain dynamically-evolving discrete spatial locations in a bounded multi-dimensional domain, is a common occurrence for two-component reaction-diffusion (RD) systems in the singular limit of a large diffusivity ratio. In previous studies of 2-D localized spot patterns for various specific well-known RD systems, the domain boundary was assumed to be impermeable to both the activator and inhibitor, and the reaction-kinetics were assumed to be spatially uniform. As an extension of this previous theory, we use formal asymptotic methods to study the existence, stability, and slow dynamics of localized spot patterns for the singularly perturbed 2-D Brusselator RD model when the domain boundary is only partially impermeable, as modeled by an inhomogeneous Robin boundary condition, or when there is an influx of inhibitor across the domain boundary. In our analysis, we will also allow for the effect of a spatially variable bulk feed term in the reaction kinetics. By applying our extended theory to the special case of one-spot patterns and ring patterns of spots inside the unit disk, we provide a detailed analysis of the effect on spot patterns of these three different sources of heterogeneity. In particular, when there is an influx of inhibitor across the boundary of the unit disk, a ring pattern of spots can become pinned to a ring-radius closer to the domain boundary. Under a Robin condition, a quasi-equilibrium ring pattern of spots is shown to exhibit a novel saddle-node bifurcation behavior in terms of either the inhibitor diffusivity, the Robin constant, or the ambient background concentration. A spatially variable bulk feed term, with a concentrated source of "fuel" inside the domain, is shown to yield a saddle-node bifurcation structure of spot equilibria, which leads to qualitatively new spot-pinning behavior. Results from our asymptotic theory are validated from full numerical simulations of the Brusselator model.

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

PubMed Central

Tang, Ai-Hui; Wang, Shi-Qiang

2009-01-01

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

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

PubMed

Tang, Ai-Hui; Wang, Shi-Qiang

2009-09-01

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

Long residence times of rapidly decomposable soil organic matter: application of a multi-phase, multi-component, and vertically resolved model (BAMS1) to soil carbon dynamics

NASA Astrophysics Data System (ADS)

Riley, W. J.; Maggi, F.; Kleber, M.; Torn, M. S.; Tang, J. Y.; Dwivedi, D.; Guerry, N.

2014-07-01

Accurate representation of soil organic matter (SOM) dynamics in Earth system models is critical for future climate prediction, yet large uncertainties exist regarding how, and to what extent, the suite of proposed relevant mechanisms should be included. To investigate how various mechanisms interact to influence SOM storage and dynamics, we developed an SOM reaction network integrated in a one-dimensional, multi-phase, and multi-component reactive transport solver. The model includes representations of bacterial and fungal activity, multiple archetypal polymeric and monomeric carbon substrate groups, aqueous chemistry, aqueous advection and diffusion, gaseous diffusion, and adsorption (and protection) and desorption from the soil mineral phase. The model predictions reasonably matched observed depth-resolved SOM and dissolved organic matter (DOM) stocks and fluxes, lignin content, and fungi to aerobic bacteria ratios. We performed a suite of sensitivity analyses under equilibrium and dynamic conditions to examine the role of dynamic sorption, microbial assimilation rates, and carbon inputs. To our knowledge, observations do not exist to fully test such a complicated model structure or to test the hypotheses used to explain observations of substantial storage of very old SOM below the rooting depth. Nevertheless, we demonstrated that a reasonable combination of sorption parameters, microbial biomass and necromass dynamics, and advective transport can match observations without resorting to an arbitrary depth-dependent decline in SOM turnover rates, as is often done. We conclude that, contrary to assertions derived from existing turnover time based model formulations, observed carbon content and Δ14C vertical profiles are consistent with a representation of SOM consisting of carbon compounds with relatively fast reaction rates, vertical aqueous transport, and dynamic protection on mineral surfaces.

Effective stochastic generator with site-dependent interactions

NASA Astrophysics Data System (ADS)

Khamehchi, Masoumeh; Jafarpour, Farhad H.

2017-11-01

It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper, we investigate this possibility by considering systems of classical particles moving on a one-dimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process, or there can be many arbitrary particles at a single site in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of an unconditioned process can be local but site-dependent. As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above-mentioned constraints.

Formation of amorphous materials

DOEpatents

Johnson, William L.; Schwarz, Ricardo B.

1986-01-01

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

Multidimensional flamelet-generated manifolds for partially premixed combustion

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

Nguyen, Phuc-Danh; Vervisch, Luc; Subramanian, Vallinayagam

2010-01-15

Flamelet-generated manifolds have been restricted so far to premixed or diffusion flame archetypes, even though the resulting tables have been applied to nonpremixed and partially premixed flame simulations. By using a projection of the full set of mass conservation species balance equations into a restricted subset of the composition space, unsteady multidimensional flamelet governing equations are derived from first principles, under given hypotheses. During the projection, as in usual one-dimensional flamelets, the tangential strain rate of scalar isosurfaces is expressed in the form of the scalar dissipation rates of the control parameters of the multidimensional flamelet-generated manifold (MFM), which ismore » tested in its five-dimensional form for partially premixed combustion, with two composition space directions and three scalar dissipation rates. It is shown that strain-rate-induced effects can hardly be fully neglected in chemistry tabulation of partially premixed combustion, because of fluxes across iso-equivalence-ratio and iso-progress-of-reaction surfaces. This is illustrated by comparing the 5D flamelet-generated manifold with one-dimensional premixed flame and unsteady strained diffusion flame composition space trajectories. The formal links between the asymptotic behavior of MFM and stratified flame, weakly varying partially premixed front, triple-flame, premixed and nonpremixed edge flames are also evidenced. (author)« less

A Modified Consumer Inkjet for Spatiotemporal Control of Gene Expression

PubMed Central

Cohen, Daniel J.; Morfino, Roberto C.; Maharbiz, Michel M.

2009-01-01

This paper presents a low-cost inkjet dosing system capable of continuous, two-dimensional spatiotemporal regulation of gene expression via delivery of diffusible regulators to a custom-mounted gel culture of E. coli. A consumer-grade, inkjet printer was adapted for chemical printing; E. coli cultures were grown on 750 µm thick agar embedded in micro-wells machined into commercial compact discs. Spatio-temporal regulation of the lac operon was demonstrated via the printing of patterns of lactose and glucose directly into the cultures; X-Gal blue patterns were used for visual feedback. We demonstrate how the bistable nature of the lac operon's feedback, when perturbed by patterning lactose (inducer) and glucose (inhibitor), can lead to coordination of cell expression patterns across a field in ways that mimic motifs seen in developmental biology. Examples of this include sharp boundaries and the generation of traveling waves of mRNA expression. To our knowledge, this is the first demonstration of reaction-diffusion effects in the well-studied lac operon. A finite element reaction-diffusion model of the lac operon is also presented which predicts pattern formation with good fidelity. PMID:19763256

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.

CITRATE 1.0: Phytoplankton continuous trait-distribution model with one-dimensional physical transport applied to the North Pacific

NASA Astrophysics Data System (ADS)

Chen, Bingzhang; Smith, Sherwood Lan

2018-02-01

Diversity plays critical roles in ecosystem functioning, but it remains challenging to model phytoplankton diversity in order to better understand those roles and reproduce consistently observed diversity patterns in the ocean. In contrast to the typical approach of resolving distinct species or functional groups, we present a ContInuous TRAiT-basEd phytoplankton model (CITRATE) that focuses on macroscopic system properties such as total biomass, mean trait values, and trait variance. This phytoplankton component is embedded within a nitrogen-phytoplankton-zooplankton-detritus-iron model that itself is coupled with a simplified one-dimensional ocean model. Size is used as the master trait for phytoplankton. CITRATE also incorporates trait diffusion for sustaining diversity and simple representations of physiological acclimation, i.e., flexible chlorophyll-to-carbon and nitrogen-to-carbon ratios. We have implemented CITRATE at two contrasting stations in the North Pacific where several years of observational data are available. The model is driven by physical forcing including vertical eddy diffusivity imported from three-dimensional general ocean circulation models (GCMs). One common set of model parameters for the two stations is optimized using the Delayed-Rejection Adaptive Metropolis-Hasting Monte Carlo (DRAM) algorithm. The model faithfully reproduces most of the observed patterns and gives robust predictions on phytoplankton mean size and size diversity. CITRATE is suitable for applications in GCMs and constitutes a prototype upon which more sophisticated continuous trait-based models can be developed.

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

Hu, Shenyang; Joshi, Vineet; Lavender, Curt A.

Experiments showed that recrystallization dramatically speeds up the gas bubble swelling kinetics in metallic UMo fuels. In this work a recrystallization model is developed to study the effect of microstructures and radiation conditions on recrystallization kinetics. The model integrates the rate theory of intra-granular gas bubble and interstitial loop evolution and a phase field model of recrystallization zone evolution. A fast passage method is employed to describe one dimensional diffusion of interstitials which have diffusivity several order magnitude larger than that of the fission gas Xe. With the model, the effect of grain sizes on recrystallization kinetics is simulated.

Computational Examination of Orientation-Dependent Morphological Evolution during the Electrodeposition and Electrodissolution of Magnesium

DOE PAGES

DeWitt, S.; Hahn, N.; Zavadil, K.; ...

2015-12-30

Here a new model of electrodeposition and electrodissolution is developed and applied to the evolution of Mg deposits during anode cycling. The model captures Butler-Volmer kinetics, facet evolution, the spatially varying potential in the electrolyte, and the time-dependent electrolyte concentration. The model utilizes a diffuse interface approach, employing the phase field and smoothed boundary methods. Scanning electron microscope (SEM) images of magnesium deposited on a gold substrate show the formation of faceted deposits, often in the form of hexagonal prisms. Orientation-dependent reaction rate coefficients were parameterized using the experimental SEM images. Three-dimensional simulations of the growth of magnesium deposits yieldmore » deposit morphologies consistent with the experimental results. The simulations predict that the deposits become narrower and taller as the current density increases due to the depletion of the electrolyte concentration near the sides of the deposits. Increasing the distance between the deposits leads to increased depletion of the electrolyte surrounding the deposit. Two models relating the orientation-dependence of the deposition and dissolution reactions are presented. Finally, the morphology of the Mg deposit after one deposition-dissolution cycle is significantly different between the two orientation-dependence models, providing testable predictions that suggest the underlying physical mechanisms governing morphology evolution during deposition and dissolution.« less

Fractional Dynamics of Single File Diffusion in Dusty Plasma Ring

NASA Astrophysics Data System (ADS)

Muniandy, S. V.; Chew, W. X.; Asgari, H.; Wong, C. S.; Lim, S. C.

2011-11-01

Single file diffusion (SFD) refers to the constrained motion of particles in quasi-one-dimensional channel such that the particles are unable to pass each other. Possible SFD of charged dust confined in biharmonic annular potential well with screened Coulomb interaction is investigated. Transition from normal diffusion to anomalous sub-diffusion behaviors is observed. Deviation from SFD's mean square displacement scaling behavior of 1/2-exponent may occur in strongly interacting systems. A phenomenological model based on fractional Langevin equation is proposed to account for the anomalous SFD behavior in dusty plasma ring.

Large-scale Instability during Gravitational Collapse with Neutrino Transport and a Core-Collapse Supernova

NASA Astrophysics Data System (ADS)

Aksenov, A. G.; Chechetkin, V. M.

2018-04-01

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (≳10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented.

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 one-dimensional heat-transport model for conduit flow in karst aquifers

USGS Publications Warehouse

Long, Andrew J.; Gilcrease, P.C.

2009-01-01

A one-dimensional heat-transport model for conduit flow in karst aquifers is presented as an alternative to two or three-dimensional distributed-parameter models, which are data intensive and require knowledge of conduit locations. This model can be applied for cases where water temperature in a well or spring receives all or part of its water from a phreatic conduit. Heat transport in the conduit is simulated by using a physically-based heat-transport equation that accounts for inflow of diffuse flow from smaller openings and fissures in the surrounding aquifer during periods of low recharge. Additional diffuse flow that is within the zone of influence of the well or spring but has not interacted with the conduit is accounted for with a binary mixing equation to proportion these different water sources. The estimation of this proportion through inverse modeling is useful for the assessment of contaminant vulnerability and well-head or spring protection. The model was applied to 7 months of continuous temperature data for a sinking stream that recharges a conduit and a pumped well open to the Madison aquifer in western South Dakota. The simulated conduit-flow fraction to the well ranged from 2% to 31% of total flow, and simulated conduit velocity ranged from 44 to 353 m/d.

3D simulations of early blood vessel formation

NASA Astrophysics Data System (ADS)

Cavalli, F.; Gamba, A.; Naldi, G.; Semplice, M.; Valdembri, D.; Serini, G.

2007-08-01

Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two-dimensional experimental vasculogenesis has been recently proposed, showing the relevance of percolation concepts and of cell cross-talk (chemotactic autocrine loop) to the understanding of this self-aggregation process. Here we study the natural 3D extension of the computational model proposed earlier, which is relevant for the investigation of the genuinely three-dimensional process of vasculogenesis in vertebrate embryos. The computational model is based on a multidimensional Burgers equation coupled with a reaction diffusion equation for a chemotactic factor and a mass conservation law. The numerical approximation of the computational model is obtained by high order relaxed schemes. Space and time discretization are performed by using TVD schemes and, respectively, IMEX schemes. Due to the computational costs of realistic simulations, we have implemented the numerical algorithm on a cluster for parallel computation. Starting from initial conditions mimicking the experimentally observed ones, numerical simulations produce network-like structures qualitatively similar to those observed in the early stages of in vivo vasculogenesis. We develop the computation of critical percolative indices as a robust measure of the network geometry as a first step towards the comparison of computational and experimental data.

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.

Comparison of Mars Science Laboratory Reaction Control System Jet Computations With Flow Visualization and Velocimetry

NASA Technical Reports Server (NTRS)

Bathel, Brett F.; Danehy, Paul M.; Johansen, Craig T.; Ashcraft, Scott W.; Novak, Luke A.

2013-01-01

Numerical predictions of the Mars Science Laboratory reaction control system jets interacting with a Mach 10 hypersonic flow are compared to experimental nitric oxide planar laser-induced fluorescence data. The steady Reynolds Averaged Navier Stokes equations using the Baldwin-Barth one-equation turbulence model were solved using the OVERFLOW code. The experimental fluorescence data used for comparison consists of qualitative two-dimensional visualization images, qualitative reconstructed three-dimensional flow structures, and quantitative two-dimensional distributions of streamwise velocity. Through modeling of the fluorescence signal equation, computational flow images were produced and directly compared to the qualitative fluorescence data.

Molecular Dynamic Simulation of Water Vapor and Determination of Diffusion Characteristics in the Pore

NASA Astrophysics Data System (ADS)

Nikonov, Eduard G.; Pavluš, Miron; Popovičová, Mária

2018-02-01

One of the varieties of pores, often found in natural or artificial building materials, are the so-called blind pores of dead-end or saccate type. Three-dimensional model of such kind of pore has been developed in this work. This model has been used for simulation of water vapor interaction with individual pore by molecular dynamics in combination with the diffusion equation method. Special investigations have been done to find dependencies between thermostats implementations and conservation of thermodynamic and statistical values of water vapor - pore system. The two types of evolution of water - pore system have been investigated: drying and wetting of the pore. Full research of diffusion coefficient, diffusion velocity and other diffusion parameters has been made.

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.

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.

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

NASA Astrophysics Data System (ADS)

Naruemon, Rueangkham; Charin, Modchang

2016-04-01

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

Programmers manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

Schoellhamer, D.H.; Jobson, H.E.

1986-01-01

A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program codes. The Programmers Manual is intended for the model user who needs to modify code either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)

Effect of Wind Velocity on Flame Spread in Microgravity

NASA Technical Reports Server (NTRS)

Prasad, Kuldeep; Olson, Sandra L.; Nakamura, Yuji; Fujita, Osamu; Nishizawa, Katsuhiro; Ito, Kenichi; Kashiwagi, Takashi; Simons, Stephen N. (Technical Monitor)

2002-01-01

A three-dimensional, time-dependent model is developed describing ignition and subsequent transition to flame spread over a thermally thin cellulosic sheet heated by external radiation in a microgravity environment. A low Mach number approximation to the Navier Stokes equations with global reaction rate equations describing combustion in the gas phase and the condensed phase is numerically solved. The effects of a slow external wind (1-20 cm/s) on flame transition are studied in an atmosphere of 35% oxygen concentration. The ignition is initiated at the center part of the sample by generating a line-shape flame along the width of the sample. The calculated results are compared with data obtained in the 10s drop tower. Numerical results exhibit flame quenching at a wind speed of 1.0 cm/s, two localized flames propagating upstream along the sample edges at 1.5 cm/s, a single line-shape flame front at 5.0 cm/s, three flames structure observed at 10.0 cm/s (consisting of a single line-shape flame propagating upstream and two localized flames propagating downstream along sample edges) and followed by two line-shape flames (one propagating upstream and another propagating downstream) at 20.0 cm/s. These observations qualitatively compare with experimental data. Three-dimensional visualization of the observed flame complex, fuel concentration contours, oxygen and reaction rate isosurfaces, convective and diffusive mass flux are used to obtain a detailed understanding of the controlling mechanism, Physical arguments based on lateral diffusive flux of oxygen, fuel depletion, oxygen shadow of the flame and heat release rate are constructed to explain the various observed flame shapes.

Generalized minimal principle for rotor filaments.

PubMed

Dierckx, Hans; Wellner, Marcel; Bernus, Olivier; Verschelde, Henri

2015-05-01

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.

Validation of a numerical method for interface-resolving simulation of multicomponent gas-liquid mass transfer and evaluation of multicomponent diffusion models

NASA Astrophysics Data System (ADS)

Woo, Mino; Wörner, Martin; Tischer, Steffen; Deutschmann, Olaf

2018-03-01

The multicomponent model and the effective diffusivity model are well established diffusion models for numerical simulation of single-phase flows consisting of several components but are seldom used for two-phase flows so far. In this paper, a specific numerical model for interfacial mass transfer by means of a continuous single-field concentration formulation is combined with the multicomponent model and effective diffusivity model and is validated for multicomponent mass transfer. For this purpose, several test cases for one-dimensional physical or reactive mass transfer of ternary mixtures are considered. The numerical results are compared with analytical or numerical solutions of the Maxell-Stefan equations and/or experimental data. The composition-dependent elements of the diffusivity matrix of the multicomponent and effective diffusivity model are found to substantially differ for non-dilute conditions. The species mole fraction or concentration profiles computed with both diffusion models are, however, for all test cases very similar and in good agreement with the analytical/numerical solutions or measurements. For practical computations, the effective diffusivity model is recommended due to its simplicity and lower computational costs.

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.

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

NASA Astrophysics Data System (ADS)

Gonzalez, M.

2018-04-01

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane

PubMed Central

Kalay, Ziya; Fujiwara, Takahiro K.; Kusumi, Akihiro

2012-01-01

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity. PMID:22479350

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.

Numerical Modelling and Simulation of Chemical Reactions in a Nano-Pulse Discharged Bubble for Water Treatment

NASA Astrophysics Data System (ADS)

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

2016-09-01

A zero-dimensional model to simulate a nano-pulse-discharged bubble in water was developed. The model consists of gas and liquid phases corresponding to the inside and outside of the bubble, respectively. The diffusions of chemical species from the gas to the liquid phase through the bubble interface was also investigated. The initial gas is Ar, but includes a little H2O and O2 in the bubble. The time evolution of the OH concentration in the liquid phase was mainly investigated as an important species for water treatment. It was shown that OH was generated in the bubble and then diffused into the liquid. With the application of a continuous nano-pulse discharge, more OH radicals were generated as the frequency increased at a low voltage for a given power consumption. supported partially by Japan Society for the Promotion of Science (JSPS) KAKENHI (No. 26249015)

Note: On the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient

NASA Astrophysics Data System (ADS)

Kalnin, Juris R.; Berezhkovskii, Alexander M.

2013-11-01

The Lifson-Jackson formula provides the effective free diffusion coefficient for a particle diffusing in an arbitrary one-dimensional periodic potential. Its counterpart, when the underlying dynamics is described in terms of an unbiased nearest-neighbor Markovian random walk on a one-dimensional periodic lattice is given by the formula obtained by Derrida. It is shown that the latter formula can be considered as a discretized version of the Lifson-Jackson formula with correctly chosen position-dependent diffusion coefficient.

Transient and diffusion analysis of HgCdTe

NASA Technical Reports Server (NTRS)

Clayton, J. C.

1982-01-01

Solute redistribution during directional solidification of HgCdTe is addressed. Both one-dimensional and two-dimensional models for solute redistribution are treated and model results compared to experiment. The central problem studied is the cause of radial inhomogeneities found in directionally solidified HgCdTe. A large scale gravity-driven interface instability, termed shape instability, is postulated to be the cause of radial inhomogeneities. Recommendations for future work, along with appropriate computer programs, are included.

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

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

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

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz-Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.

One-dimensional biomass fast pyrolysis model with reaction kinetics integrated in an Aspen Plus Biorefinery Process Model

DOE PAGES

Humbird, David; Trendewicz, Anna; Braun, Robert; ...

2017-01-12

A biomass fast pyrolysis reactor model with detailed reaction kinetics and one-dimensional fluid dynamics was implemented in an equation-oriented modeling environment (Aspen Custom Modeler). Portions of this work were detailed in previous publications; further modifications have been made here to improve stability and reduce execution time of the model to make it compatible for use in large process flowsheets. The detailed reactor model was integrated into a larger process simulation in Aspen Plus and was stable for different feedstocks over a range of reactor temperatures. Sample results are presented that indicate general agreement with experimental results, but with higher gasmore » losses caused by stripping of the bio-oil by the fluidizing gas in the simulated absorber/condenser. Lastly, this integrated modeling approach can be extended to other well-defined, predictive reactor models for fast pyrolysis, catalytic fast pyrolysis, as well as other processes.« less

One-dimensional biomass fast pyrolysis model with reaction kinetics integrated in an Aspen Plus Biorefinery Process Model

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

Humbird, David; Trendewicz, Anna; Braun, Robert

A biomass fast pyrolysis reactor model with detailed reaction kinetics and one-dimensional fluid dynamics was implemented in an equation-oriented modeling environment (Aspen Custom Modeler). Portions of this work were detailed in previous publications; further modifications have been made here to improve stability and reduce execution time of the model to make it compatible for use in large process flowsheets. The detailed reactor model was integrated into a larger process simulation in Aspen Plus and was stable for different feedstocks over a range of reactor temperatures. Sample results are presented that indicate general agreement with experimental results, but with higher gasmore » losses caused by stripping of the bio-oil by the fluidizing gas in the simulated absorber/condenser. Lastly, this integrated modeling approach can be extended to other well-defined, predictive reactor models for fast pyrolysis, catalytic fast pyrolysis, as well as other processes.« 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.

Diffusion-controlled formation and collapse of a d-dimensional A-particle island in the B-particle sea.

PubMed

Shipilevsky, Boris M

2017-06-01

We consider diffusion-controlled evolution of a d-dimensional A-particle island in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. The A-particle island is formed by a localized (point) A-source with a strength λ that acts for a finite time T. We reveal the conditions under which the island collapse time t_{c} becomes much longer than the injection period T (long-living island) and demonstrate that regardless of d the evolution of the long-living island radius r_{f}(t) is described by the universal law ζ_{f}=r_{f}/r_{f}^{M}=sqrt[eτ|lnτ|], where τ=t/t_{c} and r_{f}^{M} is the maximal island expansion radius at the front turning point t_{M}=t_{c}/e. We find that in the long-living island regime the ratio t_{c}/T changes with the increase of the injection period T by the law ∝(λ^{2}T^{2-d})^{1/d}, i.e., increases with the increase of T in the one-dimensional (1D) case, does not change with the increase of T in the 2D case and decreases with the increase of T in the 3D case. We derive the scaling laws for particles death in the long-living island and determine the limits of their applicability. We demonstrate also that these laws describe asymptotically the evolution of the d-dimensional spherical island with a uniform initial particle distribution generalizing the results obtained earlier for the quasi-one-dimensional geometry. As striking results, we present a systematic analysis of the front relative width evolution for fluctuation, logarithmically modified, and mean-field regimes, and we demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the collapse point.

A theoretical model describing the one-dimensional growth of single crystals on free sustained substrates

NASA Astrophysics Data System (ADS)

Ye, Ziran; Wang, Ke; Lu, Chenxi; Jin, Ying; Sui, Chenghua; Yan, Bo; Gao, Fan; Cai, Pinggen; Lv, Bin; Li, Yun; Chen, Naibo; Sun, Guofang; Xu, Fengyun; Ye, Gaoxiang

2018-03-01

We develop a theoretical model that interprets the growth mechanism of zinc (Zn) crystal nanorods on a liquid substrate by thermal evaporation. During deposition, Zn atoms diffuse randomly on an isotropic and quasi-free sustained substrate, the nucleation of the atoms results in the primary nanorod (or seed crystal) growth. Subsequently, a characteristic one-dimensional atomic aggregation is proposed, which leads to the accelerating growth of the crystal nanorod along its preferential growth direction until the growth terminates. The theoretical results are in good agreement with the experimental findings.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Direct reconstruction in CT-analogous pharmacokinetic diffuse fluorescence tomography: two-dimensional simulative and experimental validations

NASA Astrophysics Data System (ADS)

Wang, Xin; Zhang, Yanqi; Zhang, Limin; Li, Jiao; Zhou, Zhongxing; Zhao, Huijuan; Gao, Feng

2016-04-01

We present a generalized strategy for direct reconstruction in pharmacokinetic diffuse fluorescence tomography (DFT) with CT-analogous scanning mode, which can accomplish one-step reconstruction of the indocyanine-green pharmacokinetic-rate images within in vivo small animals by incorporating the compartmental kinetic model into an adaptive extended Kalman filtering scheme and using an instantaneous sampling dataset. This scheme, compared with the established indirect and direct methods, eliminates the interim error of the DFT inversion and relaxes the expensive requirement of the instrument for obtaining highly time-resolved date-sets of complete 360 deg projections. The scheme is validated by two-dimensional simulations for the two-compartment model and pilot phantom experiments for the one-compartment model, suggesting that the proposed method can estimate the compartmental concentrations and the pharmacokinetic-rates simultaneously with a fair quantitative and localization accuracy, and is well suitable for cost-effective and dense-sampling instrumentation based on the highly-sensitive photon counting technique.

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

NASA Astrophysics Data System (ADS)

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

1999-06-01

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

Parameterization of large-scale turbulent diffusion in the presence of both well-mixed and weakly mixed patchy layers

NASA Astrophysics Data System (ADS)

Osman, M. K.; Hocking, W. K.; Tarasick, D. W.

2016-06-01

Vertical diffusion and mixing of tracers in the upper troposphere and lower stratosphere (UTLS) are not uniform, but primarily occur due to patches of turbulence that are intermittent in time and space. The effective diffusivity of regions of patchy turbulence is related to statistical parameters describing the morphology of turbulent events, such as lifetime, number, width, depth and local diffusivity (i.e., diffusivity within the turbulent patch) of the patches. While this has been recognized in the literature, the primary focus has been on well-mixed layers, with few exceptions. In such cases the local diffusivity is irrelevant, but this is not true for weakly and partially mixed layers. Here, we use both theory and numerical simulations to consider the impact of intermediate and weakly mixed layers, in addition to well-mixed layers. Previous approaches have considered only one dimension (vertical), and only a small number of layers (often one at each time step), and have examined mixing of constituents. We consider a two-dimensional case, with multiple layers (10 and more, up to hundreds and even thousands), having well-defined, non-infinite, lengths and depths. We then provide new formulas to describe cases involving well-mixed layers which supersede earlier expressions. In addition, we look in detail at layers that are not well mixed, and, as an interesting variation on previous models, our procedure is based on tracking the dispersion of individual particles, which is quite different to the earlier approaches which looked at mixing of constituents. We develop an expression which allows determination of the degree of mixing, and show that layers used in some previous models were in fact not well mixed and so produced erroneous results. We then develop a generalized model based on two dimensional random-walk theory employing Rayleigh distributions which allows us to develop a universal formula for diffusion rates for multiple two-dimensional layers with general degrees of mixing. We show that it is the largest, most vigorous and less common turbulent layers that make the major contribution to global diffusion. Finally, we make estimates of global-scale diffusion coefficients in the lower stratosphere and upper troposphere. For the lower stratosphere, κeff ≈ 2x10-2 m2 s-1, assuming no other processes contribute to large-scale diffusion.

Cool-Flame Burning and Oscillations of Envelope Diffusion Flames in Microgravity

NASA Astrophysics Data System (ADS)

Takahashi, Fumiaki; Katta, Viswanath R.; Hicks, Michael C.

2018-05-01

The two-stage combustion, local extinction, and flame-edge oscillations have been observed in single-droplet combustion tests conducted on the International Space Station. To understand such dynamic behavior of initially enveloped diffusion flames in microgravity, two-dimensional (axisymmetric) computation is performed for a gaseous n-heptane flame using a time-dependent code with a detailed reaction mechanism (127 species and 1130 reactions), diffusive transport, and a simple radiation model (for CO2, H2O, CO, CH4, and soot). The calculated combustion characteristics vary profoundly with a slight movement of air surrounding a fuel source. In a near-quiescent environment (≤ 2 mm/s), with a sufficiently large fuel injection velocity (1 cm/s), extinction of a growing spherical diffusion flame due to radiative heat losses is predicted at the flame temperature at ≈ 1200 K. The radiative extinction is typically followed by a transition to the "cool flame" burning regime (due to the negative temperature coefficient in the low-temperature chemistry) with a reaction zone (at ≈ 700 K) in close proximity to the fuel source. By contrast, if there is a slight relative velocity (≈ 3 mm/s) between the fuel source and the air, a local extinction of the envelope diffusion flame is predicted downstream at ≈ 1200 K, followed by periodic flame-edge oscillations. At higher relative velocities (4 to 10 mm/s), the locally extinguished flame becomes steady state. The present 2D computational approach can help in understanding further the non-premixed "cool flame" structure and flame-flow interactions in microgravity environments.

Revised users manual, Pulverized Coal Gasification or Combustion: 2-dimensional (87-PCGC-2): Final report, Volume 2. [87-PCGC-2

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

Smith, P.J.; Smoot, L.D.; Brewster, B.S.

1987-12-01

A two-dimensional, steady-state model for describing a variety of reactive and non-reactive flows, including pulverized coal combustion and gasification, is presented. Recent code revisions and additions are described. The model, referred to as 87-PCGC-2, is applicable to cylindrical axi-symmetric systems. Turbulence is accounted for in both the fluid mechanics equations and the combustion scheme. Radiation from gases, walls, and particles is taken into account using either a flux method or discrete ordinates method. The particle phase is modeled in a Lagrangian framework, such that mean paths of particle groups are followed. Several multi-step coal devolatilization schemes are included along withmore » a heterogeneous reaction scheme that allows for both diffusion and chemical reaction. Major gas-phase reactions are modeled assuming local instantaneous equilibrium, and thus the reaction rates are limited by the turbulent rate mixing. A NO/sub x/ finite rate chemistry submodel is included which integrates chemical kinetics and the statistics of the turbulence. The gas phase is described by elliptic partial differential equations that are solved by an iterative line-by-line technique. Under-relaxation is used to achieve numerical stability. The generalized nature of the model allows for calculation of isothermal fluid mechanicsgaseous combustion, droplet combustion, particulate combustion and various mixtures of the above, including combustion of coal-water and coal-oil slurries. Both combustion and gasification environments are permissible. User information and theory are presented, along with sample problems. 106 refs.« less

Numerical study of chemically reacting viscous flow relevant to pulsed detonation engines

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong

2005-11-01

A computational fluid dynamics code for two-dimensional, multi-species, laminar Navier-Stokes equations is developed to simulate a recently proposed engine concept for a pulsed detonation based propulsion system and to investigate the feasibility of the engine of the concept. The governing equations that include transport phenomena such as viscosity, thermal conduction and diffusion are coupled with chemical reactions. The gas is assumed to be thermally perfect and in chemically non-equilibrium. The stiffness due to coupling the fluid dynamics and the chemical kinetics is properly taken care of by using a time-operator splitting method and a variable coefficient ordinary differential equation solver. A second-order Roe scheme with a minmod limiter is explicitly used for space descretization, while a second-order, two-step Runge-Kutta method is used for time descretization. In space integration, a finite volume method and a cell-centered scheme are employed. The first-order derivatives in the equations of transport properties are discretized by a central differencing with Green's theorem. Detailed chemistry is involved in this study. Two chemical reaction mechanisms are extracted from GRI-Mech, which are forty elementary reactions with thirteen species for a hydrogen-air mixture and twenty-seven reactions with eight species for a hydrogen-oxygen mixture. The code is ported to a high-performance parallel machine with Message-Passing Interface. Code validation is performed with chemical kinetic modeling for a stoichiometric hydrogen-air mixture, an one-dimensional detonation tube, a two-dimensional, inviscid flow over a wedge and a viscous flow over a flat plate. Detonation is initiated using a numerically simulated arc-ignition or shock-induced ignition system. Various freestream conditions are utilized to study the propagation of the detonation in the proposed concept of the engine. Investigation of the detonation propagation is performed for a pulsed detonation rocket and a supersonic combustion chamber. For a pulsed detonation rocket case, the detonation tube is embedded in a mixing chamber where an initiator is added to the main detonation chamber. Propagating detonation waves in a supersonic combustion chamber is investigated for one- and two-dimensional cases. The detonation initiated by an arc and a shock wave is studied in the inviscid and viscous flow, respectively. Various features including a detonation-shock interaction, a detonation diffraction, a base flow and a vortex are observed.

Controlling three-dimensional vortices using multiple and moving external fields

NASA Astrophysics Data System (ADS)

Das, Nirmali Prabha; Dutta, Sumana

2017-08-01

Spirals or scroll wave activities in cardiac tissues are the cause of lethal arrhythmias. The external control of these waves is thus of prime interest to scientists and physicians. In this article, we demonstrate the spatial control of scroll waves by using external electric fields and thermal gradients in experiments with the Belousov-Zhabotinsky reaction. We show that a scroll ring can be made to trace cyclic trajectories under a rotating electric field. Application of a thermal gradient in addition to the electric field deflects the motion and changes the nature of the trajectory. Our experimental results are analyzed and corroborated by numerical simulations based on an excitable reaction diffusion model.

Numerical study of transient evolution of lifted jet flames: partially premixed flame propagation and influence of physical dimensions

NASA Astrophysics Data System (ADS)

Chen, Zhi; Ruan, Shaohong; Swaminathan, Nedunchezhian

2016-07-01

Three-dimensional (3D) unsteady Reynolds-averaged Navier-Stokes simulations of a spark-ignited turbulent methane/air jet flame evolving from ignition to stabilisation are conducted for different jet velocities. A partially premixed combustion model is used involving a correlated joint probability density function and both premixed and non-premixed combustion mode contributions. The 3D simulation results for the temporal evolution of the flame's leading edge are compared with previous two-dimensional (2D) results and experimental data. The comparison shows that the final stabilised flame lift-off height is well predicted by both 2D and 3D computations. However, the transient evolution of the flame's leading edge computed from 3D simulation agrees reasonably well with experiment, whereas evident discrepancies were found in the previous 2D study. This difference suggests that the third physical dimension plays an important role during the flame transient evolution process. The flame brush's leading edge displacement speed resulting from reaction, normal and tangential diffusion processes are studied at different typical stages after ignition in order to understand the effect of the third physical dimension further. Substantial differences are found for the reaction and normal diffusion components between 2D and 3D simulations especially in the initial propagation stage. The evolution of reaction progress variable scalar gradients and its interaction with the flow and mixing field in the 3D physical space have an important effect on the flame's leading edge propagation.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Micro/nanofabricated environments for synthetic biology.

PubMed

Collier, C Patrick; Simpson, Michael L

2011-08-01

A better understanding of how confinement, crowding and reduced dimensionality modulate reactivity and reaction dynamics will aid in the rational and systematic discovery of functionality in complex biological systems. Artificial microfabricated and nanofabricated structures have helped elucidate the effects of nanoscale spatial confinement and segregation on biological behavior, particularly when integrated with microfluidics, through precise control in both space and time of diffusible signals and binding interactions. Examples of nanostructured interfaces for synthetic biology include the development of cell-like compartments for encapsulating biochemical reactions, nanostructured environments for fundamental studies of diffusion, molecular transport and biochemical reaction kinetics, and regulation of biomolecular interactions as functions of microfabricated and nanofabricated topological constraints. Copyright © 2011 Elsevier Ltd. All rights reserved.

Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning.

PubMed

Bello-Rivas, Juan M; Elber, Ron

2016-03-05

We investigated by computational means the kinetics and stationary behavior of stochastic dynamics on an ensemble of rough two-dimensional energy landscapes. There are no obvious separations of temporal scales in these systems, which constitute a simple model for the behavior of glasses and some biomaterials. Even though there are significant computational challenges present in these systems due to the large number of metastable states, the Milestoning method is able to compute their kinetic and thermodynamic properties exactly. We observe two clearly distinguished regimes in the overall kinetics: one in which diffusive behavior dominates and another that follows an Arrhenius law (despite the absence of a dominant barrier). We compare our results with those obtained with an exactly-solvable one-dimensional model, and with the results from the rough one-dimensional energy model introduced by Zwanzig. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

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)).

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.

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

Numerical investigation of the influence of electromagnetic treatment on calcium carbonate scaling rate in non-isothermal pipe flow

NASA Astrophysics Data System (ADS)

Kireev, Victor; Kovaleva, Liana; Isakov, Andrey; Alimbekova, Sofya

2017-11-01

In the present paper, an attempt to explain the mechanisms of the electromagnetic field influence on the process of formation and deposition of calcium carbonate from supersaturated brine solution has been made using numerical modeling. The one-dimensional mathematical model of the brine laminar flow through a cylindrical tube with non-uniform temperature field is written in the form of the system of transient convection-diffusion-reaction partial differential equations describing temperature field and chemical components concentrations (Ca2+, HCO3-, CaCO3). The influence of the temperature on the kinetics of formation of calcium carbonate is taken into account and it is described in accordance with the Arrhenius equation. The kinetics of the calcium carbonate precipitation on the wall of the pipe is given on the basis of the Henry isotherm. It has been established that the electromagnetic treatment of brine solution leads to a decrease of the adsorption rate constant and Henry's constant but it does not significantly influence on the chemical reaction rate of calcium carbonate formation. It also has been shown that treatment with electromagnetic field significantly reduces the amount of calcium carbonate deposits on the wall of the pipe.

Numerical modeling of pulsed laser-material interaction and of laser plume dynamics

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

Zhao, Qiang; Shi, Yina

2015-03-10

We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. A new second order accurate diffusion solver has been implemented for the thermal conduction and radiation transport on distorted mesh. The results of numerical simulation of pulsed laser ablation are presented. The influences of different processes, such as time evolution of the surfacemore » temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas are examined. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.« less

Subsurface characterization of methane production and oxidation from a New Hampshire wetland.

PubMed

Shoemaker, J K; Schrag, D P

2010-06-01

We measured the carbon isotopic composition of pore water carbon dioxide from Sallie's Fen, a New Hampshire poor fen. The isotope profiles are used in combination with a one-dimensional diffusion-reaction model to calculate rates of methane production, oxidation and transport over an annual cycle. We show how the rates vary with depth over a seasonal cycle, with methane produced deeper during the winter months and at progressively shallower depths into the summer season. The rates of methane production, constrained by the measured delta(13)C(dic) profiles, cannot explain high methane emission during the summer. We suggest that much of the methane produced during this time comes either from the unsaturated peat, or from the top 1-3 cm of saturated peat where episodic exchange with the atmosphere makes it invisible to our method.

Front propagation in one-dimensional spatially periodic bistable media

NASA Astrophysics Data System (ADS)

Löber, Jakob; Bär, Markus; Engel, Harald

2012-12-01

Front propagation in heterogeneous bistable media is studied using the Schlögl model as a representative example. Spatially periodic modulations in the parameters of the bistable kinetics are taken into account perturbatively. Depending on the ratio L/l (L is the spatial period of the heterogeneity, l is the front width), appropriate singular perturbation techniques are applied to derive an ordinary differential equation for the position of the front in the presence of the heterogeneities. From this equation, the dependence of the average propagation speed on L/l as well as on the modulation amplitude is calculated. The analytical results obtained predict velocity overshoot, different cases of propagation failure, and the propagation speed for very large spatial periods in quantitative agreement with the results of direct numerical simulations of the underlying reaction-diffusion equation.

Bistable flow occurrence in the 2D model of a steam turbine valve

NASA Astrophysics Data System (ADS)

Pavel, Procházka; Václav, Uruba

2017-09-01

The internal flow inside a steam turbine valve was investigated experimentally using PIV measurement. The valve model was proposed to be two-dimensional. The model was connected to the blow-down wind tunnel. The flow conditions were set by the different position of the valve plug. Several angles of the diffuser by diverse radii were investigated concerning flow separation and flow dynamics. It was found that the flow takes one of two possible bistable modes. The first regime is characterized by a massive flow separation just at the beginning of the diffuser section on the one side. The second regime is axisymmetric and the flow separation is not detected at all.

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Modeling of chemical vapor infiltration for ceramic composites reinforced with layered, woven fabrics

NASA Technical Reports Server (NTRS)

Chung, Gui-Yung; Mccoy, Benjamin J.

1991-01-01

A homogeneous model is developed for the chemical vapor infiltration by one-dimensional diffusion into a system of layered plies consisting of woven tows containing bundles of filaments. The model predictions of the amount of deposition and the porosity of the sample as a function of time are compared with the predictions of a recent nonhomogeneous model with aligned holes formed by the weave. The nonhomogeneous model allows for diffusion through the aligned holes, into the spaces between plies, and into the gaps around filaments; i.e., three diffusion equations apply. Relative to the nonhomogeneous results, the homogeneous model underestimates the amount of deposition, since the absence of holes and spaces allows earlier occlusion of gaps around filaments and restricts the vapor infiltration.

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Importance of Low Dimensional CeO x Nanostructures in Pt/CeO x –TiO 2 Catalysts for the Water–Gas Shift Reaction

DOE PAGES

Luo, Si; Barrio, Laura; Nguyen-Phan, Thuy-Duong; ...

2017-03-15

CO 2 and H 2 production from the water–gas shift (WGS) reaction was studied over Pt/CeO x–TiO 2 catalysts with incremental loadings of CeO x, which adopts variations in the local morphology. The lowest loading of CeO x (1 wt % to 0.5 at. %) that is configured in its smallest dimensions exhibited the best WGS activity over larger dimensional structures. We attribute this to several factors including the ultrafine dispersed one-dimensional nanocluster geometry, a large concentration of Ce 3+ and enhanced reducibility of the low loadings. We utilized several in situ experiments to monitor the active state of themore » catalyst during the WGS reaction. X-ray diffraction (XRD) results showed lattice expansion that indicated reduced ceria was prevalent during the WGS reaction. On the surface, Ce 3+ related hydroxyl groups were identified by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). The enhanced reducibility of the catalyst with the introduction of ceria was further revealed by H 2-temperature programed reduction (H 2-TPR) and good thermal stability was confirmed by in situ environmental transmission electron microscopy (ETEM). Finally, we also investigated the formation of the low dimensional structures during catalyst preparation, through a two-stage crystal growth of ceria crystallite on TiO 2 nanoparticle: fine crystallites ~1D formed at ~250 °C, followed by crystal growth into 2D chain and 3D particle from 250–400 °C.« less

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

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.

An Examination of the Evolution of Radiation and Advection Fogs

DTIC Science & Technology

1993-01-01

and fog diagnostic and prediction models have developed in sophistication so that they can reproduce fairly accurate one- or two-dimensional...occurred only by molecular diffusion near the interface created between the species during the mixing process. The rate of homogenization is minimal until...of excess vapor by molecular diffusion at the interfaces of nearly saturated air mixing in eddies is faster than the relaxation time of droplet

Tailorable Exciton Transport in Doped Peptide–Amphiphile Assemblies

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

Solomon, Lee A.; Sykes, Matthew E.; Wu, Yimin A.

Light-harvesting biomaterials are an attractive target in photovoltaics, photocatalysis, and artificial photosynthesis. Through peptide self-assembly, complex nanostructures can be engineered to study the role of chromophore organization during light absorption and energy transport. To this end, we demonstrate the one-dimensional transport of excitons along naturally occurring, light-harvesting, Zn-protoporphyrin IX chromophores within self-assembled peptide-amphiphile nanofibers. The internal structure of the nanofibers induces packing of the porphyrins into linear chains. We find that this peptide assembly can enable long-range exciton diffusion, yet it also induces the formation of excimers between adjacent molecules, which serve as exciton traps. Electronic coupling between neighboring porphyrinmore » molecules is confirmed by various spectroscopic methods. The exciton diffusion process is then probed through transient photoluminescence and absorption measurements and fit to a model for one-dimensional hopping. Because excimer formation impedes exciton hopping, increasing the interchromophore spacing allows for improved diffusivity, which we control through porphyrin doping levels. We show that diffusion lengths of over 60 nm are possible at low porphyrin doping, representing an order of magnitude improvement over the highest doping fractions.« less

Tailorable Exciton Transport in Doped Peptide-Amphiphile Assemblies.

PubMed

Solomon, Lee A; Sykes, Matthew E; Wu, Yimin A; Schaller, Richard D; Wiederrecht, Gary P; Fry, H Christopher

2017-09-26

Light-harvesting biomaterials are an attractive target in photovoltaics, photocatalysis, and artificial photosynthesis. Through peptide self-assembly, complex nanostructures can be engineered to study the role of chromophore organization during light absorption and energy transport. To this end, we demonstrate the one-dimensional transport of excitons along naturally occurring, light-harvesting, Zn-protoporphyrin IX chromophores within self-assembled peptide-amphiphile nanofibers. The internal structure of the nanofibers induces packing of the porphyrins into linear chains. We find that this peptide assembly can enable long-range exciton diffusion, yet it also induces the formation of excimers between adjacent molecules, which serve as exciton traps. Electronic coupling between neighboring porphyrin molecules is confirmed by various spectroscopic methods. The exciton diffusion process is then probed through transient photoluminescence and absorption measurements and fit to a model for one-dimensional hopping. Because excimer formation impedes exciton hopping, increasing the interchromophore spacing allows for improved diffusivity, which we control through porphyrin doping levels. We show that diffusion lengths of over 60 nm are possible at low porphyrin doping, representing an order of magnitude improvement over the highest doping fractions.

Bioturbation, advection, and diffusion of a conserved tracer in a laboratory flume

NASA Astrophysics Data System (ADS)

Work, P. A.; Moore, P. R.; Reible, D. D.

2002-06-01

Laboratory experiments indicating the relative influences of advection, diffusion, and bioturbation on transport of NaCl tracer between a stream and streambed are described. Data were collected in a recirculating flume housing a box filled with test sediments. Peclet numbers ranged from 0 to 1.5. Sediment components included a medium sand (d50 = 0.31 mm), kaolinite, and topsoil. Lumbriculus variegatus were introduced as bioturbators. Conductivity probes were employed to document the flux of the tracer solution out of the bed. Measurements are compared to one-dimensional effective diffusion models assuming one or two horizontal sediment layers. These simple models provide a good indication of tracer half-life in the bed if a suitable effective diffusion coefficient is chosen but underpredict initial flux and overpredict flux at long times. Organism activity was limited to the upper reaches of the sediment test box but eventually exerts a secondary influence on flux from deeper regions.

Modeling hexavalent chromium reduction in groundwater in field-scale transport and laboratory batch experiments

USGS Publications Warehouse

Friedly, J.C.; Davis, J.A.; Kent, D.B.

1995-01-01

A plausible and consistent model is developed to obtain a quantitative description of the gradual disappearance of hexavalent chromium (Cr(VI)) from groundwater in a small-scale field tracer test and in batch kinetic experiments using aquifer sediments under similar chemical conditions. The data exhibit three distinct timescales. Fast reduction occurs in well-stirred batch reactors in times much less than 1 hour and is followed by slow reduction over a timescale of the order of 2 days. In the field, reduction occurs on a timescale of the order of 8 days. The model is based on the following hypotheses. The chemical reduction reaction occurs very fast, and the longer timescales are caused by diffusion resistance. Diffusion into the secondary porosity of grains causes the apparent slow reduction rate in batch experiments. In the model of the field experiments, the reducing agent, heavy Fe(II)-bearing minerals, is heterogeneously distributed in thin strata located between larger nonreducing sand lenses that comprise the bulk of the aquifer solids. It is found that reducing strata of the order of centimeters thick are sufficient to contribute enough diffusion resistance to cause the observed longest timescale in the field. A one-dimensional advection/dispersion model is formulated that describes the major experimental trends. Diffusion rates are estimated in terms of an elementary physical picture of flow through a stratified medium containing identically sized spherical grains. Both reduction and sorption reactions are included. Batch simulation results are sensitive to the fraction of reductant located at or near the surface of grains, which controls the amount of rapid reduction, and the secondary porosity, which controls the rate of slow reduction observed in batch experiments. Results of Cr(VI) transport simulations are sensitive to the thickness and relative size of the reducing stratum. Transport simulation results suggest that nearly all of the reductant must be located in the reducing stratum. Within this context and as long as there is adequate reductive capacity present, the transport simulation results are insensitive to the parameters important for the batch simulations. The results illustrate how a combination of field measurements and batch laboratory studies can be used to improve predictive modeling of contaminant transport.

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.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

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

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.

Numerical investigation of the spatiotemporal distribution of chemical species in an atmospheric surface barrier-discharge

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

Hasan, M. I.; Walsh, J. L., E-mail: jlwalsh@liverpool.ac.uk

Using a one dimensional time dependent convection-reaction-diffusion model, the temporal and spatial distributions of species propagating downstream of an atmospheric pressure air surface barrier discharge was studied. It was found that the distribution of negatively charged species is more spatially spread compared to positive ions species, which is attributed to the diffusion of electrons that cool down and attach to background gas molecules, creating different negative ions downstream of the discharge region. Given the widespread use of such discharges in applications involving the remote microbial decontamination of surfaces and liquids, the transport of plasma generated reactive species away from themore » discharge region was studied by implementing mechanical convection through the discharge region. It was shown that increased convection causes the spatial distribution of species density to become uniform. It was also found that many species have a lower density close to the surface of the discharge as convection prevents their accumulation. While for some species, such as NO{sub 2}, convection causes a general increase in the density due to a reduced residence time close to the discharge region, where it is rapidly lost through reactions with OH. The impact of the applied power was also investigated, and it was found that the densities of most species, whether charged or neutral, are directly proportional to the applied power.« less

Scroll wave filaments self-wrap around unexcitable heterogeneities.

PubMed

Jiménez, Zulma A; Steinbock, Oliver

2012-09-01

Scroll waves are three-dimensional excitation vortices rotating around one-dimensional phase singularities called filaments. In experiments with a chemical reaction-diffusion system and in numerical simulations, we study the pinning of closed filament loops to inert cylindrical heterogeneities. We show that the filament wraps itself around the heterogeneity and thus avoids contraction and annihilation. This entwining steadily increases the total length of the pinned filament and reshapes the entire rotation backbone of the vortex. Self-pinning is fastest for thin cylinders with radii not much larger than the core of the unpinned rotor. The process ends when the filament is attached to the entire length of the cylinder. The possible importance of self-pinning in cardiac systems is discussed.

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

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

Samin, Adib J.

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

NASA Astrophysics Data System (ADS)

Samin, Adib J.

2016-05-01

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.

Active colloidal propulsion over a crystalline surface

NASA Astrophysics Data System (ADS)

Choudhury, Udit; Straube, Arthur V.; Fischer, Peer; Gibbs, John G.; Höfling, Felix

2017-12-01

We study both experimentally and theoretically the dynamics of chemically self-propelled Janus colloids moving atop a two-dimensional crystalline surface. The surface is a hexagonally close-packed monolayer of colloidal particles of the same size as the mobile one. The dynamics of the self-propelled colloid reflects the competition between hindered diffusion due to the periodic surface and enhanced diffusion due to active motion. Which contribution dominates depends on the propulsion strength, which can be systematically tuned by changing the concentration of a chemical fuel. The mean-square displacements (MSDs) obtained from the experiment exhibit enhanced diffusion at long lag times. Our experimental data are consistent with a Langevin model for the effectively two-dimensional translational motion of an active Brownian particle in a periodic potential, combining the confining effects of gravity and the crystalline surface with the free rotational diffusion of the colloid. Approximate analytical predictions are made for the MSD describing the crossover from free Brownian motion at short times to active diffusion at long times. The results are in semi-quantitative agreement with numerical results of a refined Langevin model that treats translational and rotational degrees of freedom on the same footing.

Temperature gradient effects on vapor diffusion in partially-saturated porous media

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

Webb, S.W.

1999-07-01

Vapor diffusion in porous media in the presence of its own liquid may be enhanced due to pore-scale processes, such as condensation and evaporation across isolated liquid islands. Webb and Ho (1997) developed one-and two-dimensional mechanistic pore-scale models of these processes in an ideal porous medium. For isothermal and isobaric boundary conditions with a concentration gradient, the vapor diffusion rate was significantly enhanced by these liquid island processes compared to a dry porous media. The influence of a temperature gradient on the enhanced vapor diffusion rate is considered in this paper. The two-dimensional pore network model which is used inmore » the present study is shown. For partially-saturated conditions, a liquid island is introduced into the top center pore. Boundary conditions on the left and right sides of the model are specified to give the desired concentration and temperature gradients. Vapor condenses on one side of the liquid island and evaporates off the other side due to local vapor pressure lowering caused by the interface curvature, even without a temperature gradient. Rather than acting as an impediment to vapor diffusion, the liquid island actually enhances the vapor diffusion rate. The enhancement of the vapor diffusion rate can be significant depending on the liquid saturation. Vapor diffusion is enhanced by up to 40% for this single liquid island compared to a dry porous medium; enhancement factors of up to an order of magnitude have been calculated for other conditions by Webb and Ho (1997). The dominant effect on the enhancement factor is the concentration gradient; the influence of the temperature gradient is smaller. The significance of these results, which need to be confirmed by experiments, is that the dominant model of enhanced vapor diffusion (EVD) by Philip and deVries (1957) predicts that temperature gradients must exist for EVD to occur. If there is no temperature gradient, there is no enhancement. The present results indicate that EVD is predominantly driven by concentration gradients; temperature gradients are less important. Therefore, the EVD model of Philip and deVries may need to be modified to reflect these results.« less

Modeling and sensitivity analysis of mass transfer in active multilayer polymeric film for food applications

NASA Astrophysics Data System (ADS)

Bedane, T.; Di Maio, L.; Scarfato, P.; Incarnato, L.; Marra, F.

2015-12-01

The barrier performance of multilayer polymeric films for food applications has been significantly improved by incorporating oxygen scavenging materials. The scavenging activity depends on parameters such as diffusion coefficient, solubility, concentration of scavenger loaded and the number of available reactive sites. These parameters influence the barrier performance of the film in different ways. Virtualization of the process is useful to characterize, design and optimize the barrier performance based on physical configuration of the films. Also, the knowledge of values of parameters is important to predict the performances. Inverse modeling and sensitivity analysis are sole way to find reasonable values of poorly defined, unmeasured parameters and to analyze the most influencing parameters. Thus, the objective of this work was to develop a model to predict barrier properties of multilayer film incorporated with reactive layers and to analyze and characterize their performances. Polymeric film based on three layers of Polyethylene terephthalate (PET), with a core reactive layer, at different thickness configurations was considered in the model. A one dimensional diffusion equation with reaction was solved numerically to predict the concentration of oxygen diffused into the polymer taking into account the reactive ability of the core layer. The model was solved using commercial software for different film layer configurations and sensitivity analysis based on inverse modeling was carried out to understand the effect of physical parameters. The results have shown that the use of sensitivity analysis can provide physical understanding of the parameters which highly affect the gas permeation into the film. Solubility and the number of available reactive sites were the factors mainly influencing the barrier performance of three layered polymeric film. Multilayer films slightly modified the steady transport properties in comparison to net PET, giving a small reduction in the permeability and oxygen transfer rate values. Scavenging capacity of the multilayer film increased linearly with the increase of the reactive layer thickness and the oxygen absorption reaction at short times decreased proportionally with the thickness of the external PET layer.

Modeling and sensitivity analysis of mass transfer in active multilayer polymeric film for food applications

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

Bedane, T.; Di Maio, L.; Scarfato, P.

The barrier performance of multilayer polymeric films for food applications has been significantly improved by incorporating oxygen scavenging materials. The scavenging activity depends on parameters such as diffusion coefficient, solubility, concentration of scavenger loaded and the number of available reactive sites. These parameters influence the barrier performance of the film in different ways. Virtualization of the process is useful to characterize, design and optimize the barrier performance based on physical configuration of the films. Also, the knowledge of values of parameters is important to predict the performances. Inverse modeling and sensitivity analysis are sole way to find reasonable values ofmore » poorly defined, unmeasured parameters and to analyze the most influencing parameters. Thus, the objective of this work was to develop a model to predict barrier properties of multilayer film incorporated with reactive layers and to analyze and characterize their performances. Polymeric film based on three layers of Polyethylene terephthalate (PET), with a core reactive layer, at different thickness configurations was considered in the model. A one dimensional diffusion equation with reaction was solved numerically to predict the concentration of oxygen diffused into the polymer taking into account the reactive ability of the core layer. The model was solved using commercial software for different film layer configurations and sensitivity analysis based on inverse modeling was carried out to understand the effect of physical parameters. The results have shown that the use of sensitivity analysis can provide physical understanding of the parameters which highly affect the gas permeation into the film. Solubility and the number of available reactive sites were the factors mainly influencing the barrier performance of three layered polymeric film. Multilayer films slightly modified the steady transport properties in comparison to net PET, giving a small reduction in the permeability and oxygen transfer rate values. Scavenging capacity of the multilayer film increased linearly with the increase of the reactive layer thickness and the oxygen absorption reaction at short times decreased proportionally with the thickness of the external PET layer.« less

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

PubMed

Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich

2013-05-17

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

Spherical Ethylene/Air Diffusion Flames Subject to Concentric DC Electric Field in Microgravity

NASA Technical Reports Server (NTRS)

Yuan, Z. -G.; Hegde, U.; Faeth, G. M.

2001-01-01

It is well known that microgravity conditions, by eliminating buoyant flow, enable many combustion phenomena to be observed that are not possible to observe at normal gravity. One example is the spherical diffusion flame surrounding a porous spherical burner. The present paper demonstrates that by superimposing a spherical electrical field on such a flame, the flame remains spherical so that we can study the interaction between the electric field and flame in a one-dimensional fashion. Flames are susceptible to electric fields that are much weaker than the breakdown field of the flame gases owing to the presence of ions generated in the high temperature flame reaction zone. These ions and the electric current of the moving ions, in turn, significantly change the distribution of the electric field. Thus, to understand the interplay between the electric field and the flame is challenging. Numerous experimental studies of the effect of electric fields on flames have been reported. Unfortunately, they were all involved in complex geometries of both the flow field and the electric field, which hinders detailed study of the phenomena. In a one-dimensional domain, however, the electric field, the flow field, the thermal field and the chemical species field are all co-linear. Thus the problem is greatly simplified and becomes more tractable.

Noise-induced drift in two-dimensional anisotropic systems

NASA Astrophysics Data System (ADS)

Farago, Oded

2017-10-01

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Electromigration of intergranular voids in metal films for microelectronic interconnects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Ravve, Igor

2003-04-01

Voids and cracks often occur in the interconnect lines of microelectronic devices. They increase the resistance of the circuits and may even lead to a fatal failure. Voids may occur inside a single grain, but often they appear on the boundary between two grains. In this work, we model and analyze numerically the migration and evolution of an intergranular void subjected to surface diffusion forces and external voltage applied to the interconnect. The grain-void interface is considered one-dimensional, and the physical formulation of the electromigration and diffusion model results in two coupled fourth-order one-dimensional time-dependent PDEs. The boundary conditions are specified at the triple points, which are common to both neighboring grains and the void. The solution of these equations uses a finite difference scheme in space and a Runge-Kutta integration scheme in time, and is also coupled to the solution of a static Laplace equation describing the voltage distribution throughout the grain. Since the voltage distribution is required only along the interface line, the two-dimensional discretization of the grain interior is not needed, and the static problem is solved by the boundary element method at each time step. The motion of the intergranular void was studied for different ratios between the diffusion and the electric field forces, and for different initial configurations of the void.

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.

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Alonso, Sergio; Strachauer, Ulrike; Radszuweit, Markus; Bär, Markus; Hauser, Marcus J. B.

2016-04-01

Self-organization in cells often manifests itself in oscillations and waves. Here, we address deformation waves in protoplasmic droplets of the plasmodial slime mould Physarum polycephalum by modelling and experiments. In particular, we extend a one-dimensional model that considered the cell as a poroelastic medium, where active tension caused mechanochemical waves that were regulated by an inhibitor (Radszuweit et al., 2013). Our extension consists of a simple, qualitative chemical reaction-diffusion model (Brusselator) that describes the regulation of the inhibitor by another biochemical species. The biochemical reaction enhances the formation of mechanochemical waves if the reaction rates and input concentrations are near or inside an oscillatory regime. The period of the waves is found to be controlled by the characteristic oscillation period, whereas their wavelength is set by mechanical parameters. The model also allows for a systematic study of the chemical activity at the onset of mechanochemical waves. We also present examples for pattern formation in protoplasmic droplets of Physarum polycephalum including global oscillations where the central region of the droplets is in antiphase to the boundary zone, as well as travelling and standing wave-like uniaxial patterns. Finally, we apply our model to reproduce these experimental results by identifying the active tension inhibitor with the intracellular calcium concentration in the Physarum droplets and by using parameter values from mechanical experiments, respectively knowledge about the properties of calcium oscillations in Physarum. The simulation results are then found to be in good agreement with the experimental observations.

A theoretical study of the global F region for June solstice, solar maximum, and low magnetic activity

NASA Technical Reports Server (NTRS)

Sojka, J. J.; Schunk, R. W.

1985-01-01

A time-dependent, three-dimensional, multi-ion model of the ionospheric F region at 120-800 km altitude is presented. Account is taken of field-aligned diffusion, cross-field electrodynamic drifts in equatorial and high latitude regions, interhemispheric flow, thermospheric winds, polar wind escape, energy-dependent chemical reactions and neutral composition changes. Attention is also given to the effects of ion production by solar EUV radiation and auroral precipitation, thermal conduction, diffusion-thermal heat flow, local heating and cooling processes, offsets between the geomagnetic and geographic poles, and bending of field lines near the magnetic equator. The model incorporates all phenomena described by previous models and can be applied to tracing magnetic storm and substorm disturbances from high to low latitudes on a global scale. Sample results are provided for ionospheric features during a June solstice, the solar maximum and in a period of low geomagnetic activity. The model will eventually be used to study coupled ionosphere-thermosphere activity.

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.

Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies.

PubMed

Luján, Emmanuel; Soto, Daniela; Rosito, María S; Soba, Alejandro; Guerra, Liliana N; Calvo, Juan C; Marshall, Guillermo; Suárez, Cecilia

2018-05-09

Mathematical modelling approaches have become increasingly abundant in cancer research. Tumour infiltration extent and its spatial organization depend both on the tumour type and stage and on the bio-physicochemical characteristics of the microenvironment. This sets a complex scenario that often requires a multidisciplinary and individually adjusted approach. The ultimate goal of this work is to present an experimental/numerical combined method for the development of a three-dimensional mathematical model with the ability to reproduce the growth and infiltration patterns of a given avascular microtumour in response to different microenvironmental conditions. The model is based on a diffusion-convection reaction equation that considers logistic proliferation, volumetric growth, a rim of proliferative cells at the tumour surface, and invasion with diffusive and convective components. The parameter values of the model were fitted to experimental results while radial velocity and diffusion coefficients were made spatially variable in a case-specific way through the introduction of a shape function and a diffusion-limited-aggregation (DLA)-derived fractal matrix, respectively, according to the infiltration pattern observed. The in vitro model consists of multicellular tumour spheroids (MTSs) of an epithelial mammary tumour cell line (LM3) immersed in a collagen I gel matrix with a standard culture medium ("naive" matrix) or a conditioned medium from adipocytes or preadipocytes ("conditioned" matrix). It was experimentally determined that both adipocyte and preadipocyte conditioned media had the ability to change the MTS infiltration pattern from collective and laminar to an individual and atomized one. Numerical simulations were able to adequately reproduce qualitatively and quantitatively both kinds of infiltration patterns, which were determined by area quantification, analysis of fractal dimensions and lacunarity, and Bland-Altman analysis. These results suggest that the combined approach presented here could be established as a new framework with interesting potential applications at both the basic and clinical levels in the oncology area.

Computational methods for diffusion-influenced biochemical reactions.

PubMed

Dobrzynski, Maciej; Rodríguez, Jordi Vidal; Kaandorp, Jaap A; Blom, Joke G

2007-08-01

We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems. Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/

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

PubMed

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

2014-10-01

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

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

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

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

Transition density of one-dimensional diffusion with discontinuous drift

NASA Technical Reports Server (NTRS)

Zhang, Weijian

1990-01-01

The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.

Diffusion with resetting inside a circle

NASA Astrophysics Data System (ADS)

Chatterjee, Abhinava; Christou, Christos; Schadschneider, Andreas

2018-06-01

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r . The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

Room-Temperature Micron-Scale Exciton Migration in a Stabilized Emissive Molecular Aggregate.

PubMed

Caram, Justin R; Doria, Sandra; Eisele, Dörthe M; Freyria, Francesca S; Sinclair, Timothy S; Rebentrost, Patrick; Lloyd, Seth; Bawendi, Moungi G

2016-11-09

We report 1.6 ± 1 μm exciton transport in self-assembled supramolecular light-harvesting nanotubes (LHNs) assembled from amphiphillic cyanine dyes. We stabilize LHNs in a sucrose glass matrix, greatly reducing light and oxidative damage and allowing the observation of exciton-exciton annihilation signatures under weak excitation flux. Fitting to a one-dimensional diffusion model, we find an average exciton diffusion constant of 55 ± 20 cm 2 /s, among the highest measured for an organic system. We develop a simple model that uses cryogenic measurements of static and dynamic energetic disorder to estimate a diffusion constant of 32 cm 2 /s, in agreement with experiment. We ascribe large exciton diffusion lengths to low static and dynamic energetic disorder in LHNs. We argue that matrix-stabilized LHNS represent an excellent model system to study coherent excitonic transport.

Onset of anomalous diffusion from local motion rules

NASA Astrophysics Data System (ADS)

de Nigris, Sarah; Carletti, Timoteo; Lambiotte, Renaud

2017-02-01

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation in animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the "flights," that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a one-dimensional lattice, "cascades" of n unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where n is drawn from a cascade distribution pn. We show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two local distributions power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

Effects of various boundary conditions on the response of Poisson-Nernst-Planck impedance spectroscopy analysis models and comparison with a continuous-time random-walk model.

PubMed

Macdonald, J Ross

2011-11-24

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.

Critical short-time dynamics in a system with interacting static and diffusive populations

NASA Astrophysics Data System (ADS)

Argolo, C.; Quintino, Yan; Gleria, Iram; Lyra, M. L.

2012-01-01

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

Flame balls dynamics in divergent channel

NASA Astrophysics Data System (ADS)

Fursenko, R.; Minaev, S.

2011-12-01

A three-dimensional reaction-diffusion model for lean low-Lewis-number premixed flames with radiative heat losses propagating in divergent channel is studied numerically. Effects of inlet gas velocity and heat-loss intensity on flame structure at low Lewis numbers are investigated. It is found that continuous flame front exists at small heat losses and the separate flame balls settled within restricted domain inside the divergent channel at large heat losses. It is shown that the time averaged flame balls coordinate may be considered as important characteristic analogous to coordinate of continuous flame stabilized in divergent channel.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

A simplified counter diffusion method combined with a 1D simulation program for optimizing crystallization conditions.

PubMed

Tanaka, Hiroaki; Inaka, Koji; Sugiyama, Shigeru; Takahashi, Sachiko; Sano, Satoshi; Sato, Masaru; Yoshitomi, Susumu

2004-01-01

We developed a new protein crystallization method has been developed using a simplified counter-diffusion method for optimizing crystallization condition. It is composed of only a single capillary, the gel in the silicon tube and the screw-top test tube, which are readily available in the laboratory. The one capillary can continuously scan a wide range of crystallization conditions (combination of the concentrations of the precipitant and the protein) unless crystallization occurs, which means that it corresponds to many drops in the vapor-diffusion method. The amount of the precipitant and the protein solutions can be much less than in conventional methods. In this study, lysozyme and alpha-amylase were used as model proteins for demonstrating the efficiency of this method. In addition, one-dimensional (1-D) simulations of the crystal growth were performed based on the 1-D diffusion model. The optimized conditions can be applied to the initial crystallization conditions for both other counter-diffusion methods with the Granada Crystallization Box (GCB) and for the vapor-diffusion method after some modification.

A Gibbs point field model for the spatial pattern of coronary capillaries

NASA Astrophysics Data System (ADS)

Karch, R.; Neumann, M.; Neumann, F.; Ullrich, R.; Neumüller, J.; Schreiner, W.

2006-09-01

We propose a Gibbs point field model for the pattern of coronary capillaries in transverse histologic sections from human hearts, based on the physiology of oxygen supply from capillaries to tissue. To specify the potential energy function of the Gibbs point field, we draw on an analogy between the equation of steady-state oxygen diffusion from an array of parallel capillaries to the surrounding tissue and Poisson's equation for the electrostatic potential of a two-dimensional distribution of identical point charges. The influence of factors other than diffusion is treated as a thermal disturbance. On this basis, we arrive at the well-known two-dimensional one-component plasma, a system of identical point charges exhibiting a weak (logarithmic) repulsive interaction that is completely characterized by a single dimensionless parameter. By variation of this parameter, the model is able to reproduce many characteristics of real capillary patterns.

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.

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.

Reduced order modeling of mechanical degradation induced performance decay in lithium-ion battery porous electrodes

DOE PAGES

Barai, Pallab; Smith, Kandler; Chen, Chien -Fan; ...

2015-06-17

In this paper, a one-dimensional computational framework is developed that can solve for the evolution of voltage and current in a lithium-ion battery electrode under different operating conditions. A reduced order model is specifically constructed to predict the growth of mechanical degradation within the active particles of the carbon anode as a function of particle size and C-rate. Using an effective diffusivity relation, the impact of microcracks on the diffusivity of the active particles has been captured. Reduction in capacity due to formation of microcracks within the negative electrode under different operating conditions (constant current discharge and constant current constantmore » voltage charge) has been investigated. At the beginning of constant current discharge, mechanical damage to electrode particles predominantly occurs near the separator. As the reaction front shifts, mechanical damage spreads across the thickness of the negative electrode and becomes relatively uniform under multiple discharge/charge cycles. Mechanical degradation under different drive cycle conditions has been explored. It is observed that electrodes with larger particle sizes are prone to capacity fade due to microcrack formation. Finally, under drive cycle conditions, small particles close to the separator and large particles close to the current collector can help in reducing the capacity fade due to mechanical degradation.« less

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

NASA Astrophysics Data System (ADS)

Zhang, Yunxin

2009-07-01

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity V and effective diffusion coefficient D of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient D of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient D from the moments of the particle's coordinate.

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

Temporal, Mauro; Canaud, Benoit; Cayzac, Witold

The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP and themore » BPS stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. Furthermore, the results provided by the two models have been compared and it is found that – close to the ignition threshold – in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.« less

Diffusion related isotopic fractionation effects with one-dimensional advective-dispersive transport.

PubMed

Xu, Bruce S; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E

2016-04-15

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining "observable" DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (Dmech/Deff). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective-dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C0/MDL ratios of 50 or higher. Much larger C0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1m) for a relatively young diffusive plume (<100years), and DRIF will not easily be detected by using the conventional sampling approach with "typical" well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where Dmech/Deff is larger than 10, DRIF effects will likely not be observable for common groundwater contaminants. Importantly, under most field conditions, Dmech/Deff≥10 is usually satisfied in the longitudinal direction, suggesting that DRIF is not likely to be observable in most groundwater systems in which contaminant transport is predominantly one-dimensional. Given the importance in the MDL it is recommended that MDL should always be explicitly reported in both modeling and field studies. Copyright © 2016. Published by Elsevier B.V.

Application of underdamped Langevin dynamics simulations for the study of diffusion from a drug-eluting stent

NASA Astrophysics Data System (ADS)

Regev, Shaked; Farago, Oded

2018-10-01

We use a one-dimensional two layer model with a semi-permeable membrane to study the diffusion of a therapeutic drug delivered from a drug-eluting stent (DES). The rate of drug transfer from the stent coating to the arterial wall is calculated by using underdamped Langevin dynamics simulations. Our results reveal that the membrane has virtually no delay effect on the rate of delivery from the DES. The work demonstrates the great potential of underdamped Langevin dynamics simulations as an easy to implement, efficient, method for solving complicated diffusion problems in systems with a spatially-dependent diffusion coefficient.

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.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Parameter extraction and transistor models

NASA Technical Reports Server (NTRS)

Rykken, Charles; Meiser, Verena; Turner, Greg; Wang, QI

1985-01-01

Using specified mathematical models of the MOSFET device, the optimal values of the model-dependent parameters were extracted from data provided by the Jet Propulsion Laboratory (JPL). Three MOSFET models, all one-dimensional were used. One of the models took into account diffusion (as well as convection) currents. The sensitivity of the models was assessed for variations of the parameters from their optimal values. Lines of future inquiry are suggested on the basis of the behavior of the devices, of the limitations of the proposed models, and of the complexity of the required numerical investigations.

Laser one-dimensional range profile and the laser two-dimensional range profile of cylinders

NASA Astrophysics Data System (ADS)

Gong, Yanjun; Wang, Mingjun; Gong, Lei

2015-10-01

Laser one-dimensional range profile, that is scattering power from pulse laser scattering of target, is a radar imaging technology. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. Laser one-dimensional range profile and laser two-dimensional range profile are called laser range profile(LRP). The laser range profile can reflect the characteristics of the target shape and surface material. These techniques were motivated by applications of laser radar to target discrimination in ballistic missile defense. The radar equation of pulse laser is given in this paper. This paper demonstrates the analytical model of laser range profile of cylinder based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cylinders are given. Laser range profiles of cylinder, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser range profiles of different pulse width of cylinder are given in this paper. The influences of geometric parameters, pulse width, attitude on the range profiles are analyzed.

Oxidation process of MoO xC y to MoO 3: kinetics and mechanism

NASA Astrophysics Data System (ADS)

Aleman-Vázquez, L. O.; Torres-García, E.; Rodríguez-Gattorno, G.; Ocotlán-Flores, J.; Camacho-López, M. A.; Cano, J. L.

2004-10-01

A non-isothermal kinetic study of the oxidation of "carbon-modified MoO3" in the temperature range of 150-550°C by simultaneous TGA-DTA was investigated. During the oxidation process, two thermal events were detected, which are associated with the oxidation of carbon in MoOxCy and MoO2 to MoO3. The model-free and model-fitting kinetic approaches have been applied to TGA experimental data. The solid state-kinetics of the oxidation of MoOxCy to MoO3 is governed by F1 (unimolecular decay), which suggests that the reaction is of the first order with respect to oxygen concentration. The constant (Ea)α value (about 115±5 kJ/mol) for this first stage can be related to the nature of the reaction site in the MoO3 matrix. This indicates that oxidation occurs in well-defined lattice position sites (energetically equivalent). On the other hand, for the second stage of oxidation, MoO2 to MoO3, the isoconversional analysis shows a complex (Ea)α dependence on (α) and reveals a typical behavior for competitive reaction. A D2 (two-dimensional diffusion) mechanism with a variable activation energy value in the range 110-200 kJ/mol was obtained. This can be interpreted as an inter-layer oxygen diffusion in the solid bulk, which does not exclude other simultaneous mechanism reactions.

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

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.

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Sunderland, P. B.; Chao, B. H.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2008-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

DMM: A MULTIGROUP, MULTIREGION ONE-SPACE-DIMENSIONAL COMPUTER PROGRAM USING NEUTRON DIFFUSION THEORY. PART II. DMM PROGRAM DESCRIPTION

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

Kavanagh, D.L.; Antchagno, M.J.; Egawa, E.K.

1960-12-31

Operating instructions are presented for DMM, a Remington Rand 1103A program using one-space-dimensional multigroup diffusion theory to calculate the reactivity or critical conditions and flux distribution of a multiregion reactor. Complete descriptions of the routines and problem input and output specifications are also included. (D.L.C.)

Roles of Diffusion Dynamics in Stem Cell Signaling and Three-Dimensional Tissue Development.

PubMed

McMurtrey, Richard J

2017-09-15

Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have ignited investigation into important aspects of molecular diffusion in 3D cellular architectures. This article describes fundamental mechanics of diffusion with equations for modeling these dynamic processes under a variety of scenarios in 3D cellular tissue constructs. The effects of these diffusion processes and resultant concentration gradients are described in the context of the major molecular signaling pathways in stem cells that both mediate and are influenced by gas and nutrient concentrations, including how diffusion phenomena can affect stem cell state, cell differentiation, and metabolic states of the cell. The application of these diffusion models and pathways is of vital importance for future studies of developmental processes, disease modeling, and tissue regeneration.

Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon

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

Ma, Fa-Jun, E-mail: Fajun.Ma@nus.edu.sg; Duttagupta, Shubham; Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576

2014-11-14

Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boronmore » diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed.« less

An Excel®-based visualization tool of 2-D soil gas concentration profiles in petroleum vapor intrusion

PubMed Central

Verginelli, Iason; Yao, Yijun; Suuberg, Eric M.

2017-01-01

In this study we present a petroleum vapor intrusion tool implemented in Microsoft® Excel® using Visual Basic for Applications (VBA) and integrated within a graphical interface. The latter helps users easily visualize two-dimensional soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, biodegradation reaction rate constant, soil characteristics and building features. This tool is based on a two-dimensional explicit analytical model that combines steady-state diffusion-dominated vapor transport in a homogeneous soil with a piecewise first-order aerobic biodegradation model, in which rate is limited by oxygen availability. As recommended in the recently released United States Environmental Protection Agency's final Petroleum Vapor Intrusion guidance, a sensitivity analysis and a simplified Monte Carlo uncertainty analysis are also included in the spreadsheet. PMID:28163564

An Excel®-based visualization tool of 2-D soil gas concentration profiles in petroleum vapor intrusion.

PubMed

Verginelli, Iason; Yao, Yijun; Suuberg, Eric M

2016-01-01

In this study we present a petroleum vapor intrusion tool implemented in Microsoft ® Excel ® using Visual Basic for Applications (VBA) and integrated within a graphical interface. The latter helps users easily visualize two-dimensional soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, biodegradation reaction rate constant, soil characteristics and building features. This tool is based on a two-dimensional explicit analytical model that combines steady-state diffusion-dominated vapor transport in a homogeneous soil with a piecewise first-order aerobic biodegradation model, in which rate is limited by oxygen availability. As recommended in the recently released United States Environmental Protection Agency's final Petroleum Vapor Intrusion guidance, a sensitivity analysis and a simplified Monte Carlo uncertainty analysis are also included in the spreadsheet.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

NASA Astrophysics Data System (ADS)

Gelß, Patrick; Matera, Sebastian; Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

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

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.

Multidimensional MnO2 nanohair-decorated hybrid multichannel carbon nanofiber as an electrode material for high-performance supercapacitors.

PubMed

Jun, Jaemoon; Lee, Jun Seop; Shin, Dong Hoon; Kim, Sung Gun; Jang, Jyongsik

2015-10-14

One-dimensional (1D)-structured nanomaterials represent one of the most attractive candidates for energy-storage systems due to their contribution to design simplicity, fast charge-transportation network, and their allowance for more accessible ion diffusion. In particular, 1D-structured nanomaterials with a highly complex inner-pore configuration enhance functionality by taking advantage of both the hollow and 1D structures. In this study, we report a MnO2 nanohair-decorated, hybrid multichannel carbon nanofiber (Mn_MCNF) fabricated via single-nozzle co-electrospinning of two immiscible polymer solutions, followed by carbonization and redox reactions. With improved ion accessibility, the optimized Mn_MCNF sample (Mn_MCNF_60 corresponding to a reaction duration time of 60 min for optimal MnO2 nanohair growth) exhibited a high specific capacitance of 855 F g(-1) and excellent cycling performance with ∼87.3% capacitance retention over 5000 cycles.

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.

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

Communication: Prediction of the rate constant of bimolecular hydrogen exchange in the water dimer using an ab initio potential energy surface.

PubMed

Wang, Yimin; Bowman, Joel M; Huang, Xinchuan

2010-09-21

We report the properties of two novel transition states of the bimolecular hydrogen exchange reaction in the water dimer, based on an ab initio water dimer potential [A. Shank et al., J. Chem. Phys. 130, 144314 (2009)]. The realism of the two transition states is assessed by comparing structures, energies, and harmonic frequencies obtained from the potential energy surface and new high-level ab initio calculations. The rate constant for the exchange is obtained using conventional transition state theory with a tunneling correction. We employ a one-dimensional approach for the tunneling calculations using a relaxed potential from the full-dimensional potential in the imaginary-frequency normal mode of the saddle point, Q(im). The accuracy of this one-dimensional approach has been shown for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H(2) reaction [Y. Wang and J. M. Bowman, J. Chem. Phys. 129, 121103 (2008)]. This approach is applied to calculate the rate constant for the H(2)O+H(2)O exchange and also for H(2)O+D(2)O→2HOD. The local zero-point energy is also obtained using diffusion Monte Carlo calculations in the space of real-frequency-saddle-point normal modes, as a function of Q(im).

Building one-dimensional oxide nanostructure arrays on conductive metal substrates for lithium-ion battery anodes.

PubMed

Jiang, Jian; Li, Yuanyuan; Liu, Jinping; Huang, Xintang

2011-01-01

Lithium ion battery (LIB) is potentially one of the most attractive energy storage devices. To meet the demands of future high-power and high-energy density requirements in both thin-film microbatteries and conventional batteries, it is challenging to explore novel nanostructured anode materials instead of conventional graphite. Compared to traditional electrodes based on nanostructure powder paste, directly grown ordered nanostructure array electrodes not only simplify the electrode processing, but also offer remarkable advantages such as fast electron transport/collection and ion diffusion, sufficient electrochemical reaction of individual nanostructures, enhanced material-electrolyte contact area and facile accommodation of the strains caused by lithium intercalation and de-intercalation. This article provides a brief overview of the present status in the area of LIB anodes based on one-dimensional nanostructure arrays growing directly on conductive inert metal substrates, with particular attention to metal oxides synthesized by an anodized alumina membrane (AAM)-free solution-based or hydrothermal methods. Both the scientific developments and the techniques and challenges are critically analyzed.

Building one-dimensional oxidenanostructure arrays on conductive metal substrates for lithium-ion battery anodes

NASA Astrophysics Data System (ADS)

Jiang, Jian; Li, Yuanyuan; Liu, Jinping; Huang, Xintang

2011-01-01

Lithium ion battery (LIB) is potentially one of the most attractive energy storage devices. To meet the demands of future high-power and high-energy density requirements in both thin-film microbatteries and conventional batteries, it is challenging to explore novel nanostructured anode materials instead of conventional graphite. Compared to traditional electrodes based on nanostructure powder paste, directly grown ordered nanostructure array electrodes not only simplify the electrode processing, but also offer remarkable advantages such as fast electron transport/collection and ion diffusion, sufficient electrochemical reaction of individual nanostructures, enhanced material-electrolyte contact area and facile accommodation of the strains caused by lithium intercalation and de-intercalation. This article provides a brief overview of the present status in the area of LIB anodes based on one-dimensional nanostructure arrays growing directly on conductive inert metal substrates, with particular attention to metal oxides synthesized by an anodized aluminamembrane (AAM)-free solution-based or hydrothermal methods. Both the scientific developments and the techniques and challenges are critically analyzed.

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.

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.

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.

Biologically Inspired Synthesis Route to Three-Dimensionally Structured Inorganic Thin Films

DOE PAGES

Schwenzer, Birgit; Morse, Daniel E.

2008-01-01

Inorganic thin films (hydroxide, oxide, and phosphate materials) that are textured on a submicron scale have been prepared from aqueous metal salt solutions at room temperature using vapor-diffusion catalysis. This generic synthesis approach mimics the essential advantages of the catalytic and structure-directing mechanisms observed for the formation of silica skeletons of marine sponges. Chemical composition, crystallinity, and the three-dimensional morphology of films prepared by this method are extremely sensitive to changes in the synthesis conditions, such as concentrations, reaction times, and the presence and nature of substrate materials. Focusing on different materials systems, the reaction mechanism for the formation ofmore » these thin films and the influence of different reaction parameters on the product are explained.« less

Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain

NASA Astrophysics Data System (ADS)

Zhou, Chao; Yu, Guoqiang; Furuya, Daisuke; Greenberg, Joel; Yodh, Arjun; Durduran, Turgut

2006-02-01

Diffuse optical correlation methods were adapted for three-dimensional (3D) tomography of cerebral blood flow (CBF) in small animal models. The image reconstruction was optimized using a noise model for diffuse correlation tomography which enabled better data selection and regularization. The tomographic approach was demonstrated with simulated data and during in-vivo cortical spreading depression (CSD) in rat brain. Three-dimensional images of CBF were obtained through intact skull in tissues(~4mm) deep below the cortex.

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem.

PubMed

Missel, P J

2000-01-01

Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38-39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina.

An axisymmetric single-path model for gas transport in the conducting airways.

PubMed

Madasu, Srinath; Borhan, All; Ultman, James S

2006-02-01

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

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.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential

NASA Astrophysics Data System (ADS)

Guérin, T.; Dean, D. S.

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F . The system is studied in the region where the force is close to the critical value Fc at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F >Fc , whereas for F

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.

A two-dimensional numerical simulation of a supersonic, chemically reacting mixing layer

NASA Technical Reports Server (NTRS)

Drummond, J. Philip

1988-01-01

Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy.

A three-dimensional spin-diffusion model for micromagnetics

PubMed Central

Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter

2015-01-01

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796

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

NASA Astrophysics Data System (ADS)

Otto, Andereas; Wang, Jian; Radons, Günter

2017-11-01

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

Spatial dynamics of a population with stage-dependent diffusion

NASA Astrophysics Data System (ADS)

Azevedo, F.; Coutinho, R. M.; Kraenkel, R. A.

2015-05-01

We explore the spatial dynamics of a population whose individuals go through life stages with very different dispersal capacities. We model it through a system of partial differential equations of the reaction-diffusion kind, with nonlinear diffusion terms that may depend on population density and on the stage. This model includes a few key biological ingredients: growth and saturation, life stage structure, small population effects, and diffusion dependent on the stage. In particular, we consider that adults exhibit two distinct classes: one highly mobile and the other less mobile but with higher fecundity rate, and the development of juveniles into one or the other depends on population density. We parametrize the model with estimated parameters of an insect species, the brown planthopper. We focus on a situation akin to an invasion of the species in a new habitat and find that the front of invasion is led by the most mobile adult class. We also show that the trade-off between dispersal and fecundity leads to invasion speed attaining its maximum at an intermediate value of the diffusion coefficient of the most mobile class.

Tuning the Ignition Performance of a Microchip Initiator by Integrating Various Al/MoO3 Reactive Multilayer Films on a Semiconductor Bridge.

PubMed

Xu, Jianbing; Tai, Yu; Ru, Chengbo; Dai, Ji; Ye, Yinghua; Shen, Ruiqi; Zhu, Peng

2017-02-15

Reactive multilayer films (RMFs) can be integrated into semiconducting electronic structures with the use of microelectromechanical systems (MEMS) technology and represent potential applications in the advancement of microscale energy-demanding systems. In this study, aluminum/molybdenum trioxide (Al/MoO 3 )-based RMFs with different modulation periods were integrated on a semiconductor bridge (SCB) using a combination of an image reversal lift-off process and magnetron sputtering technology. This produced an energetic semiconductor bridge (ESCB)-chip initiator with controlled ignition performance. The effects of the Al/MoO 3 RMFs with different modulation periods on ignition properties of the ESCB initiator were then systematically investigated in terms of flame duration, maximum flame area, and the reaction ratio of the RMFs. These microchip initiators achieved flame durations of 60-600 μs, maximum flame areas of 2.85-17.61 mm 2 , and reaction ratios of ∼14-100% (discharged with 47 μF/30 V) by simply changing the modulation periods of the Al/MoO 3 RMFs. This behavior was also consistent with a one-dimensional diffusion reaction model. The microchip initiator exhibited a high level of integration and proved to have tuned ignition performance, which can potentially be used in civilian and military applications.

Numerical Simulations of Acoustically Driven, Burning Droplets

NASA Technical Reports Server (NTRS)

Kim, H.-C.; Karagozian, A. R.; Smith, O. I.; Urban, Dave (Technical Monitor)

1999-01-01

This computational study focuses on understanding and quantifying the effects of external acoustical perturbations on droplet combustion. A one-dimensional, axisymmetric representation of the essential diffusion and reaction processes occurring in the vicinity of the droplet stagnation point is used here in order to isolate the effects of the imposed acoustic disturbance. The simulation is performed using a third order accurate, essentially non-oscillatory (ENO) numerical scheme with a full methanol-air reaction mechanism. Consistent with recent microgravity and normal gravity combustion experiments, focus is placed on conditions where the droplet is situated at a velocity antinode in order for the droplet to experience the greatest effects of fluid mechanical straining of flame structures. The effects of imposed sound pressure level and frequency are explored here, and conditions leading to maximum burning rates are identified.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Theoretical investigation of microstructure evolution and deformation of zirconium under neutron irradiation

DOE PAGES

Barashev, A. V.; Golubov, S. I.; Stoller, R. E.

2015-06-01

We studied the radiation growth of zirconium using a reaction–diffusion model which takes into account intra-cascade clustering of self-interstitial atoms and one-dimensional diffusion of interstitial clusters. The observed dose dependence of strain rates is accounted for by accumulation of sessile dislocation loops during irradiation. Moreover, the computational model developed and fitted to available experimental data is applied to study deformation of Zr single crystals under irradiation up to hundred dpa. Finally, the effect of cold work and the reasons for negative prismatic strains and co-existence of vacancy and interstitial loops are elucidated.

Aquitard contaminant storage and flux resulting from dense nonaqueous phase liquid source zone dissolution and remediation

EPA Science Inventory

A one-dimensional diffusion model was used to investigate the effects of dense non-aqueous phase liquid (DNAPL) source zone dissolution and remediation on the storage and release of contaminants from aquitards. Source zone dissolution was represented by a power-law source depleti...

A modelling approach for the heterogeneous oxidation of elastomers

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Isotopic decoupling during porous melt flow: A case-study in the Lherz peridotite

NASA Astrophysics Data System (ADS)

Le Roux, V.; Bodinier, J.-L.; Alard, O.; O'Reilly, S. Y.; Griffin, W. L.

2009-03-01

Most peridotite massifs and mantle xenoliths show a wide range of isotopic variations, often involving significant decoupling between Hf, Nd and Sr isotopes. These variations are generally ascribed either to mingling of individual components of contrasted isotopic compositions or to time integration of parent-element enrichment by percolating melts/fluids, superimposed onto previous depletion event(s). However, strong isotopic decoupling may also arise during porous flow as a result of daughter-elements fractionation during solid-liquid interaction. Although porous flow is recognized as an important process in mantle rocks, its effects on mantle isotopic variability have been barely investigated so far. The peridotites of the Lherz massif (French Pyrenees) display a frozen melt percolation front separating highly refractory harzburgites from refertilized lherzolites. Isotopic signatures observed at the melt percolation front show a strong decoupling of Hf from Nd and Sr isotopes that cannot be accounted for by simple mixing involving the harzburgite protolith and the percolating melt. Using one dimensional percolation-diffusion and percolation-reaction modeling, we show that these signatures represent transient isotopic compositions generated by porous flow. These signatures are governed by a few critical parameters such as daughter element concentrations in melt and peridotite, element diffusivity, and efficiency of isotopic homogenization rather than by the chromatographic effect of melt transport and the refertilization reaction. Subtle variations in these parameters may generate significant inter-isotopic decoupling and wide isotopic variations in mantle rocks.

Polymer diffusion in the interphase between surface and solution.

PubMed

Weger, Lukas; Weidmann, Monika; Ali, Wael; Hildebrandt, Marcus; Gutmann, Jochen Stefan; Hoffmann-Jacobsen, Kerstin

2018-05-22

Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and three-dimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N -1 ) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.

A computational model for BMP movement in sea urchin embryos.

PubMed

van Heijster, Peter; Hardway, Heather; Kaper, Tasso J; Bradham, Cynthia A

2014-12-21

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction-diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly. Copyright © 2014 Elsevier Ltd. All rights reserved.

Conceptual model analysis of interaction at a concrete-Boom Clay interface

NASA Astrophysics Data System (ADS)

Liu, Sanheng; Jacques, Diederik; Govaerts, Joan; Wang, Lian

In many concepts for deep disposal of high-level radioactive waste, cementitious materials are used in the engineered barriers. For example, in Belgium the engineered barrier system is based on a considerable amount of cementitious materials as buffer and backfill in the so-called supercontainer embedded in the hosting geological formation. A potential hosting formation is Boom Clay. Insight in the interaction between the high-pH pore water of the cementitious materials and neutral-pH Boom Clay pore water is required. Two problems are quite common for modeling of such a system. The first one is the computational cost due to the long timescale model assessments envisaged for the deep disposal system. Also a very fine grid (in sub-millimeter), especially at interfaces has to be used in order to accurately predict the evolution of the system. The second one is whether to use equilibrium or kinetic reaction models. The objectives of this paper are twofold. First, we develop an efficient coupled reactive transport code for this diffusion-dominated system by making full use of multi-processors/cores computers. Second, we investigate how sensitive the system is to chemical reaction models especially when pore clogging due to mineral precipitation is considered within the cementitious system. To do this, we selected two portlandite dissolution models, i.e., equilibrium (fastest) and diffusion-controlled model with precipitation of a calcite layer around portlandite particles (diffusion-controlled dissolution). The results show that with shrinking core model portlandite dissolution and calcite precipitation are much slower than with the equilibrium model. Also diffusion-controlled dissolution smooths out dissolution fronts compared to the equilibrium model. However, only a slight difference with respect to the clogging time can be found even though we use a very small diffusion coefficient (10-20 m2/s) in the precipitated calcite layer.

Theory of Neutron Chain Reactions: Extracts from Volume I, Diffusion and Slowing Down of Neutrons: Chapter I. Elementary Theory of Neutron Diffusion. Chapter II. Second Order Diffusion Theory. Chapter III. Slowing Down of Neutrons

DOE R&D Accomplishments Database

Weinberg, Alvin M.; Noderer, L. C.

1951-05-15

The large scale release of nuclear energy in a uranium fission chain reaction involves two essentially distinct physical phenomena. On the one hand there are the individual nuclear processes such as fission, neutron capture, and neutron scattering. These are essentially quantum mechanical in character, and their theory is non-classical. On the other hand, there is the process of diffusion -- in particular, diffusion of neutrons, which is of fundamental importance in a nuclear chain reaction. This process is classical; insofar as the theory of the nuclear chain reaction depends on the theory of neutron diffusion, the mathematical study of chain reactions is an application of classical, not quantum mechanical, techniques.

Two-dimensional free-energy surface on the exchange reaction of alkyl chloride/chloride using the QM/MM-MC method

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

Ohisa, M.; Yamataka, H.; Dupuis, Michel

2007-12-05

Two-dimensional free-energy surfaces are calculated for alkyl chloride/chloride exchange/inversion reactions: Cl- + RCl (R = Me and t-Bu) surrounded by one hundred H2O molecules as a model of solvent. The methodology of free-energy calculation by perturbation theory based on a mixed-Hamiltonian model (QM/MM) combined with Monte Carlo sampling of the solvent configurations was used to obtain the changes in solvation free energy. We devised a special procedure to analyze the two-dimensional free-energy surfaces to gain unique insight into the differences in the reaction mechanisms between the two systems. The inversion reaction path for R = t-Bu on the free-energy surfacemore » is found to proceed in an asynchronous way within a concerted framework via the ion-pair region. This is in contrast to the R = Me system that proceeds as a typical SN2 reaction. This work was supported by the U.S. Department of Energy's (DOE) Office of Basic Energy Sciences, Chemical Sciences program. The Pacific Northwest National Laboratory is operated by Battelle for DOE.« less

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.

Experimental determination of the turbulence in a liquid rocket combustion chamber

NASA Technical Reports Server (NTRS)

Hara, J.; Smith, L. O.; Partus, F. P.

1972-01-01

The intensity of turbulence and the Lagrangian correlation coefficient for a liquid rocket combustion chamber were determined experimentally using the tracer gas diffusion method. The results indicate that the turbulent diffusion process can be adequately modeled by the one-dimensional Taylor theory; however, the numerical values show significant disagreement with previously accepted values. The intensity of turbulence is higher by a factor of about two, while the Lagrangian correlation coefficient which was assumed to be unity in the past is much less than unity.

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

Modeling snow-crystal growth: a three-dimensional mesoscopic approach.

PubMed

Gravner, Janko; Griffeath, David

2009-01-01

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

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.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

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

Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface.more » We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.« less

Modeling and experimental examination of water level effects on radon exhalation from fragmented uranium ore.

PubMed

Ye, Yong-Jun; Dai, Xin-Tao; Ding, De-Xin; Zhao, Ya-Li

2016-12-01

In this study, a one-dimensional steady-state mathematical model of radon transport in fragmented uranium ore was established according to Fick's law and radon transfer theory in an air-water interface. The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula. We also designed a one-dimensional experimental apparatus for simulating radon diffusion migration in the uranium ore with various water levels to verify the mathematical model. The predicted results were in close agreement with the measured results, suggesting that the proposed model can be readily used to determine radon concentrations and exhalation rates in fragmented uranium ore with varying water levels. Copyright © 2016. Published by Elsevier Ltd.

Modeling the Role of Incisures in Vertebrate Phototransduction

PubMed Central

Caruso, Giovanni; Bisegna, Paolo; Shen, Lixin; Andreucci, Daniele; Hamm, Heidi E.; DiBenedetto, Emmanuele

2006-01-01

Phototransduction is mediated by a G-protein-coupled receptor-mediated cascade, activated by light and localized to rod outer segment (ROS) disk membranes, which, in turn, drives a diffusion process of the second messengers cGMP and Ca2+ in the ROS cytosol. This process is hindered by disks—which, however, bear physical cracks, known as incisures, believed to favor the longitudinal diffusion of cGMP and Ca2+. This article is aimed at highlighting the biophysical functional role and significance of incisures, and their effect on the local and global response of the photocurrent. Previous work on this topic regarded the ROS as well stirred in the radial variables, lumped the diffusion mechanism on the longitudinal axis of the ROS, and replaced the cytosolic diffusion coefficients by effective ones, accounting for incisures through their total patent area only. The fully spatially resolved model recently published by our group is a natural tool to take into account other significant details of incisures, including their geometry and distribution. Using mathematical theories of homogenization and concentrated capacity, it is shown here that the complex diffusion process undergone by the second messengers cGMP and Ca2+ in the ROS bearing incisures can be modeled by a family of two-dimensional diffusion processes on the ROS cross sections, glued together by other two-dimensional diffusion processes, accounting for diffusion in the ROS outer shell and in the bladelike regions comprised by the stack of incisures. Based on this mathematical model, a code has been written, capable of incorporating an arbitrary number of incisures and activation sites, with any given arbitrary distribution within the ROS. The code is aimed at being an operational tool to perform numerical experiments of phototransduction, in rods with incisures of different geometry and structure, under a wide spectrum of operating conditions. The simulation results show that incisures have a dual biophysical function. On the one hand, since incisures line up from disk to disk, they create vertical cytoplasmic channels crossing the disks, thus facilitating diffusion of second messengers; on the other hand, at least in those species bearing multiple incisures, they divide the disks into lobes like the petals of a flower, thus confining the diffusion of activated phosphodiesterase and localizing the photon response. Accordingly, not only the total area of incisures, but their geometrical shape and distribution as well, significantly influence the global photoresponse. PMID:16714347

Ducted turbine theory with right angled ducts

NASA Astrophysics Data System (ADS)

McLaren-Gow, S.; Jamieson, P.; Graham, J. M. R.

2014-06-01

This paper describes the use of an inviscid approach to model a ducted turbine - also known as a diffuser augmented turbine - and a comparison of results with a particular one-dimensional theory. The aim of the investigation was to gain a better understanding of the relationship between a real duct and the ideal diffuser, which is a concept that is developed in the theory. A range of right angled ducts, which have a rim for a 90° exit angle, were modelled. As a result, the performance of right angled ducts has been characterised in inviscid flow. It was concluded that right angled ducts cannot match the performance of their associated ideal diffuser and that the optimum rotor loading for these turbines varies with the duct dimensions.

A two-dimensional, time-dependent model of suspended sediment transport and bed reworking for continental shelves

USGS Publications Warehouse

Harris, C.K.; Wiberg, P.L.

2001-01-01

A two-dimensional, time-dependent solution to the transport equation is formulated to account for advection and diffusion of sediment suspended in the bottom boundary layer of continental shelves. This model utilizes a semi-implicit, upwind-differencing scheme to solve the advection-diffusion equation across a two-dimensional transect that is configured so that one dimension is the vertical, and the other is a horizontal dimension usually aligned perpendicular to shelf bathymetry. The model calculates suspended sediment concentration and flux; and requires as input wave properties, current velocities, sediment size distributions, and hydrodynamic sediment properties. From the calculated two-dimensional suspended sediment fluxes, we quantify the redistribution of shelf sediment, bed erosion, and deposition for several sediment sizes during resuspension events. The two-dimensional, time-dependent approach directly accounts for cross-shelf gradients in bed shear stress and sediment properties, as well as transport that occurs before steady-state suspended sediment concentrations have been attained. By including the vertical dimension in the calculations, we avoid depth-averaging suspended sediment concentrations and fluxes, and directly account for differences in transport rates and directions for fine and coarse sediment in the bottom boundary layer. A flux condition is used as the bottom boundary condition for the transport equation in order to capture time-dependence of the suspended sediment field. Model calculations demonstrate the significance of both time-dependent and spatial terms on transport and depositional patterns on continental shelves. ?? 2001 Elsevier Science Ltd. All rights reserved.

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Divergence of the long-wavelength collective diffusion coefficient in quasi-one- and quasi-two-dimensional colloidal suspensions.

PubMed

Lin, Binhua; Cui, Bianxiao; Xu, Xinliang; Zangi, Ronen; Diamant, Haim; Rice, Stuart A

2014-02-01

We report the results of experimental studies of the short-time-long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D(e)(q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D(0): H(q) ≡ D(e)(q)S(q)/D(0). We find an apparent divergence of H(q) as q → 0 with the form H(q) ∝ q(-γ) (1.7 < γ < 1.9) for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q → 0 we infer that D(e)(q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and D(e)(q) as q → 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of H(q) and D(e)(q) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that D(e)(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q(-1) as q → 0.

Design, fabrication, and testing of three-dimensionally ordered macroporous materials for pseudomorphic transformation and power storage

NASA Astrophysics Data System (ADS)

Lytle, Justin Conrad

This dissertation details my study of three-dimensionally ordered macroporous (3DOM) materials, which were prepared using polymer latex colloidal crystal templates. These solids are composed of close-packed and three-dimensionally interconnected spherical macropores surrounded by nanoscale solid wall skeletons. This unique architecture offers relatively large surface areas that are accessible by interconnected macropores, making these materials important for innovative catalysis, sensing, and separations applications. In addition, the three-dimensionally alternating dielectric structure can establish photonic stop bands that control the flow of light analogously to the restraint of electronic conduction by electronic bandgaps. Many potential applications would benefit from reducing device feature sizes from the bulk into the nanoscale regime. However, some compositions are more easily prepared as nanostructured materials than others. Therefore, it would be immensely important to develop synthetic methods of transforming solids that are more easily formed with nanoarchitectural features into compositions that are not. Pseudomorphic transformation reactions may be one solution to this problem, since they are capable of altering chemical composition while maintaining shape and structural morphology. Several compositions of inverse opal and nanostructured preforms were investigated in this work to study the effects of vapor-phase and solution-phase conversion reactions on materials with feature sizes ranging from a few nm to tens of mum. 3DOM SiO2 and WO3, nanostructured Ni, and colloidal silica sphere performs were studied to investigate the effects of preform chemistries, feature sizes and shapes, processing temperatures, and reagent ratios on overall pseudomorphic structural retention. Power storage and fuel cell devices based on nanostructured electrodes are a major example of how reducing device component feature sizes can greatly benefit applications. Bulk electrode geometries have diffusion-limited kinetics and relatively low energy and power densities. Nanostructured electrodes offer extremely short ion diffusion pathlengths and relatively numerous reaction sites. 3DOM SnO2 thin films, 3DOM Li4Ti 5O12 powders, and 3DOM carbon monoliths have been fabricated and characterized in this work as Li-ion anode materials, with 3DOM carbon exhibiting an enormous rate capability beyond similarly prepared, but non-templated, bulk carbon. Furthermore, a novel battery design that is three-dimensionally interpenetrated on the nanoscale was prepared and evaluated in this research.

Diffusiophoresis in one-dimensional solute gradients

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

Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo

Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics.more » The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.« less

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2017-09-01

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006), 10.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

Two-dimensional pH distributions and dynamics in bioturbated marine sediments

NASA Astrophysics Data System (ADS)

Zhu, Qingzhi; Aller, Robert C.; Fan, Yanzhen

2006-10-01

The seafloor is the site of intense biogeochemical and mineral dissolution-precipitation reactions which generate strong gradients in pH near the sediment-overlying water interface. These gradients are usually measured in one-dimension vertically with depth. Two-dimensional pH distributions in marine sediments were examined at high resolution (65 × 65 μm pixel) and analytical precision over areas of ˜150 to 225 cm 2 using a newly developed pH planar fluorosensor. Dramatic three-dimensional gradients, complex heterogeneity, and dynamic changes of pH occur in the surficial zone of deposits inhabited by macrofauna. pH can vary by ±2 units horizontally as well as vertically over millimeter scales. pH minima zones often form in association with redoxclines within a few millimeters of inner burrow walls, and become more pronounced with time if burrows remain stable and irrigated for extended periods. Microenvironmental pH minima also form locally around decaying biomass and relict burrow tracks, and dissipate with time (˜5 d). H + concentrations and fluxes in sandy mud show complex acid-base reaction distributions with net H + fluxes around burrows up to ˜12 nmol cm -2 d -1 and maximum net reaction rates varying between -90 (consumption) to 120 (production) μM d -1 (˜90 nmol cm -1 d -1 burrow length). Acid producing zones that surround irrigated burrows are largely balanced by acid titration zones along inner burrow walls and outer radial boundaries. The geometry and scaling of pH microenvironments are functions of diagenetic reaction rates and three-dimensional transport patterns determined by sediment properties, such as diffusive tortuosity, and by benthic community characteristics such as the abundance, mobility, and size of infauna. Previously, undocumented biogeochemical phenomena such as low pH regions associated with in-filled relict biogenic structures and burrowing tracks are readily demonstrated by two-dimensional and time-dependent images of pH and sedimentary structure.

Influence of Marangoni flows on the dynamics of isothermal A + B → C reaction fronts.

PubMed

Tiani, R; Rongy, L

2016-09-28

The nonlinear dynamics of A + B → C fronts is analyzed both numerically and theoretically in the presence of Marangoni flows, i.e., convective motions driven by surface tension gradients. We consider horizontal aqueous solutions where the three species A, B, and C can affect the surface tension of the solution, thereby driving Marangoni flows. The resulting dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection (RDC) equations for the three chemical species. We show that the dynamics of the front cannot be predicted solely on the basis of the one-dimensional reaction-diffusion profiles as is the case for buoyancy-driven convection around such fronts. We relate this observation to the structure of Marangoni flows which lead to more complex and exotic dynamics. We find in particular the surprising possibility of a reversal of the front propagation direction in time for some sets of Marangoni numbers, quantifying the influence of each chemical species concentration on the solution surface tension. We explain this reversal analytically and propose a new classification of the convective effects on A + B → C reaction fronts as a function of the Marangoni numbers. The influence of the layer thickness on the RDC dynamics is also presented. Those results emphasize the importance of flow symmetry properties when studying convective front dynamics in a given geometry.

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH 3 on Pt(1 0 0) coupled by diffusion

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2004-04-01

The Lombardo-Imbihl-Fink (LFI) ODE model of the NO+NH 3 reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH 3 and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH 3 and H.

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.

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.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

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 Review of the Ginzburg-Syrovatskii's Galactic Cosmic-Ray Propagation Model and its Leaky-Box Limit

NASA Technical Reports Server (NTRS)

Barghouty, A. F.

2012-01-01

Phenomenological models of galactic cosmic-ray propagation are based on a diffusion equation known as the Ginzburg-Syrovatskii s equation, or variants (or limits) of this equation. Its one-dimensional limit in a homogeneous volume, known as the leaky-box limit or model, is sketched here. The justification, utility, limitations, and a typical numerical implementation of the leaky-box model are examined in some detail.

Coarse analysis of collective behaviors: Bifurcation analysis of the optimal velocity model for traffic jam formation

NASA Astrophysics Data System (ADS)

Miura, Yasunari; Sugiyama, Yuki

2017-12-01

We present a general method for analyzing macroscopic collective phenomena observed in many-body systems. For this purpose, we employ diffusion maps, which are one of the dimensionality-reduction techniques, and systematically define a few relevant coarse-grained variables for describing macroscopic phenomena. The time evolution of macroscopic behavior is described as a trajectory in the low-dimensional space constructed by these coarse variables. We apply this method to the analysis of the traffic model, called the optimal velocity model, and reveal a bifurcation structure, which features a transition to the emergence of a moving cluster as a traffic jam.

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.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

PubMed

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

NASA Astrophysics Data System (ADS)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Canards and black swans in a model of a 3-D autocatalator

NASA Astrophysics Data System (ADS)

Shchepakina, E.

2005-01-01

The mathematical model of a 3-D autocatalator is studied using the geometric theory of singular perturbations, namely, the black swan and canard techniques. Critical regimes are modeled by canards (one-dimensional stable-unstable slow integral manifolds). The meaning of criticality here is as follows. The critical regime corresponds to a chemical reaction which separates the domain of self-accelerating reactions from the domain of slow reactions. A two-dimensional stable-unstable slow integral manifold (black swan) consisting entirely of canards, which simulate the critical phenomena for different initial data of the dynamical system, is constructed. It is shown that this procedure leads to the phenomenon of auto-oscillations in the chemical system. The geometric approach combined with asymptotic and numerical methods permits us to explain the strong parametric sensitivity and to obtain asymptotic representations of the critical behavior of the chemical system.

Analytical modeling of operating characteristics of premixing-prevaporizing fuel-air mixing passages. Volume 1: Analysis and results

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Chiappetta, L. M.; Edwards, D. E.; Mcvey, J. B.

1982-01-01

A model for predicting the distribution of liquid fuel droplets and fuel vapor in premixing-prevaporizing fuel-air mixing passages of the direct injection type is reported. This model consists of three computer programs; a calculation of the two dimensional or axisymmetric air flow field neglecting the effects of fuel; a calculation of the three dimensional fuel droplet trajectories and evaporation rates in a known, moving air flow; a calculation of fuel vapor diffusing into a moving three dimensional air flow with source terms dependent on the droplet evaporation rates. The fuel droplets are treated as individual particle classes each satisfying Newton's law, a heat transfer, and a mass transfer equation. This fuel droplet model treats multicomponent fuels and incorporates the physics required for the treatment of elastic droplet collisions, droplet shattering, droplet coalescence and droplet wall interactions. The vapor diffusion calculation treats three dimensional, gas phase, turbulent diffusion processes. The analysis includes a model for the autoignition of the fuel air mixture based upon the rate of formation of an important intermediate chemical species during the preignition period.

The nature of the air-cleaved mica surface

NASA Astrophysics Data System (ADS)

Christenson, Hugo K.; Thomson, Neil H.

2016-06-01

The accepted image of muscovite mica is that of an inert and atomically smooth surface, easily prepared by cleavage in an ambient atmosphere. Consequently, mica is extensively used a model substrate in many fundamental studies of surface phenomena and as a substrate for AFM imaging of biomolecules. In this review we present evidence from the literature that the above picture is not quite correct. The mica used in experimental work is almost invariably cleaved in laboratory air, where a reaction between the mica surface, atmospheric CO2 and water occurs immediately after cleavage. The evidence suggests very strongly that as a result the mica surface becomes covered by up to one formula unit of K2CO3 per nm2, which is mobile under humid conditions, and crystallises under drier conditions. The properties of mica in air or water vapour cannot be fully understood without reference to the surface K2CO3, and many studies of the structure of adsorbed water on mica surfaces may need to be revisited. With this new insight, however, the air-cleaved mica should provide exciting opportunities to study phenomena such as two-dimensional ion diffusion, electrolyte effects on surface conductivity, and two-dimensional crystal nucleation.

Critical time scales for advection-diffusion-reaction processes.

PubMed

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

2012-04-01

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

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

PubMed

Guérin, T; Dean, D S

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F

Relativistic collective diffusion in one-dimensional systems

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

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

2012-05-10

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

Competition of wormholes during the evolution of cave passages

NASA Astrophysics Data System (ADS)

Gabrovsek, Franci; Dreybrodt, Wolfgang

2017-04-01

Reactive fronts in two-dimensional plane parallel fractures, with constant head difference between input and output and with diffusion controlled first order reaction rates R = keff ṡ (Ceq - C), where keff = k ṡ (1 + ka/6D)-1, are instable to infinitesimal perturbations in fracture aperture width (1), causing spontaneous fingering of the reactive front resulting in the formation of wormholes. C is the actual concentration and Ceq the equilibrium concentration, a, is the actual aperture width of the fracture , and D the constant of molecular diffusion. Fingering happens also in plane-parallel rough fractures where it is triggered by the existence of statistically more favorable pathways. The same behavior is observed in rectangular two-dimensional networks of "one-dimensional" smooth fractures used in modeling the evolution of caves in soluble rock (2). Here the formation of caves can be regarded as the evolution of wormholes along the two-dimensional network. Once fingering has been triggered, either by instability or by roughness, many small fingers compete with each other and only a few survive. Here we investigate the competition between two seeded fingers in initially homogeneous fracture networks with identical aperture width of all fractures and also in inhomogeneous ones where the aperture widths are distributed log normally. In both cases our modeling reveals the rules of competition: By instability one of the fingers grows faster than its competitor therefore penetrating somewhat deeper. As a consequence the hydraulic head at its tip is higher than that close to the tip of the shorter finger. Therefore the fractures connecting the tip regions of both fingers carry flow from the deep finger to the tip region of its competitor. This cross-flow is replaced by increasing inflow of aggressive solution into the input of the winner, enhancing further dissolution and growth. On the other hand the cross-flow increases the head at the tip of the losing finger, and consequently decreases inflow of aggressive solution into it, thus inhibiting its further evolution. This mechanism supports further growth of the winner (wormhole) and stops the growth of its competitor. Similar competition happens in the case of several fingers competing. In any case we observe flow from the winning fingers to the loosing ones. The communication between the competitors is always established by cross flow between its tip regions. We will present various scenarios of wormhole formation, which demonstrate details of the competition of fingers arising from either the reactive instability or from the statistical distribution of fracture aperture widths. In conclusion we find that the initiation of wormholes results either from instability or from the statistical distribution of favorable pathways. Once growth of fingers has been initiated the evolution of the wormhole patterns becomes deterministic. (1) Szymczak, P., and A.J.C. Ladd (2011), The initial stages of cave formation: Beyond the one-dimensional paradigm, Earth Planet. Sci. Lett. 301, 424-432 (2) Dreybrodt, W., Gabrovšek, F., Romanov, D.(2005) Processes of Speleogenesis: A Modeling Approach. ZRC Publishing, Karst Research Institute at ZRC SAZU, Ljubljana

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

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

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

Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites

DOE PAGES

Uberuaga, Blas Pedro; Pilania, Ghanshyam

2015-07-08

Perovskite structured oxides (ABO 3) are attractive for a number of technological applications, including as superionics because of the high oxygen conductivities they exhibit. Double perovskites (AA’BB’O 6) provide even more flexibility for tailoring properties. Using accelerated molecular dynamics, we examine the role of cation ordering on oxygen vacancy mobility in one model double perovskite SrLaTiAlO 6. We find that the mobility of the vacancy is very sensitive to the cation ordering, with a migration energy that varies from 0.6 to 2.7 eV. In the extreme cases, the mobility is both higher and lower than either of the two endmore » member single perovskites. Further, the nature of oxygen vacancy diffusion, whether one-dimensional, two-dimensional, or three-dimensional, also varies with cation ordering. We correlate the dependence of oxygen mobility on cation structure to the distribution of Ti 4+ cations, which provide unfavorable environments for the positively charged oxygen vacancy. The results demonstrate the potential of using tailored double perovskite structures to precisely control the behavior of oxygen vacancies in these materials.« less

Effects of alpha stopping power modelling on the ignition threshold in a directly-driven inertial confinement fusion capsule

DOE PAGES

Temporal, Mauro; Canaud, Benoit; Cayzac, Witold; ...

2017-05-25

The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP and themore » BPS stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. Furthermore, the results provided by the two models have been compared and it is found that – close to the ignition threshold – in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.« less

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

PubMed Central

Saliba, Daniel

2016-01-01

We report the synthesis of magnesium–aluminium layered double hydroxide (LDH) using a reaction–diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium–aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’. PMID:27698034

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

Kim, G. H.; Pesaran, A.; Spotnitz, R.

To understand further the thermal abuse behavior of large format Li-ion batteries for automotive applications, the one-dimensional modeling approach formulated by Hatchard et al. was reproduced. Then it was extended to three dimensions so we could consider the geometrical features, which are critical in large cells for automotive applications. The three-dimensional model captures the shapes and dimensions of cell components and the spatial distributions of materials and temperatures, and is used to simulate oven tests, and to determine how a local hot spot can propagate through the cell. In simulations of oven abuse testing of cells with cobalt oxide cathodemore » and graphite anode with standard LiPF6 electrolyte, the three-dimensional model predicts that thermal runaway will occur sooner or later than the lumped model, depending on the size of the cell. The model results showed that smaller cells reject heat faster than larger cells; this may prevent them from going into thermal runaway under identical abuse conditions. In simulations of local hot spots inside a large cylindrical cell, the three-dimensional model predicts that the reactions initially propagate in the azimuthal and longitudinal directions to form a hollow cylinder-shaped reaction zone.« less

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Scaling hyporheic exchange and its influence on biogeochemical reactions in aquatic ecosystems

USGS Publications Warehouse

O'Connor, Ben L.; Harvey, Judson W.

2008-01-01

Hyporheic exchange and biogeochemical reactions are difficult to quantify because of the range in fluid‐flow and sediment conditions inherent to streams, wetlands, and nearshore marine ecosystems. Field measurements of biogeochemical reactions in aquatic systems are impeded by the difficulty of measuring hyporheic flow simultaneously with chemical gradients in sediments. Simplified models of hyporheic exchange have been developed using Darcy's law generated by flow and bed topography at the sediment‐water interface. However, many modes of transport are potentially involved (molecular diffusion, bioturbation, advection, shear, bed mobility, and turbulence) with even simple models being difficult to apply in complex natural systems characterized by variable sediment sizes and irregular bed geometries. In this study, we synthesize information from published hyporheic exchange investigations to develop a scaling relationship for estimating mass transfer in near‐surface sediments across a range in fluid‐flow and sediment conditions. Net hyporheic exchange was quantified using an effective diffusion coefficient (De) that integrates all of the various transport processes that occur simultaneously in sediments, and dimensional analysis was used to scale De to shear stress velocity, roughness height, and permeability that describe fluid‐flow and sediment characteristics. We demonstrated the value of the derived scaling relationship by using it to quantify dissolved oxygen (DO) uptake rates on the basis of DO profiles in sediments and compared them to independent flux measurements. The results support a broad application of the De scaling relationship for quantifying coupled hyporheic exchange and biogeochemical reaction rates in streams and other aquatic ecosystems characterized by complex fluid‐flow and sediment conditions.

The existence of minimum speed of traveling wave solutions to a non-KPP isothermal diffusion system

NASA Astrophysics Data System (ADS)

Chen, Xinfu; Liu, Guirong; Qi, Yuanwei

2017-08-01

The reaction-diffusion system at =axx - abn ,bt = Dbxx + abn, where n ≥ 1 and D > 0, arises from many real-world chemical reactions. Whereas n = 1 is the KPP type nonlinearity, which is much studied and very important results obtained in literature not only in one dimensional spatial domains, but also multi-dimensional spaces, but n > 1 proves to be much harder. One of the interesting features of the system is the existence of traveling wave solutions. In particular, for the traveling wave solution a (x , t) = a (x - vt), b (x , t) = b (x - vt), where v > 0, if we fix lim x → - ∞ ⁡ (a , b) = (0 , 1) it was proved by many authors with different bounds v* (n , D) > 0 such that a traveling wave solution exists for any v ≥v* when n > 1. For the latest progress, see [7]. That is, the traveling wave problem exhibits the mono-stable phenomenon for traveling wave of scalar equation ut =uxx + f (u) with f (0) = f (1) = 0, f (u) > 0 in (0 , 1) and, u = 0 is unstable and u = 1 is stable. A natural and significant question is whether, like the scalar case, there exists a minimum speed. That is, whether there exists a minimum speed vmin > 0 such that traveling wave solution of speed v exists iff v ≥vmin? This is an open question, in spite of many works on traveling wave of the system in last thirty years. This is duo to the reason, unlike the KPP case, the minimum speed cannot be obtained through linear analysis at equilibrium points (a , b) = (0 , 1) and (a , b) = (1 , 0). In this work, we give an affirmative answer to this question.

Diffusion of One-Dimensional Crystals in Channels of Single-Walled Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Zhigalina, V. G.; Kumskov, A. S.; Falaleev, N. S.; Vasiliev, A. L.; Kiselev, N. A.

2018-05-01

The transport of one-dimensional CuI crystals in channels of single-walled carbon nanotubes (SWCNTs) has been studied by high resolution electron microscopy. The diffusion kinetics has been investigated by counting the number of CuI atoms escaping from the nanotube channel. The diffusivity is calculated to be 6.8 × 10-21 m2/s, which corresponds to an activation-barrier height of 1 eV/atom. A comparison with the theoretically estimated height of the energy barrier for molecular transport through a graphene layer is indicative of mass transfer through vacancy defects in graphene.

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.

Correlation between discrete probability and reaction front propagation rate in heterogeneous mixtures

NASA Astrophysics Data System (ADS)

Naine, Tarun Bharath; Gundawar, Manoj Kumar

2017-09-01

We demonstrate a very powerful correlation between the discrete probability of distances of neighboring cells and thermal wave propagation rate, for a system of cells spread on a one-dimensional chain. A gamma distribution is employed to model the distances of neighboring cells. In the absence of an analytical solution and the differences in ignition times of adjacent reaction cells following non-Markovian statistics, invariably the solution for thermal wave propagation rate for a one-dimensional system with randomly distributed cells is obtained by numerical simulations. However, such simulations which are based on Monte-Carlo methods require several iterations of calculations for different realizations of distribution of adjacent cells. For several one-dimensional systems, differing in the value of shaping parameter of the gamma distribution, we show that the average reaction front propagation rates obtained by a discrete probability between two limits, shows excellent agreement with those obtained numerically. With the upper limit at 1.3, the lower limit depends on the non-dimensional ignition temperature. Additionally, this approach also facilitates the prediction of burning limits of heterogeneous thermal mixtures. The proposed method completely eliminates the need for laborious, time intensive numerical calculations where the thermal wave propagation rates can now be calculated based only on macroscopic entity of discrete probability.

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

Tsai, Shang-Min; Grosheintz, Luc; Kitzmann, Daniel

We present an open-source and validated chemical kinetics code for studying hot exoplanetary atmospheres, which we name VULCAN. It is constructed for gaseous chemistry from 500 to 2500 K, using a reduced C–H–O chemical network with about 300 reactions. It uses eddy diffusion to mimic atmospheric dynamics and excludes photochemistry. We have provided a full description of the rate coefficients and thermodynamic data used. We validate VULCAN by reproducing chemical equilibrium and by comparing its output versus the disequilibrium-chemistry calculations of Moses et al. and Rimmer and Helling. It reproduces the models of HD 189733b and HD 209458b by Mosesmore » et al., which employ a network with nearly 1600 reactions. We also use VULCAN to examine the theoretical trends produced when the temperature–pressure profile and carbon-to-oxygen ratio are varied. Assisted by a sensitivity test designed to identify the key reactions responsible for producing a specific molecule, we revisit the quenching approximation and find that it is accurate for methane but breaks down for acetylene, because the disequilibrium abundance of acetylene is not directly determined by transport-induced quenching, but is rather indirectly controlled by the disequilibrium abundance of methane. Therefore we suggest that the quenching approximation should be used with caution and must always be checked against a chemical kinetics calculation. A one-dimensional model atmosphere with 100 layers, computed using VULCAN, typically takes several minutes to complete. VULCAN is part of the Exoclimes Simulation Platform (ESP; exoclime.net) and publicly available at https://github.com/exoclime/VULCAN.« less

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Cosmic Ray Hysteresis as Evidence for Time-dependent Diffusive Processes in the Long Term Solar Modulation

NASA Technical Reports Server (NTRS)

Ogallagher, J. J.

1973-01-01

A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.

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.