High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Combined measurement of surface, grain boundary and lattice diffusion coefficients on olivine bi-crystals

NASA Astrophysics Data System (ADS)

Marquardt, Katharina; Dohmen, Ralf; Wagner, Johannes

2014-05-01

Diffusion along interface and grain boundaries provides an efficient pathway and may control chemical transport in rocks as well as their mechanical strength. Besides the significant relevance of these diffusion processes for various geologic processes, experimental data are still very limited (e.g., Dohmen & Milke, 2010). Most of these data were measured using polycrystalline materials and the formalism of LeClaire (1951) to fit integrated concentration depth profiles. To correctly apply this formalism, certain boundary conditions of the diffusion problem need to be fulfilled, e.g., surface diffusion is ignored, and furthermore the lattice diffusion coefficient has to be known from other studies or is an additional fitting parameter, which produces some ambiguity in the derived grain boundary diffusion coefficients. We developed an experimental setup where we can measure the lattice and grain boundary diffusion coefficients simultaneously but independent and demonstrate the relevance of surface diffusion for typical grain boundary diffusion experiments. We performed Mg2SiO4 bicrystal diffusion experiments, where a single grain boundary is covered by a thin-film of pure Ni2SiO4 acting as diffusant source, produced by pulsed laser deposition. The investigated grain boundary is a 60° (011)/[100]. This specific grain boundary configuration was modeled using molecular dynamics for comparison with the experimental observations in the transmission electron microscope (TEM). Both, experiment and model are in good agreement regarding the misorientation, whereas there are still some disagreements regarding the strain fields along the grain boundary that are of outmost importance for the strengths of the material. The subsequent diffusion experiments were carried out in the temperature range between 800° and 1450° C. The inter diffusion profiles were measured using the TEMs energy dispersive x-ray spectrometer standardized using the Cliff-Lorimer equation and EMPA measurements. To evaluate the obtained diffusion profiles we adapted the isolated grain boundary model, first proposed by Fisher (1951) to match several observations: (i) Anisotropic diffusion in forsterite, (ii) fast diffusion along the grain boundary, (iii) fast diffusion on the surface of the sample. The latter process is needed to explain an additional flux of material from the surface into the grain boundary. Surface and grain boundary diffusion coefficients are on the order of 10000 times faster than diffusion in the lattice. Another observation was that in some regions the diffusion profiles in the lattice were greatly extended. TEM observations suggest here that surface defects (nano-cracks, ect.) have been present, which apparently enhanced the diffusion through the bulk lattice. Dohmen, R., & Milke, R. (2010). Diffusion in Polycrystalline Materials: Grain Boundaries, Mathematical Models, and Experimental Data. Reviews in Mineralogy and Geochemistry, 72(1), 921-970. Fisher, J. C. (1951). Calculations of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion. Journal of Applied Physics, 22(1), 74-77. Le Claire, A. D. (1951). Grain boundary diffusion in metals. Philosophical Magazine A, 42(328), 468-474.

A novel CFS-PML boundary condition for transient electromagnetic simulation using a fictitious wave domain method

NASA Astrophysics Data System (ADS)

Hu, Yanpu; Egbert, Gary; Ji, Yanju; Fang, Guangyou

2017-01-01

In this study, we apply fictitious wave domain (FWD) methods, based on the correspondence principle for the wave and diffusion fields, to finite difference (FD) modeling of transient electromagnetic (TEM) diffusion problems for geophysical applications. A novel complex frequency shifted perfectly matched layer (PML) boundary condition is adapted to the FWD to truncate the computational domain, with the maximum electromagnetic wave propagation velocity in the FWD used to set the absorbing parameters for the boundary layers. Using domains of varying spatial extent we demonstrate that these boundary conditions offer significant improvements over simpler PML approaches, which can result in spurious reflections and large errors in the FWD solutions, especially for low frequencies and late times. In our development, resistive air layers are directly included in the FWD, allowing simulation of TEM responses in the presence of topography, as is commonly encountered in geophysical applications. We compare responses obtained by our new FD-FWD approach and with the spectral Lanczos decomposition method on 3-D resistivity models of varying complexity. The comparisons demonstrate that our absorbing boundary condition in FWD for the TEM diffusion problems works well even in complex high-contrast conductivity models.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

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

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Pore-scale lattice Boltzmann simulation of micro-gaseous flow considering surface diffusion effect

DOE PAGES

Wang, Junjian; Kang, Qinjun; Chen, Li; ...

2016-11-21

Some recent studies have shown that adsorbed gas and its surface diffusion have profound influence on micro-gaseous flow through organic pores in shale gas reservoirs. Here, a multiple-relaxation-time (MRT) LB model is adopted to estimate the apparent permeability of organic shale and a new boundary condition, which combines Langmuir adsorption theory with Maxwellian diffusive reflection boundary condition, is proposed to capture gas slip and surface diffusion of adsorbed gas. The simulation results match well with previous studies carried out using Molecular Dynamics (MD) and show that Maxwell slip boundary condition fails to characterize gas transport in the near wall regionmore » under the influence of the adsorbed gas. The total molar flux can be either enhanced or reduced depending on variations in adsorbed gas coverage and surface diffusion velocity. The effects of pore width, pressure as well as Langmuir properties on apparent permeability of methane transport in organic pores are further studied. It is found that the surface transport plays a significant role in determining the apparent permeability, and the variation of apparent permeability with pore size and pressure is affected by the adsorption and surface diffusion.« less

Far-field analysis of coupled bulk and boundary layer diffusion toward an ion channel entrance.

PubMed Central

Schumaker, M F; Kentler, C J

1998-01-01

We present a far-field analysis of ion diffusion toward a channel embedded in a membrane with a fixed charge density. The Smoluchowski equation, which represents the 3D problem, is approximated by a system of coupled three- and two-dimensional diffusions. The 2D diffusion models the quasi-two-dimensional diffusion of ions in a boundary layer in which the electrical potential interaction with the membrane surface charge is important. The 3D diffusion models ion transport in the bulk region outside the boundary layer. Analytical expressions for concentration and flux are developed that are accurate far from the channel entrance. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresponding to experiments of Bell and Miller (Biophys. J. 45:279, 1984). PMID:9591651

Multiscale simulation of xenon diffusion and grain boundary segregation in UO₂

DOE PAGES

Andersson, David A.; Tonks, Michael R.; Casillas, Luis; ...

2015-07-01

In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. The segregation rate is controlled by diffusion of fission gas atoms through the grains and interaction with the boundaries. Based on the mechanisms established from earlier density functional theory (DFT) and empirical potential calculations, diffusion models for xenon (Xe), uranium (U) vacancies and U interstitials in UO₂ have been derived for both intrinsic (no irradiation) and irradiation conditions. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model formore » the interaction between Xe atoms and three different grain boundaries in UO₂ (Σ5 tilt, Σ5 twist and a high angle random boundary), as derived from atomistic calculations. The present model does not attempt to capture nucleation or growth of fission gas bubbles at the grain boundaries. The point defect and Xe diffusion and segregation models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as to simulate Xe redistribution for a few simple microstructures.« less

Coupled thermo-chemical boundary conditions in double-diffusive geodynamo models at arbitrary Lewis numbers.

NASA Astrophysics Data System (ADS)

Bouffard, M.

2016-12-01

Convection in the Earth's outer core is driven by the combination of two buoyancy sources: a thermal source directly related to the Earth's secular cooling, the release of latent heat and possibly the heat generated by radioactive decay, and a compositional source due to the crystallization of the growing inner core which releases light elements into the liquid outer core. The dynamics of fusion/crystallization being dependent on the heat flux distribution, the thermochemical boundary conditions are coupled at the inner core boundary which may affect the dynamo in various ways, particularly if heterogeneous conditions are imposed at one boundary. In addition, the thermal and compositional molecular diffusivities differ by three orders of magnitude. This can produce significant differences in the convective dynamics compared to pure thermal or compositional convection due to the potential occurence of double-diffusive phenomena. Traditionally, temperature and composition have been combined into one single variable called codensity under the assumption that turbulence mixes all physical properties at an "eddy-diffusion" rate. This description does not allow for a proper treatment of the thermochemical coupling and is certainly incorrect within stratified layers in which double-diffusive phenomena can be expected. For a more general and rigorous approach, two distinct transport equations should therefore be solved for temperature and composition. However, the weak compositional diffusivity is technically difficult to handle in current geodynamo codes and requires the use of a semi-Lagrangian description to minimize numerical diffusion. We implemented a "particle-in-cell" method into a geodynamo code to properly describe the compositional field. The code is suitable for High Parallel Computing architectures and was successfully tested on two benchmarks. Following the work by Aubert et al. (2008) we use this new tool to perform dynamo simulations including thermochemical coupling at the inner core boundary as well as exploration of the infinite Lewis number limit to study the effect of a heterogeneous core mantle boundary heat flow on the inner core growth.

Pharmaceutical modulation of diffusion potentials at aqueous-aqueous boundaries under laminar flow conditions.

PubMed

Collins, Courtney J; Strutwolf, Jörg; Arrigan, Damien W M

2011-04-01

In this work, the modulation of the diffusion potential formed at the microfluidic aqueous-aqueous boundary by a pharmaceutical substance is presented. Co-flowing aqueous streams in a microchannel were used to form the stable boundary between the streams. Measurement of the open circuit potential between two silver/silver chloride electrodes enabled the diffusion potential at the boundary to be determined, which is concentration dependent. Experimental results for protonated propranolol as well as tetrapropylammonium are presented. This concept may be useful as a strategy for the detection of drug substances. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

DOE PAGES

D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; ...

2015-12-21

We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result,more » the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.« less

The first boundary-value problem for a fractional diffusion-wave equation in a non-cylindrical domain

NASA Astrophysics Data System (ADS)

Pskhu, A. V.

2017-12-01

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan- Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann- Liouville and Caputo derivatives are particular cases of results obtained here.

Laminar Diffusion Flame Studies (Ground- and Space-Based Studies)

NASA Technical Reports Server (NTRS)

Dai, Z.; El-Leathy, A. M.; Lin, K.-C.; Sunderland, P. B.; Xu, F.; Faeth, G. M.; Urban, D. L. (Technical Monitor); Yuan, Z.-G. (Technical Monitor)

2000-01-01

Laminar diffusion flames are of interest because they provide model flame systems that are far more tractable for analysis and experiments than more practical turbulent diffusion flames. Certainly, understanding flame processes within laminar diffusion flames must precede understanding these processes in more complex turbulent diffusion flames. In addition, many properties of laminar diffusion flames are directly relevant to turbulent diffusion flames using laminar flamelet concepts. Laminar jet diffusion flame shapes (luminous flame boundaries) have been of particular interest since the classical study of Burke and Schumann because they are a simple nonintrusive measurement that is convenient for evaluating flame structure predictions. Thus, consideration of laminar flame shapes is undertaken in the following, emphasizing conditions where effects of gravity are small, due to the importance of such conditions to practical applications. Another class of interesting properties of laminar diffusion flames are their laminar soot and smoke point properties (i.e., the flame length, fuel flow rate, characteristic residence time, etc., at the onset of soot appearance in the flame (the soot point) and the onset of soot emissions from the flame (the smoke point)). These are useful observable soot properties of nonpremixed flames because they provide a convenient means to rate several aspects of flame sooting properties: the relative propensity of various fuels to produce soot in flames; the relative effects of fuel structure, fuel dilution, flame temperature and ambient pressure on the soot appearance and emission properties of flames; the relative levels of continuum radiation from soot in flames; and effects of the intrusion of gravity (or buoyant motion) on emissions of soot from flames. An important motivation to define conditions for soot emissions is that observations of laminar jet diffusion flames in critical environments, e.g., space shuttle and space station facilities, cannot involve soot emitting flames in order to ensure that test chamber windows used for experimental observations are not blocked by soot deposits, thereby compromising unusually valuable experimental results. Another important motivation to define conditions where soot is present in diffusion flames is that flame chemistry, transport and radiation properties are vastly simplified when soot is absent, making such flames far more tractable for detailed numerical simulations than corresponding soot-containing flames. Motivated by these observations, the objectives of this phase of the investigation were as follows: (1) Observe flame-sheet shapes (the location of the reaction zone near phi=1) of nonluminous (soot free) laminar jet diffusion flames in both still and coflowing air and use these results to develop simplified models of flame-sheet shapes for these conditions; (2) Observe luminous flame boundaries of luminous (soot-containing) laminar jet diffusion flames in both still and coflowing air and use these results to develop simplified models of luminous flame boundaries for these conditions. In order to fix ideas here, maximum luminous flame boundaries at the laminar smoke point conditions were sought, i.e., luminous flame boundaries at the laminar smoke point; (3) Observe effects of coflow on laminar soot- and smoke-point conditions because coflow has been proposed as a means to control soot emissions and minimize the presence of soot in diffusion flames.

Simulation of xenon, uranium vacancy and interstitial diffusion and grain boundary segregation in UO 2

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

Andersson, Anders D.; Tonks, Michael R.; Casillas, Luis

2014-10-31

In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. Based on the mechanisms established from density functional theory (DFT) and empirical potential calculations 1, continuum models for diffusion of xenon (Xe), uranium (U) vacancies and U interstitials in UO 2 have been derived for both intrinsic conditions and under irradiation. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model for the interaction between Xe atoms and three different grain boundaries in UO 2 ( Σ5 tilt, Σ5more » twist and a high angle random boundary),as derived from atomistic calculations. All models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as redistribution for a few simple microstructures.« less

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.

Design-for-manufacture of gradient-index optical systems using time-varying boundary condition diffusion

NASA Astrophysics Data System (ADS)

Harkrider, Curtis Jason

2000-08-01

The incorporation of gradient-index (GRIN) material into optical systems offers novel and practical solutions to lens design problems. However, widespread use of gradient-index optics has been limited by poor correlation between gradient-index designs and the refractive index profiles produced by ion exchange between glass and molten salt. Previously, a design-for- manufacture model was introduced that connected the design and fabrication processes through use of diffusion modeling linked with lens design software. This project extends the design-for-manufacture model into a time- varying boundary condition (TVBC) diffusion model. TVBC incorporates the time-dependent phenomenon of melt poisoning and introduces a new index profile control method, multiple-step diffusion. The ions displaced from the glass during the ion exchange fabrication process can reduce the total change in refractive index (Δn). Chemical equilibrium is used to model this melt poisoning process. Equilibrium experiments are performed in a titania silicate glass and chemically analyzed. The equilibrium model is fit to ion concentration data that is used to calculate ion exchange boundary conditions. The boundary conditions are changed purposely to control the refractive index profile in multiple-step TVBC diffusion. The glass sample is alternated between ion exchange with a molten salt bath and annealing. The time of each diffusion step can be used to exert control on the index profile. The TVBC computer model is experimentally verified and incorporated into the design- for-manufacture subroutine that runs in lens design software. The TVBC design-for-manufacture model is useful for fabrication-based tolerance analysis of gradient-index lenses and for the design of manufactureable GRIN lenses. Several optical elements are designed and fabricated using multiple-step diffusion, verifying the accuracy of the model. The strength of multiple-step diffusion process lies in its versatility. An axicon, imaging lens, and curved radial lens, all with different index profile requirements, are designed out of a single glass composition.

Antimony diffusion in CdTe

DOE PAGES

Colegrove, Eric; Harvey, Steven P.; Yang, Ji -Hui; ...

2017-02-08

Group V dopants may be used for next-generation high-voltage cadmium telluride (CdTe) solar photovoltaics, but fundamental defect energetics and kinetics need to be understood. Here, antimony (Sb) diffusion is studied in single-crystal and polycrystalline CdTe under Cd-rich conditions. Diffusion profiles are determined by dynamic secondary ion mass spectroscopy and analyzed with analytical bulk and grain-boundary diffusion models. Slow bulk and fast grain-boundary diffusion are found. Density functional theory is used to understand formation energy and mechanisms. Lastly, the theory and experimental results create new understanding of group V defect kinetics in CdTe.

Modeling radiation belt electron dynamics during GEM challenge intervals with the DREAM3D diffusion model

NASA Astrophysics Data System (ADS)

Tu, Weichao; Cunningham, G. S.; Chen, Y.; Henderson, M. G.; Camporeale, E.; Reeves, G. D.

2013-10-01

a response to the Geospace Environment Modeling (GEM) "Global Radiation Belt Modeling Challenge," a 3D diffusion model is used to simulate the radiation belt electron dynamics during two intervals of the Combined Release and Radiation Effects Satellite (CRRES) mission, 15 August to 15 October 1990 and 1 February to 31 July 1991. The 3D diffusion model, developed as part of the Dynamic Radiation Environment Assimilation Model (DREAM) project, includes radial, pitch angle, and momentum diffusion and mixed pitch angle-momentum diffusion, which are driven by dynamic wave databases from the statistical CRRES wave data, including plasmaspheric hiss, lower-band, and upper-band chorus. By comparing the DREAM3D model outputs to the CRRES electron phase space density (PSD) data, we find that, with a data-driven boundary condition at Lmax = 5.5, the electron enhancements can generally be explained by radial diffusion, though additional local heating from chorus waves is required. Because the PSD reductions are included in the boundary condition at Lmax = 5.5, our model captures the fast electron dropouts over a large L range, producing better model performance compared to previous published results. Plasmaspheric hiss produces electron losses inside the plasmasphere, but the model still sometimes overestimates the PSD there. Test simulations using reduced radial diffusion coefficients or increased pitch angle diffusion coefficients inside the plasmasphere suggest that better wave models and more realistic radial diffusion coefficients, both inside and outside the plasmasphere, are needed to improve the model performance. Statistically, the results show that, with the data-driven outer boundary condition, including radial diffusion and plasmaspheric hiss is sufficient to model the electrons during geomagnetically quiet times, but to best capture the radiation belt variations during active times, pitch angle and momentum diffusion from chorus waves are required.

Role of boundary layer diffusion in vapor deposition growth of chalcogenide nanosheets: the case of GeS.

PubMed

Li, Chun; Huang, Liang; Snigdha, Gayatri Pongur; Yu, Yifei; Cao, Linyou

2012-10-23

We report a synthesis of single-crystalline two-dimensional GeS nanosheets using vapor deposition processes and show that the growth behavior of the nanosheet is substantially different from those of other nanomaterials and thin films grown by vapor depositions. The nanosheet growth is subject to strong influences of the diffusion of source materials through the boundary layer of gas flows. This boundary layer diffusion is found to be the rate-determining step of the growth under typical experimental conditions, evidenced by a substantial dependence of the nanosheet's size on diffusion fluxes. We also find that high-quality GeS nanosheets can grow only in the diffusion-limited regime, as the crystalline quality substantially deteriorates when the rate-determining step is changed away from the boundary layer diffusion. We establish a simple model to analyze the diffusion dynamics in experiments. Our analysis uncovers an intuitive correlation of diffusion flux with the partial pressure of source materials, the flow rate of carrier gas, and the total pressure in the synthetic setup. The observed significant role of boundary layer diffusions in the growth is unique for nanosheets. It may be correlated with the high growth rate of GeS nanosheets, ~3-5 μm/min, which is 1 order of magnitude higher than other nanomaterials (such as nanowires) and thin films. This fundamental understanding of the effect of boundary layer diffusions may generally apply to other chalcogenide nanosheets that can grow rapidly. It can provide useful guidance for the development of general paradigms to control the synthesis of nanosheets.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

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

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and themore » perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.« less

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

A new boundary scheme for simulation of gas flow in kerogen pores with considering surface diffusion effect

NASA Astrophysics Data System (ADS)

Wang, Lingquan; Zeng, Zhong; Zhang, Liangqi; Qiao, Long; Zhang, Yi; Lu, Yiyu

2018-04-01

Navier-Stokes (NS) equations with no-slip boundary conditions fail to realistically describe micro-flows with considering nanoscale phenomena. Particularly, in kerogen pores, slip-flow and surface diffusion are important. In this study, we propose a new slip boundary scheme for the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the slip-flow considering surface diffusion effect. Meanwhile, the second-order slip velocity can be taken into account. The predicted characteristics in a two-dimensional micro-flow, including slip-velocity, velocity distribution along the flow direction with/without surface diffusion are present. The results in this study are compared with available analytical and reference results, and good agreements are achieved.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

NASA Astrophysics Data System (ADS)

Admal, Nikhil Chandra; Po, Giacomo; Marian, Jaime

2017-12-01

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F( X,t)= F L( X,t) F P( X,t), an initial stress-free polycrystal is constructed by imposing F L to be a piecewise constant rotation field R 0( X), and F P= R 0( X)T, thereby having F( X,0)= I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.

Diurnal forcing of planetary atmospheres

NASA Technical Reports Server (NTRS)

Houben, Howard C.

1991-01-01

A free convection parameterization has been introduced into the Mars Planetary Boundary Layer Model (MPBL). Previously, the model would fail to generate turbulence under conditions of zero wind shear, even when statically unstable. This in turn resulted in erroneous results at the equator, for example, when the lack of Coriolis forcing allowed zero wind conditions. The underlying cause of these failures was the level 2 second-order turbulence closure scheme which derived diffusivities as algebraic functions of the Richardson number (the ratio of static stability to wind shear). In the previous formulation, the diffusivities were scaled by the wind shear--a convenient parameter since it is non-negative. This was the drawback that all diffusivities are zero under conditions of zero shear (viz., the free convection case). The new scheme tests for the condition of zero shear in conjunction with static instability and recalculates the diffusivities using a static stability scaling. The results for a simulation of the equatorial boundary layer at autumnal equinox are presented. (Note that after some wind shear is generated, the model reverts to the traditional diffusivity calculation.)

Effects of Refractive Index and Diffuse or Specular Boundaries on a Radiating Isothermal Layer

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Equilibrium temperatures of an absorbing-emitting layer were obtained for exposure to incident radiation and with the layer boundaries either specular or diffuse. For high refractive indices the surface condition can influence the radiative heat balance if the layer optical thickness is small. Hence for a spectrally varying absorption coefficient the layer temperature is affected if there is significant radiative energy in the spectral range with a small absorption coefficient. Similar behavior was obtained for transient radiative cooling of a layer where the results are affected by the initial temperature and hence the fraction of energy radiated in the short wavelength region where the absorption coefficient is small. The results are a layer without internal scattering. If internal scattering is significant, the radiation reaching the internal surface of a boundary is diffused and the effect of the two different surface conditions would become small.

Effect of natural convection in a horizontally oriented cylinder on NMR imaging of the distribution of diffusivity

PubMed

Mohoric; Stepisnik

2000-11-01

This paper describes the influence of natural convection on NMR measurement of a self-diffusion constant of fluid in the earth's magnetic field. To get an estimation of the effect, the Lorenz model of natural convection in a horizontally oriented cylinder, heated from below, is derived. Since the Lorenz model of natural convection is derived for the free boundary condition, its validity is of a limited value for the natural no-slip boundary condition. We point out that even a slight temperature gradient can cause significant misinterpretation of measurements. The chaotic nature of convection enhances the apparent self-diffusion constant of the liquid.

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

NASA Astrophysics Data System (ADS)

Barletti, Luigi; Negulescu, Claudia

2018-05-01

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

On the Boundary Condition Between Two Multiplying Media

DOE R&D Accomplishments Database

Friedman, F. L.; Wigner, E. P.

1944-04-19

The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

NASA Technical Reports Server (NTRS)

Shen, F.; Khodadadi, J. M.

1993-01-01

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

Prediction of Laminar and Turbulent Boundary Layer Flow Separation in V/STOL Engine Inlets

NASA Technical Reports Server (NTRS)

Chou, D. C.; Luidens, R. W.; Stockman, N. O.

1977-01-01

A description is presented of the development of the boundary layer on the lip and diffuser surface of a subsonic inlet at arbitrary operating conditions of mass flow rate, free stream velocity and incidence angle. Both laminar separation on the lip and turbulent separation in the diffuser are discussed. The agreement of the theoretical results with model experimental data illustrates the capability of the theory to predict separation. The effects of throat Mach number, inlet size, and surface roughness on boundary layer development and separation are illustrated.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

NASA Astrophysics Data System (ADS)

Hill, Peter; Shanahan, Brendan; Dudson, Ben

2017-04-01

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q → ∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions. The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined. We also demonstrate the feasibility of using the FCI approach in no n-axisymmetric configurations for a simple diffusion model in a "straight stellarator" magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius. The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells

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

Weber, Adam Z.; Newman, John

2008-08-29

In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.

Studies of the phase gradient at the boundary of the phase diffusion equation, motivated by peculiar wave patterns of rhythmic contraction in the amoeboid movement of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Iima, Makoto; Kori, Hiroshi; Nakagaki, Toshiyuki

2017-04-01

The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.

Hydrodynamic and Thermal Slip Effect on Double-Diffusive Free Convective Boundary Layer Flow of a Nanofluid Past a Flat Vertical Plate in the Moving Free Stream

PubMed Central

Khan, Waqar A.; Uddin, Md Jashim; Ismail, A. I. Md.

2013-01-01

The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters. PMID:23533566

Localized traveling pulses in natural doubly diffusive convection

NASA Astrophysics Data System (ADS)

Lo Jacono, D.; Bergeon, A.; Knobloch, E.

2017-09-01

Two-dimensional natural doubly diffusive convection in a vertical slot driven by an imposed temperature difference in the horizontal is studied using numerical continuation and direct numerical simulation. Two cases are considered and compared. In the first a concentration difference that balances thermal buoyancy is imposed in the horizontal and stationary localized structures are found to be organized in a standard snakes-and-ladders bifurcation diagram. Disconnected branches of traveling pulses TPn consisting of n ,n =1 ,2 ,⋯ , corotating cells are identified and shown to accumulate on a tertiary branch of traveling waves. With Robin or mixed concentration boundary conditions on one wall all localized states travel and the hitherto stationary localized states may connect up with the traveling pulses. The stability of the TPn states is determined and unstable TPn shown to evolve into spatio-temporal chaos. The calculations are done with no-slip boundary conditions in the horizontal and periodic boundary conditions in the vertical.

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

Flame and Soot Boundaries of Laminar Jet Diffusion Flames. Appendix A

NASA Technical Reports Server (NTRS)

Xu, F.; Dai, Z.; Faeth, G. M.; Yuan, Z.-G. (Technical Monitor); Urban, D. L. (Technical Monitor); Yuan, Z.-G. (Technical Monitor)

2002-01-01

The shapes (flame-sheet and luminous-flame boundaries) or steady weakly buoyant round hydrocarbon-fueled laminar-jet diffusion flames in still and coflowing air were studied both experimentally and theoretically. Flame-sheet shapes were measured from photographs using a CH optical filter to distinguish flame-sheet boundaries in the presence of blue CO2 and OH emissions and yellow continuum radiation from soot. Present experimental conditions included acetylene-, methane-, propane-, and ethylene-fueled flames having initial reactant temperatures of 300 K. ambient pressures of 4-50 kPa, jet-exit Reynolds numbers of 3-54, initial air/fuel velocity ratios of 0-9, and luminous flame lengths of 5-55 mm; earlier measurements for propylene- and 1,3-butadiene-fueled flames for similar conditions were considered as well. Nonbuoyant flames in still air were observed at microgravity conditions; essentially nonbuoyant flames in coflowing air were observed at small pressures to control effects of buoyancy. Predictions of luminous flame boundaries from soot luminosity were limited to laminar smoke-point conditions, whereas predictions of flame-sheet boundaries ranged from soot-free to smoke-point conditions. Flame-shape predictions were based on simplified analyses using the boundary-layer approximations along with empirical parameters to distinguish flame-sheet and luminous-flame (at the laminar smoke point) boundaries. The comparison between measurements and predictions was remarkably good and showed that both flame-sheet and luminous-flame lengths are primarily controlled by fuel flow rates with lengths in coflowing air approaching 2/3 of the lengths in still air as coflowing air velocities are increased. Finally, luminous flame lengths at laminar smoke-point conditions were roughly twice as long as flame-sheet lengths at comparable conditions because of the presence of luminous soot particles in the fuel-lean region of the flames.

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Effect of concentration boundary layers on passive solute flows in a system of two polymeric membranes positioned in vertical planes.

PubMed

Slezak, Andrzej; Jasik-Slezak, Jolanta; Dworecki, Kazimierz

2003-01-01

The results of studies of influence of concentration boundary layers on passive diffusive transport in a double-membrane osmo-diffusive cell, containing a series of two (Ml and M(r)) vertically positioned, flat, microporous and symmetric polymer membranes (Nephrophane and Cellulose IMP-1) are presented in this paper. The membranes separated three compartments (l, m, r) containing binary, heterogeneous and non-ionic solutions (aqueous solutions of glucose or ethanol) or ternary non-electrolyte solutions (glucose solutions in 0.75 mol.l-1 solution of ethanol or ethanol solutions in 0.1 mol.l-1 aqueous solution of glucose). Solution concentrations fulfilled the condition C(k)l > C(k)m > C(k)r. The intermembrane compartment (m) was an infinitesimal solution layer. The volume of the m compartment and the volumes of the external (l and r) compartments fulfilled the condition Vl = Vr approximately 170 Vm. The tests were performed for configurations A and B of a double-membrane osmo-diffusive cell. In configuration A, the solution was located behind the M(r) membrane, and water was placed behind the Ml membrane, while in configuration B this sequence was reversed. The results obtained during experiment were interpreted in the categories of convective instability, which increased the value of diffusive permeability coefficient of the system: concentration boundary layer/membrane/concentration boundary layer.

Numerical study on the thermo-chemically driven Geodynamo

NASA Astrophysics Data System (ADS)

Trümper, Tobias; Hansen, Ulrich

2014-05-01

In our numerical study we consider magneto-convection in the Earth's outer core driven by buoyancy induced by heterogeneities both in the thermal and the chemical field. The outer core is thus treated as a self-gravitating, rotating, spherical shell with unstable thermal and chemical gradients across its radius. The thermal gradient is maintained by secular cooling of the core and the release of latent heat at the inner core freezing front. Simultaneously, the concentration of the light constituents of the liquid phase increases at the inner core boundary since only a smaller fraction of the light elements can be incorporated during solidification. Thus, the inner core boundary constitutes a source of compositional buoyancy. The molecular diffusivities of the driving agents differ by some orders of magnitude so that a double-diffusive model is employed in order to study the flow dynamics of this system. We investigate the influence of different thermo-chemical driving scenarios on the structure of the flow and the internal magnetic field. A constant ratio of the diffusivities (Le=10) and a constant Ekman number (Ek=10-4) are adopted. Apart from testing different driving scenarios, the double-diffusive approach also allows to implement distinct boundary conditions on temperature and composition. Isochemical and fixed chemical flux boundary conditions are implemented in order to investigate their respective influence on the flow and magnetic field generation.

Exclusion Process with Slow Boundary

NASA Astrophysics Data System (ADS)

Baldasso, Rangel; Menezes, Otávio; Neumann, Adriana; Souza, Rafael R.

2017-06-01

We study the hydrodynamic and the hydrostatic behavior of the simple symmetric exclusion process with slow boundary. The term slow boundary means that particles can be born or die at the boundary sites, at a rate proportional to N^{-θ }, where θ > 0 and N is the scaling parameter. In the bulk, the particles exchange rate is equal to 1. In the hydrostatic scenario, we obtain three different linear profiles, depending on the value of the parameter θ ; in the hydrodynamic scenario, we obtain that the time evolution of the spatial density of particles, in the diffusive scaling, is given by the weak solution of the heat equation, with boundary conditions that depend on θ . If θ \\in (0,1), we get Dirichlet boundary conditions, (which is the same behavior if θ =0, see Farfán in Hydrostatics, statical and dynamical large deviations of boundary driven gradient symmetric exclusion processes, 2008); if θ =1, we get Robin boundary conditions; and, if θ \\in (1,∞), we get Neumann boundary conditions.

Lattice continuum and diffusional creep.

PubMed

Mesarovic, Sinisa Dj

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Lattice continuum and diffusional creep

NASA Astrophysics Data System (ADS)

Mesarovic, Sinisa Dj.

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Numerical analysis of diffusion around a suspended expressway by a multi-scale CFD model

NASA Astrophysics Data System (ADS)

kondo, Hiroaki; Asahi, Kazutake; Tomizuka, Takayuki; Suzuki, Motoo

The diffusion of NO x around Ikegami-Shinmachi crossroads, which are among the most polluted roadside areas in Japan, was analyzed with a CFD model. This is a suspended four-lane express road with a six-lane ground-level road under the expressway and another four-lane ground-level road intersecting the two roads. Three types of boundary conditions for the CFD model were tested. In the first case, the boundary conditions were given with the results from the mesoscale meteorological model; in other words, the model was multi-scale. In the second case, the boundary conditions were given with the local one-point observation. In the third case, the conditions for the wind were given with the observation, and those for the turbulence were given with the mesoscale numerical model. All of the calculations indicated high concentrations in the morning and low ones in the afternoon, but they did not indicate high concentrations in the evening. The reasons for such time variations of NO x concentrations were investigated from the viewpoints of the wind direction, velocity, and boundary layer height. The results suggested that the extremely high concentration was generated by local sources and advection from the large source area of Tokyo. On the whole, the calculation with the boundary condition with the mesoscale model appears to be better than the other calculations.

Corrosion behavior of alloy 800H (Fe-21Cr-32Ni) in supercritical water

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

Tan, Lizhen; Allen, Todd R.; Yang, Ying

2011-01-01

The effect of testing conditions (temperature, time, and oxygen content) and material's microstructure (the as-received and the grain boundary engineered conditions) on the corrosion behavior of alloy 800H in high-temperature pressurized water was studied using a variety of characterization techniques. Oxidation was observed as the primary corrosion behavior on the samples. Oxide exfoliation was significantly mitigated on the grain boundary engineered samples compared to the as-received ones. The oxide formation, including some 'mushroom-shaped oxidation', is predicted via a combination of thermodynamics and kinetics influenced by the preferential diffusion of specific species using short-cut diffusion paths.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

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

Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

2015-12-01

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated atmore » various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

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

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

NASA Astrophysics Data System (ADS)

Choquet, C.; Diédhiou, M. M.; Rosier, C.

2015-10-01

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phenomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with initial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

Flame Shapes of Nonbuoyant Laminar Jet Diffusion Flames

NASA Technical Reports Server (NTRS)

Xu, F.; Dai, Z.; Faeth, G. M.; Urban, D. L. (Technical Monitor); Yuan, Z. G. (Technical Monitor)

2001-01-01

The shapes (flame-sheet and luminous-flame boundaries) of steady nonbuoyant round hydrocarbon-fueled laminar-jet diffusion flames in still and coflowing air were studied both experimentally and theoretically. Flame-sheet shapes were measured from photographs using a CH optical filter to distinguish flame-sheet boundaries in the presence of blue CO2 and OH emissions and yellow continuum radiation from soot. Present experimental conditions included acetylene-, methane-, propane-, and ethylene-fueled flames having initial reactant temperatures of 300 K, ambient pressures of 4-50 kPa, jet exit Reynolds number of 3-54, initial air/fuel velocity ratios of 0-9 and luminous flame lengths of 5-55 mm; earlier measurements for propylene- and 1,3-butadiene-fueled flames for similar conditions were considered as well. Nonbuoyant flames in still air were observed at micro-gravity conditions; essentially nonbuoyant flames in coflowing air were observed at small pressures to control effects of buoyancy. Predictions of luminous flame boundaries from soot luminosity were limited to laminar smokepoint conditions, whereas predictions of flame-sheet boundaries ranged from soot-free to smokepoint conditions. Flame-shape predictions were based on simplified analyses using the boundary layer approximations along with empirical parameters to distinguish flame-sheet and luminous flame (at the laminar smoke point) boundaries. The comparison between measurements and predictions was remarkably good and showed that both flame-sheet and luminous-flame lengths are primarily controlled by fuel flow rates with lengths in coflowing air approaching 2/3 lengths in still air as coflowing air velocities are increased. Finally, luminous flame lengths at laminar smoke-point conditions were roughly twice as long as flame-sheet lengths at comparable conditions due to the presence of luminous soot particles in the fuel-lean region of the flames.

Flame Shapes of Nonbuoyant Laminar Jet Diffusion Flames. Appendix K

NASA Technical Reports Server (NTRS)

Xu, F.; Faeth, G. M.; Urban, D. L. (Technical Monitor); Yuan, Z.-G. (Technical Monitor)

2000-01-01

The shapes (flame-sheet and luminous-flame boundaries) of steady nonbuoyant round hydrocarbon-fueled laminar-jet diffusion flames in still and coflowing air were studied both experimentally and theoretically. Flame-sheet shapes were measured from photographs using a CH optical filter to distinguish flame-sheet boundaries in the presence of blue C02 and OH emissions and yellow continuum radiation from soot. Present experimental conditions included acetylene-, methane-, propane-, and ethylene-fueled flames having initial reactant temperatures of 300 K, ambient pressures of 4-50 kPa, jet exit Reynolds number of 3-54, initial air/fuel velocity ratios of 0-9 and luminous flame lengths of 5-55 mm; earlier measurements for propylene- and 1,3-butadiene-fueled flames for similar conditions were considered as well. Nonbuoyant flames in still air were observed at micro-gravity conditions; essentially nonbuoyant flames in coflowing air were observed at small pressures to control effects of buoyancy. Predictions of luminous flame boundaries from soot luminosity were limited to laminar smoke-point conditions, whereas predictions of flame-sheet boundaries ranged from soot-free to smoke-point conditions. Flame-shape predictions were based on simplified analyses using the boundary layer approximations along with empirical parameters to distinguish flame-sheet and luminous-flame (at the laminar smoke point) boundaries. The comparison between measurements and predictions was remarkably good and showed that both flame-sheet and luminous-flame lengths are primarily controlled by fuel flow rates with lengths in coflowing air approaching 2/3 lengths in still air as coflowing air velocities are increased. Finally, luminous flame lengths at laminar smoke-point conditions were roughly twice as long as flame-sheet lengths at comparable conditions due to the presence of luminous soot particles in the fuel-lean region of the flames.

The mobility and diffusion of ions in gases

NASA Technical Reports Server (NTRS)

Mcdaniel, E. W.; Mason, E. A.

1973-01-01

Experimental and theoretical aspects of the mobility and diffusion of ions in gases are studied in detail. Some of the subjects discussed include ion-ion interaction, boundary condition and ion and electron behavior. Also discussed in separate chapters are the problems of the diffusion coefficients and the afterglow techniques. Finally, a special chapter studies the kinetic theory of diffusion and mobility, stressing the low-, medium- and high-field theory.

Automatic Generation of Boundary Conditions Using Demons Nonrigid Image Registration for Use in 3-D Modality-Independent Elastography

PubMed Central

Ou, Jao J.; Ong, Rowena E.; Miga, Michael I.

2013-01-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method. PMID:21690002

Automatic generation of boundary conditions using demons nonrigid image registration for use in 3-D modality-independent elastography.

PubMed

Pheiffer, Thomas S; Ou, Jao J; Ong, Rowena E; Miga, Michael I

2011-09-01

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.

Verification Assessment of Flow Boundary Conditions for CFD Analysis of Supersonic Inlet Flows

NASA Technical Reports Server (NTRS)

Slater, John W.

2002-01-01

Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.

Calculation of two-dimension radial electric field in boundary plasmas by using BOUT++

NASA Astrophysics Data System (ADS)

Li, N. M.; Xu, X. Q.; Rognlien, T. D.; Gui, B.; Sun, J. Z.; Wang, D. Z.

2018-07-01

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

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

NASA Astrophysics Data System (ADS)

Wen, Zijuan; Fu, Shengmao

2009-08-01

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

Treatment of boundary conditions in through-diffusion: A case study of (85)Sr(2+) diffusion in compacted illite.

PubMed

Glaus, M A; Aertsens, M; Maes, N; Van Laer, L; Van Loon, L R

2015-01-01

Valuable techniques to measure effective diffusion coefficients in porous media are an indispensable prerequisite for a proper understanding of the migration of chemical-toxic and radioactive micropollutants in the subsurface and geosphere. The present article discusses possible pitfalls and difficulties in the classical through-diffusion technique applied to situations where large diffusive fluxes of cations in compacted clay minerals or clay rocks occur. The results obtained from a benchmark study, in which the diffusion of (85)Sr(2+) tracer in compacted illite has been studied using different experimental techniques, are presented. It is shown that these techniques may yield valuable results provided that an appropriate model is used for numerical simulations. It is further shown that effective diffusion coefficients may be systematically underestimated when the concentration at the downstream boundary is not taken adequately into account in modelling, even for very low concentrations. A criterion is derived for quasi steady-state situations, by which it can be decided whether the simplifying assumption of a zero-concentration at the downstream boundary in through-diffusion is justified or not. The application of the criterion requires, however, knowledge of the effective diffusion coefficient of the clay sample. Such knowledge is often absent or only approximately available during the planning phase of a diffusion experiment. Copyright © 2015 Elsevier B.V. All rights reserved.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

NASA Astrophysics Data System (ADS)

Homolova, V.; Watson, E. B.

2012-12-01

Diffusive fractionation of isotopes has been documented in silicate melts, aqueous fluids, and single crystals. In polycrystalline rocks, the meeting place of two grains, or grain boundaries, may also be a site of diffusive fractionation of isotopes. We have undertaken an experimental and modeling approach to investigate diffusive fractionation of lithium (Li) isotopes by grain boundary diffusion. The experimental procedure consists of packing a Ni metal capsule with predominantly ground San Carlos olivine and subjecting the capsule to 1100C and 1GPa for two days in a piston cylinder apparatus to create a nominally dry, 'dunite rock'. After this synthesis step, the capsule is sectioned and polished. One of the polished faces of the 'dunite rock' is then juxtaposed to a source material of spodumene and this diffusion couple is subject to the same experimental conditions as the synthesis step. Li abundances and isotopic profiles (ratios of count rates) were analyzed using LA-ICP-MS. Li concentrations linearly decrease away from the source from 550ppm to the average concentration of the starting olivine (2.5ppm). As a function of distance from the source, the 7Li/6Li ratio decreases to a minimum before increasing to the background ratio of the 'dunite rock'. The 7Li/6Li ratio minimum coincides with the lowest Li concentrations above average 'dunite rock' abundances. The initial decrease in the 7Li/6Li ratio is similar to that seen in other studies of diffusive fractionation of isotopes and is thought to be caused by the higher diffusivity (D) of the lighter isotope relative to the heavier isotope. The relationship between D and mass (m) is given by (D1/D2) =(m2/m1)^β, where β is an empirical fractionation factor; 1 and 2 denote the lighter and heavier isotope, respectively. A fit to the Li isotopic data reveals an effective DLi of ~1.2x10^-12 m/s^2 and a β of 0.1. Numerical modelling was utilized to elucidate the relationship between diffusive fractionation produced in the grain boundaries versus the lattices of the individual grains of the 'dunite rock'. The model assumes a linear grain boundary juxtaposed to the long side of a rectangular crystal lattice. During a simulation, the diffusant may directly enter the lattice or the grain boundary. Once in the grain boundary, the diffusant may then continue to diffuse away from the source until the end of the simulation or, alternatively, it may be incorporated into the lattice at some point during its travels down the grain boundary. The model system is similar to that considered by Whipple-LeClaire (1963) and our model results agree well with their analytical solution. Preliminary modeling results show that the distinctive minimum in the isotopic ratio is only produced when diffusive fractionation occurs in the grain boundary and not when the fractionation occurs only in the lattice. This suggests that the isotopic profile observed in the experiments may be a product of diffusive fractionation in grain boundaries. Implications of these results extend to the longevity of Li isotopic heterogeneities in the mantle, and suggest that the isotopes of other elements, which have a large relative mass difference, may also be diffusively fractionated by grain boundary diffusion.

Passive Rocket Diffuser Testing: Reacting Flow Performance of Four Second-Throat Geometries

NASA Technical Reports Server (NTRS)

Jones, Daniel R.; Allgood, Daniel C.; Saunders, Grady P.

2016-01-01

Second-throat diffusers serve to isolate rocket engines from the effects of ambient back pressure. As one of the nation's largest rocket testing facilities, the performance and design limitations of diffusers are of great interest to NASA's Stennis Space Center. This paper describes a series of tests conducted on four diffuser configurations to better understand the effects of inlet geometry and throat area on starting behavior and boundary layer separation. The diffusers were tested for a duration of five seconds with a 1455-pound thrust, LO2/GH2 thruster to ensure they each reached aerodynamic steady state. The effects of a water spray ring at the diffuser exits and a water-cooled deflector plate were also evaluated. Static pressure and temperature measurements were taken at multiple axial locations along the diffusers, and Computational Fluid Dynamics (CFD) simulations were used as a tool to aid in the interpretation of data. The hot combustion products were confirmed to enable the diffuser start condition with tighter second throats than predicted by historical cold-flow data or the theoretical normal shock method. Both aerodynamic performance and heat transfer were found to increase with smaller diffuser throats. Spray ring and deflector cooling water had negligible impacts on diffuser boundary layer separation. CFD was found to accurately capture diffuser shock structures and full-flowing diffuser wall pressures, and the qualitative behavior of heat transfer. However, the ability to predict boundary layer separated flows was not consistent.

Recursive recovery of Markov transition probabilities from boundary value data

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

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

Lattice continuum and diffusional creep

PubMed Central

2016-01-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro–Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro–Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate. PMID:27274696

Intrinsic Compressive Stress in Polycrystalline Films is Localized at Edges of the Grain Boundaries.

PubMed

Vasco, Enrique; Polop, Celia

2017-12-22

The intrinsic compression that arises in polycrystalline thin films under high atomic mobility conditions has been attributed to the insertion or trapping of adatoms inside grain boundaries. This compression is a consequence of the stress field resulting from imperfections in the solid and causes the thermomechanical fatigue that is estimated to be responsible for 90% of mechanical failures in current devices. We directly measure the local distribution of residual intrinsic stress in polycrystalline thin films on nanometer scales, using a pioneering method based on atomic force microscopy. Our results demonstrate that, at odds with expectations, compression is not generated inside grain boundaries but at the edges of gaps where the boundaries intercept the surface. We describe a model wherein this compressive stress is caused by Mullins-type surface diffusion towards the boundaries, generating a kinetic surface profile different from the mechanical equilibrium profile by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The Srolovitz-type surface diffusion that results from the stress counters the Mullins-type diffusion and stabilizes the kinetic surface profile, giving rise to a steady compression regime. The proposed mechanism of competition between surface diffusions would explain the flux and time dependency of compressive stress in polycrystalline thin films.

Intrinsic Compressive Stress in Polycrystalline Films is Localized at Edges of the Grain Boundaries

NASA Astrophysics Data System (ADS)

Vasco, Enrique; Polop, Celia

2017-12-01

The intrinsic compression that arises in polycrystalline thin films under high atomic mobility conditions has been attributed to the insertion or trapping of adatoms inside grain boundaries. This compression is a consequence of the stress field resulting from imperfections in the solid and causes the thermomechanical fatigue that is estimated to be responsible for 90% of mechanical failures in current devices. We directly measure the local distribution of residual intrinsic stress in polycrystalline thin films on nanometer scales, using a pioneering method based on atomic force microscopy. Our results demonstrate that, at odds with expectations, compression is not generated inside grain boundaries but at the edges of gaps where the boundaries intercept the surface. We describe a model wherein this compressive stress is caused by Mullins-type surface diffusion towards the boundaries, generating a kinetic surface profile different from the mechanical equilibrium profile by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The Srolovitz-type surface diffusion that results from the stress counters the Mullins-type diffusion and stabilizes the kinetic surface profile, giving rise to a steady compression regime. The proposed mechanism of competition between surface diffusions would explain the flux and time dependency of compressive stress in polycrystalline thin films.

Gas diffusion in and out of super-hydrophobic surface in transitional and turbulent boundary layers

NASA Astrophysics Data System (ADS)

Ling, Hangjian; Fu, Matthew; Hultmark, Marcus; Katz, Joseph

2017-11-01

The rate of gas diffusion in and out of a super-hydrophobic surface (SHS) located in boundary layers is investigated at varying Reynolds numbers and ambient pressures. The hierarchical SHS consists of nano-textured, 100 μm wide spanwise grooves. The boundary layers over the SHS under the Cassie-Baxter and Wenzel states as well as a smooth wall at same conditions are characterized by particle image velocimetry. The Reynolds number based on momentum thickness of the smooth wall, ReΘ0, ranges from 518 to 2088, covering transitional and turbulent boundary layer regimes. The mass diffusion rate is estimated by using microscopy to measure the time-evolution of plastron shape and volume. The data is used for calculating the Sherwood number based on smooth wall momentum thickness, ShΘ0. As expected, the diffusion rate increases linearly with the under- or super-saturation level, i.e., ShΘ0 is independent of ambient pressure. For the turbulent boundary layers, the data collapses onto ShΘ0 = 0.47ReΘ00.77 . For the transitional boundary layer, ShΘ0 is lower than the turbulent power law. When ShΘ0 is plotted against the friction Reynolds number (Reτ0) , both the transitional and turbulent boundary layer data collapse onto a single power law, ShΘ0 = 0.34Reτ00.913 . Results scaled based on Wenzel state momentum thickness show very similar trends. Sponsored by ONR.

Diffusion of phonons through (along and across) the ultrathin crystalline films

NASA Astrophysics Data System (ADS)

Šetrajčić, J. P.; Jaćimovski, S. K.; Vučenović, S. M.

2017-11-01

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film-structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is-that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Characteristic time scales for diffusion processes through layers and across interfaces

NASA Astrophysics Data System (ADS)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces.

PubMed

Carr, Elliot J

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Krogh-cylinder and infinite-domain models for washout of an inert diffusible solute from tissue.

PubMed

Secomb, Timothy W

2015-01-01

Models based on the Krogh-cylinder concept are developed to analyze the washout from tissue by blood flow of an inert diffusible solute that permeates blood vessel walls. During the late phase of washout, the outflowing solute concentration decays exponentially with time. This washout decay rate is predicted for a range of conditions. A single capillary is assumed to lie on the axis of a cylindrical tissue region. In the classic "Krogh-cylinder" approach, a no-flux boundary condition is applied on the outside of the cylinder. An alternative "infinite-domain" approach is proposed that allows for solute exchange across the boundary, but with zero net exchange. Both models are analyzed, using finite-element and analytical methods. The washout decay rate depends on blood flow rate, tissue diffusivity and vessel permeability of solute, and assumed boundary conditions. At low blood flow rates, the washout rate can exceed the value for a single well-mixed compartment. The infinite-domain approach predicts slower washout decay rates than the Krogh-cylinder approach. The infinite-domain approach overcomes a significant limitation of the Krogh-cylinder approach, while retaining its simplicity. It provides a basis for developing methods to deduce transport properties of inert solutes from observations of washout decay rates. © 2014 John Wiley & Sons Ltd.

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

The isentropic quantum drift-diffusion model in two or three space dimensions

NASA Astrophysics Data System (ADS)

Chen, Xiuqing

2009-05-01

We investigate the isentropic quantum drift-diffusion model, a fourth order parabolic system, in space dimensions d = 2, 3. First, we establish the global weak solutions with large initial value and periodic boundary conditions. Then we show the semiclassical limit by delicate interpolation estimates and compactness argument.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Grain boundary imaging, gallium diffusion and the fracture behavior of Al-Zn Alloy - An in situ study

NASA Astrophysics Data System (ADS)

Tsai, W. L.; Hwu, Y.; Chen, C. H.; Chang, L. W.; Je, J. H.; Lin, H. M.; Margaritondo, G.

2003-01-01

Phase contrast radiology using unmonochromatic synchrotron X-ray successfully imaged the grain boundaries of Al and AlZn alloy without contrast agent. Combining the high penetration of X-ray and the possibility of 3D reconstruction by tomorgraphy or stereography method, this approach can be very used for nondestructive characterization of polycrystalline materials. By examine the images with 3D perspective, we were able locate the observed void-like defects which lies exclusively on the grain boundary and identify their origin from last stage of the rolling process. We studied the Ga Liquid metal diffusion in the AlZn alloy, under different temperature and stress conditions. High resolution images, ˜2 μm, of Ga liquid metal diffusion in AlZn were obtained in real time and diffusion paths alone grain boundaries and surfaces were clearly identified. Embrittled AlZn responses to the tensile stress and fractures in a drastic different manner than the pure AlZn. These results, although very much expected from the known weakening effect of the liquid metal embrittlement demonstrated, however, that this particular radiology method is fully capable of dynamic study in the micrometer scale.

Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chew, Jia Wei

2018-02-01

In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second-order accuracy. Then, the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming [see the paragraph after Eq. (29) for the discussions of the "streaming step" in LB method]. After that, the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes. For straight boundaries, boundary nodes are directly placed at the physical boundary surface, and the present scheme is applied directly. When extending the present scheme to curved geometries, a local curvilinear coordinate system and first-order Taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface. In essence, the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface. Therefore, the advantages of the present boundary implementations are (i) the locality, i.e., no information from neighboring fluid nodes is required; (ii) the consistency, i.e., the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes, thus the three kinds of conditions are realized in a consistent way. It should be noted that the present focus is on two-dimensional cases, and theoretical derivations as well as the numerical validations are performed in the framework of the two-dimensional five-velocity lattice model.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

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.

The boundary condition for vertical velocity and its interdependence with surface gas exchange

NASA Astrophysics Data System (ADS)

Kowalski, Andrew S.

2017-07-01

The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w) in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E) and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface). This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example) but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux-gradient relationships (eddy diffusivities) requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube - with vapour transport into an overlying, horizontal airstream - was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.

Thermodynamics, Diffusion, and Structure of Mg2SiO4 forsterite grain boundaries from atomistic modeling

NASA Astrophysics Data System (ADS)

Adjaoud, O.; Marquardt, K.; Jahn, S.

2011-12-01

Most materials are not single crystals but consist of crystalline grains of various sizes, misorientated with respect to each other and joint by grain boundaries. The latter influence many of the material properties. For instance, grain boundaries are short circuits for diffusion and thus they strongly influence transport properties of materials such as electrical conductivity, or mineral growth rates, creep, or phase transform. Olivine is a major component of the Earth's upper mantle and therefore it is of considerable importance to study its physical and thermodynamic polycrystalline properties. In the present study, we have used molecular dynamics simulations to model thermodynamics, self-diffusion and structure of a series of [100] symmetric tilt grain boundaries in forsterite. The interactions between the atoms are modeled by an advanced ionic interaction potential (Jahn and Madden, 2007). The parameters of the potential are fitted to ab initio results. The model was optimized for the Ca-Mg-Al-Si-O system and shows good transferability in a wide range of pressures, temperatures, and compositions. Thermodynamics and structure were simulated at ambient conditions, and self-diffusion coefficients were determined at ambient pressure and temperatures of 1250, 1500, 1750, and 2000 K. We find that the energy and excess free volume of the grain boundaries in forsterite depend significantly on the misorientation angle of the grain boundary. One of our modeled structures is compared with an high-resolution transmission electron micrograph (HRTEM) (Heinemann et al., 2005). We relate our findings to previous studies of grain boundaries in ionic materials and in metals. For small misorientation angles (up to 22.1°), grain boundary structures consist of an array of c-edge dislocations as suggested by Heinemann et al. (2005) and their energies can be readily fit with the Read-Shockley dislocation model for grain boundaries. For high misorientation angles (32.1° and 60.8°), the cores of dislocations overlap and form repeated structural units. Similar to energies and excess free volumes, the self-diffusion coefficients of Mg and O depend significantly on the misorientation angle of the grain boundaries and they are well fitted with Arrhenius law. We compare our results to MgO grain boundary diffusion in forsterite derived from reaction rim growth experiments (Gardés and Heinrich, 2010).

Boundary Conditions for Scalar (Co)Variances over Heterogeneous Surfaces

NASA Astrophysics Data System (ADS)

Machulskaya, Ekaterina; Mironov, Dmitrii

2018-05-01

The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin-Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.

Supersonic compressor

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

Roberts, II, William Byron; Lawlor, Shawn P.; Breidenthal, Robert E.

A supersonic compressor including a rotor to deliver a gas at supersonic conditions to a diffuser. The diffuser includes a plurality of aerodynamic ducts that have converging and diverging portions, for deceleration of gas to subsonic conditions and then for expansion of subsonic gas, to change kinetic energy of the gas to static pressure. The aerodynamic ducts include vortex generating structures for controlling boundary layer, and structures for changing the effective contraction ratio to enable starting even when the aerodynamic ducts are designed for high pressure ratios, and structures for boundary layer control. In an embodiment, aerodynamic ducts are providedmore » having an aspect ratio of in excess of two to one, when viewed in cross-section orthogonal to flow direction at an entrance to the aerodynamic duct.« less

Development of a robust modeling tool for radiation-induced segregation in austenitic stainless steels

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

Yang, Ying; Field, Kevin G; Allen, Todd R.

2015-09-01

Irradiation-assisted stress corrosion cracking (IASCC) of austenitic stainless steels in Light Water Reactor (LWR) components has been linked to changes in grain boundary composition due to irradiation induced segregation (RIS). This work developed a robust RIS modeling tool to account for thermodynamics and kinetics of the atom and defect transportation under combined thermal and radiation conditions. The diffusion flux equations were based on the Perks model formulated through the linear theory of the thermodynamics of irreversible processes. Both cross and non-cross phenomenological diffusion coefficients in the flux equations were considered and correlated to tracer diffusion coefficients through Manning’s relation. Themore » preferential atomvacancy coupling was described by the mobility model, whereas the preferential atom-interstitial coupling was described by the interstitial binding model. The composition dependence of the thermodynamic factor was modeled using the CALPHAD approach. Detailed analysis on the diffusion fluxes near and at grain boundaries of irradiated austenitic stainless steels suggested the dominant diffusion mechanism for chromium and iron is via vacancy, while that for nickel can swing from the vacancy to the interstitial dominant mechanism. The diffusion flux in the vicinity of a grain boundary was found to be greatly influenced by the composition gradient formed from the transient state, leading to the oscillatory behavior of alloy compositions in this region. This work confirms that both vacancy and interstitial diffusion, and segregation itself, have important roles in determining the microchemistry of Fe, Cr, and Ni at irradiated grain boundaries in austenitic stainless steels.« less

Memoryless control of boundary concentrations of diffusing particles.

PubMed

Singer, A; Schuss, Z; Nadler, B; Eisenberg, R S

2004-12-01

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

An improved procedure for determining grain boundary diffusion coefficients from averaged concentration profiles

NASA Astrophysics Data System (ADS)

Gryaznov, D.; Fleig, J.; Maier, J.

2008-03-01

Whipple's solution of the problem of grain boundary diffusion and Le Claire's relation, which is often used to determine grain boundary diffusion coefficients, are examined for a broad range of ratios of grain boundary to bulk diffusivities Δ and diffusion times t. Different reasons leading to errors in determining the grain boundary diffusivity (DGB) when using Le Claire's relation are discussed. It is shown that nonlinearities of the diffusion profiles in lnCav-y6/5 plots and deviations from "Le Claire's constant" (-0.78) are the major error sources (Cav=averaged concentration, y =coordinate in diffusion direction). An improved relation (replacing Le Claire's constant) is suggested for analyzing diffusion profiles particularly suited for small diffusion lengths (short times) as often required in diffusion experiments on nanocrystalline materials.

A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains

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

Zhou Wei, E-mail: zhoux123@umn.edu

2013-06-15

We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than the non-degeneracy of the diffusion term. When the diffusion term, drift term, discount factor, running payoff and terminal payoff are all in the class of C{sup 1,1}( D-bar ) , the value function turns out to be the unique solution in the class of C{sub loc}{sup 1,1}(D) Intersection C{sup 0,1}( D-bar )more » to the associated degenerate Bellman equation with Dirichlet boundary data. Our approach is probabilistic.« less

A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

NASA Astrophysics Data System (ADS)

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

2014-04-01

In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O(η), which is more favorable than the error convergence of the already established Dirichlet boundary condition.

Diffusion Flame Extinction in a Low Strain Flow

NASA Technical Reports Server (NTRS)

Sutula, Jason; Jones, Joshua; Torero, Jose L.; Borlik, Jeffrey; Ezekoye, Ofodike A.

1997-01-01

Diffusion flames are of great interest in fire safety and many industrial processes. Many parameters significantly affect the flame structure, shape and stability, of particular importance are the constraints imposed by geometrical boundaries. Physical boundaries determine the characteristics of the flow, affect heat, fuel, and oxidizer transport from and towards the flame and can act as heat sinks or heat sources. As a result, the existence of a flame, its shape and nature are intimately related to the geometrical characteristics of the environment that surrounds it. The counter-flow configuration provides a constant strain flow, therefore, is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in micro-gravity conditions have begun to explore the low strain regimes. The main objective of these on-going studies is to determine the effect of radiative heat losses and variable strain on the structure and radiation-induced extinction of diffusion flames. For these programs, size, geometry, and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. Whether is the burning of condensed or gaseous fuels, for most real situations the boundaries impose a significant effect on the nature of the flame. There is, therefore, a need to better understand the effect that geometrical constraints (i.e. flow nonperpendicular to a fuel surface, heat losses to the boundaries, etc.) might have on the final characteristics of a diffusion flame. Preliminary experiments have shown that, in the absence of gravity, and depending on the distance from the flame to the boundary, three characteristically different regimes can be observed. Close to the boundary, the flame is parabolic, very thin and blue, almost soot-less. Diffusion is the main mechanism controlling fuel transport to the reaction zone, conduction towards the inlets is the main source of heat losses. As the distance increases the flame becomes linear and thickens, remaining blue at the oxidizer side and turning yellow at the fuel side. Here, convection brings fuel and oxidizer together and the reaction occurs in the viscous layer formed between the fuel and oxidizer streams. This region corresponds to the characteristic counter-flow flame where conduction and convection become negligible forms of heat losses and radiation becomes dominant. The flame in the third (mixed) region, between the two others, results from the combination of the scenarios presented above.

Non-fragile consensus algorithms for a network of diffusion PDEs with boundary local interaction

NASA Astrophysics Data System (ADS)

Xiong, Jun; Li, Junmin

2017-07-01

In this study, non-fragile consensus algorithm is proposed to solve the average consensus problem of a network of diffusion PDEs, modelled by boundary controlled heat equations. The problem deals with the case where the Neumann-type boundary controllers are corrupted by additive persistent disturbances. To achieve consensus between agents, a linear local interaction rule addressing this requirement is given. The proposed local interaction rules are analysed by applying a Lyapunov-based approach. The multiplicative and additive non-fragile feedback control algorithms are designed and sufficient conditions for the consensus of the multi-agent systems are presented in terms of linear matrix inequalities, respectively. Simulation results are presented to support the effectiveness of the proposed algorithms.

Dynamics for a diffusive prey-predator model with different free boundaries

NASA Astrophysics Data System (ADS)

Wang, Mingxin; Zhang, Yang

2018-03-01

To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect each other as time evolves, are used to describe the spreading of prey and predator. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution. Some sufficient conditions for spreading and vanishing are established. When spreading occurs, we provide the more accurate limits of (u , v) as t → ∞, and give some estimates of asymptotic spreading speeds of u , v and asymptotic speeds of g , h. Some realistic and significant spreading phenomena are found.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

TEMPERATURE DISTRIBUTION IN A DIFFUSION CLOUD CHAMBER

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

Slavic, I.; Szymakowski, J.; Stachorska, D.

1961-03-01

A diffusion cloud chamber with working conditions within a pressure range from 10 mm Hg to 2 atmospheres and at variable boundary surface temperatures in a wide interval is described. A simple procedure is described for cooling and thermoregulating the bottom of the chamber by means of vapor flow of liquid air which makes possible the achievement of temperature up to -120 deg C with stability better that plus or minus 1 deg C. A method for the measurement of temperature distribution by means of a thermistor is described, and a number of curves of the observed temperature gradient, dependentmore » on the boundary surface temperature is given. Analysis of other factors influencing the stable work of the diffusion cloud chamber was made. (auth)« less

Front propagation in a vortex lattice: dependence on boundary conditions and vortex depth.

PubMed

Beauvier, E; Bodea, S; Pocheau, A

2016-11-04

We experimentally address the propagation of reaction-diffusion fronts in vortex lattices by combining, in a Hele-Shaw cell and at low Reynolds number, forced electroconvective flows and an autocatalytic reaction in solution. We consider both vortex chains and vortex arrays, the former referring to mixed free/rigid boundary conditions for vortices and the latter to free boundary conditions. Varying the depth of the fluid layer, we observe no variation of the mean front velocities for vortex arrays and a noticeable variation for vortex chains. This questions the two-dimensional character of front propagation in low Reynolds number vortex lattices, as well as the mechanisms of this dependence.

Density functional calculation of activation energies for lattice and grain boundary diffusion in alumina

NASA Astrophysics Data System (ADS)

Lei, Yinkai; Gong, Yu; Duan, Zhiyao; Wang, Guofeng

2013-06-01

To acquire knowledge on the lattice and grain boundary diffusion processes in alumina, we have determined the activation energies of elementary O and Al diffusive jumps in the bulk crystal, Σ3(0001) grain boundaries, and Σ3(101¯0) grain boundaries of α-Al2O3 using the first-principles density functional theory method. Specifically, we calculated the activation energies for four elementary jumps of both O and Al lattice diffusion in alumina. It was predicted that the activation energy of O lattice diffusion varied from 3.58 to 5.03 eV, while the activation energy of Al lattice diffusion ranged from 1.80 to 3.17 eV. As compared with experimental measurements, the theoretical predictions of the activation energy for lattice diffusion were lower and thus implied that there might be other high-energy diffusive jumps in the experimental alumina samples. Moreover, our results suggested that the Al lattice diffusion was faster than the O lattice diffusion in alumina, in agreement with experiment observations. Furthermore, it was found from our calculations for α-Al2O3 that the activation energies of O and Al grain boundary diffusion in the high-energy Σ3(0001) grain boundaries were significantly lower than those of the lattice diffusion. In contrast, the activation energies of O and Al grain boundary diffusion in the low-energy Σ3(101¯0) grain boundaries could be even higher than those of the lattice diffusion.

Milne problem for non-absorbing medium with extremely anisotropic scattering kernel in the case of specular and diffuse reflecting boundaries

NASA Astrophysics Data System (ADS)

Güleçyüz, M. Ç.; Şenyiğit, M.; Ersoy, A.

2018-01-01

The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic scattering kernel which combines forward and backward scatterings (extremely anisotropic scattering) for a non-absorbing medium with specular and diffuse reflection boundary conditions. In order to calculate the extrapolated endpoint for the Milne problem, Legendre polynomial approximation (PN method) is applied and numerical results are tabulated for selected cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with the existing results in literature.

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

PubMed

ben-Avraham, D; Fokas, A S

2001-07-01

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

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

PubMed Central

Macklin, Paul

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Study of sorption-retarded U(VI) diffusion in Hanford silt/clay material.

PubMed

Bai, Jing; Liu, Chongxuan; Ball, William P

2009-10-15

A diffusion cell method was applied to measure the effective pore diffusion coefficient (Dp) for U(VI) under strictly controlled chemical conditions in a silt/clay sediment from the U.S. Department of Energy Hanford site, WA. "Inward-flux" diffusion studies were conducted in which [U(VI)] in both aqueous and solid phases was measured as a function of distance in the diffusion cell under conditions of constant concentration at the cell boundaries. A sequential extraction method was developed to measure sorbed contaminant U(VI) in the solid phase containing extractable background U(VI). The effect of sorption kinetics on U(VI) interparticle diffusion was evaluated by comparing sorption-retarded diffusion models with sorption described either as equilibrium or intraparticle diffusion-limited processes. Both experimental and modeling results indicated that (1) a single pore diffusion coefficient can simulate the diffusion of total aqueous U(VI), and (2) the local equilibrium assumption (LEA) is appropriate for modeling sorption-retarded diffusion under the given experimental conditions. Dp of 1.6-1.7 x 10(-6) cm2/s was estimated in aqueous solution at pH 8.0 and saturated with respect to calcite, as relevant to some subsurface regions of the Hanford site.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Shan; Liu, Zaiming

2010-03-01

In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

Compact scheme for systems of equations applied to fundamental problems of mechanics of continua

NASA Technical Reports Server (NTRS)

Klimkowski, Jerzy Z.

1990-01-01

Compact scheme formulation was used in the treatment of boundary conditions for a system of coupled diffusion and Poisson equations. Models and practical solutions of specific engineering problems arising in solid mechanics, chemical engineering, heat transfer and fuid mechanics are described and analyzed for efficiency and accuracy. Only 2-D cases are discussed and a new method of numerical treatment of boundary conditions common in the fundamental problems of mechanics of continua is presented.

The role of boundary variability in polycrystalline grain-boundary diffusion

NASA Astrophysics Data System (ADS)

Moghadam, M. M.; Rickman, J. M.; Harmer, M. P.; Chan, H. M.

2015-01-01

We investigate the impact of grain-boundary variability on mass transport in a polycrystal. More specifically, we perform both numerical and analytical studies of steady-state diffusion in prototypical microstructures in which there is either a discrete spectrum of grain-boundary activation energies or else a complex distribution of grain-boundary character, and hence a continuous spectrum of boundary activation energies. An effective diffusivity is calculated for these structures using simplified multi-state models and, for the case of a continuous spectrum, employing experimentally obtained grain-boundary energy data. We identify different diffusive regimes for these cases and quantify deviations from Arrhenius behavior using effective medium theory. Finally, we examine the diffusion kinetics of a simplified model of an interfacial layering (i.e., complexion) transition.

Modeling uptake of hydrophobic organic contaminants into polyethylene passive samplers.

PubMed

Thompson, Jay M; Hsieh, Ching-Hong; Luthy, Richard G

2015-02-17

Single-phase passive samplers are gaining acceptance as a method to measure hydrophobic organic contaminant (HOC) concentration in water. Although the relationship between the HOC concentration in water and passive sampler is linear at equilibrium, mass transfer models are needed for nonequilibrium conditions. We report measurements of organochlorine pesticide diffusion and partition coefficients with respect to polyethylene (PE), and present a Fickian approach to modeling HOC uptake by PE in aqueous systems. The model is an analytic solution to Fick's second law applied through an aqueous diffusive boundary layer and a polyethylene layer. Comparisons of the model with existing methods indicate agreement at appropriate boundary conditions. Laboratory release experiments on the organochlorine pesticides DDT, DDE, DDD, and chlordane in well-mixed slurries support the model's applicability to aqueous systems. In general, the advantage of the model is its application in the cases of well-agitated systems, low values of polyethylene-water partioning coefficients, thick polyethylene relative to the boundary layer thickness, and/or short exposure times. Another significant advantage is the ability to estimate, or at least bound, the needed exposure time to reach a desired CPE without empirical model inputs. A further finding of this work is that polyethylene diffusivity does not vary by transport direction through the sampler thickness.

Molecular Dynamics Simulations of Grain Boundary and Bulk Diffusion in Metals.

NASA Astrophysics Data System (ADS)

Plimpton, Steven James

Diffusion is a microscopic mass transport mechanism that underlies many important macroscopic phenomena affecting the structural, electrical, and mechanical properties of metals. This thesis presents results from atomistic simulation studies of diffusion both in bulk and in the fast diffusion paths known as grain boundaries. Using the principles of molecular dynamics single boundaries are studied and their structure and dynamic properties characterized. In particular, tilt boundary bicrystal and bulk models of fcc Al and bcc alpha-Fe are simulated. Diffusion coefficients and activation energies for atomic motion are calculated for both models and compared to experimental data. The influence of the interatomic pair potential on the diffusion is studied in detail. A universal relation between the melting temperature that a pair potential induces in a simulated bulk model and the potential energy barrier height for atomic hopping is derived and used to correlate results for a wide variety of pair potentials. Using these techniques grain boundary and bulk diffusion coefficients for any fcc material can be estimated from simple static calculations without the need to perform more time-consuming dynamic simulations. The influences of two other factors on grain boundary diffusion are also studied because of the interest of the microelectronics industry in the diffusion related reliability problem known as electromigration. The first factor, known to affect the self diffusion rate of Al, is the presence of Cu impurity atoms in Al tilt boundaries. The bicrystal model for Al is seeded randomly with Cu atoms and a simple hybrid Morse potential used to model the Al-Cu interaction. While some effect due to the Cu is noted, it is concluded that pair potentials are likely an inadequate approximation for the alloy system. The second factor studied is the effect of the boundary orientation angle on the diffusion rate. Symmetric bcc Fe boundaries are relaxed to find optimal structures and their diffusion coefficients calculated. Good agreement is found with the dislocation pipe model for tilt boundary diffusion.

Multistage adsorption of diffusing macromolecules and viruses

NASA Astrophysics Data System (ADS)

Chou, Tom; D'Orsogna, Maria R.

2007-09-01

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

Anomalous current in diffusive ferromagnetic Josephson junctions

NASA Astrophysics Data System (ADS)

Silaev, M. A.; Tokatly, I. V.; Bergeret, F. S.

2017-05-01

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, anomalous Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are noncoplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevented previous works based on this approximation from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe, we consider generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.

Development and Evaluation of a New Spectral Planetary Boundary-Layer Architecture for the MM5

DTIC Science & Technology

1998-08-07

I’m grateful to Dr. George Young for his suggestion to use the Bulk-Richardson technique for diagnosis of boundary-layer depth during convection, and...simulation (LES) (Wyngaard and Brost 1984). However, these profiles are not generally representative of all conditions. They are instead prescribed for...Wyngaard, J. C, and R. A. Brost , 1984: Top-down and bottom diffusion of a scalar in the convective boundary layer. J. Atmos. Sei., 44, 102-112. Zeman

The Harrison Diffusion Kinetics Regimes in Solute Grain Boundary Diffusion

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

Belova, Irina; Fiedler, T; Kulkarni, Nagraj S

2012-01-01

Knowledge of the limits of the principal Harrison kinetics regimes (Type-A, B and C) for grain boundary diffusion is very important for the correct analysis of the depth profiles in a tracer diffusion experiment. These regimes for self-diffusion have been extensively studied in the past by making use of the phenomenological Lattice Monte Carlo (LMC) method with the result that the limits are now well established. The relationship of those self-diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregationmore » on the limits is investigated with the LMC method for the well-known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type-B kinetics regime may differ from the global segregation factor.« less

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

Effect of zone size on the convergence of exact solutions for diffusion in single phase systems with planar, cylindrical or spherical geometry

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.

1981-01-01

Exact solutions for diffusion in single phase binary alloy systems with constant diffusion coefficient and zero-flux boundary condition have been evaluated to establish the optimum zone size of applicability. Planar, cylindrical and spherical interface geometry, and finite, singly infinite, and doubly infinite systems are treated. Two solutions are presented for each geometry, one well suited to short diffusion times, and one to long times. The effect of zone-size on the convergence of these solutions is discussed. A generalized form of the diffusion solution for doubly infinite systems is proposed.

Diffusion of nitrogen oxides and oxygenated volatile organic compounds through snow

NASA Astrophysics Data System (ADS)

Bartels-Rausch, T.; Ammann, M.; Schneebeli, M.; Riche, F.; Wren, S. N.

2013-12-01

Release of trace gases from surface snow on Earth drives atmospheric chemistry, especially in the Polar Regions. The exchange of atmospheric trace gases between snow or firn and atmosphere can also determine how these species are incorporated into glacial ice, which serves as archive. At low wind conditions, such fluxes between the porous surface snow and the overlaying atmosphere are driven by diffusion through the interstitial air. Here we present results from two laboratory studies where we looked at how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion of NO, NO2, HONO, methanol, and acetone on time scales up to 1 h. The diffusion through a snow sample was the direct observable of the experiments. Results for different snow types are presented, the structures of which were analysed by means of X-ray computed micro-tomography. Grain boundary content was quantified in one sample using a stereological method. The observed diffusion profiles were very well reproduced in simulations based on gas-phase diffusion and the known structure of the snow sample at temperatures above 253 K. At colder temperatures surface interactions start to dominate the diffusion. Parameterizing these in terms of adsorption to the solid ice surface gave much better agreement to the observations than the use of air - liquid partitioning coefficients. This is a central result as field and modelling studies have indicated that the partitioning to liquid water might describe the diffusion through snow much better even at cold temperatures. This will be discussed using our recent results from surface sensitive spectroscopy experiments. No changes in the diffusion was observed by increasing the number of grain boundaries in the snow sample by a factor of 7.

Pipe and grain boundary diffusion of He in UO 2

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

Galvin, C. O.T.; Cooper, M. W. D.; Fossati, P. C. M.

Molecular dynamics simulations have been conducted to study the effects of dislocations and grain boundaries on He diffusion inmore » $$\\text{U}{{\\text{O}}_{2}}$$ . Calculations were carried out for the {100}, {110} and {111} $$\\langle 1\\,1\\,0\\rangle $$ edge dislocations, the screw $$\\langle 1\\,1\\,0\\rangle $$ dislocation and Σ5, Σ13, Σ19 and Σ25 tilt grain boundaries. He diffusivity as a function of distance from the dislocation core and grain boundaries was investigated for the temperature range 2300–3000 K. An enhancement in diffusivity was predicted within 20 Å of the dislocations or grain boundaries. Further investigation showed that He diffusion in the edge dislocations follows anisotropic behaviour along the dislocation core, suggesting that pipe diffusion occurs. Here, an Arrhenius plot of He diffusivity against the inverse of temperature was also presented and the activation energy calculated for each structure, as a function of distance from the dislocation or grain boundary.« less

Pipe and grain boundary diffusion of He in UO 2

DOE PAGES

Galvin, C. O.T.; Cooper, M. W. D.; Fossati, P. C. M.; ...

2016-10-12

Molecular dynamics simulations have been conducted to study the effects of dislocations and grain boundaries on He diffusion inmore » $$\\text{U}{{\\text{O}}_{2}}$$ . Calculations were carried out for the {100}, {110} and {111} $$\\langle 1\\,1\\,0\\rangle $$ edge dislocations, the screw $$\\langle 1\\,1\\,0\\rangle $$ dislocation and Σ5, Σ13, Σ19 and Σ25 tilt grain boundaries. He diffusivity as a function of distance from the dislocation core and grain boundaries was investigated for the temperature range 2300–3000 K. An enhancement in diffusivity was predicted within 20 Å of the dislocations or grain boundaries. Further investigation showed that He diffusion in the edge dislocations follows anisotropic behaviour along the dislocation core, suggesting that pipe diffusion occurs. Here, an Arrhenius plot of He diffusivity against the inverse of temperature was also presented and the activation energy calculated for each structure, as a function of distance from the dislocation or grain boundary.« less

A Class of Solvable Stopping Games

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

Alvarez, Luis H. R.

We consider a class of Dynkin games in the case where the underlying process evolves according to a one-dimensional but otherwise general diffusion. We establish general conditions under which both the value and the saddle point equilibrium exist and under which the exercise boundaries characterizing the saddle point strategy can be explicitly characterized in terms of a pair of standard first order necessary conditions for optimality. We also analyze those cases where an extremal pair of boundaries exists and investigate the overall impact of increased volatility on the equilibrium stopping strategies and their values.

The perturbed Sparre Andersen model with a threshold dividend strategy

NASA Astrophysics Data System (ADS)

Gao, Heli; Yin, Chuancun

2008-10-01

In this paper, we consider a Sparre Andersen model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the mth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case where the inter-claim times are Erlang(2) distributed and the claim size distribution is exponential is considered in some details.

An optimal analysis for Darcy-Forchheimer 3D flow of Carreau nanofluid with convectively heated surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2018-06-01

Darcy-Forchheimer three dimensional flow of Carreau nanoliquid induced by a linearly stretchable surface with convective boundary condition has been analyzed. Buongiorno model has been employed to elaborate thermophoresis and Brownian diffusion effects. Zero nanoparticles mass flux and convective surface conditions are implemented at the boundary. The governing problems are nonlinear. Optimal homotopic procedure has been used to tackle the governing mathematical system. Graphical results clearly depict the outcome of temperature and concentration fields. Surface drag coefficients and local Nusselt number are also plotted and discussed.

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.

Grain boundary and triple junction diffusion in nanocrystalline copper

NASA Astrophysics Data System (ADS)

Wegner, M.; Leuthold, J.; Peterlechner, M.; Song, X.; Divinski, S. V.; Wilde, G.

2014-09-01

Grain boundary and triple junction diffusion in nanocrystalline Cu samples with grain sizes, , of ˜35 and ˜44 nm produced by spark plasma sintering were investigated by the radiotracer method using the 63Ni isotope. The measured diffusivities, Deff, are comparable with those determined previously for Ni grain boundary diffusion in well-annealed, high purity, coarse grained, polycrystalline copper, substantiating the absence of a grain size effect on the kinetic properties of grain boundaries in a nanocrystalline material at grain sizes d ≥ 35 nm. Simultaneously, the analysis predicts that if triple junction diffusion of Ni in Cu is enhanced with respect to the corresponding grain boundary diffusion rate, it is still less than 500ṡDgb within the temperature interval from 420 K to 470 K.

Turbine exhaust diffuser with region of reduced flow area and outer boundary gas flow

DOEpatents

Orosa, John

2014-03-11

An exhaust diffuser system and method for a turbine engine. The outer boundary may include a region in which the outer boundary extends radially inwardly toward the hub structure and may direct at least a portion of an exhaust flow in the diffuser toward the hub structure. At least one gas jet is provided including a jet exit located on the outer boundary. The jet exit may discharge a flow of gas downstream substantially parallel to an inner surface of the outer boundary to direct a portion of the exhaust flow in the diffuser toward the outer boundary to effect a radially outward flow of at least a portion of the exhaust gas flow toward the outer boundary to balance an aerodynamic load between the outer and inner boundaries.

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.

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; McCaughan, Frances E.

1998-01-01

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.

PubMed

Xiao, Perry; Imhof, Robert E

2012-10-01

Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.

Diffusive interaction of multiple surface nanobubbles: shrinkage, growth, and coarsening.

PubMed

Zhu, Xiaojue; Verzicco, Roberto; Zhang, Xuehua; Lohse, Detlef

2018-03-14

Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a single surface nanobubble has been theoretically explained, i.e. contact line pinning and gas oversaturation are required to stabilize it against diffusive dissolution [Lohse and Zhang, Phys. Rev. E, 2015, 91, 031003(R)], here we focus on the collective diffusive interaction of multiple nanobubbles. For that purpose we develop a finite difference scheme for the diffusion equation with the appropriate boundary conditions and with the immersed boundary method used to represent the growing or shrinking bubbles. After validation of the scheme against the exact results of Epstein and Plesset for a bulk bubble [J. Chem. Phys., 1950, 18, 1505] and of Lohse and Zhang for a surface bubble, the framework of these simulations is used to describe the coarsening process of competitively growing nanobubbles. The coarsening process for such diffusively interacting nanobubbles slows down with advancing time and increasing bubble distance. The present results for surface nanobubbles are also applicable for immersed surface nanodroplets, for which better controlled experimental results of the coarsening process exist.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme.

PubMed

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme

NASA Astrophysics Data System (ADS)

Ginzburg, Irina

2017-01-01

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ . Two different values Λv and Λb are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λv is adjustable for stability, accuracy, or other purposes, while the corresponding Λb(Λv) controls the primary accommodation effects. Two distinguished but similar functional relations Λb(Λv) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λb(Λv) can be identified in a few bisection iterations in given geometry. A positive solution for Λb(Λv) may not exist in pure diffusion, but a sufficiently small value of Λb significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λb also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Separation of Electric Fields Into Potential and Inductive Parts, and Implications for Radial Diffusion

NASA Astrophysics Data System (ADS)

Chan, A. A.; Ilie, R.; Elkington, S. R.; Albert, J.; Huie, W.

2017-12-01

It has been traditional to separate radiation belt radial-diffusion coefficients into two contributions: an "electrostatic" diffusion coefficient, which is assumed to be due to a potential (non-inductive) electric field, and an "electromagnetic" diffusion coefficient , which is assumed to be due to the combined effect of an inductive electric field and the corresponding time-dependent magnetic field. One difficulty in implementing this separation when using magnetospheric fields obtained from measurements, or from MHD simulations, is that only the total electric field is given; the separation of the electric field into potential and inductive parts is not readily available. In this work we separate the electric field using a numerical method based on the Helmholtz decomposition of the total motional electric field calculated by the BATS-R-US MHD code. The inner boundary for the electric potential is based on the Ridley Ionospheric Model solution and we assume floating boundary conditions in the solar wind. Using different idealized solar wind drivers, including a solar wind density that is oscillating at a single frequency or with a broad spectrum of frequencies, we calculate potential and inductive electric fields, electric and magnetic power spectral densities, and corresponding radial diffusion coefficients. Simulations driven by idealized solar wind conditions show a clear separation of the potential and inductive contributions to the power spectral densities and diffusion coefficients. Simulations with more realistic solar wind drivers are underway to better assess the use of electrostatic and electromagnetic diffusion coefficients in understanding ULF wave-particle interactions in Earth's radiation belts.

Analysis of a diffuse interface model of multispecies tumor growth

NASA Astrophysics Data System (ADS)

Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

2017-04-01

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.

Investigation of surface boundary conditions for continuum modeling of RF plasmas

NASA Astrophysics Data System (ADS)

Wilson, A.; Shotorban, B.

2018-05-01

This work was motivated by a lacking general consensus in the exact form of the boundary conditions (BCs) required on the solid surfaces for the continuum modeling of Radiofrequency (RF) plasmas. Various kinds of number and energy density BCs on solid surfaces were surveyed, and how they interacted with the electric potential BC to affect the plasma was examined in two fundamental RF plasma reactor configurations. A second-order local mean energy approximation with equations governing the electron and ion number densities and the electron energy density was used to model the plasmas. Zero densities and various combinations of drift, diffusion, and thermal fluxes were considered to set up BCs. It was shown that the choice of BC can have a significant impact on the sheath and bulk plasma. The thermal and diffusion fluxes to the surface were found to be important. A pure drift BC for dielectric walls failed to produce a sheath.

Description of jambolan (Syzygium cumini (L.)) anthocyanin extraction kinetics at different stirring frequencies of the medium using diffusion models

NASA Astrophysics Data System (ADS)

da Silva, Wilton Pereira; Nunes, Jarderlany Sousa; Gomes, Josivanda Palmeira; de Araújo, Auryclennedy Calou; e Silva, Cleide M. D. P. S.

2018-05-01

Anthocyanin extraction kinetics was described for jambolan fruits. The spherical granules obtained were dried at 40 °C and the average radius of the sphere equivalent to the granules was determined. Solid-solvent ratio was fixed at 1:20 and temperature at 35 °C. A mixture of ethyl alcohol and hydrochloric acid (85:15) was used as solvent. Experiments were conducted with the following stirring frequencies: 0, 50, 100 and 150 rpm. Two diffusion models were used to describe the extraction process. The first one used an analytical solution, with boundary condition of the first kind. The second one used a numerical solution, with boundary condition of the third kind. The second model was the most adequate, and its results were used to determine empirical equations relating the process parameters with the stirring frequency, allowing to simulate new extraction kinetics.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

A model for including thermal conduction in molecular dynamics simulations

NASA Technical Reports Server (NTRS)

Wu, Yue; Friauf, Robert J.

1989-01-01

A technique is introduced for including thermal conduction in molecular dynamics simulations for solids. A model is developed to allow energy flow between the computational cell and the bulk of the solid when periodic boundary conditions cannot be used. Thermal conduction is achieved by scaling the velocities of atoms in a transitional boundary layer. The scaling factor is obtained from the thermal diffusivity, and the results show good agreement with the solution for a continuous medium at long times. The effects of different temperature and size of the system, and of variations in strength parameter, atomic mass, and thermal diffusivity were investigated. In all cases, no significant change in simulation results has been found.

On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems.

DTIC Science & Technology

1982-02-01

I. Diaz. "Soluciones con soporte compacto para alguno. problemas semilineales". Collect. Math. 30 (1979), 141-179. -26- [121 J. I. Diaz. Tecnica de ...supersoluciones locales para problemas estacionarios no lineales: applicacion al estudio de flujoe subsonicos. Memory of the Real Academia de Ciencias...nonlinearity, nonlinear boundary conditions, dead core set, chemical reactions Work Unit Number I - Applied Analysis (1) Seccion de Matematicas

A theoretical model of grain boundary self-diffusion in metals with phase transitions (case study into titanium and zirconium)

NASA Astrophysics Data System (ADS)

Semenycheva, Alexandra V.; Chuvil'deev, Vladimir N.; Nokhrin, Aleksey V.

2018-05-01

The paper offers a model describing the process of grain boundary self-diffusion in metals with phase transitions in the solid state. The model is based on ideas and approaches found in the theory of non-equilibrium grain boundaries. The range of application of basic relations contained in this theory is shown to expand, as they can be used to calculate the parameters of grain boundary self-diffusion in high-temperature and low-temperature phases of metals with a phase transition. The model constructed is used to calculate grain boundary self-diffusion activation energy in titanium and zirconium and an explanation is provided as to their abnormally low values in the low-temperature phase. The values of grain boundary self-diffusion activation energy are in good agreement with the experiment.

Two types of diffusions at the cathode/electrolyte interface in IT-SOFCs

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

Li Zhipeng, E-mail: LI.Zhipeng@nims.go.jp; Mori, Toshiyuki; Auchterlonie, Graeme John

2011-09-15

Analytical transmission electron microscopy, in particular with the combination of energy dispersive X-ray spectroscopy (EDX) and electron energy-loss spectroscopy (EELS), has been performed to investigate the microstructure and microchemistry of the interfacial region between the cathode (La{sub 0.6}Sr{sub 0.4}Co{sub 0.8}Fe{sub 0.2}O{sub 3}, LSCF) and the electrolyte (Gd-doped ceria, GDC). Two types of diffusions, mutual diffusion between cathode and electrolyte as well as the diffusion along grain boundaries, have been clarified. These diffusions suggest that the chemical stability of LSCF and GDC are not as good as previously reported. The results are more noteworthy if we take into consideration the factmore » that such interdiffusions occur even during the sintering process of cell preparation. - Graphical Abstract: Two types of diffusions, the mutual diffusion and the diffusion along grain boundaries, occurred at the cathode/electrolyte interface of intermediate temperature solid state fuel cells, during cell preparation. The mutual diffusion is denoted by black arrows and the diffusion along grain boundaries assigned by pink arrows. Highlights: > All the cations in cathode (LSCF) and electrolyte (GDC) can mutually diffuse into each other. > Diffusing elements will segregate at grain boundaries or triple junctions around the cathode/electrolyte interface. > Two types of diffusions, the mutual diffusion and diffusion along grain boundaries, have been clarified thereafter.« less

Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent diffusion coefficient.

PubMed

Chen, Juan; Cui, Baotong; Chen, YangQuan

2018-06-11

This paper presents a boundary feedback control design for a fractional reaction diffusion (FRD) system with a space-dependent (non-constant) diffusion coefficient via the backstepping method. The contribution of this paper is to generalize the results of backstepping-based boundary feedback control for a FRD system with a space-independent (constant) diffusion coefficient to the case of space-dependent diffusivity. For the boundary stabilization problem of this case, a designed integral transformation treats it as a problem of solving a hyperbolic partial differential equation (PDE) of transformation's kernel, then the well posedness of the kernel PDE is solved for the plant with non-constant diffusivity. Furthermore, by the fractional Lyapunov stability (Mittag-Leffler stability) theory and the backstepping-based boundary feedback controller, the Mittag-Leffler stability of the closed-loop FRD system with non-constant diffusivity is proved. Finally, an extensive numerical example for this closed-loop FRD system with non-constant diffusivity is presented to verify the effectiveness of our proposed controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition. I - Incompressible flows

NASA Technical Reports Server (NTRS)

Morino, L.

1986-01-01

Using the decomposition for the infinite-space, the issue of the nonuniqueness of the Helmholtz decomposition for the problem of the three-dimensional unsteady incompressible flow around a body is considered. A representation for the velocity that is valid for both the fluid region and the region inside the boundary surface is employed, and the motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. At each instant of velocity discontinuity, vorticity is shown to be generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is shown to diffuse into the surroundings, and the no-slip conditions are automatically satisfied. A trailing edge condition must be satisfied for the solution to the Euler equations to be the limit of the solution of the Navier-Stokes equations.

Diffusion from a line source

NASA Technical Reports Server (NTRS)

Burns, R. E.

1973-01-01

The problem with predicting pollutant diffusion from a line source of arbitrary geometry is treated. The concentration at the line source may be arbitrarily varied with time. Special attention is given to the meteorological inputs which act as boundary conditions for the problem, and a mixing layer of arbitrary depth is assumed. Numerical application of the derived theory indicates the combinations of meteorological parameters that may be expected to result in high pollution concentrations.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

NASA Technical Reports Server (NTRS)

Vyas, Manan A.; Yoder, Dennis A.; Gaitonde, Datta V.

2018-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

Diffusion of drag-reducing polymer solutions within a rough-walled turbulent boundary layer

NASA Astrophysics Data System (ADS)

Elbing, Brian R.; Dowling, David R.; Perlin, Marc; Ceccio, Steven L.

2010-04-01

The influence of surface roughness on diffusion of wall-injected, drag-reducing polymer solutions within a turbulent boundary layer was studied with a 0.94 m long flat-plate test model at speeds of up to 10.6 m s-1 and Reynolds numbers of up to 9×106. The surface was hydraulically smooth, transitionally rough, or fully rough. Mean concentration profiles were acquired with planar laser induced fluorescence, which was the primary flow diagnostic. Polymer concentration profiles with high injection concentrations (≥1000 wppm) had the peak concentration shifted away from the wall, which was partially attributed to a lifting phenomenon. The diffusion process was divided into three zones—initial, intermediate, and final. Studies of polymer injection into a polymer ocean at concentrations sufficient for maximum drag reduction indicated that the maximum initial zone length is of the order of 100 boundary layer thicknesses. The intermediate zone results indicate that friction velocity and roughness height are important scaling parameters in addition to flow and injection conditions. Lastly, the current results were combined with those in Petrie et al. ["Polymer drag reduction with surface roughness in flat-plate turbulent boundary layer flow," Exp. Fluids 35, 8 (2003)] to demonstrate that the influence of polymer degradation increases with increased surface roughness.

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

NASA Astrophysics Data System (ADS)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

Kinetics of pack aluminization of nickel

NASA Technical Reports Server (NTRS)

Seigle, L. L.; Gupta, B. K.; Shankar, R.; Sarkhel, A. K.

1978-01-01

The kinetics of pack aluminization of unalloyed nickel in packs of varying aluminum activity with various halide activators were studied. Surface compositions of the coatings as functions of time, temperature, and pack composition were obtained in order to establish the boundary conditions for diffusion in the system. The structure of the packs was also examined in order to clarify the mechanism of aluminum transport. The results indicate that the kinetics of pack aluminization are controlled jointly by gas diffusion in the pack and solid diffusion in the coating. Levine and Caves' model for gas diffusion was combined with calculations of rates of diffusion in the solid to formulate a more complete theory for the kinetics of pack aluminization.

An evaluation of models of bare soil evaporation formulated with different land surface boundary conditions and assumptions

NASA Astrophysics Data System (ADS)

Smits, Kathleen M.; Ngo, Viet V.; Cihan, Abdullah; Sakaki, Toshihiro; Illangasekare, Tissa H.

2012-12-01

Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance. However, there is no agreement on the best modeling methodology to determine evaporation under different atmospheric boundary conditions. Also, there is a lack of directly measured soil evaporation data for model validation to compare these methods to establish the validity of their mathematical formulations. Thus, a need exists to systematically compare evaporation estimates using existing methods to experimental observations. The goal of this work is to test different conceptual and mathematical formulations that are used to estimate evaporation from bare soils to critically investigate various formulations and surface boundary conditions. Such a comparison required the development of a numerical model that has the ability to incorporate these boundary conditions. For this model, we modified a previously developed theory that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. Precision data under well-controlled transient heat and wind boundary conditions were generated, and results from numerical simulations were compared with experimental data. Results demonstrate that the approaches based on different boundary conditions varied in their ability to capture different stages of evaporation. All approaches have benefits and limitations, and no one approach can be deemed most appropriate for every scenario. Comparisons of different formulations of the surface boundary condition validate the need for further research on heat and vapor transport processes in soil for better modeling accuracy.

Magnetic field reconnection. [energy conversion in space plasma

NASA Technical Reports Server (NTRS)

Sonnerup, U. O.

1979-01-01

A reasonably detailed description is obtained of the current status of our understanding of magnetic field reconnection. The picture that emerges is of a process, simple in concept but extremely complicated and multifaceted in detail. Nonlinear MHD processes in the external flow region, governed by distant boundary conditions, are coupled to nonlinear microscopic plasma processes in the diffusion region, in a manner not clearly understood. It appears that reconnection may operate in entirely different ways for different plasma parameters and different external boundary conditions. Steady reconnection may be allowed in some cases, forbidden in others, with intermediate situations involving impulsive or pulsative events.

Grain boundary engineering for control of tellurium diffusion in GH3535 alloy

NASA Astrophysics Data System (ADS)

Fu, Cai-Tao; Yinling, Wang; Chu, Xiang-Wei; Jiang, Li; Zhang, Wen-Zhu; Bai, Qin; Xia, Shuang; Leng, Bin; Li, Zhi-Jun; Ye, Xiang-Xi; Liu, Fang

2017-12-01

The effect of grain boundary engineering (GBE) on the Te diffusion along the surface grain boundaries was investigated in GH3535 alloy. It can be found that GBE treatment increases obviously the fraction of low-Σ coincidence site lattice (CSL) boundaries, especially the Σ3 ones, and introduces the large-size grain clusters. When the as-received (AR) and GBE-treated (GBET) specimens were exposed to Te vapor, only Σ3 boundaries were found to be resistant to Te diffusion. From the cross section and the surface, the fewer Te-attacked grain boundaries and the thinner corrosion layer can be observed in the GBET sample. The improvement of resistance to Te diffusion in the GBET sample can be attributed to the large size grain-clusters associated with high proportion of the Σ3n boundaries.

Diffusion Of Mass In Evaporating Multicomponent Drops

NASA Technical Reports Server (NTRS)

Bellan, Josette; Harstad, Kenneth G.

1992-01-01

Report summarizes study of diffusion of mass and related phenomena occurring in evaporation of dense and dilute clusters of drops of multicomponent liquids intended to represent fuels as oil, kerosene, and gasoline. Cluster represented by simplified mathematical model, including global conservation equations for entire cluster and conditions on boundary between cluster and ambient gas. Differential equations of model integrated numerically. One of series of reports by same authors discussing evaporation and combustion of sprayed liquid fuels.

O(minus 2) grain boundary diffusion and grain growth in pure dense MgO

NASA Technical Reports Server (NTRS)

Kapadia, C. M.; Leipold, M. H.

1973-01-01

Grain growth behavior in fully dense compacts of MgO of very high purity was studied, and the results compared with other similar behaving materials. The activation energy for the intrinsic self-diffusion of Mg(2minus) is discussed along with the grain boundary diffusion of O(2minus). Grain boundary diffusion of O(2minus) is proposed as the controlling mechanism for grain growth.

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Kinetics of cellular dissolution in a Cu-Cd alloy

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

Nakkalil, R.; Gupta, S.P.

1989-07-01

Dissolution of the cellular precipitate by cell boundary migration has been studied in a Cu-2 at.% Cd alloy in the temperature range 777--878 K. Microstructural observations have revealed that the process of dissolution begins at the original position of the grain boundary as well as the cell boundary. The steady state rate of cell boundary migration decreased with decreasing temperature of dissolution and became zero at approximately 770 K, which is about 30 K below the equilibrium solves temperature. The boundary diffusivities were determined at a number of temperatures by using the theory of Petermann and Hornbogen modified for dissolution.more » The diffusivity values calculated from the experimental data are seven orders of magnitude higher than the corresponding volume diffusivities. From the temperature dependence of the diffusivity, an activation energy of 157 kJ mol{sup {minus} 1} is obtained, which is bout three-quarters of the activation energy for the bulk diffusion of Cd into Cu. From the diffusivity and activation energy values, it is concluded that the diffusion of Cd along the migrating grain boundaries control the dissolution of the cellular precipitate in this alloy.« less

Creation and perturbation of planar networks of chemical oscillators

PubMed Central

Tompkins, Nathan; Cambria, Matthew Carl; Wang, Adam L.; Heymann, Michael; Fraden, Seth

2015-01-01

Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay. PMID:26117136

Stress-sensitive tissue regeneration in viscoelastic biomaterials subjected to modulated tensile strain.

PubMed

Belfiore, Laurence A; Floren, Michael L; Paulino, Alexandre T; Belfiore, Carol J

2011-09-01

This research contribution addresses the mechanochemistry of intra-tissue mass transfer for nutrients, oxygen, growth factors, and other essential ingredients that anchorage-dependent cells require for successful proliferation on biocompatible surfaces. The unsteady state reaction-diffusion equation (i.e., modified diffusion equation) is solved according to the von Kármán-Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration are stimulated by harmonically imposed stress. The mass balance with diffusion and stress-sensitive kinetics represents a rare example where the Damköhler and Deborah numbers appear together in an effort to simulate the development of mass transfer boundary layers in porous viscoelastic biomaterials. The Boltzmann superposition integral is employed to calculate time-dependent strain in terms of the real and imaginary components of dynamic compliance for viscoelastic solids that transmit harmonic excitation to anchorage-dependent cells. Rates of nutrient consumption under stress-free conditions are described by third-order kinetics which include local mass densities of nutrients, oxygen, and attached cells that maintain dynamic equilibrium with active protein sites in the porous matrix. Thinner nutrient mass transfer boundary layers are stabilized at shorter dimensionless diffusion times when the stress-free intra-tissue Damköhler number increases above its initial-condition-sensitive critical value. The critical stress-sensitive intra-tissue Damköhler number, above which it is necessary to consider the effect of harmonic strain on nutrient consumption and tissue regeneration, is proportional to the Deborah number and corresponds to a larger fraction of the stress-free intra-tissue Damköhler number in rigid biomaterials. Copyright © 2011 Elsevier B.V. All rights reserved.

Electric-field-enhanced nutrient consumption in dielectric biomaterials that contain anchorage-dependent cells.

PubMed

Belfiore, Laurence A; Floren, Michael L; Belfiore, Carol J

2012-02-01

This research contribution addresses electric-field stimulation of intra-tissue mass transfer and cell proliferation in viscoelastic biomaterials. The unsteady state reaction-diffusion equation is solved according to the von Kármán-Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration occur in response to harmonic electric potential differences across a parallel-plate capacitor in a dielectric-sandwich configuration. The partial differential mass balance with diffusion and electro-kinetic consumption contains the Damköhler (Λ(2)) and Deborah (De) numbers. Zero-field and electric-field-sensitive Damköhler numbers affect nutrient boundary layer growth. Diagonal elements of the 2nd-rank diffusion tensor are enhanced in the presence of weak electric fields, in agreement with the formalism of equilibrium and nonequilibrium thermodynamics. Induced dipole polarization density within viscoelastic biomaterials is calculated via the real and imaginary components of the complex dielectric constant, according to the Debye equation, to quantify electro-kinetic stimulation. Rates of nutrient consumption under zero-field conditions are described by third-order kinetics that include local mass densities of nutrients, oxygen, and attached cells. Thinner nutrient boundary layers are stabilized at shorter dimensionless diffusion times when the zero-field intra-tissue Damköhler number increases above its initial-condition-sensitive critical value [i.e., {Λ(2)(zero-field)}(critical)≥53, see Eq. (23)], such that the biomaterial core is starved of essential ingredients required for successful proliferation. When tissue regeneration occurs above the critical electric-field-sensitive intra-tissue Damköhler number, the electro-kinetic contribution to nutrient consumption cannot be neglected. The critical electric-field-sensitive intra-tissue Damköhler number is proportional to the Deborah number. Copyright © 2011 Elsevier B.V. All rights reserved.

G-Jitter Induced Magnetohydrodynamics Flow of Nanofluid with Constant Convective Thermal and Solutal Boundary Conditions

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmad Izani Md.

2015-01-01

Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids. The governing transport equations are converted into non-similar equations using suitable transformations, before being solved numerically by an implicit finite difference method with quasi-linearization technique. The skin friction decreases with time, buoyancy ratio, and thermophoresis parameters while it increases with frequency, mixed convection and Brownian motion parameters. Heat transfer rate decreases with time, Brownian motion, thermophoresis and diffusion-convection parameters while it increases with the Reynolds number, frequency, mixed convection, buoyancy ratio and conduction-convection parameters. Mass transfer rate decreases with time, frequency, thermophoresis, conduction-convection parameters while it increases with mixed convection, buoyancy ratio, diffusion-convection and Brownian motion parameters. To the best of our knowledge, this is the first paper on this topic and hence the results are new. We believe that the results will be useful in designing and operating thermal fluids systems for space materials processing. Special cases of the results have been compared with published results and an excellent agreement is found. PMID:25933066

An improved design method and experimental performance of two dimensional curved wall diffusers

NASA Technical Reports Server (NTRS)

Yang, T.; Hudson, W. G.; El-Nashar, A. M.

1972-01-01

A computer design program was developed to incorporate the suction slots in solving the potential flow equations with prescribed boundary conditions. Using the contour generated from this program two Griffith diffusers were tested having area ratios AR = 3 and 4. The inlet Reynolds number ranged from 600,000 to 7 million. It was found that the slot suction required for metastable operation depends on the sidewall suction applied. Values of slot suction of 8% of the inlet flow rate was required for AR = 4 with metastable condition, provided that enough sidewall suction was applied. For AR = 3, the values of slot suction was about 25% lower than those required for AR = 4. For nearly all unseparated test runs, the effectiveness was 100% and the exit flow was uniform. In addition to the Griffith diffusers, dump and cusp diffusers of comparable area ratios were built and tested. The results obtained from these diffusers were compared with those of the Griffith diffusers. Flow separation occurred in all test runs with the dump and cusp diffusers.

Estimating Thermal Inertia with a Maximum Entropy Boundary Condition

NASA Astrophysics Data System (ADS)

Nearing, G.; Moran, M. S.; Scott, R.; Ponce-Campos, G.

2012-04-01

Thermal inertia, P [Jm-2s-1/2K-1], is a physical property the land surface which determines resistance to temperature change under seasonal or diurnal heating. It is a function of volumetric heat capacity, c [Jm-3K-1], and thermal conductivity, k [Wm-1K-1] of the soil near the surface: P=√ck. Thermal inertia of soil varies with moisture content due the difference between thermal properties of water and air, and a number of studies have demonstrated that it is feasible to estimate soil moisture given thermal inertia (e.g. Lu et al, 2009, Murray and Verhoef, 2007). We take the common approach to estimating thermal inertia using measurements of surface temperature by modeling the Earth's surface as a 1-dimensional homogeneous diffusive half-space. In this case, surface temperature is a function of the ground heat flux (G) boundary condition and thermal inertia and a daily value of P was estimated by matching measured and modeled diurnal surface temperature fluctuations. The difficulty is in measuring G; we demonstrate that the new maximum entropy production (MEP) method for partitioning net radiation into surface energy fluxes (Wang and Bras, 2011) provides a suitable boundary condition for estimating P. Adding the diffusion representation of heat transfer in the soil reduces the number of free parameters in the MEP model from two to one, and we provided a sensitivity analysis which suggests that, for the purpose of estimating P, it is preferable to parameterize the coupled MEP-diffusion model by the ratio of thermal inertia of the soil to the effective thermal inertia of convective heat transfer to the atmosphere. We used this technique to estimate thermal inertia at two semiarid, non-vegetated locations in the Walnut Gulch Experimental Watershed in southeast AZ, USA and compared these estimates to estimates of P made using the Xue and Cracknell (1995) solution for a linearized ground heat flux boundary condition, and we found that the MEP-diffusion model produced superior thermal inertia estimates. The MEP-diffusion estimates also agreed well with P estimates made using a boundary condition measured with buried flux plates. We further demonstrated the new method using diurnal surface temperature fluctuations estimated from day/night MODIS image pairs and, excluding instances where the soil was extremely dry, found a strong relationship between estimated thermal inertia and measured 5 cm soil moisture. Lu, S., Ju, Z.Q., Ren, T.S. & Horton, R. (2009). A general approach to estimate soil water content from thermal inertia. Agricultural and Forest Meteorology, 149, 1693-1698. Murray, T. & Verhoef, A. (2007). Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - I. A universal approach to calculate thermal inertia. Agricultural and Forest Meteorology, 147, 80-87. Wang, J.F. & Bras, R.L. (2011). A model of evapotranspiration based on the theory of maximum entropy production. Water Resources Research, 47. Xue, Y. & Cracknell, A.P. (1995). Advanced thermal inertia modeling. International Journal of Remote Sensing, 16, 431-446.

Temperature boundary layer profiles in turbulent Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Ching, Emily S. C.; Emran, Mohammad S.; Horn, Susanne; Shishkina, Olga

2017-11-01

Classical boundary-layer theory for steady flows cannot adequately describe the boundary layer profiles in turbulent Rayleigh-Benard convection. We have developed a thermal boundary layer equation which takes into account fluctuations in terms of an eddy thermal diffusivity. Based on Prandtl's mixing length ideas, we relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal boundary layer equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters: θ(ξ) =1/b∫0b ξ [ 1 +3a3/b3(η - arctan(η)) ] - c dη , where ξ is the similarity variable and the parameters a, b, and c are related by the condition θ(∞) = 1 . With a proper choice of the parameters, our predictions of the temperature profile are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers (Pr), from Pr=0.01 to Pr=2547.9. OS, ME and SH acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) under Grants Sh405/4-2 (Heisenberg fellowship), Sh405/3-2 and Ho 5890/1-1, respectively.

Evaporation from soils subjected to natural boundary conditions at the land-atmospheric interface

NASA Astrophysics Data System (ADS)

Smits, K.; Illngasekare, T.; Ngo, V.; Cihan, A.

2012-04-01

Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance in semiarid and arid regions. However, there is no agreement on the best methodology to determine evaporation under different boundary conditions at the land surface. This becomes critical in developing models that couples land to the atmosphere. Because it is difficult to measure evaporation from soil, with the exception of using lysimeters, numerous formulations have been proposed to establish a relationship between the rate of evaporation and soil moisture and/or soil temperature and thermal properties. Different formulations vary in how they partition available energy. A need exists to systematically compare existing methods to experimental data under highly controlled conditions not achievable in the field. The goal of this work is to perform controlled experiments under transient conditions of soil moisture, temperature and wind at the land/atmospheric interface to test different conceptual and mathematical formulations for the soil surface boundary conditions to develop appropriate numerical models to be used in simulations. In this study, to better understand the coupled water-vapor-heat flow processes in the shallow subsurface near the land surface, we modified a previously developed theory by Smits et al. [2011] that allows non-equilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. The model did not implement fitting parameters such as a vapor enhancement factor that is commonly introduced into the vapor diffusion coefficient as an arbitrary multiplication factor. In order to experimentally test the numerical formulations/code, we performed a two-dimensional physical model experiment under varying boundary conditions using test sand for which the hydraulic and thermal properties were well characterized. Precision data under well-controlled transient heat and wind boundary conditions was generated and results from numerical simulations were compared with experimental data. Results demonstrate that the boundary condition approaches varied in their ability to capture stage 1- and stage 2- evaporation. Results also demonstrated the importance of properly characterizing soil thermal properties and accounting for dry soil conditions. The contribution of film flow to hydraulic conductivity for the layer above the drying front is dominant compared to that of capillary flow, demonstrating the importance of including film flow in modeling efforts for dry soils, especially for fine grained soils. Comparisons of different formulations of the surface boundary condition validate the need for joint evaluation of heat and mass transfer for better modeling accuracy. This knowledge is applicable to many current hydrologic and environmental problems to include climate modeling and the simulation of contaminant transport and volatilization in the shallow subsurface. Smits, K. M., A. Cihan, T. Sakaki, and T. H. Illangasekare (2011). Evaporation from soils under thermal boundary conditions: Experimental and modeling investigation to compare equilibrium- and nonequilibrium-based approaches, Water Resour. Res., 47, W05540, doi:10.1029/2010WR009533.

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary.

PubMed

Lin, Zhigui; Zhu, Huaiping

2017-12-01

In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on a simplified model involving mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infected region. The spatial-temporal risk index [Formula: see text], which involves regional characteristic and time, is defined for the simplified reaction-diffusion model with the free boundary to compare with other related threshold values, including the usual basic reproduction number [Formula: see text]. Sufficient conditions for the virus to vanish or to spread are given. Our results suggest that the virus will be in a scenario of vanishing if [Formula: see text], and will spread to the whole region if [Formula: see text] for some [Formula: see text], while if [Formula: see text], the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate and other factors. Moreover, some remarks on the basic reproduction numbers and the spreading speeds are presented and compared.

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.

Discrete multi-physics simulations of diffusive and convective mass transfer in boundary layers containing motile cilia in lungs.

PubMed

Ariane, Mostapha; Kassinos, Stavros; Velaga, Sitaram; Alexiadis, Alessio

2018-04-01

In this paper, the mass transfer coefficient (permeability) of boundary layers containing motile cilia is investigated by means of discrete multi-physics. The idea is to understand the main mechanisms of mass transport occurring in a ciliated-layer; one specific application being inhaled drugs in the respiratory epithelium. The effect of drug diffusivity, cilia beat frequency and cilia flexibility is studied. Our results show the existence of three mass transfer regimes. A low frequency regime, which we called shielding regime, where the presence of the cilia hinders mass transport; an intermediate frequency regime, which we have called diffusive regime, where diffusion is the controlling mechanism; and a high frequency regime, which we have called convective regime, where the degree of bending of the cilia seems to be the most important factor controlling mass transfer in the ciliated-layer. Since the flexibility of the cilia and the frequency of the beat changes with age and health conditions, the knowledge of these three regimes allows prediction of how mass transfer varies with these factors. Copyright © 2018 Elsevier Ltd. All rights reserved.

Analysis of dangerous area of single berth oil tanker operations based on CFD

NASA Astrophysics Data System (ADS)

Shi, Lina; Zhu, Faxin; Lu, Jinshu; Wu, Wenfeng; Zhang, Min; Zheng, Hailin

2018-04-01

Based on the single process in the liquid cargo tanker berths in the state as the research object, we analyzed the single berth oil tanker in the process of VOCs diffusion theory, built network model of VOCs diffusion with Gambit preprocessor, set up the simulation boundary conditions and simulated the five detection point sources in specific factors under the influence of VOCs concentration change with time by using Fluent software. We analyzed the dangerous area of single berth oil tanker operations through the diffusion of VOCs, so as to ensure the safe operation of oil tanker.

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

NASA Astrophysics Data System (ADS)

Li, Dong; Guo, Shangjiang

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

Effects of inlet flow field conditions on the performance of centrifugal compressor diffusers: Part 1 -- Discrete-passage diffuser

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

Filipenco, V.G.; Deniz, S.; Johnston, J.M.

2000-01-01

This is Part 1 of a two-part paper considering the performance of radial diffusers for use in a high-performance centrifugal compressor. Part 1 reports on discrete-passage diffusers, while Part 2 describes a test of a straight-channel diffuser designed for equivalent duty. Two builds of discrete-passage diffuser were tested, with 30 and 38 separate passages. Both the 30 and 38 passage diffusers investigated showed comparable range of unstalled operation and similar level of overall diffuser pressure recovery. The paper concentrates on the influence of inlet flow conditions on the pressure recovery and operating range of radial diffusers for centrifugal compressor stages.more » The flow conditions examined include diffuser inlet Mach number, flow angle, blockage, and axial flow nonuniformity. The investigation was carried out in a specially built test facility, designed to provide a controlled inlet flow field to the test diffusers. The facility can provide a wide range of diffuser inlet velocity profile distortion and skew with Mach numbers up to unity and flow angles of 63 to 75 deg from the radical direction. The consequences of different averaging methods for the inlet total pressure distributions, which are needed in the definition of diffuser pressure recovery coefficient for nonuniform diffuser inlet conditions, were also assessed. The overall diffuser pressure recovery coefficient, based on suitably averaged inlet total pressure, was found to correlate well with the momentum-averaged flow angle into the diffuser. It is shown that the generally accepted sensitivity of diffuser pressure recovery performance to inlet flow distortion and boundary layer blockage can be largely attributed to inappropriate quantification of the average dynamic pressure at diffuser inlet. Use of an inlet dynamic pressure based on availability or mass-averaging in combination with definition of inlet flow angle based on mass average of the radial and tangential velocity at diffuser inlet removes this sensitivity.« less

Boundary Conditions for Diffusion-Mediated Processes within Linear Nanopores: Exact Treatment of Coupling to an Equilibrated External Fluid

DOE PAGES

Garcia, Andres; Evans, James W.

2017-04-03

In this paper, we consider a variety of diffusion-mediated processes occurring within linear nanopores, but which involve coupling to an equilibrated external fluid through adsorption and desorption. By determining adsorption and desorption rates through a set of tailored simulations, and by exploiting a spatial Markov property of the models, we develop a formulation for performing efficient pore-only simulations of these processes. Coupling to the external fluid is described exactly through appropriate nontrivial boundary conditions at the pore openings. This formalism is applied to analyze the following: (i) tracer counter permeation (TCP) where different labeled particles adsorb into opposite ends ofmore » the pore and establish a nonequilibrium steady state; (ii) tracer exchange (TE) with exchange of differently labeled particles within and outside the pore; (iii) catalytic conversion reactions where a reactant in the external fluid adsorbs into the pore and converts to a product which may desorb. The TCP analysis also generates a position-dependent generalized tracer diffusion coefficient, the form of which controls behavior in the TE and catalytic conversion processes. We focus on the regime of single-file diffusion within the pore which produces the strongest correlations and largest deviations from mean-field type behavior. Finally, behavior is quantified precisely via kinetic Monte Carlo simulations but is also captured with appropriate analytic treatments.« less

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Arnold Diffusion of Charged Particles in ABC Magnetic Fields

NASA Astrophysics Data System (ADS)

Luque, Alejandro; Peralta-Salas, Daniel

2017-06-01

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of ABC magnetic fields. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of these parameters, we obtain a normally hyperbolic invariant manifold and we apply the so-called geometric methods for a priori unstable systems developed by A. Delshams, R. de la Llave and T.M. Seara. We characterize explicitly sufficient conditions for the existence of a transition chain of invariant tori having heteroclinic connections, thus obtaining global instability (Arnold diffusion). We also check the obtained conditions in a computer-assisted proof. ABC magnetic fields are the simplest force-free-type solutions of the magnetohydrodynamics equations with periodic boundary conditions, and can be considered as an elementary model for the motion of plasma-charged particles in a tokamak.

Discontinuous Galerkin Methods for Turbulence Simulation

NASA Technical Reports Server (NTRS)

Collis, S. Scott

2002-01-01

A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.

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.

Semianalytical Solutions for Transport in Aquifer and Fractured Clay Matrix System

EPA Science Inventory

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of analytical solutions is derived based on specific initial and boundary conditions as well as ...

Numberical Solution to Transient Heat Flow Problems

ERIC Educational Resources Information Center

Kobiske, Ronald A.; Hock, Jeffrey L.

1973-01-01

Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)

Design of broadband time-domain impedance boundary conditions using the oscillatory-diffusive representation of acoustical models.

PubMed

Monteghetti, Florian; Matignon, Denis; Piot, Estelle; Pascal, Lucas

2016-09-01

A methodology to design broadband time-domain impedance boundary conditions (TDIBCs) from the analysis of acoustical models is presented. The derived TDIBCs are recast exclusively as first-order differential equations, well-suited for high-order numerical simulations. Broadband approximations are yielded from an elementary linear least squares optimization that is, for most models, independent of the absorbing material geometry. This methodology relies on a mathematical technique referred to as the oscillatory-diffusive (or poles and cuts) representation, and is applied to a wide range of acoustical models, drawn from duct acoustics and outdoor sound propagation, which covers perforates, semi-infinite ground layers, as well as cavities filled with a porous medium. It is shown that each of these impedance models leads to a different TDIBC. Comparison with existing numerical models, such as multi-pole or extended Helmholtz resonator, provides insights into their suitability. Additionally, the broadly-applicable fractional polynomial impedance models are analyzed using fractional calculus.

Numerical Modeling of High-Temperature Corrosion Processes

NASA Technical Reports Server (NTRS)

Nesbitt, James A.

1995-01-01

Numerical modeling of the diffusional transport associated with high-temperature corrosion processes is reviewed. These corrosion processes include external scale formation and internal subscale formation during oxidation, coating degradation by oxidation and substrate interdiffusion, carburization, sulfidation and nitridation. The studies that are reviewed cover such complexities as concentration-dependent diffusivities, cross-term effects in ternary alloys, and internal precipitation where several compounds of the same element form (e.g., carbides of Cr) or several compounds exist simultaneously (e.g., carbides containing varying amounts of Ni, Cr, Fe or Mo). In addition, the studies involve a variety of boundary conditions that vary with time and temperature. Finite-difference (F-D) techniques have been applied almost exclusively to model either the solute or corrodant transport in each of these studies. Hence, the paper first reviews the use of F-D techniques to develop solutions to the diffusion equations with various boundary conditions appropriate to high-temperature corrosion processes. The bulk of the paper then reviews various F-D modeling studies of diffusional transport associated with high-temperature corrosion.

Thermally induced gas flows in ratchet channels with diffuse and specular boundaries

PubMed Central

Shahabi, Vahid; Baier, Tobias; Roohi, Ehsan; Hardt, Steffen

2017-01-01

A net gas flow can be induced in the gap between periodically structured surfaces held at fixed but different temperatures when the reflection symmetry along the channel axis is broken. Such a situation arises when one surface features a ratchet structure and can be augmented by altering the boundary conditions on different parts of this surface, with some regions reflecting specularly and others diffusely. In order to investigate the physical mechanisms inducing the flow in this configuration at various Knudsen numbers and geometric configurations, direct simulation Monte Carlo (DSMC) simulations are employed using transient adaptive subcells for collision partner selection. At large Knudsen numbers the results compare favorably with analytical expressions, while for small Knudsen numbers a qualitative explanation for the flow in the strong temperature inhomogeneity at the tips of the ratchet is provided. A detailed investigation of the performance for various ratchet geometries suggests optimum working conditions for a Knudsen pump based on this mechanism. PMID:28128309

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

Evolution of passive movement in advective environments: General boundary condition

NASA Astrophysics Data System (ADS)

Zhou, Peng; Zhao, Xiao-Qiang

2018-03-01

In a previous work [16], Lou et al. studied a Lotka-Volterra competition-diffusion-advection system, where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed (no-flux boundary condition), and showed that weaker advective movements are more beneficial for species to win the competition. In this paper, we aim to extend this result to a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases. Our main approaches are to exclude the existence of co-existence (positive) steady state and to provide a clear picture on the stability of semi-trivial steady states, where we introduced new ideas and techniques to overcome the emerging difficulties. Based on these two aspects and the theory of abstract competitive systems, we achieve a complete understanding on the global dynamics.

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.

Atomisti modeling of the microstructure and transport properties of lead-free solder alloys

NASA Astrophysics Data System (ADS)

Sellers, Michael S.

Damage mechanics models of lead-free solder joints in nanoelectronics continue to improve, and in doing so begin to utilize quantitative values describing processes at the atomic level, governing phenomena like electromigration and thermomigration. In particular, knowledge of the transport properties of specific microstructures helps continuum level models fully describe these larger-scale damage phenomena via multi-scale analysis. For example, diffusivities for different types of grain boundaries (fast diffusion paths for solvent and solute atoms, and vacancies), and a description of the boundary structure as a function of temperature, are critical in modeling solder microstructure evolution and, consequently, joint behavior under extreme temperature and electric current. Moreover, for damage that develops at larger length scales, surface energies and diffusivities play important roles in characterizing void stability and morphology. Unfortunately, experiments that investigate these kind of damage phenomena in the atomistic realm are often inconsistent or unable to directly quantify important parameters. One case is the particular transport and structural properties of grain boundaries in Sn (the main component in lead-free solder alloys) and their behavior in the presence of Ag and Cu impurities. This information is crucial in determining accurate diffusivity values for the common SnAgCu (SAC) type solder. Although an average grain boundary diffusivity has been reported for polycrystalline Sn in several works, the value for grain boundary width is estimated and specific diffusivities for boundaries known to occur in Sn have not been reported, to say nothing of solute effects on Sn diffusivity and grain boundary structure. Similarly, transport properties of Sn surfaces remain relatively uninvestigated as well. These gaps and inconsistencies in atomistic data must be remedied for micro- and macro-scale modeling to improve. As a complement to experimental work and possessing the ability to fill in the gaps, molecular simulation serves to reinforce experimental predictions and provide insight into the atomistic processes that govern studied phenomena. In the present body of work, we employ molecular statics and dynamics simulations in the characterization and computation of betaSn surface energies and surface diffusivities, the determination of diffusivities and structural properties of specific betaSn grain boundaries, and the investigation of Cu and Ag solute effects on betaSn grain boundaries. In our study of betaSn surfaces, energies for low number Miller index surfaces are computed and the (100) plane is found to have the lowest un-relaxed energy. We then find that two simple hopping mechanisms dominate adatom diffusion transitions on this surface. For each, we determine hopping rates of the adatom and compute its tracer diffusivity. Our work on grain boundaries investigates the self-diffusion properties and structure of several betaSn symmetric tilt grain boundaries using molecular dynamics simulations. We find that larger diffusive widths are exhibited by higher excess potential energy grain boundaries. Diffusivities in the directions parallel to the interface plane are also computed and activation energies are found with the Arrhenius relation. These are shown to agree well with experimental data. Finally, we examine the effect that solute atoms of Ag and Cu have on the microstructure of betaSn. Excess energies of the (101) symmetric tilt betaSn grain boundary are computed as a function of solute concentration at the interface, and we show that Ag lowers the energy at a greater rate than Cu. We also quantify segregation enthalpies and critical solute concentrations (where the excess energy of the boundary is reduced to zero). The effect of solute type on shear stress is also examined, and we show that solute has a strong effect on the stabilization of higher energy grain boundaries under shear stress. We then look at the self-diffusivity of Sn in the (101) symmetric tilt betaSn grain boundary and show that adding both Ag or Cu decrease the grain boundary self-diffusivity of Sn as solute amount in the interface increases. Effects of larger concentrations of Cu in particular are also investigated.

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

Lee, Hak-Sung, E-mail: hslee@kims.re.kr; Park, Chanbum; Oh, Chang-Seok

Highlights: • We model the sample grain boundary of LiCoO2, one of important Li cathode materials. • Rigid body translation was found the asymmetric GB is more stable than symmetric GB. • The vacancy formation energy of Li and O was estimated with first principles calculations. • This model boundary can help to find a new dopant to improve Li diffusions. - Abstract: An atomic structure of LiCoO{sub 2} model grain boundary, Σ2 [1120](1102), is introduced and grain boundary energies with rigid body translations are investigated systematically to find the most stable interface structures. It is found that the coordinatedmore » structures of Co and O in the vicinity of grain boundary are strongly related to grain boundary energy. Examining nonstoichiometry at grain boundary, the defect energetics of Li and O site at grain boundary are estimated. In addition, the effect of grain boundary on Li diffusion is investigated to calculate Li diffusion across grain boundary.« less

77 FR 3255 - Notice of 229 Boundary Revision at the Paducah Gaseous Diffusion Plant

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-23

... DEPARTMENT OF ENERGY Notice of 229 Boundary Revision at the Paducah Gaseous Diffusion Plant AGENCY... areas, buildings, and other facilities of the Paducah Gaseous Diffusion Plant, located in McCracken... or upon this facility, installation, or real property of the Paducah Gaseous Diffusion Plant located...

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Turbine exhaust diffuser with a gas jet producing a coanda effect flow control

DOEpatents

Orosa, John; Montgomery, Matthew

2014-02-11

An exhaust diffuser system and method for a turbine engine includes an inner boundary and an outer boundary with a flow path defined therebetween. The inner boundary is defined at least in part by a hub structure that has an upstream end and a downstream end. The outer boundary may include a region in which the outer boundary extends radially inward toward the hub structure and may direct at least a portion of an exhaust flow in the diffuser toward the hub structure. The hub structure includes at least one jet exit located on the hub structure adjacent to the upstream end of the tail cone. The jet exit discharges a flow of gas substantially tangential to an outer surface of the tail cone to produce a Coanda effect and direct a portion of the exhaust flow in the diffuser toward the inner boundary.

Effects of degeneracy and response function in a diffusion predator-prey model

NASA Astrophysics Data System (ADS)

Li, Shanbing; Wu, Jianhua; Dong, Yaying

2018-04-01

In this paper, we consider positive solutions of a diffusion predator-prey model with a degeneracy under the Dirichlet boundary conditions. We first obtain sufficient conditions of the existence of positive solutions by the Leray-Schauder degree theory, and then analyze the limiting behavior of positive solutions as the growth rate of the predator goes to infinity and the conversion rates of the predator goes to zero, respectively. It is shown that these results for Holling II response function (i.e. m  >  0) reveal interesting contrast with that for the classical Lotka-Volterra predator-prey model (i.e. m  =  0).

Effect of progressively increasing lithium conditioning on edge transport and stability in high triangularity NSTX H-modes

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

Maingi, R.; Canik, J. M.; Bell, R. E.

A sequence of H-mode discharges with increasing levels of pre-discharge lithium evaporation (‘dose’) was conducted in high triangularity and elongation boundary shape in NSTX. Energy confinement increased, and recycling decreased with increasing lithium dose, similar to a previous lithium dose scan in medium triangularity and elongation plasmas. Data-constrained SOLPS interpretive modeling quantified the edge transport change: the electron particle diffusivity decreased by 10-30x. The electron thermal diffusivity decreased by 4x just inside the top of the pedestal, but increased by up to 5x very near the separatrix. These results provide a baseline expectation for lithium benefits in NSTX-U, which ismore » optimized for a boundary shape similar to the one in this experiment.« less

Effect of progressively increasing lithium conditioning on edge transport and stability in high triangularity NSTX H-modes

DOE PAGES

Maingi, R.; Canik, J. M.; Bell, R. E.; ...

2016-07-19

A sequence of H-mode discharges with increasing levels of pre-discharge lithium evaporation (‘dose’) was conducted in high triangularity and elongation boundary shape in NSTX. Energy confinement increased, and recycling decreased with increasing lithium dose, similar to a previous lithium dose scan in medium triangularity and elongation plasmas. Data-constrained SOLPS interpretive modeling quantified the edge transport change: the electron particle diffusivity decreased by 10-30x. The electron thermal diffusivity decreased by 4x just inside the top of the pedestal, but increased by up to 5x very near the separatrix. These results provide a baseline expectation for lithium benefits in NSTX-U, which ismore » optimized for a boundary shape similar to the one in this experiment.« less

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Bolster, Diogo

2017-04-01

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase flows, capable of handling large density and viscosity contrasts. The model is based on a diffuse-interface phase-field approach. Within this context we propose a new algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. The proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases. We test the model by applying it to four benchmark problems: (i) wetting and dewetting of a droplet on a flat surface and (ii) on a cylindrical surface, (iii) multiphase flow past a circular cylinder at an intermediate Reynolds number, and (iv) a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions. Where available, our results show good agreement with analytical solutions and/or existing experimental data, highlighting strengths of this new approach.

Intrinsic rotation from a residual stress at the boundary of a cylindrical laboratory plasma.

PubMed

Yan, Z; Xu, M; Diamond, P H; Holland, C; Müller, S H; Tynan, G R; Yu, J H

2010-02-12

An azimuthally symmetric radially sheared azimuthal flow is driven by a nondiffusive, or residual, turbulent stress localized to a narrow annular region at the boundary of a cylindrical magnetized helicon plasma device. A no-slip condition, imposed by ion-neutral flow damping outside the annular region, combined with a diffusive stress arising from turbulent and collisional viscous damping in the central plasma region, leads to net plasma rotation in the absence of momentum input.

Response of a partially penetrating well in a heterogeneous aquifer: integrated well-face flux vs. uniform well-face flux boundary conditions

NASA Astrophysics Data System (ADS)

Ruud, N. C.; Kabala, Z. J.

1997-07-01

A two-dimensional integrated well-face flux (IWFF) model is developed for computing the drawdown at the well-face and around a fully or partially penetrating well with wellbore storage, situated in a layered confined aquifer. In this model, we calculate drawdown and well-face flux distributions by numerically solving a two-dimensional diffusion equation in cylindrical coordinates subject to appropriate initial and boundary conditions and to the well-face boundary constraint of an integrated well-face flux rather than the physically inconsistent uniform well-face flux boundary condition (the UWFF model). The differences between the IWFF and UWFF models in a partially penetrating well situated in a homogeneous isotropic aquifer are insignificant for wellbore drawdown (less than 3%) but are pronounced for the well-face flux. In fact, the latter strongly deviates from uniformity as the ratio of the screen length to the aquifer thickness decreases. For partially penetrating wells situated in multilayer aquifers, significant differences between the two models may arise, especially if the screen is not located in the most conductive layer. These differences depend on the hydraulic conductivity contrast of the adjacent layers. Consequently, the uniform well-face flux boundary condition should be used with extreme caution.

MARMOT simulations of Xe segregation to grain boundaries in UO2

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

Andersson, Anders D.; Tonks, Michael; Casillas, Luis

2012-06-20

Diffusion of Xe and U in UO{sub 2} is controlled by vacancy mechanisms and under irradiation the formation of mobile vacancy clusters is important. We derive continuum thermodynamic and diffusion models for Xe and U in UO{sub 2} based on the vacancy and cluster diffusion mechanisms established from recent density functional theory (DFT) calculations. Segregation of defects to grain boundaries in UO{sub 2} is described by combining the diffusion model with models of the interaction between Xe atoms and vacancies with grain boundaries derived from separate atomistic calculations. The diffusion and segregation models are implemented in the MOOSE/MARMOT (MBM) finitemore » element (FEM) framework and we simulate Xe redistribution for a few simple microstructures. In this report we focus on segregation to grain boundaries. The U or vacancy diffusion model as well as the coupled diffusion of vacancies and Xe have also been implemented, but results are not included in this report.« less

A Validated All-Pressure Fluid Drop Model and Lewis Number Effects for a Binary Mixture

NASA Technical Reports Server (NTRS)

Harstad, K.; Bellan, J.

1999-01-01

The differences between subcritical liquid drop and supercritical fluid drop behavior are discussed. Under subcritical, evaporative high emission rate conditions, a film layer is present in the inner part of the drop surface which contributes to the unique determination of the boundary conditions; it is this film layer which contributes to the solution's convective-diffusive character. In contrast, under supercritical condition as the boundary conditions contain a degree of arbitrariness due to the absence of a surface, and the solution has then a purely diffusive character. Results from simulations of a free fluid drop under no-gravity conditions are compared to microgravity experimental data from suspended, large drop experiments at high, low and intermediary temperatures and in a range of pressures encompassing the sub-and supercritical regime. Despite the difference between the conditions of the simulations and experiments (suspension vs. free floating), the time rate of variation of the drop diameter square is remarkably well predicted in the linear curve regime. The drop diameter is determined in the simulations from the location of the maximum density gradient, and agrees well with the data. It is also shown that the classical calculation of the Lewis number gives qualitatively erroneous results at supercritical conditions, but that an effective Lewis number previously defined gives qualitatively correct estimates of the length scales for heat and mass transfer at all pressures.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Numerical modeling of crystal growth in Bridgman device

NASA Astrophysics Data System (ADS)

Vompe, Dmitry Aleksandrovich

1997-12-01

The standard model for the growth of a crystal from a pure substance or diluted binary mixture contains transport equations for heat and phase change conditions at the solidification front. A numerical method is constructed for simulations of crystal growth in a vertical Bridgman device. The method is based on a boundary fitting technique in which melted and solidified regions are mapped onto a fixed rectangular logical domain. The Alternating Directions scheme (ADI) is used to treat the diffusive terms implicitly, with explicit methods are used for the remaining terms in the mapped temperature equations with variable coefficients. The nonlinear equation for the solid/liquid interface motion is solved by the modified Euler technique. Results obtained from the calculations have been used to study the influence of various boundary conditions imposed on the sidewalls and the top and bottom of the ampoule. Conditions are identified that lead to a steadily growing crystal and results are compared with an asymptotic one- dimensional model. Criteria based on ampoule length and boundary conditions being derived and compared with a previously developed one-dimensional model. Various cases have been considered to determine conditions for maintaining a nearly flat interface. It was found that the interface amplitude can be decreased by a factor of 100 (even 1,000) by optimizing temperature boundary conditions.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map

PubMed Central

Callegari, S.; Lake, G. R.; Tkachenko, N.; Weissmann, J. D.; Zollikofer, Ch. P. E.

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas. PMID:28085882

Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi

1996-01-01

An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map.

PubMed

Petersen, W P; Callegari, S; Lake, G R; Tkachenko, N; Weissmann, J D; Zollikofer, Ch P E

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher-Kolmogorov-Petrovski-Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Boundary conditions for a one-sided numerical model of evaporative instabilities in sessile drops of ethanol on heated substrates

NASA Astrophysics Data System (ADS)

Semenov, Sergey; Carle, Florian; Medale, Marc; Brutin, David

2017-12-01

The work is focused on obtaining boundary conditions for a one-sided numerical model of thermoconvective instabilities in evaporating pinned sessile droplets of ethanol on heated substrates. In the one-sided model, appropriate boundary conditions for heat and mass transfer equations are required at the droplet surface. Such boundary conditions are obtained in the present work based on a derived semiempirical theoretical formula for the total droplet's evaporation rate, and on a two-parametric nonisothermal approximation of the local evaporation flux. The main purpose of these boundary conditions is to be applied in future three-dimensional (3D) one-sided numerical models in order to save a lot of computational time and resources by solving equations only in the droplet domain. Two parameters, needed for the nonisothermal approximation of the local evaporation flux, are obtained by fitting computational results of a 2D two-sided numerical model. Such model is validated here against parabolic flight experiments and the theoretical value of the total evaporation rate. This study combines theoretical, experimental, and computational approaches in convective evaporation of sessile droplets. The influence of the gravity level on evaporation rate and contributions of different mechanisms of vapor transport (diffusion, Stefan flow, natural convection) are shown. The qualitative difference (in terms of developing thermoconvective instabilities) between steady-state and unsteady numerical approaches is demonstrated.

Downstream boundary effects on the frequency of self-excited oscillations in transonic diffuser flows

NASA Astrophysics Data System (ADS)

Hsieh, T.

1986-10-01

Investigation of downstream boundary effects on the frequency of self-excited oscillations in two-dimensional, separated transonic diffuser flows were conducted numerically by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equation with two equation turbulence models. It was found that the flow fields are very sensitive to the location of the downstream boundary. Extension of the diffuser downstream boundary significantly reduces the frequency and amplitude of oscillations for pressure, velocity, and shock. The existence of a suction slot in the experimental setpup obscures the physical downstream boundary and therefore presents a difficulty for quantitative comparisons between computation and experiment.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Evidence That Descending Cortical Axons Are Essential for Thalamocortical Axons to Cross the Pallial-Subpallial Boundary in the Embryonic Forebrain

PubMed Central

Chen, Yijing; Magnani, Dario; Theil, Thomas; Pratt, Thomas; Price, David J.

2012-01-01

Developing thalamocortical axons traverse the subpallium to reach the cortex located in the pallium. We tested the hypothesis that descending corticofugal axons are important for guiding thalamocortical axons across the pallial-subpallial boundary, using conditional mutagenesis to assess the effects of blocking corticofugal axonal development without disrupting thalamus, subpallium or the pallial-subpallial boundary. We found that thalamic axons still traversed the subpallium in topographic order but did not cross the pallial-subpallial boundary. Co-culture experiments indicated that the inability of thalamic axons to cross the boundary was not explained by mutant cortex developing a long-range chemorepulsive action on thalamic axons. On the contrary, cortex from conditional mutants retained its thalamic axonal growth-promoting activity and continued to express Nrg-1, which is responsible for this stimulatory effect. When mutant cortex was replaced with control cortex, corticofugal efferents were restored and thalamic axons from conditional mutants associated with them and crossed the pallial-subpallial boundary. Our study provides the most compelling evidence to date that cortical efferents are required to guide thalamocortical axons across the pallial-subpallial boundary, which is otherwise hostile to thalamic axons. These results support the hypothesis that thalamic axons grow from subpallium to cortex guided by cortical efferents, with stimulation from diffusible cortical growth-promoting factors. PMID:22412988

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio

2009-07-01

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.

Diffusion model validation and interpretation of stable isotopes in river and lake ice

USGS Publications Warehouse

Ferrick, M.G.; Calkins, D.J.; Perron, N.M.; Cragin, J.H.; Kendall, C.

2002-01-01

The stable isotope stratigraphy of river- and lake-ice archives winter hydroclimatic conditions, and can potentially be used to identify changing water sources or to provide important insights into ice formation processes and growth rates. However, accurate interpretations rely on known isotopic fractionation during ice growth. A one-dimensional diffusion model of the liquid boundary layer adjacent to an advancing solid interface, originally developed to simulate solute rejection by growing crystals, has been used without verification to describe non-equilibrium fractionation during congelation ice growth. Results are not in agreement, suggesting the presence of important uncertainties. In this paper we seek validation of the diffusion model for this application using large-scale laboratory experiments with controlled freezing rates and frequent sampling. We obtained consistent, almost constant, isotopic boundary layer thicknesses over a representative range of ice growth rates on both quiescent and well-mixed water. With the 18O boundary layer thickness from the laboratory, the model successfully quantified reduced river-ice growth rates relative to those of a nearby lake. These results were more representative and easier to obtain than those of a conventional thermal ice-growth model. This diffusion model validation and boundary layer thickness determination provide a powerful tool for interpreting the stable isotope stratigraphy of floating ice. The laboratory experiment also replicated successive fractionation events in response to a freeze-thaw-refreeze cycle, providing a mechanism for apparent ice fractionation that exceeds equilibrium. Analysis of the composition of snow ice and frazil ice in river and lake cores indicated surprising similarities between these ice forms. Published in 2002 by John Wiley & Sons, Ltd.

Determination of gaseous fission product behavior near the cerium dioxide Σ 3 (111)/[11 bar0] tilt grain boundary via first-principles study

NASA Astrophysics Data System (ADS)

Xi, Jianqi; Liu, Bin; Xu, Haixuan; Zhang, Yanwen; Weber, William J.

2018-02-01

Grain boundaries (GBs) are the most abundant structural defects in nanostructured nuclear fuels and play an important role in determining fission product behavior, which further affects the performance of nuclear fuels. In this work, cerium dioxide (CeO2) is used as a surrogate material for mixed oxide fuels to understand gaseous fission product behavior, specifically Xe. First-principles calculations are employed to comprehensively study the behavior of Xe and trap sites for Xe near the Σ 3 (111)/[11 bar0] grain boundary in CeO2, which will provide guidance on overall trends for Xe stability and diffusion at grain boundaries vs in the bulk. Significant segregation behavior of trap sites, regardless of charge states, is observed near the GB. This is mainly ascribed to the local atomic structure near the GB, which results in weaker bond strength and more negative segregation energies. For Xe, however, the segregation profile near the GB is different. Our calculations show that, as the size of trap sites increases, the segregation propensity of Xe is reduced. In addition, under hyper-stoichiometric conditions, the solubility of Xe trapped at the GB is significantly higher than that in the bulk, suggesting higher Xe concentration than that in the bulk. The results of this work demonstrate that the diffusion mechanism of Xe in CeO2 is comparable to that in UO2. The diffusion activation energies of Xe atoms in the Σ 3 GB are lower than that in the bulk CeO2. These results suggest that the diffusivity of Xe atoms is higher along the GB than that in the bulk, which enhances the aggregation of Xe atoms near the GB.

Rotational Diffusion Depends on Box Size in Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-06-07

We show that the rotational dynamics of proteins and nucleic acids determined from molecular dynamics simulations under periodic boundary conditions suffer from significant finite-size effects. We remove the box-size dependence of the rotational diffusion coefficients by adding a hydrodynamic correction k B T/6 ηV with k B Boltzmann's constant, T the absolute temperature, η the solvent shear viscosity, and V the box volume. We show that this correction accounts for the finite-size dependence of the rotational diffusion coefficients of horse-heart myoglobin and a B-DNA dodecamer in aqueous solution. The resulting hydrodynamic radii are in excellent agreement with experiment.

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

Integration of plume and puff diffusion models/application of CFD

NASA Astrophysics Data System (ADS)

Mori, Akira

The clinical symptoms of patients and other evidences of a gas poisoning accident inside an industrial building strongly suggested an abrupt influx of engine exhaust from a construction vehicle which was operating outside in the open air. But the obviously high level of gas concentration could not be well explained by any conventional steady-state gas diffusion models. The author used an unsteady-state continuous Puff Model to simulate the time-wise changes in air stream with the pollutant gas being continuously emitted, and successfully reproduced the observed phenomena. The author demonstrates that this diffusion formula can be solved analytically by the use of error function as long as the change in wind velocity is stepwise, and clarifies the accurate differences between the unsteady- and steady-states and their convergence profiles. Also, the relationship between the Puff and Plume Models is discussed. The case study included a computational fluid dynamics (CFD) analysis to estimate the steady-state air stream and the gas concentration pattern in the affected area. It is well known that clear definition of the boundary conditions is key to successful CFD analysis. The author describes a two-step use of CFD: the first step to define the boundary conditions and the second to determine the steady-state air stream and the gas concentration pattern.

Construction of Fluid - solid Coupling Model with Improved Richards - BP & Its Engineering Application

NASA Astrophysics Data System (ADS)

Xie, Chengyu; Jia, Nan; Shi, Dongping; Lu, Hao

2017-10-01

In order to study the slurry diffusion law during grouting, Richards unsaturated-saturated model was introduced, the definition of the grouting model is clear, the Richards model control equation was established, And the BP neural network was introduced, the improved fluid-solid coupling model was constructed, Through the use of saturated - unsaturated seepage flow model, As well as the overflow boundary iterative solution of the mixed boundary conditions, the free surface is calculated. Engineering practice for an example, with the aid of multi - field coupling analysis software, the diffusion law of slurry was simulated numerically. The results show that the slurry diffusion rule is affected by grouting material, initial pressure and other factors. When the slurry starts, it flows in the cracks along the upper side of the grouting hole, when the pressure gradient is reduced to the critical pressure, that is, to the lower side of the flow, when the slurry diffusion stability, and ultimately its shape like an 8. The slurry is spread evenly from the overall point of view, from the grouting mouth toward the surrounding evenly spread, it gradually reaches saturation by non-saturation, and it is not a purely saturated flow, when the slurry spread and reach a saturated state, the diffusion time is the engineering grouting time.

A study of the determination of grain boundary diffusivity and energy through the thermally grown oxide ridges on a Fe-22Cr alloy surface

NASA Astrophysics Data System (ADS)

Lin, Yu; Laughlin, David E.; Zhu, Jingxi

2017-03-01

The grain boundaries (GBs) present in polycrystalline materials are important with respect to materials behaviour and properties. During the transient stage of oxidation, the higher GB diffusivity results in heterogeneous oxidation structures in the form of oxide ridges that emerge along the alloy GBs. In an attempt to delve into the more fundamental aspects of the GBs, such as GB energy, the size of the oxide ridges was quantitatively measured by atomic force microscopy on the post oxidation surface of a Fe-22 wt % Cr alloy after an oxidation exposure at 800 °C in dry air. The GB diffusivity was calculated utilising the ridge size data and the relationship between the GB diffusivity and the GB characteristics was determined. Furthermore, the GB energy was calculated from the GB diffusivity data, also to make comparison with the data available in the literature. The absolute value of the calculated GB energy was quite close to the values reported in the literature. However, compared to the extremely low temperature (0 K) data-set from the literature, the data-set obtained from this study showed much less spread. The smaller variation range may be attributed to the higher temperature condition (1073 K) in this study.

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

PubMed

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

2007-10-07

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

Multiscale Methods for Nuclear Reactor Analysis

NASA Astrophysics Data System (ADS)

Collins, Benjamin S.

The ability to accurately predict local pin powers in nuclear reactors is necessary to understand the mechanisms that cause fuel pin failure during steady state and transient operation. In the research presented here, methods are developed to improve the local solution using high order methods with boundary conditions from a low order global solution. Several different core configurations were tested to determine the improvement in the local pin powers compared to the standard techniques, that use diffusion theory and pin power reconstruction (PPR). Two different multiscale methods were developed and analyzed; the post-refinement multiscale method and the embedded multiscale method. The post-refinement multiscale methods use the global solution to determine boundary conditions for the local solution. The local solution is solved using either a fixed boundary source or an albedo boundary condition; this solution is "post-refinement" and thus has no impact on the global solution. The embedded multiscale method allows the local solver to change the global solution to provide an improved global and local solution. The post-refinement multiscale method is assessed using three core designs. When the local solution has more energy groups, the fixed source method has some difficulties near the interface: however the albedo method works well for all cases. In order to remedy the issue with boundary condition errors for the fixed source method, a buffer region is used to act as a filter, which decreases the sensitivity of the solution to the boundary condition. Both the albedo and fixed source methods benefit from the use of a buffer region. Unlike the post-refinement method, the embedded multiscale method alters the global solution. The ability to change the global solution allows for refinement in areas where the errors in the few group nodal diffusion are typically large. The embedded method is shown to improve the global solution when it is applied to a MOX/LEU assembly interface, the fuel/reflector interface, and assemblies where control rods are inserted. The embedded method also allows for multiple solution levels to be applied in a single calculation. The addition of intermediate levels to the solution improves the accuracy of the method. Both multiscale methods considered here have benefits and drawbacks, but both can provide improvements over the current PPR methodology.

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(00 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

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.

Numerical modeling of the sound fields in urban squares

NASA Astrophysics Data System (ADS)

Kang, Jian

2005-06-01

This paper studies the basic characteristics of sound fields in urban squares surrounded by reflecting building façades and the effectiveness of architectural changes and urban design options. A radiosity model and an image source model are developed, and a parametric study is carried out in hypothetical squares. The results show that the reverberation time (RT) is rather even in a square, whereas the early decay time (EDT) is very low in the near field, and then becomes close to RT after a rapid increase. Compared to diffuse boundaries, with geometrical boundaries the RT and EDT are significantly longer and the sound pressure level (SPL) attenuation with distance is generally smaller unless the height/side ratio is high. With a boundary diffusion coefficient of 0.2, the sound field is already close to that resulting from purely diffusely reflecting boundaries. The SPL in far field is typically 6-9 dB lower if the square side is doubled; 8 dB lower if the height of building façades is decreased from 50 m to 6 m (diffuse boundaries); 5 dB (diffuse boundaries) or 2 dB (geometrical boundaries) lower if the length/width ratio is increased from 1 to 4; and 10-12 dB lower if the boundary absorption coefficient is increased from 0.1 to 0.9. .

Numerical modeling of the sound fields in urban squares.

PubMed

Kang, Jian

2005-06-01

This paper studies the basic characteristics of sound fields in urban squares surrounded by reflecting building façades and the effectiveness of architectural changes and urban design options. A radiosity model and an image source model are developed, and a parametric study is carried out in hypothetical squares. The results show that the reverberation time (RT) is rather even in a square, whereas the early decay time (EDT) is very low in the near field, and then becomes close to RT after a rapid increase. Compared to diffuse boundaries, with geometrical boundaries the RT and EDT are significantly longer and the sound pressure level (SPL) attenuation with distance is generally smaller unless the height/side ratio is high. With a boundary diffusion coefficient of 0.2, the sound field is already close to that resulting from purely diffusely reflecting boundaries. The SPL in far field is typically 6-9 dB lower if the square side is doubled; 8 dB lower if the height of building façades is decreased from 50 m to 6 m (diffuse boundaries); 5 dB (diffuse boundaries) or 2 dB (geometrical boundaries) lower if the length/width ratio is increased from 1 to 4; and 10-12 dB lower if the boundary absorption coefficient is increased from 0.1 to 0.9.

Non-dispersive carrier transport in molecularly doped polymers and the convection-diffusion equation

NASA Astrophysics Data System (ADS)

Tyutnev, A. P.; Parris, P. E.; Saenko, V. S.

2015-08-01

We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection-diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.

Numerical study of photon migration in the presence of a void region using the radiative transfer and diffusion equations

NASA Astrophysics Data System (ADS)

Miyakawa, Erina; Fujii, Hiroyuki; Hattori, Kiyohito; Tatekura, Yuki; Kobayashi, Kazumichi; Watanabe, Masao

2016-12-01

Diffuse optical tomography (DOT), which is still under development, has a potential to enable non-invasive diagnoses of thyroid cancers in the human neck using the near-infrared light. This modality needs a photon migration model because scattered light is used. There are two types of photon migration models: the radiative transport equation (RTE) and diffusion equation (DE). The RTE can describe photon migration in the human neck with accuracy, while the DE enables an efficient calculation. For developing the accurate and efficient model of photon migration, it is crucial to investigate a condition where the DE holds in a scattering medium including a void region under the refractive-index mismatch at the void boundary because the human neck has a trachea (void region) and the refractive indices are different between the human neck and trachea. Hence, in this paper, we compare photon migration using the RTE with that using the DE in the medium. The numerical results show that the DE is valid under the refractive-index match at the void boundary even though the void region is near the source and detector positions. Under the refractive-index mismatch at the boundary, the numerical results using the DE disagree with those using the RTE when the void region is near the source and detector positions. This is probably because the anisotropy of the light scattering remains around the void boundary.

Immersed boundary methods for simulating fluid-structure interaction

NASA Astrophysics Data System (ADS)

Sotiropoulos, Fotis; Yang, Xiaolei

2014-02-01

Fluid-structure interaction (FSI) problems commonly encountered in engineering and biological applications involve geometrically complex flexible or rigid bodies undergoing large deformations. Immersed boundary (IB) methods have emerged as a powerful simulation tool for tackling such flows due to their inherent ability to handle arbitrarily complex bodies without the need for expensive and cumbersome dynamic re-meshing strategies. Depending on the approach such methods adopt to satisfy boundary conditions on solid surfaces they can be broadly classified as diffused and sharp interface methods. In this review, we present an overview of the fundamentals of both classes of methods with emphasis on solution algorithms for simulating FSI problems. We summarize and juxtapose different IB approaches for imposing boundary conditions, efficient iterative algorithms for solving the incompressible Navier-Stokes equations in the presence of dynamic immersed boundaries, and strong and loose coupling FSI strategies. We also present recent results from the application of such methods to study a wide range of problems, including vortex-induced vibrations, aquatic swimming, insect flying, human walking and renewable energy. Limitations of such methods and the need for future research to mitigate them are also discussed.

Effective transient behaviour of inclusions in diffusion problems

NASA Astrophysics Data System (ADS)

Brassart, Laurence; Stainier, Laurent

2018-06-01

This paper is concerned with the effective transport properties of heterogeneous media in which there is a high contrast between the phase diffusivities. In this case the transient response of the slow phase induces a memory effect at the macroscopic scale, which needs to be included in a macroscopic continuum description. This paper focuses on the slow phase, which we take as a dispersion of inclusions of arbitrary shape. We revisit the linear diffusion problem in such inclusions in order to identify the structure of the effective (average) inclusion response to a chemical load applied on the inclusion boundary. We identify a chemical creep function (similar to the creep function of viscoelasticity), from which we construct estimates with a reduced number of relaxation modes. The proposed estimates admit an equivalent representation based on a finite number of internal variables. These estimates allow us to predict the average inclusion response under arbitrary time-varying boundary conditions at very low computational cost. A heuristic generalisation to concentration-dependent diffusion coefficient is also presented. The proposed estimates for the effective transient response of an inclusion can serve as a building block for the formulation of multi-inclusion homogenisation schemes.

Effect of the computational domain size and shape on the self-diffusion coefficient in a Lennard-Jones liquid.

PubMed

Kikugawa, Gota; Ando, Shotaro; Suzuki, Jo; Naruke, Yoichi; Nakano, Takeo; Ohara, Taku

2015-01-14

In the present study, molecular dynamics (MD) simulations on the monatomic Lennard-Jones liquid in a periodic boundary system were performed in order to elucidate the effect of the computational domain size and shape on the self-diffusion coefficient measured by the system. So far, the system size dependence in cubic computational domains has been intensively investigated and these studies showed that the diffusion coefficient depends linearly on the inverse of the system size, which is theoretically predicted based on the hydrodynamic interaction. We examined the system size effect not only in the cubic cell systems but also in rectangular cell systems which were created by changing one side length of the cubic cell with the system density kept constant. As a result, the diffusion coefficient in the direction perpendicular to the long side of the rectangular cell significantly increases more or less linearly with the side length. On the other hand, the diffusion coefficient in the direction along the long side is almost constant or slightly decreases. Consequently, anisotropy of the diffusion coefficient emerges in a rectangular cell with periodic boundary conditions even in a bulk liquid simulation. This unexpected result is of critical importance because rectangular fluid systems confined in nanospace, which are present in realistic nanoscale technologies, have been widely studied in recent MD simulations. In order to elucidate the underlying mechanism for this serious system shape effect on the diffusion property, the correlation structures of particle velocities were examined.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Modeling condensation with a noncondensable gas for mixed convection flow

NASA Astrophysics Data System (ADS)

Liao, Yehong

2007-05-01

This research theoretically developed a novel mixed convection model for condensation with a noncondensable gas. The model developed herein is comprised of three components: a convection regime map; a mixed convection correlation; and a generalized diffusion layer model. These components were developed in a way to be consistent with the three-level methodology in MELCOR. The overall mixed convection model was implemented into MELCOR and satisfactorily validated with data covering a wide variety of test conditions. In the development of the convection regime map, two analyses with approximations of the local similarity method were performed to solve the multi-component two-phase boundary layer equations. The first analysis studied effects of the bulk velocity on a basic natural convection condensation process and setup conditions to distinguish natural convection from mixed convection. It was found that the superimposed velocity increases condensation heat transfer by sweeping away the noncondensable gas accumulated at the condensation boundary. The second analysis studied effects of the buoyancy force on a basic forced convection condensation process and setup conditions to distinguish forced convection from mixed convection. It was found that the superimposed buoyancy force increases condensation heat transfer by thinning the liquid film thickness and creating a steeper noncondensable gas concentration profile near the condensation interface. In the development of the mixed convection correlation accounting for suction effects, numerical data were obtained from boundary layer analysis for the three convection regimes and used to fit a curve for the Nusselt number of the mixed convection regime as a function of the Nusselt numbers of the natural and forced convection regimes. In the development of the generalized diffusion layer model, the driving potential for mass transfer was expressed as the temperature difference between the bulk and the liquid-gas interface using the Clausius-Clapeyron equation. The model was developed on a mass basis instead of a molar basis to be consistent with general conservation equations. It was found that vapor diffusion is not only driven by a gradient of the molar fraction but also a gradient of the mixture molecular weight at the diffusion layer.

A numerical method for the solution of internal pipe/channel flows in laminar or turbulent motion

NASA Astrophysics Data System (ADS)

Lourenco, L.; Essers, J. A.

1981-11-01

A computer program which is useful in the solution of problems of internal turbulent or laminar flow without recirculation is described. The flow is treated in terms of parabolic boundary layer differential equations. The eddy diffusivity concept is used to model turbulent stresses. Two turbulent models are available: the Prandtl mixing length model and the Nee-Kovasznay model for the effective viscosity. Fluid is considered incompressible, but little program modification is needed to treat compressible flows. Initial conditions are prescribed as well as the boundary conditions. The differencing scheme employed is fully implicit for the dependent variables. This allows the use of relatively large forward steps without stability problems.

Modified chloride diffusion model for concrete under the coupling effect of mechanical load and chloride salt environment

NASA Astrophysics Data System (ADS)

Lei, Mingfeng; Lin, Dayong; Liu, Jianwen; Shi, Chenghua; Ma, Jianjun; Yang, Weichao; Yu, Xiaoniu

2018-03-01

For the purpose of investigating lining concrete durability, this study derives a modified chloride diffusion model for concrete based on the odd continuation of boundary conditions and Fourier transform. In order to achieve this, the linear stress distribution on a sectional structure is considered, detailed procedures and methods are presented for model verification and parametric analysis. Simulation results show that the chloride diffusion model can reflect the effects of linear stress distribution of the sectional structure on the chloride diffusivity with reliable accuracy. Along with the natural environmental characteristics of practical engineering structures, reference value ranges of model parameters are provided. Furthermore, a chloride diffusion model is extended for the consideration of multi-factor coupling of linear stress distribution, chloride concentration and diffusion time. Comparison between model simulation and typical current research results shows that the presented model can produce better considerations with a greater universality.

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Diffusion-coupled cohesive interface simulations of stress corrosion intergranular cracking in polycrystalline materials

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

Pu, Chao; Gao, Yanfei; Wang, Yanli

To study the stress corrosion intergranular cracking mechanism, a diffusion-coupled cohesive zone model (CZM) is proposed for the simulation of the stress-assisted diffusional process along grain boundaries and the mechanical response of grain boundary sliding and separation. This simulation methodology considers the synergistic effects of impurity diffusion driven by pressure gradient and degradation of grain boundary strength by impurity concentration. The diffusion-coupled CZM is combined with crystal plasticity finite element model (CPFEM) to simulate intergranular fracture of polycrystalline material under corrosive environment. Significant heterogeneity of the stress field and extensive impurity accumulation is observed at grain boundaries and junction points.more » Deformation mechanism maps are constructed with respect to the grain boundary degradation factor and applied strain rate, which dictate the transition from internal to near-surface intergranular fracture modes under various strain amplitudes and grain sizes.« less

Turbine exhaust diffuser flow path with region of reduced total flow area

DOEpatents

Orosa, John A.

2012-12-25

An exhaust diffuser system and method for a turbine engine includes an inner boundary and an outer boundary with a flow path defined therebetween. The inner boundary is defined at least in part by a hub that has an upstream end and a downstream end. The outer boundary has a region in which the outer boundary extends radially inward toward the hub. The region can begin at a point that is substantially aligned with the downstream end of the hub or, alternatively, at a point that is proximately upstream of the downstream end of the hub. The region directs at least a portion of an exhaust flow in the diffuser toward the hub. As a result, the exhaust diffuser system and method can achieve the performance of a long hub system while enjoying the costs of a short hub system.

On the protein crystal formation as an interface-controlled process with prototype ion-channeling effect.

PubMed

Siódmiak, Jacek; Uher, Jan J; Santamaría-Holek, Ivan; Kruszewska, Natalia; Gadomski, Adam

2007-08-01

A superdiffusive random-walk action in the depletion zone around a growing protein crystal is considered. It stands for a dynamic boundary condition of the growth process and competes steadily with a quasistatic, curvature-involving (thermodynamic) free boundary condition, both of them contributing to interpret the (mainly late-stage) growth process in terms of a prototype ion-channeling effect. An overall diffusion function contains quantitative signatures of both boundary conditions mentioned and indicates whether the new phase grows as an orderly phase or a converse scenario occurs. This situation can be treated in a quite versatile way both numerically and analytically, within a generalized Smoluchowski framework. This study can help in (1) elucidating some dynamic puzzles of a complex crystal formation vs biomolecular aggregation, also those concerning ion-channel formation, and (2) seeing how ion-channel-type dynamics of non-Markovian nature may set properly the pace of model (dis)ordered protein aggregation.

Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels

NASA Astrophysics Data System (ADS)

Zhu, Huayang; Jackson, Gregory

2000-11-01

Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.

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

Barbante, Paolo; Frezzotti, Aldo; Gibelli, Livio

The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviationsmore » of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.« less

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.

Diffusion of volatile organics through porous snow: impact of surface adsorption and grain boundaries

NASA Astrophysics Data System (ADS)

Bartels-Rausch, T.; Wren, S. N.; Schreiber, S.; Riche, F.; Schneebeli, M.; Ammann, M.

2013-07-01

Release of trace gases from surface snow on earth drives atmospheric chemistry, especially in the polar regions. The gas-phase diffusion of methanol and of acetone through the interstitial air of snow was investigated in a well-controlled laboratory study in the temperature range of 223 to 263 K. The aim of this study was to evaluate how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion on timescales up to 1 h. The diffusive loss of these two volatile organics into packed snow samples was measured using a chemical ionization mass spectrometer. The structure of the snow was analysed by means of X-ray-computed micro-tomography. The observed diffusion profiles could be well described based on gas-phase diffusion and the known structure of the snow sample at temperatures ≥ 253 K. At colder temperatures, surface interactions start to dominate the diffusive transport. Parameterizing these interactions in terms of adsorption to the solid ice surface, i.e. using temperature-dependent air-ice partitioning coefficients, better described the observed diffusion profiles than the use of air-liquid partitioning coefficients. No changes in the diffusive fluxes were observed by increasing the number of grain boundaries in the snow sample by a factor of 7, indicating that for these volatile organic trace gases, uptake into grain boundaries does not play a role on the timescale of diffusion through porous surface snow. For this, a snow sample with an artificially high amount of ice grains was produced and the grain boundary surface measured using thin sections. In conclusion, we have shown that the diffusivity can be predicted when the structure of the snowpack and the partitioning of the trace gas to solid ice is known.

The transition from diffuse to focused extension: Modeled evolution of the West Antarctic Rift system

NASA Astrophysics Data System (ADS)

Huerta, Audrey D.; Harry, Dennis L.

2007-03-01

Two distinct stages of extension are recognized in the West Antarctic Rift system (WARS). During the first stage, beginning in the Late Cretaceous, extension was broadly distributed throughout much of West Antarctica. A second stage of extension in the late Paleogene was focused primarily in the Victoria Land Basin, near the boundary with the East Antarctic craton. The transition to focused extension was roughly coeval with volcanic activity and strike-slip faulting in the adjacent Transantarctic Mountains. This spatial and temporal correspondence suggests that the transition in extensional style could be the result of a change in plate motions or impingement of a plume. Here we use finite element models to study the processes and conditions responsible for the two-stage evolution of rifting in the WARS. Model results indicate that the transition from a prolonged period of broadly distributed extension to a later period of focused rifting did not require a change in the regional stress regime (changes in plate motion), or deep mantle thermal state (impingement of a plume). Instead, we attribute the transition from diffuse to focused extension to an early stage dominated by the initially weak accreted lithosphere of West Antarctica, and a later stage that concentrated around a secondary weakness located at the boundary between the juvenile West Antarctica lithosphere and Precambrian East Antarctic craton. The modeled transition in extension from the initially weak West Antarctica region to the secondary weakness at the West Antarctic-East Antarctic boundary is precipitated by strengthening of the West Antarctica lithosphere during syn-extensional thinning and cooling. The modeled syn-extensional strengthening of the WARS lithosphere promotes a wide-rift mode of extension between 105 and ˜ 65 Ma. By ˜ 65 Ma most of the extending WARS region becomes stronger than the area immediately adjacent to the East Antarctic craton and extension becomes concentrated near the East Antarctic/West Antarctic boundary, forming the Victoria Land Basin region. Mantle necking in this region leads to syn-extensional weakening that promotes a narrow-rift mode of extension that becomes progressively more focused with time, resulting in formation of the Terror Rift in the western Victoria Land Basin. The geodynamic models demonstrate that the transition from diffuse to focused extension occurs only under a limited set of initial and boundary conditions, and is particularly sensitive to the pre-rift thermal state of the crust and upper mantle. Models that predict diffuse extension in West Antarctica followed by localization of rifting near the boundary between East and West Antarctica require upper mantle temperatures of 730 ± 50 °C and sufficient concentration of heat producing elements in the crust to account for ˜ 50% of the upper mantle temperature. Models with upper mantle temperatures < ca. 680 °C and/or less crustal heat production initially undergo diffuse extension in West Antarctica, and quickly develop a lithospheric neck at the model edge furthest from East Antarctica. Models with upper mantle temperatures > ca. 780 °C do not develop focused rifts, and predict indefinite diffuse extension in West Antarctica.

Meso-scale anisotropic hydrogen segregation near grain-boundaries in polycrystalline nickel characterized by EBSD/SIMS

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

Oudriss, A.; Le Guernic, Solenne; Wang, Zhaoying

2016-02-15

To study anisotropic hydrogen segregation and diffusion in nickel polycrystalline, Secondary Ion Mass Spectrometry (SIMS) and Electron Back Scattered Diffraction (EBSD) are integrated to investigate hydrogen distribution around grain boundaries. Hydrogen distribution in pre-charged samples were correlated with grain boundary character by integrating high-resolution grain microstructure from EBSD inverse pole figure map and low-resolution hydrogen concentration profile map from SIMS. This multimodal imaging instrumentation shows that grain boundaries in nickel can be categorized into two families based on behavior of hydrogen distribution crossing grain boundary: the first one includes random grain boundaries with fast hydrogen diffusivity, showing a sharp gapmore » for hydrogen concentration profile cross the grain boundaries. The second family are special Σ3n grain boundaries with low hydrogen diffusivity, showing a smooth gradient of hydrogen concentration cross the grain boundary. Heterogeneous hydrogen distributions due to grain boundary family revealed by SIMS/EBSD on mesoscale further validate the recent hydrogen permeation data and anisotropic ab-initio calculations in nanoscale. The results highlight the fact that grain boundaries character impacts hydrogen distribution significantly.« less

Grain boundary diffusion behaviors in hot-deformed Nd2Fe14B magnets by PrNd-Cu low eutectic alloys

NASA Astrophysics Data System (ADS)

Tang, Xu; Chen, Renjie; Li, Ming; Jin, Chaoxiang; Yin, Wenzong; Lee, Don; Yan, Aru

2018-01-01

High coercivity of hot-deformed Nd2Fe14B magnets was obtained by grain boundary diffusion. Comparable squareness and similar magnetic properties for samples diffusing from side and pole surfaces show little discrepancies if quantities of the infiltrated PrNd-Cu low eutectic alloys is enough to obtain sufficient diffusion. However, the microstructures and higher characteristic peak ratios show preferable orientation of grains near surfaces of the sample diffused from side surfaces than that from pole surfaces. Amorphous Nd-rich phases and crystal Fe-rich phases were both observed in the diffused magnets. The enhancement of coercivity is considered to be resulted from grain boundary optimization and magnetic isolation which is caused by the thickened nonmagnetic intergranular phases.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Theory of a time-dependent heat diffusion determination of thermal diffusivities with a single temperature measurement

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

Perez, R. B.; Carroll, R. M.; Sisman, O.

1971-02-01

A method to measure the thermal diffusivity of reactor fuels during irradiation is developed, based on a time-dependent heat diffusion equation. With this technique the temperature is measured at only one point in the fuel specimen. This method has the advantage that it is not necessary to know the heat generation (a difficult evaluation during irradiation). The theory includes realistic boundary conditions, applicable to actual experimental systems. The parameters are the time constants associated with the first two time modes in the temperature-vs-time curve resulting from a step change in heat input to the specimen. With the time constants andmore » the necessary material properties and dimensions of the specimen and specimen holder, the thermal diffusivity of the specimen can be calculated.« less

Radial diffusion with outer boundary determined by geosynchronous measurements: Storm and post-storm intervals

NASA Astrophysics Data System (ADS)

Chu, F.; Haines, P.; Hudson, M.; Kress, B.; Freidel, R.; Kanekal, S.

2007-12-01

Work is underway by several groups to quantify diffusive radial transport of radiation belt electrons, including a model for pitch angle scattering losses to the atmosphere. The radial diffusion model conserves the first and second adiabatic invariants and breaks the third invariant. We have developed a radial diffusion code which uses the Crank Nicholson method with a variable outer boundary condition. For the radial diffusion coefficient, DLL, we have several choices, including the Brautigam and Albert (JGR, 2000) diffusion coefficient parameterized by Kp, which provides an ad hoc measure of the power level at ULF wave frequencies in the range of electron drift (mHz), breaking the third invariant. Other diffusion coefficient models are Kp-independent, fixed in time but explicitly dependent on the first invariant, or energy at a fixed L, such as calculated by Elkington et al. (JGR, 2003) and Perry et al. (JGR, 2006) based on ULF wave model fields. We analyzed three periods of electron flux and phase space density (PSD) enhancements inside of geosynchronous orbit: March 31 - May 31, 1991, and July 2004 and Nov 2004 storm intervals. The radial diffusion calculation is initialized with a computed phase space density profile for the 1991 interval using differential flux values from the CRRES High Energy Electron Fluxmeter instrument, covering 0.65 - 7.5 MeV. To calculate the initial phase space density, we convert Roederer L* to McIlwain's L- parameter using the ONERA-DESP program. A time averaged model developed by Vampola1 from the entire 14 month CRRES data set is applied to the July 2004 and Nov 2004 storms. The online CRESS data for specific orbits and the Vampola-model flux are both expressed in McIlwain L-shell, while conversion to L* conserves phase space density in a distorted non-dipolar magnetic field model. A Tsyganenko (T04) magnetic field model is used for conversion between L* and L. The outer boundary PSD is updated using LANL GEO satellite fluxes. After calculating the phase space density time evolution for the two storms and post-injection interval (March 31 - May 31, 1991), we compare results with SAMPEX measurements. A better match with SAMPEX measurements is obtained with a variable outer boundary, also with a Kp-dependent diffusion coefficient, and finally with an energy and L-dependent loss term (Summers et al., JGR, 2004), than with a time-independent diffusion coefficient and a simple Kp-parametrized loss rate and location of the plasmapause. Addition of a varying outer boundary which incorporates measured fluxes at geosynchronous orbit using L* has the biggest effect of the three parametrized variations studied. 1Vampola, A.L., 1996, The ESA Outer Zone Electron Model Update, Environment Modelling for Spaced-based Applications, ESA SP-392, ESTEC, Nordwijk, NL, pp. 151-158, W. Burke and T.-D. Guyenne, eds.

Solid-state diffusion-controlled growth of the phases in the Au-Sn system

NASA Astrophysics Data System (ADS)

Baheti, Varun A.; Kashyap, Sanjay; Kumar, Praveen; Chattopadhyay, Kamanio; Paul, Aloke

2018-01-01

The solid state diffusion-controlled growth of the phases is studied for the Au-Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn4 phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn4 phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

USDA-ARS?s Scientific Manuscript database

Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

Dynamics of flow control in an emulated boundary layer-ingesting offset diffuser

NASA Astrophysics Data System (ADS)

Gissen, A. N.; Vukasinovic, B.; Glezer, A.

2014-08-01

Dynamics of flow control comprised of arrays of active (synthetic jets) and passive (vanes) control elements , and its effectiveness for suppression of total-pressure distortion is investigated experimentally in an offset diffuser, in the absence of internal flow separation. The experiments are conducted in a wind tunnel inlet model at speeds up to M = 0.55 using approach flow conditioning that mimics boundary layer ingestion on a Blended-Wing-Body platform. Time-dependent distortion of the dynamic total-pressure field at the `engine face' is measured using an array of forty total-pressure probes, and the control-induced distortion changes are analyzed using triple decomposition and proper orthogonal decomposition (POD). These data indicate that an array of the flow control small-scale synthetic jet vortices merge into two large-scale, counter-rotating streamwise vortices that exert significant changes in the flow distortion. The two most energetic POD modes appear to govern the distortion dynamics in either active or hybrid flow control approaches. Finally, it is shown that the present control approach is sufficiently robust to reduce distortion with different inlet conditions of the baseline flow.

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

NASA Astrophysics Data System (ADS)

Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, D. Scott

2018-05-01

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame-flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier-Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the 'exact' numerical integration of the governing equations, comparing predictions of the various flame properties.

A finite element model development for simulation of the impact of slab thickness, joints, and membranes on indoor radon concentration.

PubMed

Muñoz, E; Frutos, B; Olaya, M; Sánchez, J

2017-10-01

The focus of this study is broadly to define the physics involved in radon generation and transport through the soil and other materials using different parameter-estimation tools from the literature. The effect of moisture in the soil and radon transport via water in the pore space was accounted for with the application of a porosity correction coefficient. A 2D finite element model is created, which reproduces the diffusion and advection mechanisms resulting from specified boundary conditions. A comparison between the model and several analytical and numerical solutions obtained from the literature and field studies validates the model. Finally, the results demonstrate that the model can predict radon entry through different building boundary conditions, such as concrete slabs with or without joints, variable slab thicknesses and diffusion coefficients, and the use of several radon barrier membranes. Cracks in the concrete or the radon barrier membrane have been studied to understand how indoor concentration is affected by these issues. Copyright © 2017 Elsevier Ltd. All rights reserved.

Growth and Interaction of Colloid Nuclei

NASA Astrophysics Data System (ADS)

Lam, Michael-Angelo; Khusid, Boris; Meyer, William; Kondic, Lou

2017-11-01

We study evolution of colloid systems under zero-gravity conditions. In particular, we focus on the regime where there is a coexistence between a liquid and a solid state. Under zero gravity, the dominating process in the bulk of the fluid phase and the solid phase is diffusion. At the moving solid/liquid interface, osmotic pressure is balanced by surface tension, as well as balancing fluxes (conservation of mass) with the kinematics of nuclei growth (Wilson-Frenkel law). Due to the highly nonlinear boundary condition at the moving boundary, care has to be taken when performing numerical simulations. In this work, we present a nonlinear model for colloid nuclei growth. Numerical simulations using a finite volume method are compared with asymptotic analysis of the governing equation and experimental results for nuclei growth. Novel component in our numerical simulations is the inclusion of nonlinear (collective) diffusion terms that depend on the chemical potentials of the colloid in the solid and fluid phase. The results include growth and dissolution of a single colloidal nucleus, as well as evolution of multiple interacting nuclei. Supported by NASA Grant No. NNX16AQ79G.

Spreading and vanishing in a West Nile virus model with expanding fronts

NASA Astrophysics Data System (ADS)

Tarboush, Abdelrazig K.; Lin, ZhiGui; Zhang, MengYun

2017-05-01

In this paper, we study a simplified version of a West Nile virus model discussed by Lewis et al. [28], which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number $R_0$ for the non-spatial epidemic model is defined and a threshold parameter $R_0 ^D$ for the corresponding problem with null Dirichlet boundary condition is introduced. We consider a free boundary problem with coupled system, which describes the diffusion of birds by a PDE and the movement of mosquitoes by a ODE. The risk index $R_0^F (t)$ associated with the disease in spatial setting is represented. Sufficient conditions for the WNv to eradicate or to spread are given. The asymptotic behavior of the solution to system when the spreading occurs are considered. It is shown that the initial number of infected populations, the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus. Numerical simulations are presented to illustrate the analytical results.

Understanding the Effects of Lower Boundary Conditions and Eddy Diffusion on the Ionosphere-Thermosphere System

NASA Astrophysics Data System (ADS)

Malhotra, G.; Ridley, A. J.; Marsh, D. R.; Wu, C.; Paxton, L. J.

2017-12-01

The exchange of energy between lower atmospheric regions with the ionosphere-thermosphere (IT) system is not well understood. A number of studies have observed day-to-day and seasonal variabilities in the difference between data and model output of various IT parameters. It is widely speculated that the forcing from the lower atmosphere, variability in weather systems and gravity waves that propagate upward from troposphere into the upper mesosphere and lower thermosphere (MLT) may be responsible for these spatial and temporal variations in the IT region, but their exact nature is unknown. These variabilities can be interpreted in two ways: variations in state (density, temperature, wind) of the upper mesosphere or spatial and temporal changes in the small-scale mixing, or Eddy diffusion that is parameterized within the model.In this study, firstly, we analyze the sensitivity of the thermospheric and ionospheric states - neutral densities, O/N2, total electron content (TEC), peak electron density, and peak electron height - to various lower boundary conditions in the Global Ionosphere Thermosphere Model (GITM). We use WACCM-X and GSWM to drive the lower atmospheric boundary in GITM at 100 km, and compare the results with the current MSIS-driven version of GITM, analyzing which of these simulations match the measurements from GOCE, GUVI, CHAMP, and GPS-derived TEC best. Secondly, we analyze the effect of eddy diffusion in the IT system. The turbulence due to eddy mixing cannot be directly measured and it is a challenge to completely characterize its linear and non-linear effects from other influences, since the eddy diffusion both influences the composition through direct mixing and the temperature structure due to turbulent conduction changes. In this study we input latitudinal and seasonal profiles of eddy diffusion into GITM and then analyze the changes in the thermospheric and ionospheric parameters. These profiles will be derived from both WACC-X simulations and direct observations of errors between the model and data such as GUVI O/N2 ratios and TEC data. In each case, the model results will be compared to data to determine the improvement.

Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd-Fe-B magnets

NASA Astrophysics Data System (ADS)

Li, W.; Zhou, Q.; Zhao, L. Z.; Wang, Q. X.; Zhong, X. C.; Liu, Z. W.

2018-04-01

A systematic investigation on the anisotropic grain boundary diffusion in sintered Nd-Fe-B magnets is carried out by micromagnetic simulation. The results indicate that the critical reason for the anisotropic diffusion effect is not the difference in the amount of Dy diffused along different directions but the macroscopic demagnetizing field. The diffusion parallel to the easy axis from both pole surfaces of the magnet can increase the nucleation fields in the two major regions with large macroscopic demagnetizing fields, where the reverse domains can nucleate easily. As a consequence, the grain boundary diffusion along the directions parallel to the easy axis from two pole surfaces is more effective to improve the coercivity of the magnets than that along other directions. It is also found that, to enhance the coercivity, only a limited diffusion depth is required. The present result is in good agreement with the recent experimental findings.

Ultra-fast grain boundary diffusion and its contribution to surface segregation on a martensitic steel. Experiments and modeling

NASA Astrophysics Data System (ADS)

Christien, F.; Le Gall, R.

2011-09-01

Phosphorus surface segregation was measured by Auger Electron Spectroscopy on a 17-4 PH martensitic stainless steel at 450, 550 and 600 °C. Surface segregation was shown to be much faster than expected which was attributed to a high contribution of phosphorus diffusion along the former austenitic grain boundaries. A model of surface segregation was developed following the Darken-du Plessis approach and taking account of both bulk and grain boundary solute diffusion. The phosphorus grain boundary diffusion coefficient in 17-4 PH was estimated: DGB< = 6.2 10 4 exp(- 157 kJ mol - 1 /RT)cm 2 s - 1 . It is found to be more than three orders of magnitude higher in 17-4 PH steel than in α-iron.

Grain-boundary type and distribution in silicon carbide coatings and wafers

NASA Astrophysics Data System (ADS)

Cancino-Trejo, Felix; López-Honorato, Eddie; Walker, Ross C.; Ferrer, Romelia Salomon

2018-03-01

Silicon carbide is the main diffusion barrier against metallic fission products in TRISO (tristructural isotropic) coated fuel particles. The explanation of the accelerated diffusion of silver through SiC has remained a challenge for more than four decades. Although, it is now well accepted that silver diffuse through SiC by grain boundary diffusion, little is known about the characteristics of the grain boundaries in SiC and how these change depending on the type of sample. In this work five different types (coatings and wafers) of SiC produced by chemical vapor deposition were characterized by electron backscatter diffraction (EBSD). The SiC in TRISO particles had a higher concentration of high angle grain boundaries (aprox. 70%) compared to SiC wafers, which ranged between 30 and 60%. Similarly, SiC wafers had a higher concentration of low angle grain boundaries ranging between 15 and 30%, whereas TRISO particles only reached values of around 7%. The same trend remained when comparing the content of coincidence site lattice (CSL) boundaries, since SiC wafers showed a concentration of more than 30%, whilst TRISO particles had contents of around 20%. In all samples the largest fractions of CSL boundaries (3 ≤ Σ ≤ 17) were the Σ3 boundaries. We show that there are important differences between the SiC in TRISO particles and SiC wafers which could explain some of the differences observed in diffusion experiments in the literature.

Cs diffusion in SiC high-energy grain boundaries

NASA Astrophysics Data System (ADS)

Ko, Hyunseok; Szlufarska, Izabela; Morgan, Dane

2017-09-01

Cesium (Cs) is a radioactive fission product whose release is of concern for Tristructural-Isotropic fuel particles. In this work, Cs diffusion through high energy grain boundaries (HEGBs) of cubic-SiC is studied using an ab-initio based kinetic Monte Carlo (kMC) model. The HEGB environment was modeled as an amorphous SiC, and Cs defect energies were calculated using the density functional theory (DFT). From defect energies, it was suggested that the fastest diffusion mechanism is the diffusion of Cs interstitial in an amorphous SiC. The diffusion of Cs interstitial was simulated using a kMC model, based on the site and transition state energies sampled from the DFT. The Cs HEGB diffusion exhibited an Arrhenius type diffusion in the range of 1200-1600 °C. The comparison between HEGB results and the other studies suggests not only that the GB diffusion dominates the bulk diffusion but also that the HEGB is one of the fastest grain boundary paths for the Cs diffusion. The diffusion coefficients in HEGB are clearly a few orders of magnitude lower than the reported diffusion coefficients from in- and out-of-pile samples, suggesting that other contributions are responsible, such as radiation enhanced diffusion.

Mathematical modeling of liquid/liquid hollow fiber membrane contactor accounting for interfacial transport phenomena: Extraction of lanthanides as a surrogate for actinides

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

Rogers, J.D.

1994-08-04

This report is divided into two parts. The second part is divided into the following sections: experimental protocol; modeling the hollow fiber extractor using film theory; Graetz model of the hollow fiber membrane process; fundamental diffusive-kinetic model; and diffusive liquid membrane device-a rigorous model. The first part is divided into: membrane and membrane process-a concept; metal extraction; kinetics of metal extraction; modeling the membrane contactor; and interfacial phenomenon-boundary conditions-applied to membrane transport.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Composite and Component Plates, Plate Non-rigidity, and the Steadiness of Plate Motion From Marine Geophysical and Space Geodetic Data

NASA Astrophysics Data System (ADS)

Gordon, R. G.; Argus, D. F.; DeMets, C.

2017-12-01

Plate tectonic theory has evolved since its birth 50 years ago. In particular, we now recognize that some of the originally proposed plates such as the Indo-Australia plate, the Africa plate, and the America plate are what we term "composite" plates—entities that contain no traditionally defined narrow plate boundaries, but are composed of multiple approximately rigid regions, which we term "component" plates, separated by diffuse plate boundaries. The best example of a composite plate is the Indo-Australia composite plate, which consists of the India, Capricorn, Australia, and Macquarie component plates and multiple intervening diffuse oceanic plate boundaries. The poles of relative rotation between component plates tend to lie in their mutual diffuse plate boundary. Outside of diffuse boundaries, plate rigidity has proven to be an excellent approximation, but the non-closure of some plate circuits indicates that stable plate interiors have a small but significant non-rigidity that may add up to 1 to 2 mm/a across any individual plate and may be partly due to horizontal thermal contraction of oceanic lithosphere. The greatest observational challenge to plate rigidity is posed by the Pacific-Cocos-Nazca plate circuit, which fails closure by 15 ±4 mm/a. The most rapid deformation of the plates observed with space geodesy is generated by solid Earth's viscous response to unloading of the late Pleistocene ice sheets. Differences between different realizations of global plate velocities from space geodesy appear in some cases to be due to differing assumptions about the motion of the geocenter, which affects estimated plate relative angular velocities and estimated vertical motion at geodetic sites. Comparison of space geodetic and marine geophysical plate motion rates and directions has demonstrated that plate motion is nearly steady, which allows plate boundary conditions to be applied to inter-seismic strain accumulation due to locking of specific faults. In detail it appears, however, that plate velocities over the past few decades have in several cases been significantly different from plate motions averaged over geologic time. Some of the largest changes have been decreases in rates across convergent plate boundaries: Nazca-South America and the velocities of Nubia, Arabia, and India relative to Eurasia.

Predictions and Verification of an Isotope Marine Boundary Layer Model

NASA Astrophysics Data System (ADS)

Feng, X.; Posmentier, E. S.; Sonder, L. J.; Fan, N.

2017-12-01

A one-dimensional (1D), steady state isotope marine boundary layer (IMBL) model is constructed. The model includes meteorologically important features absent in Craig and Gordon type models, namely height-dependent diffusion/mixing and convergence of subsiding external air. Kinetic isotopic fractionation results from this height-dependent diffusion which starts as pure molecular diffusion at the air-water interface and increases linearly with height due to turbulent mixing. The convergence permits dry, isotopically depleted air subsiding adjacent to the model column to mix into ambient air. In δD-δ18O space, the model results fill a quadrilateral, of which three sides represent 1) vapor in equilibrium with various sea surface temperatures (SSTs) (high d18O boundary of quadrilateral); 2) mixture of vapor in equilibrium with seawater and vapor in the subsiding air (lower boundary depleted in both D and 18O); and 3) vapor that has experienced the maximum possible kinetic fractionation (high δD upper boundary). The results can be plotted in d-excess vs. δ18O space, indicating that these processes all cause variations in d-excess of MBL vapor. In particular, due to relatively high d-excess in the descending air, mixing of this air into the MBL causes an increase in d-excess, even without kinetic isotope fractionation. The model is tested by comparison with seven datasets of marine vapor isotopic ratios, with excellent correspondence; >95% of observational data fall within the quadrilateral area predicted by the model. The distribution of observations also highlights the significant influence of vapor from the nearby converging descending air on isotopic variations in the MBL. At least three factors may explain the <5% of observations that fall slightly outside of the predicted region in both δD-δ18O and d-excess - δ18O space: 1) variations in seawater isotopic ratios, 2) variations in isotopic composition of subsiding air, and 3) influence of sea spray. The model can be used for understanding the effects of boundary layer processes and meteorological conditions on isotopic composition of vapor within, and vapor fluxes through the MBL, and how changes in moisture source regions affect the isotopic composition of precipitation. The model can be applied to modern as well as paleo- climate conditions.

Monte Carlo Modeling of VLWIR HgCdTe Interdigitated Pixel Response

NASA Astrophysics Data System (ADS)

D'Souza, A. I.; Stapelbroek, M. G.; Wijewarnasuriya, P. S.

2010-07-01

Increasing very long-wave infrared (VLWIR, λ c ≈ 15 μm) pixel operability was approached by subdividing each pixel into four interdigitated subpixels. High response is maintained across the pixel, even if one or two interdigitated subpixels are deselected (turned off), because interdigitation provides that the preponderance of minority carriers photogenerated in the pixel are collected by the selected subpixels. Monte Carlo modeling of the photoresponse of the interdigitated subpixel simulates minority-carrier diffusion from carrier creation to recombination. Each carrier generated at an appropriately weighted random location is assigned an exponentially distributed random lifetime τ i, where < τ i> is the bulk minority-carrier lifetime. The minority carrier is allowed to diffuse for a short time d τ, and the fate of the carrier is decided from its present position and the boundary conditions, i.e., whether the carrier is absorbed in a junction, recombined at a surface, reflected from a surface, or recombined in the bulk because it lived for its designated lifetime. If nothing happens, the process is then repeated until one of the boundary conditions is attained. The next step is to go on to the next carrier and repeat the procedure for all the launches of minority carriers. For each minority carrier launched, the original location and boundary condition at fatality are recorded. An example of the results from Monte Carlo modeling is that, for a 20- μm diffusion length, the calculated quantum efficiency (QE) changed from 85% with no subpixels deselected, to 78% with one subpixel deselected, 67% with two subpixels deselected, and 48% with three subpixels deselected. Demonstration of the interdigitated pixel concept and verification of the Monte Carlo modeling utilized λ c(60 K) ≈ 15 μm HgCdTe pixels in a 96 × 96 array format. The measured collection efficiency for one, two, and three subelements selected, divided by the collection efficiency for all four subelements selected, matched that calculated using Monte Carlo modeling.

Very Efficient High-order Hyperbolic Schemes for Time-dependent Advection Diffusion Problems: Third-, Fourth-, and Sixth-order

DTIC Science & Technology

2014-07-07

boundary condition (x ¼ 7p =2; j ¼ 2p; U ¼ 1; m ¼ 1) on N ¼ 10 uniform nodes (Dt ¼ 0:01.) Table 10 Unsteady linear advection–diffusion problem with periodic...500 3rd 55 2 4th 55 2 6th 55 2 1000 3rd 116 2 4th 116 2 6th 116 2 Table 11 Unsteady linear advection–diffusion problem with oscillatory BC (x ¼ 7p =2; a...dependent problem with oscillatory BC (x ¼ 7p =2; a ¼ 1.) using the third-order RD-GT scheme with the BDF3 time discretization. Number of nodes Dt (BDF3

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Finite element modelling of creep cavity filling by solute diffusion

NASA Astrophysics Data System (ADS)

Versteylen, C. D.; Szymański, N. K.; Sluiter, M. H. F.; van Dijk, N. H.

2018-04-01

In recently discovered self healing creep steels, open-volume creep cavities are filled by the precipitation of supersaturated solute. These creep cavities form on the grain boundaries oriented perpendicular to the applied stress. The presence of a free surface triggers a flux of solute from the matrix, over the grain boundaries towards the creep cavities. We studied the creep cavity filling by finite element modelling and found that the filling time critically depends on (i) the ratio of diffusivities in the grain boundary and the bulk, and (ii) on the ratio of the intercavity distance and the cavity size. For a relatively large intercavity spacing 3D transport is observed when the grain boundary and volume diffusivities are of a similar order of magnitude, while a 2D behaviour is observed when the grain boundary diffusivity is dominant. Instead when the intercavity distance is small, the transport behaviour tends to a 1D behaviour in all cases, as the amount of solute available in the grain boundary is insufficient. A phase diagram with the transition lines is constructed.

Plume meander and dispersion in a stable boundary layer

NASA Astrophysics Data System (ADS)

Hiscox, April L.; Miller, David R.; Nappo, Carmen J.

2010-11-01

Continuous lidar measurements of elevated plume dispersion and corresponding micrometeorology data are analyzed to establish the relationship between plume behavior and nocturnal boundary layer dynamics. Contrasting nights of data from the JORNADA field campaign in the New Mexico desert are analyzed. The aerosol lidar measurements were used to separate the plume diffusion (plume spread) from plume meander (displacement). Mutiresolution decomposition was used to separate the turbulence scale (<90 s) from the submesoscale (>90 s). Durations of turbulent kinetic energy stationarity and the wind steadiness were used to characterize the local scale and submesoscale turbulence. Plume meander, driven by submesoscale wind motions, was responsible for most of the total horizontal plume dispersion in weak and variable winds and strong stability. This proportion was reduced in high winds (i.e., >4 m s-1), weakly stable conditions but remained the dominant dispersion mechanism. The remainder of the plume dispersion in all cases was accounted for by internal spread of the plume, which is a small eddy diffusion process driven by turbulence. Turbulence stationarity and the wind steadiness are demonstrated to be closely related to plume diffusion and plume meander, respectively.

Effect of Gravity Level on the Particle Shape and Size During Zeolite Crystal Growth

NASA Technical Reports Server (NTRS)

Song, Hong-Wei; Ilebusi, Olusegun J.; Sacco, Albert, Jr.

2003-01-01

A microscopic diffusion model is developed to represent solute transport in the boundary layer of a growing zeolite crystal. This model is used to describe the effect of gravity on particle shape and solute distribution. Particle dynamics and crystal growth kinetics serve as the boundary conditions of flow and convection-diffusion equations. A statistical rate theory is used to obtain the rate of solute transport across the growing interface, which is expressed in terms of concentration and velocity of solute species. Microgravity can significantly decrease the solute velocity across the growing interface compared to its earth-based counterpart. The extent of this reduction highly depends on solute diffusion constant in solution. Under gravity, the flow towards the crystal enhances solute transport rate across the growing interface while the flow away from crystals reduces this rate, suggesting a non-uniform growth rate and thus an elliptic final shape. However, microgravity can significantly reduce the influence of flow and obtain a final product with perfect spherical shape. The model predictions compare favorably with the data of space experiment of zeolites grown in space.

Gas exchange across the air-sea interface

NASA Astrophysics Data System (ADS)

Hasse, L.; Liss, P. S.

1980-10-01

The physics of gas exchange at the air-sea interface are reviewed. In order to describe the transfer of gases in the liquid near the boundary, a molecular plus eddy diffusivity concept is used, which has been found useful for smooth flow over solid surfaces. From consideration of the boundary conditions, a similar dependence of eddy diffusivity on distance from the interface can be derived for the flow beneath a gas/liquid interface, at least in the absence of waves. The influence of waves is then discussed. It is evident from scale considerations that the effect of gravity waves is small. It is known from wind tunnel work that capillary waves enhance gas transfer considerably. The existing hypotheses are apparently not sufficient to explain the observations. Examination of field data is even more frustrating since the data do not show the expected increase of gas exchange with wind speed.

Creep of quartz by dislocation and grain boundary processes

NASA Astrophysics Data System (ADS)

Fukuda, J. I.; Holyoke, C. W., III; Kronenberg, A. K.

2015-12-01

Wet polycrystalline quartz aggregates deformed at temperatures T of 600°-900°C and strain rates of 10-4-10-6 s-1 at a confining pressure Pc of 1.5 GPa exhibit plasticity at low T, governed by dislocation glide and limited recovery, and grain size-sensitive creep at high T, governed by diffusion and sliding at grain boundaries. Quartz aggregates were HIP-synthesized, subjecting natural milky quartz powder to T=900°C and Pc=1.5 GPa, and grain sizes (2 to 25 mm) were varied by annealing at these conditions for up to 10 days. Infrared absorption spectra exhibit a broad OH band at 3400 cm-1 due to molecular water inclusions with a calculated OH content (~4000 ppm, H/106Si) that is unchanged by deformation. Rate-stepping experiments reveal different stress-strain rate functions at different temperatures and grain sizes, which correspond to differing stress-temperature sensitivities. At 600-700°C and grain sizes of 5-10 mm, flow law parameters compare favorably with those for basal plasticity and dislocation creep of wet quartzites (effective stress exponents n of 3 to 6 and activation enthalpy H* ~150 kJ/mol). Deformed samples show undulatory extinction, limited recrystallization, and c-axis maxima parallel to the shortening direction. Similarly fine-grained samples deformed at 800°-900°C exhibit flow parameters n=1.3-2.0 and H*=135-200 kJ/mol corresponding to grain size-sensitive Newtonian creep. Deformed samples show some undulatory extinction and grain sizes change by recrystallization; however, grain boundary deformation processes are indicated by the low value of n. Our experimental results for grain size-sensitive creep can be compared with models of grain boundary diffusion and grain boundary sliding using measured rates of silicon grain boundary diffusion. While many quartz mylonites show microstructural and textural evidence for dislocation creep, results for grain size-sensitive creep may apply to very fine-grained (<10 mm) quartz mylonites.

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

Stagg, Alan K; Yoon, Su-Jong

This report describes the Consortium for Advanced Simulation of Light Water Reactors (CASL) work conducted for completion of the Thermal Hydraulics Methods (THM) Level 3 Milestone THM.CFD.P11.02: Hydra-TH Extensions for Multispecies and Thermosolutal Convection. A critical requirement for modeling reactor thermal hydraulics is to account for species transport within the fluid. In particular, this capability is needed for modeling transport and diffusion of boric acid within water for emergency, reactivity-control scenarios. To support this need, a species transport capability has been implemented in Hydra-TH for binary systems (for example, solute within a solvent). A species transport equation is solved formore » the species (solute) mass fraction, and both thermal and solutal buoyancy effects are handled with specification of a Boussinesq body force. Species boundary conditions can be specified with a Dirichlet condition on mass fraction or a Neumann condition on diffusion flux. To enable enhanced species/fluid mixing in turbulent flow, the molecular diffusivity for the binary system is augmented with a turbulent diffusivity in the species transport calculation. The new capabilities are demonstrated by comparison of Hydra-TH calculations to the analytic solution for a thermosolutal convection problem, and excellent agreement is obtained.« less

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

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

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

Numerical Determination of Critical Conditions for Thermal Ignition

NASA Technical Reports Server (NTRS)

Luo, W.; Wake, G. C.; Hawk, C. W.; Litchford, R. J.

2008-01-01

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

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

Guerrier, C.; Holcman, D., E-mail: david.holcman@ens.fr; Mathematical Institute, Oxford OX2 6GG, Newton Institute

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationallymore » greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.« less

Grain boundary grooving induced by the anisotropic surface drift diffusion driven by the capillary and electromigration forces: Simulations

NASA Astrophysics Data System (ADS)

Akyildiz, Oncu; Omer Ogurtani, Tarik

2011-08-01

The morphological evolution kinetics of a bicrystal thin film induced by anisotropic surface drift diffusion and driven by the applied electrostatic field is investigated via self consistent dynamical computer simulations. The physico-mathematical model, which is based upon the irreversible thermodynamic treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], provided us with auto-control on the otherwise free-motion of the triple junction at the intersection of the grooving surface and the grain boundary, without having any a priori assumption on the equilibrium dihedral angles. The destruction of the symmetry of the freshly formed grain boundary grooves under the anisotropic surface diffusion driven by the concurrent action of the capillarity and electromigration is observed. After prolonged exposure times the applied electric field above the well defined threshold level modifies Mullins' familiar stationary state time law as, t¯1/4, and causes the premature termination of the groove penetration because of the current crowding at the tips of counteracting grain boundary-grooves initiated on both sides of the test modulus. That finding indicates that the electromigration plays the same role as a healing agent [T. O. Ogurtani, J. Appl. Phys. 106, 053503 (2009)] in arresting the thermal grooving, thereby avoiding the premature interconnect failure as in the case of surface roughening and crack initiation caused by compressive stress gradients. The role of the electromigration and wetting parameter on the ridge/slit formations are thoroughly investigated in this study and the prerequisite conditions are also identified.

Rectified Brownian movement in molecular and cell biology

NASA Astrophysics Data System (ADS)

Fox, Ronald F.

1998-02-01

A unified model is presented for rectified Brownian movement as the mechanism for a variety of putatively chemomechanical energy conversions in molecular and cell biology. The model is established by a detailed analysis of ubiquinone transport in electron transport chains and of allosteric conformation changes in proteins. It is applied to P-type ATPase ion transporters and to a variety of rotary arm enzyme complexes. It provides a basis for the dynamics of actin-myosin cross-bridges in muscle fibers. In this model, metabolic free energy does no work directly, but instead biases boundary conditions for thermal diffusion. All work is done by thermal energy, which is harnessed at the expense of metabolic free energy through the establishment of the asymmetric boundary conditions.

Performance Characteristics of Plane-Wall Two-Dimensional Diffusers

NASA Technical Reports Server (NTRS)

Reid, Elliott G

1953-01-01

Experiments have been made at Stanford University to determine the performance characteristics of plane-wall, two-dimensional diffusers which were so proportioned as to insure reasonable approximation of two-dimensional flow. All of the diffusers had identical entrance cross sections and discharged directly into a large plenum chamber; the test program included wide variations of divergence angle and length. During all tests a dynamic pressure of 60 pounds per square foOt was maintained at the diffuser entrance and the boundary layer there was thin and fully turbulent. The most interesting flow characteristics observed were the occasional appearance of steady, unseparated, asymmetric flow - which was correlated with the boundary-layer coalescence - and the rapid deterioration of flow steadiness - which occurred as soon as the divergence angle for maximum static pressure recovery was exceeded. Pressure efficiency was found to be controlled almost exclusively by divergence angle, whereas static pressure recovery was markedly influenced by area ratio (or length) as well as divergence angle. Volumetric efficiency. diminished as area ratio increased, and at a greater rate with small lengths than with large ones. Large values of the static-pressure-recovery coefficient were attained only with long diffusers of large area ratio; under these conditions pressure efficiency was high and. volumetric efficiency low. Auxiliary tests with asymmetric diffusers demonstrated that longitudinal pressure gradient, rather than wall divergence angle, controlled flow separation. Others showed that the addition of even a short exit duct of uniform section augmented pressure recovery. Finally, it was found that the installation of a thin, central, longitudinal partition suppressed flow separation in short diffusers and thereby improved pressure recovery

Insight into the grain boundary effect on the ionic transport of yttria-stabilized zirconia at elevated temperatures from a molecular modeling perspective

NASA Astrophysics Data System (ADS)

Chang, Kai-Shiun; Lin, Yi-Feng; Tung, Kuo-Lun

A molecular dynamics (MD) simulation is used to reveal the grain boundary effect on the ionic transport of yttria-stabilized zirconia (YSZ). The oxygen ion displacements and diffusivities of the ideal and grain boundary-inserted YSZ models are analyzed at elevated temperatures. An optimized Y 2O 3 concentration within YSZ for the best ionic conductivity is achieved by balancing the trade-off between the increased vacancies and the decreased accessible free space. The mass transfer resistance of the grain boundary in YSZ can be more easily found at higher temperatures by observing the oxygen ion diffusivities or traveling trajectories. At lower temperatures, the grain interior and the grain boundary control the ionic transport. In contrast, the grain boundary effect on the diffusion barrier is gradually eliminated at elevated temperatures. The modeled results in this work agree well with previous experimental data.

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.

Transport of ions in presence of induced electric field and electrostatic turbulence - Source of ions injected into ring current

NASA Technical Reports Server (NTRS)

Cladis, J. B.; Francis, W. E.

1985-01-01

The transport of ions from the polar ionosphere to the inner magnetosphere during stormtime conditions has been computed using a Monte Carlo diffusion code. The effect of the electrostatic turbulence assumed to be present during the substorm expansion phase was simulated by a process that accelerated the ions stochastically perpendicular to the magnetic field with a diffusion coefficient proportional to the energization rate of the ions by the induced electric field. This diffusion process was continued as the ions were convected from the plasma sheet boundary layer to the double-spiral injection boundary. Inward of the injection boundary, the ions were convected adiabatically. By using as input an O(+) flux of 2.8 x 10 to the 8th per sq cm per s (w greater than 10 eV) and an H(+) flux of 5.5 x 10 to the 8th per sq cm per s (w greater than 0.63 eV), the computed distribution functions of the ions in the ring current were found to be in good agreement, over a wide range in L (4 to 8), with measurements made with the ISEE-1 satellite during a storm. This O(+) flux and a large part of the H(+) flux are consistent with the DE satellite measurements of the polar ionospheric outflow during disturbed times.

Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation

NASA Astrophysics Data System (ADS)

Sun, Linan; Shi, Junping; Wang, Yuwen

2013-08-01

In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied.

Electromigration in Cu(Al) and Cu(Mn) damascene lines

NASA Astrophysics Data System (ADS)

Hu, C.-K.; Ohm, J.; Gignac, L. M.; Breslin, C. M.; Mittal, S.; Bonilla, G.; Edelstein, D.; Rosenberg, R.; Choi, S.; An, J. J.; Simon, A. H.; Angyal, M. S.; Clevenger, L.; Maniscalco, J.; Nogami, T.; Penny, C.; Kim, B. Y.

2012-05-01

The effects of impurities, Mn or Al, on interface and grain boundary electromigration (EM) in Cu damascene lines were investigated. The addition of Mn or Al solute caused a reduction in diffusivity at the Cu/dielectric cap interface and the EM activation energies for both Cu-alloys were found to increase by about 0.2 eV as compared to pure Cu. Mn mitigated and Al enhanced Cu grain boundary diffusion; however, no significant mitigation in Cu grain boundary diffusion was observed in low Mn concentration samples. The activation energies for Cu grain boundary diffusion were found to be 0.74 ± 0.05 eV and 0.77 ± 0.05 eV for 1.5 μm wide polycrystalline lines with pure Cu and Cu (0.5 at. % Mn) seeds, respectively. The effective charge number in Cu grain boundaries Z*GB was estimated from drift velocity and was found to be about -0.4. A significant enhancement in EM lifetimes for Cu(Al) or low Mn concentration bamboo-polycrystalline and near-bamboo grain structures was observed but not for polycrystalline-only alloy lines. These results indicated that the existence of bamboo grains in bamboo-polycrystalline lines played a critical role in slowing down the EM-induced void growth rate. The bamboo grains act as Cu diffusion blocking boundaries for grain boundary mass flow, thus generating a mechanical stress-induced back flow counterbalancing the EM force, which is the equality known as the "Blech short length effect."

Oxygen diffusion in nanocrystalline yttria-stabilized zirconia: the effect of grain boundaries.

PubMed

De Souza, Roger A; Pietrowski, Martha J; Anselmi-Tamburini, Umberto; Kim, Sangtae; Munir, Zuhair A; Martin, Manfred

2008-04-21

The transport of oxygen in dense samples of yttria-stabilized zirconia (YSZ), of average grain size d approximately 50 nm, has been studied by means of 18O/16O exchange annealing and secondary ion mass spectrometry (SIMS). Oxygen diffusion coefficients (D*) and oxygen surface exchange coefficients (k*) were measured for temperatures 673

Escape driven by alpha-stable white noises.

PubMed

Dybiec, B; Gudowska-Nowak, E; Hänggi, P

2007-02-01

We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Lévy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Lévy white noise parameters. Depending on the value of the skewness beta of the Lévy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of Lévy noise, exhibiting a marked discontinuity at alpha=1. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.

The island dynamics model on parallel quadtree grids

NASA Astrophysics Data System (ADS)

Mistani, Pouria; Guittet, Arthur; Bochkov, Daniil; Schneider, Joshua; Margetis, Dionisios; Ratsch, Christian; Gibou, Frederic

2018-05-01

We introduce an approach for simulating epitaxial growth by use of an island dynamics model on a forest of quadtree grids, and in a parallel environment. To this end, we use a parallel framework introduced in the context of the level-set method. This framework utilizes: discretizations that achieve a second-order accurate level-set method on non-graded adaptive Cartesian grids for solving the associated free boundary value problem for surface diffusion; and an established library for the partitioning of the grid. We consider the cases with: irreversible aggregation, which amounts to applying Dirichlet boundary conditions at the island boundary; and an asymmetric (Ehrlich-Schwoebel) energy barrier for attachment/detachment of atoms at the island boundary, which entails the use of a Robin boundary condition. We provide the scaling analyses performed on the Stampede supercomputer and numerical examples that illustrate the capability of our methodology to efficiently simulate different aspects of epitaxial growth. The combination of adaptivity and parallelism in our approach enables simulations that are several orders of magnitude faster than those reported in the recent literature and, thus, provides a viable framework for the systematic study of mound formation on crystal surfaces.

Augmenting ejector endwall effects. [V/STOL aircraft

NASA Technical Reports Server (NTRS)

Porter, J. L.; Squyers, R. A.

1979-01-01

Rectangular inlet ejectors which had multiple hypermixing nozzles for their primary jets were investigated for the effects of endwall blowing on thrust augmentation performance. The ejector configurations tested had both straight wall and active boundary layer control type diffusers. Endwall flows were energized and controlled by simple blowing jets suitably located in the ejector. Both the endwall and boundary layer control diffuser blowing rates were varied to determine optimum performance. High area ratio diffusers with insufficient endwall blowing showed endwall separation and rapid degradation of thrust performance. Optimized values of diffuser boundary layer control and endwall nozzle blowing rates in an ejector augmenter were shown to achieve high levels of augmentation performance for maximum compactness.

Recombination activity of grain boundaries in high-performance multicrystalline Si during solar cell processing

NASA Astrophysics Data System (ADS)

Adamczyk, Krzysztof; Søndenâ, Rune; Stokkan, Gaute; Looney, Erin; Jensen, Mallory; Lai, Barry; Rinio, Markus; Di Sabatino, Marisa

2018-02-01

In this work, we applied internal quantum efficiency mapping to study the recombination activity of grain boundaries in High Performance Multicrystalline Silicon under different processing conditions. Wafers were divided into groups and underwent different thermal processing, consisting of phosphorus diffusion gettering and surface passivation with hydrogen rich layers. After these thermal treatments, wafers were processed into heterojunction with intrinsic thin layer solar cells. Light Beam Induced Current and Electron Backscatter Diffraction were applied to analyse the influence of thermal treatment during standard solar cell processing on different types of grain boundaries. The results show that after cell processing, most random-angle grain boundaries in the material are well passivated, but small-angle grain boundaries are not well passivated. Special cases of coincidence site lattice grain boundaries with high recombination activity are also found. Based on micro-X-ray fluorescence measurements, a change in the contamination level is suggested as the reason behind their increased activity.

Effect of boundary heat flux on columnar formation in binary alloys: A phase-field study

NASA Astrophysics Data System (ADS)

Du, Lifei; Zhang, Peng; Yang, Shaomei; Chen, Jie; Du, Huiling

2018-02-01

A non-isothermal phase-field model was employed to simulate the columnar formation during rapid solidification in binary Ni-Cu alloy. Heat flux at different boundaries was applied to investigate the temperature gradient effect on the morphology, concentration and temperature distributions during directional solidifications. With the heat flux input/extraction from boundaries, coupling with latent heat release and initial temperature gradient, temperature distributions are significantly changed, leading to solute diffusion changes during the phase-transition. Thus, irregular columnar structures are formed during the directional solidification, and the concentration distribution in solid columnar arms could also be changed due to the different growing speeds and temperature distributions at the solid-liquid interfaces. Therefore, applying specific heat conditions at the solidifying boundaries could be an efficient way to control the microstructure during solidifications.

Grain boundary diffusion of Dy films prepared by magnetron sputtering for sintered Nd–Fe–B magnets

NASA Astrophysics Data System (ADS)

Chen, W.; Luo, J. M.; Guan, Y. W.; Huang, Y. L.; Chen, M.; Hou, Y. H.

2018-05-01

Dy films, deposited on the surface of sintered Nd–Fe–B magnets by magnetron sputtering, were employed for grain boundary diffusion source. High coercivity sintered Nd–Fe–B magnets were successfully prepared. Effects of sputtering power and grain boundary diffusion processes (GBDP) on the microstructure and magnetic properties were investigated in detail. The dense and uniform Dy films were beneficial to prepare high coercivity magnets by GBDP. The maximum coercivity value of 1189 kA m‑1 could be shown, which was an amplification of 22.3%, compared with that of as-prepared Nd–Fe–B magnet. Furthermore, the improved remanence and maximum energy product were also achieved through tuning grain boundary diffusion processes. Our results demonstrated that the formation of (Nd, Dy)2Fe14B shell surrounding Nd2Fe14B grains and fine, uniform and continuous intergranular RE-rich phases jointly contribute to the improved coercivity.

Sucrose diffusion in aqueous solution

PubMed Central

Murray, Benjamin J.

2016-01-01

The diffusion of sugar in aqueous solution is important both in nature and in technological applications, yet measurements of diffusion coefficients at low water content are scarce. We report directly measured sucrose diffusion coefficients in aqueous solution. Our technique utilises a Raman isotope tracer method to monitor the diffusion of non-deuterated and deuterated sucrose across a boundary between the two aqueous solutions. At a water activity of 0.4 (equivalent to 90 wt% sucrose) at room temperature, the diffusion coefficient of sucrose was determined to be approximately four orders of magnitude smaller than that of water in the same material. Using literature viscosity data, we show that, although inappropriate for the prediction of water diffusion, the Stokes–Einstein equation works well for predicting sucrose diffusion under the conditions studied. As well as providing information of importance to the fundamental understanding of diffusion in binary solutions, these data have technological, pharmaceutical and medical implications, for example in cryopreservation. Moreover, in the atmosphere, slow organic diffusion may have important implications for aerosol growth, chemistry and evaporation, where processes may be limited by the inability of a molecule to diffuse between the bulk and the surface of a particle. PMID:27364512

An experimental study of the role of particle diffusive convection on the residence time of volcanic ash clouds

NASA Astrophysics Data System (ADS)

Deal, E.; Carazzo, G.; Jellinek, M.

2013-12-01

The longevity of volcanic ash clouds generated by explosive volcanic plumes is difficult to predict. Diffusive convective instabilities leading to the production of internal layering are known to affect the stability and longevity of these clouds, but the detailed mechanisms controlling particle dynamics and sedimentation are poorly understood. We present results from a series of analog experiments reproducing diffusive convection in a 2D (Hele-Shaw) geometry, which allow us to constrain conditions for layer formation, sedimentation regime and cloud residence time as a function of only the source conditions. We inject a turbulent particle-laden jet sideways into a tank containing a basal layer of salt water and an upper layer of fresh water, which ultimately spreads as a gravity current. After the injection is stopped, particles in suspension settle through the cloud to form particle boundary layers (PBL) at the cloud base. We vary the initial particle concentration of the plume and the injection velocity over a wide range of conditions to identify and characterize distinct regimes of sedimentation. Our experiments show that convective instabilities driven as a result of differing diffusivities of salt and particles lead to periodic layering over a wide range of conditions expected in nature. The flux of particles from layered clouds and the thicknesses of the layers are understood using classical theory for double diffusive convection adjusted for the hydrodynamic diffusion of particles. Although diffusive convection increases sedimentation rates for the smallest particles (<30 μm) its overall effect is to extend the cloud residence time to several hours by maintaining larger particles in suspension within the layers, which is several orders of magnitude longer than expected when considering individual settling rates.

A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis

2014-04-01

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

Creation and Analysis of Atomic Structures for CdTe Bi-crystal Interfaces by the Grain Boundary Genie

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

Buurma, Christopher; Sen, Fatih G.; Paulauskas, Tadas

2015-01-01

Grain boundaries (GB) in poly-CdTe solar cells play an important role in species diffusion, segregation, defect formation, and carrier recombination. While the creation of specific high-symmetry interfaces can be straight forward, the creation of general GB structures in many material systems is difficult if periodic boundary conditions are to be enforced. Here we describe a novel algorithm and implementation to generate initial general GB structures for CdTe in an automated way, and we investigate some of these structures using density functional theory (DFT). Example structures include those with bi-crystals already fabricated for comparison, and those planning to be investigated inmore » the future.« less

Diffusion Behaviour in Superconducting Ti/Au bilayers for SAFARI TES Detectors

NASA Astrophysics Data System (ADS)

van der Heijden, N. J.; Khosropanah, P.; van der Kuur, J.; Ridder, M. L.

2014-08-01

Controlling the critical temperature () of Ti/Au bilayers is vital in the development of practical TES detectors. Previously empirical studies have been done on aging effects in Ti/Au and other superconducting bilayers but no link with theory has been made. Here we attempt to explain the change in with a diffusion mechanism. The change in has been measured for a set of Ti/Au bilayer samples that have been given a variety of bake-out treatments, where we found a trend that can be partly explained by an inter-diffusion mechanism. With an empirical model based on diffusion a safe zone can be defined as a region of bake-out treatments, where the is not affected beyond the requirements. This will shine light on the bake-out and the storage condition boundaries of these detectors.

Molecular Diagnostics of Diffusive Boundary Layers

NASA Astrophysics Data System (ADS)

Rawlings, J. M. C.; Hartquist, T. W.

1997-10-01

We have examined the chemistry in thin (<~0.01 pc) boundary layers between dark star-forming cores and warm, shocked T Tauri winds on the assumption that turbulence-driven diffusion occurs within them. The results indicate that emissions from C+, CH, OH, H2O and the J = 6 --> 5 transition of CO, among others, may serve as diagnostics of the boundary layers.

DIFFUSION IN THE VICINITY OF STANDARD-DESIGN NUCLEAR POWER PLANTS-I. WIND-TUNNEL EVALUATION OF DIFFUSIVE CHARACTERISTICS OF A SIMULATED SUBURBAN NEUTRAL ATMOSPHERIC BOUNDARY LAYER

EPA Science Inventory

A large meteorological wind tunnel was used to simulate a suburban atmospheric boundary layer. The model-prototype scale was 1:300 and the roughness length was approximately 1.0 m full scale. The model boundary layer simulated full scale dispersion from ground-level and elevated ...

Negativly streched premixed flames

NASA Astrophysics Data System (ADS)

Krikunova, A. I.; Saveliev, A. S.; Son, E. E.

2018-01-01

An experimental study of gravity effect on the blow-off and flash-back borders of the conical methane-air flame (normal and ring-stabilized) was performed. The influence of the preferential diffusion on the flame behavior in vicinity of flash-back boundaries was observed. Under conditions at Lewis number Le > 1, the radius of curvature of the flame tip increased gradually approaching flash-back boundaries while for the lean methane-air flames (Le < 1) the radius decreased abruptly. It was shown that the burning velocity for lean flames is less than that for reach ones, so the flash-back occurs at higher strains.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

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

Heat Diffusion in Gases, Including Effects of Chemical Reaction

NASA Technical Reports Server (NTRS)

Hansen, C. Frederick

1960-01-01

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

Ion Current Rectification, Limiting and Overlimiting Conductances in Nanopores

PubMed Central

van Oeffelen, Liesbeth; Van Roy, Willem; Idrissi, Hosni; Charlier, Daniel; Lagae, Liesbet; Borghs, Gustaaf

2015-01-01

Previous reports on Poisson-Nernst-Planck (PNP) simulations of solid-state nanopores have focused on steady state behaviour under simplified boundary conditions. These are Neumann boundary conditions for the voltage at the pore walls, and in some cases also Donnan equilibrium boundary conditions for concentrations and voltages at both entrances of the nanopore. In this paper, we report time-dependent and steady state PNP simulations under less restrictive boundary conditions, including Neumann boundary conditions applied throughout the membrane relatively far away from the nanopore. We simulated ion currents through cylindrical and conical nanopores with several surface charge configurations, studying the spatial and temporal dependence of the currents contributed by each ion species. This revealed that, due to slow co-diffusion of oppositely charged ions, steady state is generally not reached in simulations or in practice. Furthermore, it is shown that ion concentration polarization is responsible for the observed limiting conductances and ion current rectification in nanopores with asymmetric surface charges or shapes. Hence, after more than a decade of collective research attempting to understand the nature of ion current rectification in solid-state nanopores, a relatively intuitive model is retrieved. Moreover, we measured and simulated current-voltage characteristics of rectifying silicon nitride nanopores presenting overlimiting conductances. The similarity between measurement and simulation shows that overlimiting conductances can result from the increased conductance of the electric double-layer at the membrane surface at the depletion side due to voltage-induced polarization charges. The MATLAB source code of the simulation software is available via the website http://micr.vub.ac.be. PMID:25978328

Determination of gaseous fission product behavior near the cerium dioxide Σ 3 (111)/[1 1 ¯ 0] tilt grain boundary via first-principles study

DOE PAGES

Xi, Jianqi; Liu, Bin; Xu, Haixuan; ...

2017-12-02

We presenmore » t that grain boundaries (GBs) are the most abundant structural defects in nanostructured nuclear fuels and play an important role in determining fission product behavior, which further affects the performance of nuclear fuels. In this work, cerium dioxide (CeO 2) is used as a surrogate material for mixed oxide fuels to understand gaseous fission product behavior, specifically Xe. First-principles calculations are employed to comprehensively study the behavior of Xe and trap sites for Xe near the Σ 3 (111)/[1 1 ¯ 0] grain boundary in CeO 2, which will provide guidance on overall trends for Xe stability and diffusion at grain boundaries vs in the bulk. Significant segregation behavior of trap sites, regardless of charge states, is observed near the GB. This is mainly ascribed to the local atomic structure near the GB, which results in weaker bond strength and more negative segregation energies. For Xe, however, the segregation profile near the GB is different. Our calculations show that, as the size of trap sites increases, the segregation propensity of Xe is reduced. In addition, under hyper-stoichiometric conditions, the solubility of Xe trapped at the GB is significantly higher than that in the bulk, suggesting higher Xe concentration than that in the bulk. The results of this work demonstrate that the diffusion mechanism of Xe in CeO 2 is comparable to that in UO 2. The diffusion activation energies of Xe atoms in the Σ3GB are lower than that in the bulk CeO 2. Lastly, these results suggest that the diffusivity of Xe atoms is higher along the GB than that in the bulk, which enhances the aggregation of Xe atoms near the GB.« less

Determination of gaseous fission product behavior near the cerium dioxide Σ 3 (111)/[1 1 ¯ 0] tilt grain boundary via first-principles study

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

Xi, Jianqi; Liu, Bin; Xu, Haixuan

We presenmore » t that grain boundaries (GBs) are the most abundant structural defects in nanostructured nuclear fuels and play an important role in determining fission product behavior, which further affects the performance of nuclear fuels. In this work, cerium dioxide (CeO 2) is used as a surrogate material for mixed oxide fuels to understand gaseous fission product behavior, specifically Xe. First-principles calculations are employed to comprehensively study the behavior of Xe and trap sites for Xe near the Σ 3 (111)/[1 1 ¯ 0] grain boundary in CeO 2, which will provide guidance on overall trends for Xe stability and diffusion at grain boundaries vs in the bulk. Significant segregation behavior of trap sites, regardless of charge states, is observed near the GB. This is mainly ascribed to the local atomic structure near the GB, which results in weaker bond strength and more negative segregation energies. For Xe, however, the segregation profile near the GB is different. Our calculations show that, as the size of trap sites increases, the segregation propensity of Xe is reduced. In addition, under hyper-stoichiometric conditions, the solubility of Xe trapped at the GB is significantly higher than that in the bulk, suggesting higher Xe concentration than that in the bulk. The results of this work demonstrate that the diffusion mechanism of Xe in CeO 2 is comparable to that in UO 2. The diffusion activation energies of Xe atoms in the Σ3GB are lower than that in the bulk CeO 2. Lastly, these results suggest that the diffusivity of Xe atoms is higher along the GB than that in the bulk, which enhances the aggregation of Xe atoms near the GB.« less

Comment on: Diffusion through a slab

NASA Astrophysics Data System (ADS)

Gieseler, U. D. J.; Kirk, J. G.

1997-05-01

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick and Kuščer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalized to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

NASA Astrophysics Data System (ADS)

Geng, Hao; Deng, Wei-Yin; Ren, Yue-Jiao; Sheng, Li; Xing, Ding-Yu

2016-09-01

We show that by integrating out the electric field and incorporating proper boundary conditions, a Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General analytical formulas of the conductance in D = 1,2,3 dimensions are obtained, which recover the Boltzmann-Drude formula and Landauer-Büttiker formula in the diffusive and ballistic limits, respectively. This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena, when the quantum interference effect is not important. Project supported by the National Basic Research Program of China (Grant Nos. 2015CB921202 and 2014CB921103) and the National Natural Science Foundation of China (Grant No. 11225420).

Diffusion mechanisms in chemical vapor-deposited iridium coated on chemical vapor-deposited rhenium

NASA Technical Reports Server (NTRS)

Hamilton, J. C.; Yang, N. Y. C.; Clift, W. M.; Boehme, D. R.; Mccarty, K. F.; Franklin, J. E.

1992-01-01

Radiation-cooled rocket thruster chambers have been developed which use CVD Re coated with CVD Ir on the interior surface that is exposed to hot combustion gases. The Ir serves as an oxidation barrier which protects the structural integrity-maintaining Re at elevated temperatures. The diffusion kinetics of CVD materials at elevated temperatures is presently studied with a view to the prediction and extension of these thrusters' performance limits. Line scans for Ir and Re were fit on the basis of a diffusion model, in order to extract relevant diffusion constants; the fastest diffusion process is grain-boundary diffusion, where Re diffuses down grain boundaries in the Ir overlayer.

Creep crack growth by grain boundary cavitation under monotonic and cyclic loading

NASA Astrophysics Data System (ADS)

Wen, Jian-Feng; Srivastava, Ankit; Benzerga, Amine; Tu, Shan-Tung; Needleman, Alan

2017-11-01

Plane strain finite deformation finite element calculations of mode I crack growth under small scale creep conditions are carried out. Attention is confined to isothermal conditions and two time histories of the applied stress intensity factor: (i) a monononic increase to a plateau value subsequently held fixed; and (ii) a cyclic time variation. The crack growth calculations are based on a micromechanics constitutive relation that couples creep deformation and damage due to grain boundary cavitation. Grain boundary cavitation, with cavity growth due to both creep and diffusion, is taken as the sole failure mechanism contributing to crack growth. The influence on the crack growth rate of loading history parameters, such as the magnitude of the applied stress intensity factor, the ratio of the applied minimum to maximum stress intensity factors, the loading rate, the hold time and the cyclic loading frequency, are explored. The crack growth rate under cyclic loading conditions is found to be greater than under monotonic creep loading with the plateau applied stress intensity factor equal to its maximum value under cyclic loading conditions. Several features of the crack growth behavior observed in creep-fatigue tests naturally emerge, for example, a Paris law type relation is obtained for cyclic loading.

Grain Boundaries Act as Solid Walls for Charge Carrier Diffusion in Large Crystal MAPI Thin Films.

PubMed

Ciesielski, Richard; Schäfer, Frank; Hartmann, Nicolai F; Giesbrecht, Nadja; Bein, Thomas; Docampo, Pablo; Hartschuh, Achim

2018-03-07

Micro- and nanocrystalline methylammonium lead iodide (MAPI)-based thin-film solar cells today reach power conversion efficiencies of over 20%. We investigate the impact of grain boundaries on charge carrier transport in large crystal MAPI thin films using time-resolved photoluminescence (PL) microscopy and numerical model calculations. Crystal sizes in the range of several tens of micrometers allow for the spatially and time resolved study of boundary effects. Whereas long-ranged diffusive charge carrier transport is observed within single crystals, no detectable diffusive transport occurs across grain boundaries. The observed PL transients are found to crucially depend on the microscopic geometry of the crystal and the point of observation. In particular, spatially restricted diffusion of charge carriers leads to slower PL decay near crystal edges as compared to the crystal center. In contrast to many reports in the literature, our experimental results show no quenching or additional loss channels due to grain boundaries for the studied material, which thus do not negatively affect the performance of the derived thin-film devices.

An Experimental Investigation of Forced Mixing of a Turbulent Boundary Layer in an Annular Diffuser. Ph.D. Thesis - Ohio State Univ.; [for boundary layer control

NASA Technical Reports Server (NTRS)

Shaw, R. J.

1979-01-01

The forced mixing process of a turbulent boundary layer in an axisymmetric annular diffuser using conventional wing-like vortex generators was studied. Flow field measurements were made at four axial locations downstream of the vortex generators. At each axial location, a total of 25 equally spaced profiles were measured behind three consecutive vortex generators which formed two pairs of vortex generators. Hot film anemometry probes measured the boundary layer turbulence structure at the same locations where pressure measurements were made. Both single and cross film probes were used. The diffuser turbulence data was teken only for a nominal inlet Mach number of 0.3. Three vortex generator configurations were tested. The differences between configurations involved changes in size and relative vortex generator positions. All three vortex generator configurations tested provided increases in diffuser performance. Distinct differences in the boundary layer integral properties and skin friction levels were noted between configurations. The axial turbulence intensity and Reynolds stress profiles measured displayed similarities in trends but differences in levels for the three configurations.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dow, J. W.

1972-01-01

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

NASA Astrophysics Data System (ADS)

Fetecau, Constatin; Shah, Nehad Ali; Vieru, Dumitru

2017-12-01

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

Diffusion of volatile organics through porous snow: impact of surface adsorption and grain boundaries

NASA Astrophysics Data System (ADS)

Bartels-Rausch, T.; Wren, S. N.; Schreiber, S.; Riche, F.; Schneebeli, M.; Ammann, M.

2013-03-01

Release of trace gases from surface snow on Earth drives atmospheric chemistry, especially in the polar regions. The gas-phase diffusion of methanol and of acetone through the interstitial air of snow was investigated in a well-controlled laboratory study in the temperature range of 223 to 263 K. The aim of this study was to evaluate how the structure of the snowpack, the interaction of the trace gases with the snow surface, and the grain boundaries influence the diffusion on timescales up to 1 h. The diffusive loss of these two volatile organics into packed snow samples was measured using a chemical ionization mass spectrometer. The structure of the snow was analyzed by means of X-ray computed micro-tomography. The observed diffusion profiles could be well described based on gas-phase diffusion and the known structure of the snow sample at temperatures ≥ 253 K. At colder temperatures surface interactions start to dominate the diffusive transport. Parameterizing these interactions in terms of adsorption to the solid ice surface, i.e. using temperature dependent air-ice partitioning coefficients, better described the observed diffusion profiles than the use of air-liquid partitioning coefficients. No changes in the diffusive fluxes were observed by increasing the number of grain boundaries in the snow sample by a factor of 7, indicating that for these volatile organic trace gases, uptake into grain boundaries does not play a role on the timescale of diffusion through porous surface snow. In conclusion, we have shown that the diffusivity can be predicted when the structure of the snowpack and the partitioning of the trace gas to solid ice is known.

Sensing and Active Flow Control for Advanced BWB Propulsion-Airframe Integration Concepts

NASA Technical Reports Server (NTRS)

Fleming, John; Anderson, Jason; Ng, Wing; Harrison, Neal

2005-01-01

In order to realize the substantial performance benefits of serpentine boundary layer ingesting diffusers, this study investigated the use of enabling flow control methods to reduce engine-face flow distortion. Computational methods and novel flow control modeling techniques were utilized that allowed for rapid, accurate analysis of flow control geometries. Results were validated experimentally using the Techsburg Ejector-based wind tunnel facility; this facility is capable of simulating the high-altitude, high subsonic Mach number conditions representative of BWB cruise conditions.

Many-body calculations of low energy eigenstates in magnetic and periodic systems with self healing diffusion Monte Carlo: steps beyond the fixed-phase

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

Reboredo, Fernando A.

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\\bf 79}, 195117 (2009), Reboredo, {\\it ibid.} {\\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. A recursive optimization algorithm is derived from the time evolution of the mixed probability density. The mixed probability density is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weigh allows the amplitude of the fix-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC andmore » the fixed-phase approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\\bf 71}, 2777 (1993)]. When used recursively it improves simultaneously the node and phase. The algorithm is demonstrated to converge to the nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The method is also applied to obtain low energy excitations with magnetic field or periodic boundary conditions. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.« less

Experimental Evidence for Fast Lithium Diffusion and Isotope Fractionation in Water-bearing Rhyolitic Melts at Magmatic Conditions

NASA Astrophysics Data System (ADS)

Cichy, S. B.; Till, C. B.; Roggensack, K.; Hervig, R. L.; Clarke, A. B.

2015-12-01

The aim of this work is to extend the existing database of experimentally-determined lithium diffusion coefficients to more natural cases of water-bearing melts at the pressure-temperature range of the upper crust. In particular, we are investigating Li intra-melt and melt-vapor diffusion and Li isotope fractionation, which have the potential to record short-lived magmatic processes (seconds to hours) in the shallow crust, especially during decompression-induced magma degassing. Hydrated intra-melt Li diffusion-couple experiments on Los Posos rhyolite glass [1] were performed in a piston cylinder at 300 MPa and 1050 °C. The polished interfaces between the diffusion couples were marked by addition of Pt powder for post-run detection. Secondary ion mass spectrometry analyses indicate that lithium diffuses extremely fast in the presence of water. Re-equilibration of a hydrated ~2.5 mm long diffusion-couple experiment was observed during the heating period from room temperature to the final temperature of 1050 °C at a rate of ~32 °C/min. Fractionation of ~40‰ δ7Li was also detected in this zero-time experiment. The 0.5h and 3h runs show progressively higher degrees of re-equilibration, while the isotope fractionation becomes imperceptible. Li contamination was observed in some experiments when flakes filed off Pt tubing were used to mark the diffusion couple boundary, while the use of high purity Pt powder produced better results and allowed easier detection of the diffusion-couple boundary. The preliminary lithium isotope fractionation results (δ7Li vs. distance) support findings from [2] that 6Li diffuses substantially faster than 7Li. Further experimental sets are in progress, including lower run temperatures (e.g. 900 °C), faster heating procedure (~100 °C/min), shorter run durations and the extension to mafic systems. [1] Stanton (1990) Ph.D. thesis, Arizona State Univ., [2] Richter et al. (2003) GCA 67, 3905-3923.

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

PubMed Central

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

2012-01-01

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

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Investigation of Perforated Convergent-divergent Diffusers with Initial Boundary Layer

NASA Technical Reports Server (NTRS)

Weinstein, Maynard I

1950-01-01

An experimental investigation was made at Mach number 1.90 of the performance of a series of perforated convergent-divergent supersonic diffusers operating with initial boundary layer, which was induced and controlled by lengths of cylindrical inlets affixed to the diffusers. Supercritical mass-flow and peak total-pressure recoveries were decreased slightly by use of the longest inlets (4 inlet diameters in length). Combinations of cylindrical inlets, perforated diffusers, and subsonic diffuser were evaluated as simulated wind tunnels having second throats. Comparisons with noncontracted configurations of similar scale indicated conservatively computed power reductions of 25 percent.

The angular distribution of diffusely backscattered light

NASA Astrophysics Data System (ADS)

Vera, M. U.; Durian, D. J.

1997-03-01

The diffusion approximation predicts the angular distribution of light diffusely transmitted through an opaque slab to depend only on boundary reflectivity, independent of scattering anisotropy, and this has been verified by experiment(M.U. Vera and D.J. Durian, Phys. Rev. E 53) 3215 (1996). Here, by contrast, we demonstrate that the angular distribution of diffusely backscattered light depends on scattering anisotropy as well as boundary reflectivity. To model this observation scattering anisotropy is added to the diffusion approximation by a discontinuity in the photon concentration at the source point that is proportional to the average cosine of the scattering angle. We compare the resulting predictions with random walk simulations and with measurements of diffusely backscattered intensity versus angle for glass frits and aqueous suspensions of polystyrene spheres held in air or immersed in a water bath. Increasing anisotropy and boundary reflectivity each tend to flatten the predicted distributions, and for different combinations of anisotropy and reflectivity the agreement between data and predictions ranges from qualitatively to quantitatively good.

Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos

NASA Astrophysics Data System (ADS)

Meng, Lili; Li, Xinfu; Zhang, Guang

2017-12-01

In this paper, a discrete rational fration population model with the Dirichlet boundary conditions will be considered. According to the discrete maximum principle and the sub- and supper-solution method, the necessary and sufficient conditions of uniqueness and existence of positive steady state solutions will be obtained. In addition, the dynamical behavior of a special two patch metapopulation model is investigated by using the bifurcation method, the center manifold theory, the bifurcation diagrams and the largest Lyapunov exponent. The results show that there exist the pitchfork, the flip bifurcations, and the chaos. Clearly, these phenomena are caused by the simple diffusion. The theoretical analysis of chaos is very imortant, unfortunately, there is not any results in this hand. However, some open problems are given.

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

NASA Astrophysics Data System (ADS)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

Diffuse Extension of the Southern Mariana Margin: Implications for Subduction Zone Infancy and Plate Tectonics

NASA Astrophysics Data System (ADS)

Martinez, F.; Stern, R. J.; Kelley, K. A.; Ohara, Y.; Sleeper, J. D.; Ribeiro, J. M.; Brounce, M. N.

2017-12-01

Opening of the southern Mariana margin takes place in contrasting modes: Extension normal to the trench forms crust that is passively accreted to a rigid Philippine Sea plate and forms along focused and broad accretion axes. Extension also occurs parallel to the trench and has split apart an Eocene-Miocene forearc terrain accreting new crust diffusely over a 150-200 km wide zone forming a pervasive volcano-tectonic fabric oriented at high angles to the trench and the backarc spreading center. Earthquake seismicity indicates that the forearc extension is active over this broad area and basement samples date young although waning volcanic activity. Diffuse formation of new oceanic crust and lithosphere is unusual; in most oceanic settings extension rapidly focuses to narrow plate boundary zones—a defining feature of plate tectonics. Diffuse crustal accretion has been inferred to occur during subduction zone infancy, however. We hypothesize that, in a near-trench extensional setting, the continual addition of water from the subducting slab creates a weak overriding hydrous lithosphere that deforms broadly. This process counteracts mantle dehydration and strengthening proposed to occur at mid-ocean ridges that may help to focus deformation and melt delivery to narrow plate boundary zones. The observations from the southern Mariana margin suggest that where lithosphere is weakened by high water content narrow seafloor spreading centers cannot form. These conditions likely prevail during subduction zone infancy, explaining the diffuse contemporaneous volcanism inferred in this setting.

Experiments on tandem diffusers with boundary-layer suction applied in between

NASA Technical Reports Server (NTRS)

Barna, P. S.

1979-01-01

Experiments were performed on conical diffusers of various configurations with the same, but rather unusually large, 16:1 area ratio. Because available performance data on diffusers fall short of very large area ratio configurations, an unconventional design, consisting of two diffusers following each other in tandem, was proposed. Both diffusers had the same area ratio of 4:1, but had different taper angles. While for the first diffuser (called leading) the angle remained constant, for the second (called follower), the taper angle was stepped up to higher values. Boundary layer control, by way of suction, was applied between the diffusers, and a single slot suction ring was inserted between them. The leading diffuser had an enclosed nominal divergence angle 2 theta = 5 degrees, while the follower diffusers had either 10, 20, 30, or 40 degrees, respectively, giving 4 combinations. The experiments were performed at four different Reynolds numbers with various suction rates. The rates indicate a general improvement in the performance of all diffusers with boundary layer suction. It appears that the improvement of the pressure recovery depends on both the Reynolds number and the suction rate, and the largest increase, 0.075, was found at the lowest R sub e when the follower divergence was 2 theta = 40 degrees.

Simulations of the vortex in the Dellenback abrupt expansion, resembling a hydro turbine draft tube operating at part-load

NASA Astrophysics Data System (ADS)

Nilsson, H.

2012-11-01

This work presents an OpenFOAM case-study, based on the experimental studies of the swirling flow in the abrupt expansion by Dellenback et al.[1]. The case yields similar flow conditions as those of a helical vortex rope in a hydro turbine draft tube working at part-load. The case-study is set up similar to the ERCOFTAC Conical Diffuser and Centrifugal Pump OpenFOAM case-studies [2,3], making all the files available and the results fully reproducable using OpenSource software. The mesh generation is done using m4 scripting and the OpenFOAM built-in blockMesh mesh generator. The swirling inlet boundary condition is specified as an axi-symmetric profile. The outlet boundary condition uses the zeroGradient condition for all variables except for the pressure, which uses the fixed mean value boundary condition. The wall static pressure is probed at a number of locations during the simulations, and post-processing of the time-averaged solution is done using the OpenFOAM sample utility. Gnuplot scripts are provided for plotting the results. The computational results are compared to one of the operating conditions studied by Dellenback, and measurements for all the experimentally studied operating conditions are available in the case-study. Results from five cases are here presented, based on the kEpsilon model, the kOmegaSST model, and a filtered version of the same kOmegaSST model, named kOmegaSSTF [4,5]. Two different inlet boundary conditions are evaluated. It is shown that kEpsilon and kOmegaSST give steady solutions, while kOmegaSSTF gives a highly unsteady solution. The time-averaged solution of the kOmegaSSTF model is much more accurate than the other models. The kEpsilon and kOmegaSST models are thus unable to accurately model the effect of the large-scale unsteadiness, while kOmegaSSTF resolves those scales and models only the smaller scales. The use of two different boundary conditions shows that the boundary conditions are more important than the choice between kEpsilon and kOmegaSST, for the results just after the abrupt expansion.

Disorder-induced transition from grain boundary to bulk dominated ionic diffusion in pyrochlores

DOE PAGES

Perriot, Romain; Dholabhai, Pratik P.; Uberuaga, Blas P.

2017-05-04

In this paper, we use molecular dynamics simulations to investigate the role of grain boundaries (GBs) on ionic diffusion in pyrochlores, as a function of the GB type, chemistry of the compound, and level of cation disorder. We observe that the presence of GBs promotes oxygen transport in ordered and low-disordered systems, as the GBs are found to have a higher concentration of mobile carriers with higher mobilities than in the bulk. Thus, in ordered samples, the ionic diffusion is 2D, localized along the grain boundary. When cation disorder is introduced, bulk carriers begin to contribute to the overall diffusion,more » while the GB contribution is only slightly enhanced. In highly disordered samples, the diffusive behavior at the GBs is bulk-like, and the two contributions (bulk vs. GB) can no longer be distinguished. There is thus a transition from 2D/GB dominated oxygen diffusivity to 3D/bulk dominated diffusivity versus disorder in pyrochlores. Finally, these results provide new insights into the possibility of using internal interfaces to enhance ionic conductivity in nanostructured complex oxides.« less

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

A Theory for Stability and Buzz Pulsation Amplitude in Ram Jets and an Experimental Investigation Including Scale Effects

NASA Technical Reports Server (NTRS)

Trimpi, Robert L

1956-01-01

From a theory developed on a quasi-one-dimensional-flow basis, it is found that the stability of the ram jet is dependent upon the instantaneous values of mass flow and total pressure recovery of the supersonic diffuser and immediate neighboring subsonic diffuser. Conditions for stable and unstable flow are presented. The theory developed in the report is in agreement with the experimental data of NACA-TN-3506 and NACA-RM-L50K30. A simple theory for predicting the approximate amplitude of small pressure pulsation in terms of mass-flow decrement from minimum-stable mass flow is developed and found to agree with experiments. Cold-flow tests at a Mach number of 1.94 of ram-jet models having scale factors of 3.15:1 and Reynolds number ratios of 4.75:1 with several supersonic diffuser configurations showed only small variations in performance between geometrically similar models. The predominant variation in steady-flow performance resulted from the larger boundary layer in the combustion chamber of the low Reynolds number models. The conditions at which buzz originated were nearly the same for the same supersonic diffuser (cowling-position angle) configurations in both large and small diameter models. There was no appreciable variation in stability limits of any of the models when the combustion-chamber length was increased by a factor of three. The unsteady-flow performance and wave patterns were also similar when considered on a reduced-frequency basis determined from the relative lengths of the model. The negligible effect of Reynolds number on stability of the off-design configurations was not anticipated in view of the importance of boundary layer to stability, and this result should not be construed to be generally applicable. (author)

Finite element analysis of ion transport in solid state nuclear waste form materials

NASA Astrophysics Data System (ADS)

Rabbi, F.; Brinkman, K.; Amoroso, J.; Reifsnider, K.

2017-09-01

Release of nuclear species from spent fuel ceramic waste form storage depends on the individual constituent properties as well as their internal morphology, heterogeneity and boundary conditions. Predicting the release rate is essential for designing a ceramic waste form, which is capable of effectively storing the spent fuel without contaminating the surrounding environment for a longer period of time. To predict the release rate, in the present work a conformal finite element model is developed based on the Nernst Planck Equation. The equation describes charged species transport through different media by convection, diffusion, or migration. And the transport can be driven by chemical/electrical potentials or velocity fields. The model calculates species flux in the waste form with different diffusion coefficient for each species in each constituent phase. In the work reported, a 2D approach is taken to investigate the contributions of different basic parameters in a waste form design, i.e., volume fraction, phase dispersion, phase surface area variation, phase diffusion co-efficient, boundary concentration etc. The analytical approach with preliminary results is discussed. The method is postulated to be a foundation for conformal analysis based design of heterogeneous waste form materials.

Probing the oxidation kinetics of small permalloy particles

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

Dong, Xiaolei; Song, Xiao; Yin, Shiliu

2017-02-15

The oxidation of permalloys is important to apply in a wide range. The oxidation and diffusion mechanisms of small permalloy particles with different Fe content are studied by using thermal gravimetric analysis (TGA) and microstructure characterizations. Fe{sub 2}O{sub 3}/(Ni, Fe){sub 3}O{sub 4} plays a key role in the morphology evolution and diffusion mechanisms of small NiFe particles upon oxidation. The activation energies of grain boundary diffusion for the NiFe alloys increase from 141 kJ/mol to 208 kJ/mol as the Fe content increases from 0 to ~50 wt%. We have developed a diffusion process resolved temperature programed oxidation (PR-TPO) analysis method.more » Three diffusion mechanisms have been recognized by using this method: In addition to the grain boundary diffusion and lattice diffusion, our TGA analysis suggests that the phase conversion from Fe{sub 2}O{sub 3} to (Ni, Fe){sub 3}O{sub 4} induces diffusion change and affects the diffusion process at the intermediate temperature. Relevant oxidation kinetics and diffusion mechanisms are discussed. - Graphical abstract: The oxidation mechanisms of small Permalloy particles with different Fe content is studied by using thermal gravimetric analysis (TGA) and microstructure characterizations. The activation energies of grain boundary diffusion for the NiFe alloys increases from 140 kJ/mol to 208 kJ/mol as the Fe content increases from 0 to 50 wt% as determined by TGA. We have developed a diffusion process resolved temperature programed oxidation (DPR-TPO) analysis method, and three diffusion mechanisms have been recognized by using this method: In addition to the well-known grain boundary diffusion and lattice diffusion, we found that the phase conversion from Fe{sub 2}O{sub 3} to (Ni, Fe){sub 3}O{sub 4} will induce diffusion changes and affect the diffusion process at the intermediate temperature. The diffusion processes can be characterized by the corresponding characteristic peak temperatures in temperature programmed oxidation (TPO) analysis. This work not only give insight knowledge about the oxidation and diffusion processes of small permalloy particles, but also, provides a useful tool for analyzing solid-gas reactions of other materials. - Highlights: • The oxidation kinetics of small NiFe particles were studied by using thermoanalysis. • Grain boundary, lattice, and phase conversion induced diffusions were recognized. • The activation energy of oxidation increases with the Fe content in the alloy. • Each diffusion process corresponds to a characteristic temperature in TPO analysis. • NiFe alloys with ~5–10 wt% Fe content have the lowest oxidation rates.« less

Barrier mechanism of multilayers graphene coated copper against atomic oxygen irradiation

NASA Astrophysics Data System (ADS)

Zhang, Haijing; Ren, Siming; Pu, Jibin; Xue, Qunji

2018-06-01

Graphene has been demonstrated as a protective coating for Cu under ambient condition because of its high impermeability and light-weight oxidation barrier. However, it lacks the research of graphene as a protective coating in space environment. Here, we experimentally and theoretically study the oxidation behavior of graphene-coated Cu in vacuum atomic oxygen (AO) condition. After AO irradiation, the experimental results show multilayer graphene has better anti-oxidation than monolayer graphene. Meanwhile, the calculation results show the oxidation appeared on the graphene's grain boundaries or the film's vacancy defects for the monolayer graphene coated Cu foil. Moreover, the calculation results show the oxidation process proceeds slowly in multilayers because of the matched defects overlaps each other to form a steric hindrance to suppress the O atom diffusion in the vertical direction, and the mismatched defects generates potential energy barriers for interlayer to suppress the O atom diffusion in the horizontal direction. Hence, multilayer graphene films could serve as protection coatings to prevent diffusion of O atom.

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.

Analysis of the electron-beam-induced current of a polycrystalline p-n junction when the diffusion lengths of the material on either side of a grain boundary differ

NASA Technical Reports Server (NTRS)

Von Roos, O.; Luke, K. L.

1984-01-01

The short circuit current generated by the electron beam of a scanning electron microscope in p-n junctions is reduced by enhanced recombination at grain boundaries in polycrystalline material. Frequently, grain boundaries separate the semiconductor into regions possessing different minority carrier life times. This markedly affects the short circuit current I(sc) as a function of scanning distance from the grain boundary. It will be shown theoretically that (1) the minimum of the I(sc) in crossing the grain boundary with the scanning electron beam is shifted away from the grain boundary toward the region with smaller life time (shorter diffusion length), (2) the magnitude of the minimum differs markedly from those calculated under the assumption of equal diffusion lengths on either side of the grain boundary, and (3) the minimum disappears altogether for small surface recombination velocities (s less than 10,000 cm/s). These effects become negligible, however, for large recombination velocities s at grain boundaries. For p-type silicon this happens for s not less than 100,000 cm/s.

Modeling Biogeochemical Cycling of Heavy Metals in Lake Coeur d'Alene Sediments

NASA Astrophysics Data System (ADS)

Sengor, S. S.; Spycher, N.; Belding, E.; Curthoys, K.; Ginn, T. R.

2005-12-01

Mining of precious metals since the late 1800's have left Lake Coeur d'Alene (LCdA) sediments heavily enriched with toxic metals, including Cd, Cu, Pb, and Zn. Indigenous microbes however are capable of catalyzing reactions that detoxify the benthic and aqueous lake environments, and thus constitute an important driving component in the biogeochemical cycles of these metals. Here we report on the development of a quantitative model of transport, fate, exposure and effects of toxic compounds on benthic microbial communities at LCdA. First, chemical data from the LCdA area have been compiled from multiple sources to investigate trends in chemical occurrence, as well as to define model boundary conditions. The model is structured as 1-D diffusive reactive transport model to simulate spatial and temporal distribution of metals through the benthic sediments. Inorganic reaction processes included in the model are aqueous speciation, surface complexation, mineral precipitation/dissolution and abiotic redox reactions. Simulations with and without surface complexation are carried out to evaluate the effect of sorption and the conservative behaviour of metals within the benthic sediments under abiotic and purely diffusive transport. The 1-D inorganic diffusive transport model is then coupled to a biotic reaction network including consortium biodegradation kinetics with multiple electron acceptors, product toxicity, and energy partitioning. Multiyear simulations are performed, with water column chemistry established as a boundary condition from extant data, to explore the role of biogeochemical dynamics on benthic fluxes of metals in the long term.

Interpreting the Weibull fitting parameters for diffusion-controlled release data

NASA Astrophysics Data System (ADS)

Ignacio, Maxime; Chubynsky, Mykyta V.; Slater, Gary W.

2017-11-01

We examine the diffusion-controlled release of molecules from passive delivery systems using both analytical solutions of the diffusion equation and numerically exact Lattice Monte Carlo data. For very short times, the release process follows a √{ t } power law, typical of diffusion processes, while the long-time asymptotic behavior is exponential. The crossover time between these two regimes is determined by the boundary conditions and initial loading of the system. We show that while the widely used Weibull function provides a reasonable fit (in terms of statistical error), it has two major drawbacks: (i) it does not capture the correct limits and (ii) there is no direct connection between the fitting parameters and the properties of the system. Using a physically motivated interpolating fitting function that correctly includes both time regimes, we are able to predict the values of the Weibull parameters which allows us to propose a physical interpretation.

Effect of the scattering delay on time-dependent photon migration in turbid media.

PubMed

Yaroslavsky, I V; Yaroslavsky, A N; Tuchin, V V; Schwarzmaier, H J

1997-09-01

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.

Diffusion of molecules and macromolecules in thylakoid membranes.

PubMed

Kirchhoff, Helmut

2014-04-01

The survival and fitness of photosynthetic organisms is critically dependent on the flexible response of the photosynthetic machinery, harbored in thylakoid membranes, to environmental changes. A central element of this flexibility is the lateral diffusion of membrane components along the membrane plane. As demonstrated, almost all functions of photosynthetic energy conversion are dependent on lateral diffusion. The mobility of both small molecules (plastoquinone, xanthophylls) as well as large protein supercomplexes is very sensitive to changes in structural boundary conditions. Knowledge about the design principles that govern the mobility of photosynthetic membrane components is essential to understand the dynamic response of the photosynthetic machinery. This review summarizes our knowledge about the factors that control diffusion in thylakoid membranes and bridges structural membrane alterations to changes in mobility and function. This article is part of a Special Issue entitled: Dynamic and ultrastructure of bioenergetic membranes and their components. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

The effects of inlet temperature and turbulence characteristics on the flow development inside a gas turbine exhaust diffuser

NASA Astrophysics Data System (ADS)

Bomela, Christian Loangola

The overall industrial gas turbine efficiency is known to be influenced by the pressure recovery in the exhaust system. The design and, subsequently, the performance of an industrial gas turbine exhaust diffuser largely depend on its inflow conditions dictated by the turbine last stage exit flow state and the restraints of the diffuser internal geometry. Recent advances in Computational Fluid Dynamics (CFD) tools and the availability of computer hardware at an affordable cost made the virtual tool a very attractive one for the analysis of fluid flow through devices like a diffuser. In this backdrop, CFD analyses of a typical industrial gas turbine hybrid exhaust diffuser, consisting of an annular diffuser followed by a conical portion, have been carried out with the purpose of improving the performance of these thermal devices using an open-source CFD code "OpenFOAM". The first phase in the research involved the validation of the CFD approach using OpenFOAM by comparing CFD results against published benchmark experimental data. The numerical results closely captured the flow reversal and the separated boundary layer at the shroud wall where a steep velocity gradient has been observed. The standard k --epsilon turbulence model slightly over-predicted the mean velocity profile in the casing boundary layer while slightly under-predicted it in the reversed flow region. A reliable prediction of flow characteristics in this region is very important as the presence of the annular diffuser inclined wall has the most dominant effect on the downstream flow development. The core flow region and the presence of the hub wall have only a minor influence as reported by earlier experimental studies. Additional simulations were carried out in the second phase to test the veracity of other turbulence models; these include RNG k--epsilon, the SST k--o, and the Spalart-Allmaras turbulence models. It was found that a high resolution case with 47.5 million cells using the SST k--o turbulence model produced a mean flow velocity profile at the middle of the annular diffuser portion that had the best overall match with the experiment. The RNG k --epsilon, however, better predicted the diffuser performance along the exhaust diffuser length by means of the pressure recovery coefficient. These results were obtained using uniform inflow conditions and steady-state simulations. As such, the last phase of our investigations involved varying the inflow parameters like the turbulence intensity, the inlet flow temperature, and the flow angularity, which constitute important characteristics of the turbine blade wake, to investigate their impact on the diffuser design and performance. These isothermal CFD simulations revealed that by changing the flow temperature from 15 to 427°C, the pressure recovery coefficient significantly increased. However, it has been shown that the increase of temperature had no effects on the size of the reversed flow region and the thickness of the separated casing boundary layer, although the flow appears to be more turbulent. Furthermore, it has been established that an optimum turbulence intensity of about 4% produced comparable diffuser performance as the experiment. We also found that a velocity angle of about 2.5° at the last turbine stage will ensure a better exhaust diffuser performance.

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.

Solvent and solute ingress into hydrogels resolved by a combination of imaging techniques

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

Wagner, D.; Burbach, J.; Egelhaaf, S. U.

2016-05-28

Using simultaneous neutron, fluorescence, and optical brightfield transmission imaging, the diffusion of solvent, fluorescent dyes, and macromolecules into a crosslinked polyacrylamide hydrogel was investigated. This novel combination of different imaging techniques enables us to distinguish the movements of the solvent and fluorescent molecules. Additionally, the swelling or deswelling of the hydrogels can be monitored. From the sequence of images, dye and solvent concentrations were extracted spatially and temporally resolved. Diffusion equations and different boundary conditions, represented by different models, were used to quantitatively analyze the temporal evolution of these concentration profiles and to determine the diffusion coefficients of solvent andmore » solutes. Solute size and network properties were varied and their effect was investigated. Increasing the crosslinking ratio or partially drying the hydrogel was found to hinder solute diffusion due to the reduced pore size. By contrast, solvent diffusion seemed to be slightly faster if the hydrogel was only partially swollen and hence solvent uptake enhanced.« less

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-06-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Technical Reports Server (NTRS)

Saunders, B. V.; Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Application of the perfectly matched layer in 2.5D marine controlled-source electromagnetic modeling

NASA Astrophysics Data System (ADS)

Li, Gang; Han, Bo

2017-09-01

For the traditional framework of EM modeling algorithms, the Dirichlet boundary is usually used which assumes the field values are zero at the boundaries. This crude condition requires that the boundaries should be sufficiently far away from the area of interest. Although cell sizes could become larger toward the boundaries as electromagnetic wave is propagated diffusively, a large modeling area may still be necessary to mitigate the boundary artifacts. In this paper, the complex frequency-shifted perfectly matched layer (CFS-PML) in stretching Cartesian coordinates is successfully applied to 2.5D frequency-domain marine controlled-source electromagnetic (CSEM) field modeling. By using this PML boundary, one can restrict the modeling area of interest to the target region. Only a few absorbing layers surrounding the computational area can effectively depress the artificial boundary effect without losing the numerical accuracy. A 2.5D marine CSEM modeling scheme with the CFS-PML is developed by using the staggered finite-difference discretization. This modeling algorithm using the CFS-PML is of high accuracy, and shows advantages in computational time and memory saving than that using the Dirichlet boundary. For 3D problem, this computation time and memory saving should be more significant.

Compositional changes of minerals associated with dynamic recrystallizatin

NASA Astrophysics Data System (ADS)

Yund, Richard A.; Tullis, Jan

1991-09-01

The rate of compositional and isotopic exchange between minerals may be enhanced significantly if the rock is deformed simultaneously. The enhanced exchange rate may result from a reduction in grain size (shorter distance for volume diffusion), dissolution and growth of grains by diffusion creep (pressure solution), or the movement of high-angle grain boundaries through strained grains during recrystallization in the dislocation creep regime. The migration of high-angle grain boundaries provides high diffusivity paths for the rapid exchange of components during recrystallization. The operation of the latter process has been demonstrated by deforming aggregates consisting of two plagioclases (An1 and An79) at 900°C, 1 GPa confining pressure, and a strain rate of ˜2x10-6s-1. The polygonal, recrystallized grains were analyzed using an analytical transmission electron microscope and have a variable but often intermediate composition. At the conditions of these experiments, the volume interdiffusion rate of NaSi/CaAl is too slow to produce any observable chemical change, and microstructural-chemical relations indicate that the contribution from diffusion creep was insignificant except for initially fine-grained (2 10 μm) aggregates. These results indicate that strain-induced recrystallization can be an effective mechanism for enhancing the kinetics of metamorphic reactions and for resetting the isotope systematics of minerals such as feldspars, pyroxenes, and amphiboles.

Numerical study of the effects of Planetary Boundary Layer structure on the pollutant dispersion within built-up areas.

PubMed

Miao, Yucong; Liu, Shuhua; Zheng, Yijia; Wang, Shu; Liu, Zhenxin; Zhang, Bihui

2015-06-01

The effects of different Planetary Boundary Layer (PBL) structures on pollutant dispersion processes within two idealized street canyon configurations and a realistic urban area were numerically examined by a Computational Fluid Dynamics (CFD) model. The boundary conditions of different PBL structures/conditions were provided by simulations of the Weather Researching and Forecasting model. The simulated results of the idealized 2D and 3D street canyon experiments showed that the increment of PBL instability favored the downward transport of momentum from the upper flow above the roof to the pedestrian level within the street canyon. As a result, the flow and turbulent fields within the street canyon under the more unstable PBL condition are stronger. Therefore, more pollutants within the street canyon would be removed by the stronger advection and turbulent diffusion processes under the unstable PBL condition. On the contrary, more pollutants would be concentrated in the street canyon under the stable PBL condition. In addition, the simulations of the realistic building cluster experiments showed that the density of buildings was a crucial factor determining the dynamic effects of the PBL structure on the flow patterns. The momentum field within a denser building configuration was mostly transported from the upper flow, and was more sensitive to the PBL structures than that of the sparser building configuration. Finally, it was recommended to use the Mellor-Yamada-Nakanishi-Niino (MYNN) PBL scheme, which can explicitly output the needed turbulent variables, to provide the boundary conditions to the CFD simulation. Copyright © 2015. Published by Elsevier B.V.

The multiple roles of small-angle tilt grain boundaries in annihilating radiation damage in SiC

DOE PAGES

Jiang, Hao; Wang, Xing; Szlufarska, Izabela

2017-02-09

Lattice defects generated by radiation damage can diffuse to grain boundaries (GBs) and be annihilated at GBs. However, the precise role of GBs in annihilating the segregated defects remains unclear. Here, we employed multi-scale models to determine how interstitials are annihilated at small-angle tilt GBs (STGBs) in SiC. First of all, we found the pipe diffusion of interstitials in STGBs is slower than bulk diffusion. This is because the increased interatomic distance at dislocation cores raises the migration barrier of interstitial dumbbells. Furthermore, we found both the annihilation of interstitials at jogs and jog nucleation from clusters are diffusion-controlled andmore » can occur under off-stoichiometric interstitial fluxes. Finally, a dislocation line model is developed to predict the role of STGBs in annihilating radiation damage. This model includes defect flux to GBs, pipe diffusion in STGBs, and the interaction of defects with jogs. The model predicts the role of STGBs in annihilating defects depends on the rate of defects segregation to and diffusion along STGBs. STGBs mainly serve as diffusion channel for defects to reach other sinks when defect diffusivity is high at boundaries. As a result, when defect diffusivity is low, most of the defects segregated to STGBs are annihilated by dislocation climb.« less

The multiple roles of small-angle tilt grain boundaries in annihilating radiation damage in SiC

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

Jiang, Hao; Wang, Xing; Szlufarska, Izabela

Lattice defects generated by radiation damage can diffuse to grain boundaries (GBs) and be annihilated at GBs. However, the precise role of GBs in annihilating the segregated defects remains unclear. Here, we employed multi-scale models to determine how interstitials are annihilated at small-angle tilt GBs (STGBs) in SiC. First of all, we found the pipe diffusion of interstitials in STGBs is slower than bulk diffusion. This is because the increased interatomic distance at dislocation cores raises the migration barrier of interstitial dumbbells. Furthermore, we found both the annihilation of interstitials at jogs and jog nucleation from clusters are diffusion-controlled andmore » can occur under off-stoichiometric interstitial fluxes. Finally, a dislocation line model is developed to predict the role of STGBs in annihilating radiation damage. This model includes defect flux to GBs, pipe diffusion in STGBs, and the interaction of defects with jogs. The model predicts the role of STGBs in annihilating defects depends on the rate of defects segregation to and diffusion along STGBs. STGBs mainly serve as diffusion channel for defects to reach other sinks when defect diffusivity is high at boundaries. As a result, when defect diffusivity is low, most of the defects segregated to STGBs are annihilated by dislocation climb.« less

Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment

NASA Astrophysics Data System (ADS)

Illien, Pierre; Bénichou, Olivier; Oshanin, Gleb; Sarracino, Alessandro; Voituriez, Raphaël

2018-05-01

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Diffusing wave spectroscopy studies of gelling systems

NASA Astrophysics Data System (ADS)

Horne, David S.

1991-06-01

The recognition that the transmission of light through a concentrated, opaque system can be treated as a diffusion process has extended the application of photon correlation techniques to the study of particle size, mobility and interactions in such systems. Solutions of the photon diffusion equation are sensitive to the boundary conditions imposed by the geometry of the scattering apparatus. The apparatus, incorporating a bifurcated fiber optic bundle for light transmission between source, sample and detector, takes advantage of the particularly simple solution for a back-scattering configuration. Its ability to measure particle size using monodisperse polystyrene latices and to respond to concentration dependent particle interactions in a study of casein micelle mobility in skim and concentrated milks is demonstrated. Finally, the changes in dynamic light scattering behavior occurring during colloidal gel formation are described and discussed.

Stability of a diffuse linear pinch with axial boundaries

NASA Technical Reports Server (NTRS)

Einaudi, G.; Van Hoven, G.

1981-01-01

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Metzler, Ralf; Oshanin, Gleb

2017-10-01

We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.

Viscosity of dilute suspensions of rigid bead arrays at low shear: accounting for the variation in hydrodynamic stress over the bead surfaces.

PubMed

Allison, Stuart A; Pei, Hongxia

2009-06-11

In this work, we examine the viscosity of a dilute suspension of irregularly shaped particles at low shear. A particle is modeled as a rigid array of nonoverlapping beads of variable size and geometry. Starting from a boundary element formalism, approximate account is taken of the variation in hydrodynamic stress over the surface of the individual beads. For a touching dimer of two identical beads, the predicted viscosity is lower than the exact value by 5.2%. The methodology is then applied to several other model systems including tetramers of variable conformation and linear strings of touching beads. An analysis is also carried out of the viscosity and translational diffusion of several dilute amino acids and diglycine in water. It is concluded that continuum hydrodynamic modeling with stick boundary conditions is unable to account for the experimental viscosity and diffusion data simultaneously. A model intermediate between "stick" and "slip" could possibly reconcile theory and experiment.

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.

Application of Laser Ranging and VLBI Data to a Study of Plate Tectonic Driving Forces

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The conditions under which changes in plate driving or resistive forces associated with plate boundary earthquakes are measurable with laser ranging or very long base interferometry were investigated. Aspects of plate forces that can be characterized by such measurements were identified. Analytic solutions for two dimensional stress diffusion in a viscoelastic plate following earthquake faulting on a finite fault, finite element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting, and quantitative constraints from modeling of global intraplate stress on the magnitude of deviatoric stress in the lithosphere are among the topics discussed.

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).

Simulation of temperature distribution in tumor Photothermal treatment

NASA Astrophysics Data System (ADS)

Zhang, Xiyang; Qiu, Shaoping; Wu, Shulian; Li, Zhifang; Li, Hui

2018-02-01

The light transmission in biological tissue and the optical properties of biological tissue are important research contents of biomedical photonics. It is of great theoretical and practical significance in medical diagnosis and light therapy of disease. In this paper, the temperature feedback-controller was presented for monitoring photothermal treatment in realtime. Two-dimensional Monte Carlo (MC) and diffuse approximation were compared and analyzed. The results demonstrated that diffuse approximation using extrapolated boundary conditions by finite element method is a good approximation to MC simulation. Then in order to minimize thermal damage, real-time temperature monitoring was appraised by proportional-integral-differential (PID) controller in the process of photothermal treatment.

A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging

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

Nguyen, Dang Van; NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex; Li, Jing-Rebecca, E-mail: jingrebecca.li@inria.fr

2014-04-15

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution atmore » the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.« less

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model.

PubMed

Billon, Alexis; Foy, Cédric; Picaut, Judicaël; Valeau, Vincent; Sakout, Anas

2008-06-01

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Effects of Atmospheric Conditions and the Land/Atmospheric Interface on Transport of Chemical Vapors from Subsurface Sources

NASA Astrophysics Data System (ADS)

Rice, A. K.; Smits, K. M.; Cihan, A.; Howington, S. E.; Illangasekare, T. H.

2013-12-01

Understanding the movement of chemical vapors and gas through variably saturated soil subjected to atmospheric thermal and mass flux boundary conditions at the land/atmospheric interface is important to many applications, including landmine detection, methane leakage during natural gas production from shale and CO2 leakage from deep geologic storage. New, advanced technologies exist to sense chemical signatures and gas leakage at the land/atmosphere interface, but interpretation of sensor signals remains a challenge. Chemical vapors are subject to numerous interactions while migrating through the soil environment, masking source conditions. The process governing movement of gases through porous media is often assumed to be Fickian diffusion through the air phase with minimal quantification of other processes, such as convective gas flow and temporal or spatial variation in soil moisture. Vapor migration is affected by atmospheric conditions (e.g. humidity, temperature, wind velocity), soil thermal and hydraulic properties and contaminant properties, all of which are physically and thermodynamically coupled. The complex coupling of two drastically different flow regimes in the subsurface and atmosphere is commonly ignored in modeling efforts, or simplifying assumptions are made to treat the systems as de-coupled. Experimental data under controlled laboratory settings are lacking to refine the theory for proper coupling and complex treatment of vapor migration through porous media in conversation with atmospheric flow and climate variations. Improving fundamental understanding and accurate quantification of these processes is not feasible in field settings due to lack of controlled initial and boundary conditions and inability to fully characterize the subsurface at all relevant scales. The goal of this work is to understand the influence of changes in atmospheric conditions to transport of vapors through variably saturated soil. We have developed a tank apparatus with a network of soil and atmospheric sensors and a head space for air flow to simulate the atmospheric boundary layer. Experiments were performed under varying temperature values at the soil surface bounded by the atmospheric boundary layer. The model of Smits et al. [2011], accounting for non-equilibrium phase change and coupled heat, water vapor and liquid water flux through soil, was amended to include organic vapor in the gas phase and migration mechanisms often overlooked in models (thermal and Knudsen diffusion, density driven advection). Experimental results show increased vapor mass flux across the soil/atmospheric interface due to heat applied from the atmosphere and coupling of heat and mass transfer in the shallow subsurface for both steady and diurnal temperature patterns. Comparison of model results to experimental data shows dynamic interactions between transport in porous media and boundary conditions. Results demonstrate the value of considering interactions of the atmosphere and subsurface to better understand chemical gas transport through unsaturated soils and the land/atmospheric interface.

Capillary Flow of Liquid Metals in Brazing

NASA Astrophysics Data System (ADS)

Dehsara, Mohammad

Capillary flow is driven or controlled by capillary forces, exerted at the triple line where the fluid phases meet the solid boundary. Phase field (PF) models naturally accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. Moreover, they are uniquely suited for modeling of topological discontinuities which often arise during capillary flows. In this study, we consider diffusive triple line motion within two PF models: the compositionally compressible (CC) and the incompressible (IC) models. We derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. The CC model, applied to the fluids of dissimilar mass densities, exhibits a computational instability at the triple line. The IC model perfectly represents the analytic equilibria. We develop the parameter identification procedure and show that the triple line kinetics can be well represented by the IC model's diffusive boundary condition. The IC model is first tested by benchmarking the phase-field and experimental kinetics of water, and silicone oil spreading over the glass plates in which two systems do not interact with the substrate. Then, two high-temperature physical settings involving spreading of the molten Al-Si alloy: one over a rough wetting substrate, the other over a non-wetting substrate are modeled in a T-joint structure which is a typical geometric configuration for many brazing and soldering applications. Surface roughness directly influences the spreading of the molten metal by causing break-ups of the liquid film and trapping the liquid away from the joint. In the early stages of capillary flow over non-wetting surface, the melting and flow are concurrent, so that the kinetics of wetting is strongly affected by the variations in effective viscosity of the partially molten metal. We define adequate time-dependent functions for the variations of Al-Si alloy viscosity and triple line mobility to describe the wetting kinetics.

Competitive separation of di- vs. mono-valent cations in electrodialysis: effects of the boundary layer properties.

PubMed

Kim, Younggy; Walker, W Shane; Lawler, Desmond F

2012-05-01

In electrodialysis desalination, the boundary layer near ion-exchange membranes is the limiting region for the overall rate of ionic separation due to concentration polarization over tens of micrometers in that layer. Under high current conditions, this sharp concentration gradient, creating substantial ionic diffusion, can drive a preferential separation for certain ions depending on their concentration and diffusivity in the solution. Thus, this study tested a hypothesis that the boundary layer affects the competitive transport between di- and mono-valent cations, which is known to be governed primarily by the partitioning with cation-exchange membranes. A laboratory-scale electrodialyzer was operated at steady state with a mixture of 10mM KCl and 10mM CaCl(2) at various flow rates. Increased flows increased the relative calcium transport. A two-dimensional model was built with analytical solutions of the Nernst-Planck equation. In the model, the boundary layer thickness was considered as a random variable defined with three statistical parameters: mean, standard deviation, and correlation coefficient between the thicknesses of the two boundary layers facing across a spacer. Model simulations with the Monte Carlo method found that a greater calcium separation was achieved with a smaller mean, greater standard deviation, or more negative correlation coefficient. The model and experimental results were compared for the cationic transport number as well as the current and potential relationship. The mean boundary layer thickness was found to decrease from 40 to less than 10 μm as the superficial water velocity increased from 1.06 to 4.24 cm/s. The standard deviation was greater than the mean thickness at slower water velocities and smaller at faster water velocities. Copyright © 2012 Elsevier Ltd. All rights reserved.

On the use of reverse Brownian motion to accelerate hybrid simulations

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

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategiesmore » for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.« less

The Turbulent Flow in Diffusers of Small Divergence Angle

NASA Technical Reports Server (NTRS)

Gourzhienko, G. A.

1947-01-01

The turbulent flow in a conical diffuser represents the type of turbulent boundary layer with positive longitudinal pressure gradient. In contrast to the boundary layer problem, however, it is not necessary that the pressure distribution along the limits of the boundary layer(along the axis of the diffuser) be given, since this distribution can be obtained from the computation. This circumstance, together with the greater simplicity of the problem as a whole, provides a useful basis for the study of the extension of the results of semiempirical theories to the case of motion with a positive pressure gradient. In the first part of the paper,formulas are derived for the computation of the velocity and.pressure distributions in the turbulent flow along, and at right angles to, the axis of a diffuser of small cone angle. The problem is solved.

Product interactions and feedback in diffusion-controlled reactions

NASA Astrophysics Data System (ADS)

Roa, Rafael; Siegl, Toni; Kim, Won Kyu; Dzubiella, Joachim

2018-02-01

Steric or attractive interactions among reactants or between reactants and inert crowders can substantially influence the total rate of a diffusion-influenced reaction in the liquid phase. However, the role of the product species, which has typically different physical properties than the reactant species, has been disregarded so far. Here we study the effects of reactant-product and product-product interactions as well as asymmetric diffusion properties on the rate of diffusion-controlled reactions in the classical Smoluchowski-setup for chemical transformations at a perfect catalytic sphere. For this, we solve the diffusion equation with appropriate boundary conditions coupled by a mean-field approach on the second virial level to account for the particle interactions. We find that all particle spatial distributions and the total rate can change significantly, depending on the diffusion and interaction properties of the accumulated products. Complex competing and self-regulating (homeostatic) or self-amplifying effects are observed for the system, leading to both decrease and increase in the rates, as the presence of interacting products feeds back to the reactant flux and thus the rate with which the products are generated.

Diffusion induced atomic islands on the surface of Ni/Cu nanolayers

NASA Astrophysics Data System (ADS)

Takáts, Viktor; Csik, Attila; Hakl, József; Vad, Kálmán

2018-05-01

Surface islands formed by grain-boundary diffusion has been studied in Ni/Cu nanolayers by in-situ low energy ion scattering spectroscopy, X-ray photoelectron spectroscopy, scanning probe microscopy and ex-situ depth profiling based on ion sputtering. In this paper a new experimental approach of measurement of grain-boundary diffusion coefficients is presented. Appearing time of copper atoms diffused through a few nanometer thick nickel layer has been detected by low energy ion scattering spectroscopy with high sensitivity. The grain-boundary diffusion coefficient can be directly calculated from this appearing time without using segregation factors in calculations. The temperature range of 423-463 K insures the pure C-type diffusion kinetic regime. The most important result is that surface coverage of Ni layer by Cu atoms reaches a maximum during annealing and stays constant if the annealing procedure is continued. Scanning probe microscopy measurements show a Volmer-Weber type layer growth of Cu layer on the Ni surface in the form of Cu atomic islands. Depth distribution of Cu in Ni layer has been determined by depth profile analysis.

Field theory and diffusion creep predictions in polycrystalline aggregates

NASA Astrophysics Data System (ADS)

Villani, A.; Busso, E. P.; Forest, S.

2015-07-01

In polycrystals, stress-driven vacancy diffusion at high homologous temperatures leads to inelastic deformation. In this work, a novel continuum mechanics framework is proposed to describe the strain fields resulting from such a diffusion-driven process in a polycrystalline aggregate where grains and grain boundaries are explicitly considered. The choice of an anisotropic eigenstrain in the grain boundary region provides the driving force for the diffusive creep processes. The corresponding inelastic strain rate is shown to be related to the gradient of the vacancy flux. Dislocation driven deformation is then introduced as an additional mechanism, through standard crystal plasticity constitutive equations. The fully coupled diffusion-mechanical model is implemented into the finite element method and then used to describe the biaxial creep behaviour of FCC polycrystalline aggregates. The corresponding results revealed for the first time that such a coupled diffusion-stress approach, involving the gradient of the vacancy flux, can accurately predict the well-known macroscopic strain rate dependency on stress and grain size in the diffusion creep regime. They also predict strongly heterogeneous viscoplastic strain fields, especially close to grain boundaries triple junctions. Finally, a smooth transition from Herring and Coble to dislocation creep behaviour is predicted and compared to experimental results for copper.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Pattern formation study of dissolution-driven convection

NASA Astrophysics Data System (ADS)

Aljahdaly, Noufe; Hadji, Layachi

2017-11-01

A three-dimensional pattern formation analysis is performed to investigate the dissolution-driven convection induced by the sequestration of carbon dioxide. We model this situation by considering a Rayleigh-Taylor like base state consisting of carbon-rich heavy brine overlying a carbon-free layer and seek, through a linear stability analysis, the instability threshold conditions as function of the thickness of the CO2-rich brine layer. Our model accounts for carbon diffusion anisotropy, permeability dependence on depth and the presence of a first order chemical reaction between the carbon-rich brine and host mineralogy. A small amplitude nonlinear stability analysis is performed to isolate the preferred regular pattern and solute flux conditions at the interface. The latter are used to derive equations for the time and space evolution of the interface as it migrates upward. We quantify the terminal time when the interface reaches the top boundary as function of the type of solute boundary conditions at the top boundary thereby also quantifying the beginning of the shutdown regime. The analysis will also shed light on the development of the three-dimensional fingering pattern that is observed when the constant flux regime is attained.

Effect of Reynolds number and saturation level on gas diffusion in and out of a superhydrophobic surface

NASA Astrophysics Data System (ADS)

Ling, Hangjian; Katz, Joseph; Fu, Matthew; Hultmark, Marcus

2017-12-01

This experimental study investigates the effects of ambient pressure and Reynolds number on the volume of a plastron in a superhydrophobic surface (SHS) due to compression and gas diffusion. The hierarchical SHS consists of nanotextured, ˜100 μm wide spanwise grooves. Microscopic observations measure the time evolution of interface height and contact angle. The water tunnel tests are performed both without flow as well as in transitional and turbulent boundary layers at several Reynolds numbers. Particle image velocimetry is used for estimating the wall shear stress and calculating the momentum thickness for the SHSs under Cassie-Baxter (CB) and Wenzel states as well as a smooth wall at the same conditions. Holographic microscopy is used for determining the wall shear stress directly for one of the CB cases. The mass diffusion rate is calculated from changes to the plastron volume when the liquid is under- or supersaturated. For stationary water, the mass diffusion is slow. With increasing pressure, the interface is initially pinned and then migrates into the groove with high advancing contact angle. Upon subsequent decrease in pressure, the interface migrates upward at a shallow angle and, after being pinned to the tip corner, becomes convex. With flow and exposure to undersaturated liquid, the diffusion-induced wetting also involves pinned and downward migration states, followed by shrinkage of the plastron until it decreases below the resolution limit. The corresponding changes to the velocity profile indicate a transition from slight drag reduction to significant drag increase. In supersaturated water starting at a Wenzel state, a bubble grows from one of the bottom corners until it reaches the other side of the groove. Subsequently, dewetting involves upward migration of the interface, pinning to the tip corners, and formation of a convex interface. The diffusion rate increases with the level of under- or supersaturation and with the Reynolds number. A power law relation, S hΘ 0=0.47 ReΘ0 0.77 , is obtained for the turbulent flow regime using the smooth wall momentum thickness for calculating the Sherwood (S hΘ 0 ) and Reynolds (R eΘ 0 ) numbers. This relation agrees with published diffusion rates for smooth wall turbulent boundary layers. However, the mass diffusion rate is lower than this prediction in the transitional boundary layer. When S hΘ 0 is plotted against the friction Reynolds number (R eτ 0 ) instead, both the transitional and turbulent boundary layer results collapse onto a single power law, S hΘ 0=0.34 Reτ0 0.913 . This trend suggests that turbulent diffusion and wall friction are correlated. The relation between Sherwood number and momentum thickness Reynolds number persists if length scales of the Wenzel state are used instead of those of the smooth wall. However, trends with the friction Reynolds number change slightly.

Roles of Vacancy/Interstitial Diffusion and Segregation in the Microchemistry at Grain Boundaries of Irradiated Fe-Cr-Ni alloys

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

Yang, Ying; Field, Kevin G.; Allen, Todd R.

2016-02-23

A detailed analysis of the diffusion fluxes near and at grain boundaries of irradiated Fe–Cr–Ni alloys, induced by preferential atom-vacancy and atom-interstitial coupling, is presented. The diffusion flux equations were based on the Perks model formulated through the linear theory of the thermodynamics of irreversible processes. The preferential atom-vacancy coupling was described by the mobility model, whereas the preferential atom-interstitial coupling was described by the interstitial binding model. The composition dependence of the thermodynamic factor was modeled using the CALPHAD approach. The calculated fluxes up to 10 dpa suggested the dominant diffusion mechanism for chromium and iron is via vacancy,more » while that for nickel can swing from the vacancy to the interstitial dominant mechanism. The diffusion flux in the vicinity of a grain boundary was found to be greatly modified by the segregation induced by irradiation, leading to the oscillatory behavior of alloy compositions in this region.« less

Viscous diffusion of vorticity in unsteady wall layers using the diffusion velocity concept

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

Strickland, J.H.; Kempka, S.N.; Wolfe, W.P.

1995-03-01

The primary purpose of this paper is to provide a careful evaluation of the diffusion velocity concept with regard to its ability to predict the diffusion of vorticity near a moving wall. A computer code BDIF has been written which simulates the evolution of the vorticity field near a wall of infinite length which is moving in an arbitrary fashion. The simulations generated by this code are found to give excellent results when compared to several exact solutions. We also outline a two-dimensional unsteady viscous boundary layer model which utilizes the diffusion velocity concept and is compatible with vortex methods.more » A primary goal of this boundary layer model is to minimize the number of vortices generated on the surface at each time step while achieving good resolution of the vorticity field near the wall. Preliminary results have been obtained for simulating a simple two-dimensional laminar boundary layer.« less

A level-set method for two-phase flows with moving contact line and insoluble surfactant

NASA Astrophysics Data System (ADS)

Xu, Jian-Jun; Ren, Weiqing

2014-04-01

A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by Ren et al. (2010) [37]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by Xu et al. (2012) [54] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.

Survival probability for a diffusive process on a growing domain

NASA Astrophysics Data System (ADS)

Simpson, Matthew J.; Sharp, Jesse A.; Baker, Ruth E.

2015-04-01

We consider the motion of a diffusive population on a growing domain, 0

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

NASA Astrophysics Data System (ADS)

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

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

A first-passage scheme for determination of overall rate constants for non-diffusion-limited suspensions

NASA Astrophysics Data System (ADS)

Lu, Shih-Yuan; Yen, Yi-Ming

2002-02-01

A first-passage scheme is devised to determine the overall rate constant of suspensions under the non-diffusion-limited condition. The original first-passage scheme developed for diffusion-limited processes is modified to account for the finite incorporation rate at the inclusion surface by using a concept of the nonzero survival probability of the diffusing entity at entity-inclusion encounters. This nonzero survival probability is obtained from solving a relevant boundary value problem. The new first-passage scheme is validated by an excellent agreement between overall rate constant results from the present development and from an accurate boundary collocation calculation for the three common spherical arrays [J. Chem. Phys. 109, 4985 (1998)], namely simple cubic, body-centered cubic, and face-centered cubic arrays, for a wide range of P and f. Here, P is a dimensionless quantity characterizing the relative rate of diffusion versus surface incorporation, and f is the volume fraction of the inclusion. The scheme is further applied to random spherical suspensions and to investigate the effect of inclusion coagulation on overall rate constants. It is found that randomness in inclusion arrangement tends to lower the overall rate constant for f up to the near close-packing value of the regular arrays because of the inclusion screening effect. This screening effect turns stronger for regular arrays when f is near and above the close-packing value of the regular arrays, and consequently the overall rate constant of the random array exceeds that of the regular array. Inclusion coagulation too induces the inclusion screening effect, and leads to lower overall rate constants.

Solute partitioning under continuous cooling conditions as a cooling rate indicator. [in lunar rocks

NASA Technical Reports Server (NTRS)

Onorato, P. I. K.; Hopper, R. W.; Yinnon, H.; Uhlmann, D. R.; Taylor, L. A.; Garrison, J. R.; Hunter, R.

1981-01-01

A model of solute partitioning in a finite body under conditions of continuous cooling is developed for the determination of cooling rates from concentration profile data, and applied to the partitioning of zirconium between ilmenite and ulvospinel in the Apollo 15 Elbow Crater rocks. Partitioning in a layered composite solid is described numerically in terms of concentration profiles and diffusion coefficients which are functions of time and temperature, respectively; a program based on the model can be used to calculate concentration profiles for various assumed cooling rates given the diffusion coefficients in the two phases and the equilibrium partitioning ratio over a range of temperatures. In the case of the Elbow Rock gabbros, the cooling rates are calculated from measured concentration ratios 10 microns from the interphase boundaries under the assumptions of uniform and equilibrium initial conditions at various starting temperatures. It is shown that the specimens could not have had uniform concentrations profiles at the previously suggested initial temperature of 1350 K. It is concluded that even under conditions where the initial temperature, grain sizes and solute diffusion coefficients are not well characterized, the model can be used to estimate the cooling rate of a grain assemblage to within an order of magnitude.

Diffuser for augmenting a wind turbine

DOEpatents

Foreman, Kenneth M.; Gilbert, Barry L.

1984-01-01

A diffuser for augmenting a wind turbine having means for energizing the boundary layer at several locations along the diffuser walls is improved by the addition of a short collar extending radially outward from the outlet of the diffuser.

Measuring the viscosity of whole bovine lens using a fiber optic oxygen sensing system

PubMed Central

Thao, Mai T.; Perez, Daniel; Dillon, James

2014-01-01

Purpose To obtain a better understanding of oxygen and nutrient transport within the lens, the viscosity of whole lenses was investigated using a fiber optic oxygen sensor (optode). The diffusion coefficient of oxygen was calculated using the Stokes-Einstein equation at the slip boundary condition. Methods The optode was used to measure the oxygen decay signal in samples consisting of different glycerol/water solutions with known viscosities. The oxygen decay signal was fitted to a double exponential decay rate equation, and the lifetimes (tau) were calculated. It was determined that the tau-viscosity relationship is linear, which served as the standard curve. The same procedure was applied to fresh bovine lenses, and the unknown viscosity of the bovine lens was calculated from the tau-viscosity relationship. Results The average viscosity in a whole bovine lens was determined to be 5.74±0.88 cP by our method. Using the Stokes-Einstein equation at the slip boundary condition, the diffusion coefficient for oxygen was calculated to be 8.2 × 10−6 cm2/s. Conclusions These data indicate a higher resistance to flow for oxygen and nutrients in the lens than what is currently assumed in the literature. Overall, this study allows a better understanding of oxygen transport within the lens. PMID:24505211

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

PubMed

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

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

Stokes flow inside an evaporating liquid line for any contact angle

NASA Astrophysics Data System (ADS)

Petsi, A. J.; Burganos, V. N.

2008-09-01

Evaporation of droplets or liquid films lying on a substrate induces internal viscous flow, which affects the transport of suspended particles and, thus, the final deposit profile in numerous applications. In this work, the problem of Stokes flow inside a two-dimensional droplet, representing the cross section of an evaporating liquid line lying on a flat surface, is considered. The stream function formulation is adopted, leading to the biharmonic equation in bipolar coordinates. A solution in closed form is obtained for any contact angle in (0,π) and is, thus, valid for both hydrophilic and hydrophobic substrates. The solution can be used with any type of evaporation mechanism, including diffusion, convection, or kinetically controlled modes. Both pinned and depinned contact lines are considered. For the boundary conditions to be compatible at the contact lines, the Navier slip boundary condition is applied on the substrate. Numerical results are presented for kinetically and diffusion controlled evaporation. For pinned contact lines, the flow inside the evaporating liquid line is directed towards the edges, thus, promoting the coffee stain phenomenon. In the case of depinned contact lines and contact angle less than π/2 , the flow is directed towards the center of the droplet, whereas, for strongly hydrophobic substrates it is directed outwards.

Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

NASA Astrophysics Data System (ADS)

Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy

2017-11-01

Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.

Singular solution of the Feller diffusion equation via a spectral decomposition.

PubMed

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Singular solution of the Feller diffusion equation via a spectral decomposition

NASA Astrophysics Data System (ADS)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

Multiscale model of metal alloy oxidation at grain boundaries

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

Sushko, Maria L.; Alexandrov, Vitali Y.; Schreiber, Daniel K.

2015-06-07

High temperature intergranular oxidation and corrosion of metal alloys is one of the primary causes of materials degradation in nuclear systems. In order to gain insights into grain boundary oxidation processes, a mesoscale metal alloy oxidation model at experimentally relevant length scales is established by combining quantum Density Functional Theory (DFT) and mesoscopic Poisson-Nernst-Planck/classical DFT with predictions focused on Ni alloyed with either Cr or Al. Analysis of species and fluxes at steady-state conditions indicates that the oxidation process involves vacancy-mediated transport of Ni and the minor alloying element to the oxidation front and the formation of stable metal oxides.more » The simulations further demonstrate that the mechanism of oxidation for Ni-5Cr and Ni-4Al is qualitatively different. Intergranular oxidation of Ni-5Cr involves the selective oxidation of the minor element and not matrix Ni, due to slower diffusion of Ni relative to Cr in the alloy and due to the significantly smaller energy gain upon the formation of nickel oxide compared to that of Cr2O3. This essentially one-component oxidation process results in continuous oxide formation and a monotonic Cr vacancy distribution ahead of the oxidation front, peaking at alloy/oxide interface. In contrast, Ni and Al are both oxidized in Ni-4Al forming a mixed spinel NiAl2O4. Different diffusivities of Ni and Al give rise to a complex elemental distribution in the vicinity of the oxidation front. Slower diffusing Ni accumulates in the oxide and metal within 3 nm of the interface, while Al penetrates deeper into the oxide phase. Ni and Al are both depleted from the region 3–10 nm ahead of the oxidation front creating voids. The oxide microstructure is also different. Cr2O3 has a plate-like structure with 1.2 - 1.7 nm wide pores running along the grain boundary, while NiAl2O4 has 1.5 nm wide pores in the direction parallel to the grain boundary and 0.6 nm pores in the perpendicular direction providing an additional pathway for oxygen diffusion through the oxide.« less

In-situ observation of impurity diffusion boundary layer in silicon Czochralski growth

NASA Astrophysics Data System (ADS)

Kakimoto, Koichi; Eguchi, Minoru; Watanabe, Hisao; Hibiya, Taketoshi

1990-01-01

In-situ observation of the impurity diffusion boundary layer during single crystal growth of indium-doped silicon was carried out by X-ray radiography. The difference in the transmitted X-ray image compared with molten silicon just beneath the crystal-melt interface was attributed to the concentration of indium impurities having a larger absorption coefficient. The intensity profile of the transmitted X-ray can be reproduced by a transmittance calculation that considers the meniscus shape and impurity distribution. The impurity distribution profile near the crystal-melt interface was estimated using the Burton-Prim-Slichter (BPS) equation. The observed impurity diffusion boundary layer thickness was about 0.5 mm. It was found that the boundary layer thickness was not constant in the radial direction, which cannot be explained by the BPS theory, since it is based on a one-dimensional calculation.

Direct simulation of groundwater age

USGS Publications Warehouse

Goode, Daniel J.

1996-01-01

A new method is proposed to simulate groundwater age directly, by use of an advection-dispersion transport equation with a distributed zero-order source of unit (1) strength, corresponding to the rate of aging. The dependent variable in the governing equation is the mean age, a mass-weighted average age. The governing equation is derived from residence-time-distribution concepts for the case of steady flow. For the more general case of transient flow, a transient governing equation for age is derived from mass-conservation principles applied to conceptual “age mass.” The age mass is the product of the water mass and its age, and age mass is assumed to be conserved during mixing. Boundary conditions include zero age mass flux across all noflow and inflow boundaries and no age mass dispersive flux across outflow boundaries. For transient-flow conditions, the initial distribution of age must be known. The solution of the governing transport equation yields the spatial distribution of the mean groundwater age and includes diffusion, dispersion, mixing, and exchange processes that typically are considered only through tracer-specific solute transport simulation. Traditional methods have relied on advective transport to predict point values of groundwater travel time and age. The proposed method retains the simplicity and tracer-independence of advection-only models, but incorporates the effects of dispersion and mixing on volume-averaged age. Example simulations of age in two idealized regional aquifer systems, one homogeneous and the other layered, demonstrate the agreement between the proposed method and traditional particle-tracking approaches and illustrate use of the proposed method to determine the effects of diffusion, dispersion, and mixing on groundwater age.

Modeling of various heat adapter plate 4 and 6 array for optimization of thermoelectric generator element using modified diffusion equation

NASA Astrophysics Data System (ADS)

Defrianto; Tambunan, W.; Lazuardi

2017-07-01

The use of waste heat from exhaust gas and converting it to electricity is now an alternative to harvest a cheap and clean energy. Thermoelectric generator (TEG) has the ability to directly recover such waste heat and generate electricity. The aim of this study is to simulate the heat transfer on the aluminum adapter plate for homogeneity temperature distribution coupled with hot side of TEG type 40-40-10/100 from Firma Eureka and adjust their high temperatures to the TEG operating temperature to avoid the element damage. Modelling was carried out using MATLAB modified diffusion equation with Dirichlet boundary conditions at defined temperature which has been set at the ends of the heat source at 463K and 373K ± 10% on the hot side of the TEG element. The use of nylon insulated material is modeled after Neumann boundary condition in which the temperature gradient is ∂T/∂n = 0 out of boundary. Realization of the modelling is done by designing a heat conductive plate using software ACAD 2015 and converted into a binary file format of Mathlab to form a finite element mesh with geometry variations of solid model. The solid cubic model of aluminum adapter plate has a dimension of 40mm length, 40mm width and also 20mm, 30mm and 40mm thickness arranged in two arrays of 2×2 and 2×3 of TEG elements. Results showed a temperature decrease about 40.95% and 50.02% respectively from the initial source and appropriate with TEG temperature tolerance.

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions

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

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

2016-10-13

We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomainmore » $$\\Omega^{hs}$$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $$\\Omega^{hs}$$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $$\\Omega^{hs}$$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.« less

Direct measurement of concentration distribution within the boundary layer of an ion-exchange membrane.

PubMed

Choi, Jae-Hwan; Park, Jin-Soo; Moon, Seung-Hyeon

2002-07-15

In this study the concentration distributions within the diffusion boundary layer were obtained by directly measuring the potential drops while the currents (under- and overlimiting) passed through the Neosepta CMX cation-exchange membrane (Tokuyama Corp., Japan). Potential drops according to the distance from the membrane surface on the depleted side were measured using a microelectrode to obtain the concentration profile. From the concentration profiles obtained, it was observed that the diffusion boundary layers existed in the range of 300-350 microm, which reasonably coincide with the theoretical diffusion boundary layer thickness calculated from the limiting current density. Although there were some deviations between the concentrations determined from the Nernst model and those from experiments, it was confirmed that the Nernst model effectively depicts the transport phenomena in the ion-exchange membrane system. In addition it was found that the salt concentration at the membrane surface increased when the currents applied exceeded the limiting current. It is thought that the concentration polarization formed in the diffusion boundary layer at currents near or lower than the limiting current was disturbed by a turbulent convection when the current was greater than the limiting current. As a consequence, the concentration at the membrane surface increased to a sufficient level for generation of the overlimiting current.

Brownian dynamics simulations on a hypersphere in 4-space

NASA Astrophysics Data System (ADS)

Nissfolk, Jarl; Ekholm, Tobias; Elvingson, Christer

2003-10-01

We describe an algorithm for performing Brownian dynamics simulations of particles diffusing on S3, a hypersphere in four dimensions. The system is chosen due to recent interest in doing computer simulations in a closed space where periodic boundary conditions can be avoided. We specifically address the question how to generate a random walk on the 3-sphere, starting from the solution of the corresponding diffusion equation, and we also discuss an efficient implementation based on controlled approximations. Since S3 is a closed manifold (space), the average square displacement during a random walk is no longer proportional to the elapsed time, as in R3. Instead, its time rate of change is continuously decreasing, and approaches zero as time becomes large. We show, however, that the effective diffusion coefficient can still be obtained from the time dependence of the square displacement.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

NASA Technical Reports Server (NTRS)

Dusenbery, P. B.; Lyons, L. R.

1988-01-01

The quasi-linear diffusion of particles from resonant interactions with a spectrum of electrostatic waves is investigated theoretically, extending results obtained for no magnetic field and for strong magnetic fields to cases where the ambient magnetic field which organizes azimuthally symmetric wave and particle distributions does not have to be taken into consideration in evaluating the local interaction. The derivation of the governing equations is explained, and numerical results are presented in extensive graphs and characterized in detail. Slow-mode ion-acoustic waves are shown to be unstable under the plasma conditions studied, and the dependence of resonant-ion diffusion rates with pitch angle, speed, and the distribution of wave energy in wavenumber space is explored. The implications of the present findings for theoretical models of the earth bow shock and plasma-sheet boundary layer are indicated.

Improved diffuser for augmenting a wind turbine

DOEpatents

Foreman, K.M.; Gilbert, B.L.

A diffuser for augmenting a wind turbine having means for energizing the boundary layer at several locations along the diffuser walls is improved by the addition of a short collar extending radially outward from the outlet of the diffuser.

Dynamical Generation of the Transition Zone in the Earth's Mantle

NASA Astrophysics Data System (ADS)

Hansen, U.; Stemmer, K.

2005-12-01

The internal structure of the Earth is made up by a series of layers, though it is unclear how many layers exist and if there are layers invisible to remote sensing techniques. The transition zone is likely to be a boundary layer separating the convective systems in the lower and upper mantle. It seems likely that currently there is some mass exchange across this boundary, rather than the two systems beeing strictly separated.a Double-diffusive convection(d.d.c) is a vital mechanism which can generate layered structure and may thus be an important mmical machinery behind the formation of the transition zone. Double-diffusive convection determines the dynamics of systems whose density is influenced by at least two components with different molecular diffusivities.In the mantle, composition and temperature play the role of those two components. By means of numerical experiments we demonstrate that under mantle relevant conditions d.d.c typically leads to the formation of a transition zone. The calculations encompass two- and three dimensional Cartesian geometries as well as fully 3D spherical domains. We have further included strongly temperature dependent viscosity and find that this leads to even more pronounced layering. In most cases a layered flow pattern emerges, where two layers with a transition zone in between resembles a quasistationary state. Thus, the transition zone can be the result of a self organization process of the convective flow in the mantle. The presence of a phase transition further helps to stabilize the boundary against overturning, even on a time scale on the order of the age of the Earth.

Wind direction variability in Afternoon and Sunset Turbulence

NASA Astrophysics Data System (ADS)

Nilsson, Erik; Lothon, Marie; Lohou, Fabienne; Mahrt, Larry

2014-05-01

Understanding wind direction (WD) variability better is important for several reasons. Air pollution models need information about how variable wind direction is in different conditions (Davies and Thomson 1999). Accurate predictions of dispersion are important for human health and safety and allow for adaptation planning (Nagle et al. 2011). Other applications include horizontal diffusion, efficiency and fatigue of wind machines and air-sea interaction (Mahrt 2011). Most studies of wind direction variability have focused on nocturnal conditions because of greater variability in light winds. Modelling WD variability in transition periods when both mean wind speed and variance of the wind components are in a state of change can, however, also be very challenging and has not been the focus of earlier studies. The evening transitioning to the nocturnal boundary layer can play an important role in the diffusion process of pollutants and scalars emitted at surface and transported within the atmosphere. The Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) field campaign that took place in southern France in June and July 2011 focused on the decaying turbulence of the late afternoon boundary layer and related issues (Lothon et al. 2012). We analyse field measurements from BLLAST to investigate WD variability in the evening transition period. Standard deviations of horizontal wind direction fluctuations in the lowest 60 m of the boundary layer have been examined for dependence on mean wind speed, higher order moments and averaging time. Measurement results are interpreted using measured and idealized probability density functions of horizontal wind vectors. These are also used to develop analytical functions describing how WD variability depends on wind speed, variance and other controlling factors in the atmospheric boundary layer. References: Davies B.M., Thomson D.J., 1999. Comparison of some parameterizations of wind direction variability with observations, Atmospheric Enviroment 33, 4909-4917. Lothon M. et al., 2012. The Boundary-Layer Late Afternoon and Sunset Turbulence field experiment, Proc. of the 20th Symposium on Boundary-Layers and Turbulence, 7-13 July, Boston, MA, USA. Mahrt L., 2011. Surface Wind Direction Variability, Journal of Applied Meteorology and Climatology 50. 144-152. Nagle J.C., 2011. Adapting to Pollution, Research Roundtable on Climate Change, Adaptation, and Enviromental Law, Northwestern Law Searle Center, Legal and Regulatory Studies 7-18 April, IL, USA.

Areal-averaged trace gas emission rates from long-range open-path measurements in stable boundary layer conditions

NASA Astrophysics Data System (ADS)

Schäfer, K.; Grant, R. H.; Emeis, S.; Raabe, A.; von der Heide, C.; Schmid, H. P.

2012-07-01

Measurements of land-surface emission rates of greenhouse and other gases at large spatial scales (10 000 m2) are needed to assess the spatial distribution of emissions. This can be readily done using spatial-integrating micro-meteorological methods like flux-gradient methods which were evaluated for determining land-surface emission rates of trace gases under stable boundary layers. Non-intrusive path-integrating measurements are utilized. Successful application of a flux-gradient method requires confidence in the gradients of trace gas concentration and wind, and in the applicability of boundary-layer turbulence theory; consequently the procedures to qualify measurements that can be used to determine the flux is critical. While there is relatively high confidence in flux measurements made under unstable atmospheres with mean winds greater than 1 m s-1, there is greater uncertainty in flux measurements made under free convective or stable conditions. The study of N2O emissions of flat grassland and NH3 emissions from a cattle lagoon involves quality-assured determinations of fluxes under low wind, stable or night-time atmospheric conditions when the continuous "steady-state" turbulence of the surface boundary layer breaks down and the layer has intermittent turbulence. Results indicate that following the Monin-Obukhov similarity theory (MOST) flux-gradient methods that assume a log-linear profile of the wind speed and concentration gradient incorrectly determine vertical profiles and thus flux in the stable boundary layer. An alternative approach is considered on the basis of turbulent diffusivity, i.e. the measured friction velocity as well as height gradients of horizontal wind speeds and concentrations without MOST correction for stability. It is shown that this is the most accurate of the flux-gradient methods under stable conditions.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Daily, Michael; Baker, Nathan A.

2015-05-07

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Unified path integral approach to theories of diffusion-influenced reactions

NASA Astrophysics Data System (ADS)

Prüstel, Thorsten; Meier-Schellersheim, Martin

2017-08-01

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

Effects of Electrical Current and External Stress on the Electromigration of Intermetallic Compounds Between the Flip-Chip Solder and Copper Substrate

NASA Astrophysics Data System (ADS)

Chen, Wei-Jhen; Lee, Yue-Lin; Wu, Ti-Yuan; Chen, Tzu-Ching; Hsu, Chih-Hui; Lin, Ming-Tzer

2018-01-01

This study investigated the effects of electric current and external stress on electromigration of intermetallic compounds (IMC) between solder and copper substrate. Different samples were tested under three different sets of conditions: (1) thermal aging only, (2) thermal aging with electric current ,where resistivity changes were measured using four-point probe measurements, (3) thermal aging with electric current and external stress provided using a four-point bending apparatus. The micro-structural changes in the samples were observed. The results were closely examined; particularly the coupling effect of electric current and external stress to elucidate the electromigration mechanism, as well as the formation of IMC in the samples. For thermal-aging-only samples, the IMC growth mechanism was controlled by grain boundary diffusion. Meanwhile, for thermal aging and applied electric current samples, the IMC growth mechanism was dominated by volume diffusion and interface reaction. Lastly, the IMC growth mechanism in the electric current and external stress group was dominated by grain boundary diffusion with grain growth. The results reveal that the external stress/strain and electric current play a significant role in the electromigration of copper-tin IMC. The samples exposed to tensile stress have reduced electromigration, while those subjected under compressive stress have enhanced electromigration.

Diffusion of Drag-Reducing Polymers within a High-Reynolds-Number, Rough-Wall Turbulent Boundary Layer

NASA Astrophysics Data System (ADS)

Elbing, Brian; Perlin, Marc; Dowling, David; Solomon, Michael; Ceccio, Steven

2008-11-01

Two experiments were conducted to investigate polymer drag reduction (PDR) within high Reynolds number (to 200 million based on downstream distance), rough-wall turbulent boundary layers. The first experiment was conducted at the U.S. Navy's Large Cavitation Channel on a 12.9 m long flat-plate at speeds to 20 m/s with the surface hydraulically smooth and fully rough. Local skin-friction measurements on the smooth and rough surfaces had maximum PDR levels of 65 and 75 percent, respectively. However, PDR decreased with increasing downstream distance and flow speed more rapidly on the rough surface, and at the top speed no measureable level of PDR was observed. The roughness-induced increased diffusion was quantified with near-wall concentration measurements and the second experiment, which measured concentration profiles on a 0.94 m long flat-plate with three surface conditions: smooth, 240-grit, and 60-grit sandpaper. The increased diffusion does not fully explain the smooth-rough PDR differences observed in the first experiment. Rheological analysis of drawn samples from the first experiment indicates that polymer degradation (chain scission) could be responsible for the remaining loss of rough-wall PDR. These results have implications for the cost effectiveness of PDR for surface ships.

Scalar conservation and boundedness in simulations of compressible flow

NASA Astrophysics Data System (ADS)

Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

2017-11-01

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

Continuous time random walk with local particle-particle interaction

NASA Astrophysics Data System (ADS)

Xu, Jianping; Jiang, Guancheng

2018-05-01

The continuous time random walk (CTRW) is often applied to the study of particle motion in disordered media. Yet most such applications do not allow for particle-particle (walker-walker) interaction. In this paper, we consider a CTRW with particle-particle interaction; however, for simplicity, we restrain the interaction to be local. The generalized Chapman-Kolmogorov equation is modified by introducing a perturbation function that fluctuates around 1, which models the effect of interaction. Subsequently, a time-fractional nonlinear advection-diffusion equation is derived from this walking system. Under the initial condition of condensed particles at the origin and the free-boundary condition, we numerically solve this equation with both attractive and repulsive particle-particle interactions. Moreover, a Monte Carlo simulation is devised to verify the results of the above numerical work. The equation and the simulation unanimously predict that this walking system converges to the conventional one in the long-time limit. However, for systems where the free-boundary condition and long-time limit are not simultaneously satisfied, this convergence does not hold.

A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

USGS Publications Warehouse

Moran, B.; Kulkarni, S.S.; Reeves, H.W.

2007-01-01

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.

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

Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variablesmore » are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.« less

Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions

NASA Astrophysics Data System (ADS)

Zeeshan, A.; Shehzad, N.; Ellahi, R.

2018-03-01

The motivation of the current article is to explore the energy activation in MHD radiative Couette-Poiseuille flow nanofluid in horizontal channel with convective boundary conditions. The mathematical model of Buongiorno [1] effectively describes the current flow analysis. Additionally, the impact of chemical reaction is also taken in account. The governing flow equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with analytical (HAM) technique. The influence of dimensionless convergence parameter like Brownian motion parameter, radiation parameter, buoyancy ratio parameter, dimensionless activation energy, thermophoresis parameter, temperature difference parameter, dimensionless reaction rate, Schmidt number, Brinkman number, Biot number and convection diffusion parameter on velocity, temperature and concentration profiles are discussed graphically and in tabular form. From the results, it is elaborate that the nanoparticle concentration is directly proportional to the chemical reaction with activation energy and the performance of Brownian motion on nanoparticle concentration gives reverse pattern to that of thermophoresis parameter.

Alternating currents and shear waves in viscous electronics

NASA Astrophysics Data System (ADS)

Semenyakin, M.; Falkovich, G.

2018-02-01

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (ac) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current parallel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for dc current across a strip with a no-stress boundary, there are only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions.

Electrical properties of polycrystalline olivine: evidence for grain boundary transport

NASA Astrophysics Data System (ADS)

Ten Grotenhuis, S. M.; Drury, M. R.; Peach, C. J.; Spiers, C. J.

2003-12-01

The physical and chemical properties of grain boundaries are known to play an important role in determining the electrical properties of polycrystalline oxides. Grain boundaries can either enhance conductivity if the transport of charge carriers along the grain boundaries is faster than through the lattice, or grain boundaries can reduce conductivity if the grain boundaries block the transport of charge carriers. The purpose of the experiments presented here is to deduce the mechanisms responsible for electrical conductivity in fine-grained forsterite, the Mg-end member of olivine, in order to get a better understanding of the contribution of grain boundary transport, of the properties of the grain boundaries, and to determine any relation between grain size and conductivity. A relationship between grain size and conductivity at high temperature could potentially be used to interpret zones of anomalous conductivity in the upper mantle. The materials studied consist of fine-grained forsterite (Mg2SiO4) with a minor amount (5%) of enstatite (MgSiO3) added. The electrical conductivity of three melt-free synthetic polycrystalline samples, with grain sizes between 1.1 and 4.7 mm, was measured at temperatures up to 1470° C. The complex impedance plots display one clear arc, indicating a single dominant conduction mechanism. Bulk conductivity is inversely proportional to the grain size of the different samples. This relation suggests that grain boundary diffusion of the charge carriers is controlling the electrical conductivity of the samples. The activation energy for diffusion of the charge carriers lies between 315 and 323 kJ/mol. This resembles previous data on grain boundary diffusion of Mg in forsterite and grain boundary diffusion creep. A geometrical model of less conducting cubic grains and more conducting grain boundaries agrees well with the experimental data. This model is applied to a natural mantle shear zone to predict the conductivity contrast between fine-grained shear zones and less deformed regions in the lithosphere. Upper mantle shear zones are predicted to have 1.5 to 2 orders of magnitude higher conductivity than less deformed regions in the lithosphere. This may mean that fine-grained shear zones can be detected using magnetotelluric methods.

Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants

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

Zhang, Zhen, E-mail: matzz@nus.edu.sg; Xu, Shixin, E-mail: matxs@nus.edu.sg; Ren, Weiqing, E-mail: matrw@nus.edu.sg

2014-06-15

A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as wellmore » as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically.« less

Influence of definition of impeller-vaneless diffuser boundary on physical validity of numerical simulations of viscid flow in the vaneless diffuser of a centrifugal compressor: A short review of case studies

NASA Astrophysics Data System (ADS)

Kabalyk, K.; Kryllowicz, W.

2017-09-01

The study aims to work out a set of recommendations for setting a proper distance between the trailing edge of impeller and the interface boundary, which on the one hand would not be too large to overpredict the impeller efficiency and not too short to introduce artificial wake-like flow structures at diffuser inlet on the other. Three individual two-element stages belonging to three different types known as medium- and low-flow coefficient stages are studied. Besides of the design flow coefficient, the focus is on the influence of impeller tip Mach number on the optimal location of the boundary.

Self-diffusion of polycrystalline ice Ih under confining pressure: Hydrogen isotope analysis using 2-D Raman imaging

NASA Astrophysics Data System (ADS)

Noguchi, Naoki; Kubo, Tomoaki; Durham, William B.; Kagi, Hiroyuki; Shimizu, Ichiko

2016-08-01

We have developed a high-resolution technique based on micro Raman spectroscopy to measure hydrogen isotope diffusion profiles in ice Ih. The calibration curve for quantitative analysis of deuterium in ice Ih was constructed using micro Raman spectroscopy. Diffusion experiments using diffusion couples composed of dense polycrystalline H2O and D2O ice were carried out under a gas confining pressure of 100 MPa (to suppress micro-fracturing and pore formation) at temperatures from 235 K to 245 K and diffusion times from 0.2 to 94 hours. Two-dimensional deuterium profiles across the diffusion couples were determined by Raman imaging. The location of small spots of frost from room air could be detected from the shapes of the Raman bands of OH and OD stretching modes, which change because of the effect of the molar ratio of deuterium on the molecular coupling interaction. We emphasize the validity for screening the impurities utilizing the coupling interaction. Some recrystallization and grain boundary migration occurred in recovered diffusion couples, but analysis of two-dimensional diffusion profiles of regions not affected by grain boundary migration allowed us to measure a volume diffusivity for ice at 100 MPa of (2.8 ± 0.4) ×10-3exp[ -57.0 ± 15.4kJ /mol RT ] m2 /s (R is the gas constant, T is temperature). Based on ambient pressure diffusivity measurements by others, this value indicates a high (negative) activation volume for volume diffusivity of -29.5 cm3/mol or more. We can also constrain the value of grain boundary diffusivity in ice at 100 MPa to be <104 that of volume diffusivity.

Diffusivity in Alumina Scales Grown on Al-MAX Phases

NASA Technical Reports Server (NTRS)

Smialek, James L.

2014-01-01

Ti3AlC2, Ti2AlC, and Cr2AlC are oxidation resistant MAX phase compounds distinguished by the formation of protective Al2O3 scales with well controlled kinetics. A modified Wagner treatment was used to obtain interfacial grain boundary diffusivity, deltaD(sub gb,O,int.), from scale growth rates and corresponding grain size. It is based on the p(O2)(exp -1/6) dependency of the double charged oxygen vacancy and oxygen diffusivity, coupled with the effective diffusion constant for short circuit grain boundary paths. Data from the literature for MAX phases was analyzed accordingly, and deltaD(sub gb,O,int.) was found to nearly coincide with the Arrhenius line developed for Zr-doped FeCrAl, where: deltaD(sub gb,O,int.) = 1.8x10(exp -10) exp(-375 kJ/RT) cubic meters/s. Furthermore, this oxidation relation suggests the more general format applicable to bulk samples under ambient conditions: deltaD(sub gb,O) = 7.567x10(exp -8) exp(-544 kJ/RT) p(O2)(exp -1/6) cubic meters/[s x Pa(exp -1/6)]. Data from many other FeCrAl(X) studies were similarly assessed to show general agreement with the relation for deltaD(sub gb,O,int.). This analysis reinforces the view that protective alumina scales grow by similar mechanisms for these Al-MAX phases and oxidation resistant FeCrAl alloys.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

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

Densification kinetics of nanocrystalline zirconia powder using microwave and spark plasma sintering--a comparative study.

PubMed

Vasylkiv, Oleg; Demirskyi, Dmytro; Sakka, Yoshio; Ragulya, Andrey; Borodianska, Hanna

2012-06-01

Two-stage densification process of nanosized 3 mol% yttria-stabilized zirconia (3Y-SZ) polycrystalline compacts during consolidation via microwave and spark-plasma sintering have been observed. The values of activation energies obtained for microwave and spark-plasma sintering 260-275 kJ x mol(-1) are quite similar to that of conventional sintering of zirconia, suggesting that densification during initial stage is controlled by the grain-boundary diffusion mechanism. The sintering behavior during microwave sintering was significantly affected by preliminary pressing conditions, as the surface diffusion mechanism (230 kJ x mol(-1)) is active in case of cold-isostatic pressing procedure was applied.

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

PubMed Central

Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360

Strain localization and fabric development in polycrystalline anorthite + melt by water diffusion in an axial deformation experiment

NASA Astrophysics Data System (ADS)

Fukuda, Jun-ichi; Muto, Jun; Nagahama, Hiroyuki

2018-01-01

We performed two axial deformation experiments on synthetic polycrystalline anorthite samples with a grain size of 3 μm and 5 vol% Si-Al-rich glass at 900 °C, a confining pressure of 1.0 GPa, and a strain rate of 10-4.8 s-1. One sample was deformed as-is (dry); in the other sample, two half-cut samples (two cores) with 0.15 wt% water at the boundary were put together in the apparatus. The mechanical data for both samples were essentially identical with a yield strength of 700 MPa and strain weakening of 500 MPa by 20% strain. The dry sample appears to have been deformed by distributed fracturing. Meanwhile, the water-added sample shows plastic strain localization in addition to fracturing and reaction products composed of zoisite grains and SiO2 materials along the boundary between the two sample cores. Infrared spectra of the water-added sample showed dominant water bands of zoisite. The maximum water content was 1500 wt ppm H2O at the two-core boundary, which is the same as the added amount. The water contents gradually decreased from the boundaries to the sample interior, and the gradient fitted well with the solution of the one-dimensional diffusion equation. The determined diffusion coefficient was 7.4 × 10-13 m2/s, which agrees with previous data for the grain boundary diffusion of water. The anorthite grains in the water-added sample showed no crystallographic preferred orientation. Textural observations and water diffusion indicate that water promotes the plastic deformation of polycrystalline anorthite by grain-size-sensitive creep as well as simultaneous reactions. We calculated the strain rate evolution controlled by water diffusion in feldspar aggregates surrounded by a water source. We assumed water diffusion in a dry rock mass with variable sizes. Diffused water weakens a rock mass with time under compressive stress. The calculated strain rate decreased from 10-10 to 10-15 s-1 with an increase in the rock mass size to which water is supplied from < 1 m to 1 km and an increase in the time of water diffusion from < 1 to 10,000 years. This indicates a decrease in the strain rate in a rock mass with increasing deformation via water diffusion.

Aerodynamically induced radial forces in a centrifugal gas compressor: Part 2 -- Computational investigation

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

Flathers, M.B.; Bache, G.E.

1999-10-01

Radial loads and direction of a centrifugal gas compressor containing a high specific speed mixed flow impeller and a single tongue volute were determined both experimentally and computationally at both design and off-design conditions. The experimental methodology was developed in conjunction with a traditional ASME PTC-10 closed-loop test to determine radial load and direction. The experimental study is detailed in Part 1 of this paper (Moore and Flathers, 1998). The computational method employs a commercially available, fully three-dimensional viscous code to analyze the impeller and the volute interaction. An uncoupled scheme was initially used where the impeller and volute weremore » analyzed as separate models using a common vaneless diffuser geometry. The two calculations were then repeated until the boundary conditions at a chosen location in the common vaneless diffuser were nearly the same. Subsequently, a coupled scheme was used where the entire stage geometry was analyzed in one calculation, thus eliminating the need for manual iteration of the two independent calculations. In addition to radial load and direction information, this computational procedure also provided aerodynamic stage performance. The effect of impeller front face and rear face cavities was also quantified. The paper will discuss computational procedures, including grid generation and boundary conditions, as well as comparisons of the various computational schemes to experiment. The results of this study will show the limitations and benefits of Computational Fluid Dynamics (CFD) for determination of radial load, direction, and aerodynamic stage performance.« less

Modeling the transport of organic chemicals between polyethylene passive samplers and water in finite and infinite bath conditions.

PubMed

Tcaciuc, A Patricia; Apell, Jennifer N; Gschwend, Philip M

2015-12-01

Understanding the transfer of chemicals between passive samplers and water is essential for their use as monitoring devices of organic contaminants in surface waters. By applying Fick's second law to diffusion through the polymer and an aqueous boundary layer, the authors derived a mathematical model for the uptake of chemicals into a passive sampler from water, in finite and infinite bath conditions. The finite bath model performed well when applied to laboratory observations of sorption into polyethylene (PE) sheets for various chemicals (polycyclic aromatic hydrocarbons, polychlorinated biphenyls [PCBs], and dichlorodiphenyltrichloroethane [DDT]) and at varying turbulence levels. The authors used the infinite bath model to infer fractional equilibration of PCB and DDT analytes in field-deployed PE, and the results were nearly identical to those obtained using the sampling rate model. However, further comparison of the model and the sampling rate model revealed that the exchange of chemicals was inconsistent with the sampling rate model for partially or fully membrane-controlled transfer, which would be expected in turbulent conditions or when targeting compounds with small polymer diffusivities and small partition coefficients (e.g., phenols, some pesticides, and others). The model can be applied to other polymers besides PE as well as other chemicals and in any transfer regime (membrane, mixed, or water boundary layer-controlled). Lastly, the authors illustrate practical applications of this model such as improving passive sampler design and understanding the kinetics of passive dosing experiments. © 2015 SETAC.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical approach to describe complementary drying of banana slices osmotically dehydrated

NASA Astrophysics Data System (ADS)

da Silva Júnior, Aluízio Freire; da Silva, Wilton Pereira; de Farias Aires, Juarez Everton; Farias Aires, Kalina Lígia C. A.

2018-02-01

In this work, diffusion model was used to describe the water loss in the complementary drying process of cylindrical slices of banana pretreated by osmotic dehydration. A numerical solution has been proposed for the diffusion equation in cylindrical coordinates, which was obtained through the Finite Volume Method. The diffusion equation was discretized assuming that the effective water diffusivity and the dimensions of a finite cylinder may vary; also considering the boundary condition of the third kind. The banana slices were cut in length of about 1.00 cm and average radius 1.70 cm before osmotic pretreatment, and completed the pretreatment with length of about 0.74 cm and average radius 1.40 cm. The complementary drying was carried out in a kiln with circulation and air exchange. Drying temperatures were the same as used in the osmotic pretreatment (40 to 70 °C). The proposed model described well the water loss, with good statistical indicators for all fits.

Magnon diffusion theory for the spin Seebeck effect in ferromagnetic and antiferromagnetic insulators

NASA Astrophysics Data System (ADS)

Rezende, Sergio M.; Azevedo, Antonio; Rodríguez-Suárez, Roberto L.

2018-05-01

In magnetic insulators, spin currents are carried by the elementary excitations of the magnetization: spin waves or magnons. In simple ferromagnetic insulators there is only one magnon mode, while in two-sublattice antiferromagnetic insulators (AFIs) there are two modes, which carry spin currents in opposite directions. Here we present a theory for the diffusive magnonic spin current generated in a magnetic insulator layer by a thermal gradient in the spin Seebeck effect. We show that the formulations describing magnonic perturbation using a position-dependent chemical potential and those using a magnon accumulation are completely equivalent. Then we develop a drift–diffusion formulation for magnonic spin transport treating the magnon accumulation governed by the Boltzmann transport and diffusion equations and considering the full boundary conditions at the surfaces and interfaces of an AFI/normal metal bilayer. The theory is applied to the ferrimagnetic yttrium iron garnet and to the AFIs MnF2 and NiO, providing good quantitative agreement with experimental data.

Nanostructural evolution and behavior of H and Li in ion-implanted γ-LiAlO 2

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

Jiang, Weilin; Zhang, Jiandong; Edwards, Danny J.

In-situ He+ ion irradiation is performed under a helium ion microscope to study nanostructural evolution in polycrystalline gamma-LiAlO2 pellets. Various locations within a grain, across grain boundaries and at a cavity are selected. The results exhibit He bubble formation, grain-boundary cracking, nanoparticle agglomeration, increasing surface brightness with dose, and material loss from the surface. Similar brightening effects at grain boundaries are also observed under a scanning electron microscope. Li diffusion and loss from polycrystalline gamma-LiAlO2 is faster than its monocrystalline counterpart during H2+ ion implantation at elevated temperatures. There is also more significant H diffusion and release from polycrystalline pelletsmore » during thermal annealing of 300 K implanted samples. Grain boundaries and cavities could provide a faster pathway for H and Li diffusion. H release is slightly faster from the 573 K implanted monocrystalline gamma-LiAlO2 during annealing at 773 K. Metal hydrides could be formed preferentially along the grain boundaries to immobilize hydrogen.« less

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/

A Semi-Analytical Model for Dispersion Modelling Studies in the Atmospheric Boundary Layer

NASA Astrophysics Data System (ADS)

Gupta, A.; Sharan, M.

2017-12-01

The severe impact of harmful air pollutants has always been a cause of concern for a wide variety of air quality analysis. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to a constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height. In the present model, a method of eigen-function expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first order ordinary differential equations with a coefficient matrix depending on the downwind distance. The solution of this system, in general, can be expressed in terms of Peano-baker series which is not easy to compute, particularly when the coefficient matrix becomes non-commutative (Martin et al., 1967). An approach based on Taylor's series expansion is introduced to find the numerical solution of first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The performance of the model is evaluated with the diffusion datasets from Copenhagen (Gryning et al., 1987) and Hanford (Doran et al., 1985). In addition, the proposed method is used to deduce three dimensional concentrations by considering the Gaussian distribution in crosswind direction, which is also evaluated with diffusion data corresponding to a continuous point source.

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

PubMed Central

2012-01-01

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

Local measurement of thermal conductivity and diffusivity.

PubMed

Hurley, David H; Schley, Robert S; Khafizov, Marat; Wendt, Brycen L

2015-12-01

Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness for extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representatives of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agreed closely with the literature values. A distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility.

Mechanisms of high-temperature, solid-state flow in minerals and ceramics and their bearing on the creep behavior of the mantle

USGS Publications Warehouse

Kirby, S.H.; Raleigh, C.B.

1973-01-01

The problem of applying laboratory silicate-flow data to the mantle, where conditions can be vastly different, is approached through a critical review of high-temperature flow mechanisms in ceramics and their relation to empirical flow laws. The intimate association of solid-state diffusion and high-temperature creep in pure metals is found to apply to ceramics as well. It is shown that in ceramics of moderate grain size, compared on the basis of self-diffusivity and elastic modulus, normalized creep rates compare remarkably well. This comparison is paralleled by the near universal occurrence of similar creep-induced structures, and it is thought that the derived empirical flow laws can be associated with dislocation creep. Creep data in fine-grained ceramics, on the other hand, are found to compare poorly with theories involving the stress-directed diffusion of point defects and have not been successfully correlated by self-diffusion rates. We conclude that these fine-grained materials creep primarily by a quasi-viscous grain-boundary sliding mechanism which is unlikely to predominate in the earth's deep interior. Creep predictions for the mantle reveal that under most conditions the empirical dislocation creep behavior predominates over the mechanisms involving the stress-directed diffusion of point defects. The probable role of polymorphic transformations in the transition zone is also discussed. ?? 1973.

Numerical Solution of Moving Phase Boundary and Diffusion-Induced Stress of Sn Anode in the Lithium-Ion Battery

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

Chen, Chun-Hao; Chason, Eric; Guduru, Pradeep R.

Here, we have previously observed a large transient stress in Sn film anodes at the beginning of the Sn-Li 2Sn 5 phase transformation. To understand this behavior, we use numerical modeling to simulate the kinetics of the 1-D moving boundary and Li diffusion in the Sn anodes. A mixture of diffusion-controlled and interface-controlled kinetics is found. The Li concentration in the Li 2Sn 5 phase remains near a steady-state profile as the phase boundary propagates, whereas the Li diffusion in Sn is more complicated. Li continuously diffuses into the Sn layer and produces a supersaturation; the Li can then diffusemore » toward the Sn/Li 2Sn 5 interface and contribute to further phase transformation. Finally, the evolution of Li concentration in the Sn induces strain which involves rate-dependent plasticity and elastic unloading, resulting in the complex stress evolution that is observed. In the long term, the measured stress is dominated by the stress in the growing Li 2Sn 5 phase.« less

Numerical Solution of Moving Phase Boundary and Diffusion-Induced Stress of Sn Anode in the Lithium-Ion Battery

DOE PAGES

Chen, Chun-Hao; Chason, Eric; Guduru, Pradeep R.

2017-08-02

Here, we have previously observed a large transient stress in Sn film anodes at the beginning of the Sn-Li 2Sn 5 phase transformation. To understand this behavior, we use numerical modeling to simulate the kinetics of the 1-D moving boundary and Li diffusion in the Sn anodes. A mixture of diffusion-controlled and interface-controlled kinetics is found. The Li concentration in the Li 2Sn 5 phase remains near a steady-state profile as the phase boundary propagates, whereas the Li diffusion in Sn is more complicated. Li continuously diffuses into the Sn layer and produces a supersaturation; the Li can then diffusemore » toward the Sn/Li 2Sn 5 interface and contribute to further phase transformation. Finally, the evolution of Li concentration in the Sn induces strain which involves rate-dependent plasticity and elastic unloading, resulting in the complex stress evolution that is observed. In the long term, the measured stress is dominated by the stress in the growing Li 2Sn 5 phase.« less

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

NASA Astrophysics Data System (ADS)

Jennissen, Herbert P.

2005-10-01

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

A Multispectral Bidirectional Reflectance Distribution Function Study of Human Skin for Improved Dismount Detection

DTIC Science & Technology

2011-03-01

electromagnetic spectrum. With the availability of multispectral and hyperspectral systems, both spatial and spectral information for a scene are...an image. The boundary conditions for NDGRI and NDSI are set from diffuse spectral reflectance values for the range of skin types determined in [28...wearing no standard uniform and blending into the urban population. To assist with enemy detection and tracking, imaging systems that acquire spectral

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

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

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

2016-03-11

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

3-D Modeling of Directional Solidification of a Non-Dilute Alloy with Temperature and Concentration Fields Coupling via Materials Properties Dependence and via Double Diffusive Convection

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1998-01-01

Numerical simulation of the HgCdTe growth by the vertical Bridgman method was performed using FIDAP finite element code. Double-diffusive melt convection is analyzed, as the primary factor at controls inhomogeneity of the solidified material. Temperature and concentration fields in the model are also coupled via material properties, such as thermal and solutal expansion coefficients with the dependence on both temperature and concentration, and melting temperature evaluation from pseudobinary CdTe-HgTe phase diagram. Experimental measurements were used to obtain temperature boundary conditions. Parametric study of the melt convection dependence on the gravity conditions was undertaken. It was found, that the maximum convection velocity in the melt can be reduced under certain conditions. Optimal conditions to obtain a near flat solidified interface are discussed. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D calculations are compared with previous 2- D findings. A video film featuring 3-D melt convection will be presented.

Initiation and growth of the discontinuous precipitation reaction at [0 1 1] symmetric tilt boundaries in Cu-Be alloy bicrystals

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

Monzen, R.; Watanabe, C.; Mino, D.

2005-02-01

The initiation and growth of discontinuous precipitation (DP) at [0 1 1] symmetric tilt boundaries in Cu-0.75 wt% Be alloy bicrystals have been studied. Transmission electron microscopy revealed that {gamma} precipitates tended to nucleate at a boundary in such a manner that their habit plane, (1 1 2){sub {alpha}} or (4 4 5){sub {alpha}}, with one of the adjoining grains lay as close as possible to the boundary. The habit plane with a low energy formed on both sides of the precipitates behind an initially migrating boundary, indicating the importance of the existence of the low-energy habit plane for themore » initial boundary migration. The incubation period to initiate DP and cell growth rate for a boundary show a good correlation with the energy of the boundary. A kinetic analysis of DP using the models of Turnbull, and Petermann and Hornbogen has yielded boundary diffusion data. A higher-energy boundary has a higher diffusivity with a smaller activation energy.« less

A diffuse plate boundary model for Indian Ocean tectonics

NASA Technical Reports Server (NTRS)

Wiens, D. A.; Demets, C.; Gordon, R. G.; Stein, S.; Argus, D.

1985-01-01

It is suggested that motion along the virtually aseismic Owen fracture zone is negligible, so that Arabia and India are contained within a single Indo-Arabian plate divided from the Australian plate by a diffuse boundary. The boundary is a zone of concentrated seismicity and deformation commonly characterized as 'intraplate'. The rotation vector of Australia relative to Indo-Arabia is consistent with the seismologically observed 2 cm/yr of left-lateral strike-slip along the Ninetyeast Ridge, north-south compression in the Central Indian Ocean, and the north-south extension near Chagos.

Surface evolution in bare bamboo-type metal lines under diffusion and electric field effects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Nathan, Menachem; Ravve, Igor

2003-07-01

Irregularities such as voids and cracks often occur in bamboo-type metal lines of microelectronic interconnects. They increase the resistance of the circuits, and may even lead to a fatal failure. In this work, we analyze numerically the electromigration of an unpassivated bamboo-type line with pre-existing irregularities in its top surface (also called a grain-void interface). The bamboo line is subjected to surface diffusion forces and external electric fields. Under these forces, initial defects may either heal or become worse. The grain-void interface is considered to be one-dimensional, and the physical formulation of an electromigration and diffusion model results in two coupled, fourth order, one-dimensional time-dependent PDEs, with the boundary conditions imposed at the electrode points and at the triple point, which belongs to two neighboring grains and the void. These equations are discretized by finite differences on a regular grid in space, and by a Runge-Kutta integration scheme in time, and solved simultaneously with a static Laplace equation describing the voltage distribution throughout each grain, when the substrate conductivity is neglected. Since the voltage distribution is required only along an 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 interface line is studied for different ratios between diffusion and electric field forces, and for different initial configurations of the grain-void interface. We study plain and tilted contour lines, considering positive and negative tilts with respect to the external electric field, a stepped contour with field lines entering or exiting the 'step', and a number of modifications of the classical Mullins problem of thermal grooving. We also consider a two-grain Mullins problem with a normal and tilted boundary between the grains, examining positive and negative tilts.

Planetary Boundary Layer Patterns, Height Variability and their Controls over the Indian Subcontinent with respect to Monsoon

NASA Astrophysics Data System (ADS)

Sathyanadh, A.; Karipot, A.; Prabhakaran, T.

2016-12-01

Planetary boundary layer (PBL) height and its controlling factors undergo large variations at different spatio-temporal scales over land regions. In the present study, Modern Era Retrospective analysis for Research and Applications (MERRA) data products are used to investigate variations of PBL height and its controls in relation to different phases of Indian monsoon. MERRA PBL height validations carried out against those estimated from radiosonde and Global Positioning System Radio Occultation atmospheric profiles revealed fairly good agreement. Different PBL patterns are identified in terms of maximum height, its time of occurrence and growth rate, and they vary with respect to geographical locations, terrain characteristics and monsoon circulation. The pre-monsoon boundary layers are the deepest over the region, often exceeding 4 km and grow at a rate of approximately 400 m hr-1. Large nocturnal BL depths, possibly related to weakly convective residual layers, are another feature noted during dry conditions. Monsoon BLs are generally shallower, except where rainfall is scanty. The break-monsoon periods have slightly deeper BLs than the active monsoon phase. The controlling factors for the observed boundary layer behaviour are investigated using supplementary MERRA datasets. Evaporative fraction is found to have dominant control on the PBL height varying with seasons and regions. The characteristics and controls of wet and dry boundary layer regimes over inland and coastal locations are different. The fractional diffusion (ratio of non-local and total diffusion) coefficient analyses indicated that enhanced entrainment during monsoon contributes to reduction in PBLH unlike in the dry period. The relationship between controls and PBLH are better defined over inland than coastal regions. The wavelet cross spectral analysis revealed temporal variations in dominant contributions from the controlling factors at different periodicities during the course of the year.

Chemokinetic accumulation of human neutrophils on immune complex-coated substrata: analysis at a boundary

PubMed Central

1984-01-01

The locomotory behavior of human blood neutrophil leukocytes was studied at a boundary between two surfaces with different chemokinetic properties. This was achieved by time-lapse cinematography of neutrophils moving on coverslips coated with BSA, then part-coated with immune complexes by adding anti-BSA IgG with a straight-line boundary between the BSA and the immune complexes. Cell locomotion was filmed in microscopic fields bisected by the boundary, and kinetic behavior was assessed by comparing speed (orthokinesis), turning behavior (klinokinesis), and the rate of diffusion of the cells on each side of the boundary, using a recently described mathematical analysis of kinesis. In the absence of serum or complement, the proportion of motile cells and their speed and rate of diffusion were greater on BSA than on antiBSA, but there was no consistent difference in turning behavior between cells on the two surfaces. The immune complexes were therefore negatively chemokinetic in comparison with BSA, and this resulted from a negative orthokinesis with little or no contribution from klinokinesis. As would be predicted theoretically, this resulted in gradual accumulation of cells on the immune complexes even in the absence of a chemotactic factor. In further studies, a parallel plate flow chamber was used to show that, under conditions of flow, neutrophils accumulated much more rapidly on a surface coated with BSA- anti-BSA than on BSA alone. Moreover, neutrophils on immune complex- coated surfaces lost their ability to form rosettes with IgG-coated erythrocytes. This suggests that neutrophils on immune complex-coated surfaces redistribute their Fc receptors (RFc gamma) to the under surface, and that the lowered speed of locomotion is due to tethering of neutrophils by substratum-bound IgG-Fc. PMID:6490719

NMR-based diffusion pore imaging.

PubMed

Laun, Frederik Bernd; Kuder, Tristan Anselm; Wetscherek, Andreas; Stieltjes, Bram; Semmler, Wolfhard

2012-08-01

Nuclear magnetic resonance (NMR) diffusion experiments offer a unique opportunity to study boundaries restricting the diffusion process. In a recent Letter [Phys. Rev. Lett. 107, 048102 (2011)], we introduced the idea and concept that such diffusion experiments can be interpreted as NMR imaging experiments. Consequently, images of closed pores, in which the spins diffuse, can be acquired. In the work presented here, an in-depth description of the diffusion pore imaging technique is provided. Image artifacts due to gradient profiles of finite duration, field inhomogeneities, and surface relaxation are considered. Gradients of finite duration lead to image blurring and edge enhancement artifacts. Field inhomogeneities have benign effects on diffusion pore images, and surface relaxation can lead to a shrinkage and shift of the pore image. The relation between boundary structure and the imaginary part of the diffusion weighted signal is analyzed, and it is shown that information on pore coherence can be obtained without the need to measure the phase of the diffusion weighted signal. Moreover, it is shown that quite arbitrary gradient profiles can be used for diffusion pore imaging. The matrices required for numerical calculations are stated and provided as supplemental material.

Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium

NASA Astrophysics Data System (ADS)

Sadeghi, Pegah; Safavinejad, Ali

2017-11-01

Radiative entropy generation through a gray absorbing, emitting, and scattering planar medium at radiative equilibrium with diffuse-gray walls is investigated. The radiative transfer equation and radiative entropy generation equations are solved using discrete ordinates method. Components of the radiative entropy generation are considered for two different boundary conditions: two walls are at a prescribed temperature and mixed boundary conditions, which one wall is at a prescribed temperature and the other is at a prescribed heat flux. The effect of wall emissivities, optical thickness, single scattering albedo, and anisotropic-scattering factor on the entropy generation is attentively investigated. The results reveal that entropy generation in the system mainly arises from irreversible radiative transfer at wall with lower temperature. Total entropy generation rate for the system with prescribed temperature at walls remarkably increases as wall emissivity increases; conversely, for system with mixed boundary conditions, total entropy generation rate slightly decreases. Furthermore, as the optical thickness increases, total entropy generation rate remarkably decreases for the system with prescribed temperature at walls; nevertheless, for the system with mixed boundary conditions, total entropy generation rate increases. The variation of single scattering albedo does not considerably affect total entropy generation rate. This parametric analysis demonstrates that the optical thickness and wall emissivities have a significant effect on the entropy generation in the system at radiative equilibrium. Considering the parameters affecting radiative entropy generation significantly, provides an opportunity to optimally design or increase overall performance and efficiency by applying entropy minimization techniques for the systems at radiative equilibrium.

The diffusive boundary layer of sediments: oxygen microgradients over a microbial mat

NASA Technical Reports Server (NTRS)

Jorgensen, B. B.; Des Marais, D. J.

1990-01-01

Oxygen microelectrodes were used to analyze the distribution of the diffusive boundary layer (DBL) at the sediment-water interface in relation to surface topography and flow velocity. The sediment, collected from saline ponds, was covered by a microbial mat that had high oxygen consumption rate and well-defined surface structure. Diffusion through the DBL constituted an important rate limitation to the oxygen uptake of the sediment. The mean effective DBL thickness decreased from 0.59 to 0.16 mm as the flow velocity of the overlying water was increased from 0.3 to 7.7 cm s-1 (measured 1 cm above the mat). The oxygen uptake rate concurrently increased from 3.9 to 9.4 nmol cm-2 min-1. The effects of surface roughness and topography on the thickness and distribution of the DBL were studied by three-dimensional mapping of the sediment-water interface and the upper DBL boundary at 0.1-mm spatial resolution. The DBL boundary followed mat structures that had characteristic dimensions > 1/2 DBL thickness but the DBL had a dampened relief relative to the mat. The effective surface area of the sediment-water interface and of the upper DBL boundary were 31 and 14% larger, respectively, than a flat plane. Surface topography thereby increased the oxygen flux across the sediment-water interface by 49% relative to a one-dimensional diffusion flux calculated from the vertical oxygen microgradients.

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

PubMed

Sabelnikov, V A; Lipatnikov, A N

2014-09-01

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

Phonon coupling to dynamic short-range polar order in a relaxor ferroelectric near the morphotropic phase boundary

DOE PAGES

John A. Schneeloch; Xu, Zhijun; Winn, B.; ...

2015-12-28

We report neutron inelastic scattering experiments on single-crystal PbMg 1/3Nb 2/3O 3 doped with 32% PbTiO 3, a relaxor ferroelectric that lies close to the morphotropic phase boundary. When cooled under an electric field E∥ [001] into tetragonal and monoclinic phases, the scattering cross section from transverse acoustic (TA) phonons polarized parallel to E weakens and shifts to higher energy relative to that under zero-field-cooled conditions. Likewise, the scattering cross section from transverse optic (TO) phonons polarized parallel to E weakens for energy transfers 4 ≤ ℏω ≤ 9 meV. However, TA and TO phonons polarized perpendicular to E showmore » no change. This anisotropic field response is similar to that of the diffuse scattering cross section, which, as previously reported, is suppressed when polarized parallel to E but not when polarized perpendicular to E. Lastly, our findings suggest that the lattice dynamics and dynamic short-range polar correlations that give rise to the diffuse scattering are coupled.« less

Oxygen vacancy diffusion in bulk SrTiO3 from density functional theory calculations

DOE PAGES

Zhang, Lipeng; Liu, Bin; Zhuang, Houlong; ...

2016-04-01

Point defects and point defect diffusion contribute significantly to the properties of perovskite materials. However, even for the prototypical case of oxygen vacancies in SrTiO 3 (STO), predictions vary widely. Here we present a comprehensive and systematic study of the diffusion barriers for this material. We use density functional theory (DFT) and assess the role of different cell sizes, density functionals, and charge states. Our results show that vacancy-induced octahedral rotations, which are limited by the boundary conditions of the supercell, can significantly affect the computed oxygen vacancy diffusion energy barrier. The diffusion energy barrier of a charged oxygen vacancymore » is lower than that of a neutral one. Unexpectedly, we find that with increasing supercell size, the effects of the oxygen vacancy charge state, the type of DFT exchange and correlation functional on the energy barrier diminish, and the different DFT predictions asymptote to a value in the range of 0.39-0.49 eV. This work provides important insight and guidance that should be considered for investigations of point defect diffusion in other perovskite materials and in oxide superlattices.« less

A finite volume method for trace element diffusion and partitioning during crystal growth

NASA Astrophysics Data System (ADS)

Hesse, Marc A.

2012-09-01

A finite volume method on a uniform grid is presented to compute the polythermal diffusion and partitioning of a trace element during the growth of a porphyroblast crystal in a uniform matrix and in linear, cylindrical and spherical geometry. The motion of the crystal-matrix interface and the thermal evolution are prescribed functions of time. The motion of the interface is discretized and it advances from one cell boundary to next as the prescribed interface position passes the cell center. The appropriate conditions for the flux across the crystal-matrix interface are derived from discrete mass conservation. Numerical results are benchmarked against steady and transient analytic solutions for isothermal diffusion with partitioning and growth. Two applications illustrate the ability of the model to reproduce observed rare-earth element patterns in garnets (Skora et al., 2006) and water concentration profiles around spherulites in obsidian (Watkins et al., 2009). Simulations with diffusion inside the growing crystal show complex concentration evolutions for trace elements with high diffusion coefficients, such as argon or hydrogen, but demonstrate that rare-earth element concentrations in typical metamorphic garnets are not affected by intracrystalline diffusion.

Hydrodynamics of Bacterial Cooperation

NASA Astrophysics Data System (ADS)

Petroff, A.; Libchaber, A.

2012-12-01

Over the course of the last several decades, the study of microbial communities has identified countless examples of cooperation between microorganisms. Generally—as in the case of quorum sensing—cooperation is coordinated by a chemical signal that diffuses through the community. Less well understood is a second class of cooperation that is mediated through physical interactions between individuals. To better understand how the bacteria use hydrodynamics to manipulate their environment and coordinate their actions, we study the sulfur-oxidizing bacterium Thiovulum majus. These bacteria live in the diffusive boundary layer just above the muddy bottoms of ponds. As buried organic material decays, sulfide diffuses out of the mud. Oxygen from the pond diffuses into the boundary layer from above. These bacteria form communities—called veils— which are able to transport nutrients through the boundary layer faster than diffusion, thereby increasing their metabolic rate. In these communities, bacteria attach to surfaces and swim in place. As millions of bacteria beat their flagella, the community induces a macroscopic fluid flow, which mix the boundary layer. Here we present experimental observations and mathematical models that elucidate the hydrodynamics linking the behavior of an individual bacterium to the collective dynamics of the community. We begin by characterizing the flow of water around an individual bacterium swimming in place. We then discuss the flow of water and nutrients around a small number of individuals. Finally, we present observations and models detailing the macroscopic dynamics of a Thiovulum veil.

Optimal policy for value-based decision-making.

PubMed

Tajima, Satohiro; Drugowitsch, Jan; Pouget, Alexandre

2016-08-18

For decades now, normative theories of perceptual decisions, and their implementation as drift diffusion models, have driven and significantly improved our understanding of human and animal behaviour and the underlying neural processes. While similar processes seem to govern value-based decisions, we still lack the theoretical understanding of why this ought to be the case. Here, we show that, similar to perceptual decisions, drift diffusion models implement the optimal strategy for value-based decisions. Such optimal decisions require the models' decision boundaries to collapse over time, and to depend on the a priori knowledge about reward contingencies. Diffusion models only implement the optimal strategy under specific task assumptions, and cease to be optimal once we start relaxing these assumptions, by, for example, using non-linear utility functions. Our findings thus provide the much-needed theory for value-based decisions, explain the apparent similarity to perceptual decisions, and predict conditions under which this similarity should break down.

Optimal policy for value-based decision-making

PubMed Central

Tajima, Satohiro; Drugowitsch, Jan; Pouget, Alexandre

2016-01-01

For decades now, normative theories of perceptual decisions, and their implementation as drift diffusion models, have driven and significantly improved our understanding of human and animal behaviour and the underlying neural processes. While similar processes seem to govern value-based decisions, we still lack the theoretical understanding of why this ought to be the case. Here, we show that, similar to perceptual decisions, drift diffusion models implement the optimal strategy for value-based decisions. Such optimal decisions require the models' decision boundaries to collapse over time, and to depend on the a priori knowledge about reward contingencies. Diffusion models only implement the optimal strategy under specific task assumptions, and cease to be optimal once we start relaxing these assumptions, by, for example, using non-linear utility functions. Our findings thus provide the much-needed theory for value-based decisions, explain the apparent similarity to perceptual decisions, and predict conditions under which this similarity should break down. PMID:27535638

Purging of multilayer insulation by gas diffusion

NASA Technical Reports Server (NTRS)

Sumner, I. E.; Spuckler, C. M.

1976-01-01

An experimental investigation was conducted to determine the time required to purge a multilayer insulation (MLI) panel with gaseous helium by means of gas diffusion to obtain a condensable (nitrogen) gas concentration of less than 1 percent within the panel. Two flat, rectangular MLI panel configurations, one incorporating a butt joint, were tested. The insulation panels consisted of 15 double-aluminized Mylar radiation shields separated by double silk net spacers. The test results indicated that the rate which the condensable gas concentration at the edge or at the butt joint of an MLI panel was reduced was a significant factor in the total time required to reduce the condensable gas concentration within the panel to less than 1 percent. The experimental data agreed well with analytical predictions made by using a simple, one-dimensional gas diffusion model in which the boundary conditions at the edge of the MLI panel were time dependent.

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

Synchronized shocks in an inhomogeneous exclusion process

NASA Astrophysics Data System (ADS)

Arita, Chikashi

2015-11-01

We study an exclusion process with 4 segments, which was recently introduced by T. Banerjee, N. Sarkar and A. Basu (J. Stat. Mech. (2015) P01024). The segments have hopping rates 1, r(<1) , 1 and r, respectively. In a certain parameter region, two shocks appear, which are not static but synchronized. We explore dynamical properties of each shock and correlation of shocks, by means of the so-called second-class particle. The mean-squared displacement of shocks has three diffusive regimes, and the asymptotic diffusion coefficient is different from the known formula. In some time interval, it also exhibits sub-diffusion, being proportional to t1/2 . Furthermore we introduce a correlation function and a crossover time, in order to quantitatively characterize the synchronization. We numerically estimate the dynamical exponent for the crossover time. We also revisit the 2-segment case and the open boundary condition for comparison.

ANALYSIS OF THE MOMENTS METHOD EXPERIMENT

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

Kloster, R.L.

1959-09-01

Monte Cario calculations show the effects of a plane water-air boundary on both fast neutron and gamma dose rates. Multigroup diffusion theory calculation for a reactor source shows the effects of a plane water-air boundary on thermal neutron dose rate. The results of Monte Cario and multigroup calculations are compared with experimental values. The predicted boundary effect for fast neutrons of 7.3% agrees within 16% with the measured effect of 6.3%. The gamma detector did not measure a boundary effect because it lacked sensitivity at low energies. However, the effect predicted for gamma rays of 5 to 10% is asmore » large as that for neutrons. An estimate of the boundary effect for thermal neutrons from a PoBe source is obtained from the results of muitigroup diffusion theory calcuiations for a reactor source. The calculated boundary effect agrees within 13% with the measured values. (auth)« less

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.

Simulations of Xe and U diffusion in UO2

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

Andersson, Anders D.; Vyas, Shyam; Tonks, Michael R.

2012-09-10

Diffusion of xenon (Xe) and uranium (U) in UO{sub 2} is controlled by vacancy mechanisms and under irradiation the formation of mobile vacancy clusters is important. Based on the vacancy and cluster diffusion mechanisms established from density functional theory (DFT) calculations, we derive continuum thermodynamic and diffusion models for Xe and U in UO{sub 2}. In order to capture the effects of irradiation, vacancies (Va) are explicitly coupled to the Xe and U dynamics. Segregation of defects to grain boundaries in UO{sub 2} is described by combining the bulk diffusion model with models of the interaction between Xe atoms andmore » vacancies with grain boundaries, which were derived from atomistic calculations. The diffusion and segregation models were implemented in the MOOSE-Bison-Marmot (MBM) finite element (FEM) framework and the Xe/U redistribution was simulated for a few simple microstructures.« less

Diffusion and related transport mechanisms in brain tissue

NASA Astrophysics Data System (ADS)

Nicholson, Charles

2001-07-01

Diffusion plays a crucial role in brain function. The spaces between cells can be likened to the water phase of a foam and many substances move within this complicated region. Diffusion in this interstitial space can be accurately modelled with appropriate modifications of classical equations and quantified from measurements based on novel micro-techniques. Besides delivering glucose and oxygen from the vascular system to brain cells, diffusion also moves informational substances between cells, a process known as volume transmission. Deviations from expected results reveal how local uptake, degradation or bulk flow may modify the transport of molecules. Diffusion is also essential to many therapies that deliver drugs to the brain. The diffusion-generated concentration distributions of well-chosen molecules also reveal the structure of brain tissue. This structure is represented by the volume fraction (void space) and the tortuosity (hindrance to diffusion imposed by local boundaries or local viscosity). Analysis of these parameters also reveals how the local geometry of the brain changes with time or under pathological conditions. Theoretical and experimental approaches borrow from classical diffusion theory and from porous media concepts. Earlier studies were based on radiotracers but the recent methods use a point-source paradigm coupled with micro-sensors or optical imaging of macromolecules labelled with fluorescent tags. These concepts and methods are likely to be applicable elsewhere to measure diffusion properties in very small volumes of highly structured but delicate material.

Diffusion in coronas around clinopyroxene: modelling with local equilibrium and steady state, and a non-steady-state modification to account for zoned actinolite-hornblende

NASA Astrophysics Data System (ADS)

Ashworth, J. R.; Birdi, J. J.; Emmett, T. F.

1992-01-01

Retrograde coronas of Caledonian age, between clinopyroxene and plagioclase in the Jotun Nappe Complex, Norway, illustrate the effects of diffusion kinetics on mineral distributions among layers and on the compositions of hornblende-actinolite. One corona type comprises a symplectite of epidote + quartz adjacent to plagioclase, and a less well-organized intergrowth of amphibole + quartz replacing clinopyroxene. The observed mineral proportions imply an open-system reaction, but the similarity of Al/Si ratios in reactant plagioclase and product symplectite indicates approximate conservation of Al2O3 and SiO2. The largest inferred open-system flux is a loss of CaO, mostly derived from consumption of clinopyroxene. The approximate layer structure, Pl|Ep + Qtz|Hbl + Qtz|Act±Hbl + Qtz|Cpx, is modelled using the theory of steady-state diffusion-controlled growth with local equilibrium. To obtain a solution, it is necessary to use a reactant plagioclase composition which takes into account aluminous (epidote) inclusions. The results indicate that, in terms of Onsager diffusion coefficients L ii , Ca is more mobile than AL ( L CaCa/ L AlAl≳3.) (where ≳ means greater than or approximately equal to). This behaviour of Ca is comparable with that of Mg in previously studied coronas around olivine. Si is non-diffusing in the present modelling, because of silica saturation. Oxidation of some Fe2+ to Fe3+ occurs within the corona. Mg diffuses towards its source (clinopyroxene) to maintain local equilibrium. Other coronas consist of two layers, hornblende adjacent to plagioclase and zoned amphibole + quartz adjacent to clinopyroxene. In the zoned layer, actinolitic hornblende forms relict patches, separated from quartz blebs by more aluminous hornblende. A preliminary steady-state, local-equilibrium model of grain-boundary diffusion explains the formation of low-Al and high-Al layers as due to Al immobility. Zoning and replacement are qualitatively explained in terms of evolution of actinolite to more stable aluminous compositions. This is modelled by a non-steady-state modification of the theory, retaining local equilibrium in grain boundaries while relatively steep zoning profiles develop in grain interiors through slow intracrystalline diffusion. Replacement of actinolite by hornblende does not require a change in P- T conditions if actinolite is a kinetically determined, non-equilibrium product. The common preservation of a sharp contact between hornblende and actionolite layers may be explained by ineffectiveness of intracrystalline diffusion: according to the theory, given sufficient grain-boundary Al flux, a metastable actinolite + quartz layer in contact with hornblende may be diffusionally stable and may continue to grow in a steady state.

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations.

PubMed

Rugonyi, Sandra

2008-04-01

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.

Turing instability in reaction-diffusion systems with nonlinear diffusion

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

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

2013-10-15

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

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

DOE PAGES

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

2015-09-30

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

Diffusion at the boundary between the film and substrate upon the electrocrystallization of zinc on a copper substrate

NASA Astrophysics Data System (ADS)

Shtapenko, E. Ph.; Zabludovsky, V. A.; Dudkina, V. V.

2015-03-01

In this paper, we present the results of experimental investigations of the diffusion layer formed at the film-substrate interface upon the electrodeposition of zinc films on a copper substrate. The investigations have shown that, in the transient layer, the deposited metal is diffused into the material of the substrate. The depth of the diffusion layer and, consequently, the concentrations of the incorporated zinc atoms depend strongly on the conditions of electrocrystallization, which vary from 1.5 μm when using direct current to 4 μm when using direct current in combination with laser-stimulated deposition (LSD). The X-ray diffraction investigations of the transient layer at the film-substrate interface have shown that, upon electrocrystallization using pulsed current in rigid regimes with the application of the LSD, a CuZn2 phase is formed in the diffusion layer. This indicates that the diffusion of zinc into copper occurs via two mechanisms, i.e., grainboundary and bulk. The obtained values of the coefficient of diffusion of zinc adatoms in polycrystalline copper are equal to 1.75 × 10-15 m2/s when using direct current and 1.74 × 10-13 m2/s when using LSD.

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-09-30

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

Reproducing the observed energy-dependent structure of Earth's electron radiation belts during storm recovery with an event-specific diffusion model

DOE PAGES

Ripoll, J. -F.; Reeves, Geoffrey D.; Cunningham, Gregory Scott; ...

2016-06-11

Here, we present dynamic simulations of energy-dependent losses in the radiation belt “slot region” and the formation of the two-belt structure for the quiet days after the 1 March storm. The simulations combine radial diffusion with a realistic scattering model, based data-driven spatially and temporally resolved whistler-mode hiss wave observations from the Van Allen Probes satellites. The simulations reproduce Van Allen Probes observations for all energies and L shells (2–6) including (a) the strong energy dependence to the radiation belt dynamics (b) an energy-dependent outer boundary to the inner zone that extends to higher L shells at lower energies andmore » (c) an “S-shaped” energy-dependent inner boundary to the outer zone that results from the competition between diffusive radial transport and losses. We find that the characteristic energy-dependent structure of the radiation belts and slot region is dynamic and can be formed gradually in ~15 days, although the “S shape” can also be reproduced by assuming equilibrium conditions. The highest-energy electrons (E > 300 keV) of the inner region of the outer belt (L ~ 4–5) also constantly decay, demonstrating that hiss wave scattering affects the outer belt during times of extended plasmasphere. Through these simulations, we explain the full structure in energy and L shell of the belts and the slot formation by hiss scattering during storm recovery. We show the power and complexity of looking dynamically at the effects over all energies and L shells and the need for using data-driven and event-specific conditions.« less

Do We Really Need Sinusoidal Surface Temperatures to Apply Heat Tracing Techniques to Estimate Streambed Fluid Fluxes?

NASA Astrophysics Data System (ADS)

Luce, C. H.; Tonina, D.; Applebee, R.; DeWeese, T.

2017-12-01

Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes, thermal conductivity, or bed surface elevation from temperature time series in streambeds are that the solution assumes that 1) the surface boundary condition is a sine wave or nearly so, and 2) there is no gradient in mean temperature with depth. Concerns on these subjects are phrased in various ways, including non-stationarity in frequency, amplitude, or phase. Although the mathematical posing of the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we re-derive the inverse solution of the 1-D advection-diffusion equation starting with an arbitrary surface boundary condition for temperature. In doing so, we demonstrate the frequency-independence of the solution, meaning any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes, gradients in the mean temperature with depth, or `non-stationary' amplitude and frequency (or phase) do not actually represent violations of assumptions, and they should not cause errors in estimates when using one of the suite of existing solution methods derived based on a single frequency. Misattribution of errors to these issues constrains progress on solving real sources of error. Numerical and physical experiments are used to verify this conclusion and consider the utility of information at `non-standard' frequencies and multiple frequencies to augment the information derived from time series of temperature.

Mathematical modelling of the Phloem: the importance of diffusion on sugar transport at osmotic equilibrium.

PubMed

Payvandi, S; Daly, K R; Zygalakis, K C; Roose, T

2014-11-01

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.

Damage Accumulation in Silica Glass Nanofibers.

PubMed

Bonfanti, Silvia; Ferrero, Ezequiel E; Sellerio, Alessandro L; Guerra, Roberto; Zapperi, Stefano

2018-06-06

The origin of the brittle-to-ductile transition, experimentally observed in amorphous silica nanofibers as the sample size is reduced, is still debated. Here we investigate the issue by extensive molecular dynamics simulations at low and room temperatures for a broad range of sample sizes, with open and periodic boundary conditions. Our results show that small sample-size enhanced ductility is primarily due to diffuse damage accumulation, that for larger samples leads to brittle catastrophic failure. Surface effects such as boundary fluidization contribute to ductility at room temperature by promoting necking, but are not the main driver of the transition. Our results suggest that the experimentally observed size-induced ductility of silica nanofibers is a manifestation of finite-size criticality, as expected in general for quasi-brittle disordered networks.

Three-dimensional Monte Carlo model of pulsed-laser treatment of cutaneous vascular lesions

NASA Astrophysics Data System (ADS)

Milanič, Matija; Majaron, Boris

2011-12-01

We present a three-dimensional Monte Carlo model of optical transport in skin with a novel approach to treatment of side boundaries of the volume of interest. This represents an effective way to overcome the inherent limitations of ``escape'' and ``mirror'' boundary conditions and enables high-resolution modeling of skin inclusions with complex geometries and arbitrary irradiation patterns. The optical model correctly reproduces measured values of diffuse reflectance for normal skin. When coupled with a sophisticated model of thermal transport and tissue coagulation kinetics, it also reproduces realistic values of radiant exposure thresholds for epidermal injury and for photocoagulation of port wine stain blood vessels in various skin phototypes, with or without application of cryogen spray cooling.

Forest Canopy Processes in a Regional Chemical Transport Model

NASA Astrophysics Data System (ADS)

Makar, Paul; Staebler, Ralf; Akingunola, Ayodeji; Zhang, Junhua; McLinden, Chris; Kharol, Shailesh; Moran, Michael; Robichaud, Alain; Zhang, Leiming; Stroud, Craig; Pabla, Balbir; Cheung, Philip

2016-04-01

Forest canopies have typically been absent or highly parameterized in regional chemical transport models. Some forest-related processes are often considered - for example, biogenic emissions from the forests are included as a flux lower boundary condition on vertical diffusion, as is deposition to vegetation. However, real forest canopies comprise a much more complicated set of processes, at scales below the "transport model-resolved scale" of vertical levels usually employed in regional transport models. Advective and diffusive transport within the forest canopy typically scale with the height of the canopy, and the former process tends to dominate over the latter. Emissions of biogenic hydrocarbons arise from the foliage, which may be located tens of metres above the surface, while emissions of biogenic nitric oxide from decaying plant matter are located at the surface - in contrast to the surface flux boundary condition usually employed in chemical transport models. Deposition, similarly, is usually parameterized as a flux boundary condition, but may be differentiated between fluxes to vegetation and fluxes to the surface when the canopy scale is considered. The chemical environment also changes within forest canopies: shading, temperature, and relativity humidity changes with height within the canopy may influence chemical reaction rates. These processes have been observed in a host of measurement studies, and have been simulated using site-specific one-dimensional forest canopy models. Their influence on regional scale chemistry has been unknown, until now. In this work, we describe the results of the first attempt to include complex canopy processes within a regional chemical transport model (GEM-MACH). The original model core was subdivided into "canopy" and "non-canopy" subdomains. In the former, three additional near-surface layers based on spatially and seasonally varying satellite-derived canopy height and leaf area index were added to the original model structure. Process methodology for deposition, biogenic emissions, shading, vertical diffusion, advection, chemical reactive environment and particle microphysics were modified to account for expected conditions within the forest canopy and the additional layers. The revised and original models were compared for a 10km resolution domain covering North America, for a one-month duration simulation. The canopy processes were found to have a very significant impact on model results. We will present a comparison to network observations which suggests that forest canopy processes may account for previously unexplained local and regional biases in model ozone predictions noted in GEM-MACH and other models. The impact of the canopy processes on NO2, PM2.5, and SO2 performance will also be presented and discussed.

A transfer function type of simplified electrochemical model with modified boundary conditions and Padé approximation for Li-ion battery: Part 1. lithium concentration estimation

NASA Astrophysics Data System (ADS)

Yuan, Shifei; Jiang, Lei; Yin, Chengliang; Wu, Hongjie; Zhang, Xi

2017-06-01

To guarantee the safety, high efficiency and long lifetime for lithium-ion battery, an advanced battery management system requires a physics-meaningful yet computationally efficient battery model. The pseudo-two dimensional (P2D) electrochemical model can provide physical information about the lithium concentration and potential distributions across the cell dimension. However, the extensive computation burden caused by the temporal and spatial discretization limits its real-time application. In this research, we propose a new simplified electrochemical model (SEM) by modifying the boundary conditions for electrolyte diffusion equations, which significantly facilitates the analytical solving process. Then to obtain a reduced order transfer function, the Padé approximation method is adopted to simplify the derived transcendental impedance solution. The proposed model with the reduced order transfer function can be briefly computable and preserve physical meanings through the presence of parameters such as the solid/electrolyte diffusion coefficients (Ds&De) and particle radius. The simulation illustrates that the proposed simplified model maintains high accuracy for electrolyte phase concentration (Ce) predictions, saying 0.8% and 0.24% modeling error respectively, when compared to the rigorous model under 1C-rate pulse charge/discharge and urban dynamometer driving schedule (UDDS) profiles. Meanwhile, this simplified model yields significantly reduced computational burden, which benefits its real-time application.