Measurement of Solute Diffusion Behavior in Fractured Waste Glass Media

International Nuclear Information System (INIS)

Saripalli, Kanaka P.; Lindberg, Michael J.; Meyer, Philip D.

2008-01-01

Determination of aqueous phase diffusion coefficients of solutes through fractured media is essential for understanding and modeling contaminants transport at many hazardous waste disposal sites. No methods for earlier measurements are available for the characterization of diffusion in fractured glass blocks. We report here the use of time-lag diffusion experimental method to assess the diffusion behavior of three different solutes (Cs, Sr and Pentafluoro Benzoic Acid or PFBA) in fractured, immobilized low activity waste (ILAW) glass forms. A fractured media time-lag diffusion experimental apparatus that allows the measurement of diffusion coefficients has been designed and built for this purpose. Use of time-lag diffusion method, a considerably easier experimental method than the other available methods, was not previously demonstrated for measuring diffusion in any fractured media. Hydraulic conductivity, porosity and diffusion coefficients of a solute were experimentally measured in fractured glass blocks using this method for the first time. Results agree with the range of properties reported for similar rock media earlier, indicating that the time-lag experimental method can effectively characterize the diffusion coefficients of fractured ILAW glass media

Analytical solutions of one-dimensional advection–diffusion

Indian Academy of Sciences (India)

Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the ...

Thermal diffusivity of samarium-gadolinium zirconate solid solutions

International Nuclear Information System (INIS)

Pan, W.; Wan, C.L.; Xu, Q.; Wang, J.D.; Qu, Z.X.

2007-01-01

We synthesized samarium-gadolinium zirconate solid solutions and determined their thermal diffusivities, Young's moduli and thermal expansion coefficients, which are very important for their application in thermal barrier coatings. Samarium-gadolinium zirconate solid solutions have extremely low thermal diffusivity between 20 and 600 deg. C. The solid solutions have lower Young's moduli and higher thermal expansion coefficients than those of pure samarium and gadolinium zirconates. This combination of characteristics is promising for the application of samarium and gadolinium zirconates in gas turbines. The mechanism of phonon scattering by point defects is discussed

Diffusion of nanoparticles in solution through elastomeric membrane

International Nuclear Information System (INIS)

Zemzem, Mohamed; Vinches, Ludwig; Hallé, Stéphane

2017-01-01

Diffusion phenomena encountered in mass transfer of liquids play an important role in many technological processes of polymer manufacturing and use. In addition and alongside the notable growth of nanoparticles use, particularly when in suspension in liquid solutions, it has become important to pay some attention to their interactions with polymeric structures. The aim of this work is to evaluate some diffusion parameters of gold nanoparticle solutions as well as of their liquid carrier (water) through elastomeric membranes. Gravimetric method was chosen as the main technique to quantify swelling phenomena and to assess kinetic properties. The dynamic liquid uptake measurements were conducted on gold nanoparticles (5 nm and 50 nm in diameter) in aqueous solutions when brought into contact with two types of nitrile material samples. Results showed that diffusion mechanism of the liquids lies between Fickian and sub-Fickian modes. Slight deviations were noticed with the gold nanoparticle solutions. A growth in liquid interaction with the rubbery structure in presence of the nanoparticles was also observed from comparison of K factor (characteristic of the elastomer-liquid interaction). Difference between the characteristics of the two membranes was also reported using this parameter. Besides, diffusion coefficients testified the impact of the membrane thickness on the penetration process, while no significant effect of the nature of the nanoparticle solution can be seen on this coefficient. (paper)

Diffusion of nanoparticles in solution through elastomeric membrane

Science.gov (United States)

Zemzem, Mohamed; Vinches, Ludwig; Hallé, Stéphane

2017-04-01

Diffusion phenomena encountered in mass transfer of liquids play an important role in many technological processes of polymer manufacturing and use. In addition and alongside the notable growth of nanoparticles use, particularly when in suspension in liquid solutions, it has become important to pay some attention to their interactions with polymeric structures. The aim of this work is to evaluate some diffusion parameters of gold nanoparticle solutions as well as of their liquid carrier (water) through elastomeric membranes. Gravimetric method was chosen as the main technique to quantify swelling phenomena and to assess kinetic properties. The dynamic liquid uptake measurements were conducted on gold nanoparticles (5 nm and 50 nm in diameter) in aqueous solutions when brought into contact with two types of nitrile material samples. Results showed that diffusion mechanism of the liquids lies between Fickian and sub-Fickian modes. Slight deviations were noticed with the gold nanoparticle solutions. A growth in liquid interaction with the rubbery structure in presence of the nanoparticles was also observed from comparison of K factor (characteristic of the elastomer-liquid interaction). Difference between the characteristics of the two membranes was also reported using this parameter. Besides, diffusion coefficients testified the impact of the membrane thickness on the penetration process, while no significant effect of the nature of the nanoparticle solution can be seen on this coefficient.

Conformational analysis of a Chlamydia-specific disaccharide {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo-(2{sup {yields}}O)-allyl in aqueous solution and bound to a monoclonal antibody: Observation of intermolecular transfer NOEs

Energy Technology Data Exchange (ETDEWEB)

Sokolowski, Tobias; Haselhorst, Thomas; Scheffler, Karoline [Medizinische Universitaet, Institut fuer Chemie (Germany); Weisemann, Ruediger [Bruker Analytik GmbH, Silberstreifen (Germany); Kosma, Paul [Institut fuer Chemie der Universitaet fuer Bodenkultur Wien (Austria); Brade, Helmut; Brade, Lore [Forschungszentrum Borstel, Zentrum fuer Medizin und Biowissenschaften Parkallee 22 (Germany); Peters, Thomas [Medizinische Universitaet, Institut fuer Chemie (Germany)

1998-07-15

The disaccharide {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo (Kdo: 3-deoxy-d-manno-oct-2-ulosonic acid) represents a genus-specific epitope of the lipopolysaccharide of the obligate intracellular human pathogen Chlamydia. The conformation of the synthetically derived disaccharide {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo-(2{sup {yields}}O)-allyl was studied in aqueous solution, and complexed to a monoclonal antibody S25-2. Various NMR experiments based on the detection of NOEs (or transfer NOEs) and ROEs (or transfer ROEs) were performed. A major problem was the extensive overlap of almost all {sup 1}H NMR signals of {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo-(2{sup {yields}}O)-allyl. To overcome this difficulty, HMQC-NOESY and HMQC-trNOESY experiments were employed. Spin diffusion effects were identified using trROESY experiments, QUIET-trNOESY experiments and MINSY experiments. It was found that protein protons contribute to the observed spin diffusion effects. At 800 MHz, intermolecular trNOEs were observed between ligand protons and aromatic protons in the antibody binding site. From NMR experiments and Metropolis Monte Carlo simulations, it was concluded that {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo-(2{sup {yields}}O)-allyl in aqueous solution exists as a complex conformational mixture. Upon binding to the monoclonal antibody S25-2, only a limited range of conformations is available to {alpha}-Kdo-(2{sup {yields}}8)-{alpha}-Kdo-(2{sup {yields}}O)-allyl. These possible bound conformations were derived from a distance geometry analysis using transfer NOEs as experimental constraints. It is clear that a conformation is selected which lies within a part of the conformational space that is highly populated in solution. This conformational space also includes the conformation found in the crystal structure. Our results provide a basis for modeling studies of the antibody-disaccharide complex.

Anomalous diffusion in niobium. Study of solute diffusion mechanism of iron in niobium

International Nuclear Information System (INIS)

Ablitzer, D.

1977-01-01

In order to explain anomalously high diffusion velocities observed for iron diffusion in niobium, the following parameters were measured: isotope effect, b factor (which expresses the effect of iron on niobium self-diffusion), self-diffusion coefficient of niobium, solute diffusion coefficient of iron in niobium. The results obtained show that neither pure vacancy models, nor diffusion in the lattice defects (dislocations, sub-boundaries, grain boundaries), nor pure interstitialy mechanisms, nor simple or cyclic exchange mechanisms agree with experiments. A mechanism is proposed which considers an equilibrium between substitution iron atoms and interstitial iron atoms. The diffusion of iron then occurs through interstitial vancancy pairs [fr

Free diffusion of translation of macromolecules in solution with the rayleigh interferometer; Diffusion libre de translation des macromolecules en solution, par interferometrie de rayleigh

Energy Technology Data Exchange (ETDEWEB)

Leger, J J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1969-07-01

The aim of this study is to develop a rapid and accurate measurement, with the Rayleigh interferometer, of the free diffusion coefficient of translation of macromolecules in solution. After having explained the choice of a diffusion cell with laminar lateral flow, and explained the principle of the Rayleigh interferometer, a semi-automatic technique of free diffusion are then introduced. Solutions are proposed for systems composed of two or three components, such as biopolymers. The paper ends by drafting the possible treatment of recorded experimental data by means of electronic computer. (author) [French] Cette etude a ete entreprise pour mettre au point une methode precise et rapide de mesure, par interferometre de Rayleigh, du coefficient de diffusion libre de translation des macromolecules en solution. Apres avoir justifie le choix d'une cellule de diffusion a ecoulement laminaire lateral et explique le principe de l'interferometre de Rayleigh, l'auteur decrit une technique semi-automatique d'enregistrement des cliches d'interference. Il introduit ensuite les equations differentielles de diffusion libre et propose des solutions pour les systemes a deux et trois composants applicables aux biopolymeres. L'article se termine par une esquisse concernant le traitement des donnees experimentales enregistrees au moyen du calcul electronique. (auteur)

Traveling wave solutions for reaction-diffusion systems

DEFF Research Database (Denmark)

Lin, Zhigui; Pedersen, Michael; Tian, Canrong

2010-01-01

This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions...

Solutes and cells - aspects of advection-diffusion-reaction phenomena in biochips

DEFF Research Database (Denmark)

Vedel, Søren

2012-01-01

the dependencies on density. This shows that the varied single-cell behavior including the overall modulations imposed by density arise as a natural consequence of pseudopod-driven motility in a social context. The final subproject concerns the combined effects of advection, diffusion and reaction of several......Cell’), and the overall title of the project is Solutes and cells — aspects of advection-diffusion-reaction phenomena in biochips. The work has consisted of several projects focusing on theory, and to some extend analysis of experimental data, with advection-diffusion-reaction phenomena of solutes as the recurring theme...... quantitatively interpret the proximal concentration of specific solutes, and integrate this to achieve biological functions. In three specific examples, the author and co-workers have investigated different aspects of the influence of advection, diffusion and reaction on solute distributions, as well...

The analytical solution to the 1D diffusion equation in heterogeneous media

International Nuclear Information System (INIS)

Ganapol, B.D.; Nigg, D.W.

2011-01-01

The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)

Solution of diffusion equation in deformable spheroids

Energy Technology Data Exchange (ETDEWEB)

Ayyoubzadeh, Seyed Mohsen [Department of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Safari, Mohammad Javad, E-mail: iFluka@gmail.com [Department of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Vosoughi, Naser [Department of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

2011-05-15

Research highlights: > Developing an explicit solution for the diffusion equation in spheroidal geometry. > Proving an orthogonality relation for spheroidal eigenfunctions. > Developing a relation for the extrapolation distance in spheroidal geometry. > Considering the sphere and slab as limiting cases for a spheroid. > Cross-validation of the analytical solution with Monte Carlo simulations. - Abstract: The time-dependent diffusion of neutrons in a spheroid as a function of the focal distance has been studied. The solution is based on an orthogonal basis and an extrapolation distanced related boundary condition for the spheroidal geometry. It has been shown that spheres and disks are two limiting cases for the spheroids, for which there is a smooth transition for the systems properties between these two limits. Furthermore, it is demonstrated that a slight deformation from a sphere does not affect the fundamental mode properties, to the first order. The calculations for both multiplying and non-multiplying media have been undertaken, showing good agreement with direct Monte Carlo simulations.

Numerical solution of a reaction-diffusion equation

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2000-01-01

The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

Mutual diffusion of sodium hyaluranate in aqueous solutions

International Nuclear Information System (INIS)

Veríssimo, Luís M.P.; Valada, Teresa I.C.; Sobral, Abilio J.F.N.; Azevedo, Eduarda E.F.G.; Azevedo, Maria L.G.; Ribeiro, Ana C.F.

2014-01-01

Highlights: • Binary diffusion coefficients for the systems containing sodium hyaluronate. • Influence of the aggregation on diffusion of the sodium hyaluronate in the aqueous media. • Estimation of the thermodynamic and mobility factors from mutual diffusion. -- Abstract: The Taylor dispersion technique has been used for measuring mutual diffusion coefficients of sodium hyaluronate in aqueous solutions at T = 298.15 K, and concentrations ranging from (0.00 to 0.50) g · dm −3 . The results are interpreted on the basis of Nernst, and Onsager and Fuoss theoretical equations. From the diffusion coefficient at infinitesimal concentration, the limiting ionic conductivity and the tracer diffusion coefficient of hyaluronate ion were estimated. These studies have been complemented by molecular mechanics calculations

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

Solid solution strengthening and diffusion in nickel- and cobalt-based superalloys

Energy Technology Data Exchange (ETDEWEB)

Rehman, Hamad ur

2016-07-01

Nickel and cobalt-based superalloys with a γ-γ{sup '} microstructure are known for their excellent creep resistance at high temperatures. Their microstructure is engineered using different alloying elements, that partition either to the fcc γ matrix or to the ordered γ{sup '} phase. In the present work the effect of alloying elements on their segregation behaviour in nickel-based superalloys, diffusion in cobalt-based superalloys and the temperature dependent solid solution strengthening in nickel-based alloys is investigated. The effect of dendritic segregation on the local mechanical properties of individual phases in the as-cast, heat treated and creep deformed state of a nickel-based superalloy is investigated. The local chemical composition is characterized using Electron Probe Micro Analysis and then correlated with the mechanical properties of individual phases using nanoindentation. Furthermore, the temperature dependant solid solution hardening contribution of Ta, W and Re towards fcc nickel is studied. The room temperature hardening is determined by a diffusion couple approach using nanoindentation and energy dispersive X-ray analysis for relating hardness to the chemical composition. The high temperature properties are determined using compression strain rate jump tests. The results show that at lower temperatures, the solute size is prevalent and the elements with the largest size difference with nickel, induce the greatest hardening consistent with a classical solid solution strengthening theory. At higher temperatures, the solutes interact with the dislocations such that the slowest diffusing solute poses maximal resistance to dislocation glide and climb. Lastly, the diffusion of different technically relevant solutes in fcc cobalt is investigated using diffusion couples. The results show that the large atoms diffuse faster in cobalt-based superalloys similar to their nickel-based counterparts.

Solid solution strengthening and diffusion in nickel- and cobalt-based superalloys

International Nuclear Information System (INIS)

Rehman, Hamad ur

2016-01-01

Nickel and cobalt-based superalloys with a γ-γ ' microstructure are known for their excellent creep resistance at high temperatures. Their microstructure is engineered using different alloying elements, that partition either to the fcc γ matrix or to the ordered γ ' phase. In the present work the effect of alloying elements on their segregation behaviour in nickel-based superalloys, diffusion in cobalt-based superalloys and the temperature dependent solid solution strengthening in nickel-based alloys is investigated. The effect of dendritic segregation on the local mechanical properties of individual phases in the as-cast, heat treated and creep deformed state of a nickel-based superalloy is investigated. The local chemical composition is characterized using Electron Probe Micro Analysis and then correlated with the mechanical properties of individual phases using nanoindentation. Furthermore, the temperature dependant solid solution hardening contribution of Ta, W and Re towards fcc nickel is studied. The room temperature hardening is determined by a diffusion couple approach using nanoindentation and energy dispersive X-ray analysis for relating hardness to the chemical composition. The high temperature properties are determined using compression strain rate jump tests. The results show that at lower temperatures, the solute size is prevalent and the elements with the largest size difference with nickel, induce the greatest hardening consistent with a classical solid solution strengthening theory. At higher temperatures, the solutes interact with the dislocations such that the slowest diffusing solute poses maximal resistance to dislocation glide and climb. Lastly, the diffusion of different technically relevant solutes in fcc cobalt is investigated using diffusion couples. The results show that the large atoms diffuse faster in cobalt-based superalloys similar to their nickel-based counterparts.

Effect of potassium chloride on diffusion of theophylline at T = 298.15 K

Energy Technology Data Exchange (ETDEWEB)

Santos, Cecilia I.A.V., E-mail: cecilia.alves@uah.e [Departamento de Quimica Fisica, Facultad de Farmacia, Universidad de Alcala, 28871 Alcala de Henares, Madrid (Spain); Lobo, Victor M.M., E-mail: vlobo@ci.uc.p [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal); Esteso, Miguel A., E-mail: miguel.esteso@uah.e [Departamento de Quimica Fisica, Facultad de Farmacia, Universidad de Alcala, 28871 Alcala de Henares, Madrid (Spain); Ribeiro, Ana C.F., E-mail: anacfrib@ci.uc.p [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal)

2011-06-15

Research highlights: {yields} Mutual diffusion coefficients of theophylline in aqueous dilute solutions. {yields} Influence of the presence of potassium chloride in the aqueous media. {yields} Estimation of the association constant, K, between THP and KCl. - Abstract: Ternary mutual diffusion coefficients measured by Taylor dispersion method (D{sub 11}, D{sub 22}, D{sub 12}, and D{sub 21}) are reported for aqueous solutions of KCl + theophylline (THP) at T = 298.15 K at carrier concentrations from (0.000 to 0.010) mol {center_dot} dm{sup -3}, for each solute. These diffusion coefficients have been measured having in mind a better understanding of the structure of these systems and the thermodynamic behavior of potassium chloride and theophylline in solution. For example, from these data it will be possible to make conclusions about the influence of this electrolyte in diffusion of THP and to estimate some parameters, such as the diffusion coefficient of the aggregate between KCl and THP.

Predictability of solute transport in diffusion-controlled hydrogeologic regimes

International Nuclear Information System (INIS)

Gillham, R.W.; Cherry, J.A.

1983-01-01

Hydrogeologic regimes that are favourable for the subsurface management of low-level radioactive wastes must have transport properties that will limit the migration velocity of contaminants to some acceptably low value. Of equal importance, for the purpose of impact assessment and licensing, is the need to be able to predict, with a reasonable degree of certainty and over long time periods, what the migration velocity of the various contaminants of interest will be. This paper presents arguments to show that in addition to having favourable velocity characteristics, transport in saturated, diffusion-controlled hydrogeologic regimes is considerably more predictable than in the most common alternatives. The classical transport models for unsaturated, saturated-advection-controlled and saturated-diffusion-controlled environments are compared, with particular consideration being given to the difficulties associated with the characterization of the respective transport parameters. Results are presented which show that the diffusion of non-reactive solutes and solutes that react according to a constant partitioning ratio (K/sub d/) are highly predictable under laboratory conditions and that the diffusion coefficients for the reactive solutes can be determined with a reasonable degree of accuracy from independent measurements of bulk density, porosity, distribution coefficient and tortuosity. Field evidence is presented which shows that the distribution of environmental isotopes and chloride in thick clayey deposits is consistent with a diffusion-type transport process in these media. These results are particularly important in that they not only demonstrate the occurrence of diffusion-controlled hydrogeologic regimes, but they also demonstrate the predictability of the migration characteristics over very long time periods

Asymptotic solutions of diffusion models for risk reserves

Directory of Open Access Journals (Sweden)

S. Shao

2003-01-01

Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.

Solute redistribution in dendritic solidification with diffusion in the solid

Science.gov (United States)

Ganesan, S.; Poirier, D. R.

1989-01-01

An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion is characterized by the instantaneous and average diffusion parameters. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. Numerical results are presented as an approximate model, which is used to predict the average diffusion parameter and calculate the composition of the interdendritic liquid during solidification.

Periodic solutions in reaction–diffusion equations with time delay

International Nuclear Information System (INIS)

Li, Li

2015-01-01

Spatial diffusion and time delay are two main factors in biological and chemical systems. However, the combined effects of them on diffusion systems are not well studied. As a result, we investigate a nonlinear diffusion system with delay and obtain the existence of the periodic solutions using coincidence degree theory. Moreover, two numerical examples confirm our theoretical results. The obtained results can also be applied in other related fields

Semianalytic Solution of Space-Time Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

ANOVA-HDMR structure of the higher order nodal diffusion solution

International Nuclear Information System (INIS)

Bokov, P. M.; Prinsloo, R. H.; Tomasevic, D. I.

2013-01-01

Nodal diffusion methods still represent a standard in global reactor calculations, but employ some ad-hoc approximations (such as the quadratic leakage approximation) which limit their accuracy in cases where reference quality solutions are sought. In this work we solve the nodal diffusion equations utilizing the so-called higher-order nodal methods to generate reference quality solutions and to decompose the obtained solutions via a technique known as High Dimensional Model Representation (HDMR). This representation and associated decomposition of the solution provides a new formulation of the transverse leakage term. The HDMR structure is investigated via the technique of Analysis of Variance (ANOVA), which indicates why the existing class of transversely-integrated nodal methods prove to be so successful. Furthermore, the analysis leads to a potential solution method for generating reference quality solutions at a much reduced calculational cost, by applying the ANOVA technique to the full higher order solution. (authors)

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

International Nuclear Information System (INIS)

Indekeu, Joseph O; Smets, Ruben

2017-01-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

International Nuclear Information System (INIS)

Guo, Ran; Du, Jiulin

2015-01-01

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

Energy Technology Data Exchange (ETDEWEB)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.

Counterion self-diffusion in polyelectrolyte solutions

Science.gov (United States)

Schipper, F. J. M.; Hollander, J. G.; Leyte, J. C.

1997-12-01

The self-diffusion coefficient of 0953-8984/9/50/019/img1, tetra-methylammonium 0953-8984/9/50/019/img2, tetra-ethylammonium 0953-8984/9/50/019/img3, tetra-propylammonium 0953-8984/9/50/019/img4 and tetra-butylammonium 0953-8984/9/50/019/img5 in solutions of the weak polymethacrylic acid (PMA) were measured with PFG NMR. No additional salt was present in any of the experiments. The polyion concentration and degree of neutralization were varied. The maximum relative counterion self-diffusion coefficient against polyion concentration, that was reported earlier, was observed for both alkali and tetra-alkylammonium 0953-8984/9/50/019/img6 counterions. We propose that the maximum is due to the combination of the obstruction by the polyion and the changing counterion distribution at increasing polyion concentration. An explanation of this proposal is offered in terms of the Poisson - Boltzmann - Smoluchowski (PBS) model for polyelectrolytes. Qualitative agreement of this model with experiment was found for the dependence of the counterion self-diffusion coefficient on the degree of neutralization of the polyion, on counterion radius and on polyion concentration, over a concentration range from 0.01 to 1 0953-8984/9/50/019/img7. Adaption of the theoretical obstruction, to fit the self-diffusion data of the solvent, also greatly improves the model predictions on the counterion self-diffusion.

On matrix diffusion: formulations, solution methods and qualitative effects

Science.gov (United States)

Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi

Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme

Iterative solutions of finite difference diffusion equations

International Nuclear Information System (INIS)

Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

1981-01-01

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

Modified micro-diffusion method for 15N-enriched soil solutions

International Nuclear Information System (INIS)

Aigner, M.

2000-01-01

The preparation of solutions for determination of 15 N/ 14 N isotope ratios is described, with special reference to dilute samples. A micro-diffusion method has been simplified to be more suitable for rapid isotope-ratio determination in soil solutions collected in tensionics. Ammonia expelled during micro-diffusion is captured on acidified filter discs fixed to the caps of gas-tight vials. The discs are transferred to tin capsules for shipment to the Soil Science Unit for 15 N-enrichment determination. (author)

Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions

International Nuclear Information System (INIS)

Ohtani, Nobuo

1976-01-01

A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)

Transport of neutral solute across articular cartilage: the role of zonal diffusivities.

Science.gov (United States)

Arbabi, V; Pouran, B; Weinans, H; Zadpoor, A A

2015-07-01

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute Iodixanol into cartilage was monitored using calibrated microcomputed tomography micro-CT images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Numerical solution of non-linear diffusion problems

International Nuclear Information System (INIS)

Carmen, A. del; Ferreri, J.C.

1998-01-01

This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

Solution of two energy-group neutron diffusion equation by triangular elements

International Nuclear Information System (INIS)

Correia Filho, A.

1981-01-01

The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

KAUST Repository

CARRILLO, JOSÉ ANTONIO

2012-12-01

A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.

Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

International Nuclear Information System (INIS)

Chakraverty, S.; Tapaswini, Smita

2014-01-01

The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < α ≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases. (general)

Free diffusion of translation of macromolecules in solution with the rayleigh interferometer

International Nuclear Information System (INIS)

Leger, J.J.

1969-01-01

The aim of this study is to develop a rapid and accurate measurement, with the Rayleigh interferometer, of the free diffusion coefficient of translation of macromolecules in solution. After having explained the choice of a diffusion cell with laminar lateral flow, and explained the principle of the Rayleigh interferometer, a semi-automatic technique of free diffusion are then introduced. Solutions are proposed for systems composed of two or three components, such as biopolymers. The paper ends by drafting the possible treatment of recorded experimental data by means of electronic computer. (author) [fr

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

OpenAIRE

Elsaid, A.; Abdel Latif, M. S.; Maneea, M.

2016-01-01

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on ...

Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

Indian Academy of Sciences (India)

constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

Calculated yields of ammonia in the radiolysis of deoxygenated solutions of glycylglycine

International Nuclear Information System (INIS)

Bolch, W.E.; Turner, J.E.; Yoshida, H.; Jacobson, K.B.

1988-01-01

This paper presents detailed Monte Carlo simulations of physical and chemical interactions occurring within electron tracks in deoxygenated solutions of glycylglycine. Hydrated electrons produced within these tracks react with the solute to produce ammonia and a peptide secondary free radical. Calculated yields of ammonia are presented for a range of solute concentrations and electron energies. Excellent agreement is found between calculated and measured yields of ammonia in solutions irradiated by 250-kVp x-rays and 60 Co gamma rays. 12 refs., 5 figs

Solutions for a diffusion equation with a backbone term

International Nuclear Information System (INIS)

Tateishi, A A; Lenzi, E K; Ribeiro, H V; Evangelista, L R; Mendes, R S; Da Silva, L R

2011-01-01

We investigate the diffusion equation ∂ t ρ=D y ∂ y 2 ρ+D x ∂ x 2 ρ+ D-bar x δ(y)∂ x μ ρ subjected to the boundary conditions ρ(±∞,y;t)=0 and ρ(x,±∞;t)=0, and the initial condition ρ(x,y;0)= ρ-hat (x,y). We obtain exact solutions in terms of the Green function approach and analyze the mean square displacement in the x and y directions. This analysis shows an anomalous spreading of the system which is characterized by different diffusive regimes connected to anomalous diffusion

Understanding diffusion of intrinsically disordered proteins in polymer solutions: A disorder plus collapse model

Directory of Open Access Journals (Sweden)

Juan Wang

2017-11-01

Full Text Available Understanding diffusion of intrinsically disordered proteins (IDPs under crowded environments is of ubiquitous importance to modelling related dynamics in biological systems. In the present work, we proposed a theoretical framework to study the diffusion behavior of IDPs in polymer solutions. IDP is modeled as an ensemble of particles with a wide range of gyration radius subject to Flory-Fisk distribution, where the collapse effect which leads to the shrink of IDP due to polymer crowding is included. The diffusion coefficient of IDP is calculated as the average, denoted by 〈D〉, over the values of the particle samples. By properly incorporating the scaling relations for diffusion coefficient of nanoparticle (NP in polymer solutions, we are able to evaluate 〈D〉 straightforwardly and reveal the disorder and collapse effects on IDP’s diffusion in an explicit manner. Particular attentions are paid on comparison between the diffusion coefficient of an IDP and that of a NP. Results demonstrate that both disorder and collapse can enhance IDP diffusion rate. Our analysis shows that the crossover behavior reported by experiments can be actually a general phenomenon, namely, while a NP with smaller size than that of an IDP diffuses faster in simple solutions, the IDP may become the faster one under crowded conditions. We apply our theory to analyze the diffusion of several types of IDP in a few different polymer solutions. Good agreements between the theoretical results and the experimental data are obtained.

An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

Energy Technology Data Exchange (ETDEWEB)

Fisher, A. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bailey, D. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kaiser, T. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eder, D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gunney, B. T. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Masters, N. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Koniges, A. E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Anderson, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-02-01

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L₂ norm.

Solitary wave solutions of selective nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

The quasi-diffusive approximation in transport theory: Local solutions

International Nuclear Information System (INIS)

Celaschi, M.; Montagnini, B.

1995-01-01

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

Existence and stability of periodic solutions for a delayed prey-predator model with diffusion effects

Directory of Open Access Journals (Sweden)

Hongwei Liang

2016-01-01

Full Text Available Existence and stability of spatially periodic solutions for a delay prey-predator diffusion system are concerned in this work. We obtain that the system can generate the spatially nonhomogeneous periodic solutions when the diffusive rates are suitably small. This result demonstrates that the diffusion plays an important role on deriving the complex spatiotemporal dynamics. Meanwhile, the stability of the spatially periodic solutions is also studied. Finally, in order to verify our theoretical results, some numerical simulations are also included.

Shape functions for separable solutions to cross-field diffusion problems

International Nuclear Information System (INIS)

Luning, C.D.; Perry, W.L.

1984-01-01

The shape function S(x), which arises in the study of nonlinear diffusion for cross-field diffusion in plasmas, satisfies the equation S''(x)+lambdaa(x)S/sup α/(x) = 0, 0 0. In the cases of physical interest a(x) possesses an integrable singularity at some point in (0,1) but is otherwise continuous. Existence of a positive solution to this problem is established

Intraparticle diffusion of rare earths in porous ion exchanger rounding by EDTA solution

International Nuclear Information System (INIS)

Ling Daren; Xie Weije

1991-01-01

The self-diffusion of rate earth (RE) isotopes in porous cation exchangers with various radii or different pore structures rounding by EDTA solution was studied. The intraparticle effective diffusivity De was calculated by Boyd's method and Kataoka's bi-disperse pore model, and through further calculation the solid phase diffusivity Dg and macropore diffusivity Dp were also obtained. (author)

On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle

International Nuclear Information System (INIS)

Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.

2011-01-01

In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)

Temperature effects on solute diffusion and adsorption in differently compacted kaolin clay

DEFF Research Database (Denmark)

Mon, Ei Ei; Hamamoto, Shoichiro; Kawamoto, Ken

2016-01-01

Effects of soil temperature on the solute diffusion process in soils are important since subsurface temperature variation affects solute transport such as a fertilizer movement, leaching of salt, and pollutant movement to groundwater aquifers. However, the temperature dependency on the solute dif...

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.

Differential constraints and exact solutions of nonlinear diffusion equations

International Nuclear Information System (INIS)

Kaptsov, Oleg V; Verevkin, Igor V

2003-01-01

The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries

Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

Science.gov (United States)

Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

2002-01-01

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

On Solution of a Fractional Diffusion Equation by Homotopy Transform Method

International Nuclear Information System (INIS)

Salah, A.; Hassan, S.S.A.

2012-01-01

The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

Science.gov (United States)

Ge, Xian-Hui; Sin, Sang-Jin; Tian, Yu; Wu, Shao-Feng; Wu, Shang-Yu

2018-01-01

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ black hole is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension d, exponents z and θ. Remarkably, the case d = θ and z = 2 is a very special in that the charge diffusion D c is a constant and the energy diffusion D e might be ill-defined, but v B 2 τ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

Long-term solute diffusion in a granite block immersed in sea water

International Nuclear Information System (INIS)

Jefferies, N.L.

1988-01-01

Solute diffusion profiles for Cl - , Br - , F - and SO 4 -- have been measured in a granite block which was immersed in the sea at Falmouth, Cornwall, for 30 years. Leachable concentrations of Cl - and Br - were found to be higher in the block than in quarry samples of granite, which demonstrates that solutes from the sea water have diffused into the block. The Cl - and Br - profiles within the block were flat, implying that equilibrium has been reached between the seawater and granite porewater. The apparent diffusion coefficient and the solute accessible porosity have been estimated from these profiles, and these were used to calculate the intrinsic diffusion coefficient which was then compared with previously obtained laboratory data. Concentration profiles for F - and S0 4 -- indicate that these elements have high concentrations at the margins of the block (to depths of up to 15 cm) and are in the process of diffusing outwards into the surrounding seawater. The initially high porewater concentrations of F - and SO 4 -- in the block are believed to result from weathering of the granite prior to its immersion in the sea, due to the breakdown of primary minerals such as pyrite and the micas. F - and SO 4 -- sorptivity has been estimated from an analysis of the porewater concentration profiles. This preliminary experiment has demonstrated the potential for the measurement of solute migration in granite, as a result of the rock having been immersed in seawater. This work is part of the CEC project MIRAGE (radionuclide migration in the geosphere)- Second phase (1985-89) Research area 'Natural analogues'

Comparison of nanoparticle diffusion using fluorescence correlation spectroscopy and differential dynamic microscopy within concentrated polymer solutions

Science.gov (United States)

Shokeen, Namita; Issa, Christopher; Mukhopadhyay, Ashis

2017-12-01

We studied the diffusion of nanoparticles (NPs) within aqueous entangled solutions of polyethylene oxide (PEO) by using two different optical techniques. Fluorescence correlation spectroscopy, a method widely used to investigate nanoparticle dynamics in polymer solution, was used to measure the long-time diffusion coefficient (D) of 25 nm radius particles within high molecular weight, Mw = 600 kg/mol PEO in water solutions. Differential dynamic microscopy (DDM) was used to determine the wave-vector dependent dynamics of NPs within the same polymer solutions. Our results showed good agreement between the two methods, including demonstration of normal diffusion and almost identical diffusion coefficients obtained by both techniques. The research extends the scope of DDM to study the dynamics and rheological properties of soft matter at a nanoscale. The measured diffusion coefficients followed a scaling theory, which can be explained by the coupling between polymer dynamics and NP motion.

Parallel solutions of the two-group neutron diffusion equations

International Nuclear Information System (INIS)

Zee, K.S.; Turinsky, P.J.

1987-01-01

Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

Energy Technology Data Exchange (ETDEWEB)

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)

2015-08-15

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

International Nuclear Information System (INIS)

th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Samin, Adib; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Lahti, Erik; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Zhang, Jinsuo

2015-01-01

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes

Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media

Directory of Open Access Journals (Sweden)

Yu Bai

2015-01-01

Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.

A new scaling for the rotational diffusion of molecular probes in polymer solutions.

Science.gov (United States)

Qing, Jing; Chen, Anpu; Zhao, Nanrong

2017-12-13

In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study. The mean-field theory for depletion effect and semi-empirical scaling equation for the macroscopic viscosity of polymer solutions are properly incorporated to specify the space-dependent concentration and viscosity profiles in the vicinity of the probe surface. Following the scheme of classical fluid mechanics, we numerically evaluate the shear torque exerted on the probes, which then allows us to further calculate the rotational diffusion coefficient D r . Particular attention is given to the scaling behavior of the retardation factor R rot ≡ D/D r with D being the diffusion coefficient in pure solvent. We find that R rot has little relevance to the macroscopic viscosity of the polymer solution, while it can be well featured by the characteristic length scale r h /δ, i.e. the ratio between the hydrodynamic radius of the probe r h and the depletion thickness δ. Correspondingly, we obtain a novel scaling form for the rotational retardation factor, following R rot = exp[a(r h /δ) b ] with rather robust parameters of a ≃ 0.51 and b ≃ 0.56. We apply the theory to an extensive calculation for various probes in specific polymer solutions of poly(ethylene glycol) (PEG) and dextran. Our theoretical results show good agreements with the experimental data, and clearly demonstrate the validity of the new scaling form. In addition, the difference of the scaling behavior between translational and rotational diffusions is clarified, from which we conclude that the depletion effect plays a more significant role on the local rotational diffusion rather than the long-range translation diffusion.

Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

Directory of Open Access Journals (Sweden)

Povstenko YZ

2011-01-01

Full Text Available Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time , the Hankel transform with respect to the radial coordinate , the finite Fourier transform with respect to the angular coordinate , and the exponential Fourier transform with respect to the spatial coordinate . Numerical results are illustrated graphically.

Analytical solution to the hybrid diffusion-transport equation

International Nuclear Information System (INIS)

Nanneh, M.M.; Williams, M.M.R.

1986-01-01

A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

Energy Technology Data Exchange (ETDEWEB)

Telfeyan, Katherine Christina [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ware, Stuart Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-11-06

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Science.gov (United States)

Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.

2018-02-01

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

Directory of Open Access Journals (Sweden)

Said Kouachi

2001-10-01

Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].

The structure and diffusion behaviour of the neurotransmitter γ-aminobutyric acid (GABA) in neutral aqueous solutions

International Nuclear Information System (INIS)

Rodrigo, M.M.; Esteso, M.A.; Barros, M.F.; Verissimo, L.M.P.; Romero, C.M.; Suarez, A.F.; Ramos, M.L.; Valente, A.J.M.; Burrows, H.D.; Ribeiro, A.C.F.

2017-01-01

Highlights: • Diffusion coefficients and densities of binary aqueous solutions of γ-aminobutyric acid (GABA). • Dependence on both shape and size of GABA on its diffusion. • Interactions intramolecular and the solute-water interactions in these systems. - Abstract: GABA (γ-aminobutyric acid) is a non-protein amino acid with important physiological properties, and with considerable relevance to the food and pharmaceutical industries. Particular interest has focused on its role as an inhibitory neurotransmitter in the mammalian cerebral cortex. In this paper, we report density and mutual diffusion coefficients of GABA in non-buffered aqueous solutions (0.001–0.100) mol·dm −3 at 298.15 K. Under these conditions, 1 H and 13 C NMR spectroscopy and pH measurements show that it is present predominantly as a monomeric zwitterionic species. Diffusion coefficients have been computed assuming that this behaves as the binary system GABA/water. From density and intermolecular diffusion coefficients measurements, the molar volume, hydrodynamic radii, R h , diffusion coefficients at infinitesimal concentration, D 0 , activity coefficients and the thermodynamic factors, F T , have been estimated. Within experimental error, the hydrodynamic volume calculated from this is identical to the molar volume obtained from density measurements. From the NMR spectra and literature data, it is suggested that this amino acid diffuses in aqueous solution as a curved, coil-like hydrated zwitterionic entity.

Communication: Modeling of concentration dependent water diffusivity in ionic solutions: Role of intermolecular charge transfer

Energy Technology Data Exchange (ETDEWEB)

Yao, Yi; Berkowitz, Max L., E-mail: maxb@unc.edu, E-mail: ykanai@unc.edu; Kanai, Yosuke, E-mail: maxb@unc.edu, E-mail: ykanai@unc.edu [Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 (United States)

2015-12-28

The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na{sup +} and K{sup +} ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.

Numerical fluid solutions for nonlocal electron transport in hot plasmas: Equivalent diffusion versus nonlocal source

International Nuclear Information System (INIS)

Colombant, Denis; Manheimer, Wallace

2010-01-01

Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

Science.gov (United States)

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Solution-diffusion with defects model for pressure-assisted forward osmosis

KAUST Repository

Duan, Jintang

2014-11-01

An osmosis transport model is presented that combines the standard internal and external concentration polarization equations in the forward osmosis (FO) field with the selective layer transport equations first proposed by Sherwood in 1967. The Sherwood model describes water flux as the sum of a solute-selective, diffusive component driven by the sum of osmotic pressure and hydraulic pressure differences, and a nonselective, convective component driven by hydraulic pressure difference only. This solution-diffusion with defects (SDWD) model and the solution-diffusion (SD) model were compared against data collected using polyamide thin-film-composite (PA-TFC) and integrally-skinned asymmetric cellulose triacetate (CTA) membranes, evaluated in various configurations. When tested with pure water on the porous support side and 1.5. M (π=72.7. bar) sodium chloride solution on the selective layer side, applying 1.25. bar of hydraulic pressure to the porous support side increased water flux by an order of magnitude for PA-TFC membranes, but had negligible effect on CTA membrane flux. These large flux variations can be explained by the SDWD model, but not the SD model. To confirm the existence of defects, a PA-TFC membrane was coated with a uniform, highly water-permeable, nonselective polymer. After coating to block convection through defects, the influence of hydraulic pressure on water flux through this membrane essentially disappeared. Water flux through these defects is low (<1% of total water flux for PA-TFC membranes) and of little consequence in practical FO or reverse osmosis (RO) applications. But in pressure-assisted forward osmosis (PAFO) or pressure-retarded osmosis (PRO), convective transport through defects affects the solute concentration difference across the membrane selective layer, increasing or decreasing water flux through defect-free regions. The presence of defects may explain why membrane power density in PRO is lower than that predicted based on

Interaction between lactose and cadmium chloride in aqueous solutions as seen by diffusion coefficients measurements

International Nuclear Information System (INIS)

Verissimo, Luis M.P.; Gomes, Joselaine C.S.; Romero, Carmen; Esteso, Miguel A.; Sobral, Abilio J.F.N.; Ribeiro, Ana C.F.

2013-01-01

Highlights: ► Diffusion coefficients of aqueous systems containing lactose and cadmium chloride. ► Influence of the lactose on the diffusion of cadmium chloride. ► Interactions between Cd 2+ and lactose. -- Abstract: Diffusion coefficients of an aqueous system containing cadmium chloride 0.100 mol · dm −3 and lactose at different concentrations at 25 °C have been measured, using a conductimetric cell and an automatic apparatus to follow diffusion. The cell relies on an open-ended capillary method and a conductimetric technique is used to follow the diffusion process by measuring the resistance of a solution inside the capillaries, at recorded times. From these results and by ab initio calculations, it was possible to obtain a better understanding of the effect of lactose on transport of cadmium chloride in aqueous solutions

A general solution in the cylindrical coordinates system for the diffusion of a radionuclide in homogeneous and isotropic solids

CERN Document Server

Ribeiro, F B

1999-01-01

Solutions of the diffusion equation in cylindrical coordinates are presented for a radionuclide produced by the decay of a not diffusing parent isotope with arbitrary activity distribution. General initial and Dirichlet boundary conditions are considered and the diffusion equation is solved for a finite cylinder. Solutions corresponding to two particular boundary conditions that can be imposed in laboratory diffusion coefficient measurements are presented. An analysis of the speed of convergence and of the series truncation error is done for these particular solutions. An example of the escape to production ratio derived from one of the solutions is also presented.

A general solution in the cylindrical coordinates system for the diffusion of a radionuclide in homogeneous and isotropic solids

International Nuclear Information System (INIS)

Ribeiro, Fernando Brenha

1999-01-01

Solutions of the diffusion equation in cylindrical coordinates are presented for a radionuclide produced by the decay of a not diffusing parent isotope with arbitrary activity distribution. General initial and Dirichlet boundary conditions are considered and the diffusion equation is solved for a finite cylinder. Solutions corresponding to two particular boundary conditions that can be imposed in laboratory diffusion coefficient measurements are presented. An analysis of the speed of convergence and of the series truncation error is done for these particular solutions. An example of the escape to production ratio derived from one of the solutions is also presented

Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

International Nuclear Information System (INIS)

Litvinenko, Yuri E.; Effenberger, Frederic

2014-01-01

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

Evolution of density profiles for reaction-diffusion processes

International Nuclear Information System (INIS)

Ondarza-Rovira, R.

1990-01-01

The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

A comparison of certain variational solutions of neutron diffusion equation

International Nuclear Information System (INIS)

Altiparmakov, D.V.; Milgram, M.S.

1987-01-01

Using the R-function theory and the variational method of Kantorovich, an approximate solution of the neutron diffusion equation is constructed for a homogeneous spatial domain of arbitrary shape. Calculations have been carried out by five different types of trial functions for certain characteristic domains of polygonal shape (square, triangle, hexagon, rhombus nad L-shaped domain). In the case of non-convex polygons, the consequence of the R-function solution is very poor and a separate treatment of singularity seems to be necessary. Compared to the R-function solution, the singular function development is mathematically more complicated but superior in respect to convergence rate. (author)

An analytical solution describing the shape of a yield stress material subjected to an overpressure

DEFF Research Database (Denmark)

Hovad, Emil; Spangenberg, Jon; Larsen, P.

2016-01-01

as well as the spread length and height of the material when deformed in a box due to gravity. In the present work, the analytical solution is extended with the addition of an overpressure that acts over the entire body of the material. This extension enables finding the shape of a yield stress material......Many fluids and granular materials are able to withstand a limited shear stress without flowing. These materials are known as yields stress materials. Previously, an analytical solution was presented to quantify the yield stress for such materials. The yields stress is obtained based on the density...... with known density and yield stress when for instance deformed under water or subjected to a forced air pressure....

Bulk diffusion and solubility of silver and nickel in lead, lead-silver and lead-nickel solid solutions

International Nuclear Information System (INIS)

Amenzou-Badrour, H.; Moya, G.; Bernardini, J.

1988-01-01

The results of a study of solubility and bulk diffusion of /sup 110/Ag and /sup 63/Ni in lead, lead-silver and lead-nickel solid solutions in the temperature range 220 to 88 0 C are reported. Owing to the low solubility of silver and nickel in lead, Fick's solution corresponding to the boundary condition of a constant concentration of solute at the surface has been used. Depth profile concentration analysis suggests a fundamental difference between the diffusion mechanisms of silver and nickel. Since silver penetration profiles in pure lead give diffusion coefficients independent of the penetration depth and silver concentration, it is suggested that slight decreases of silver diffusivity in lead-silver solid solutions have no significance. This implies that the interstitial silver atoms do not associate significantly with each other to form Ag-Ag dimers. In contrast, different behaviors of /sup 63/Ni depth profile concentration in pure lead and saturated PbNi solid solutions agree with a Ni-Ni interaction leading to the formation of less mobile dimers near the surface in pure lead

An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

International Nuclear Information System (INIS)

Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.

2009-01-01

In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

On the solutions of fractional reaction-diffusion equations

Directory of Open Access Journals (Sweden)

Jagdev Singh

2013-05-01

Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.

Direct rotating ring-disk measurement of the sodium borohydride diffusion coefficient in sodium hydroxide solutions

Energy Technology Data Exchange (ETDEWEB)

Chatenet, M. [Laboratoire d' Electrochimie et de Physico-chimie des Materiaux et des Interfaces, LEPMI, UMR 5631 CNRS/Grenoble-INP/UJF, 1130 rue de la piscine, BP75, 38402 Saint Martin d' Heres Cedex (France)], E-mail: Marian.Chatenet@phelma.grenoble-inp.fr; Molina-Concha, M.B. [Laboratoire d' Electrochimie et de Physico-chimie des Materiaux et des Interfaces, LEPMI, UMR 5631 CNRS/Grenoble-INP/UJF, 1130 rue de la piscine, BP75, 38402 Saint Martin d' Heres Cedex (France); El-Kissi, N. [Laboratoire de Rheologie, UMR 5520 CNRS/Grenoble-INP/UJF, 1301 rue de la piscine, 38041 Grenoble Cedex 9 (France); Parrour, G.; Diard, J.-P. [Laboratoire d' Electrochimie et de Physico-chimie des Materiaux et des Interfaces, LEPMI, UMR 5631 CNRS/Grenoble-INP/UJF, 1130 rue de la piscine, BP75, 38402 Saint Martin d' Heres Cedex (France)

2009-07-15

This paper presents the experimental determination of the diffusion coefficient of borohydride anion and solution kinematic viscosity for a large panel of NaOH + NaBH{sub 4} electrolytic solutions relevant for use as anolyte in Direct Borohydride Fuel Cells (DBFC). The diffusion coefficients have been measured by the transit-time technique on gold rotating ring-disk electrodes, and verified using other classical techniques reported in the literature, namely the Levich method and Electrochemical Impedance Spectroscopy on a gold RDE, or chronoamperometry at a gold microdisk. The agreement between these methods is generally good. The diffusion coefficients measured from the RRDE technique are however ca. twice larger than those previously reported in the literature (e.g. ca. 3 x 10{sup -5} cm{sup 2} s{sup -1} in 1 M NaOH + 0.01 M NaBH{sub 4} at 25 deg. C in the present study vs. ca. 1.6 x 10{sup -5} cm{sup 2} s{sup -1} in 1 M NaOH + 0.02 M NaBH{sub 4} at 30 deg. C in the literature, as measured by chronoamperometry at a gold microsphere), which is thoroughly discussed. Our measurements using chronoamperometry at a gold microdisk showed that such technique can yield diffusion coefficient values below what expected. The origin of such finding is explained in the frame of the formation of both a film of boron-oxide(s) at the surface of the (static) gold microdisk and the generation of H{sub 2} bubbles at the electrode surface (as a result of the heterogeneous hydrolysis at Au), which alter the access to the electrode surface and thus prevents efficient measurements. Such film formation and H{sub 2} bubbles generation is not so much of an issue for rotating electrodes thanks to the convection of electrolyte which sweeps the electrode surface. In addition, should such film be present, the transit-time determination technique on a RRDE displays the advantage of not being very sensible to its presence: the parameter measured is the time taken by a perturbation generated the

Direct rotating ring-disk measurement of the sodium borohydride diffusion coefficient in sodium hydroxide solutions

International Nuclear Information System (INIS)

Chatenet, M.; Molina-Concha, M.B.; El-Kissi, N.; Parrour, G.; Diard, J.-P.

2009-01-01

This paper presents the experimental determination of the diffusion coefficient of borohydride anion and solution kinematic viscosity for a large panel of NaOH + NaBH 4 electrolytic solutions relevant for use as anolyte in Direct Borohydride Fuel Cells (DBFC). The diffusion coefficients have been measured by the transit-time technique on gold rotating ring-disk electrodes, and verified using other classical techniques reported in the literature, namely the Levich method and Electrochemical Impedance Spectroscopy on a gold RDE, or chronoamperometry at a gold microdisk. The agreement between these methods is generally good. The diffusion coefficients measured from the RRDE technique are however ca. twice larger than those previously reported in the literature (e.g. ca. 3 x 10 -5 cm 2 s -1 in 1 M NaOH + 0.01 M NaBH 4 at 25 deg. C in the present study vs. ca. 1.6 x 10 -5 cm 2 s -1 in 1 M NaOH + 0.02 M NaBH 4 at 30 deg. C in the literature, as measured by chronoamperometry at a gold microsphere), which is thoroughly discussed. Our measurements using chronoamperometry at a gold microdisk showed that such technique can yield diffusion coefficient values below what expected. The origin of such finding is explained in the frame of the formation of both a film of boron-oxide(s) at the surface of the (static) gold microdisk and the generation of H 2 bubbles at the electrode surface (as a result of the heterogeneous hydrolysis at Au), which alter the access to the electrode surface and thus prevents efficient measurements. Such film formation and H 2 bubbles generation is not so much of an issue for rotating electrodes thanks to the convection of electrolyte which sweeps the electrode surface. In addition, should such film be present, the transit-time determination technique on a RRDE displays the advantage of not being very sensible to its presence: the parameter measured is the time taken by a perturbation generated the disk to reach the ring trough a distance several orders

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

Science.gov (United States)

Burden, Conrad J; Tang, Yurong

2016-12-01

We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

Diffusion-accelerated solution of the 2-D x-y Sn equations with linear-bilinear nodal differencing

International Nuclear Information System (INIS)

Wareing, T.A.; Walters, W.F.; Morel, J.E.

1994-01-01

Recently a new diffusion-synthetic acceleration scheme was developed for solving the 2-D S n Equations in x-y geometry with bilinear-discontinuous finite element spatial discretization using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differs from previous methods in that it is conditional efficient for problems with isotropic or nearly isotropic scattering. We have used the same bilinear-discontinuous diffusion scheme, and associated solution technique, to accelerate the x-y geometry S n equations with linear-bilinear nodal spatial differencing. We find that this leads to an unconditionally efficient solution method for problems with isotropic or nearly isotropic scattering. computational results are given which demonstrate this property

Comparison of finite-difference and variational solutions to advection-diffusion problems

International Nuclear Information System (INIS)

Lee, C.E.; Washington, K.E.

1984-01-01

Two numerical solution methods are developed for 1-D time-dependent advection-diffusion problems on infinite and finite domains. Numerical solutions are compared with analytical results for constant coefficients and various boundary conditions. A finite-difference spectrum method is solved exactly in time for periodic boundary conditions by a matrix operator method and exhibits excellent accuracy compared with other methods, especially at late times, where it is also computationally more efficient. Finite-system solutions are determined from a conservational variational principle with cubic spatial trial functions and solved in time by a matrix operator method. Comparisons of problems with few nodes show excellent agreement with analytical solutions and exhibit the necessity of implementing Lagrangian conservational constraints for physically-correct solutions. (author)

Self-diffusion in electrolyte solutions a critical examination of data compiled from the literature

CERN Document Server

Mills, R

1989-01-01

This compilation - the first of its kind - fills a real gap in the field of electrolyte data. Virtually all self-diffusion data in electrolyte solutions as reported in the literature have been examined and the book contains over 400 tables covering diffusion in binary and ternary aqueous solutions, in mixed solvents, and of non-electrolytes in various solvents.An important feature of the compilation is that all data have been critically examined and their accuracy assessed. Other features are an introductory chapter in which the methods of measurement are reviewed; appendices containing tables

An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst

2011-01-01

Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

Temperature jump boundary conditions in radiation diffusion

International Nuclear Information System (INIS)

Alonso, C.T.

1976-12-01

The radiation diffusion approximation greatly simplifies radiation transport problems. Yet the application of this method has often been unnecessarily restricted to optically thick regions, or has been extended through the use of such ad hoc devices as flux limiters. The purpose of this paper is to review and draw attention to the use of the more physically appropriate temperature jump boundary conditions for extending the range of validity of the diffusion approximation. Pioneering work has shown that temperature jump boundary conditions remove the singularity in flux that occurs in ordinary diffusion at small optical thicknesses. In this review paper Deissler's equations for frequency-dependent jump boundary conditions are presented and specific geometric examples are calculated analytically for steady state radiation transfer. When jump boundary conditions are applied to radiation diffusion, they yield exact solutions which are naturally flux- limited and geometry-corrected. We believe that the presence of temperature jumps on source boundaries is probably responsible in some cases for the past need for imposing ad hoc flux-limiting constraints on pure diffusion solutions. The solution for transfer between plane slabs, which is exact to all orders of optical thickness, also provides a useful tool for studying the accuracy of computer codes

Analytic solution for one-dimensional diffusion of radionuclides from a waste package

International Nuclear Information System (INIS)

Oliver, D.L.

1985-01-01

This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated

Diffusion kinetics and spinodal decay of quasi-equilibrium solid solutions

International Nuclear Information System (INIS)

Zakharov, M.A.

2000-01-01

Phenomenological theory for rearrangement of solid solutions with the hierarchy of the component atomic mobilities is elaborated in the approximation of the local equilibrium. The hydrodynamic stage of the evolution of these solutions is studied as a sequence of quasi-equilibrium states characterized by implementation of some conditions of the total equilibrium. On the basis of separation of fast and slow constituents of diffusion and on the basis of the method of reduced description one derived equation for evolution of separations of fast components in quasi-equilibrium solid solutions at the arbitrary stages of rearrangement in terms of the generalized lattice model taking account of the proper volumes of the components. The conditions of the stability of quasi-equilibrium solutions to the spinodal decomposition are determined and the equations of metastability boundaries of such systems are derived [ru

Contribution to the study of the interfacial diffusion

International Nuclear Information System (INIS)

Perinet, Francois.

1975-07-01

The diffusion behaviour of matrix-precipitate boundaries is the same as that of interphase boundaries prepared by welding. Therefore the latter can be used to measure diffusivity along interphase boundaries. Diffusion rates of silver along copper-silver interfaces prepared by welding single crystals have been measured. The interfacial diffusion coefficients deduced through different analytical solutions of the diffusion equations, yield for the activation energy and the frequency factor values close to: Q(i)=65kcal/mole Dsub(i)sup(o) delta=100cm 3 .s -1 . These results seem to indicate that, in agreement with Bondy's and Job's previous results, the activation energies for interfacial diffusion are high. Furthermore it is shown that the misorientation between the two phases building the interface has an influence on the measured diffusion coefficients [fr

Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system

International Nuclear Information System (INIS)

Kudryashov, Nikolay A.; Zakharchenko, Anastasia S.

2014-01-01

A system of equations for description of the Belousov–Zhabotinskii chemical reaction is considered. The Painlevé analysis of this reaction–diffusion system is studied. Exact traveling wave solutions of the system for the Belousov–Zhabotinskii reaction are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given

Finite Volume Scheme for Double Convection-Diffusion Exchange of Solutes in Bicarbonate High-Flux Hollow-Fiber Dialyzer Therapy

Directory of Open Access Journals (Sweden)

Kodwo Annan

2012-01-01

Full Text Available The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers.

On the role of specific interactions in the diffusion of nanoparticles in aqueous polymer solutions.

Science.gov (United States)

Mun, Ellina A; Hannell, Claire; Rogers, Sarah E; Hole, Patrick; Williams, Adrian C; Khutoryanskiy, Vitaliy V

2014-01-14

Understanding nanoparticle diffusion within non-Newtonian biological and synthetic fluids is essential in designing novel formulations (e.g., nanomedicines for drug delivery, shampoos, lotions, coatings, paints, etc.), but is presently poorly defined. This study reports the diffusion of thiolated and PEGylated silica nanoparticles, characterized by small-angle neutron scattering, in solutions of various water-soluble polymers such as poly(acrylic acid) (PAA), poly(N-vinylpyrrolidone) (PVP), poly(ethylene oxide) (PEO), and hydroxyethylcellulose (HEC) probed using NanoSight nanoparticle tracking analysis. Results show that the diffusivity of nanoparticles is affected by their dimensions, medium viscosity, and, in particular, the specific interactions between nanoparticles and the macromolecules in solution; strong attractive interactions such as hydrogen bonding hamper diffusion. The water-soluble polymers retarded the diffusion of thiolated particles in the order PEO > PVP > PAA > HEC whereas for PEGylated silica particles retardation followed the order PAA > PVP = HEC > PEO. In the absence of specific interactions with the medium, PEGylated nanoparticles exhibit enhanced mobility compared to their thiolated counterparts despite some increase in their dimensions.

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

Science.gov (United States)

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Localized modulated wave solutions in diffusive glucose–insulin systems

Energy Technology Data Exchange (ETDEWEB)

Mvogo, Alain, E-mail: mvogal_2009@yahoo.fr [Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Tambue, Antoine [The African Institute for Mathematical Sciences (AIMS) and Stellenbosch University, 6-8 Melrose Road, Muizenberg 7945 (South Africa); Center for Research in Computational and Applied Mechanics (CERECAM), and Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch (South Africa); Ben-Bolie, Germain H. [Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon); Kofané, Timoléon C. [Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon)

2016-06-03

We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet β-cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale expansion in the semi-discrete approximation, we show that the insulin dynamics can be governed by the complex Ginzburg–Landau equation. The localized solutions of this equation are reported. The results suggest from the biophysical point of view that the insulin propagates in pancreatic islet β-cells using both temporal and spatial dimensions in the form of localized modulated waves. - Highlights: • The dynamics of an array of diffusively coupled pancreatic islet beta-cells is investigated. • Through the multiple scale expansion, we show that the insulin dynamics can be governed by the complex Ginzburg–Landau equation. • Localized modulated waves are obtained for the insulin dynamics.

Fluorescence quantum yield of thioflavin T in rigid isotropic solution and incorporated into the amyloid fibrils.

Directory of Open Access Journals (Sweden)

Anna I Sulatskaya

Full Text Available In this work, the fluorescence of thioflavin T (ThT was studied in a wide range of viscosity and temperature. It was shown that ThT fluorescence quantum yield varies from 0.0001 in water at room temperature to 0.28 in rigid isotropic solution (T/η→0. The deviation of the fluorescence quantum yield from unity in rigid isotropic solution suggests that fluorescence quantum yield depends not only on the ultra-fast oscillation of ThT fragments relative to each other in an excited state as was suggested earlier, but also depends on the molecular configuration in the ground state. This means that the fluorescence quantum yield of the dye incorporated into amyloid fibrils must depend on its conformation, which, in turn, depends on the ThT environment. Therefore, the fluorescence quantum yield of ThT incorporated into amyloid fibrils can differ from that in the rigid isotropic solution. In particular, the fluorescence quantum yield of ThT incorporated into insulin fibrils was determined to be 0.43. Consequently, the ThT fluorescence quantum yield could be used to characterize the peculiarities of the fibrillar structure, which opens some new possibilities in the ThT use for structural characterization of the amyloid fibrils.

Diffusion and localization of o-Ps in Dsub(2)O determined from positron annihilation in SDS micellar solutions

International Nuclear Information System (INIS)

Vass, Sz.; Kajcsos, Zs.; Molnar, B.

1985-04-01

A microscopic diffusion model is presented for the determination of orthopositronium (o-Ps) lifetime in micellar solutions. Among other parameters, the lifetime density function depends on the o-Ps diffusion coefficient in the water phase. Orthopositronium diffusion coefficients are determined by fitting this lifetime density function to positron annihilation spectra obtained from 1 mol/dmsup(3) solution of sodium dodecylsulphate (SDS) in Dsub(2)O at different temperatures. The activation energy of the o-Ps diffusion in Dsub(2)O obtained from the Arrhenius-plot as Esub(a)=(0.9sub(22)+-0.1sub(03)) eV indicates strong localization. (author)

Entire solutions of a diffusive and competitive Lotka–Volterra type system with nonlocal delays

International Nuclear Information System (INIS)

Wang, Mingxin; Lv, Guangying

2010-01-01

This paper is concerned with the entire solution of a diffusive and competitive Lotka–Volterra type system with nonlocal delays. The existence of the entire solution is proved by transforming the system with nonlocal delays to a four-dimensional system without delay and using the comparing argument and the sub-super-solution method. Here an entire solution means a classical solution defined for all space and time variables, which behaves as two wave fronts coming from both sides of the x-axis

The Generalized Maxwell-Stefan Model Coupled with Vacancy Solution Theory of Adsorption for Diffusion in Zeolites

Directory of Open Access Journals (Sweden)

Seyyed Milad Salehi

2014-01-01

Full Text Available It seems using the Maxwell-Stefan (M-S diffusion model in combination with the vacancy solution theory (VST and the single-component adsorption data provides a superior, qualitative, and quantitative prediction of diffusion in zeolites. In the M-S formulation, thermodynamic factor (Г is an essential parameter which must be estimated by an adsorption isotherm. Researchers usually utilize the simplest form of adsorption isotherms such as Langmuir or improved dual-site Langmuir, which eventually cannot predict the real behavior of mixture diffusion particularly at high concentrations of adsorbates because of ignoring nonideality in the adsorbed phase. An isotherm model with regard to the real behavior of the adsorbed phase, which is based on the vacancy solution theory (VST and considers adsorbate-adsorbent interactions, is employed. The objective of this study is applying vacancy solution theory to pure component data, calculating thermodynamic factor (Г, and finally evaluating the simulation results by comparison with literature. Vacancy solution theory obviously predicts thermodynamic factor better than simple models such as dual-site Langmuir.

Exact solution of a model for diffusion particles and longitudinal dispersion in packed beds

International Nuclear Information System (INIS)

Rasmuson, A.; Neretnieks, I.

1979-08-01

An analytical solution of a model for diffusion in particles and longitudinal despersion in porous media is derived. The solution is obtained by the method of Laplace transform. The result is expressed as an infinite integral of five deminsionless quanitities. The extension for a decaying species is given. (authors)

Influence of microemulsion-mucin interaction on the fate of microemulsions diffusing through pig gastric mucin solutions.

Science.gov (United States)

Zhang, Jianbin; Lv, Yan; Wang, Bing; Zhao, Shan; Tan, Mingqian; Lv, Guojun; Ma, Xiaojun

2015-03-02

Mucus layer, a selective diffusion barrier, has an important effect on the fate of drug delivery systems in the gastrointestinal tract. To study the fate of microemulsions in the mucus layer, four microemulsion formulations with different particle sizes and lipid compositions were prepared. The microemulsion-mucin interaction was demonstrated by the fluorescence resonance energy transfer (FRET) method. Moreover, the microemulsions were observed aggregated into micron-sized emulsions by laser confocal microscopy. We concluded the microemulsion-mucin interaction not only led to microemulsions closely adhered to mucins but also destroyed the structure of microemulsions. At last, the diffusion of blank microemulsions and microemulsion-carried drugs (resveratrol and hymecromone) through mucin solutions was determined by the fluorescence recovery after photobleaching (FRAP) method and the Franz diffusion cell method. The results demonstrated the diffusion of microemulsions was significantly hindered by mucin solutions. The particle size of microemulsions had a negligible effect on the diffusion coefficients. However, the type of lipid played an important role, which could form hydrophobic interactions with mucins. Interestingly, microemulsion-carried drugs with different core/shell locations seemed to suffer different fates in the mucin solutions. The drug incorporated in the oil core of microemulsions, resveratrol, was transported through the mucus layer by the carriers, while the drug incorporated in the surfactant shell of microemulsions, hymecromone, was separated from the carriers and diffused toward the epithelium in the form of free molecules.

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

Science.gov (United States)

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.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

An analytic solution for one-dimensional diffusion of radionuclides from a waste package

International Nuclear Information System (INIS)

1985-01-01

This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated. 6 refs., 2 figs., 2 tabs

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

Directory of Open Access Journals (Sweden)

Matthew J Simpson

Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

The charge effect on the hindrance factors for diffusion and convection of a solute in pores: II

Energy Technology Data Exchange (ETDEWEB)

Akinaga, Takeshi; O-tani, Hideyuki; Sugihara-Seki, Masako, E-mail: r091077@kansai-u.ac.jp [Department of Pure and Applied Physics, Kansai University, Yamate-cho, Suita, Osaka 564-8680 (Japan)

2012-10-15

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e. the Debye-Hueckel equation. (paper)

Effects of Land-Applied Ammonia Scrubber Solutions on Yield, Nitrogen Uptake, Soil Test Phosphorus, and Phosphorus Runoff.

Science.gov (United States)

Martin, Jerry W; Moore, Philip A; Li, Hong; Ashworth, Amanda J; Miles, Dana M

2018-03-01

Ammonia (NH) scrubbers reduce amounts of NH and dust released from animal rearing facilities while generating nitrogen (N)-rich solutions, which may be used as fertilizers. The objective of this study was to determine the effects of various NH scrubber solutions on forage yields, N uptake, soil-test phosphorus (P), and P runoff. A small plot study was conducted using six treatments: (i) an unfertilized control, (ii) potassium bisulfate (KHSO) scrubber solution, (iii) aluminum sulfate [Al(SO) ⋅14HO, alum] scrubber solution, (iv) sodium bisulfate (NaHSO) scrubber solution, (v) sulfuric acid (HSO) scrubber solution, and (vi) ammonium nitrate (NHNO) fertilizer. The scrubber solutions were obtained from ARS Air Scrubbers attached to commercial broiler houses. All N sources were applied at a rate of 112 kg N ha. Plots were harvested approximately every 4 wk and soil-test P measurements were made, then a rainfall simulation study was conducted. Cumulative forage yields were greater ( scrubber solutions than for alum (6.7 Mg ha) or HSO (6.5 Mg ha) scrubber solutions or for NHNO (6.9 Mg ha). All N sources resulted in higher yields than the control (5.1 Mg ha). The additional potassium in the KHSO treatment likely resulted in higher yields. Although Mehlich-III-extractable P was not affected, water-extractable P in soil was lowered by the alum-based scrubber solution, which also resulted in lower P runoff. This study demonstrates that N captured using NH scrubbers is a viable N fertilizer. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.

Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems

International Nuclear Information System (INIS)

Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.

1995-01-01

In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

Science.gov (United States)

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Analytical solution to the diffusion, sorption and decay chain equation in a saturated porous medium between two reservoirs

International Nuclear Information System (INIS)

Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario

2015-01-01

The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain

Multigrid solution of the convection-diffusion equation with high-Reynolds number

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jun [George Washington Univ., Washington, DC (United States)

1996-12-31

A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.

Solution of the diffusion equation in the GPT theory by the Laplace transform technique

International Nuclear Information System (INIS)

Lemos, R.S.M.; Vilhena, M.T.; Segatto, C.F.; Silva, M.T.

2003-01-01

In this work we present a analytical solution to the auxiliary and importance functions attained from the solution of a multigroup diffusion problem in a multilayered slab by the Laplace Transform technique. We also obtain the the transcendental equation for the effective multiplication factor, resulting from the application of the boundary and interface conditions. (author)

FURFURAL YIELD AND DECOMPOSITION IN SODIUM 2,4DIMETHYLBENZENESULFONATE--SULFURIC ACID--WATER SOLUTIONS.

Science.gov (United States)

Batch-type microreactors (about 1/40 milliliter of reactants) were used to measure furfural yields from acidified xylose solutions containing sodium...It was found that presence of the salt did not affect the quantity of furfural produced, but greatly increased the rate of formation. The regular...increase in rate of furfural formation was directly related to the increase in the rate xylose decomposition, and furfural yields for all salt and acid

Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

Science.gov (United States)

Liu, Ping; Shi, Junping

2018-01-01

The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

Digital simulation of an enrichment process for solutions by means of an advection-diffusion chamber

International Nuclear Information System (INIS)

Artucio, G.; Suarez, R.; Uruguay Catholic University)

1995-01-01

An ab-initio digital simulation of the space-time dynamics of the concentration field of a solute in an advection-diffusion chamber is done. Some questions related to the digital simulation of the concentration field using the analytical solution obtained in a previous paper are discussed

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

2014-01-01

Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative

Computational modeling for the angular reconstruction of monoenergetic neutron flux in non-multiplying slabs using synthetic diffusion approximation

International Nuclear Information System (INIS)

Mansur, Ralph S.; Barros, Ricardo C.

2011-01-01

We describe a method to determine the neutron scalar flux in a slab using monoenergetic diffusion model. To achieve this goal we used three ingredients in the computational code that we developed on the Scilab platform: a spectral nodal method that generates numerical solution for the one-speed slab-geometry fixed source diffusion problem with no spatial truncation errors; a spatial reconstruction scheme to yield detailed profile of the coarse-mesh solution; and an angular reconstruction scheme to yield approximately the neutron angular flux profile at a given location of the slab migrating in a given direction. Numerical results are given to illustrate the efficiency of the offered code. (author)

Solution of the multilayer multigroup neutron diffusion equation in cartesian geometry by fictitious borders power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)

2017-05-15

In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.

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

Science.gov (United States)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

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

Diffusion Dominant Solute Transport Modelling in Fractured Media Under Deep Geological Environment - 12211

Energy Technology Data Exchange (ETDEWEB)

Kwong, S. [National Nuclear Laboratory (United Kingdom); Jivkov, A.P. [Research Centre for Radwaste and Decommissioning and Modelling and Simulation Centre, University of Manchester (United Kingdom)

2012-07-01

Deep geologic disposal of high activity and long-lived radioactive waste is gaining increasing support in many countries, where suitable low permeability geological formation in combination with engineered barriers are used to provide long term waste contaminant and minimise the impacts to the environment and risk to the biosphere. This modelling study examines the solute transport in fractured media under low flow velocities that are relevant to a deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes. The effects of water velocity in the fracture, matrix porosity and diffusion on solute transport are investigated and discussed. Some illustrative modelled results are presented to demonstrate the use of the model to examine the effects of media degradation on solute transport, under the influences of hydrogeological (diffusion dominant) and microbially mediated chemical processes. The challenges facing the prediction of long term degradation such as cracks evolution, interaction and coalescence are highlighted. The potential of a novel microstructure informed modelling approach to account for these effects is discussed, particularly with respect to investigating multiple phenomena impact on material performance. The GRM code is used to examine the effects of media degradation for a geological waste disposal package, under the combined hydrogeological (diffusion dominant) and chemical effects in low groundwater flow conditions that are typical of deep geological disposal systems. An illustrative reactive transport modelling application demonstrates the use of the code to examine the interplay of kinetic controlled biogeochemical reactive processes with advective and diffusive transport, under the influence of media degradation. The initial model results are encouraging which show the

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

Science.gov (United States)

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)(0divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables. While the solution for normal diffusion problems is, at most, divergent as t-->0 , 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 .

Probing the Interplay of Size, Shape, and Solution Environment in Macromolecular Diffusion Using a Simple Refraction Experiment

Science.gov (United States)

Mankidy, Bijith D.; Coutinho, Cecil A.; Gupta, Vinay K.

2010-01-01

The diffusion coefficient of polymers is a critical parameter in biomedicine, catalysis, chemical separations, nanotechnology, and other industrial applications. Here, measurement of macromolecular diffusion in solutions is described using a visually instructive, undergraduate-level optical refraction experiment based on Weiner's method. To…

A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor

Directory of Open Access Journals (Sweden)

B. Godongwana

2010-01-01

Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

Directory of Open Access Journals (Sweden)

Narcisa Apreutesei

2014-05-01

Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

Single molecule diffusion and the solution of the spherically symmetric residence time equation.

Science.gov (United States)

Agmon, Noam

2011-06-16

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Science.gov (United States)

Watkins, James M.; DePaolo, Donald J.; Ryerson, Frederick J.; Peterson, Brook T.

2011-06-01

Molecular diffusion in natural volcanic liquids discriminates between isotopes of major ions (e.g., Fe, Mg, Ca, and Li). Although isotope separation by diffusion is expected on theoretical grounds, the dependence on mass is highly variable for different elements and in different media. Silicate liquid diffusion experiments using simple liquid compositions were carried out to further probe the compositional dependence of diffusive isotopic discrimination and its relationship to liquid structure. Two diffusion couples consisting of the mineral constituents anorthite (CaAl 2Si 2O 8; denoted AN), albite (NaAlSi 3O 8; denoted AB), and diopside (CaMgSi 2O 6; denoted DI) were held at 1450 °C for 2 h and then quenched to ambient pressure and temperature. Major-element as well as Ca and Mg isotope profiles were measured on the recovered quenched glasses. In both experiments, Ca diffuses rapidly with respect to Si. In the AB-AN experiment, D Ca/ D Si ≈ 20 and the efficiency of isotope separation for Ca is much greater than in natural liquid experiments where D Ca/ D Si ≈ 1. In the AB-DI experiment, D Ca/ D Si ≈ 6 and the efficiency of isotope separation is between that of the natural liquid experiments and the AB-AN experiment. In the AB-DI experiment, D Mg/ D Si ≈ 1 and the efficiency of isotope separation for Mg is smaller than it is for Ca yet similar to that observed for Mg in natural liquids. The results from the experiments reported here, in combination with results from natural volcanic liquids, show clearly that the efficiency of diffusive separation of Ca isotopes is systematically related to the solvent-normalized diffusivity - the ratio of the diffusivity of the cation ( D Ca) to the diffusivity of silicon ( D Si). The results on Ca isotopes are consistent with available data on Fe, Li, and Mg isotopes in silicate liquids, when considered in terms of the parameter D cation/ D Si. Cations diffusing in aqueous solutions display a similar relationship

Aqueous pathways dominate permeation of solutes across Pisum sativum seed coats and mediate solute transport via diffusion and bulk flow of water.

Science.gov (United States)

Niemann, Sylvia; Burghardt, Markus; Popp, Christian; Riederer, Markus

2013-05-01

The permeability of seed coats to solutes either of biological or anthropogenic origin plays a major role in germination, seedling growth and seed treatment by pesticides. An experimental set-up was designed for investigating the mechanisms of seed coat permeation, which allows steady-state experiments with isolated seed coats of Pisum sativum. Permeances were measured for a set of organic model compounds with different physicochemical properties and sizes. The results show that narrow aqueous pathways dominate the diffusion of solutes across pea seed coats, as indicated by a correlation of permeances with the molecular sizes of the compounds instead of their lipophilicity. Further indicators for an aqueous pathway are small size selectivity and a small effect of temperature on permeation. The application of an osmotic water potential gradient across isolated seed coats leads to an increase in solute transfer, indicating that the aqueous pathways form a water-filled continuum across the seed coat allowing the bulk flow of water. Thus, the uptake of organic solutes across pea testae has two components: (1) by diffusion and (2) by bulk water inflow, which, however, is relevant only during imbibition. © 2012 Blackwell Publishing Ltd.

Application of finite Fourier transformation for the solution of the diffusion equation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

Solution of two group neutron diffusion equation by using homotopy analysis method

International Nuclear Information System (INIS)

Cavdar, S.

2010-01-01

The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.

assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

International Nuclear Information System (INIS)

Esmail, S.F.H.

2011-01-01

The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

Determination of the Solute Diffusion Coefficient by the Droplet Migration Method

Energy Technology Data Exchange (ETDEWEB)

Shan Liu; Jing Teng; Jeongyun Choi

2007-07-01

Further analysis of droplet migration in a temperature gradient field indicates that different terms can be used to evaluate the solute diffusion coefficient in liquid (D{sub L}) and that there exists a characteristic curve that can describe the motion of all the droplets for a given composition and temperature gradient. Critical experiments are subsequently conducted in succinonitrile (SCN)-salol and SCN-camphor transparent alloys in order to observe dynamic migration processes of a number of droplets. The derived diffusion coefficients from different terms are the same within experimental error. For SCN-salol alloys, D{sub L} = (0.69 {+-} 0.05) x 10{sup -3} mm{sup 2}/s, and for SCN-camphor alloys, D{sub L} = (0.24 {+-} 0.02) x 10{sup -3} mm{sup 2}/s.

Influence of liquid structure on diffusive isotope separation in molten silicates and aqueous solutions

Energy Technology Data Exchange (ETDEWEB)

Watkins, J.M.; DePaolo, D.J.; Ryerson, F.J.; Peterson, B.

2011-03-01

}/D{sub Si}. Cations diffusing in aqueous solutions display a similar relationship between isotopic separation efficiency and D{sub cation} =D{sub H 2 O} , although the efficiencies are smaller than in silicate liquids. Our empirical relationship provides a tool for predicting the magnitude of diffusive isotopic effects in many geologic environments and a basis for a more comprehensive theory of isotope separation in liquid solutions. We present a conceptual model for the relationship between diffusivity and liquid structure that is consistent with available data.

Test of the 'glymphatic' hypothesis demonstrates diffusive and aquaporin-4-independent solute transport in rodent brain parenchyma.

Science.gov (United States)

Smith, Alex J; Yao, Xiaoming; Dix, James A; Jin, Byung-Ju; Verkman, Alan S

2017-08-21

Transport of solutes through brain involves diffusion and convection. The importance of convective flow in the subarachnoid and paravascular spaces has long been recognized; a recently proposed 'glymphatic' clearance mechanism additionally suggests that aquaporin-4 (AQP4) water channels facilitate convective transport through brain parenchyma. Here, the major experimental underpinnings of the glymphatic mechanism were re-examined by measurements of solute movement in mouse brain following intracisternal or intraparenchymal solute injection. We found that: (i) transport of fluorescent dextrans in brain parenchyma depended on dextran size in a manner consistent with diffusive rather than convective transport; (ii) transport of dextrans in the parenchymal extracellular space, measured by 2-photon fluorescence recovery after photobleaching, was not affected just after cardiorespiratory arrest; and (iii) Aqp4 gene deletion did not impair transport of fluorescent solutes from sub-arachnoid space to brain in mice or rats. Our results do not support the proposed glymphatic mechanism of convective solute transport in brain parenchyma.

Contribution to the study of the role of diffusion in the growth of crystals from solution; Contribution a l'etude du role de la diffusion dans la croissance des cristaux a partir de solution

Energy Technology Data Exchange (ETDEWEB)

Quivy, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1965-12-01

In the case of the two-dimensional growth of crystals from solution, the concentration distribution could be explained on the basis of Fick diffusion equation. The limiting conditions are defined in a satisfactory way, and the curves of equal concentration in the solution surrounding the crystal are calculated using a resistance network device. These curves are similar to the observed interference fringes. The limiting conditions are different according as to whether the type of crystal growth is regular or dendritic. In this work the growth rate of the crystal faces in solution has been measured for various substances. These direct measurements were carried out using a micrometric eye-piece and chrono-photographs. The interferential method using polarized light has been used for determining the concentration distribution in the neighbourhood of the crystal; it was thereby possible, knowing the diffusion coefficient, to calculate the growth rate and to observe the existence of a disagreement, of the order of two, with the direct measurements. This discrepancy can even attain a value of ten in the case of very soluble substances; these latter have been studied by R. ITTI. (author) [French] Dans le cas de la croissance a deux dimensions de cristaux a partir de solution, la distribution des concentrations pouvait etre expliquee a partir de l'equation de diffusion de FICK. En fixant les conditions aux limites de facon convenable, on calcule, au moyen d'un dispositif a reseaux resistifs, les courbes d'egale concentration de la solution entourant le cristal. On constate que ces courbes sont semblables aux franges d'interferences observees. Les conditions aux limites sont differentes suivant que le type de croissance du cristal est regulier ou dendritique. Dans ce travail, on a egalement mesure les vitesses de croissance des faces cristallines a partir de solutions, en employant differentes substances. Ces mesures directes ont ete effectuees au moyen d'un oculaire

Communication: Relationship between solute localization and diffusion in a dynamically constrained polymer system

Energy Technology Data Exchange (ETDEWEB)

Saylor, David M.; Jawahery, Sudi; Silverstein, Joshua S.; Forrey, Christopher [Center for Devices and Radiological Health, FDA, Silver Spring, Maryland 20993 (United States)

2016-07-21

We investigate the link between dynamic localization, characterized by the Debye–Waller factor, 〈u{sup 2}〉, and solute self-diffusivity, D, in a polymer system using atomistic molecular dynamics simulations and vapor sorption experiments. We find a linear relationship between lnD and 1/〈u{sup 2}〉 over more than four decades of D, encompassing most of the glass formation regime. The observed linearity is consistent with the Langevin dynamics in a periodically varying potential field and may offer a means to rapidly assess diffusion based on the characterization of dynamic localization.

On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation

Directory of Open Access Journals (Sweden)

Yuri Luchko

2017-12-01

Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

International Nuclear Information System (INIS)

Ragusa, J. C.

2004-01-01

In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

Solution of multigroup diffusion equations in cylindrical configuration by local polynomial approximation

International Nuclear Information System (INIS)

Jakab, J.

1979-05-01

Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)

Diffuse neutron scattering study of metallic interstitial solid solutions

International Nuclear Information System (INIS)

Barberis, P.

1991-10-01

We studied two interstitial solid solutions (Ni-C(1at%) and Nb-O(2at%) and two stabilized zirconia (ZrO2-CaO(13.6mol%) and ZrO2-Y2O3(9.6mol%) by elastic diffuse neutron scattering. We used polarized neutron scattering in the case of the ferromagnetic Ni-based sample, in order to determine the magnetic perturbation induced by the C atoms. Measurements were made on single crystals in the Laboratoire Leon Brillouin (CEA-CNRS, Saclay, France). An original algorithm to deconvolve time-of-flight spectra improved the separation between elastically and inelastically scattered intensities. In the case of metallic solutions, we used a simple non-linear model, assuming that interstitials are isolated and located in octahedral sites. Results are: - in both compounds, nearest neighbours are widely displaced away from the interstitial, while next nearest neighbours come slightly closer. - the large magnetic perturbation induced by carbon in Nickel decreases with increasing distance on the three first neighbour shells and is in good agreement with the total magnetization variation. - no chemical order between solute atoms could be evidenced. Stabilized zirconia exhibit a strong correlation between chemical order and the large displacements around vacancies and dopants. (Author). 132 refs., 38 figs., 13 tabs

Diffusive transport of strontium-85 in sand-bentonite mixtures

International Nuclear Information System (INIS)

Gillham, R.W.; Robin, M.J.L.; Dytynyshyn, D.J.

1983-06-01

Diffusion experiments have been used to determine the transport of 85 Sr in sand-bentonite mixtures. The diffusion experiments were performed on one natural soil (Chalk River sand) and on seven mixtures of bentonite and silica sand, containing from 0 percent to 100 percent bentonite. Two non-reactive solutes ( 36 Cl and 3 H) and one reactive solute ( 85 Sr) were used in the study. The experiments with non-reactive solutes yielded estimates of tortuosity factors. Retardation factors were obtained from experimental porosities, experimental bulk densities, and from batch distribution coefficients (Ksub(d)). These Ksub(d) values are a simple way of describing the solute/medium reaction, and are based on the assumption that the cation-exchange reaction may be described by a linear adsorption isotherm passing through the origin. The results demonstrate that, for practical purposes and for our experimental conditions, the use of the distribution coefficient provides a convenient means of calculating the effective diffusion coefficient for 85 Sr. The porosity and bulk density were also found to have a considerable influence on the effective diffusion coefficient, through the retardation factor. Mixtures containing 5-10 percent bentonite were found to be more effective in retarding 85 Sr than either sand alone, or mixtures containing more bentonite. In the soils of higher bentonite content, the effect of increased cation-exchange capacity was balanced by a decreasing ratio of bulk density to porosity

Sample-averaged biexciton quantum yield measured by solution-phase photon correlation.

Science.gov (United States)

Beyler, Andrew P; Bischof, Thomas S; Cui, Jian; Coropceanu, Igor; Harris, Daniel K; Bawendi, Moungi G

2014-12-10

The brightness of nanoscale optical materials such as semiconductor nanocrystals is currently limited in high excitation flux applications by inefficient multiexciton fluorescence. We have devised a solution-phase photon correlation measurement that can conveniently and reliably measure the average biexciton-to-exciton quantum yield ratio of an entire sample without user selection bias. This technique can be used to investigate the multiexciton recombination dynamics of a broad scope of synthetically underdeveloped materials, including those with low exciton quantum yields and poor fluorescence stability. Here, we have applied this method to measure weak biexciton fluorescence in samples of visible-emitting InP/ZnS and InAs/ZnS core/shell nanocrystals, and to demonstrate that a rapid CdS shell growth procedure can markedly increase the biexciton fluorescence of CdSe nanocrystals.

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

Science.gov (United States)

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

2018-01-01

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

Bifurcation structure of positive stationary solutions for a Lotka-Volterra competition model with diffusion I

Science.gov (United States)

Kan-On, Yukio

2007-04-01

This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.

General solution of the aerosol dynamic equation: growth and diffusion processes

International Nuclear Information System (INIS)

Elgarayhi, A.; Elhanbaly, A.

2004-01-01

The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated

Verification of a dust transport model against theoretical solutions in multidimensional advection diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Xu, Z., E-mail: zhanjie.xu@kit.ed [Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany); Travis, J.R. [Ingenieurbuero DuBois-Pitzer-Travis, 63071 Offenbach (Germany); Breitung, W.; Jordan, T. [Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany)

2010-12-15

Potentially explosive dust aerosol mobilization in the vacuum vessel is an important safety issue of the ITER facility, especially in scenarios of loss of vacuum accidents. Therefore dust mobilization modeling is ongoing in Research Center Karlsuhe. At first the aerosol particle model in the GASFLOW computer code is introduced briefly. To verify the particle model, a series of particle diffusion problems are simulated in one-, two- and three-dimensions. In each problem a particle source is initially exposed to an advective gas flow. Then a dust cloud is formed in the down stream. To obtain the theoretical solution about the particle concentration in the dust cloud, the governing diffusion partial differential equations with an additional advection term are solved by using Green's function method. Different spatial and temporal characters about the particle sources are also considered, e.g., instantaneous or continuous sources, line, or volume sources and so forth. The GASFLOW simulation results about the particle concentrations and the corresponding Green's function solutions are compared case by case. Very good agreements are found between the theoretical solutions and the GASGLOW simulations, when the drag force between the micron-sized particles and the conveying gas flow meets the Stokes' law about resistance. This situation is corresponding to a very small Reynolds number based on the particle diameter, with a negligible inertia effect of the particles. This verification work shows that the particle model of the GASFLOW code can reproduce numerically particle transport and diffusion in a good way.

On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion

International Nuclear Information System (INIS)

Iyiola, O.S.; Tasbozan, O.; Kurt, A.; Çenesiz, Y.

2017-01-01

In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative.

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

Science.gov (United States)

Liang, Yingjie; Chen, Wen; Magin, Richard L.

2016-07-01

Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

Fast solution of neutron diffusion problem by reduced basis finite element method

International Nuclear Information System (INIS)

Chunyu, Zhang; Gong, Chen

2018-01-01

Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.

Periodic solutions for a two-species nonautonomous competition system with diffusion and impulses

International Nuclear Information System (INIS)

Dong Lingzhen; Chen Lansun; Shi Peilin

2007-01-01

By re-estimating the upper bound of ∫ 0 ω e u i (t) dt (i=1,2), we generalize a result about the existence of a positive periodic solution for a two-species nonautonomous patchy competition system with time delay. Based on that system, we consider the impulsive harvesting and stocking, and establish a two-species nonautonomous competition Lotka-Volterra system with diffusion and impulsive effects. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. At last, two examples are given to demonstrate our results

On positive periodic solution of periodic competition Lotka-Volterra system with time delay and diffusion

International Nuclear Information System (INIS)

Sun Wen; Chen Shihua; Hong Zhiming; Wang Changping

2007-01-01

A two-species periodic competition Lotka-Volterra system with time delay and diffusion is investigated. Some sufficient conditions of the existence of positive periodic solution are established for the system by using the continuation theorem of coincidence degree theory

Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration

International Nuclear Information System (INIS)

Brown, Peter N.; Shumaker, Dana E.; Woodward, Carol S.

2005-01-01

We present a solution method for fully implicit radiation diffusion problems discretized on meshes having millions of spatial zones. This solution method makes use of high order in time integration techniques, inexact Newton-Krylov nonlinear solvers, and multigrid preconditioners. We explore the advantages and disadvantages of high order time integration methods for the fully implicit formulation on both two- and three-dimensional problems with tabulated opacities and highly nonlinear fusion source terms

Solution of the atmospheric diffusion equation with a realistic diffusion coefficient and time dependent mixing height

International Nuclear Information System (INIS)

Mayhoub, A.B.; Etman, S.M.

1997-01-01

One dimensional model for the dispersion of a passive atmospheric contaminant (neglecting chemical reactions) in the atmospheric boundary layer is introduced. The differential equation representing the dispersion of pollutants is solved on the basis of gradient-transfer theory (K- theory). The present approach deals with a more appropriate and realistic profile for the diffusion coefficient K, which is expressed in terms of the friction velocity U, the vertical coordinate z and the depth of the mixing layer h, which is taken time dependent. After some mathematical simplification, the equation analytic obtained solution can be easily applied to case study concerning atmospheric dispersion of pollutants

Solution of the neutron diffusion equation at two groups of energy by method of triangular finite elements

International Nuclear Information System (INIS)

Correia Filho, A.

1981-04-01

The Neutron Diffusion Equation at two groups of energy is solved with the use of the Finite - Element Method with first order triangular elements. The program EFTDN (Triangular Finite Elements on Neutron Diffusion) was developed using the language FORTRAN IV. The discrete formulation of the Diffusion Equation is obtained with the application of the Galerkin's Method. In order to solve the eigenvalue - problem, the Method of the Power is applied and, with the purpose of the convergence of the results, Chebshev's polynomial expressions are applied. On the solution of the systems of equations Gauss' Method is applied, divided in two different parts: triangularization of the matrix of coeficients and retrosubstitution taking in account the sparsity of the system. Several test - problems are solved, among then two P.W.R. type reactors, the ZION-1 with 1300 MWe and the 2D-IAEA - Benchmark. Comparision of results with standard solutions show the validity of application of the EFM and precision of the results. (Author) [pt

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

Measurement of the thermal diffusivity and speed of sound of hydrothermal solutions via the laser-induced grating technique

International Nuclear Information System (INIS)

Butenhoff, T.J.

1994-01-01

Hydrothermal processing is being developed as a method for organic destruction for the Hanford Site in Washington. Hydrothermal processing refers to the redox reactions of chemical compounds in supercritical or near-supercritical aqueous solutions. In order to design reactors for the hydrothermal treatment of complicated mixtures found in the Hanford wastes, engineers need to know the thermophysical properties of the solutions under hydrothermal conditions. The author used the laser-induced grating technique to measure the thermal diffusivity and speed of sound of hydrothermal solutions. In this non-invasive optical technique, a transient grating is produced in the hydrothermal solution by optical absorption from two crossed time-coincident nanosecond laser pulses. The grating is probed by measuring the diffraction efficiency of a third laser beam. The grating relaxes via thermal diffusion, and the thermal diffusivity can be determined by measuring the decay of the grating diffraction efficiency as a function of the pump-probe delay time. In addition, intense pump pulses produce counterpropagating acoustic waves that appear as large undulations in the transient grating decay spectrum. The speed of sound in the sample is simply the grating fringe spacing divided by the undulation period. The cell is made from a commercial high pressure fitting and is equipped with two diamond windows for optical access. Results are presented for dilute dye/water solutions with T = 400 C and pressures between 20 and 70 MPa

[Analyze nanofiltration separation rule of chlorogenic acid from low concentration ethanol by Donnan effect and solution-diffusion effect].

Science.gov (United States)

Li, Cun-Yu; Liu, Li-Cheng; Jin, Li-Yang; Li, Hong-Yang; Peng, Guo-Ping

2017-07-01

To separate chlorogenic acid from low concentration ethanol and explore the influence of Donnan effect and solution-diffusion effect on the nanofiltration separation rule. The experiment showed that solution pH and ethanol volume percent had influences on the separation of chlorogenic acid. Within the pH values from 3 to 7 for chlorogenic acid in 30% ethanol, the rejection rate of chlorogenic acid was changed by 70.27%. Through the response surface method for quadratic regression model, an interaction had been found in molecule weight cut-off, pH and ethanol volume percent. In fixed nanofiltration apparatus, the existence states of chlorogenic acid determinedits separation rules. With the increase of ethanol concentration, the free form chlorogenic acid was easily adsorbed, dissolved on membrane surface and then caused high transmittance due to the solution-diffusion effect. However, at the same time, due to the double effects of Donnan effect and solution-diffusion effect, the ionic state of chlorogenic acid was hard to be adsorbed in membrane surface and thus caused high rejection rate. The combination of Box-Behnken design and response surface analysis can well optimize the concentrate process by nanofiltration, and the results showed that nanofiltration had several big advantages over the traditional vacuum concentrate technology, meanwhile, and solved the problems of low efficiency and serious component lossesin the Chinese medicines separation process for low concentration organic solvent-water solution. Copyright© by the Chinese Pharmaceutical Association.

Improved diffusivity of NaOH solution in autohydrolyzed poplar sapwood chips for chemi-mechanical pulp production.

Science.gov (United States)

Zhang, Honglei; Hou, Qingxi; Liu, Wei; Yue, Zhen; Jiang, Xiaoya; Ma, Xixi

2018-07-01

This work investigated the changes in the physical structure of autohydrolyzed poplar sapwood chips and the effect on the subsequent alkali liquor diffusion properties for chemi-mechanical pulping (CMP). An alkali impregnation process was conducted by using the autohydrolyzed poplar sapwood with different levels of autohydrolysis intensity. The results showed that the volume porosity, water constraint capacity, and saturated water absorption of the autohydrolyzed poplar sapwood chips increased. Also, the effective capillary cross-sectional area (ECCSA) in the radial direction and the diffusion coefficients of NaOH solution in both the radial and axial directions all increased. Autohydrolysis pretreatment enhanced the alkali liquor diffusion properties in poplar sapwood chips, and the diffusion coefficient was increased more greatly in the radial direction than that in the axial direction. Copyright © 2018 Elsevier Ltd. All rights reserved.

New self-similar radiation-hydrodynamics solutions in the high-energy density, equilibrium diffusion limit

International Nuclear Information System (INIS)

Lane, Taylor K; McClarren, Ryan G

2013-01-01

This work presents semi-analytic solutions to a radiation-hydrodynamics problem of a radiation source driving an initially cold medium. Our solutions are in the equilibrium diffusion limit, include material motion and allow for radiation-dominated situations where the radiation energy is comparable to (or greater than) the material internal energy density. As such, this work is a generalization of the classical Marshak wave problem that assumes no material motion and that the radiation energy is negligible. Including radiation energy density in the model serves to slow down the wave propagation. The solutions provide insight into the impact of radiation energy and material motion, as well as present a novel verification test for radiation transport packages. As a verification test, the solution exercises the radiation–matter coupling terms and their v/c treatment without needing a hydrodynamics solve. An example comparison between the self-similar solution and a numerical code is given. Tables of the self-similar solutions are also provided. (paper)

Charge effects on hindrance factors for diffusion and convection of solute in pores I

Energy Technology Data Exchange (ETDEWEB)

O-tani, Hideyuki [Graduate School of Science and Engineering, Kansai University, Yamate-cho, Suita, Osaka 564-8680 (Japan); Akinaga, Takeshi; Sugihara-Seki, Masako, E-mail: ga8d002@kansai-u.ac.jp [Department of Pure and Applied Physics, Kansai University, Yamate-cho, Suita, Osaka 564-8680 (Japan)

2011-12-01

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Larsen, Edward W.

2004-01-01

The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions

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

Science.gov (United States)

Al Noufaey, K. S.

2018-06-01

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

Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

Directory of Open Access Journals (Sweden)

S. Das

2013-12-01

Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

Diffusion in solids

International Nuclear Information System (INIS)

Tiwari, G.P.; Kale, G.B.; Patil, R.V.

1999-01-01

The article presents a brief survey of process of diffusion in solids. It is emphasised that the essence of diffusion is the mass transfer through the atomic jumps. To begin with formal equations for diffusion coefficient are presented. This is followed by discussions on mechanisms of diffusion. Except for solutes which form interstitial solid solution, diffusion in majority of cases is mediated through exchange of sites between an atom and its neighbouring vacancy. Various vacancy parameters such as activation volume, correlation factor, mass effect etc are discussed and their role in establishing the mode of diffusion is delineated. The contribution of dislocations and grain boundaries in diffusion process is brought out. The experimental determination of different types of diffusion coefficients are described. Finally, the pervasive nature of diffusion process in number of commercial processes is outlined to show the importance of diffusion studies in materials science and technology. (author)

Diffusion Dominant Solute Transport Modelling In Deep Repository Under The Effect of Emplacement Media Degradation - 13285

International Nuclear Information System (INIS)

Kwong, S.; Jivkov, A.P.

2013-01-01

Deep geologic disposal of high activity and long-lived radioactive waste is being actively considered and pursued in many countries, where low permeability geological formations are used to provide long term waste contaminant with minimum impact to the environment and risk to the biosphere. A multi-barrier approach that makes use of both engineered and natural barriers (i.e. geological formations) is often used to further enhance the containment performance of the repository. As the deep repository system subjects to a variety of thermo-hydro-chemo-mechanical (THCM) effects over its long 'operational' lifespan (e.g. 0.1 to 1.0 million years, the integrity of the barrier system will decrease over time (e.g. fracturing in rock or clay)). This is broadly referred as media degradation in the present study. This modelling study examines the effects of media degradation on diffusion dominant solute transport in fractured media that are typical of deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes, while the effects of degradation is studied using a pore network model that considers the media diffusivity and network changes. Model results are presented to demonstrate the use of a 3D pore-network model, using a novel architecture, to calculate macroscopic properties of the medium such as diffusivity, subject to pore space changes as the media degrade. Results from a reactive transport model of a representative geological waste disposal package are also presented to demonstrate the effect of media property change on the solute migration behaviour, illustrating the complex interplay between kinetic biogeochemical processes and diffusion dominant transport. The initial modelling results demonstrate the feasibility of a coupled modelling approach (using pore-network model and reactive

Generalized Analytical Treatment Of The Source Strength In The Solution Of The Diffusion Equation

International Nuclear Information System (INIS)

Essa, Kh.S.M.; EI-Otaify, M.S.

2007-01-01

The source release strength (which is an integral part of the mathematical formulation of the diffusion equation) together with the boundary conditions leads to three different forms of the diffusion equation. The obtained forms have been solved analytically under different boundary conditions, by using transformation of axis, cosine, and Fourier transformation. Three equivalent alternative mathematical formulations of the problem have been obtained. The estimated solution of the concentrations at the ground source has been used for comparison with observed concentrations data for SF 6 tracer experiments in low wind and unstable conditions at lIT Delhi sports ground. A good agreement between estimated and observed concentrations is found

Multigrid solution of diffusion equations on distributed memory multiprocessor systems

International Nuclear Information System (INIS)

Finnemann, H.

1988-01-01

The subject is the solution of partial differential equations for simulation of the reactor core on high-performance computers. The parallelization and implementation of nodal multigrid diffusion algorithms on array and ring configurations of the DIRMU multiprocessor system is outlined. The particular iteration scheme employed in the nodal expansion method appears similarly efficient in serial and parallel environments. The combination of modern multi-level techniques with innovative hardware (vector-multiprocessor systems) provides powerful tools needed for real time simulation of physical systems. The parallel efficiencies range from 70 to 90%. The same performance is estimated for large problems on large multiprocessor systems being designed at present. (orig.) [de

The KASY synthesis programme for the approximative solution of the 3-dimensional neutron diffusion equation

International Nuclear Information System (INIS)

Buckel, G.; Wouters, R. de; Pilate, S.

1977-01-01

The synthesis code KASY for an approximate solution of the three-dimensional neutron diffusion equation is described; the state of the art as well as envisaged program extensions and the application to tasks from the field of reactor designing are dealt with. (RW) [de

Effects of land-applied ammonia scrubber solutions on yield, nitrogen uptake, soil test phosphorus and phosphorus runoff

Science.gov (United States)

Ammonia (NH3) scrubbers reduce amounts of NH3 and dust released from animal rearing facilities, while generating nitrogen (N) rich solutions, which may be used as fertilizer. The objective of this study was to determine the effects of various NH3 scrubber solutions on yields, N uptake by forage, so...

Analytical modal diffusion theory based on flux separability

International Nuclear Information System (INIS)

Segev, M.

1987-01-01

The theory provides for an iterative solution of the mathematical problem of generating the assembly-wise power distribution in a LWR through the solution of the 2-group, multidimensional, diffusion equation. The companion problems of assembly pre-homogenization and of pin power reconstruction are of no direct concern presently. The theoretical development stems from the assumption of flux separability in X, Y and Z. The assumption derives from the notion that separability holds in a great part of the interior of a LWR assembly. More important, well accurate power maps are generated with a code based on the theoretical develpment yielded by the basic assumption

Principles and implementation of diffusion-weighted and diffusion tensor imaging

International Nuclear Information System (INIS)

Roberts, Timothy P.L.; Schwartz, E.S.

2007-01-01

We review the physiological basis of diffusion-weighted imaging and discuss the implementation of diffusion-weighted imaging pulse sequences and the subsequent postprocessing to yield quantitative estimations of diffusion parameters. We also introduce the concept of directionality of ''apparent'' diffusion in vivo and the means of assessing such anisotropy quantitatively. This in turn leads to the methodological application of diffusion tensor imaging and the subsequent postprocessing, known as tractography. The following articles deal with the clinical applications enabled by such methodologies. (orig.)

Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence

Energy Technology Data Exchange (ETDEWEB)

Diamond, Kevin R; Farrell, Thomas J; Patterson, Michael S [Department of Medical Physics, Juravinski Cancer Centre and McMaster University, 699 Concession Street, Hamilton, Ontario L8V 5C2 (Canada)

2003-12-21

Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance were calculated by diffusion theory and Monte Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS{sub 4}), Photofrin or meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride (TPPS{sub 4}). The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelengthwas recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS{sub 4} and TPPS{sub 4} were calculated to be 0.59 {+-} 0.03 and 0.121 {+-} 0

Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence

International Nuclear Information System (INIS)

Diamond, Kevin R; Farrell, Thomas J; Patterson, Michael S

2003-01-01

Steady-state diffusion theory models of fluorescence in tissue have been investigated for recovering fluorophore concentrations and fluorescence quantum yield. Spatially resolved fluorescence, excitation and emission reflectance were calculated by diffusion theory and Monte Carlo simulations, and measured using a multi-fibre probe on tissue-simulating phantoms containing either aluminium phthalocyanine tetrasulfonate (AlPcS 4 ), Photofrin or meso-tetra-(4-sulfonatophenyl)-porphine dihydrochloride (TPPS 4 ). The accuracy of the fluorophore concentration and fluorescence quantum yield recovered by three different models of spatially resolved fluorescence were compared. The models were based on: (a) weighted difference of the excitation and emission reflectance, (b) fluorescence due to a point excitation source or (c) fluorescence due to a pencil beam excitation source. When literature values for the fluorescence quantum yield were used for each of the fluorophores, the fluorophore absorption coefficient (and hence concentration) at the excitation wavelengthwas recovered with a root-mean-square accuracy of 11.4% using the point source model of fluorescence and 8.0% using the more complicated pencil beam excitation model. The accuracy was calculated over a broad range of optical properties and fluorophore concentrations. The weighted difference of reflectance model performed poorly, with a root-mean-square error in concentration of about 50%. Monte Carlo simulations suggest that there are some situations where the weighted difference of reflectance is as accurate as the other two models, although this was not confirmed experimentally. Estimates of the fluorescence quantum yield in multiple scattering media were also made by determining independently from the fitted absorption spectrum and applying the various diffusion theory models. The fluorescence quantum yields for AlPcS 4 and TPPS 4 were calculated to be 0.59 ± 0.03 and 0.121 ± 0.001 respectively using the point

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.

2014-01-06

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.; Al-Mulla, Noah

2014-01-01

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Yield Behavior of Solution Treated and Aged Ti-6Al-4V

Science.gov (United States)

Ring, Andrew J.; Baker, Eric H.; Salem, Jonathan A.; Thesken, John C.

2014-01-01

Post yield uniaxial tension-compression tests were run on a solution treated and aged (STA), titanium 6-percent aluminum 4-percent vanadium (Ti-6Al-4V) alloy to determine the yield behavior on load reversal. The material exhibits plastic behavior almost immediately on load reversal implying a strong Bauschinger effect. The resultant stress-strain data was compared to a 1D mechanics model and a finite element model used to design a composite overwrapped pressure vessel (COPV). Although the models and experimental data compare well for the initial loading and unloading in the tensile regime, agreement is lost in the compressive regime due to the Bauschinger effect and the assumption of perfect plasticity. The test data presented here are being used to develop more accurate cyclic hardening constitutive models for future finite element design analysis of COPVs.

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Eternal solutions to a singular diffusion equation with critical gradient absorption

International Nuclear Information System (INIS)

Iagar, Razvan Gabriel; Laurençot, Philippe

2013-01-01

The existence of non-negative radially symmetric eternal solutions of exponential self-similar type u(t, x) = e −pβt/(2−p) f β (|x|e −βt ; β) is investigated for the singular diffusion equation with critical gradient absorption ∂ t u−Δ p u+|∇u| p/2 =0  in (0,∞)×R N , where 2N/(N + 1) < p < 2. Such solutions are shown to exist only if the parameter β ranges in a bounded interval (0, β * ], which is in sharp contrast to well-known singular diffusion equations, such as ∂ t φ − Δ p φ = 0 when p = 2N/(N + 1), N ⩾ 1, or the porous medium equation ∂ t φ − Δφ m  = 0 when m = (N − 2)/N, N ⩾ 3. Moreover, the profile f(r; β) decays to zero as r → ∞ in a faster way for β = β * than for β ∈ (0, β * ) but the algebraic leading order is the same in both cases. In fact, for large r, f(r; β * ) decays as r −p/(2−p) while f(r; β) behaves as (log r) 2/(2−p) r −p/(2−p) when β ∈ (0, β * ). (paper)

Influence of convection on the diffusive transport and sieving of water and small solutes across the peritoneal membrane.

Science.gov (United States)

Asghar, Ramzana B; Diskin, Ann M; Spanel, Patrik; Smith, David; Davies, Simon J

2005-02-01

The three-pore model of peritoneal membrane physiology predicts sieving of small solutes as a result of the presence of a water-exclusive pathway. The purpose of this study was to measure the diffusive and convective components of small solute transport, including water, under differing convection. Triplicate studies were performed in eight stable individuals using 2-L exchanges of bicarbonate buffered 1.36 or 3.86% glucose and icodextrin. Diffusion of water was estimated by establishing an artificial gradient of deuterated water (HDO) between blood/body water and the dialysate. (125)RISA (radio-iodinated serum albumin) was used as an intraperitoneal volume marker to determine the net ultrafiltration and reabsorption of fluid. The mass transfer area coefficient (MTAC) for HDO and solutes was estimated using the Garred and Waniewski equations. The MTAC of HDO calculated for 1.36% glucose and icodextrin were similar (36.8 versus 39.7 ml/min; P = 0.3), whereas for other solutes, values obtained using icodextrin were consistently higher (P solutes is a reflection of their sieving. The increase in the MTAC of water and urea associated with an increase in convection is most likely due to increased mixing within the interstitium.

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

International Nuclear Information System (INIS)

Ceolin, C.; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T.

2015-01-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

Energy Technology Data Exchange (ETDEWEB)

Ceolin, C., E-mail: celina.ceolin@gmail.com [Universidade Federal de Santa Maria (UFSM), Frederico Westphalen, RS (Brazil). Centro de Educacao Superior Norte; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T., E-mail: celina.ceolin@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2015-07-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

Hydration and rotational diffusion of levoglucosan in aqueous solutions

Science.gov (United States)

Corezzi, S.; Sassi, P.; Paolantoni, M.; Comez, L.; Morresi, A.; Fioretto, D.

2014-05-01

Extended frequency range depolarized light scattering measurements of water-levoglucosan solutions are reported at different concentrations and temperatures to assess the effect of the presence and distribution of hydroxyl groups on the dynamics of hydration water. The anhydro bridge, reducing from five to three the number of hydroxyl groups with respect to glucose, considerably affects the hydration properties of levoglucosan with respect to those of mono and disaccharides. In particular, we find that the average retardation of water dynamics is ≈3-4, that is lower than ≈5-6 previously found in glucose, fructose, trehalose, and sucrose. Conversely, the average number of retarded water molecules around levoglucosan is 24, almost double that found in water-glucose mixtures. These results suggest that the ability of sugar molecules to form H-bonds through hydroxyl groups with surrounding water, while producing a more effective retardation, it drastically reduces the spatial extent of the perturbation on the H-bond network. In addition, the analysis of the concentration dependence of the hydration number reveals the aptitude of levoglucosan to produce large aggregates in solution. The analysis of shear viscosity and rotational diffusion time suggests a very short lifetime for these aggregates, typically faster than ≈20 ps.

Formation of solid solution during mutual diffusion of tungsten and molybdenum in the process of sintering

International Nuclear Information System (INIS)

Timofeeva, A.A.; Bulat, I.B.; Voronin, Yu.V.; Fedoseev, G.K.; Karasev, V.M.

1984-01-01

A process of a solid solution homogenization during sintering of W-15Mo and W-5Mo alloys is studied by the methods of density measurements, analysis of the X-ray lines physical broadening and determination of crystalline lattice constant. Study of the process of solid solution formation under conditions of powder composite sintering is shown to be conducted with account of peculiarities of tungsten and molybdenum mutual diffusion in the investigated temperature range of concentrations

Solution of the advection-diffusion equation for a nonhomogeneous and nonstationary Planetary Boundary Layer by GILTT (Generalized Integral Laplace Transform Technique)

International Nuclear Information System (INIS)

Mello, Kelen Berra de

2005-02-01

In this work is shown the solution of the advection-diffusion equation to simulate a pollutant dispersion in the Planetary Boundary Layer. The solution is obtained through of the GILTT (Generalized Integral Laplace Transform Technique) analytic method and of the numerical inversion Gauss Quadrature. The validity of the solution is proved using concentration obtained from the model with concentration obtained for Copenhagen experiment. In this comparison was utilized potential and logarithmic wind profile and eddy diffusivity derived by Degrazia et al (1997) [17] and (2002) [19]. The best results was using the potential wind profile and the eddy diffusivity derived by Degrazia et al (1997). The vertical velocity influence is shown in the plume behavior of the pollutant concentration. Moreover, the vertical and longitudinal velocity provided by Large Eddy Simulation (LES) was stood in the model to simulate the turbulent boundary layer more realistic, the result was satisfactory when compared with contained in the literature. (author)

Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids

International Nuclear Information System (INIS)

Ragusa, Jean C.

2015-01-01

In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement

Yields of hydrogen peroxide from the reaction of hydroxyl radical with organic compounds in solution and ice

Directory of Open Access Journals (Sweden)

T. Hullar

2011-07-01

Full Text Available Hydrogen peroxide (HOOH is a significant oxidant in atmospheric condensed phases (e.g., cloud and fog drops, aqueous particles, and snow that also photolyzes to form hydroxyl radical (^•OH. ^•OH can react with organics in aqueous phases to form organic peroxyl radicals and ultimately reform HOOH, but the efficiency of this process in atmospheric aqueous phases, as well as snow and ice, is not well understood. We investigate HOOH formation from ^•OH attack on 10 environmentally relevant organic compounds: formaldehyde, formate, glycine, phenylalanine, benzoic acid, octanol, octanal, octanoic acid, octanedioic acid, and 2-butoxyethanol. Liquid and ice samples with and without nitrate (as an ^•OH source were illuminated using simulated solar light, and HOOH formation rates were measured as a function of pH and temperature. For most compounds, the formation rate of HOOH without nitrate was the same as the background formation rate in blank water (i.e., illumination of the organic species does not produce HOOH directly, while formation rates with nitrate were greater than the water control (i.e., reaction of ^•OH with the organic species forms HOOH. Yields of HOOH, defined as the rate of HOOH production divided by the rate of ^•OH production, ranged from essentially zero (glycine to 0.24 (octanal, with an average of 0.12 ± 0.05 (95 % CI. HOOH production rates and yields were higher at lower pH values. There was no temperature dependence of the HOOH yield for formaldehyde or octanedioic acid between −5 to 20 °C and ice samples had approximately the same HOOH yield as the aqueous solutions. In contrast, HOOH yields in formate solutions were higher at 5 and 10 °C compared to −5 and 20 °C. Yields of HOOH in ice for solutions containing nitrate and either phenylalanine, benzoate, octanal, or octanoic acid were indistinguishable from zero. Our HOOH yields were approximately

Isolated effects of external bath osmolality, solute concentration, and electrical charge on solute transport across articular cartilage.

Science.gov (United States)

Pouran, Behdad; Arbabi, Vahid; Zadpoor, Amir A; Weinans, Harrie

2016-12-01

The metabolic function of cartilage primarily depends on transport of solutes through diffusion mechanism. In the current study, we use contrast enhanced micro-computed tomography to determine equilibrium concentration of solutes through different cartilage zones and solute flux in the cartilage, using osteochondral plugs from equine femoral condyles. Diffusion experiments were performed with two solutes of different charge and approximately equal molecular weight, namely iodixanol (neutral) and ioxaglate (charge=-1) in order to isolate the effects of solute's charge on diffusion. Furthermore, solute concentrations as well as bath osmolality were changed to isolate the effects of steric hindrance on diffusion. Bath concentration and bath osmolality only had minor effects on the diffusion of the neutral solute through cartilage at the surface, middle and deep zones, indicating that the diffusion of the neutral solute was mainly Fickian. The negatively charged solute diffused considerably slower through cartilage than the neutral solute, indicating a large non-Fickian contribution in the diffusion of charged molecules. The numerical models determined maximum solute flux in the superficial zone up to a factor of 2.5 lower for the negatively charged solutes (charge=-1) as compared to the neutral solutes confirming the importance of charge-matrix interaction in diffusion of molecules across cartilage. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

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

Energy Technology Data Exchange (ETDEWEB)

Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)

2016-01-15

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

Diffusion-enhanced Förster resonance energy transfer and the effects of external quenchers and the donor quantum yield.

Science.gov (United States)

Jacob, Maik H; Dsouza, Roy N; Ghosh, Indrajit; Norouzy, Amir; Schwarzlose, Thomas; Nau, Werner M

2013-01-10

effective FRET rate and the recovered donor-acceptor distance depend on the quantum yield, most strongly in the absence of diffusion, which has to be accounted for in the interpretation of distance trends monitored by FRET.

A numerical solution for a class of time fractional diffusion equations with delay

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

Ionic Diffusion and Kinetic Homogeneous Chemical Reactions in the Pore Solution of Porous Materials with Moisture Transport

DEFF Research Database (Denmark)

Johannesson, Björn

2009-01-01

Results from a systematic continuum mixture theory will be used to establish the governing equations for ionic diffusion and chemical reactions in the pore solution of a porous material subjected to moisture transport. The theory in use is the hybrid mixture theory (HMT), which in its general form......’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...

Solving the neutron diffusion equation on combinatorial geometry computational cells for reactor physics calculations

International Nuclear Information System (INIS)

Azmy, Y. Y.

2004-01-01

An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)

On weak solutions to a diffuse interface model of a binary mixture of compressible fluids

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2016-01-01

Roč. 9, č. 1 (2016), s. 173-183 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Euler-Cahn-Hilliard system * weak solution * diffuse interface model Subject RIV: BA - General Mathematics Impact factor: 0.781, year: 2016 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=12093

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

Energy Technology Data Exchange (ETDEWEB)

Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand); Fichtner, Horst; Walter, Dominik [Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum (Germany)

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.

Development of a coarse mesh code for the solution of two group static diffusion problems

International Nuclear Information System (INIS)

Barros, R.C. de.

1985-01-01

This new coarse mesh code designed for the solution of 2 and 3 dimensional static diffusion problems, is based on an alternating direction method which consists in the solution of one dimensional problem along each coordinate direction with leakage terms for the remaining directions estimated from previous interactions. Four versions of this code have been developed: AD21 - 2D - 1/4, AD21 - 2D - 4/4, AD21 - 3D - 1/4 and AD21 - 3D - 4/4; these versions have been designed for 2 and 3 dimensional problems with or without 1/4 symmetry. (Author) [pt

Activation energy of tracer-diffusion of manganese ions (Mn2+) in alkali metal chloride solutions

International Nuclear Information System (INIS)

Borhade, A.V.

2000-01-01

The activation energy of the tracer diffusion of Mn 2+ ions in alkali chloride solutions (0.1M) has been determined in agar gel medium (1-2.5%) over the temperature range of 25 - 45 deg C. The decrease in the value of the Arrhenius parameters, E and D 0 , with gel percentage is explained on the basis of the transition state theory. Further, the activation energy as a function of electrolyte concentration is also investigated using 1% agar gel in the temperature range of 25 - 45 deg C. In both the cases, the activation energies are determined by the least square fitting of the diffusion coefficient data obtained at various temperatures through the Arrhenius plots. (author)

Diffusion Influenced Adsorption Kinetics.

Science.gov (United States)

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.

Homotopy analysis method for neutron diffusion calculations

International Nuclear Information System (INIS)

Cavdar, S.

2009-01-01

The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on a fundamental concept in differential geometry and topology, the homotopy. It has proved useful for problems involving algebraic, linear/non-linear, ordinary/partial differential and differential-integral equations being an analytic, recursive method that provides a series sum solution. It has the advantage of offering a certain freedom for the choice of its arguments such as the initial guess, the auxiliary linear operator and the convergence control parameter, and it allows us to effectively control the rate and region of convergence of the series solution. HAM is applied for the fixed source neutron diffusion equation in this work, which is a part of our research motivated by the question of whether methods for solving the neutron diffusion equation that yield straightforward expressions but able to provide a solution of reasonable accuracy exist such that we could avoid analytic methods that are widely used but either fail to solve the problem or provide solutions through many intricate expressions that are likely to contain mistakes or numerical methods that require powerful computational resources and advanced programming skills due to their very nature or intricate mathematical fundamentals. Fourier basis are employed for expressing the initial guess due to the structure of the problem and its boundary conditions. We present the results in comparison with other widely used methods of Adomian Decomposition and Variable Separation.

Experimental test of depth dependence of solutions for time-resolved diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Laidevant, A.; Da Silva, A.; Moy, J.P.; Berger, M.; Dinten, J.M

2004-07-01

The determination of optical properties of a semi-infinite medium such as biological tissue has been widely investigated by many authors. Reflectance formulas can be derived from the diffusion equation for different boundary conditions at the medium-air interface. This quantity can be measured at the medium surface. For realistic objects, such as a mouse, tissue optical properties can realistically only be determined at the object surface. However, near the surface diffusion approximation is weak and boundary models have to be considered. In order to investigate the validity of the time resolved reflectance approach at the object boundary, we have estimated optical properties of a liquid semi-infinite medium by this method for different boundary conditions and different fiber's position beneath the surface. The time-correlated single photon counting (TCSPC) technique is used to measure the reflectance curve. Our liquid phantoms are made of water, Intra-lipid and Ink. Laser light is delivered by a pulsed laser diode. Measurements are then fitted to theoretical solutions expressed as a function of source and detector's depth and distance. By taking as reference the optical properties obtained from the infinite model for fibers deeply immersed, influence of the different boundary conditions and bias induced are established for different fibers' depth and a variety of solutions. This influence is analysed by comparing evolution of the reflectance models, as well as estimations of absorption and scattering coefficients. According to this study we propose a strategy for determining optical properties of a solid phantom where measurements can only be realized at the surface. (authors)

A development of simulation and analytical program for through-diffusion experiments for a single layer of diffusion media

International Nuclear Information System (INIS)

Sato, Haruo

2001-01-01

A program (TDROCK1. FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual. (author)

The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

Diffusion of inorganic ion aqueous solution into hydrophilic polymer fiber and molecular orientation

International Nuclear Information System (INIS)

Kawaguchi, Akio

2001-01-01

The adsorption process of iodine to nylon 6 (polyamide-6), as well as deiodination process, has been an issue of controversy in the past half century from the view points related to the conversion of hydrogen bonding (α phase vs. γ phase). In the researches since late '80s, it has been revealed that the adsorption or inclusion of iodine to polyamides causes formations of various kind of structures to be called complexes whether they are crystalline or amorphous, and the formation of complex is reflected on the physical properties (especially on adsorption and ion mobility). Among them, it has been reported about both the doubly-oriented samples and the non-oriented samples that the ion diffusion causes molecular chain orientation during the complex formation. In the present experiment the change of molecular orientation in the early stage of the complex formation is studied by the time-resolved measurement with synchrotron radiation facility at SPring-8. Through-view and edge-view diffraction patterns of doubly oriented nylon 6 and non-oriented one were measured at 0.1 nm wavelength introducing I2-KI aqueous solution. It is observed that the formation of complex (i.e. diffusion of polyiodine) is attained in about 0.3 to 0.4 sec. even in non-oriented sample. From the analysis of the diffraction behavior, it is summarized that the inclusion of iodine into the crystalline phase of nylon 6 is possible from either sides of the molecular directions, namely normal diffusion and parallel diffusion. It is concluded that the diffusion and adsorption of inorganic ions including polyiodine to polyamide causes not only the formation of complexes in the crystalline phase but also give motive force to change structure in the surrounding non-crystalline region. (S. Funahashi)

Influence of fructose on the diffusion of potassium hydrogen phosphate in aqueous solutions at 25 °C

International Nuclear Information System (INIS)

Verissimo, Luis M.P.; Teigão, Joana M.M.; Ramos, M. Luísa; Burrows, Hugh D.; Esteso, Miguel A.; Ribeiro, Ana C.F.

2016-01-01

Highlights: • Diffusion coefficients of aqueous systems of fructose and potassium hydrogen phosphate measured with Lobo’s cell. • Influence of the fructose on the diffusion of potassium hydrogen phosphate. • Interactions between of hydrogen phosphate anion and fructose. - Abstract: Diffusion coefficients have been measured at 25 °C for potassium hydrogen phosphate (K_2HPO_4, 0.101 mol kg"−"1) in aqueous solutions containing various concentrations of fructose from (0.001 to 0.101) mol kg"−"1, using a conductimetric cell (the Lobo cell) coupled to an automatic data acquisition system. Significant effects of fructose were observed on the diffusion of K_2HPO_4 in these mixtures, which are attributed to the interaction between HPO_4"2"− anion (or other protonated forms) and fructose. Support for this comes from "1H and "1"3C NMR spectroscopy, which are compatible with binding between the anomeric forms of D-fructose and the HPO_4"2"− anion.

Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

High-Yield Production of Levulinic Acid from Pretreated Cow Dung in Dilute Acid Aqueous Solution

Directory of Open Access Journals (Sweden)

Jialei Su

2017-02-01

Full Text Available Agricultural waste cow dung was used as feedstock for the production of a high value–added chemical levulinic acid (LA in dilute acid aqueous solutions. A high LA yield of 338.9 g/kg was obtained from the pretreated cow dung, which was much higher than that obtained from the crude cow dung (135 g/kg, mainly attributed to the breakage of the lignin fraction in the lignocellulose structure of the cow dung by potassium hydroxide (KOH pretreatment, and thus enhanced the accessibility of cow dung to the acid sites in the catalytic reaction. Meanwhile, another value-added chemical formic acid could be obtained with a yield of ca. 160 g/kg in the process, implying a total production of ca. 500 g/kg yield for LA and formic acid from the pretreated cow dung with the proposed process. The developed process was shown to be tolerant to high initial substrate loading with a satisfied LA yield. This work provides a promising strategy for the value-increment utilization of liglocellulosic agricultural residues.

Thermal expansion and thermal diffusivity properties of Co-Si solid solutions and intermetallic compounds

International Nuclear Information System (INIS)

Ruan, Ying; Li, Liuhui; Gu, Qianqian; Zhou, Kai; Yan, Na; Wei, Bingbo

2016-01-01

Highlights: • Length change difference between rapidly and slowly solidified Co-Si alloy occurs at high temperature. • Generally CTE increases with an increasing Si content. • The thermal diffusion abilities are CoSi 2 > Co 95 Si 5 > Co 90 Si 10 > Co 2 Si > CoSi if T exceeds 565 K. • All the CTE and thermal diffusivity variations with T satisfy linear or polynomial relations. - Abstract: The thermal expansion of Co-Si solid solutions and intermetallic compounds was measured via dilatometric method, compared with the results of first-principles calculations, and their thermal diffusivities were investigated using laser flash method. The length changes of rapidly solidified Co-Si alloys are larger than those of slowly solidified alloys when temperature increases to around 1000 K due to the more competitive atom motion. The coefficient of thermal expansion (α) of Co-Si alloy increases with an increasing Si content, except that the coefficient of thermal expansion of Co 95 Si 5 influenced by both metastable structure and allotropic transformation is lower than that of Co 90 Si 10 at a higher temperature. The thermal expansion abilities of Co-Si intermetallic compounds satisfy the relationship of Co 2 Si > CoSi > CoSi 2 , and the differences of the coefficients of thermal expansion between them increase with the rise of temperature. The thermal diffusivity of CoSi 2 is evidently larger than the values of other Co-Si alloys. If temperature exceeds 565 K, their thermal diffusion abilities are CoSi 2 > Co 95 Si 5 > Co 90 Si 10 > Co 2 Si > CoSi. All the coefficient of thermal expansion and thermal diffusivity variations with temperature satisfy linear or polynomial relations.

Diffusion coefficients of gaseous scavengers in organic liquids used in radiation chemistry

International Nuclear Information System (INIS)

Luthjens, L.H.; De Leng, H.C.; Warman, J.M.; Hummel, A.

1990-01-01

Diffusion coefficients have been measured of some gaseous scavengers commonly used in radiation chemical studies: CO 2 , NH 3 , SF 6 and O 2 in trans-decalin, cyclohexane, isooctane and n-hexane, and CO 2 in cis-decalin, at 25 0 C. A modified diaphragm cell method has been used in order to limit the time needed for a measurement to about 6 h. Analysis of the results yields a simple semi-empirical predictive relation for the diffusion coefficient of a (gaseous) solute A in an organic solvent B. Diffusion coefficients calculated using the simple relation appear to give results in fair agreement with published values, over a range of organic solvents including alcohols, and over a range of temperatures. Some measured and predicted values are discussed with reference to results from the literature. (author)

Correlation effects in diffusion: a new approach

International Nuclear Information System (INIS)

Benoist, Pierre; Lafore, Pierre; Bocquet, J.-L.

1975-11-01

All the methods used up to now to solve the correlation problems are approximate: they do not allow the defect causing the migration to walk to infinity in the crystal. The new method of the present study enables to solve rigorously the correlation problems with the use of double Laplace-Fourier transforms. The method yields both: a compact formulation of all the problems previously treated by other investigators; a solution for problems still unresolved (influence of vacancy concentration on the correlation factor for self diffusion) or too much sophisticated to be treated by the previous methods (dissociated interstitial...) [fr

Design guidelines for H-Darrieus wind turbines: Optimization of the annual energy yield

International Nuclear Information System (INIS)

Bianchini, Alessandro; Ferrara, Giovanni; Ferrari, Lorenzo

2015-01-01

Highlights: • Proposal for a new design criterion for H-Darrieus turbines based on the energy-yield maximization. • 21,600 design cases analyzed to identify the best solutions for each installation site (i.e. average wind speed). • Critical analysis of the best design choices in terms of turbine shape, dimensions, airfoils and constraints. • Notable energy increase provided by the new design approach. • Each site requires a specific turbine concept to optimize the energy yield. - Abstract: H-Darrieus wind turbines are gaining popularity in the wind energy market, particularly as they are thought to represent a suitable solution even in unconventional installation areas. To promote the diffusion of this technology, industrial manufacturers are continuously proposing new and appealing exterior solutions, coupled with tempting rated-power offers. The actual operating conditions of a rotor over a year can be, however, very different from the nominal one and strictly dependent on the features of the installation site. Based on these considerations, a turbine optimization oriented to maximize the annual energy yield, instead of the maximum power, is thought to represent a more interesting solution. With this goal in mind, 21,600 test cases of H-Darrieus rotors were compared on the basis of their energy-yield capabilities for different annual wind distributions in terms of average speed. The wind distributions were combined with the predicted performance maps of the rotors obtained with a specifically developed numerical code based on a Blade Element Momentum (BEM) approach. The influence on turbine performance of the cut-in speed was accounted for, as well as the limitations due to structural loads (i.e. maximum rotational speed and maximum wind velocity). The analysis, carried out in terms of dimensionless parameters, highlighted the aerodynamic configurations able to ensure the largest annual energy yield for each wind distribution and set of aerodynamic

Root-induced Changes in the Rhizosphere of Extreme High Yield Tropical Rice: 2. Soil Solution Chemical Properties

Directory of Open Access Journals (Sweden)

Mitsuru Osaki

2012-09-01

Full Text Available Our previous studies showed that the extreme high yield tropical rice (Padi Panjang produced 3-8 t ha-1 without fertilizers. We also found that the rice yield did not correlate with some soil properties. We thought that it may be due to ability of root in affecting soil properties in the root zone. Therefore, we studied the extent of rice root in affecting the chemical properties of soil solution surrounding the root zone. A homemade rhizobox (14x10x12 cm was used in this experiment. The rhizobox was vertically segmented 2 cm interval using nylon cloth that could be penetrated neither root nor mycorrhiza, but, soil solution was freely passing the cloth. Three soils of different origins (Kuin, Bunipah and Guntung Papuyu were used. The segment in the center was sown with 20 seeds of either Padi Panjang or IR64 rice varieties. After emerging, 10 seedlings were maintained for 5 weeks. At 4 weeks after sowing, some chemical properties of the soil solution were determined. These were ammonium (NH4+, nitrate (NO3-, phosphorus (P and iron (Fe2+ concentrations and pH, electric conductivity (EC and oxidation reduction potential (ORP. In general, the plant root changed solution chemical properties both in- and outside the soil rhizosphere. The patterns of changes were affected by the properties of soil origins. The release of exudates and change in ORP may have been responsible for the changes soil solution chemical properties.

The analytical benchmark solution of spatial diffusion kinetics in source driven systems for homogeneous media

International Nuclear Information System (INIS)

Oliveira, F.L. de; Maiorino, J.R.; Santos, R.S.

2007-01-01

This paper describes a closed form solution obtained by the expansion method for the general time dependent diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. Thus, first an analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent without precursors was also solved and the results inter compared with results obtained by the previous one group models for a given fast homogeneous media, and different types of source transients. The results are being compared with the obtained by numerical methods. (author)

Molecular theory for nuclear magnetic relaxation in protein solutions and tissue; Surface diffusion and free-volume analogy

Energy Technology Data Exchange (ETDEWEB)

Kimmich, R; Nusser, W; Gneiting, T [Ulm Universitaet (Federal Republic of Germany). Sektion Kernresonanzspektroskopie

1990-04-01

A model theory is presented explaining a series of striking phenomena observed with nuclear magnetic relaxation in protein systems such as solutions or tissue. The frequency, concentration and temperature dependences of proton or deuteron relaxation times of protein solutions and tissue are explained. It is concluded that the translational diffusion of water molecules along the rugged surfaces of proteins and, to a minor degree, protein backbone fluctuations are crucial processes. The rate limiting factor of macromolecular tumbling is assumed to be given by the free water content in a certain analogy to the free-volume model of Cohen ad Turnbull. There are two characteristic water mass fractions indicating the saturation of the hydration shells and the onset of protein tumbling. A closed and relatively simple set of relaxation formulas is presented. The potentially fractal nature of the diffusion of water molecules on the protein surface is discussed. (author). 43 refs.; 4 figs.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

Science.gov (United States)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

OpenAIRE

Fagioli, Simone; Radici, Emanuela

2018-01-01

We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\\infty} \\cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelti...

Traveling wave solutions of a biological reaction-convection-diffusion equation model by using $(G'/G$ expansion method

Directory of Open Access Journals (Sweden)

Shahnam Javadi

2013-07-01

Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

A new model of anomalous phosphorus diffusion in silicon

International Nuclear Information System (INIS)

Budil, M.; Poetzl, H.; Stingeder, G.; Grasserbauer, M.

1989-01-01

A model is presented to describe the 'kink and tail' diffusion of phosphorus. The diffusion behaviour of phosphorus is expplained by the motion of phosphorus-interstitial and phosphorus-vacancy pairs in different charge states. The model yields the enhancement of diffusion in the tail region depending on surface concentration. Furthermore it yields the same selfdiffusion coefficient for interstitials as the gold diffusion experiments. A transformation of the diffusion equation was found to reduce the number of simulation equations. (author) 7 refs., 5 figs

An axisymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples.

Science.gov (United States)

Takeda, M; Hiratsuka, T; Ito, K; Finsterle, S

2011-04-25

Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an

An asixymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples

Energy Technology Data Exchange (ETDEWEB)

Takeda, M.; Hiratsuka, T.; Ito, K.; Finsterle, S.

2011-02-01

Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an

Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.

Science.gov (United States)

Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner

2017-01-01

We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.

Conservative diffusions

International Nuclear Information System (INIS)

Carlen, E.A.

1984-01-01

In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions. These diffusions are formally given by stochastic differential equations with extremely singular coefficients. Using PDE methods, we prove the existence of solutions. This reult provides a rigorous basis for stochastic mechanics. (orig.)

A variational nodal diffusion method of high accuracy; Varijaciona nodalna difuziona metoda visoke tachnosti

Energy Technology Data Exchange (ETDEWEB)

Tomasevic, Dj; Altiparmarkov, D [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)

1988-07-01

A variational nodal diffusion method with accurate treatment of transverse leakage shape is developed and presented in this paper. Using Legendre expansion in transverse coordinates higher order quasi-one-dimensional nodal equations are formulated. Numerical solution has been carried out using analytical solutions in alternating directions assuming Legendre expansion of the RHS term. The method has been tested against 2D and 3D IAEA benchmark problem, as well as 2D CANDU benchmark problem. The results are highly accurate. The first order approximation yields to the same order of accuracy as the standard nodal methods with quadratic leakage approximation, while the second order reaches reference solution. (author)

Dynamic and structural characterisation of micellar solutions of surfactants by spin relaxation and translational diffusion

International Nuclear Information System (INIS)

Mahieu, Nathalie

1992-01-01

The work reported in this research thesis aimed at characterizing micellar phases formed by some surfactants (sodium carboxylates) in aqueous solution. After some recalls on nuclear magnetic resonance dealing with spin relaxation (longitudinal relaxation, transverse relaxation, relaxation in the rotating coordinate system, and crossed relaxation), and comments on the dipolar mechanism responsible of relaxation phenomena, the author presents the methods used for relaxation parameter measurement and the data processing software issued from experiments. He presents experiments which allowed the self-diffusion coefficient to be measured, reports data processing, and addresses problems of special diffusion and of coherence transfers during diffusion measurements. Results of proton relaxation measurements are then presented and discussed. They are used to determine the micellar state of the studied carboxylates. The case of the oleate is also addressed. Measurements of carbon-13 relaxation times are reported, and exploited in terms of structural parameters by using the Relaxator software. An original method of the hetero-nuclear Overhauser method is presented, and used to assess the average distance between water molecules and micelle surface [fr

Impurity diffusion of cobalt in plutonium

International Nuclear Information System (INIS)

Charissoux, Christian; Calais, Daniel.

1975-01-01

The sectioning method for investigation of the impurity diffusion of 60 Co in the fcc and bcc phases of plutonium gives the following results: 344-426 deg C: D=1.2x10 -2 exp(-12700/RT)cm 2 /s in delta Pu(fcc); 484-621 deg C: D=1.4x10 -3 exp(-9900/RT)cm 2 /s in epsilon Pu(bcc). Cobalt is a fast diffuser in plutonium; the diffusion coefficient being unaffected by phase changes delta'→delta; delta'→epsilon, the diffusion mechanism is probably dissociative in both phases, the solute becoming interstitial by: solute (substitution) reversible solute (interstitial) + vacancy [fr

The numerical analysis of eigenvalue problem solutions in the multigroup diffusion theory

International Nuclear Information System (INIS)

Woznick, Z.I.

1994-01-01

In this paper a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations is described. Usually the solution method is based on the system of inner and outer iterations. The presented matrix formalism allows us to visualize clearly, how the used matrix splitting influences the structure of the matrix in an eigenvalue problem to be solved as well as the independence between inner and outer iterations within global iterations. To keep the page limit, the present version of the paper consists only with first three of five sections given in the original paper under the same title (which will be published soon). (author). 13 refs

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

KAUST Repository

Almeida, Regina C.

2010-08-01

A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems

KAUST Repository

Almeida, Regina C.; Oden, J. Tinsley

2010-01-01

A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.

On Diffusion and Permeation

KAUST Repository

Peppin, Stephen S. L.

2009-01-01

Diffusion and permeation are discussed within the context of irreversible thermodynamics. A new expression for the generalized Stokes-Einstein equation is obtained which links the permeability to the diffusivity of a two-component solution and contains the poroelastic Biot-Willis coefficient. The theory is illustrated by predicting the concentration and pressure profiles during the filtration of a protein solution. At low concentrations the proteins diffuse independently while at higher concentrations they form a nearly rigid porous glass through which the fluid permeates. The theoretically determined pressure drop is nonlinear in the diffusion regime and linear in the permeation regime, in quantitative agreement with experimental measurements. © 2009 Walter de Gruyter, Berlin, New York.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

International Nuclear Information System (INIS)

Kriventsev, Vladimir

2000-09-01

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

Directory of Open Access Journals (Sweden)

Pratibha Joshi

2014-12-01

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

Distributed order reaction-diffusion systems associated with Caputo derivatives

Science.gov (United States)

Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

2014-08-01

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables

A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

International Nuclear Information System (INIS)

Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

On the Aharonov-Bohm diffusion

International Nuclear Information System (INIS)

Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75

1993-07-01

The diffusion of a charged particle by a singular flux tube is revisited. A simple and rigourous derivation shows that the action of the propagator on an incident plane wave precisely yields the Aharonov-Bohm diffusion amplitude. The forward diffusion is discussed as well as the singularity of the interaction at the position of the flux tube. (orig.)

Solution of the diffusion equations for several groups by the finite elements method

International Nuclear Information System (INIS)

Arredondo S, C.

1975-01-01

The code DELFIN has been implemented for the solution of the neutrons diffusion equations in two dimensions obtained by applying the approximation of several groups of energy. The code works with any number of groups and regions, and can be applied to thermal reactors as well as fast reactor. Providing it with the diffusion coefficients, the effective sections and the fission spectrum we obtain the results for the systems multiplying constant and the flows of each groups. The code was established using the method of finite elements, which is a form of resolution of the variational formulation of the equations applying the Ritz-Galerkin method with continuous polynomial functions by parts, in one case of the Lagrange type with rectangular geometry and up to the third grade. The obtained results and the comparison with the results in the literature, permit to reach the conclusion that it is convenient, to use the rectangular elements in all the cases where the geometry permits it, and demonstrate also that the finite elements method is better than the finite differences method. (author)

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

Energy Technology Data Exchange (ETDEWEB)

Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

1994-12-31

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

Science.gov (United States)

Nefedov, N. N.; Nikulin, E. I.

2018-01-01

A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

Exact solution of the nucleons diffusion equation with increase inelastic cross section

International Nuclear Information System (INIS)

Portella, H.M.

1985-01-01

The successive aproximations method is applied to obtain an exact and compact analytical solution of the differential equation wich describes the diffusion of nucleonic component in the atmosphere, when the inelastic cross section of the air interaction nucleon-nucleus increases with the energy. The result is compared with the experimental data wich have been obtained in Chacaltaya (x=540g/cm 2 ) by the Brazil - Japan cooperation using emulsion chambers. The value of the constant a measurement of the variation of the cross section with the energy, that makes the best adjustment of the result found out with the experimental data is between 0.05 and 0.06. (M.C.K.) [pt

Analytical solution of spatial kinetics of the diffusion model for subcritical homogeneous systems driven by external source

International Nuclear Information System (INIS)

Oliveira, Fernando Luiz de

2008-01-01

This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients. (author)

Diffusion through statically compacted clay

International Nuclear Information System (INIS)

Ho, C.L.; Shebl, M.A.A.

1994-01-01

This paper presents experimental work on the effect of compaction on contaminant flow through clay liners. The experimental program included evaluation of soil properties, compaction, permeability and solute diffusion. A permeameter was built of non reactive materials to test samples compacted at different water contents and compactive efforts. The flow of a permeating solute, LiCl, was monitored. Effluent samples were collected for solute concentration measurements. The concentrations were measured by performing atomic adsorption tests. The analyzed results showed different diffusion characteristics when compaction conditions changed. At each compactive effort, permeability decreased as molding water content increased. Consequently, transit time (measured at relative concentration 50%) increased and diffusivity decreased. As compactive effort increased for soils compacted dry of optimum, permeability and diffusion decreased. On the other hand, as compactive effort increased for soils compacted wet of optimum, permeability and diffusivity increased. Tortuosity factor was indirectly measured from the diffusion and retardation rate. Tortuosity factor also decreased as placement water content was increased from dry of optimum to wet of optimum. Then decreases were more pronounced for low compactive effort tests. 27 refs., 7 figs., 5 tabs

A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

International Nuclear Information System (INIS)

Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

Numerical modelling of random walk one-dimensional diffusion

International Nuclear Information System (INIS)

Vamos, C.; Suciu, N.; Peculea, M.

1996-01-01

The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies

Coarse-grain parallel solution of few-group neutron diffusion equations

International Nuclear Information System (INIS)

Sarsour, H.N.; Turinsky, P.J.

1991-01-01

The authors present a parallel numerical algorithm for the solution of the finite difference representation of the few-group neutron diffusion equations. The targeted architectures are multiprocessor computers with shared memory like the Cray Y-MP and the IBM 3090/VF, where coarse granularity is important for minimizing overhead. Most of the work done in the past, which attempts to exploit concurrence, has concentrated on the inner iterations of the standard outer-inner iterative strategy. This produces very fine granularity. To coarsen granularity, the authors introduce parallelism at the nested outer-inner level. The problem's spatial domain was partitioned into contiguous subregions and assigned a processor to solve for each subregion independent of all other subregions, hence, processors; i.e., each subregion is treated as a reactor core with imposed boundary conditions. Since those boundary conditions on interior surfaces, referred to as internal boundary conditions (IBCs), are not known, a third iterative level, the recomposition iterations, is introduced to communicate results between subregions

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Modeling the diffusion magnetic resonance imaging signal inside neurons

International Nuclear Information System (INIS)

Nguyen, D V; Li, J R; Grebenkov, D S; Le Bihan, D

2014-01-01

The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times

Solution based synthesis of perovskite-type oxide films and powders

International Nuclear Information System (INIS)

McHale, J.M. Jr.

1995-01-01

Conventional solid state reactions are diffusion limited processes that require high temperatures and long reaction times to reach completion. In this work, several solution based methods were utilized to circumvent this diffusion limited reaction and achieve product formation at lower temperatures. The solution methods studied all have the common goal of trapping the homogeneity inherent in a solution and transferring this homogeneity to the solid state, thereby creating a solid atomic mixture of reactants. These atomic mixtures can yield solid state products through diffusionless mechanisms. The effectiveness of atomic mixtures in solid state synthesis was tested on three classes of materials, varying in complexity. A procedure was invented for obtaining the highly water soluble salt, titanyl nitrate, TiO(NO 3 ) 2 , in crystalline form, which allowed the production of titanate materials by freeze drying. The freeze drying procedures yielded phase pure, nanocrystalline BaTiO 3 and the complete SYNROC-B phase assemblage after ten minute heat treatments at 600 C and 1,100 C, respectively. Two novel methods were developed for the solution based synthesis of Ba 2 YCu 3 O 7-x and Bi 2 Sr 2 Ca 2 Cu 3 O 10 . Thin and thick films of Ba 2 YCu 3 O 7-x and Bi 2 Sr 2 Ca 2 Cu 3 O 10 were synthesized by an atmospheric pressure, chemical vapor deposition technique. Liquid ammonia solutions of metal nitrates were atomized with a stream of N 2 O and ignited with a hydrogen/oxygen torch. The resulting flame was used to coat a substrate with superconducting material. Bulk powders of Ba 2 YCu 3 O 7-x and Bi 2 Sr 2 Ca 2 Cu 3 O 10 were synthesized through a novel acetate glass method. The materials prepared were characterized by XRD, TEM, SEM, TGA, DTA, magnetic susceptibility and electrical resistivity measurements

Diffusion properties of conventional and calcium-sensitive MRI contrast agents in the rat cerebral cortex.

Science.gov (United States)

Hagberg, Gisela E; Mamedov, Ilgar; Power, Anthony; Beyerlein, Michael; Merkle, Hellmut; Kiselev, Valerij G; Dhingra, Kirti; Kubìček, Vojtĕch; Angelovski, Goran; Logothetis, Nikos K

2014-01-01

Calcium-sensitive MRI contrast agents can only yield quantitative results if the agent concentration in the tissue is known. The agent concentration could be determined by diffusion modeling, if relevant parameters were available. We have established an MRI-based method capable of determining diffusion properties of conventional and calcium-sensitive agents. Simulations and experiments demonstrate that the method is applicable both for conventional contrast agents with a fixed relaxivity value and for calcium-sensitive contrast agents. The full pharmacokinetic time-course of gadolinium concentration estimates was observed by MRI before, during and after intracerebral administration of the agent, and the effective diffusion coefficient D* was determined by voxel-wise fitting of the solution to the diffusion equation. The method yielded whole brain coverage with a high spatial and temporal sampling. The use of two types of MRI sequences for sampling of the diffusion time courses was investigated: Look-Locker-based quantitative T(1) mapping, and T(1) -weighted MRI. The observation times of the proposed MRI method is long (up to 20 h) and consequently the diffusion distances covered are also long (2-4 mm). Despite this difference, the D* values in vivo were in agreement with previous findings using optical measurement techniques, based on observation times of a few minutes. The effective diffusion coefficient determined for the calcium-sensitive contrast agents may be used to determine local tissue concentrations and to design infusion protocols that maintain the agent concentration at a steady state, thereby enabling quantitative sensing of the local calcium concentration. Copyright © 2014 John Wiley & Sons, Ltd.

Simulation of effects of redox and precipitation on diffusion of uranium solution species in backfill

International Nuclear Information System (INIS)

Carnahan, C.L.

1987-12-01

This investigation addresses the problem of prediction of the rate of migration of redox-sensitive solution species within packing and backfill materials under conditions of variable oxidation potential. Effects of changes of oxidation potential and precipitation of stable uranium compounds during diffusion of uranium from a region of high oxidation potential into a region of low oxidation potential were simulated numerically. Questions of particular interest addressed in the investigation were the existence of a moving ''redox front'' and the influence of precipitation-dissolution processes on uranium migration. The simulations showed that no expanding redox fronts existed at any simulated time up to 3.2 x 10 5 years (10 13 s). In simulations where precipitation of stable solids was not allowed, variations of oxidation potential did not affect total uranium concentrations in solution. Concentration profiles could be predicted simply by diffusion of the (constant) source concentrations. In simulations where precipitation of stable solids was allowed, uraninite and calcium uranate accumulated at the source-transport domain interface, while coffinite penetrated further into the transport domain. Total uranium concentrations in regions of precipitation were determined by solubilities of the precipitated solids, and were six to seven orders of magnitude lower than those in the simulations without precipitation, throughout the domain of transport. 14 refs., 7 figs., 2 tabs

Chemical order-disorder in alloys. Study by neutrons diffuse diffusion

International Nuclear Information System (INIS)

Novion, C. de; Beuneu, B.

1993-01-01

Applications of neutrons diffuse diffusion for short distance chemical order in FCC transition metals solid solutions (Pd-V, Ni-V, Ni-Cr) and understoichiometric carbides or nitrides of transition metals (TiC 1-x , NbC 1-x , TiN 1-x ) are shortly presented with theoretical and experimental aspects. (A.B.)

Photogeneration of H2O2 in SPEEK/PVA aqueous polymer solutions.

Science.gov (United States)

Little, Brian K; Lockhart, PaviElle; Slaten, B L; Mills, G

2013-05-23

Photolysis of air-saturated aqueous solutions containing sulphonated poly(ether etherketone) and poly(vinyl alcohol) results in the generation of hydrogen peroxide. Consumption of oxygen and H2O2 formation are initially concurrent processes with a quantum yield of peroxide generation of 0.02 in stirred or unstirred solutions within the range of 7 ≤ pH ≤ 9. The results are rationalized in terms of O2 reduction by photogenerated α-hydroxy radicals of the polymeric ketone in competition with radical-radical processes that consume the macromolecular reducing agents. Generation of H2O2 is controlled by the photochemical transformation that produces the polymer radicals, which is most efficient in neutral and slightly alkaline solutions. Quenching of the excited state of the polyketone by both H3O(+) and OH(-) affect the yields of the reducing macromolecular radicals and of H2O2. Deprotonation of the α-hydroxy polymeric radicals at pH > 9 accelerate their decay and contribute to suppressing the peroxide yields in basic solutions. Maxima in [H2O2] are observed when illuminations are performed with static systems, where O2 reduction is faster than diffusion of oxygen into the solutions. Under such conditions H2O2 can compete with O2 for the reducing radicals resulting in a consumption of the peroxide.

Polyamide–thallium selenide composite materials via temperature and pH controlled adsorption–diffusion method

International Nuclear Information System (INIS)

Ivanauskas, Remigijus; Samardokas, Linas; Mikolajunas, Marius; Virzonis, Darius; Baltrusaitis, Jonas

2014-01-01

Graphical abstract: Single phase polyamide–thallium selenide hybrid functional materials were synthesized for solar energy conversion. - Highlights: • Thallium selenide–polyamide composite materials surfaces synthesized. • Mixed phase composition confirmed by XRD. • Increased temperature resulted in a denser surface packing. • Urbach energies correlated with AFM showing decreased structural disorder. • Annealing in N 2 at 100 °C yielded a single TlSe phase. - Abstract: Composite materials based on III–VI elements are promising in designing efficient photoelectronic devices, such as thin film organic–inorganic solar cells. In this work, TlSe composite materials were synthesized on a model polymer polyamide using temperature and pH controlled adsorption–diffusion method via (a) selenization followed by (b) the exposure to the group III metal (Tl) salt solution and their surface morphological, chemical and crystalline phase information was determined with particular focus on their corresponding structure–optical property relationship. XRD analysis yielded a complex crystalline phase distribution which correlated well with the optical and surface morphological properties measured. pH 11.3 and 80 °C yielded well defined, low structural disorder composite material surface. After annealing in N 2 at 100 °C, polycrystalline PA-Tl x Se y composite materials yielded a single TlSe phase due to the enhanced diffusion and reaction of thallium ions into the polymer. The method described here can be used to synthesize variety of binary III–VI compounds diffused into the polymer at relatively low temperatures and low overall cost, thus providing for a flexible synthesis route for novel composite solar energy harvesting materials

Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part I: Analytical solutions with the extended method of moments.

Science.gov (United States)

Ginzburg, Irina; Vikhansky, Alexander

2018-05-01

The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive-flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic configurations: diffusion process and Darcy flow through two porous blocks in "series", straight and radial Poiseuille flow, porous flow governed by the Stokes-Brinkman-Darcy channel equation and a fracture surrounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Péclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous

The PLUS family: A set of computer programs to evaluate analytical solutions of the diffusion equation and thermoelasticity

International Nuclear Information System (INIS)

Montan, D.N.

1987-02-01

This report is intended to describe, document and provide instructions for the use of new versions of a set of computer programs commonly referred to as the PLUS family. These programs were originally designed to numerically evaluate simple analytical solutions of the diffusion equation. The new versions include linear thermo-elastic effects from thermal fields calculated by the diffusion equation. After the older versions of the PLUS family were documented a year ago, it was realized that the techniques employed in the programs were well suited to the addition of linear thermo-elastic phenomena. This has been implemented and this report describes the additions. 3 refs., 14 figs

Impact of the solution ionic strength on strontium diffusion through the Callovo-Oxfordian clayrocks: An experimental and modeling study

International Nuclear Information System (INIS)

Savoye, S.; Beaucaire, C.; Grenut, B.; Fayette, A.

2015-01-01

Highlights: • HTO and 85 Sr diffusion is studied in clayrocks under increasing ionic strengths. • Sr diffusive flux is 5 times higher than HTO under standard porewater ionic strength. • Sr diffusive flux is reduced when the porewater ionic strength increases. • The Sr diffusive evolution is qualitatively reproduced by a surface diffusion model. - Abstract: Diffusion of cations in clayrocks is widely investigated, because deep clay-rich formations are currently considered as one of the potential host rocks for radioactive waste repositories. However, several authors have already reported that sorbing cations seem to diffuse at rates larger than those predicted by a simple pore diffusion model from their sorption coefficients and from the diffusive flux of non-sorbing water tracers. This process has been attributed to the migration of cations within the electrical double layer, next to the mineral surfaces, called the surface diffusion phenomenon. The aim of this work was to verify whether this “enhanced” cation diffusion compared to neutral species was observed for strontium and, if so, to what extent this effect might vary with the salinity of the synthetic solutions. These questions were addressed by performing batch sorption, through-diffusion and out-diffusion experiments on rock samples from the Callovo-Oxfordian claystone formation (France). The results showed that there was a good agreement of the distribution ratios (R D ) determined on crushed and intact rocks by batch and through-diffusion methods with a R D decrease related to the increase of the sodium concentration, a sorption competitor. Such a trend was also well reproduced by means of a geochemical modeling based on the multi-site ion exchange (MSIE) theory. Moreover, the “enhanced” diffusion for strontium was clearly observed in this study: the Sr diffusive flux was almost five times higher than that for HTO in the cell with the lowest ionic strength, and diminished to less than 1

Phosphorus removal from aqueous solution in parent and aluminum-modified eggshells: thermodynamics and kinetics, adsorption mechanism, and diffusion process.

Science.gov (United States)

Guo, Ziyan; Li, Jiuhai; Guo, Zhaobing; Guo, Qingjun; Zhu, Bin

2017-06-01

Parent and aluminum-modified eggshells were prepared and characterized with X-ray diffraction, specific surface area measurements, infrared spectroscopy, zeta potential, and scanning electron microscope, respectively. Besides, phosphorus adsorptions in these two eggshells at different temperatures and solution pH were carried out to study adsorption thermodynamics and kinetics as well as the mechanisms of phosphorus adsorption and diffusion. The results indicated that high temperature was favorable for phosphorus adsorption in parent and aluminum-modified eggshells. Alkaline solution prompted phosphorus adsorption in parent eggshell, while the maximum adsorption amount was achievable at pH 4 in aluminum-modified eggshell. Adsorption isotherms of phosphorus in these eggshells could be well described by Langmuir and Freundlich models. Phosphorus adsorption amounts in aluminum-modified eggshell were markedly higher compared to those in parent eggshell. Adsorption heat indicated that phosphorus adsorption in parent eggshell was a typically physical adsorption process, while chemical adsorption mechanism of ion exchange between phosphorus and hydroxyl groups on the surface of eggshells was dominated in aluminum-modified eggshell. The time-resolved uptake curves showed phosphorus adsorption in aluminum-modified eggshell was significantly faster than that in parent eggshell. Moreover, there existed two clear steps in time-resolved uptake curves of phosphorus in parent eggshell. Based on pseudo-second order kinetic model and intraparticle diffusion model, we inferred more than one process affected phosphorus adsorption. The first process was the diffusion of phosphorus through water to external surface and the opening of pore channel in the eggshells, and the second process was mainly related to intraparticle diffusion.

Numerical solution of multigroup diffuse equations of one-dimensional geometry

International Nuclear Information System (INIS)

Pavelesku, M.; Adam, S.

1975-01-01

The one-dimensional diffuse theory is used for reactor physics calculations of fast reactors. Computer program based on the one-dimensional diffuse theory is speedy and not memory consuming. The algorithm is described for the three-zone fast reactor criticality computation in one-dimensional diffusion approximation. This algorithm is realised on IBM 370/135 computer. (I.T.)

The Green’s functions for peridynamic non-local diffusion

Science.gov (United States)

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Size, shape, and diffusivity of a single Debye-Hückel polyelectrolyte chain in solution

Science.gov (United States)

Soysa, W. Chamath; Dünweg, B.; Prakash, J. Ravi

2015-08-01

Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporation of the Rotne-Prager-Yamakawa tensor. Simulation results are interpreted in the light of the Odjik, Skolnick, Fixman, Khokhlov, and Khachaturian blob scaling theory (Everaers et al., Eur. Phys. J. E 8, 3 (2002)) which predicts that all solution properties are determined by just two scaling variables—the number of electrostatic blobs X and the reduced Debye screening length, Y. We identify three broad regimes, the ideal chain regime at small values of Y, the blob-pole regime at large values of Y, and the crossover regime at intermediate values of Y, within which the mean size, shape, and diffusivity exhibit characteristic behaviours. In particular, when simulation results are recast in terms of blob scaling variables, universal behaviour independent of the choice of bead-spring chain parameters, and the number of blobs X, is observed in the ideal chain regime and in much of the crossover regime, while the existence of logarithmic corrections to scaling in the blob-pole regime leads to non-universal behaviour.

Formulation of Low Peclet Number Based Grid Expansion Factor for the Solution of the Convection Diffusion Equation

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A. Abdullah

2018-04-01

Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.

Association and Diffusion of Li(+) in Carboxymethylcellulose Solutions for Environmentally Friendly Li-ion Batteries.

Science.gov (United States)

Casalegno, Mosè; Castiglione, Franca; Passarello, Marco; Mele, Andrea; Passerini, Stefano; Raos, Guido

2016-07-21

Carboxymethylcellulose (CMC) has been proposed as a polymeric binder for electrodes in environmentally friendly Li-ion batteries. Its physical properties and interaction with Li(+) ions in water are interesting not only from the point of view of electrode preparation-processability in water is one of the main reasons for its environmental friendliness-but also for its possible application in aqueous Li-ion batteries. We combine molecular dynamics simulations and variable-time pulsed field gradient spin-echo (PFGSE) NMR spectroscopy to investigate Li(+) transport in CMC-based solutions. Both the simulations and experimental results show that, at concentrations at which Li-CMC has a gel-like consistency, the Li(+) diffusion coefficient is still very close to that in water. These Li(+) ions interact preferentially with the carboxylate groups of CMC, giving rise to a rich variety of coordination patterns. However, the diffusion of Li(+) in these systems is essentially unrestricted, with a fast, nanosecond-scale exchange of the ions between CMC and the aqueous environment. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

Science.gov (United States)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Total variation regularization for a backward time-fractional diffusion problem

International Nuclear Information System (INIS)

Wang, Liyan; Liu, Jijun

2013-01-01

Consider a two-dimensional backward problem for a time-fractional diffusion process, which can be considered as image de-blurring where the blurring process is assumed to be slow diffusion. In order to avoid the over-smoothing effect for object image with edges and to construct a fast reconstruction scheme, the total variation regularizing term and the data residual error in the frequency domain are coupled to construct the cost functional. The well posedness of this optimization problem is studied. The minimizer is sought approximately using the iteration process for a series of optimization problems with Bregman distance as a penalty term. This iteration reconstruction scheme is essentially a new regularizing scheme with coupling parameter in the cost functional and the iteration stopping times as two regularizing parameters. We give the choice strategy for the regularizing parameters in terms of the noise level of measurement data, which yields the optimal error estimate on the iterative solution. The series optimization problems are solved by alternative iteration with explicit exact solution and therefore the amount of computation is much weakened. Numerical implementations are given to support our theoretical analysis on the convergence rate and to show the significant reconstruction improvements. (paper)

Diffusion coefficients of nickel chloride in aqueous solutions of lactose at T = 298.15 K and T = 310.15 K

International Nuclear Information System (INIS)

Ribeiro, Ana C.F.; Gomes, Joselaine C.S.; Barros, Marisa C.F.; Lobo, Victor M.M.; Esteso, Miguel A.

2011-01-01

Binary mutual diffusion coefficients (interdiffusion coefficients) of nickel chloride in water at T = 298.15 K and T = 310.15 K, and at concentrations between (0.000 and 0.100) mol · dm -3 , using a Taylor dispersion method have been measured. These data are discussed on the basis of the Onsager-Fuoss and Pikal models. The equivalent conductance at infinitesimal concentration of the nickel ion in these solutions at T = 310.15 K has been estimated using these results. Through the same technique, ternary mutual diffusion coefficients (D 11 , D 22 , D 12 , and D 21 ) for aqueous solutions containing NiCl 2 and lactose, at T = 298.15 K and T = 310.15 K, and at different carrier concentrations were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of NiCl 2 in different media.

Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation

International Nuclear Information System (INIS)

Muresan, Cristian; Vaillon, Rodolphe; Menezo, Christophe; Morlot, Rodolphe

2004-01-01

The coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation is solved. The collimated and diffuse components problems are treated separately. The solution for diffuse radiation is obtained by using a composite discrete ordinates method and includes the development of adaptive directional quadratures to overcome the difficulties usually encountered at the interfaces. The complete radiation numerical model is validated against the predictions obtained by using the Monte Carlo method

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

Directory of Open Access Journals (Sweden)

Ida de Bonis

2017-09-01

Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

A tracer diffusion model derived from microstructure

International Nuclear Information System (INIS)

Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus

2012-01-01

Document available in extended abstract form only. Full text of publication follows: Numerous attempts have been made to explain the tracer diffusion of various solutes in compacted clays. These attempts have commonly suffered from an inability to describe the diffusion of uncharged and charged solutes with a single unified model. Here, an internally consistent approach to describing the diffusion of solutes in a heterogeneous porous medium, such as compacted bentonite, in terms of its microstructure is presented. The microstructure is taken to be represented by a succession of unit cells, which consist of two consecutive regions (Do, 1996). In the first region, the diffusion is viewed to occur in two parallel paths: one through microcrystalline units (micropores) and the other through meso-pores between the microcrystalline units. Solutes exiting these two paths are then joined together to continue diffusing through the second, disordered, region, connecting the two adjacent microcrystalline units. Adsorption (incl. co-ion exclusion) is thought to occur in the micropores, whereas meso-pores and the disordered region accommodate free species alone. Co-ions are also assumed to experience transfer resistance into and out of the micropores, which is characterized in the model by a transmission coefficient. Although the model is not new per se, its application to compacted clays has never been attempted before. It is shown that in the limit of strong adsorption, the effective diffusivity is limited from above only by the microstructural parameters of the model porous medium. As intuitive and logical as this result may appear, it has not been proven before. In the limit of vanishing disordered region, the effective diffusivity is no longer explicitly constrained by any of the model parameters. The tortuosity of the diffusion path, i.e. the quotient of the actual diffusion path length in the porous-medium coordinates and the characteristic length of the laboratory frame

Adsorption and diffusion of plutonium in soil

International Nuclear Information System (INIS)

Relyea, J.F.; Brown, D.A.

1978-01-01

The behavior of plutonium in soil--water systems was studied by measuring its apparent diffusion coefficient in the aqueous and solid phases and by finding the adsorption--desorption relationships between soil and solution. Apparent diffusion coefficients of plutonium in soil were measured using a quick-freeze method. Aqueous diffusion was studied in a capillary-tube diffusion cell. Adsorption studies were done by equilibrating a tagged soil--water mixture on a rotary shaker before centrifuging and sampling. As expected from high adsorption coefficients (Kd) (300--10,000), the apparent diffusion coefficients were low compared with normal soil cations (1.4 x 10 -8 cm 2 /sec in a sandy soil to less than 2.4 x 10 -11 cm 2 /sec in a silt loam). The Kd of plutonium in aqueous solution containing the chelate ethylenediaminetetraacetic acid (EDTA) was reduced compared with the Kd in dilute HNO 3 . As the EDTA concentration was increased, the Kd was decreased. The chelate diethylenetriaminepentaacetic acid (DTPA) reduced the Kd more than EDTA at comparable concentrations. The aqueous diffusion coefficients varied from 3.1 x 10 -7 cm 2 /sec in a solution extracted from the silt loam up to 2.7 x 10 -5 cm 2 /sec in a solution extracted from the sandy soil

Interface methods for hybrid Monte Carlo-diffusion radiation-transport simulations

International Nuclear Information System (INIS)

Densmore, Jeffery D.

2006-01-01

Discrete diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo simulations in diffusive media. An important aspect of DDMC is the treatment of interfaces between diffusive regions, where DDMC is used, and transport regions, where standard Monte Carlo is employed. Three previously developed methods exist for treating transport-diffusion interfaces: the Marshak interface method, based on the Marshak boundary condition, the asymptotic interface method, based on the asymptotic diffusion-limit boundary condition, and the Nth-collided source technique, a scheme that allows Monte Carlo particles to undergo several collisions in a diffusive region before DDMC is used. Numerical calculations have shown that each of these interface methods gives reasonable results as part of larger radiation-transport simulations. In this paper, we use both analytic and numerical examples to compare the ability of these three interface techniques to treat simpler, transport-diffusion interface problems outside of a more complex radiation-transport calculation. We find that the asymptotic interface method is accurate regardless of the angular distribution of Monte Carlo particles incident on the interface surface. In contrast, the Marshak boundary condition only produces correct solutions if the incident particles are isotropic. We also show that the Nth-collided source technique has the capacity to yield accurate results if spatial cells are optically small and Monte Carlo particles are allowed to undergo many collisions within a diffusive region before DDMC is employed. These requirements make the Nth-collided source technique impractical for realistic radiation-transport calculations

Diffusion Coefficients of Several Aqueous Alkanolamine Solutions

NARCIS (Netherlands)

Snijder, Erwin D.; Riele, Marcel J.M. te; Versteeg, Geert F.; Swaaij, W.P.M. van

1993-01-01

The Taylor dispersion technique was applied for the determination of diffusion coefficients of various systems. Experiments with the system KCl in water showed that the experimental setup provides accurate data. For the alkanolamines monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine

Investigation of the uranium-molybdenum diffusion in body centered {gamma} solid solutions; Etude de la diffusion uranium-molybdene dans la solution solide {gamma} cubique centree

Energy Technology Data Exchange (ETDEWEB)

Adda, Y; Mairy, C; Bouchet, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires; Philibert, J [IRSID, 78 - Saint-Germain-en-Laye (France)

1958-07-01

The body centered {gamma} phase uranium-molybdenum intermetallic diffusion has been studied by different technical methods: micrography, electronic microanalyser, microhardness. The values of several numbers of penetration coefficients are given, and their physical significations has been discussed. The diffusion coefficients, the frequency factor and activation energies has been determined for each concentration. After determination of the Kirkendall effect in this system, we calculated the intrinsic diffusion coefficient of uranium and molybdenum. (author) [French] La dilution intermetallique uranium-molybdene, en phase {gamma} cubique centree, a ete etudiee au moyen de differentes techniques: micrographie, microsonde electronique, microdurete. Les valeurs d'un certain nombre de coefficients de penetration sont donnees et leur signification physique discutee. Les coefficients de diffusion, les facteurs de frequence et les energies d'activation ont ete determines pour chaque concentration. Apres avoir mis en evidence un effet Kirkendall dans ce systeme, on a calcule les coefficients de diffusion intrinseques de l'uranium et du molybdene. (auteur)

MAGNETIC QUENCHING OF TURBULENT DIFFUSIVITY: RECONCILING MIXING-LENGTH THEORY ESTIMATES WITH KINEMATIC DYNAMO MODELS OF THE SOLAR CYCLE

International Nuclear Information System (INIS)

Munoz-Jaramillo, Andres; Martens, Petrus C. H.; Nandy, Dibyendu

2011-01-01

The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double-step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory, which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work, we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric average of the dynamically quenched diffusivity. This bridges the gap between dynamically quenched and kinematic dynamo models, supporting their usage as viable tools for understanding the solar magnetic cycle.

Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems

International Nuclear Information System (INIS)

Ma, Z.; Whitley, R.D.; Wang, N.H.L.

1996-01-01

A generalized parallel pore and surface diffusion model for multicomponent adsorption and liquid chromatography is formulated and solved numerically. Analytical solution for first- and second-order central moments for a pulse on a plateau input is used as benchmarks for the numerical solutions. Theoretical predictions are compared with experimental data for two systems: ion-exchange of strontium, sodium, and calcium in a zeolite and competitive adsorption of two organics on activated carbon. In a linear isotherm region of single-component systems, both surface and pore diffusion cause symmetric spreading in breakthrough curves. In a highly nonlinear isotherm region, however, surface diffusion causes pronounced tailing in breakthrough curves; the larger the step change in concentration, the more pronounced tailing, in contrast to relatively symmetric breakthroughs due to pore diffusion. If only a single diffusion mechanism is assumed in analyzing the data of parallel diffusion systems, a concentration-dependent apparent surface diffusivity or pore diffusivity results; for a convex isotherm, the apparent surface diffusivity increases, whereas the apparent pore diffusivity decreases with increasing concentration. For a multicomponent nonlinear system, elution order can change if pore diffusion dominates for a low-affinity solute, whereas surface diffusion dominates for a high-affinity solute

Polyamide–thallium selenide composite materials via temperature and pH controlled adsorption–diffusion method

Energy Technology Data Exchange (ETDEWEB)

Ivanauskas, Remigijus; Samardokas, Linas [Department of Physical and Inorganic Chemistry, Kaunas University of Technology, Radvilenu str. 19, Kaunas LT-50254 (Lithuania); Mikolajunas, Marius; Virzonis, Darius [Department of Technology, Kaunas University of Technology, Panevezys Faculty, Daukanto 12, 35212 Panevezys (Lithuania); Baltrusaitis, Jonas, E-mail: job314@lehigh.edu [Department of Chemical and Biomolecular Engineering, Lehigh University, B336 Iacocca Hall, 111 Research Drive, Bethlehem, PA 18015 (United States)

2014-10-30

Graphical abstract: Single phase polyamide–thallium selenide hybrid functional materials were synthesized for solar energy conversion. - Highlights: • Thallium selenide–polyamide composite materials surfaces synthesized. • Mixed phase composition confirmed by XRD. • Increased temperature resulted in a denser surface packing. • Urbach energies correlated with AFM showing decreased structural disorder. • Annealing in N{sub 2} at 100 °C yielded a single TlSe phase. - Abstract: Composite materials based on III–VI elements are promising in designing efficient photoelectronic devices, such as thin film organic–inorganic solar cells. In this work, TlSe composite materials were synthesized on a model polymer polyamide using temperature and pH controlled adsorption–diffusion method via (a) selenization followed by (b) the exposure to the group III metal (Tl) salt solution and their surface morphological, chemical and crystalline phase information was determined with particular focus on their corresponding structure–optical property relationship. XRD analysis yielded a complex crystalline phase distribution which correlated well with the optical and surface morphological properties measured. pH 11.3 and 80 °C yielded well defined, low structural disorder composite material surface. After annealing in N{sub 2} at 100 °C, polycrystalline PA-Tl{sub x}Se{sub y} composite materials yielded a single TlSe phase due to the enhanced diffusion and reaction of thallium ions into the polymer. The method described here can be used to synthesize variety of binary III–VI compounds diffused into the polymer at relatively low temperatures and low overall cost, thus providing for a flexible synthesis route for novel composite solar energy harvesting materials.

Modeling long-term leaching experiments of full scale cemented wastes: effect of solution composition on diffusion

International Nuclear Information System (INIS)

Borkel, C.; Montoya, V.; Kienzler, B.

2015-01-01

The code PHREECQ V3.1 has been used to simulate leaching experiments performed with cemented simulated waste products in tap water for more than 30 years. In this work the main focus is related with the leaching of Cs explained by diffusion processes. A simplifying model using the code PHREECQ V3.1 was used to investigate the influence of different parameters on the release of Cs from the cement solid to the leaching solution. The model setup bases on four main assumptions: a) the solid as well as the distribution of Cs is homogeneous and of isotropic texture, b) there is no preferential direction regarding cement degradation or water intrusion into the solid, c) the pore space is entirely connected and d) Cs adsorption to the cement or container is negligible. In the modeling the constraint of charge balance was stressed. Effective diffusion coefficients (D e ) were obtained analytically and from modeling the diffusive release of Cs from cemented waste simulates. The obtained values D e for Cs leaching are in perfect agreement with the values published in literature. Contradictory results to diffusive release were obtained from XRD analysis of the solids, suggesting that water may not have penetrated the cement monoliths entirely, but only to some centimeters depth. XRD analysis have been done to determine the solid phases present in cement and are used to help outlining strength and weaknesses of the different models

A solution of the thermal neutron diffusion equation for a two-region cyclindrical system program for ODRA-1305 computer

International Nuclear Information System (INIS)

Drozdowicz, K.; Woznicka, U.

1982-01-01

The program in FORTRAN for the ODRA-1305 computer is described. The dependence of the decay constant of the thermal neutron flux upon the dimensions of the two-region concentric cylindrical system is the result of the program. The solution (with a constant neutron flux in the inner medium assumed) is generally obtained in the one-group diffusion approximation by the method of the perturbation calculation. However, the energy distribution of the thermal neutron flux and the diffusion cooling are taken into account. The program is written for the case when the outer medium is hydrogenous. The listing of the program and an example of calculation results are included. (author)

Diffusion coefficients of rare earth elements in fcc Fe: A first-principles study

Science.gov (United States)

Wang, Haiyan; Gao, Xueyun; Ren, Huiping; Chen, Shuming; Yao, Zhaofeng

2018-01-01

The diffusion data and corresponding detailed insights are particularly important for the understanding of the related kinetic processes in Fe based alloys, e.g. solute strengthening, phase transition, solution treatment etc. We present a density function theory study of the diffusivity of self and solutes (La, Ce, Y and Nb) in fcc Fe. The five-frequency model was employed to calculate the microscopic parameters in the correlation factors of the solute diffusion. The interactions of the solutes with the first nearest-neighbor vacancy (1nn) are all attractive, and can be well understood on the basis of the combination of the strain-relief effects and the electronic effects. It is found that among the investigated species, Ce is the fastest diffusing solute in fcc Fe matrix followed by Nb, and the diffusion coefficients of these two solutes are about an order of magnitude higher than that of Fe self-diffusion. And the results show that the diffusion coefficient of La is slightly higher than that of Y, and both species are comparable to that of Fe self-diffusion.

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

Science.gov (United States)

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.

Diffusion coefficients of nickel chloride in aqueous solutions of lactose at T = 298.15 K and T = 310.15 K

Energy Technology Data Exchange (ETDEWEB)

Ribeiro, Ana C.F., E-mail: anacfrib@ci.uc.p [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal); Gomes, Joselaine C.S., E-mail: leidygomes18@hotmail.co [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal); Barros, Marisa C.F., E-mail: marisa.barros@gmail.co [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal); Lobo, Victor M.M., E-mail: vlobo@ci.uc.p [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal); Esteso, Miguel A., E-mail: miguel.esteso@uah.e [Departamento de Quimica Fisica, Facultad de Farmacia, Universidad de Alcala, 28871, Alcala de Henares (Madrid) (Spain)

2011-03-15

Binary mutual diffusion coefficients (interdiffusion coefficients) of nickel chloride in water at T = 298.15 K and T = 310.15 K, and at concentrations between (0.000 and 0.100) mol {center_dot} dm{sup -3}, using a Taylor dispersion method have been measured. These data are discussed on the basis of the Onsager-Fuoss and Pikal models. The equivalent conductance at infinitesimal concentration of the nickel ion in these solutions at T = 310.15 K has been estimated using these results. Through the same technique, ternary mutual diffusion coefficients (D{sub 11}, D{sub 22}, D{sub 12}, and D{sub 21}) for aqueous solutions containing NiCl{sub 2} and lactose, at T = 298.15 K and T = 310.15 K, and at different carrier concentrations were also measured. These data permit us to have a better understanding of the structure of these systems and the thermodynamic behaviour of NiCl{sub 2} in different media.

Solution of the Multigroup-Diffusion equation by the response matrix method

International Nuclear Information System (INIS)

Oliveira, C.R.E.

1980-10-01

A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt

A consistent transported PDF model for treating differential molecular diffusion

Science.gov (United States)

Wang, Haifeng; Zhang, Pei

2016-11-01

Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.

Nonequilibrium free diffusion in seed leachate

Science.gov (United States)

Ortiz G., Luis; Riquelme P., Pablo; Guzmán, R.

2013-11-01

In this work, we use a Schlieren-like Near Field Scattering (SNFS) setup to study nonequilibrium free diffusion behavior of a colloidal solution obtained from seeds leachate. The main objective is to compare the temporal behavior of the diffusion coefficient of seed leachate with an electric conductivity based vigor test. SNFS sizing measurements, based on Mie theory, were carried out to ensure its reliability and sensitivity. Then, we performed a typical nonequilibrium free diffusion experiment of a glycerol-water mixture. In this way, we confirmed that SNFS setup is sensitive to giant concentration fluctuations of nanocolloidal solutions. The results obtained in this stage reproduce properly the data reported elsewhere in literature. Moreover, seed leachate diffuse, in water, in a similar way that glycerol does. In both cases we used the same method (dynamic structure factor) to determine thermo-physical properties. We show that time evolution of diffusion coefficient of Lupinus Albus leachate exhibits three defined regimes as electric conductivity measurements. The results also exhibit a correspondence between the behavior of the diffusion coefficient and electric conductivity values of the two regions in the temporal range studied. Finally, we discuss biological processes involved in germination that could modulate this dependence, and the role played by the electrolytic nature of solutes.

Applicability of the Galerkin method to the approximate solution of the multigroup diffusion equation

International Nuclear Information System (INIS)

Obradovic, D.

1970-04-01

In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)

Analytical solution of the multigroup neutron diffusion kinetic equation in one-dimensional cartesian geometry by the integral transform technique

International Nuclear Information System (INIS)

Ceolin, Celina

2010-01-01

The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)

Electro-regeneration of Ce(IV) in real spent Cr-etching solutions

International Nuclear Information System (INIS)

Chen, Te-San; Huang, Kuo-Lin

2013-01-01

Highlights: • An electrochemical process is used to regenerate Ce(IV) in real (hazardous) spent TFT-LCD Cr-etching solutions. • The Ce(IV) yield on tested anodes was in order BDD > Pt > DSA. • A Neosepta CMX separator was better than Nafion ones to be used in the process. • The activation energy on Pt was 10.7 kJ/mol. • The obtained parameters are useful to design reactors for 100% Ce(IV) regeneration in real spent Cr-etching solutions. -- Abstract: This paper presents the electro-regeneration of Ce(IV) in real (hazardous) spent thin-film transistor liquid-crystal display (TFT-LCD) Cr-etching solutions. In addition to Ce(III) > Ce(IV) in diffusivity, a quasi-reversible behavior of Ce(III)/Ce(IV) was observed at both boron-doped diamond (BDD) and Pt disk electrodes. The Ce(IV) yield on Pt increased with increasing current density, and the best current efficiency (CE) was obtained at 2 A/2.25 cm 2 . The performance in terms of Ce(IV) yield and CE of tested anodes was in order BDD > Pt > dimensional stable anode (DSA). At 2 A/2.25 cm 2 on Pt and 40 °C for 90 min, the Ce(IV) yield, CE and apparent rate constant (k) for Ce(III) oxidation were 81.4%, 21.8% and 3.17 × 10 −4 s −1 , respectively. With the increase of temperature, the Ce(IV) yield, CE, and k increased (activation energy = 10.7 kJ/mol), but the specific electricity consumption decreased. The Neosepta CMX membrane was more suitable than Nafion-117 and Nafion-212 to be used as the separator of the Ce(IV) regeneration process. The obtained parameters are useful to design divided batch reactors for the Ce(IV) electro-regeneration in real spent Cr-etching solutions

Tracer diffusion study in binary alloys

International Nuclear Information System (INIS)

Bocquet, Jean-Louis

1973-01-01

The diffusional properties of dilute alloys are quite well described with 5 vacancy jump frequencies: the diffusion experiments allow as to determine only 3 jump frequency ratios. The first experiment set, found by Howard and Manning, was used in order to determine the 3 frequency ratios in the dilute Cu-Fe alloy. N.V. Doan has shown that the isotope effect measurements may be replaced by easier electromigration experiments: this new method was used with success for the dilute Ag-Zn and Ag-Cd alloys. Two effects which take place in less dilute alloys cannot be explained with the 5 frequency model, these are: the linear enhancement of solute diffusion and the departure from linear enhancement of solvent diffusion versus solute concentration. To explain these effects, we have had to take account of the influence of solute pairs on diffusion via 53 new vacancy jump frequencies. Diffusion in a concentrated alloy can be described with a quasi-chemical approach: we show that a description with 'surrounded atoms' allows the simultaneous explanation of the thermodynamical properties of the binary solid solution, the dependence of atomic jump frequencies with respect to the local concentration of the alloy. In this model, the two atomic species have a jump frequency spectrum at their disposal, which seems to greatly modify Manning's correlation analysis. (author) [fr

Influence of a fertilizer solution on yield and quality of bread wheat in Guadalquivir Valley (Córdoba, Spain)

Science.gov (United States)

Concepción Benítez, M.; González, José Luis; Tejada, Manuel

2014-05-01

The use of by-products of food industries in agricultural practices has become a routine over the last few decades. The addition of beet vinasse, by-products of the two sep olive mill process and by-products of defatted sunflower flour, etc., to soils is a common agricultural practice, since sensible use has been reported to improve the physical, chemical and biological aspects of the soil and to increase harvest yield, and in many cases harvest quality Previous research carried out by the authors (Ordóñez et al., 2001) examined a process whereby a protein concentrate is obtained from defatted sunflower flour. In this process, floating liquid phosphorus, potassium contents and smaller amounts of humic substances and nitrogen are obtained. The potential application of this solution as a fertiliser has been evaluated on rye grass, confirming that its effects are comparable to those produced by a nutritional solution in terms of phosphorus and potassium foliar levels. The experiment was performed on soil classified as Typic Haploxererts located in the Middle Valley of the river Guadalquivir Cajeme wheat (Triticum aestivum var) variety was used at a dose of 180 kg seeds / ha. For both crop, four fertiliser treatments were applied in triplicate to randomly distributed 7 x 8 m plots. The greatest positive effect of applying the experimental phospho-potassic solution was found for the leaf levels of K, in maturity; this influence was most significant when the highest dosage of said solution. With reference to the levels of N, P and K in wheat grain, the levels of potassium were significantly different for all the fertilising treatments, and the plot fertilised with the highest dosage of the experimental phospho-potassic solution presented the highest values. As for the data obtained for harvest yield and quality, the addition of the experimental solution was observed to have a significantly positive influence (but only in the highest dosages) on the production levels.

Kinetics of polymer degradation in solution. 6. Laser flash photolysis and pulse radiolysis studies of polymethylvinylketone in solution using the light scattering detection method

Energy Technology Data Exchange (ETDEWEB)

Lindenau, D; Beavan, S W; Beck, G; Schnabel, W [Hahn-Meitner-Institut fuer Kernforschung Berlin G.m.b.H. (Germany, F.R.)

1977-01-01

Polymethylvinylketone (PMVK) was irradiated in solution with 2 ..mu..s pulses of 15 MeV electrons or with 15 ns flashes of 262 nm light. The change of the intensity of the light scattered by the solution (LSI) after the irradiation was measured. For the radiolysis experiments, a main chain scission process tausub(1/2) (decr) approximately 20 ..mu..s) and a subsequent crosslinking process (tausub(1/2) (incr) approximately 0.4 sec) could be discriminated. The LSI change pertaining to the main chain degradation was found to be due to disentanglement diffusion, whereas the LSI change pertaining to the crosslinking process could be correlated to a chemical reaction. The rate constant for combination of lateral macroradicals in acetone solution was estimated as 2 k/sub 2/ - (4.5 +- 1.5)10/sup 6/ M/sup -1/ sec/sup -1/. Stationary irradiation with /sup 60/Co-..gamma..-rays showed that PMVK is predominantly crosslinked to form a macrogel when irradiated in the solid state or in solution at concentrations greater than 100 g/l. At lower concentrations, microgel formation occurred. Photolysis of PMVK in solution yielded only main chain degradation. The LSI change was found to be due to disentanglement diffusion as during radiolysis. It was concluded that the same mechanism for main chain rupture is operative as in radiolysis. Stationary irradiations with uv light (lambda > 260 nm ) resulted in main chain degradation; no indication of crosslinking was obtained.

Effect of mycorrhiza and phosphorus content in nutrient solution on the yield and nutritional status of tomato plants grown on rockwool or coconut coir

Directory of Open Access Journals (Sweden)

Iwona Kowalska

2015-03-01

Full Text Available Effects of P level in nutrient solution and the colonization of roots by arbuscular mycorrhizal fungi (AMF on P uptake by tomato plants, their nutritional status, yield and quality of fruits were studied. Plants were grown on rockwool or coconut coir. Inoculation by a mixture of several AMF species was performed three times during the growing period. The mycorrhizal frequency in roots inoculated with AMF amounted to 35.79 – 50.82%. The highest level of mycorrhiza was found in plants receiving nutrient solution with a lower concentration of P. Among the experimental factors, only P level influenced the fruit yield, being higher from plants receiving a nutrient solution with a higher P level. A higher concentration of P in nutrient solution imposed better nutritional status of plants. Higher contents of ascorbic acid and total soluble sugars were found in fruits collected from inoculated plants, grown on rockwool.

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection-diffusion equation

Science.gov (United States)

Cholet, Cybèle; Charlier, Jean-Baptiste; Moussa, Roger; Steinmann, Marc; Denimal, Sophie

2017-07-01

The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection-diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection-diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space - between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) - as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit-matrix exchanges, inducing a complex water mixing effect in the saturated zone

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Directory of Open Access Journals (Sweden)

C. Cholet

2017-07-01

Full Text Available The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection–diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection–diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space – between the two reaches located in the unsaturated zone (R1, and in the zone that is both unsaturated and saturated (R2 – as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions and localized infiltration in the secondary conduit network (tributaries in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit–matrix exchanges, inducing a complex water mixing effect

Solution of the multigroup neutron diffusion Eigenvalue problem in slab geometry by modified power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática

2017-07-01

We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description.

Science.gov (United States)

Shetty, Anil N; Chiang, Sharon; Maletic-Savatic, Mirjana; Kasprian, Gregor; Vannucci, Marina; Lee, Wesley

2014-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal-Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

Burger, Martin

2010-01-01

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.

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

Science.gov (United States)

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.

On the solution of reaction-diffusion equations with double diffusivity

Directory of Open Access Journals (Sweden)

B. D. Aggarwala

1987-01-01

Full Text Available In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.

Atomistically informed solute drag in Al–Mg

International Nuclear Information System (INIS)

Zhang, F; Curtin, W A

2008-01-01

Solute drag in solute-strengthened alloys, caused by diffusion of solute atoms around moving dislocations, controls the stress at deformation rates and temperatures useful for plastic forming processes. In the technologically important Al–Mg alloys, the solute drag stresses predicted by classical theories are much larger than experiments, which is resolved in general by eliminating the singularity of the dislocation core via Peierls–Nabarro-type models. Here, the drag stress versus dislocation velocity is computed numerically using a realistic dislocation core structure obtained from an atomistic model to investigate the role of the core and obtain quantitative stresses for comparison with experiment. The model solves a discrete diffusion equation in a reference frame moving with the dislocation, with input solute enthalpies and diffusion activation barriers in the core computed by or estimated from atomistic studies. At low dislocation velocities, the solute drag stress is controlled by bulk solute diffusion because the core diffusion occurs too quickly. In this regime, the drag stress can be obtained using a Peierls–Nabarro model with a core spreading parameter tuned to best match the atomistic models. At intermediate velocities, both bulk and core diffusion can contribute to the drag, leading to a complex stress–velocity relationship showing two peaks in stress. At high velocities, the drag stress is controlled solely by diffusion within and across the core. Like the continuum models, the drag stress is nearly linear in solute concentration. The Orowan relationship is used to connect dislocation velocity to deformation strain rate. Accounting for the dependence of mobile dislocation density on stress, the simulations are in good agreement with experiments on Al–Mg alloys over a range of concentrations and temperatures

Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

International Nuclear Information System (INIS)

Alonso-Vargas, G.

1991-01-01

A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)

Application of a numerical transport correction in diffusion calculations

International Nuclear Information System (INIS)

Tomatis, Daniele; Dall'Osso, Aldo

2011-01-01

Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)

Temperature and concentration calibration of aqueous polyvinylpyrrolidone (PVP solutions for isotropic diffusion MRI phantoms.

Directory of Open Access Journals (Sweden)

Friedrich Wagner

Full Text Available To use the "apparent diffusion coefficient" (Dapp as a quantitative imaging parameter, well-suited test fluids are essential. In this study, the previously proposed aqueous solutions of polyvinylpyrrolidone (PVP were examined and temperature calibrations were obtained. For example, at a temperature of 20°C, Dapp ranged from 1.594 (95% CI: 1.593, 1.595 μm2/ms to 0.3326 (95% CI: 0. 3304, 0.3348 μm2/ms for PVP-concentrations ranging from 10% (w/w to 50% (w/w using K30 polymer lengths. The temperature dependence of Dapp was found to be so strong that a negligence seems not advisable. The temperature dependence is descriptively modelled by an exponential function exp(c2 (T - 20°C and the determined c2 values are reported, which can be used for temperature calibration. For example, we find the value 0.02952 K-1 for 30% (w/w PVP-concentration and K30 polymer length. In general, aqueous PVP solutions were found to be suitable to produce easily applicable and reliable Dapp-phantoms.

On a novel iterative method to compute polynomial approximations to Bessel functions of the first kind and its connection to the solution of fractional diffusion/diffusion-wave problems

International Nuclear Information System (INIS)

Yuste, Santos Bravo; Abad, Enrique

2011-01-01

We present an iterative method to obtain approximations to Bessel functions of the first kind J p (x) (p > -1) via the repeated application of an integral operator to an initial seed function f 0 (x). The class of seed functions f 0 (x) leading to sets of increasingly accurate approximations f n (x) is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree s, it yields a polynomial of degree s + 2, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function f 0 (x) = 1. This set of polynomials is useful not only for the computation of J p (x) but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.

Diffusion and mass transfer

CERN Document Server

Vrentas, James S

2013-01-01

The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedime...

The influence of the primary solutes in the study of the yield of alpha/beta discrimination in 241 Am and 210 Po

International Nuclear Information System (INIS)

Rodriguez, L.; Grau Carles, A.

1997-01-01

We have studied the yields in efficiency and alpha/beta discrimination for two commercial cocktails, Ultima-Gold''TM AB and Insta-Gel and three laboratory-made mixtures made of Insta-Gel and naphthalene, pyrene or 9,10-diphenylanthracene. Also, we have tested the samples made of radioactive solutions of ''241 Am and ''210 Po in HNO 3 of different concentrations in all scintillator solutions. (Author)

The relevance of light diffusion profiles for interstitial PDT using light-diffusing optical fibers

Science.gov (United States)

Stringasci, Mirian D.; Fortunato, Thereza C.; Moriyama, Lilian T.; Vollet Filho, José Dirceu; Bagnato, Vanderlei S.; Kurachi, Cristina

2017-02-01

Photodynamic therapy (PDT) is a technique used for several tumor types treatment. Light penetration on biological tissue is one limiting factor for PDT applied to large tumors. An alternative is using interstitial PDT, in which optical fibers are inserted into tumors. Cylindrical diffusers have been used in interstitial PDT. Light emission of different diffusers depends on the manufacturing process, size and optical properties of fibers, which make difficult to establish an adequate light dosimetry, since usually light profile is not designed for direct tissue-fiber contact. This study discusses the relevance of light distribution by a cylindrical diffuser into a turbid lipid emulsion solution, and how parts of a single diffuser contribute to illumination. A 2 cm-long cylindrical diffuser optical fiber was connected to a diode laser (630 nm), and the light spatial distribution was measured by scanning the solution with a collection probe. From the light field profile generated by a 1 mm-long intermediary element of a 20 mm-long cylindrical diffuser, recovery of light distribution for the entire diffuser was obtained. PDT was performed in rat healthy liver for a real treatment outcome analysis. By using computational tools, a typical necrosis profile generated by the irradiation with such a diffuser fiber was reconstructed. The results showed that it was possible predicting theoretically the shape of a necrosis profile in a healthy, homogeneous tissue with reasonable accuracy. The ability to predict the necrosis profile obtained from an interstitial illumination by optical diffusers has the potential improve light dosimetry for interstitial PDT.

Terahertz Conductivity within Colloidal CsPbBr3 Perovskite Nanocrystals: Remarkably High Carrier Mobilities and Large Diffusion Lengths.

Science.gov (United States)

Yettapu, Gurivi Reddy; Talukdar, Debnath; Sarkar, Sohini; Swarnkar, Abhishek; Nag, Angshuman; Ghosh, Prasenjit; Mandal, Pankaj

2016-08-10

Colloidal CsPbBr3 perovskite nanocrystals (NCs) have emerged as an excellent light emitting material in last one year. Using time domain and time-resolved THz spectroscopy and density functional theory based calculations, we establish 3-fold free carrier recombination mechanism, namely, nonradiative Auger, bimolecular electron-hole recombination, and inefficient trap-assisted recombination in 11 nm sized colloidal CsPbBr3 NCs. Our results confirm a negligible influence of surface defects in trapping charge carriers, which in turn results into desirable intrinsic transport properties, from the perspective of device applications, such as remarkably high carrier mobility (∼4500 cm(2) V(-1) s(-1)), large diffusion length (>9.2 μm), and high luminescence quantum yield (80%). Despite being solution processed and possessing a large surface to volume ratio, this combination of high carrier mobility and diffusion length, along with nearly ideal photoluminescence quantum yield, is unique compared to any other colloidal quantum dot system.

Diffusion-kinetic theories for LET effects on the radiolysis of water

International Nuclear Information System (INIS)

Pimblott, S.M.; LaVerne, J.A.

1994-01-01

Diffusion-kinetic methods are used to investigate the effects of incident particle linear energy transfer (LET) on the radiolysis of water and aqueous solutions. Chemically realistic deterministic diffusion-kinetic calculations examining the scavenging capacity dependences of the scavenged yield of e aq - and of OH demonstrate that the scavenged yields are related to the underlying time-dependent kinetics in the absence of the scavenger by a simple Laplace transform relationship. This relationship is also shown to link the effect of an e eq - scavenger on the formation of H 2 with the time dependence of H 2 production in the absence of the scavenger. The simple Laplace relationship does not work well when applied to H 2 O 2 formation in high-LET particle tracks even though such a relationship is valid with low-LET particles. It is found that while the secondary reaction of H 2 O 2 with e aq - can be neglected in low-LET particle radiolysis, it is of considerable significance in the tracks produced by high-LET particles. The increased importance of this reaction with increasing LET is the major reason for the failure of the Laplace relationship for H 2 O 2 . 55 refs., 9 figs., 2 tabs

Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

International Nuclear Information System (INIS)

Valdes Parra, J.J.

1986-01-01

One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)

Radiolysis of Aqueous Toluene Solutions

International Nuclear Information System (INIS)

Christensen, H.C.; Gustafson, R.

1971-04-01

Aqueous toluene solutions have been irradiated with Co γ-rays. In unbuffered solutions the various cresol isomers are formed in a total yield of 0.45, 0.87 and 0.94 molecules/100 eV absorbed energy in argon-, N 2 O- and air - saturated solutions, respectively. The yields are reduced in acid (pH 3) solutions (G 0.14, 0.14 and 0.52, respectively) but the reduction is compensated by the formation of 1,2-di-phenylethane in yields of 0.49 and 1.60 in argon- and N 2 O-saturated solutions, respectively. Benzyl radicals are formed through an acid catalysed water elimination reaction from the initially formed hydroxymethylcyclohexadienyl radical. Phenyltolylmethanes, dimethylbiphenyls and partly reduced dimers are also formed during the radiolysis. Hydrogen is formed in the same yield as the molecular yield, g(H 2 ). Xylene isomers and benzene are formed in trace quantities. The most remarkable effects of the addition of Fe(III) ions to deaerated acid toluene solutions are the formation of benzyl alcohol and benzaldehyde and an increase in the yield of 1,2-diphenylethane

A new analytical solution to the diffusion problem: Fourier series ...

African Journals Online (AJOL)

This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.

Interaction between diffusion and chemical stresses

International Nuclear Information System (INIS)

Yang Fuqian

2005-01-01

The present work studies the interaction between chemical stresses and diffusion. A new relation between hydrostatic stress and concentration of solute atoms is established. For a solid free of action of body force, the Laplacian of the hydrostatic stress is proportional to the Laplacian of the concentration of solute atoms, that is, deviation of the hydrostatic stress from its local average is proportional to deviation of the local concentration of solute atoms. A general relationship among surface concentration of solute atoms, normal stress and surface deformation of a solid is then derived, in which the normal stress is dependent on the mean curvature of the undeformed surface and tangential components of the surface displacement. A closed-form solution of the steady state concentration of solute atoms in a thin plate is obtained. It turns out that linear distribution of solute atoms in the plate is non-existent due to the interaction between chemical stresses and diffusion

Enhanced diffusion of polycyclic aromatic hydrocarbons in artificial and natural aqueous solutions

DEFF Research Database (Denmark)

Mayer, Philipp; Fernqvist, M.M.; Christensen, P.S.

2007-01-01

Uptake of hydrophobic organic compounds into organisms is often limited by the diffusive transport through a thin boundary layer. Therefore, a microscale diffusion technique was applied to determine the diffusive mass transfer of 12 polycyclic aromatic hydrocarbons through water, air, surfactant...

Assessment of protein solution versus crystal structure determination using spin- diffusion-suppressed NOE and heteronuclear relaxation data

International Nuclear Information System (INIS)

LeMaster, David M.

1997-01-01

A spin-diffusion-suppressed NOE buildup series has been measured for E. coli thioredoxin.The extensive 13C and 15N relaxation data previously reported for this protein allow for direct interpretation of dynamical contributions to the 1H-1H cross-relaxation rates for a large proportion of the NOE cross peaks. Estimates of the average accuracy for these derived NOE distances are bounded by 4% and 10%, based on a comparison to the corresponding X-ray distances. An independent fluctuation model is proposed for prediction of the dynamical corrections to 1H-1H cross-relaxation rates, based solely on experimental structural and heteronuclear relaxation data. This analysis is aided by the demonstration that heteronuclear order parameters greater than 0.6 depend only on the variance of the H-X bond orientation,independent of the motional model in either one- or two-dimensional diffusion (i.e., 1- S2 = 3/4 sin2 2 θσ). The combination of spin-diffusion-suppressed NOE data and analysis of dynamical corrections to 1H-1H cross-relaxation rates based on heteronuclear relaxation data has allowed for a detailed interpretation of various discrepancies between the reported solution and crystal structures

Thermal diffusion and separation of isotopes; Diffusion thermique et separation d'isotopes

Energy Technology Data Exchange (ETDEWEB)

Fournier, Andre

1944-03-30

After a review of the various processes used to separate isotopes or at least to obtain mixes with a composition different from the natural proportion, this research addresses the use of thermal diffusion. The author reports a theoretical study of gas thermal diffusion and of the Clusius-Dickel method. In the second part, he reports the enrichment of methane with carbon-13, and of ammoniac with nitrogen-15. The next part reports the experimental study of thermal diffusion of liquids and solutions, and the enrichment of carbon tetra-chloride with chlorine-37. The author then proposes an overview of theories of thermal diffusion in liquid phase (hydrodynamic theory, kinetic theory, theory of caged molecules)

Exposure to buffer solution alters tendon hydration and mechanics.

Science.gov (United States)

Safa, Babak N; Meadows, Kyle D; Szczesny, Spencer E; Elliott, Dawn M

2017-08-16

A buffer solution is often used to maintain tissue hydration during mechanical testing. The most commonly used buffer solution is a physiological concentration of phosphate buffered saline (PBS); however, PBS increases the tissue's water content and decreases its tensile stiffness. In addition, solutes from the buffer can diffuse into the tissue and interact with its structure and mechanics. These bathing solution effects can confound the outcome and interpretation of mechanical tests. Potential bathing solution artifacts, including solute diffusion, and their effect on mechanical properties, are not well understood. The objective of this study was to measure the effects of long-term exposure of rat tail tendon fascicles to several concentrations (0.9-25%) of NaCl, sucrose, polyethylene glycol (PEG), and SPEG (NaCl+PEG) solutions on water content, solute diffusion, and mechanical properties. We found that with an increase in solute concentration the apparent water content decreased for all solution types. Solutes diffused into the tissue for NaCl and sucrose, however, no solute diffusion was observed for PEG or SPEG. The mechanical properties changed for both NaCl solutions, in particular after long-term (8h) incubation the modulus and equilibrium stress decreased compared to short-term (15min) for 25% NaCl, and the cross sectional area increased for 0.9% NaCl. However, the mechanical properties were unchanged for both PEG and SPEG except for minor alterations in stress relaxation parameters. This study shows that NaCl and sucrose buffer solutions are not suitable for long-term mechanical tests. We therefore propose using PEG or SPEG as alternative buffer solutions that after long-term incubation can maintain tissue hydration without solute diffusion and produce a consistent mechanical response. Copyright © 2017 Elsevier Ltd. All rights reserved.

Exact Solution of Fractional Diffusion Model with Source Term used in Study of Concentration of Fission Product in Uranium Dioxide Particle

International Nuclear Information System (INIS)

Fang Chao; Cao Jianzhu; Sun Lifeng

2011-01-01

The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide (UO 2 ) particle is built. The adsorption effect of the fission product on the surface of the UO 2 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor. (nuclear physics)

Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation

International Nuclear Information System (INIS)

Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro

2013-01-01

This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper)

Radiation Re-solution Calculation in Uranium-Silicide Fuels

International Nuclear Information System (INIS)

Matthews, Christopher; Andersson, Anders David Ragnar; Unal, Cetin

2017-01-01

The release of fission gas from nuclear fuels is of primary concern for safe operation of nuclear power plants. Although the production of fission gas atoms can be easily calculated from the fission rate in the fuel and the average yield of fission gas, the actual diffusion, behavior, and ultimate escape of fission gas from nuclear fuel depends on many other variables. As fission gas diffuses through the fuel grain, it tends to collect into intra-granular bubbles, as portrayed in Figure 1.1. These bubbles continue to grow due to absorption of single gas atoms. Simultaneously, passing fission fragments can cause collisions in the bubble that result in gas atoms being knocked back into the grain. This so called ''re-solution'' event results in a transient equilibrium of single gas atoms within the grain. As single gas atoms progress through the grain, they will eventually collect along grain boundaries, creating inter-granular bubbles. As the inter-granular bubbles grow over time, they will interconnect with other grain-face bubbles until a pathway is created to the outside of the fuel surface, at which point the highly pressurized inter-granular bubbles will expel their contents into the fuel plenum. This last process is the primary cause of fission gas release. From the simple description above, it is clear there are several parameters that ultimately affect fission gas release, including the diffusivity of single gas atoms, the absorption and knockout rate of single gas atoms in intra-granular bubbles, and the growth and interlinkage of intergranular bubbles. Of these, the knockout, or re-solution rate has an particularly important role in determining the transient concentration of single gas atoms in the grain. The re-solution rate will be explored in the following sections with regards to uranium-silicide fuels in order to support future models of fission gas bubble behavior.

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

Probability representations of a class of two-way diffusions

Energy Technology Data Exchange (ETDEWEB)

Clifford, P.; Green, N.J.P. [Department of Statistics, University of Oxford, Oxford (United Kingdom); Feng, J.F. [COGS, Sussex University, Brighton (United Kingdom); Wei, G. [Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong (China)

2002-07-19

There has been little progress in the analysis of two-way diffusion in the last few decades due to the difficulties brought by the interface section similar to a free boundary condition. In this paper, however, the equivalent probability model is considered and the interface section is precisely described by an integral equation. The solution of two-way diffusion is then expressed in an integral form with the integrand being the solution of a classical first passage time model and the solution of a one-dimensional integral equation which is relatively easier to solve. The exact expression of the two-way diffusion enables us to find the explicit solution of the model with infinite horizontal boundaries and without drifting. (author)

Radiolysis of Aqueous Toluene Solutions

Energy Technology Data Exchange (ETDEWEB)

Christensen, H C; Gustafson, R

1971-04-15

Aqueous toluene solutions have been irradiated with Co gamma-rays. In unbuffered solutions the various cresol isomers are formed in a total yield of 0.45, 0.87 and 0.94 molecules/100 eV absorbed energy in argon-, N{sub 2}O- and air - saturated solutions, respectively. The yields are reduced in acid (pH 3) solutions (G = 0.14, 0.14 and 0.52, respectively) but the reduction is compensated by the formation of 1,2-di-phenylethane in yields of 0.49 and 1.60 in argon- and N{sub 2}O-saturated solutions, respectively. Benzyl radicals are formed through an acid catalysed water elimination reaction from the initially formed hydroxymethylcyclohexadienyl radical. Phenyltolylmethanes, dimethylbiphenyls and partly reduced dimers are also formed during the radiolysis. Hydrogen is formed in the same yield as the molecular yield, g(H{sub 2}). Xylene isomers and benzene are formed in trace quantities. The most remarkable effects of the addition of Fe(III) ions to deaerated acid toluene solutions are the formation of benzyl alcohol and benzaldehyde and an increase in the yield of 1,2-diphenylethane

Suitability of various materials for porous filters in diffusion experiments

Energy Technology Data Exchange (ETDEWEB)

Aldaba, David; Vidal, Miquel; Rigol, Anna [Univ. de Barcelona (Spain). Dept. de Quimica Analitica; Glaus, Martin; Van Loon, Luc [Paul Scherrer Institut, Villigen PSI (Switzerland). Lab. for Waste Management; Leupin, Olivier [Nagra, Wettingen (Switzerland)

2014-10-01

The suitability of different porous materials (stainless steel, VYCOR {sup registered} glass, Al{sub 2}O{sub 3} and PEEK) for use as confining filters in diffusion experiments was evaluated by measuring the effective diffusion coefficients (D{sub e}) of neutral (HTO) and ionic solutes (Na{sup +}, Cs{sup +}, Sr{sup 2+}, Cl{sup -}, SeO{sub 4}{sup 2-}) in the materials in through-diffusion experiments. For stainless steel filters, the D{sub e} values of the target solutes correlated satisfactorily with their bulk diffusion coefficient in water (D{sub w}); thus, the diffusion process in the stainless steel filters was primarily controlled by the diffusivity of the solvated ions. For the remaining materials, the D{sub e} and D{sub w} values were also correlated for the target solutes, and the geometric factors were in the sequence: VYCOR {sup registered} glass < Al{sub 2}O{sub 3} < PEEK. Stainless steel and VYCOR {sup registered} glass were the most appropriate materials because of their high D{sub e} values, but a specific interaction of caesium with VYCOR {sup registered} glass was hypothesised because the D{sub e} values obtained for this solute were slightly higher than expected.

Transport tensors in perfectly aligned low-density fluids: Self-diffusion and thermal conductivity

International Nuclear Information System (INIS)

Singh, G. S.; Kumar, B.

2001-01-01

The modified Taxman equation for the kinetic theory of low-density fluids composed of rigid aspherical molecules possessing internal degrees of freedom is generalized to obtain the transport tensors in a fluid of aligned molecules. The theory takes care of the shape of the particles exactly but the solution has been obtained only for the case of perfectly aligned hard spheroids within the framework of the first Sonine polynomial approximation. The expressions for the thermal-conductivity components have been obtained for the first time whereas the self-diffusion components obtained here turn out to be exactly the same as those derived by Kumar and Masters [Mol. Phys. >81, 491 (1994)] through the solution of the Lorentz-Boltzmann equation. All our expressions yield correct results in the hard-sphere limit

Diffusion along and around dislocations; Diffusion le long et autour des dislocations

Energy Technology Data Exchange (ETDEWEB)

Brebec, G [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1965-07-01

We have gathered together in this text some solutions for Fick's equations applicable to diffusion in dislocations. The problems is fairly similar to that of grain boundaries but in this case a further difficulty arises, purely mathematical in fact, due to the supposedly cylindrical shape of the perturbed region around a dislocation. It follows that Fick's equation is used in the form: {partial_derivative}C/{partial_derivative}t=D[{partial_derivative}{sup 2}C/{partial_derivative}r{sup 2}+1/r{partial_derivative}C/{partial_derivative} r + {partial_derivative}{sup 2}C/{partial_derivative}z{sup 2}] in order to express simply the limiting conditions and so that the solution takes into account the symmetry of revolution of the system. This very much complicates the final form of the results. We give here as an illustration a solution obtained using the same hypotheses and making the same approximations as those employed by WHIPPLE for his grain boundary work. Unfortunately the final form is not suitable for a numerical calculation. By making grosser approximations, such a those used by FISHER, it is possible to determine the parameter D/(a{sup 2}D'); the same result as for grain boundary is found i.e that the logarithm of the mean concentration varies linearly with penetration, the slope of this straight line is proportional to {radical}(D/(a{sup 2}D')) Finally we give the exact solution for a platelet of finite thickness assuming that the diffusion in the defect less crystal is negligible and that the surface diffusion is infinitely fast. This is the problem dealt with by HENDRIGKSON and MACHLIN. We arrive at conclusions different to those obtained by these two authors. (author) [French] Nous avons groupe dans ce texte quelques solutions des equations de Fick applicables a la diffusion dans les dislocations. Le probleme est assez analogue a celui des joints de grains mais il s'introduit ici une difficulte supplementaire, d'ailleurs purement mathematique, due au fait de

Predicting diffusivities in dense fluid mixtures

Directory of Open Access Journals (Sweden)

C. DARIVA

1999-09-01

Full Text Available In this work the Enskog solution of the Boltzmann equation, as corrected by Speedy, together with the Weeks-Chandler-Andersen (WCA perturbation theory of liquids is employed in correlating and predicting self-diffusivities of dense fluids. Afterwards this theory is used to estimate mutual diffusion coefficients of solutes at infinite dilution in sub and supercritical solvents. We have also investigated the behavior of Fick diffusion coefficients in the proximity of a binary vapor-liquid critical point since this subject is of great interest for extraction purposes. The approach presented here, which makes use of a density and temperature dependent hard-sphere diameter, is shown to be excellent for predicting diffusivities in dense pure fluids and fluid mixtures. The calculations involved highly nonideal mixtures as well as systems with high molecular asymmetry. The predicted diffusivities are in good agreement with the experimental data for the pure and binary systems. The methodology proposed here makes only use of pure component information and density of mixtures. The simple algebraic relations are proposed without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent mixtures.

Resolution of the time dependent P{sub n} equations by a Godunov type scheme having the diffusion limit; Resolution des equations P{sub n} instationnaires par un schema de type Godunov, ayant la limite diffusion

Energy Technology Data Exchange (ETDEWEB)

Cargo, P.; Samba, G

2007-07-01

We consider the P{sub n} model to approximate the transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it gives the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by L. Gosse to solve the P{sub 1} model without absorption term. Moreover, it has the well-balanced property: it preserves the steady solutions of the system. (authors)

Efficient estimation of diffusion during dendritic solidification

Science.gov (United States)

Yeum, K. S.; Poirier, D. R.; Laxmanan, V.

1989-01-01

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing the computed results with the results of an analytical solution derived by Kobayashi (1988) for the assumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a parabolic rate of the advancement of the solid/liquid interface. The flexibility of the method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.

On the application of finite element method in the solution of steady state diffusion equation

International Nuclear Information System (INIS)

Ono, S.

1982-01-01

The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

Diffusion in the special theory of relativity.

Science.gov (United States)

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Nonlinear diffusion problem arising in plasma physics

International Nuclear Information System (INIS)

Berryman, J.G.; Holland, C.J.

1978-01-01

In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented

Drift-Diffusion Equation

Directory of Open Access Journals (Sweden)

K. Banoo

1998-01-01

equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

Diffusive gradient in thin FILMS (DGT) compared with soil solution and labile uranium fraction for predicting uranium bioavailability to ryegrass.

Science.gov (United States)

Duquène, L; Vandenhove, H; Tack, F; Van Hees, M; Wannijn, J

2010-02-01

The usefulness of uranium concentration in soil solution or recovered by selective extraction as unequivocal bioavailability indices for uranium uptake by plants is still unclear. The aim of the present study was to test if the uranium concentration measured by the diffusive gradient in thin films (DGT) technique is a relevant substitute for plant uranium availability in comparison to uranium concentration in the soil solution or uranium recovered by ammonium acetate. Ryegrass (Lolium perenne L. var. Melvina) is grown in greenhouse on a range of uranium spiked soils. The DGT-recovered uranium concentration (C(DGT)) was correlated with uranium concentration in the soil solution or with uranium recovered by ammonium acetate extraction. Plant uptake was better predicted by the summed soil solution concentrations of UO(2)(2+), uranyl carbonate complexes and UO(2)PO(4)(-). The DGT technique did not provide significant advantages over conventional methods to predict uranium uptake by plants. Copyright 2009 Elsevier Ltd. All rights reserved.

Diffusive gradient in thin FILMS (DGT) compared with soil solution and labile uranium fraction for predicting uranium bioavailability to ryegrass

Energy Technology Data Exchange (ETDEWEB)

Duquene, L. [SCK-CEN, Biosphere Impact Studies, Boeretang 200, B-2400 Mol (Belgium); Vandenhove, H., E-mail: hvandenh@sckcen.b [SCK-CEN, Biosphere Impact Studies, Boeretang 200, B-2400 Mol (Belgium); Tack, F. [Ghent University, Laboratory for Analytical Chemistry and Applied Ecochemistry, Coupure Links 653, B-9000 Gent (Belgium); Van Hees, M.; Wannijn, J. [SCK-CEN, Biosphere Impact Studies, Boeretang 200, B-2400 Mol (Belgium)

2010-02-15

The usefulness of uranium concentration in soil solution or recovered by selective extraction as unequivocal bioavailability indices for uranium uptake by plants is still unclear. The aim of the present study was to test if the uranium concentration measured by the diffusive gradient in thin films (DGT) technique is a relevant substitute for plant uranium availability in comparison to uranium concentration in the soil solution or uranium recovered by ammonium acetate. Ryegrass (Lolium perenne L. var. Melvina) is grown in greenhouse on a range of uranium spiked soils. The DGT-recovered uranium concentration (C{sub DGT}) was correlated with uranium concentration in the soil solution or with uranium recovered by ammonium acetate extraction. Plant uptake was better predicted by the summed soil solution concentrations of UO{sub 2}{sup 2+}, uranyl carbonate complexes and UO{sub 2}PO{sub 4}{sup -}. The DGT technique did not provide significant advantages over conventional methods to predict uranium uptake by plants.

Diffusive gradient in thin FILMS (DGT) compared with soil solution and labile uranium fraction for predicting uranium bioavailability to ryegrass

International Nuclear Information System (INIS)

Duquene, L.; Vandenhove, H.; Tack, F.; Van Hees, M.; Wannijn, J.

2010-01-01

The usefulness of uranium concentration in soil solution or recovered by selective extraction as unequivocal bioavailability indices for uranium uptake by plants is still unclear. The aim of the present study was to test if the uranium concentration measured by the diffusive gradient in thin films (DGT) technique is a relevant substitute for plant uranium availability in comparison to uranium concentration in the soil solution or uranium recovered by ammonium acetate. Ryegrass (Lolium perenne L. var. Melvina) is grown in greenhouse on a range of uranium spiked soils. The DGT-recovered uranium concentration (C DGT ) was correlated with uranium concentration in the soil solution or with uranium recovered by ammonium acetate extraction. Plant uptake was better predicted by the summed soil solution concentrations of UO 2 2+ , uranyl carbonate complexes and UO 2 PO 4 - . The DGT technique did not provide significant advantages over conventional methods to predict uranium uptake by plants.

Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes

International Nuclear Information System (INIS)

Larsen, E.W.; Morel, J.E.; Miller, W.F. Jr.

1987-01-01

We present an asymptotic analysis of spatial differencing schemes for the discrete-ordinates equations, for diffusive media with spatial cells that are not optically thin. Our theoretical tool is an asymptotic expansion that has previously been used to describe the transform from analytic transport to analytic diffusion theory for such media. To introduce this expansion and its physical rationale, we first describe it for the analytic discrete-ordinates equations. Then, we apply the expansion to the spatially discretized discrete-ordinates equations, with the spatial mesh scaled in either of two physically relevant ways such that the optical thickness of the spatial cells is not small. If the result of either expansion is a legitimate diffusion description for either the cell-averaged or cell-edge fluxes, then we say that the approximate flux has the appropriate diffusion limit; otherwise, we say it does not. We consider several transport differencing schemes that are applicable in neutron transport and thermal radiation applications. We also include numerical results which demonstrate the validity of our theory and show that differencing schemes that do have a particular diffusion limit are substantially more accurate, in the regime described by the limit, than those that do not. copyright 1987 Academic Press, Inc

Mutual diffusion coefficients of L-glutamic acid and monosodium L-glutamate in aqueous solutions at T = 298.15 K

International Nuclear Information System (INIS)

Ribeiro, Ana C.F.; Rodrigo, M.M.; Barros, Marisa C.F.; Verissimo, Luis M.P.; Romero, Carmen; Valente, Artur J.M.; Esteso, Miguel A.

2014-01-01

Highlights: • Interdiffusion coefficients of L-glutamic acid and sodium L-glutamate were measured. • The L-glutamic acid behaves as a monoprotic weak acid. • The sodium L-glutamate shows a symmetrical 1:1 non-associated behaviour. • Limiting diffusion coefficients and ionic conductivities were estimated. • Diffusion coefficients were discussed on the basis of the Onsager–Fuoss equations. - Abstract: Mutual diffusion coefficient values for binary aqueous solutions of both L-glutamic acid (H 2 Glu) and sodium L-glutamate (NaHGlu) were measured with the Taylor dispersion technique, at T = 298.15 K, and concentrations ranging from (0.001 to 0.100) mol · dm −3 . The results were discussed on the basis of the Onsager–Fuoss and the Nernst theoretical equations, by considering the H 2 Glu as a weak acid (monoprotic acid, with K 2 = 5.62 · 10 −5 ). The smaller values found for the acid with respect to those of the salt, confirm this association hypothesis. From the diffusion coefficient values at infinitesimal concentration, limiting ionic conductivities as well as the hydrodynamic radius of the hydrogen glutamate ion (HGlu − ) were derived and analyzed in terms of the chain methylene groups. The effect of different phenomena, such as association or complexation, were also taken into consideration and discussed. Values for the dissociation degree for H 2 Glu were also estimated

Carbon isotope exchange between gaseous CO2 and thin solution films: Artificial cave experiments and a complete diffusion-reaction model

Science.gov (United States)

Hansen, Maximilian; Scholz, Denis; Froeschmann, Marie-Louise; Schöne, Bernd R.; Spötl, Christoph

2017-08-01

Speleothem stable carbon isotope (δ13C) records provide important paleoclimate and paleo-environmental information. However, the interpretation of these records in terms of past climate or environmental change remains challenging because of various processes affecting the δ13C signals. A process that has only been sparsely discussed so far is carbon isotope exchange between the gaseous CO2 of the cave atmosphere and the dissolved inorganic carbon (DIC) contained in the thin solution film on the speleothem, which may be particularly important for strongly ventilated caves. Here we present a novel, complete reaction diffusion model describing carbon isotope exchange between gaseous CO2 and the DIC in thin solution films. The model considers all parameters affecting carbon isotope exchange, such as diffusion into, out of and within the film, the chemical reactions occurring within the film as well as the dependence of diffusion and the reaction rates on isotopic mass and temperature. To verify the model, we conducted laboratory experiments under completely controlled, cave-analogue conditions at three different temperatures (10, 20, 30 °C). We exposed thin (≈0.1 mm) films of a NaHCO3 solution with four different concentrations (1, 2, 5 and 10 mmol/l, respectively) to a nitrogen atmosphere containing a specific amount of CO2 (1000 and 3000 ppmV). The experimentally observed temporal evolution of the pH and δ13C values of the DIC is in good agreement with the model predictions. The carbon isotope exchange times in our experiments range from ca. 200 to ca. 16,000 s and strongly depend on temperature, film thickness, atmospheric pCO2 and the concentration of DIC. For low pCO2 (between 500 and 1000 ppmV, as for strongly ventilated caves), our time constants are substantially lower than those derived in a previous study, suggesting a potentially stronger influence of carbon isotope exchange on speleothem δ13C values. However, this process should only have an

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

Science.gov (United States)

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.

An Investigation into Solution Verification for CFD-DEM

Energy Technology Data Exchange (ETDEWEB)

Fullmer, William D. [National Energy Technology Lab. (NETL), AECOM, Morgantown, WV (United States); Musser, Jordan [National Energy Technology Lab. (NETL), Morgantown, WV (United States)

2017-10-01

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6^th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

Solution based preparation of Perovskite-type oxide films and powders

Energy Technology Data Exchange (ETDEWEB)

McHale, Jr., James M. [Temple Univ., Philadelphia, PA (United States). Dept. of Chemistry

1995-04-01

Conventional solid state reactions are diffusion limited processes that require high temperatures and long reaction times to reach completion. In this work, several solution based methods were utilized to circumvent this diffusion limited reaction and achieve product formation at lower temperatures. The solution methods studied all have the common goal of trapping the homogeneity inherent in a solution and transferring this homogeneity to the solid state, thereby creating a solid atomic mixture of reactants. These atomic mixtures can yield solid state products through "diffusionless" mechanisms. The effectiveness of atomic mixtures in solid state synthesis was tested on three classes of materials, varying in complexity. A procedure was invented for obtaining the highly water soluble salt, titanyl nitrate, TiO(NO₃)₂, in crystalline form, which allowed the production of titanate materials by freeze drying. The freeze drying procedures yielded phase pure, nanocrystalline BaTiO₃ and the complete SYNROC-B phase assemblage after ten minute heat treatments at 600{degrees}C and 1100{degrees}C, respectively. Two novel methods were developed for the solution based synthesis of Ba₂YCu₃O_7-x and Bi₂Sr₂Ca₂Cu₃O₁₀. Thin and thick films of Ba₂YCu₃O_7-x and Bi₂Sr₂Ca₂u₃O₁₀ were synthesized by an atmospheric pressure, chemical vapor deposition technique. Liquid ammonia solutions of metal nitrates were atomized with a stream of N₂O and ignited with a hydrogen/oxygen torch. The resulting flame was used to coat a substrate with superconducting material. Bulk powders of Ba₂YCu₃O_7-x and Bi₂Sr₂Ca₂Cu₃O₁₀ were synthesized through a novel acetate glass method. The materials prepared were

Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow.

Science.gov (United States)

Holter, Karl Erik; Kehlet, Benjamin; Devor, Anna; Sejnowski, Terrence J; Dale, Anders M; Omholt, Stig W; Ottersen, Ole Petter; Nagelhus, Erlend Arnulf; Mardal, Kent-André; Pettersen, Klas H

2017-09-12

The brain lacks lymph vessels and must rely on other mechanisms for clearance of waste products, including amyloid [Formula: see text] that may form pathological aggregates if not effectively cleared. It has been proposed that flow of interstitial fluid through the brain's interstitial space provides a mechanism for waste clearance. Here we compute the permeability and simulate pressure-mediated bulk flow through 3D electron microscope (EM) reconstructions of interstitial space. The space was divided into sheets (i.e., space between two parallel membranes) and tunnels (where three or more membranes meet). Simulation results indicate that even for larger extracellular volume fractions than what is reported for sleep and for geometries with a high tunnel volume fraction, the permeability was too low to allow for any substantial bulk flow at physiological hydrostatic pressure gradients. For two different geometries with the same extracellular volume fraction the geometry with the most tunnel volume had [Formula: see text] higher permeability, but the bulk flow was still insignificant. These simulation results suggest that even large molecule solutes would be more easily cleared from the brain interstitium by diffusion than by bulk flow. Thus, diffusion within the interstitial space combined with advection along vessels is likely to substitute for the lymphatic drainage system in other organs.

Formation of calcium phosphates by vapour diffusion in highly concentrated ionic micro-droplets

Energy Technology Data Exchange (ETDEWEB)

Iafisco, M. [Alma Mater Studiorum Universita di Bologna, Dipartimento di Chimica ' ' G. Ciamician' ' , Via Selmi 2, 40126 Bologna (Italy); Universita del Piemonte Orientale, Dipartimento di Scienze Mediche, Via Solaroli 4, 28100 Novara (Italy); Delgado-Lopez, J.M.; Gomez-Morales, J.; Hernandez-Hernandez, M.A.; Rodriguez-Ruiz, I. [Laboratorio de Estudios Cristalograficos, IACT CSIC-UGR, Edificio Lopez Neyra, Avenida del Conocimiento, s/n 18100 Armilla (Spain); Roveri, N. [Alma Mater Studiorum Universita di Bologna, Dipartimento di Chimica ' ' G. Ciamician' ' , Via Selmi 2, 40126 Bologna (Italy)

2011-08-15

In this work we have used the sitting drop vapour diffusion technique, employing the ''crystallization mushroom '' to analyze the evolution of calcium phosphate crystallization in micro-droplets containing high initial concentrations of Ca{sup 2+} and HPO{sub 4}{sup 2-}. The decomposition of NH{sub 4}HCO{sub 3} solution produces vapours of NH{sub 3} and CO{sub 2} which diffuse through the droplets containing an aqueous solution of Ca(CH{sub 3}COO){sub 2} and (NH{sub 4}){sub 2}HPO{sub 4}. The result is the increase of pH by means of the diffusion of NH{sub 3} gas and the doping of the calcium phosphate with CO{sub 3}{sup 2-} ions by means of the diffusion of CO{sub 2} gas. The pH of the crystallization process is monitored and the precipitates at different times are characterized by XRD, FTIR, TGA, SEM and TEM techniques. The slow increase of pH and the high concentration of Ca{sup 2+} and HPO{sub 4}{sup 2-} in the droplets induce the crystallization of three calcium phosphate phases: dicalcium phosphate dihydrate (DCPD, brushite), octacalcium phosphate (OCP) and carbonate-hydroxyapatite (HA). The amount of HA nanocrystals with needle-like morphology and dimensions of about 100 nm, closely resembling the inorganic phase of bones, gradually increases, with the precipitation time up to 7 days, whereas the amount of DCPD, growing along the b axis, increases up to 3 days. Then, DCDP crystals start to hydrolyze yielding OCP nanoribbons and HA nanocrystals. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Understanding deterministic diffusion by correlated random walks

International Nuclear Information System (INIS)

Klages, R.; Korabel, N.

2002-01-01

Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulae we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coefficients in terms of dynamical correlations. (author)

Exact solutions of some coupled nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

From quantum stochastic differential equations to Gisin-Percival state diffusion

Science.gov (United States)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Vectorized and multitasked solution of the few-group neutron diffusion equations

International Nuclear Information System (INIS)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-01-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. For the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model

Ion diffusion in compacted bentonite

Energy Technology Data Exchange (ETDEWEB)

Lehikoinen, J. [VTT Chemical Technology, Espoo (Finland)

1999-03-01

In the study, a two-dimensional molecular-level diffusion model, based on a modified form of the Gouy-Chapman (GC) theory of the electrical double layers, for hydrated ionic species in compacted bentonite was developed. The modifications to the GC theory, which forms the very kernel of the diffusion model, stem from various non-conventional features: ionic hydration, dielectric saturation, finite ion-sizes and specific adsorption. The principal objectives of the study were met. With the aid of the consistent diffusion model, it is a relatively simple matter to explain the experimentally observed macroscopic exclusion for anions as well as the postulated, but greatly controversial, surface diffusion for cations. From purely theoretical grounds, it was possible to show that the apparent diffusivities of cations, anions and neutral molecules (i) do not exhibit order-or-magnitude differences, and (ii) are practically independent of the solution ionic strength used and, consequently, of the distribution coefficient, K{sub d}, unless they experience specific binding onto the substrate surface. It was also of interest to investigate the equilibrium anionic concentration distribution in the pore geometry of the GMM model as a function of the solution ionic strength, and to briefly speculate its consequences to diffusion. An explicit account of the filter-plate effect was taken by developing a computerised macroscopic diffusion model, which is based upon the very robust and efficient Laplace Transform Finite-Difference technique. Finally, the inherent limitations as well as the potential fields of applications of the models were addressed. (orig.) 45 refs.

Ion diffusion in compacted bentonite

International Nuclear Information System (INIS)

Lehikoinen, J.

1999-03-01

In the study, a two-dimensional molecular-level diffusion model, based on a modified form of the Gouy-Chapman (GC) theory of the electrical double layers, for hydrated ionic species in compacted bentonite was developed. The modifications to the GC theory, which forms the very kernel of the diffusion model, stem from various non-conventional features: ionic hydration, dielectric saturation, finite ion-sizes and specific adsorption. The principal objectives of the study were met. With the aid of the consistent diffusion model, it is a relatively simple matter to explain the experimentally observed macroscopic exclusion for anions as well as the postulated, but greatly controversial, surface diffusion for cations. From purely theoretical grounds, it was possible to show that the apparent diffusivities of cations, anions and neutral molecules (i) do not exhibit order-or-magnitude differences, and (ii) are practically independent of the solution ionic strength used and, consequently, of the distribution coefficient, K d , unless they experience specific binding onto the substrate surface. It was also of interest to investigate the equilibrium anionic concentration distribution in the pore geometry of the GMM model as a function of the solution ionic strength, and to briefly speculate its consequences to diffusion. An explicit account of the filter-plate effect was taken by developing a computerised macroscopic diffusion model, which is based upon the very robust and efficient Laplace Transform Finite-Difference technique. Finally, the inherent limitations as well as the potential fields of applications of the models were addressed. (orig.)

Scale dependence of the effective matrix diffusion coefficient: Evidence and preliminary interpretation

International Nuclear Information System (INIS)

Liu, Hui-Hai; Zhang, Yingqi; Molz, Fred J.

2006-01-01

The exchange of solute mass (through molecular diffusion) between fluid in fractures and fluid in the rock matrix is called matrix diffusion. Owing to the orders-of-magnitude slower flow velocity in the matrix compared to fractures, matrix diffusion can significantly retard solute transport in fractured rock, and therefore is an important process for a variety of problems, including remediation of subsurface contamination and geological disposal of nuclear waste. The effective matrix diffusion coefficient (molecular diffusion coefficient in free water multiplied by matrix tortuosity) is an important parameter for describing matrix diffusion, and in many cases largely determines overall solute transport behavior. While matrix diffusion coefficient values measured from small rock samples in the laboratory are generally used for modeling field-scale solute transport in fractured rock (Boving and Grathwohl, 2001), several research groups recently have independently found that effective matrix diffusion coefficients much larger than laboratory measurements are needed to match field-scale tracer-test data (Neretnieks, 2002; Becker and Shapiro, 2000; Shapiro, 2001; Liu et al., 2003, 2004a). In addition to the observed enhancement, Liu et al. (2004b), based on a relatively small number of field-test results, reported that the effective matrix diffusion coefficient might be scale dependent, and, like permeability and dispersivity, it seems to increases with test scale. This scale-dependence has important implications for large-scale solute transport in fractured rock. Although a number of mechanisms have been proposed to explain the enhancement of the effective matrix diffusion coefficient, the potential scale dependence and its mechanisms are not fully investigated at this stage. The major objective of this study is to again demonstrate (based on more data published in the literature than those used in Liu et al. [2004b]) the potential scale dependence of the effective

Scale Dependence of the Effective Matrix Diffusion Coefficient : Evidence and Preliminary Interpretation

International Nuclear Information System (INIS)

H.H. Liu; Y. Zhang

2006-01-01

The exchange of solute mass (through molecular diffusion) between fluid in fractures and fluid in the rock matrix is called matrix diffusion. Owing to the orders-of-magnitude slower flow velocity in the matrix compared to fractures, matrix diffusion can significantly retard solute transport in fractured rock, and therefore is an important process for a variety of problems, including remediation of subsurface contamination and geological disposal of nuclear waste. The effective matrix diffusion coefficient (molecular diffusion coefficient in free water multiplied by matrix tortuosity) is an important parameter for describing matrix diffusion, and in many cases largely determines overall solute transport behavior. While matrix diffusion coefficient values measured from small rock samples in the laboratory are generally used for modeling field-scale solute transport in fractured rock (Boving and Grathwohl, 2001), several research groups recently have independently found that effective matrix diffusion coefficients much larger than laboratory measurements are needed to match field-scale tracer-test data (Neretnieks, 2002; Becker and Shapiro, 2000; Shapiro, 2001; Liu et al., 2003,2004a). In addition to the observed enhancement, Liu et al. (2004b), based on a relatively small number of field-test results, reported that the effective matrix diffusion coefficient might be scale dependent, and, like permeability and dispersivity, it seems to increases with test scale. This scale-dependence has important implications for large-scale solute transport in fractured rock. Although a number of mechanisms have been proposed to explain the enhancement of the effective matrix diffusion coefficient, the potential scale dependence and its mechanisms are not fully investigated at this stage. The major objective of this study is to again demonstrate (based on more data published in the literature than those used in Liu et al. [2004b]) the potential scale dependence of the effective

Tracer concentration contours in grain lattice and grain boundary diffusion

International Nuclear Information System (INIS)

Kim, Y. S.; Olander, D. R.

1997-01-01

Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low burn-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination). (author)

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

International Nuclear Information System (INIS)

Khotylev, V.A.; Hoogenboom, J.E.

1996-01-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

Energy Technology Data Exchange (ETDEWEB)

Khotylev, V.A.; Hoogenboom, J.E. [Delft Univ. of Technology, Interfaculty Reactor Inst., Delft (Netherlands)

1996-07-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

Perturbation on diffusion problems in domain with interfaces

International Nuclear Information System (INIS)

Watson, F.V.

1985-01-01

A perturbative type algorithm for the solution of linear diffusion equation at two dimensions, in domain with interfaces is presented. The perturbative scheme should be assembled in the weak formulation of diffusion equation, even if the strong solution exists, and when it is taken in terms superiors to first order, it should be calculated analytically, in one of the dimensions to avoid problems of slow convergence. (M.C.K.) [pt

Diffusion of Fission Product Elements in Compacted Bentonite

International Nuclear Information System (INIS)

Pratomo-Budiman-Sastrowardoyo; Dewi-Susilowati; Dadang-Suganda

2000-01-01

Study on diffusion of fission product in compacted bentonite has been conducted. The information about mobilities of these elements have been obtained from the studies resulted in many countries. It is presented that the diffusion coefficient was varied by the function of solution phase condition as well as the nature of bentonite. It is also showed that the diffusion coefficient decreased by the increasing of density, as well as the increasing of montmorillonite content in bentonite. The ratio of bentonite/silica-sand used, was related to the increasing of elements mobility. In many case variation of diffusion coefficient was related to the variation of pH, redox condition, and the presence of complex ant in solution phase. The lower diffusion coefficient could give the higher retardation factor, which is a favorable factor to retard the radionuclides release from a disposal facility to geosphere. (author)

Interspecies Ion Diffusion Studies using DT, DT(3He), and DT(H) Implosions

Science.gov (United States)

Kim, Y.; Herrmann, H. W.; Schmitt, M. J.; Kagan, G.; McEvoy, A. M.; Hoffman, N. M.; Gales, S.; Leatherland, A.; Gatu Johnson, M.; Frenje, J.; Glevov, V. Yu; Forrest, C.

2015-11-01

Anomalous ICF yield degradation has been observed from gas fills containing mixtures (i.e., D(3He), DT(3He), D(Ar), and even DT). Interspecies ion diffusion theory has been suggested as a possible cause resulting from gradient-driven diffusion (i.e., pressure, electric potential, and temperature) which forces lower mass ions away from core and higher mass ions toward core. The theory predicts hydrogen addition to deuterium or tritium should result in increased yield compared to expected yield, which is opposite to 3He addition. At Omega laser facility, we have tested hydro-equivalent fills of DT, DT(3He), and DT(H) with the assumption that same fuel mass and particle pressure will provide identical convergence. Preliminary results verify a factor of 2 yield reduction relative to scaling when 3He added to DT. At DT(H) case, however, no significant yield degradation or a slight yield enhancement was observed which agrees with the interspecies ion diffusion theory. Detailed experiment results and simulation are needed to confirm the initial observation.

Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

KAUST Repository

Carrillo, J. A.; Desvillettes, L.; Fellner, K.

2009-01-01

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a Continuous Coagulation-Fragmentation Model with Diffusion

KAUST Repository

Carrillo, J. A.

2009-10-30

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

Yields of 2-deoxy-D-gluconic, D-gluconic and other sugar acids in gamma-irradiated aqueous solutions of D-glucose. [Gamma rays

Energy Technology Data Exchange (ETDEWEB)

Esterbauer, H; Schubert, J; Sanders, E B; Sweeley, C C [Pittsburgh Univ., Pa. (USA); Michigan State Univ., East Lansing (USA). Dept. of Biochemistry)

1977-03-01

The yields of 2-deoxy-D-gluconic, D-gluconic and other sugar acids from /sup 60/Co-gamma irradiated (dose-rate = 4 Krads/min) D-glucose solutions are reported. The acids produced upon radiolysis were separated from glucose and neutral products by anion exchange, assayed by gas chromatography of the trimethylsilyl derivatives, and definitive identification made by mass spectrometry. In He degassed, irradiated 0.055 M glucose G(2-deoxy-D-gluconic acid) = 0.62 and G(D-gluconic acid) = 0.20. The approximate G values for the other identified acids are: glyceric acid 0.03, 2-deoxy-tetronic acid 0.04, tetronic acid 0.03, 4-deoxypentonic acid 0.02, deoxyketogluconic acid 0.17. In N/sub 2/O saturated glucose solutions D-gluconic acid yields increased by a factor of approximately 1.9 while that of 2-deoxy-D-gluconic acid increased by a factor of only approximately 1.1.

Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

CERN Document Server

Cherniha, Roman

2017-01-01

This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception,...

Size dependent diffusive parameters and tensorial diffusion equations in neutronic models for optically small nuclear systems

International Nuclear Information System (INIS)

Premuda, F.

1983-01-01

Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

Entropy methods for diffusive partial differential equations

CERN Document Server

Jüngel, Ansgar

2016-01-01

This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.

Phenomenology of polymer solution dynamics

National Research Council Canada - National Science Library

Phillies, George D. J

2011-01-01

... solutions, not dilute solutions or polymer melts. From centrifugation and solvent dynamics to viscosity and diffusion, experimental measurements and their quantitative representations are the core of the discussion...

Reaction diffusion in chromium-zircaloy-2 system

International Nuclear Information System (INIS)

Xiang Wenxin; Ying Shihao

2001-01-01

Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound

TRANSIENT ANOMALOUS SUB-DIFFUSION ON BOUNDED DOMAINS

OpenAIRE

MEERSCHAERT, MARK M.; NANE, ERKAN; VELLAISAMY, P.

2012-01-01

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

Gas-induced friction and diffusion of rigid rotors

Science.gov (United States)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures

International Nuclear Information System (INIS)

Sobolev, S.L.

2014-01-01

An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal diffusion equations of hyperbolic type and describes the transition to complete solute trapping and diffusionless solidification at a finite interface velocity in accordance with experimental data and molecular dynamic simulation. -- Highlights: •We propose the diffusion-stress coupling model for binary solidification. •The coupling arises at deep undercooling. •With diffusive dynamics, the models result in parabolic transfer equations. •With the wavelike dynamics, the models lead to hyperbolic transfer equations. •The coupling strongly affects the solute partition coefficient

Effect of cation nature of Cl2- yields in pulse radiolysis of alkali metal chloride aqueous solutions

International Nuclear Information System (INIS)

Kabakchi, S.A.; Zansokhova, A.A.; Pikaev, A.K.

1975-01-01

A study is made of the amount of Cl 2 - formed during a pulsating radiolysis of potassium, rubidium and cesium chlorides in aqueous solutions saturated with air. An equation is presented relating the yield of Cl 2 - and the concentration of the starting materials. Various mechanisms describing the radiolysis of neutral aqueous solutions of the chlorides are proposed. The observed effect of the cation on the efficiency of Cl 2 - formations favours the mechanism according to which Cl 2 - forms through the reaction of Cl - ion with a ''hole''. Due to charge migration in the conductivity zone the electron transfer reaction either goes steadily by jumps. As a result of the interaction between the ''hole'' and water [H 3 O + ...OH] a complex is formed from a hydrogen ion and OH radical, which are united trhough the hydrogen bond. Disturbance of the hydrogen bond structure should increase the probability of disintegration of the complex

Double diffusivity model under stochastic forcing

Science.gov (United States)

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

a metabolic wastage model for the rate-yield trade off

Indian Academy of Sciences (India)

A METABOLIC WASTAGE MODEL FOR THE RATE-YIELD TRADE OFF. There is a growth limiting step in which an intermediate metabolite (m) has to hit a target molecule (t). ... D= rate of diffusing out. S= the rate of formation of the metabolite. The equilibrium loss decides the yield. The no. of activated targets decide the rate ...

Osmosis and Diffusion

Science.gov (United States)

Sack, Jeff

2005-01-01

OsmoBeaker is a CD-ROM designed to enhance the learning of diffusion and osmosis by presenting interactive experimentation to the student. The software provides several computer simulations that take the student through different scenarios with cells, having different concentrations of solutes in them.

Diffusiophoresis in one-dimensional solute gradients

International Nuclear Information System (INIS)

Ault, Jesse T.; Warren, Patrick B.; Shin, Sangwoo; Stone, Howard A.

2017-01-01

Here, the diffusiophoretic motion of suspended colloidal particles under one-dimensional solute gradients is solved using numerical and analytical techniques. Similarity solutions are developed for the injection and withdrawal dynamics of particles into semi-infinite pores. Furthermore, a method of characteristics formulation of the diffusion-free particle transport model is presented and integrated to realize particle trajectories. Analytical solutions are presented for the limit of small particle diffusiophoretic mobility Γ p relative to the solute diffusivity D s for particle motions in both semi-infinite and finite domains. Results confirm the build up of local maxima and minima in the propagating particle front dynamics. The method of characteristics is shown to successfully predict particle motions and the position of the particle front, although it fails to accurately predict suspended particle concentrations in the vicinity of sharp gradients, such as at the particle front peak seen in some injection cases, where particle diffusion inevitably plays an important role. Results inform the design of applications in which the use of applied solute gradients can greatly enhance particle injection into and withdrawal from pores.

Benchmarks for multicomponent diffusion and electrochemical migration

DEFF Research Database (Denmark)

Rasouli, Pejman; Steefel, Carl I.; Mayer, K. Ulrich

2015-01-01

In multicomponent electrolyte solutions, the tendency of ions to diffuse at different rates results in a charge imbalance that is counteracted by the electrostatic coupling between charged species leading to a process called “electrochemical migration” or “electromigration.” Although not commonly...... not been published to date. This contribution provides a set of three benchmark problems that demonstrate the effect of electric coupling during multicomponent diffusion and electrochemical migration and at the same time facilitate the intercomparison of solutions from existing reactive transport codes...

Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

Directory of Open Access Journals (Sweden)

Nauman Raza

2013-01-01

Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

Neutron diffusion approximation solution for the the three layer borehole cylindrical geometry. Pt. 1. Theoretical description

International Nuclear Information System (INIS)

Czubek, J.A.; Woznicka, U.

1997-01-01

A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n + 2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R 1 surrounded by the intermediate region (e.g. mud cake) of thickness (R 2 -R 1 ) and finally surrounded by the geological formation which spreads from R 2 up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author)

A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor

Directory of Open Access Journals (Sweden)

B. Godongwana

2015-01-01

Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

Metal ions diffusion through polymeric matrices: A total reflection X-ray fluorescence study

International Nuclear Information System (INIS)

Boeykens, S.; Caracciolo, N.; D'Angelo, M.V.; Vazquez, C.

2006-01-01

This work proposes the use of X-ray fluorescence with total reflection geometry to explore the metal ions transport in aqueous hydrophilic polymer solutions. It is centered in the study of polymer concentration influence on ion diffusion. This subject is relevant to various and diverse applications, such as drug controlled release, microbiologic corrosion protection and enhanced oil recovery. It is anticipated that diffusion is influenced by various factors in these systems, including those specific to the diffusing species, such as charge, shape, molecular size, and those related to the structural complexity of the matrix as well as any specific interaction between the diffusing species and the matrix. The diffusion of nitrate salts of Ba and Mn (same charge, different hydrodynamic radii) through water-swollen polymeric solutions and gels in the 0.01% to 1% concentration ranges was investigated. The measurements of the metal concentration were performed by TXRF analysis using the scattered radiation by the sample as internal standard. Results are discussed according to different physical models for solute diffusion in polymeric solutions

Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems

OpenAIRE

Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus

2017-01-01

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...

A Mathematical Model of Solute Coupled Water Transport in Toad Intestine Incorporating Recirculation of the Actively Transported Solute

DEFF Research Database (Denmark)

Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær

2000-01-01

those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute......A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing...... increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux...

Effective diffusion in time-periodic linear planar flow

International Nuclear Information System (INIS)

Indeikina, A.; Chang, H.

1993-01-01

It is shown that when a point source of solute is inserted into a time-periodic, unbounded linear planar flow, the large-time, time-average transport of the solute can be described by classical anisotropic diffusion with constant effective diffusion tensors. For a given vorticity and forcing period, elongational flow is shown to be the most dispersive followed by simple shear and rotational flow. Large-time diffusivity along the major axis of the time-average concentration ellipse, whose alignment is predicted from the theory, is shown to increase with vorticity for all flows and decrease with increasing forcing frequency for elongational flow and simple shear. For the interesting case of rotational flow, there exist discrete resonant frequencies where the time-average major diffusivity reaches local maxima equal to the time-average steady flow case with zero forcing frequency

Origin of the reversed yield asymmetry in Mg-rare earth alloys at high temperature

International Nuclear Information System (INIS)

Hidalgo-Manrique, P.; Herrera-Solaz, V.; Segurado, J.; Llorca, J.; Gálvez, F.; Ruano, O.A.; Yi, S.B.; Pérez-Prado, M.T.

2015-01-01

The mechanical behaviour in tension and compression of an extruded Mg–1 wt.% Mn–1 wt.% Nd (MN11) alloy was studied along the extrusion direction in the temperature range −175 °C to 300 °C at both quasi-static and dynamic strain rates. Microstructural analysis revealed that the as-extruded bar presents a recrystallized microstructure and a weak texture that remain stable in the whole temperature range. A remarkable reversed yield stress asymmetry was observed above 150 °C, with the compressive yield stress being significantly higher than the tensile yield stress. The origin of this anomalous reversed yield stress asymmetry, which to date remains unknown, was investigated through the analysis of the macro and microtexture development during deformation, as well as by means of crystal plasticity finite element simulations of a representative volume element of the polycrystal. The critical resolved shear stresses of slip and twining for simulated single crystals were obtained as a function of the temperature by means of an inverse optimisation strategy. Experimental and simulation results suggest that the reversed yield asymmetry may be primarily attributed to the non-Schmid behaviour of pyramidal 〈c + a〉 slip, which is the dominant deformation mechanism at high temperatures. It is proposed, furthermore, that the asymmetry is enhanced at quasi-static strain rates by the stronger interaction of 〈c + a〉 dislocations with the diffusing solute atoms and particles in compression than in tension

Diffusion with Varying Drag; the Runaway Problem.

Science.gov (United States)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

Diffusion with varying drag; the runaway problem

International Nuclear Information System (INIS)

Rollins, D.K.

1986-01-01

The motion of electrons in an ionized plasma of electrons and ions in an external electric field is studied. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron-runaway phenomenon. The electric field is treated as a small perturbation. Various diffusion coefficients are considered for the one dimensional problem, and the runaway current is determined as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coeffient decays with velocity are then considered. To determine the runaway current, the equivalent Schroedinger eigenvalue problem is analyzed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching, a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem

Effects of solution volume on hydrogen production by pulsed spark discharge in ethanol solution

Energy Technology Data Exchange (ETDEWEB)

Xin, Y. B.; Sun, B., E-mail: sunb88@dlmu.edu.cn; Zhu, X. M.; Yan, Z. Y.; Liu, H.; Liu, Y. J. [College of Environmental Science and Engineering, Dalian Maritime University, Dalian 116026 (China)

2016-07-15

Hydrogen production from ethanol solution (ethanol/water) by pulsed spark discharge was optimized by varying the volume of ethanol solution (liquid volume). Hydrogen yield was initially increased and then decreased with the increase in solution volume, which achieved 1.5 l/min with a solution volume of 500 ml. The characteristics of pulsed spark discharge were studied in this work; the results showed that the intensity of peak current, the rate of current rise, and energy efficiency of hydrogen production can be changed by varying the volume of ethanol solution. Meanwhile, the mechanism analysis of hydrogen production was accomplished by monitoring the process of hydrogen production and the state of free radicals. The analysis showed that decreasing the retention time of gas production and properly increasing the volume of ethanol solution can enhance the hydrogen yield. Through this research, a high-yield and large-scale method of hydrogen production can be achieved, which is more suitable for industrial application.

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

Science.gov (United States)

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

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

Proof of existence of global solutions for m-component reaction-diffusion systems with mixed boundary conditions via the Lyapunov functional method

International Nuclear Information System (INIS)

Abdelmalek, Salem; Kouachi, Said

2007-01-01

To prove global existence for solutions of m-component reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions and nonhomogeneous Robin boundary conditions. The purpose of this paper is to prove the existence of a global solution using a single inequality for the polynomial growth condition of the reaction terms. Our technique is based on the construction of polynomial functionals. This result generalizes those obtained recently by Kouachi et al (at press), Kouachi (2002 Electron. J. Diff. Eqns 2002 1), Kouachi (2001 Electron. J. Diff. Eqns 2001 1) and independently by Malham and Xin (1998 Commun. Math. Phys. 193 287)

A spatial structural derivative model for ultraslow diffusion

Directory of Open Access Journals (Sweden)

Xu Wei