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.

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

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 treatment of implicit continuum diffusion

Science.gov (United States)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

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.

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)

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

Raffinate treatment at the Portsmouth Gaseous Diffusion Plant

International Nuclear Information System (INIS)

Acox, T.A.

1983-01-01

Raffinate solutions, which contain uranium, technetium, nitrates, and lesser amounts of heavy metals, are produced in the decontamination and uranium recovery operations at the Portsmouth Gaseous Diffusion Plant. These solutions are presently being placed in temporary storage until three treatment facilities are constructed which will produce an environmentally acceptable effluent from the raffinate. These facilities are: (1) The Heavy Metals Precipitation Facility; (2) The Technetium Ion Exchange Facility; and (3) The Biodenitrification Pilot Plant. When the facilities are completed, the raffinate will be treated in 500 gallon batches. The first treatment is the heavy metals precipitation by caustic addition and filtering. The effluent proceeds to the ion exchange columns where the technetium is removed by adsorption onto a strongly basic, anion exchange resin which has been converted to the hydroxyl form. Following ion exchange, the solution is transported to the biodenitrification pilot plant. The biodenitrification column is a fluidized-bed using bacteria-laden coal particles as the denitrifying media. The resulting effluent should meet the limits established by the US EPA for all metals and nitrate. Technetium will be 98+% removed and the uranium concentration will be less than one milligram per liter. 13 references

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.

Singular solution of the Feller diffusion equation via a spectral decomposition

Science.gov (United States)

Gan, Xinjun; Waxman, David

2015-01-01

Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

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)

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.

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.

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)

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)

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.

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

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 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)

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].

Evaluation of water, sucrose and minerals effective diffusivities during osmotic treatment of pork in sugar beet molasses

Directory of Open Access Journals (Sweden)

Nićetin Milica R.

2015-01-01

Full Text Available Effective diffusivities of water, sucrose and minerals in osmotic treatment of pork cubes (M. triceps brachii were calculated using Response Surface Methodology (RSM, with respect to temperature (20, 35 and 50oC and concentration of sugar beet molasses, (60, 70 and 80% w/w. The numerical solution of Fick's' law for unsteady-state mass transfer in a perfect cube configuration was used to calculate the effective diffusivities of water, sucrose and minerals (Na, K, Ca and Mg. Zugarramurdi and Lupin's model was used to predict the equilibrium condition, which was shown to be appropriate for water loss and solute uptake during osmotic treatment. Effective diffusivity of water was found to be in the range of 6.95×10-10 - 8.03×10-10 m2s-1, the sucrose effective diffusivity was between 6.39×10-10 and 8.25×10-10 m2s-1, while diffusivities for minerals were in the range 6.34×10-10 - 8.82×10-10 m2s-1, for Na, 6.27×10-10 - 7.43×10-10 m2s-1, for K, 6.44×10-10 - 8.94×10-10 m2s-1, for Ca and 3.47×10-10 - 5.66×10-10 m2s-1, for Mg. [Projekat Ministarstva nauke Republike Srbije, br. TR 31055

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.

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)

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.

New diffusion-like solutions of one-speed transport equations in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.

1988-01-01

Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ψ(r, μ) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted. (author)

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

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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.

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)

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

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

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.

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

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.

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

Mathematical Simulation of the Process of Aerobic Treatment of Wastewater under Conditions of Diffusion and Mass Transfer Perturbations

Science.gov (United States)

Bomba, A. Ya.; Safonik, A. P.

2018-03-01

A mathematical model of the process of aerobic treatment of wastewater has been refined. It takes into account the interaction of bacteria, as well as of organic and biologically nonoxidizing substances under conditions of diffusion and mass transfer perturbations. An algorithm of the solution of the corresponding nonlinear perturbed problem of convection-diffusion-mass transfer type has been constructed, with a computer experiment carried out based on it. The influence of the concentration of oxygen and of activated sludge on the quality of treatment is shown. Within the framework of the model suggested, a possibility of automated control of the process of deposition of impurities in a biological filter depending on the initial parameters of the water medium is suggested.

Mathematical Simulation of the Process of Aerobic Treatment of Wastewater under Conditions of Diffusion and Mass Transfer Perturbations

Science.gov (United States)

Bomba, A. Ya.; Safonik, A. P.

2018-05-01

A mathematical model of the process of aerobic treatment of wastewater has been refined. It takes into account the interaction of bacteria, as well as of organic and biologically nonoxidizing substances under conditions of diffusion and mass transfer perturbations. An algorithm of the solution of the corresponding nonlinear perturbed problem of convection-diffusion-mass transfer type has been constructed, with a computer experiment carried out based on it. The influence of the concentration of oxygen and of activated sludge on the quality of treatment is shown. Within the framework of the model suggested, a possibility of automated control of the process of deposition of impurities in a biological filter depending on the initial parameters of the water medium is suggested.

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.

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.

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)

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)

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

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

HRCT of diffuse interstitial pneumonia during treatment

International Nuclear Information System (INIS)

Takahashi, Masashi; Sano, Akira; Imanaka, Kazufumi

1989-01-01

HRCT was carried out in twenty patients with diffuse interstitial pneumonia: 13 cases of IIP, 3 of BOOP, 2 of drug-induced pneumonia, 1 of rheumatoid lung and acute interstitial pneumonia of unknown origin. With special attention to inflammatory activity, the patients underwent HRCT periodically during the treatment. Correlative investigation between HRCT image and grade of accumulation in 67 Ga scintigraphy was also performed. Response to steroid therapy was clearly reflected on HRCT image, that was shown as decreasing pulmonary density or thinning of honeycomb wall. HRCT is considered to be useful in assessing the activity of diffuse interstitial pneumonia. (author)

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)

Treatment of knee diffuse pigmented villonodular synovitis under the arthroscopy with radiotherapy

International Nuclear Information System (INIS)

Peng Wei; Huang Xunwu; Guan Changyong; Yu Fangyuan; Zhang Bo

2011-01-01

Objective: To evaluate arthroscopy plus radiotherapy in the treatment of diffuse pigmented villonodular synovitis of the knee. Methods: A total of 10 cases of diffuse pigmented villonodular synovitis of the knee were treated under the arthroscopy combined with postoperative radiotherapy. These patients were followed up for 12-36 months, and were evaluated as to the effect of treatment. Results: According to the Lysholm criteria, the score was (53.5 ± 11.6) and(85.7 ± 10.7) respectively before surgery and at the last followup. Conclusion: Arthroscopical synovectomy with a combined application of postoperative radiotherapy is an effective treatment for diffuse pigmented vilionoclular synovitis of the knee. (authors)

Lattice diffusion of a single molecule in solution

Science.gov (United States)

Ruggeri, Francesca; Krishnan, Madhavi

2017-12-01

The ability to trap a single molecule in an electrostatic potential well in solution has opened up new possibilities for the use of molecular electrical charge to study macromolecular conformation and dynamics at the level of the single entity. Here we study the diffusion of a single macromolecule in a two-dimensional lattice of electrostatic traps in solution. We report the ability to measure both the size and effective electrical charge of a macromolecule by observing single-molecule transport trajectories, typically a few seconds in length, using fluorescence microscopy. While, as shown previously, the time spent by the molecule in a trap is a strong function of its effective charge, we demonstrate here that the average travel time between traps in the landscape yields its hydrodynamic radius. Tailoring the pitch of the lattice thus yields two different experimentally measurable time scales that together uniquely determine both the size and charge of the molecule. Since no information is required on the location of the molecule between consecutive departure and arrival events at lattice sites, the technique is ideally suited to measurements on weakly emitting entities such as single molecules.

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

Hybrid diffusive/PVD treatments to improve the tribological resistance of Ti-6Al-4V.

Science.gov (United States)

Marin, E; Offoiach, R; Lanzutti, A; Regis, M; Fusi, S; Fedrizzi, L

2014-01-01

Titanium alloys are nowadays used for a wide range of biomedical applications thanks to their combination of high mechanical resistance, high corrosion resistance and biocompatibility. Nevertheless, the applicability of titanium alloys is sometimes limited due to their low microhardness and tribological resistance. Thus the titanium alloys cannot be successfully applied to prosthetic joint couplings. A wide range of surface treatments, in particular PVD coatings such as CrN and TiN, have been used in order to improve the tribological behaviour of titanium alloys. However, the low microhardness of the titanium substrate often results in coating failure due to cracks and delamination. For this reason, hybrid technologies based on diffusive treatments and subsequent PVD coatings may improve the overall coating resistance. In this work, conventional PVD coatings of CrN or TiCN, deposited on Titanium Grade 5, were characterized and then combined with a standard thermal diffusive nitriding treatment in order to improve the tribological resistance of the titanium alloys and avoid coating delamination. The different treatments were studied by means of scanning electron microscopy both on the sample surface and in cross-section. In-depth composition profiles were obtained using glow discharge optical emission spectrometry (GDOES) and localized energy dispersive X-ray diffraction on linear scan-lines. The microhardness and adhesion properties of the different treatments were evaluated using Vickers microhardness tests at different load conditions. The indentations were observed by means of SEM in order to evaluate delaminated areas and the crack's shape and density. The tribological behaviour of the different treatments was tested in dry conditions and in solution, in alternate pin-on-flat configuration, with a frequency of 0.5 Hz. After testing, the surface was investigated by means of stylus profilometry and SEM both on the surface and in cross-section. The standalone PVD

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.

Solution treatment of fast reactor claddings

International Nuclear Information System (INIS)

Miura, Makoto; Nagaki, Hiroshi; Koyama, Masahiro

1974-01-01

The fuel cladding tubes for Joyo (experimental FBR) are required to be a material corresponding to AISI Type 316 and cold-rolled after solution treatment. It is necessary to have no precipitation of carbide and to make the grain size smaller than ASTM No.6. It is very difficult to obtain the fine grains without the precipitation, however. In this connection, the behavior of carbide solution at high temperature and the annealing behavior of the material cold-worked and solution-treated were studied. The following matters are described: the solid solubility line of AISI Type 316; the behavior of carbide at solution treatment temperature; and the annealing behavior of the cold-worked material. (Mori, K.)

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.

Treatment outcome in early diffuse cutaneous systemic sclerosis

DEFF Research Database (Denmark)

Herrick, Ariane L; Pan, Xiaoyan; Peytrignet, Sébastien

2017-01-01

OBJECTIVES: The rarity of early diffuse cutaneous systemic sclerosis (dcSSc) makes randomised controlled trials very difficult. We aimed to use an observational approach to compare effectiveness of currently used treatment approaches. METHODS: This was a prospective, observational cohort study...

Diffuse plasma treatment of polyamide 66 fabric in atmospheric pressure air

International Nuclear Information System (INIS)

Li, Lee; Peng, Ming-yang; Teng, Yun; Gao, Guozhen

2016-01-01

Graphical abstract: - Highlights: • A cylindrical-electrode nanosecond-pulse diffuse-discharge reactor is presented. • Large-scale non-thermal plasmas were generated steadily in atmospheric air. • Treated PA66 fabric is etched with oxygen-containing group increases. • The hydrophily of treated PA66 fabric improves effectively. • Extending the treatment time is a method to reduce the treatment frequency. - Abstract: The polyamide 66 (PA66) fabrics are hard to be colored or glued in industrial production due to the poor hydrophily. Diffuse plasma is a kind of non-thermal plasma generated at atmospheric pressure in air. This paper proposes that large-scale diffuse plasma generated between wire electrodes can be employed for improving the hydrophily of PA66 fabrics. A repetitive nanosecond-pulse diffuse-discharge reactor using a cylindrical wire electrode configuration is presented, which can generate large-scale non-thermal plasmas steadily at atmospheric pressure without any barrier dielectric. Then the reactor is used to treat PA66 fabrics in different discharge conditions. The hydrophilicity property of modified PA66 is measured by wicking test method. The modified PA66 is also analyzed by atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS) to prove the surface changes in physical microstructure and chemical functional groups, respectively. What's more, the effects of treatment time and treatment frequency on surface modification are investigated and discussed.

Metallurgical study of low-temperature plasma carbon diffusion treatments for stainless steels

International Nuclear Information System (INIS)

Lewis, D.B.; Leyland, A.; Stevenson, P.R.; Cawley, J.; Matthews, A.

1993-01-01

We recently reported a novel low-temperature carbon diffusion technique for surface hardening of stainless steels. The treatment was shown to provide benefits in terms of abrasive wear resistance. There is also evidence to suggest that by performing diffusion treatments at low temperatures (i.e. below 400 C), these benefits can be achieved without compromising corrosion resistance. Here a variety of surface analysis and depth profiling techniques have been used to determine the physical and mechanical properties of carbon-rich layers produced on a range of stainless steel substrate materials. X-ray diffraction (XRD) was employed to determine the crystallographic structure, whilst wavelength dispersive X-ray analysis (WDX) and glow discharge optical spectroscopy (GDOS) gave information on the concentration and distribution of the diffused species within the treated layers. A variety of carbide-based structures was detected, including the expected M 23 C 6 and, more surprisingly, M 3 C. Optical and electron microscopy techniques were used to provide information on layer morphology. The surfaces produced by the low-temperature carbon-diffusion process generally exhibit a distinct diffusion layer of between 1 and 20 μm, depending on the material and the treatment conditions. Austenitic stainless steels appear to give the best response to treatment, however other types of stainless steel can be treated, particularly if the microstructure contains above 5% retained austenite. Here we discuss the changes in mechanical and metallurgical properties provided by this technique and its potential value for treatment of both austenitic and other stainless steel substrate materials. (orig.)

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

Abatement vs. treatment for efficient diffuse source water pollution management in terrestrial-marine systems.

Science.gov (United States)

Roebeling, P C; Cunha, M C; Arroja, L; van Grieken, M E

2015-01-01

Marine ecosystems are affected by water pollution originating from coastal catchments. The delivery of water pollutants can be reduced through water pollution abatement as well as water pollution treatment. Hence, sustainable economic development of coastal regions requires balancing of the marginal costs from water pollution abatement and/or treatment and the associated marginal benefits from marine resource appreciation. Water pollution delivery reduction costs are, however, not equal across abatement and treatment options. In this paper, an optimal control approach is developed and applied to explore welfare maximizing rates of water pollution abatement and/or treatment for efficient diffuse source water pollution management in terrestrial-marine systems. For the case of diffuse source dissolved inorganic nitrogen water pollution in the Tully-Murray region, Queensland, Australia, (agricultural) water pollution abatement cost, (wetland) water pollution treatment cost and marine benefit functions are determined to explore welfare maximizing rates of water pollution abatement and/or treatment. Considering partial (wetland) treatment costs and positive water quality improvement benefits, results show that welfare gains can be obtained, primarily, through diffuse source water pollution abatement (improved agricultural management practices) and, to a minor extent, through diffuse source water pollution treatment (wetland restoration).

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.

[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.

Conductivity enhancement of silver nanowire networks via simple electrolyte solution treatment and solvent washing

Science.gov (United States)

Gu, Jiahui; Wang, Xuelin; Chen, Hongtao; Yang, Shihua; Feng, Huanhuan; Ma, Xing; Ji, Hongjun; Wei, Jun; Li, Mingyu

2018-06-01

As a promising replacement material for indium tin oxide in flexible electronics, silver nanowires (AgNWs) usually need complicated post-treatment to reduce the high contact resistance across the intersections when used as transparent conductive films. In this work, a widely applicable nano-joining method for improving the overall conductivity of AgNW networks with different kinds of electrolyte solutions is presented. By treatment with an electrolyte solution with appropriate ionic strengths, the insulating surfactant layer (polyvinylpyrrolidone, PVP) on the AgNWs could be desorbed, and the AgNW network could be densified. The sheet resistance of the AgNW film on a glass slide is reduced by 60.9% (from 67.5 to 26.4 Ohm sq‑1) with a transmittance of 92.5%. High-resolution transmission electron microscopy analysis indicates that atomic diffusion occurs at the intersection of two AgNWs. Thus, metallurgical bonding on the nanometer scale is achieved across the junctions of the AgNWs, leading to a significant enhancement in the conductivity of the AgNW network.

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.

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.

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

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

Problems with Discontinuous Diffusion/Dispersion Coefficients

Directory of Open Access Journals (Sweden)

Stefano Ferraris

2012-01-01

accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.

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

Grain boundary diffusion in terms of the tempered fractional calculus

International Nuclear Information System (INIS)

Sibatov, R.T.; Svetukhin, V.V.

2017-01-01

Mathematical treatment of grain-boundary diffusion based on the model first proposed by Fisher is usually formulated in terms of normal diffusion equations in a two-component nonhomogeneous medium. On the other hand, fractional equations of anomalous diffusion proved themselves to be useful in description of grain-boundary diffusion phenomena. Moreover, the most important propagation regime predicted by Fisher's model demonstrates subdiffusive behavior. However, the direct link between fractional approach and the Fisher model and its modifications has not found yet. Here, we fill this gap and show that solution of fractional subdiffusion equation offers general properties of classical solutions obtained by Whipple and Suzuoka. The tempered fractional approach is a convenient tool for studying precipitation in granular materials as the tempered subdiffusion limited process. - Highlights: • The link connected fractional diffusion approach and Fisher's model of grain-boundary diffusion is derived. • The subdiffusion exponent of grain-boundary diffusion can differ from 1/2. • Nucleation in granular materials is modeled by the process limited by tempered subdiffusion.

Grain boundary diffusion in terms of the tempered fractional calculus

Energy Technology Data Exchange (ETDEWEB)

Sibatov, R.T., E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432017, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation); Svetukhin, V.V. [Ulyanovsk State University, 432017, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation); Institute of Nanotechnology and Microelectronics of the Russian Academy of Sciences, 115487, 18 Nagatinskaya str., Moscow (Russian Federation)

2017-06-28

Mathematical treatment of grain-boundary diffusion based on the model first proposed by Fisher is usually formulated in terms of normal diffusion equations in a two-component nonhomogeneous medium. On the other hand, fractional equations of anomalous diffusion proved themselves to be useful in description of grain-boundary diffusion phenomena. Moreover, the most important propagation regime predicted by Fisher's model demonstrates subdiffusive behavior. However, the direct link between fractional approach and the Fisher model and its modifications has not found yet. Here, we fill this gap and show that solution of fractional subdiffusion equation offers general properties of classical solutions obtained by Whipple and Suzuoka. The tempered fractional approach is a convenient tool for studying precipitation in granular materials as the tempered subdiffusion limited process. - Highlights: • The link connected fractional diffusion approach and Fisher's model of grain-boundary diffusion is derived. • The subdiffusion exponent of grain-boundary diffusion can differ from 1/2. • Nucleation in granular materials is modeled by the process limited by tempered subdiffusion.

The use of ion-selective membranes for the recovery of sulphuric acid out of contaminated solutions. Comparing electrodialysis, electro electrodialysis and diffusion dialysis

International Nuclear Information System (INIS)

Cattoir, S.

1998-02-01

The amount of waste arising from dismantled reactors is minimized by decontamination processes. These processes result in contaminated effluents, containing acid and metal salts. The quantity of final waste can be substantially reduced when the acid is extracted out of the decontamination effluents prior to neutralisation. This report discusses three membrane techniques for the displacement of acids out of mixed acid/salt solutions: electrodialysis (ED), electro electrodialysis (EED) and diffusion dialysis (DD). EED uses an electrical potential difference across an anion-selective membrane; DD uses a concentration difference across an anion-selective membrane; ED uses an electrical potential difference, across an anion- and a cation-selective membrane. EED can displace up to 90% of the sulphuric acid, the amount of metal ions in the displaced-acid solution is less than 1% of the ions in the original contaminated solution. Treatment costs are estimated to about 18 Belgian Francs per litre. In DD the purity of the displaced acid is comparable to EED. Treatment costs are about 21 Belgian Francs per litre. In ED 90% acid-displacement is easily reached, but 5% metal ions are also displaced. Treatment costs are about 6 Belgian Francs per litre. Therefore, in spite of the lower purity of the resulting acid, ED is economically speaking the best choice

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.

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.)

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.

Analytically solvable models of reaction-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)

2004-05-01

We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.

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)

[Surgical treatment of diffuse adult orbital lymphangioma: two case studies].

Science.gov (United States)

Berthout, A; Jacomet, P V; Putterman, M; Galatoire, O; Morax, S

2008-12-01

Orbital lymphangioma is a rare vascular malformation; it is a benign but severe anomaly because of its infiltrative, diffuse, and hemorrhagic nature, and its high morbidity rate. Surgical resection is a real challenge on account of the intricate architecture of the lesion. The authors report their surgical experience concerning two cases of diffuse orbital lymphangioma whose diagnosis was established in adulthood and whose surgical treatment was successful. Two patients presented with adult orbital lymphangioma. Progression was slow during the first decade and then was quickly followed by complications: major exorbitism, compressive optic neuropathy, and corneal exposure. Neuroimaging showed a diffuse and cystic orbital malformation. Surgical resection was performed as completely as possible, in one case with a Krönlein orbitotomy and in the other case only via a conjunctive route. An aspirate drain was put in the orbit for 48 h so as to prevent dead spaces forming after resection, an essential risk factor of hemorrhagic or cystic recurrence. Systemic corticotherapy was administered for the 5 days following surgery. The resection was total in one case and subtotal in the other. The surgical follow-up was uneventful with an excellent aesthetic result and an improvement in visual acuity. After 12 months, no tumoral or hemorrhagic recurrence was noted. The surgical treatment of orbital lymphangiomas is challenging because of their infiltrative nature. In diffuse forms, a complete resection is rarely possible because of the risk of sacrificing visual function. In the two cases reported herein, the resection of the extraconal portion was complete, but the intraconal portion was completely removed only in one case. Using the aspirate drain, negative pressure was maintained in the orbital cavity, preventing the formation of chocolate cysts induced by surgery. Although the clinical result was very satisfying, long-term follow-up is necessary to evaluate recurrence

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.

Sustainable Zero-Valent Metal (ZVM Water Treatment Associated with Diffusion, Infiltration, Abstraction, and Recirculation

Directory of Open Access Journals (Sweden)

David D.J. Antia

2010-09-01

Full Text Available Socio-economic, climate and agricultural stress on water resources have resulted in increased global demand for water while at the same time the proportion of potential water resources which are adversely affected by sodification/salinisation, metals, nitrates, and organic chemicals has increased. Nano-zero-valent metal (n-ZVM injection or placement in aquifers offers a potential partial solution. However, n-ZVM application results in a substantial reduction in aquifer permeability, which in turn can reduce the amount of water that can be abstracted from the aquifer. This study using static diffusion and continuous flow reactors containing n-ZVM and m-ZVM (ZVM filaments, filings and punchings has established that the use of m-ZVM does not result in a reduction in aquifer permeability. The experimental results are used to design and model m-ZVM treatment programs for an aquifer (using recirculation or static diffusion. They also provide a predictive model for water quality associated with specific abstraction rates and infiltration/injection into an aquifer. The study demonstrates that m-ZVM treatment requires 1% of the weight required for n-ZVM treatment for a specific flow rate. It is observed that 1 t Fe0 will process 23,500 m3 of abstracted or infiltrating water. m-ZVM is able to remove >80% of nitrates from flowing water and adjust the water composition (by reduction in an aquifer to optimize removal of nitrates, metals and organic compounds. The experiments demonstrate that ZVM treatment of an aquifer can be used to reduce groundwater salinity by 20 –> 45% and that an aquifer remediation program can be designed to desalinate an aquifer. Modeling indicates that widespread application of m-ZVM water treatment may reduce global socio-economic, climate and agricultural stress on water resources. The rate of oxygen formation during water reduction [by ZVM (Fe0, Al0 and Cu0] controls aquifer permeability, the associated aquifer pH, aquifer Eh

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

Our Treatment Results of Circumscribed and Diffuse Choroidal Hemangiomas

Directory of Open Access Journals (Sweden)

Esra Savku

2013-08-01

Full Text Available Purpose: To discuss our treatment results of choroidal hemangiomas. Material and Method: The records of 39 cases of choroidal hemangioma followed up at our clinic between July 1999–October 2012 were reviewed retrospectively. Asymptomatic cases were followed up. Symptomatic cases with subretinal fluid and impaired vision received treatment. Results: Mean age of the 39 patients was 44 (12-80 years. Thirty-five of 39 cases had circumscribed choroidal hemangioma, and 4 cases had diffuse choroidal hemangioma. Sturge-Weber syndrome was present in 3 cases with diffuse choroidal hemangioma. Cases with circumscribed choroidal hemangioma and minimal subretinal fluid were treated with TTT in 11 cases, PDT in 12 cases, and PDT+TTT in 1 case. Cases with circumscribed choroidal hemangioma and excessive subretinal fluid were treated with Ru-106 plaque radiotherapy in 1 case, Ru-106 plaque radiotherapy+TTT in 1 case, EBRT in 3 cases, and TTT+EBRT in 1 case. One painful blind eye with neovascular glaucoma and complicated cataract was enucleated. Cases with diffuse choroidal hemangioma and excessive subretinal fluid were treated with Ru-106 plaque radiotherapy+TTT in 1 case and EBRT in 1 case. Ahmed glaucoma valve implantation and FAKO emulsification were applied to a case with neovascular glaucoma and complicated cataract. Complete resorption of subretinal fluid was achieved in 23 (72% of treated 32 cases. When mean initial tumor thickness was 2.6 mm (0.5-6, mean final tumor thickness was 1.4 mm (0-6. When mean initial visual acuity (LogMAR was 1.5 (0-3, mean final visual acuity was 1.1 (0-3. No recurrence was observed. Discussion: The amount of the subretinal fluid determines the method of treatment in circumscribed choroidal hemangioma. While TTT and PDT are effective treatment modalities for minimal subretinal fluid, plaque radiotherapy and EBRT are applied in cases with excessive subretinal fluid. Combination therapies may be necessary according to the

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)

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.

Treatment for hydrazine-containing waste water solution

Science.gov (United States)

Yade, N.

1986-01-01

The treatment for waste solutions containing hydrazine is presented. The invention attempts oxidation and decomposition of hydrazine in waste water in a simple and effective processing. The method adds activated charcoal to waste solutions containing hydrazine while maintaining a pH value higher than 8, and adding iron salts if necessary. Then, the solution is aerated.

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.

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.

Change in Identity Diffusion and Psychopathology in a Specialized Inpatient Treatment for Borderline Personality Disorder.

Science.gov (United States)

Sollberger, Daniel; Gremaud-Heitz, Daniela; Riemenschneider, Anke; Agarwalla, Puspa; Benecke, Cord; Schwald, Oliver; Küchenhoff, Joachim; Walter, Marc; Dammann, Gerhard

2015-01-01

Patients with borderline personality disorder (BPD) show various psychopathological symptoms and suffer especially from disturbance in their identity. The purpose of the study was to investigate changes-particularly in affective BPD symptoms and identity diffusion-during a structured, disorder-specific inpatient treatment (DST) that combined a psychodynamic transference-focused psychotherapy approach with modules of dialectical behavioural skills training. In a prospective, two-group comparison trial, 44 patients with BPD were assessed with questionnaires addressing identity diffusion and state, as well as trait affective psychopathology, before and after 12 weeks of inpatient treatment. Thirty-two patients received DST, whereas 12 patients were given inpatient treatment-as-usual (TAU). The patients were allocated in a non-random procedure for two groups, in order of admission and availability of treatment options in the DST unit. In the pre-post-comparison, the DST group showed a significant decrease in identity diffusion (p borderline symptomatology and in the personality structure feature of identity diffusion. This highlights the significance of a short-term specific inpatient therapy for BPD. A structured, disorder-specific inpatient treatment of patients diagnosed with borderline personality disorder (BPD) combined a psychodynamic transference-focused psychotherapy treatment approach (focusing on pathological features in personality organization, particularly on non-integrated images of self and others) with modules of dialectical behavioural skills training. This treatment is associated with a decrease in identity diffusion of these patients after 12 weeks of treatment. The treatment is also related to a significant decrease in borderline typical psychopathological symptoms such as depressive symptoms, as well as an improvement in state anger. The outcomes of this structured, disorder-specific inpatient treatment of severely ill BPD patients indicated

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...

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

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.

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)

Handling and treatment of low-level radioactive wastes from gaseous diffusion plants in the United States of America

International Nuclear Information System (INIS)

Wing, J.F.; Behrend, J.E.

1984-01-01

Gaseous diffusion plants in the United States of America currently generate very small quantities of low-level radioactive wastes. These wastes consist primarily of airborne effluent solid trapping media and liquid scrubber solutions, liquid effluent treatment sludges, waste oils and solvents, scrap metals and conventional combustible wastes such as floor sweepings, cleaning rags and shoe covers. In addition to waste emanating from current operations, large quantities of scrap metal generated during the Cascade Improvement Program are stored above ground at each of the diffusion plants. The radionuclides of primary concern are uranium and 99 Tc. Current radioactive waste treatment consists of uranium dissolution in weak acids followed by chemical precipitation and/or solvent extraction for uranium recovery. Current disposal operations consist of above ground storage of scrap metals, shallow land burial of inorganic solids and incineration of combustible wastes. With increased emphasis on reducing the potential for off-site radiological dose, several new treatment and disposal options are being studied and new projects are being planned. One project of particular interest involves the installation of a high temperature incinerator to thermally degrade hazardous organic wastes contaminated with low-level radioactive wastes. Other technologies being studied include fixation of uranium-bearing sludges in concrete before burial, decontamination of scrap metals by smelting and use of specially engineered centralized burial grounds. (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...

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.

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.

Treatment of uranyl nitrate and flouride solutions

International Nuclear Information System (INIS)

Rodrigo Otero, A.; Rodrigo Vilaseca, F.; Morales Calvo, G.

1977-01-01

A theoretical study on the fluoride complexes contained in uranyl and aluminium solutions has been carried out. Likewise concentration limits and Duhring diagrams for those solutions have been experimentally established. As a result, the optimum operation conditions for concentration by evaporation in the treatment plant, have been deduced. (Author) 12 refs

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.

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.)

Time-Dependent Diffusion MRI in Cancer: Tissue Modeling and Applications

Directory of Open Access Journals (Sweden)

Olivier Reynaud

2017-11-01

Full Text Available In diffusion weighted imaging (DWI, the apparent diffusion coefficient (ADC has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times/frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a in the short time regime, disentangling structural and diffusive tissue properties, and (b near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts, a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS and diffusivities are assessed. The proper modeling of tissue membrane permeability—hardly a newcomer in the field, but lacking applications—and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter

Time-dependent diffusion MRI in cancer: tissue modeling and applications

Science.gov (United States)

Reynaud, Olivier

2017-11-01

In diffusion weighted imaging (DWI), the apparent diffusion coefficient has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD) is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times / frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a) in the short time regime, disentangling structural and diffusive tissue properties, and (b) near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts), a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT) are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS) and diffusivities are assessed. The proper modeling of tissue membrane permeability – hardly a newcomer in the field, but lacking applications - and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter estimation (i

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

Treatment planning using tailored and standard cylindrical light diffusers for photodynamic therapy of the prostate

International Nuclear Information System (INIS)

Rendon, Augusto; Lilge, Lothar; Beck, J Christopher

2008-01-01

Interstitial photodynamic therapy (PDT) has seen a rebirth, partially prompted by the development of photosensitizers with longer absorption wavelengths that enable the treatment of larger tissue volumes. Here, we study whether using diffusers with customizable longitudinal emission profiles, rather than conventional ones with flat emission profiles, improves our ability to conform the light dose to the prostate. We present a modified Cimmino linear feasibility algorithm to solve the treatment planning problem, which improves upon previous algorithms by (1) correctly minimizing the cost function that penalizes deviations from the prescribed light dose, and (2) regularizing the inverse problem. Based on this algorithm, treatment plans were obtained under a variety of light delivery scenarios using 5-15 standard or tailored diffusers. The sensitivity of the resulting light dose distributions to uncertainties in the optical properties, and the placement of diffusers was also studied. We find that tailored diffusers only marginally outperform conventional ones in terms of prostate coverage and rectal sparing. Furthermore, it is shown that small perturbations in optical properties can lead to large changes in the light dose distribution, but that those changes can be largely corrected with a simple light dose re-normalization. Finally, we find that prostate coverage is only minimally affected by small changes in diffuser placement. Our results suggest that prostate PDT is not likely to benefit from the use of tailored diffusers. Other locations with more complex geometries might see a better improvement

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

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.

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.

The Functional Diffusion Map: An Imaging Biomarker for the Early Prediction of Cancer Treatment Outcome

Directory of Open Access Journals (Sweden)

Bradford A. Moffat

2006-04-01

Full Text Available Functional diffusion map (fDM has been recently reported as an early and quantitative biomarker of clinical brain tumor treatment outcome. This MRI approach spatially maps and quantifies treatment-induced changes in tumor water diffusion values resulting from alterations in cell density/cell membrane function and microenvironment. This current study was designed to evaluate the capability of fDM for preclinical evaluation of dose escalation studies and to determine if these changes were correlated with outcome measures (cell kill and overall survival. Serial T2-weighted and diffusion MRI were carried out on rodents with orthotopically implanted 9L brain tumors receiving three doses of 1,3-bis(2-chloroethyl-1-nitrosourea (6.65, 13.3, and 26.6 mg/kg, i.p.. All images were coregistered to baseline T2-weighted images for fDM analysis. Analysis of tumor fDM data on day 4 posttreatment detected dosedependent changes in tumor diffusion values, which were also found to be spatially dependent. Histologic analysis of treated tumors confirmed spatial changes in cellularity as observed by fDM. Early changes in tumor diffusion values were found to be highly correlative with drug dose and independent biologic outcome measures (cell kill and survival. Therefore, the fDM imaging biomarker for early prediction of treatment efficacy can be used in the drug development process.

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

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)

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

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.)

Diffusion tensor imaging with direct cytopathological validation: characterisation of decorin treatment in experimental juvenile communicating hydrocephalus.

Science.gov (United States)

Aojula, Anuriti; Botfield, Hannah; McAllister, James Patterson; Gonzalez, Ana Maria; Abdullah, Osama; Logan, Ann; Sinclair, Alexandra

2016-05-31

In an effort to develop novel treatments for communicating hydrocephalus, we have shown previously that the transforming growth factor-β antagonist, decorin, inhibits subarachnoid fibrosis mediated ventriculomegaly; however decorin's ability to prevent cerebral cytopathology in communicating hydrocephalus has not been fully examined. Furthermore, the capacity for diffusion tensor imaging to act as a proxy measure of cerebral pathology in multiple sclerosis and spinal cord injury has recently been demonstrated. However, the use of diffusion tensor imaging to investigate cytopathological changes in communicating hydrocephalus is yet to occur. Hence, this study aimed to determine whether decorin treatment influences alterations in diffusion tensor imaging parameters and cytopathology in experimental communicating hydrocephalus. Moreover, the study also explored whether diffusion tensor imaging parameters correlate with cellular pathology in communicating hydrocephalus. Accordingly, communicating hydrocephalus was induced by injecting kaolin into the basal cisterns in 3-week old rats followed immediately by 14 days of continuous intraventricular delivery of either human recombinant decorin (n = 5) or vehicle (n = 6). Four rats remained as intact controls and a further four rats served as kaolin only controls. At 14-days post-kaolin, just prior to sacrifice, routine magnetic resonance imaging and magnetic resonance diffusion tensor imaging was conducted and the mean diffusivity, fractional anisotropy, radial and axial diffusivity of seven cerebral regions were assessed by voxel-based analysis in the corpus callosum, periventricular white matter, caudal internal capsule, CA1 hippocampus, and outer and inner parietal cortex. Myelin integrity, gliosis and aquaporin-4 levels were evaluated by post-mortem immunohistochemistry in the CA3 hippocampus and in the caudal brain of the same cerebral structures analysed by diffusion tensor imaging. Decorin significantly

Albedo-adjusted fast-neutron diffusion coefficients in reactor reflectors

International Nuclear Information System (INIS)

Terney, W.B.

1975-01-01

In the newer, larger pressurized-water reactor cores, the calculated power distributions are fairly sensitive to the number of neutron groups used and to the treatment of the reflector cross sections. Comparisons between transport and diffusion calculations show that the latter substantially underpredict the reflector albedos in the fast (top) group and that the power distribution is shifted toward the core center when compared to 4-group transport theory results. When the fast-neutron diffusion coefficients are altered to make the transport- and diffusion-theory albedos agree, the power distributions are also brought into agreement. An expression for the fast-neutron diffusion coefficients in reflector regions has been derived such that the diffusion calculation reproduces the albedo obtained from a transport solution. In addition, a correction factor for mesh effects applicable to coarse mesh problems is presented. The use of the formalism gives the correct albedos and improved power distributions. (U.S.)

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

Cleaning of diffusion bonding surface by argon ion bombardment treatment

International Nuclear Information System (INIS)

Wang, Airu; Ohashi, Osamu; Yamaguchi, Norio; Aoki, Masanori; Higashi, Yasuo; Hitomi, Nobuteru

2003-01-01

The specimens of oxygen-free high conductivity copper, SUS304L stainless steel and pure iron were treated by argon ion bombardment and then were bonded by diffusion bonding method. The effects of argon ion bombardment treatment on faying surface morphology, tensile strength of bonding joints and inclusions at the fracture surface were investigated. The results showed that argon ion bombardment treatment was effective to remove the oxide film and contamination at the faying surface and improve the quality of joints. The tensile strength of the bonded joints was improved, and minimum bonding temperature to make the metallic bonding at the interface was lowered by argon ion bombardment treatment. At the joints with argon ion bombardment treatment, ductile fractured surface was seen and the amount of inclusions was obviously decreased

High-resolution neutron spectroscopy on protein solution samples

International Nuclear Information System (INIS)

Grimaldo, M.; Henning, M.; Roosen-Runge, F.; Seydel, T.; Jalarvo, N.; Zamponi, M.; Zanini, F.; Zhang, F.; Schreiber, F.

2015-01-01

Proteins in solution are subject to a complex superposition of global translational and rotational diffusion as well as internal relaxations covering a wide range of time scales. With the advent of new high-flux neutron spectrometers in combination with enhanced analysis frameworks it has become possible to separate these different contributions. We discuss new approaches to the analysis by presenting example spectra and fits from data recorded on the backscattering spectrometers IN16, IN16B, and BASIS on the same protein solution sample. We illustrate the separation of the rotational and translational diffusion contribution, the accurate treatment of the solvent contribution, and the extraction of information on internal fluctuations. We also highlight the progress made in passing from second- to third-generation backscattering spectrometers. (authors)

Formation of crystalline InGaO₃(ZnO)n nanowires via the solid-phase diffusion process using a solution-based precursor.

Science.gov (United States)

Guo, Yujie; Van Bilzen, Bart; Locquet, Jean Pierre; Seo, Jin Won

2015-12-11

One-dimensional single crystalline InGaO3(ZnO)n (IGZO) nanostructures have great potential for various electrical and optical applications. This paper demonstrates for the first time, to our knowledge, a non-vacuum route for the synthesis of IGZO nanowires by annealing ZnO nanowires covered with solution-based IGZO precursor. This method results in nanowires with highly periodic IGZO superlattice structure. The phase transition of IGZO precursor during thermal treatment was systematically studied. Transmission electron microscopy studies reveal that the formation of the IGZO structure is driven by anisotropic inter-diffusion of In, Ga, and Zn atoms, and also by the crystallization of the IGZO precursor. Optical measurements using cathodoluminescence and UV-vis spectroscopy confirm that the nanowires consist of the IGZO compound with wide optical band gap and suppressed luminescence.

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

Measurement of Retinalamin diffusion coefficient in human sclera by optical spectroscopy

Science.gov (United States)

Genina, Elina A.; Bashkatov, Alexey N.; Zubkova, Elena A.; Kamenskikh, Tatiana G.; Tuchin, Valery V.

2008-12-01

The use of cytomedines (such as Retinalamin) in clinical practice has shown high effectiveness of the medicaments in ophthalmology. The study of diffusion of Retinalamin in scleral tissue is important for estimation of a drug dose delivered into inner tissue of eye, time of drug action, etc. In vitro measurements of spectral reflectance of sclera interacting with aqueous solution of Retinalamin have been carried out. Ten human sclera samples were included in the study. The results of the experiments have shown that penetration of Retinalamin into scleral tissue leads to the decrease of scleral reflectance due to optical immersion. Estimation of diffusion coefficient of studied solution has been made on the basis of analysis of optical reflectance dynamics of the sclera samples. The diffusion coefficient of Retinalamin in human scleral tissue was evaluated as (1.82±0.14)×10 -6 cm 2/s. The results are important for treatment of partial optic atrophy observed at primary open-angle glaucoma and others eye diseases.

Study of physicochemical processes and parameters of regime of diffusion brazing of niobium with titanium, zirconium and vanadium

International Nuclear Information System (INIS)

Grishin, V.L.; Lashko, S.V.

1986-01-01

Physicochemical processes at diffusion brazing of niobium with titanium, zirconium and vanadium, producing continious series of solid solutions with niobium are studied. Diffusion coefficients, time of isothermal crystallization of soldered welds, as well as the duration of homogenized thermal treatment of soldered welds necessary to provide the given temperature of weld unsoldering

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

Directory of Open Access Journals (Sweden)

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.

Treatment of pediatric molluscum contagiosum with 10% potassium hydroxide solution.

Science.gov (United States)

Can, Burce; Topaloğlu, Filiz; Kavala, Mukaddes; Turkoglu, Zafer; Zindancı, Ilkin; Sudogan, Sibel

2014-06-01

Molluscum contagiosum (MC) is a common cutaneous viral infection of the skin that is frequently seen in children. Although lesions can resolve spontaneously, treatment is mandatory because of the psychological effect of widespread lesions in children. Potassium hydroxide (KOH) is a strong alkali that has been used by dermatologists for a long time in identifying the fungal infections from skin scrapings. We evaluated 40 children with MC for the safety and efficacy of treatment with topical 10% KOH aqueous solution. Parents were instructed to apply a 10% KOH aqueous solution, twice daily, with a cotton stick to all lesions. Treatment was continued till the lesions showed signs of inflammation or superficial ulceration. Assessments of response and side effects were performed at the end of week 2, week 4, week 8 and week 12. We found complete clearance of lesions in 37 (92.5%) patients receiving topical 10%KOH solution after a mean period of four weeks. Three children dropped out of the study; two children reported severe stinging of the lesions and discontinued the treatment; the other patient developed hypopigmentation during the treatment. Local side effects were observed in 12 children (32.4%). Even though 10% KOH solution is associated with some local side effects, it is a safe, effective, inexpensive and noninvasive alternative treatment of MC in children.

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.

Decontamination of waste radioactive polluted solutions in radiation treatment

International Nuclear Information System (INIS)

Simova, G.; Boyadzhiev, A.; Mikhajlov, M.G.; Shopov, N.

1979-01-01

The decontamination capacity of solutions of the trivial cleaning Bulgarian preparations ''Mipro'', ''Sana'', ''Synthek'' and ''Univer'' for different surfaces (steel, glass, PVC and linoleum) contaminated with cesium-134, strontium-85 or cerium-144 chlorides, was studied. Concentrations from 5 to 15 g/l of the solutions used in this study displayed a degree of cleaning over 90%. Higher concentration of the solution does not improve its cleaning capacity. For evaluation of foam formation by the solutions, the so called ''foam column stability coefficient'' has been adopted. This coefficient represents the ratio between the height of the foam column and the time of its half life, referred to the time for the foam column formation when blown through with a constant air current. On the basis of this index, solutions of the preparation ''Mipro'' proved to be the best ones for decontamination - in the whole investigated concentration span, the foam column stability coefficient for the solutions of this preparation is with two orders lower than the respective coefficient of the other preparations. It was experimentally established that radiation treatment of radio-contaminated solutions reduces the foam column stability coefficient. Radiation treatment should be carried out in a gamma field, realizing at least one megarad within an acceptable for the liquid wastes time period. (A.B.)

INFLUENCE VARIOUS REAGENTS ON THE MOLECULAR DIFFUSION INDEX OF SUCROSE FROM BEET

Directory of Open Access Journals (Sweden)

N. G. Kulneva

2015-01-01

Full Text Available Food products from vegetable raw materials play a special role in the food industry. Sugar is one of the strategically important products. The significance of its is great due to its wide use in confectionery, bakery, liquor, canning, biochemical, pharmaceutical and other branches of human activity. Effective development of the domestic sugar industry depends on the terms of competition with European partners. Production of granulated sugar includes a significant amount of energy-intensive and technologically complex operations, one of which is the extraction of sucrose from beet chips by means of hot countercurrent extraction. The most important criterion for the extraction process efficiency evaluation is the coefficient of molecular diffusion. The efficiency of using of beet chips thermo chemical processing before extraction depending on the quality of processed beet was investigated. It was found out that when using a low quality beet the diffusion coefficient decreases compared to healthy beet. The use of solutio ns of some salts for beet chips heat treatment has an overall positive effect on the diffusion coefficient. A method for recovering sucrose from beet with the use of compounds of Al2(SO4, Ca(SO4, and (NH42SO4 as the extractants was proposed. It was found out that beet samples treatment with solutions of proposed salts provides a sucrose smooth transition from the pores of sugar beet tissue into the extractant due to intense convective washout. It is caused by the high degree of tissue cells plasmolysis achieved in its processing with solutions of proposed reagents. The results obtained indicate a significant increase of the sucrose diffusion coefficient in the ammonium sulfate solution used as the extractant.

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

Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

KAUST Repository

Alzahrani, Hasnaa H.

2016-07-26

A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.

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

Diffusive counter dispersion of mass in bubbly media.

Science.gov (United States)

Goldobin, Denis S; Brilliantov, Nikolai V

2011-11-01

We consider a liquid bearing gas bubbles in a porous medium. When gas bubbles are immovably trapped in a porous matrix by surface-tension forces, the dominant mechanism of transfer of gas mass becomes the diffusion of gas molecules through the liquid. Essentially, the gas solution is in local thermodynamic equilibrium with vapor phase all over the system, i.e., the solute concentration equals the solubility. When temperature and/or pressure gradients are applied, diffusion fluxes appear and these fluxes are faithfully determined by the temperature and pressure fields, not by the local solute concentration, which is enslaved by the former. We derive the equations governing such systems, accounting for thermodiffusion and gravitational segregation effects, which are shown not to be neglected for geological systems-marine sediments, terrestrial aquifers, etc. The results are applied for the treatment of non-high-pressure systems and real geological systems bearing methane or carbon dioxide, where we find a potential possibility of the formation of gaseous horizons deep below a porous medium surface. The reported effects are of particular importance for natural methane hydrate deposits and the problem of burial of industrial production of carbon dioxide in deep aquifers.

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)

Formation of crystalline InGaO_3(ZnO)_n nanowires via the solid-phase diffusion process using a solution-based precursor

International Nuclear Information System (INIS)

Guo, Yujie; Seo, Jin Won; Bilzen, Bart Van; Locquet, Jean Pierre

2015-01-01

One-dimensional single crystalline InGaO_3(ZnO)_n (IGZO) nanostructures have great potential for various electrical and optical applications. This paper demonstrates for the first time, to our knowledge, a non-vacuum route for the synthesis of IGZO nanowires by annealing ZnO nanowires covered with solution-based IGZO precursor. This method results in nanowires with highly periodic IGZO superlattice structure. The phase transition of IGZO precursor during thermal treatment was systematically studied. Transmission electron microscopy studies reveal that the formation of the IGZO structure is driven by anisotropic inter-diffusion of In, Ga, and Zn atoms, and also by the crystallization of the IGZO precursor. Optical measurements using cathodoluminescence and UV-vis spectroscopy confirm that the nanowires consist of the IGZO compound with wide optical band gap and suppressed luminescence. (paper)

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

Diffuse Urticarial Reaction Associated with Titanium Dioxide Following Laser Tattoo Removal Treatments.

Science.gov (United States)

Willardson, Hal Bret; Kobayashi, Todd T; Arnold, Jason G; Hivnor, Chad M; Bowen, Casey D

2017-03-01

Local and generalized allergic reactions following laser tattoo removal have been documented, but are rare. To our knowledge, this is the fourth documented case of widespread urticarial eruptions following laser tattoo removal treatment. Unlike previously documented cases, this patient's reaction was found to be associated with titanium dioxide within the tattoo and her symptoms were recalcitrant to medical therapy. A 46-year-old female experienced diffuse urticarial plaques, erythema, and pruritis following multiple laser tattoo removal treatments with an Nd:YAG laser. The systemic allergic reaction was recalcitrant to increasing doses of antihistamines and corticosteroids. The tattoo was finally surgically excised. The excised tissue was analyzed by scanning electron microscopy and energy-dispersive X-ray analysis and contained high levels of titanium dioxide. Two weeks following the excision, and without the use of medical therapy, the patient had complete resolution of her generalized urticaria. Ours is the first documented case of a diffuse urticarial reaction following laser tattoo removal treatments that shows a strong association to titanium dioxide within the tattoo pigment. Herein, we describe a novel surgical approach to treat recalcitrant generalized allergic reaction to tattoo pigment.

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)

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)

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

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)

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)

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

Diffusion-sensitive optical coherence tomography for real-time monitoring of mucus thinning treatments

Science.gov (United States)

Blackmon, Richard L.; Kreda, Silvia M.; Sears, Patrick R.; Ostrowski, Lawrence E.; Hill, David B.; Chapman, Brian S.; Tracy, Joseph B.; Oldenburg, Amy L.

2016-03-01

Mucus hydration (wt%) has become an increasingly useful metric in real-time assessment of respiratory health in diseases like cystic fibrosis and COPD, with higher wt% indicative of diseased states. However, available in vivo rheological techniques are lacking. Gold nanorods (GNRs) are attractive biological probes whose diffusion through tissue is sensitive to the correlation length of comprising biopolymers. Through employment of dynamic light scattering theory on OCT signals from GNRs, we find that weakly-constrained GNR diffusion predictably decreases with increasing wt% (more disease-like) mucus. Previously, we determined this method is robust against mucus transport on human bronchial epithelial (hBE) air-liquid interface cultures (R2=0.976). Here we introduce diffusion-sensitive OCT (DS-OCT), where we collect M-mode image ensembles, from which we derive depth- and temporally-resolved GNR diffusion rates. DS-OCT allows for real-time monitoring of changing GNR diffusion as a result of topically applied mucus-thinning agents, enabling monitoring of the dynamics of mucus hydration never before seen. Cultured human airway epithelial cells (Calu-3 cell) with a layer of endogenous mucus were doped with topically deposited GNRs (80x22nm), and subsequently treated with hypertonic saline (HS) or isotonic saline (IS). DS-OCT provided imaging of the mucus thinning response up to a depth of 600μm with 4.65μm resolution, over a total of 8 minutes in increments of >=3 seconds. For both IS and HS conditions, DS-OCT captured changes in the pattern of mucus hydration over time. DS-OCT opens a new window into understanding mechanisms of mucus thinning during treatment, enabling real-time efficacy feedback needed to optimize and tailor treatments for individual patients.

Plasma surface treatment of Cu by nanosecond-pulse diffuse discharges in atmospheric air

Science.gov (United States)

Cheng, ZHANG; Jintao, QIU; Fei, KONG; Xingmin, HOU; Zhi, FANG; Yu, YIN; Tao, SHAO

2018-01-01

Nanosecond-pulse diffuse discharges could provide high-density plasma and high-energy electrons at atmospheric pressure. In this paper, the surface treatment of Cu by nanosecond-pulse diffuse discharges is conducted in atmospheric air. Factors influencing the water contact angle (WCA), chemical composition and microhardness, such as the gap spacing and treatment time, are investigated. The results show that after the plasma surface treatment, the WCA considerably decreases from 87° to 42.3°, and the surface energy increases from 20.46 mJ m-2 to 66.28 mJ m-2. Results of energy dispersive x-ray analysis show that the concentration of carbon decreases, but the concentrations of oxygen and nitrogen increase significantly. Moreover, the microhardness increases by approximately 30% after the plasma treatment. The aforementioned changes on the Cu surface indicate the plasma surface treatment enhances the hydrophilicity and microhardness, and it cleans the carbon and achieves oxidization on the Cu surface. Furthermore, by increasing the gap spacing and treatment time, better treatment effects can be obtained. The microhardness in the case of a 2.5 cm gap is higher than that in the case of a 3 cm gap. More oxygen and nitrogen species appear on the Cu surface for the 2.5 cm gap treatment than for the 3 cm gap treatment. The WCA significantly decreases with the treatment time when it is no longer than 90 s, and then it reaches saturation. In addition, more oxygen-containing and nitrogen-containing groups appear after extended plasma treatment time. They contribute to the improvement of the hydrophilicity and oxidation on the Cu surface.

Bilateral diffuse lamellar keratitis triggered by permanent eyeliner tattoo treatment: A case report.

Science.gov (United States)

Lu, Cheng-Wei; Liu, Xiu-Fen; Zhou, Dan-Dan; Kong, Yu-Jiao; Qi, Xiao-Feng; Liu, Tao-Tao; Qu, Ting; Pan, Xiao-Tao; Liu, Cong; Hao, Ji-Long

2017-07-01

Diffuse lamellar keratitis (DLK) is a sterile inflammation of the cornea, which may occur after laser-assisted in situ keratomileusis (LASIK) surgery. Little is known about the association of DLK with permanent eyeliner tattoo. The present case report describes the case of a 37-year-old Chinese woman who developed severe foreign body sensation in both eyes 1 week after receiving bilateral permanent eyeliner tattoo treatment. The patient had received bilateral LASIK surgery 10 years previously. Slit-lamp biomicroscopy revealed diffused granular infiltrates precipitated around the edge of the corneal flaps in both eyes. After topical treatment, DLK persisted. Therefore, the patient underwent surgery to remove the corneal epithelium around the DLK lesion. There was no recurrence of the disease during the 3-month observation period. To our knowledge, this is the first case report describing a case of late-onset of DLK that was triggered by permanent eyeliner tattoo. Doctors should be aware of the diagnosis and treatment of this complication associated with the application of permanent eyeliner tattoo as the popularity of this cosmetic procedure increases.

Efficacy of bromfenac sodium ophthalmic solution for treatment of dry eye disease.

Science.gov (United States)

Fujishima, Hiroshi; Fuseya, Miki; Ogata, Masarou; Murat, Dogru

2015-01-01

To evaluate the efficacy of bromfenac sodium ophthalmic solution (BF) in patients with dry eye disease (DED) inadequately controlled by monotherapy with artificial tears (ATs). An investigator-oriented trial with a single-arm, nonrandomized, open-label design. Twenty-six patients, who showed no symptomatic improvement of DED after 1 month of AT treatment, were enrolled. Bromfenac sodium ophthalmic solution was administered adjunctively with AT for 1 month. The BF treatment was then discontinued, and AT treatment alone was continued for 3 months. The signs and symptoms were evaluated at the beginning of BF treatment (Pre), at the end of the combined BF and AT treatment (BF1M), and at 1 and 3 months after discontinuation of BF treatment (Po1M and Po3M, respectively). The dryness scores at BF1M were significantly improved compared with Pre (P ophthalmic solution has improved the dryness of the eye and signs of DED through its anti-inflammatory effects. Nonsteroidal anti-inflammatory drugs were suitable as anti-inflammatory ophthalmic solutions for patients with DED.

Assessment of early treatment response to neoadjuvant chemotherapy in breast cancer using non-mono-exponential diffusion models: a feasibility study comparing the baseline and mid-treatment MRI examinations

Energy Technology Data Exchange (ETDEWEB)

Bedair, Reem; Manavaki, Roido; Gill, Andrew B.; Abeyakoon, Oshaani; Gilbert, Fiona J. [University of Cambridge, Department of Radiology, School of Clinical Medicine, Cambridge (United Kingdom); Priest, Andrew N.; Patterson, Andrew J. [Cambridge University Hospitals NHS Foundation Trust, Department of Radiology, Addenbrookes Hospital, Cambridge (United Kingdom); McLean, Mary A. [Cambridge University Hospitals NHS Foundation Trust, Department of Radiology, Addenbrookes Hospital, Cambridge (United Kingdom); University of Cambridge, Li Ka Shing Centre, Cancer Research UK Cambridge Institute, Cambridge (United Kingdom); Graves, Martin J. [University of Cambridge, Department of Radiology, School of Clinical Medicine, Cambridge (United Kingdom); Cambridge University Hospitals NHS Foundation Trust, Department of Radiology, Addenbrookes Hospital, Cambridge (United Kingdom); Griffiths, John R. [University of Cambridge, Li Ka Shing Centre, Cancer Research UK Cambridge Institute, Cambridge (United Kingdom)

2017-07-15

To assess the feasibility of the mono-exponential, bi-exponential and stretched-exponential models in evaluating response of breast tumours to neoadjuvant chemotherapy (NACT) at 3 T. Thirty-six female patients (median age 53, range 32-75 years) with invasive breast cancer undergoing NACT were enrolled for diffusion-weighted MRI (DW-MRI) prior to the start of treatment. For assessment of early response, changes in parameters were evaluated on mid-treatment MRI in 22 patients. DW-MRI was performed using eight b values (0, 30, 60, 90, 120, 300, 600, 900 s/mm{sup 2}). Apparent diffusion coefficient (ADC), tissue diffusion coefficient (D{sub t}), vascular fraction (Florin), distributed diffusion coefficient (DDC) and alpha (α) parameters were derived. Then t tests compared the baseline and changes in parameters between response groups. Repeatability was assessed at inter- and intraobserver levels. All patients underwent baseline MRI whereas 22 lesions were available at mid-treatment. At pretreatment, mean diffusion coefficients demonstrated significant differences between groups (p < 0.05). At mid-treatment, percentage increase in ADC and DDC showed significant differences between responders (49 % and 43 %) and non-responders (21 % and 32 %) (p = 0.03, p = 0.04). Overall, stretched-exponential parameters showed excellent repeatability. DW-MRI is sensitive to baseline and early treatment changes in breast cancer using non-mono-exponential models, and the stretched-exponential model can potentially monitor such changes. (orig.)

Assessment of early treatment response to neoadjuvant chemotherapy in breast cancer using non-mono-exponential diffusion models: a feasibility study comparing the baseline and mid-treatment MRI examinations

International Nuclear Information System (INIS)

Bedair, Reem; Manavaki, Roido; Gill, Andrew B.; Abeyakoon, Oshaani; Gilbert, Fiona J.; Priest, Andrew N.; Patterson, Andrew J.; McLean, Mary A.; Graves, Martin J.; Griffiths, John R.

2017-01-01

To assess the feasibility of the mono-exponential, bi-exponential and stretched-exponential models in evaluating response of breast tumours to neoadjuvant chemotherapy (NACT) at 3 T. Thirty-six female patients (median age 53, range 32-75 years) with invasive breast cancer undergoing NACT were enrolled for diffusion-weighted MRI (DW-MRI) prior to the start of treatment. For assessment of early response, changes in parameters were evaluated on mid-treatment MRI in 22 patients. DW-MRI was performed using eight b values (0, 30, 60, 90, 120, 300, 600, 900 s/mm"2). Apparent diffusion coefficient (ADC), tissue diffusion coefficient (D_t), vascular fraction (Florin), distributed diffusion coefficient (DDC) and alpha (α) parameters were derived. Then t tests compared the baseline and changes in parameters between response groups. Repeatability was assessed at inter- and intraobserver levels. All patients underwent baseline MRI whereas 22 lesions were available at mid-treatment. At pretreatment, mean diffusion coefficients demonstrated significant differences between groups (p < 0.05). At mid-treatment, percentage increase in ADC and DDC showed significant differences between responders (49 % and 43 %) and non-responders (21 % and 32 %) (p = 0.03, p = 0.04). Overall, stretched-exponential parameters showed excellent repeatability. DW-MRI is sensitive to baseline and early treatment changes in breast cancer using non-mono-exponential models, and the stretched-exponential model can potentially monitor such changes. (orig.)

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

X-Ray Characterization of Non-Equilibrium Solid Solutions

International Nuclear Information System (INIS)

Brown, A.; Rosdahl, Oe.

1975-01-01

The Rudman approach to composition line broadening in X-ray diffraction patterns, originally designed for the study of diffusion in alloys, is seen to provide a basis for characterizing inhomogeneous solid solutions. Limitations, imposed on this treatment when the cell dimensions of the primary components differ by less than 0.1 A, are attributable to experimental effects such as instrument broadening. These limitations can be overcome by a rigorous numerical treatment of the measured data. Thus, separate elimination of the Kα 2 radiation component followed by iterative deconvolution are advocated for the recovery of the intrinsic broadening. This course of action is made possible chiefly through the availability of large, fast memory computers and primary data recorded in the form of a step scan on punched paper tape. The characteristics of inhomogeneous solid solutions made available by the above treatment are the identity of closely similar, solid solution phases, the frequency distribution curve for a chosen component, and the degree of homogeneity of the X-ray sample

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)

Increased risk of gastric adenocarcinoma after treatment of primary gastric diffuse large B-cell lymphoma

International Nuclear Information System (INIS)

Inaba, Koji; Morota, Madoka; Mayahara, Hiroshi; Ito, Yoshinori; Sumi, Minako; Uno, Takashi; Itami, Jun; Kushima, Ryoji; Murakami, Naoya; Kuroda, Yuuki; Harada, Ken; Kitaguchi, Mayuka; Yoshio, Kotaro; Sekii, Shuhei; Takahashi, Kana

2013-01-01

There have been sporadic reports about synchronous as well as metachronous gastric adenocarcinoma and primary gastric lymphoma. Many reports have dealt with metachronous gastric adenocarcinoma in mucosa-associated lymphoid tissue lymphoma of stomach. But to our knowledge, there have been no reports that document the increased incidence of metachronous gastric adenocarcinoma in patients with gastric diffuse large B-cell lymphoma. This retrospective study was conducted to estimate the incidence of metachronous gastric adenocarcinoma after primary gastric lymphoma treatment, especially in diffuse large B-cell lymphoma. The retrospective cohort study of 139 primary gastric lymphoma patients treated with radiotherapy at our hospital. Mean observation period was 61.5 months (range: 3.7-124.6 months). Patients profile, characteristics of primary gastric lymphoma and metachronous gastric adenocarcinoma were retrieved from medical records. The risk of metachronous gastric adenocarcinoma was compared with the risk of gastric adenocarcinoma in Japanese population. There were 10 (7.2%) metachronous gastric adenocarcinoma patients after treatment of primary gastric lymphomas. It was quite high risk compared with the risk of gastric carcinoma in Japanese population of 54.7/100,000. Seven patients of 10 were diffuse large B-cell lymphoma and other 3 patients were mixed type of diffuse large B-cell lymphoma and mucosa associated lymphoid tissue lymphoma. Four patients of 10 metachronous gastric adenocarcinomas were signet-ring cell carcinoma and two patients died of gastric adenocarcinoma. Metachronous gastric adenocarcinoma may have a more malignant potential than sporadic gastric adenocarcinoma. Old age, Helicobacter pylori infection and gastric mucosal change of chronic gastritis and intestinal metaplasia were possible risk factors for metachronous gastric adenocarcinoma. There was an increased risk of gastric adenocarcinoma after treatment of primary gastric lymphoma

Treatment of plutonium-bearing solutions: A brief survey of the DOE complex

International Nuclear Information System (INIS)

Conner, C.; Chamberlain, D.B.; Chen, L.; Vandegrift, G.F.

1995-03-01

With the abrupt shutdown of some DOE facilities, a significant volume of in-process material was left in place and still requires treatment for interim storage. Because the systems containing these process streams have deteriorated since shutdown, a portable system for treating the solutions may be useful. A brief survey was made of the DOE complex on the need for a portable treatment system to treat plutonium-bearing solutions. A survey was completed to determine (1) the compositions and volumes of solutions and heels present, (2) the methods that have been used to treat these solutions and heels in the past, and (3) the potential problems that exist in removing and treating these solutions. Based on the surveys and on the Defense Nuclear Facilities Safety Board Recommendation 94-1, design criteria for a portable treatment system were generated

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.

Absence of saturation of void growth in rate theory with anisotropic diffusion

CERN Document Server

Hudson, T S; Sutton, A P

2002-01-01

We present a first attempt at solution the problem of the growth of a single void in the presence of anisotropically diffusing radiation induced self-interstitial atom (SIA) clusters. In order to treat a distribution of voids we perform ensemble averaging over the positions of centres of voids using a mean-field approximation. In this way we are able to model physical situations in between the Standard Rate Theory (SRT) treatment of swelling (isotropic diffusion), and the purely 1-dimensional diffusion of clusters in the Production Bias Model. The background absorption by dislocations is however treated isotropically, with a bias for interstitial cluster absorption assumed similar to that of individual SIAs. We find that for moderate anisotropy, unsaturated void growth is characteristic of this anisotropic diffusion of clusters. In addition we obtain a higher initial void swelling rate than predicted by SRT whenever the diffusion is anisotropic.

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)

Diffusive Silicon Nanopore Membranes for Hemodialysis Applications.

Directory of Open Access Journals (Sweden)

Steven Kim

Full Text Available Hemodialysis using hollow-fiber membranes provides life-sustaining treatment for nearly 2 million patients worldwide with end stage renal disease (ESRD. However, patients on hemodialysis have worse long-term outcomes compared to kidney transplant or other chronic illnesses. Additionally, the underlying membrane technology of polymer hollow-fiber membranes has not fundamentally changed in over four decades. Therefore, we have proposed a fundamentally different approach using microelectromechanical systems (MEMS fabrication techniques to create thin-flat sheets of silicon-based membranes for implantable or portable hemodialysis applications. The silicon nanopore membranes (SNM have biomimetic slit-pore geometry and uniform pores size distribution that allow for exceptional permeability and selectivity. A quantitative diffusion model identified structural limits to diffusive solute transport and motivated a new microfabrication technique to create SNM with enhanced diffusive transport. We performed in vitro testing and extracorporeal testing in pigs on prototype membranes with an effective surface area of 2.52 cm2 and 2.02 cm2, respectively. The diffusive clearance was a two-fold improvement in with the new microfabrication technique and was consistent with our mathematical model. These results establish the feasibility of using SNM for hemodialysis applications with additional scale-up.

Diffusive Silicon Nanopore Membranes for Hemodialysis Applications

Science.gov (United States)

Kim, Steven; Feinberg, Benjamin; Kant, Rishi; Chui, Benjamin; Goldman, Ken; Park, Jaehyun; Moses, Willieford; Blaha, Charles; Iqbal, Zohora; Chow, Clarence; Wright, Nathan; Fissell, William H.; Zydney, Andrew; Roy, Shuvo

2016-01-01

Hemodialysis using hollow-fiber membranes provides life-sustaining treatment for nearly 2 million patients worldwide with end stage renal disease (ESRD). However, patients on hemodialysis have worse long-term outcomes compared to kidney transplant or other chronic illnesses. Additionally, the underlying membrane technology of polymer hollow-fiber membranes has not fundamentally changed in over four decades. Therefore, we have proposed a fundamentally different approach using microelectromechanical systems (MEMS) fabrication techniques to create thin-flat sheets of silicon-based membranes for implantable or portable hemodialysis applications. The silicon nanopore membranes (SNM) have biomimetic slit-pore geometry and uniform pores size distribution that allow for exceptional permeability and selectivity. A quantitative diffusion model identified structural limits to diffusive solute transport and motivated a new microfabrication technique to create SNM with enhanced diffusive transport. We performed in vitro testing and extracorporeal testing in pigs on prototype membranes with an effective surface area of 2.52 cm2 and 2.02 cm2, respectively. The diffusive clearance was a two-fold improvement in with the new microfabrication technique and was consistent with our mathematical model. These results establish the feasibility of using SNM for hemodialysis applications with additional scale-up. PMID:27438878

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.

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...

Improvement of stress-rupture life of GTD-111 by second solution heat treatment

International Nuclear Information System (INIS)

Yang, Caixiong; Xu, Yulai; Zhang, Zixing; Nie, Heng; Xiao, Xueshan; Jia, Guoqing; Shen, Zhi

2013-01-01

Highlights: ► The second solution heat treatment promoted the solution of γ–γ′ eutectic into γ matrix. ► The volume fraction of γ′ increases significantly after adding the second solution heat treatment. ► The improved stress-rupture life is primarily due to the increased volume fraction of γ′ phase. -- Abstract: An added second solution heat treatment was conducted to investigate its effects on the microstructures and stress-rupture properties of GTD-111. The microstructures were analyzed by scanning electron microscope after each step of heat treatments. The stress-rupture life of GTD-111 dramatically increases from about 180 to 288 h at 871 °C/310 MPa after adding a second solution heat treatment. The added second solution heat treatment promoted the solution of γ–γ′ eutectic into γ matrix, and facilitated the nucleation and precipitate of the secondary γ′ particles. The distribution of γ′ phase becomes much denser, the width of γ matrix channel is also reduced, and the volume fraction of γ′ phase significantly increases from about 29.3% to 44.2%. The improved stress-rupture life is primarily due to the increased volume fraction of γ′ phase. The carbides mainly consist of MC and a small amount of M 23 C 6 , which may prevent the dislocation moving and/or grain boundary sliding, and further improve the stress-rupture properties of GTD-111.

Serial diffusion-weighted MRI correlates with clinical course and treatment response in children with intracranial pus collections

International Nuclear Information System (INIS)

Fanning, Noel F.; Laffan, Eoghan E.; Shroff, Manohar M.

2006-01-01

Accurate assessment of treatment response in children with intracranial pus collections is vital to guide appropriate therapy and reduce morbidity and mortality. To correlate serial MR-measurable changes in diffusion-weighted imaging (DWI) with clinical response to treatment. We retrospectively reviewed clinical notes, conventional MR sequences and DWI in eight children with intracranial pus collections. Trace DWI signal intensity and apparent diffusion coefficient (ADC) values were compared at three time points: at initial diagnosis (eight children, 13 collections), at follow-up during continued clinical infection (three children, sp collections), and at follow-up when clinical infection had resolved (seven children, 12 collections). At initial diagnosis all patients were septic and collections showed restricted diffusion (mean ADC 0.61±0.15 x 10 -3 mm 2 /s). Patients with persistent clinical sepsis at follow-up DWI had collections with persistent low ADC values (0.66±0.21 x 10 -3 mm 2 /s), significantly (P -3 mm 2 /s, P<0.01) compared both to patients with signs of continued sepsis and to normal gray matter values. Persistent restricted diffusion in pus collections correlates with continued sepsis. Treatment response is associated with clinical resolution of sepsis and ADC value elevation significantly above normal gray matter values. (orig.)

Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

Directory of Open Access Journals (Sweden)

Przemysław Korohoda

2013-01-01

Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.

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.

Diquafosol ophthalmic solution for dry eye treatment.

Science.gov (United States)

Nakamura, Masatsugu; Imanaka, Takahiro; Sakamoto, Asuka

2012-07-01

There has been rapid progress in our understanding of dry eye pathogenesis, as well as the development of improved diagnostic clinical tests. Various types of dry eye treatment drugs have been developed. This review summarizes the basic and clinical research carried out in the development of diquafosol for ophthalmic use. Diquafosol is a dinucleotide, purinoreceptor P2Y(2) receptor agonist. Basic pharmacological studies have shown that it acts on P2Y(2) receptors at the ocular surface, to promote tear and mucin secretion via elevated intracellular Ca(2+) concentrations. Diquafosol also improves tear and mucin secretion in experimental dry eye models. Based on the results of laboratory experiments, the authors conducted a series of clinical studies in patients with dry eye disease. Diquafosol was effective in the treatment of dry eye disease at an optimal dose of 3% six times a day. In comparison to commercially available 0.1% sodium hyaluronate ophthalmic solution, 3% diquafosol ophthalmic solution showed non-inferiority in improving corneal fluorescein staining scores and superiority in improving keratoconjunctival Rose Bengal staining scores. Diquafosol ophthalmic solution has a novel mechanism of action that is characterized by its stimulatory effects on tear and mucin secretion. This drug has the potential to be effective in patients with tear film instability and short break-up time type of dry eye, which are essential factors in dry eye pathogenesis.

One-velocity neutron diffusion calculations based on a two-group reactor model

Energy Technology Data Exchange (ETDEWEB)

Bingulac, S; Radanovic, L; Lazarevic, B; Matausek, M; Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

Many processes in reactor physics are described by the energy dependent neutron diffusion equations which for many practical purposes can often be reduced to one-dimensional two-group equations. Though such two-group models are satisfactory from the standpoint of accuracy, they require rather extensive computations which are usually iterative and involve the use of digital computers. In many applications, however, and particularly in dynamic analyses, where the studies are performed on analogue computers, it is preferable to avoid iterative calculations. The usual practice in such situations is to resort to one group models, which allow the solution to be expressed analytically. However, the loss in accuracy is rather great particularly when several media of different properties are involved. This paper describes a procedure by which the solution of the two-group neutron diffusion. equations can be expressed analytically in the form which, from the computational standpoint, is as simple as the one-group model, but retains the accuracy of the two-group treatment. In describing the procedure, the case of a multi-region nuclear reactor of cylindrical geometry is treated, but the method applied and the results obtained are of more general application. Another approach in approximate solution of diffusion equations, suggested by Galanin is applicable only in special ideal cases.

Diffusion-weighted magnetic resonance imaging: biomarker for treatment response in oncology

Directory of Open Access Journals (Sweden)

Maria Luiza Testa

2013-06-01

Full Text Available The authors report a case where a quantitative assessment of the apparent diffusion coefficient (ADC of liver metastasis in a patient undergoing chemotherapy has shown to be an effective early marker for predicting therapeutic response, anticipating changes in tumor size. A lesion with lower initial ADC value and early increase in such value in the course of the treatment tends to present a better therapeutic response.

Diffusion simulation of ferric ions in dosemeter Fricke-gel with variable diffusion coefficient

International Nuclear Information System (INIS)

Milani, Caio Jacob; Bevilacqua, Joyce da Silva; Rodrigues Junior, Orlando

2014-01-01

Dosimetry using dosimeters Fricke-xylenol-Gel (FXG) allows confirmation and better understanding of radiotherapy treatments. The technique involves the evaluation of volumes irradiated by magnetic resonance imaging (MRI) or CT-optical. In both cases, the time spent between the irradiation and measurement is an important factor that directly influences the results. The quality of the images can be compromised by the mobility of ferric ions (Fe 3+), formed during the interaction of radiation with matter, increasing the uncertainty in determining the isodose. In this work, we simulated the dynamic involving ferric ions formed in one irradiated region irradiated in a two-dimensional domain with a variable diffusion coefficient. This phenomenon is modeled by a differential equation and solved numerically by an efficient algorithm that generalizes the Crank-Nicolson method. The stability and consistency of the method guarantee the convergence of the numerical solution for a predefined tolerance based in the choice of discretization steps of time and space. Different continuous functions were chosen to represent the diffusion coefficient and graphical views of the phenomenon are presented for a better understanding of the process

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)

Rescue pre-operative treatment with Lugol's solution in uncontrolled Graves' disease.

Science.gov (United States)

Calissendorff, Jan; Falhammar, Henrik

2017-05-01

Graves' disease is a common cause of hyperthyroidism. Three therapies have been used for decades: pharmacologic therapy, surgery and radioiodine. In case of adverse events, especially agranulocytosis or hepatotoxicity, pre-treatment with Lugol's solution containing iodine/potassium iodide to induce euthyroidism before surgery could be advocated, but this has rarely been reported. All patients hospitalised due to uncontrolled hyperthyroidism at the Karolinska University Hospital 2005-2015 and treated with Lugol's solution were included. All electronic files were carefully reviewed manually, with focus on the cause of treatment and admission, demographic data, and effects of iodine on thyroid hormone levels and pulse frequency. Twenty-seven patients were included. Lugol's solution had been chosen due to agranulocytosis in 9 (33%), hepatotoxicity in 2 (7%), other side effects in 11 (41%) and poor adherence to medication in 5 (19%). Levels of free T4, free T3 and heart rate decreased significantly after 5-9 days of iodine therapy (free T4 53-20 pmol/L, P  = 0.0002; free T3 20-6.5 pmol/L, P  = 0.04; heart rate 87-76 beats/min P  = 0.0007), whereas TSH remained unchanged. Side effects were noted in 4 (15%) (rash n  = 2, rash and vomiting n  = 1, swelling of fingers n  = 1). Thyroidectomy was performed in 26 patients (96%) and one was treated with radioiodine; all treatments were without serious complications. Treatment of uncontrolled hyperthyroidism with Lugol's solution before definitive treatment is safe and it decreases thyroid hormone levels and heart rate. Side effects were limited. Lugol's solution could be recommended pre-operatively in Graves' disease with failed medical treatment, especially if side effects to anti-thyroid drugs have occurred. © 2017 The authors.

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.

Characteristics and applications of diffuse discharge of water electrode in air

Science.gov (United States)

Wenzheng, LIU; Tahan, WANG; Xiaozhong, CHEN; Chuanlong, MA

2018-01-01

Plasma water treatment technology, which aims to produce strong oxidizing reactive particles that act on the gas-liquid interface by way of discharging, is used to treat the organic pollutants that do not degrade easily in water. This paper presents a diffuse-discharge plasma water treatment method, which is realized by constructing a conical air gap through an uneven medium layer. The proposed method uses water as one electrode, and a dielectric barrier discharge electrode is constructed by using an uneven dielectric. The electric field distribution in the discharge space will be uneven, wherein the long gap electric field will have a smaller intensity, while the short one will have a larger intensity. A diffuse glow discharge is formed in the cavity. With this type of plasma water treatment equipment, a methyl orange solution with a concentration of 10 mg l-1 was treated, and the removal rate was found to reach 88.96%.

SOLUTION TREATMENT EFFECT ON MICROSTRUCTURE AND MECHANICAL PROPERTIES OF AUTOMOTIVE CAST ALLOY

Directory of Open Access Journals (Sweden)

Eva Tillová

2012-02-01

Full Text Available The contribution describes influence of the heat treatment (solution treatment at temperature 545°C and 565°C with different holding time 2, 4, 8, 16 and 32 hours; than water quenching at 40°C and natural aging at room temperature during 24 hours on mechanical properties (tensile strength and Brinell hardness and microstructure of the secondary AlSi12Cu1Fe automotive cast alloy. Mechanical properties were measured in line with EN ISO. A combination of different analytical techniques (light microscopy, scanning electron microscopy (SEM were therefore been used for study of microstructure. Solution treatment led to changes in microstructure includes the spheroidization and coarsening of eutectic silicon. The dissolution of precipitates and the precipitation of finer hardening phase further increase the hardness and tensile strength of the alloy. Optimal solution treatment (545°C/4 hours most improves mechanical properties and there mechanical properties are comparable with mechanical properties of primary AlSi12Cu1Fe alloy. Solution treatment at 565 °C caused testing samples distortion, local melting process and is not applicable for this secondary alloy with 12.5 % Si.

Conversion of the reducing substances and the indices of sugar solutions

Directory of Open Access Journals (Sweden)

V. A. Golybin

2017-01-01

Full Text Available Investigated the extent of adsorption removal of calcium carbonate pigments - products of conversion of the reducing substances in different conditions of the preceding limestone processing flow. Also carried out experiments on the influence of the conditions of conversion of the reducing substances in the process of lime treatment on the filtration characteristics of the solutions after the first carbonation. As the criterion was accepted the value of the filtration coefficient. Found that by subjecting the conversion of reducing substances in the process managed lime processing, it is necessary in the course of the subsequent carbonization to ensure maximum adsorption of the formed secondary products – it is possible to achieve a satisfactory filtration of the investigated solutions. It is shown that the largest absolute removal of the dyes obtained after high temperature lime treatment, however, the composition of the products of disintegration to a greater extent accumulate high molecular weight compounds which deteriorate the filtration performance of solutions. In the solutions after the combination of the lime treatment in the process of carbonization is achieved the maximum effect of adsorption with the minimum remaining shares of conversion products, including high-molecular substances, which favorably affect the parameters of the filtering. The combination possibilities of the model of purification of diffusion juice with warm-hot lime treatment is limited to receive the filtered juice in the processing of raw materials with a purity of beet juice 82 % or less, you need to enter a 3.5% Cao, which is unacceptable. To ensure sustainable results of the adsorption of conversion products reducing substances and satisfactory filtering carbonated solutions are to intensify the processes of combined lime processing diffusion juice at the optimum distribution of the reagent.

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...

Measuring Charge Carrier Diffusion in Coupled Colloidal Quantum Dot Solids

KAUST Repository

Zhitomirsky, David

2013-06-25

Colloidal quantum dots (CQDs) are attractive materials for inexpensive, room-temperature-, and solution-processed optoelectronic devices. A high carrier diffusion length is desirable for many CQD device applications. In this work we develop two new experimental methods to investigate charge carrier diffusion in coupled CQD solids under charge-neutral, i.e., undepleted, conditions. The methods take advantage of the quantum-size-effect tunability of our materials, utilizing a smaller-bandgap population of quantum dots as a reporter system. We develop analytical models of diffusion in 1D and 3D structures that allow direct extraction of diffusion length from convenient parametric plots and purely optical measurements. We measure several CQD solids fabricated using a number of distinct methods and having significantly different doping and surface ligand treatments. We find that CQD materials recently reported to achieve a certified power conversion efficiency of 7% with hybrid organic-inorganic passivation have a diffusion length of 80 ± 10 nm. The model further allows us to extract the lifetime, trap density, mobility, and diffusion coefficient independently in each material system. This work will facilitate further progress in extending the diffusion length, ultimately leading to high-quality CQD solid semiconducting materials and improved CQD optoelectronic devices, including CQD solar cells. © 2013 American Chemical Society.

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)

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

A simple model of carcinogenic mutations with time delay and diffusion.

Science.gov (United States)

Piotrowska, Monika Joanna; Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan

2013-06-01

In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. The model essentially follows the idea of Ahangar and Lin (2003) where mutations in three different environmental conditions, namely favorable, competitive and unfavorable, were considered. We focus on the unfavorable conditions that can result from a given treatment, e.g. chemotherapy. Included delay stands for the interactions between benign and other cells. We compare the dynamics of ODEs system, the system with delay and the system with delay and diffusion. We mainly focus on the dynamics when a positive steady state exists. The system which is globally stable in the case without the delay and diffusion is destabilized by increasing delay, and therefore the underlying kinetic dynamics becomes oscillatory due to a Hopf bifurcation for appropriate values of the delay. This suggests the occurrence of spatially non-homogeneous periodic solutions for the system with the delay and diffusion.

X-Ray Characterization of Non-Equilibrium Solid Solutions

Energy Technology Data Exchange (ETDEWEB)

Brown, A; Rosdahl, Oe

1975-07-01

The Rudman approach to composition line broadening in X-ray diffraction patterns, originally designed for the study of diffusion in alloys, is seen to provide a basis for characterizing inhomogeneous solid solutions. Limitations, imposed on this treatment when the cell dimensions of the primary components differ by less than 0.1 A, are attributable to experimental effects such as instrument broadening. These limitations can be overcome by a rigorous numerical treatment of the measured data. Thus, separate elimination of the Kalpha{sub 2} radiation component followed by iterative deconvolution are advocated for the recovery of the intrinsic broadening. This course of action is made possible chiefly through the availability of large, fast memory computers and primary data recorded in the form of a step scan on punched paper tape. The characteristics of inhomogeneous solid solutions made available by the above treatment are the identity of closely similar, solid solution phases, the frequency distribution curve for a chosen component, and the degree of homogeneity of the X-ray sample

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)

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.

Fractional diffusion equations and anomalous diffusion

CERN Document Server

Evangelista, Luiz Roberto

2018-01-01

Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

Technical solutions for waste treatment in the Belene project

International Nuclear Information System (INIS)

Büttner, K.; Eichhorn, H.

2011-01-01

Outline: In June 2010 NUKEM Technologies GmbH was awarded a contract from ATOMSTROYEXPORT JSC to perform the complete work package related to designing and completion of the equipment for treatment of radioactive waste on the turn-key basis for Belene NPP. Technical Solutions: Waste Streams and Technologies at UKC and UKS; Concentration Plant; Thermal Treatment of Resins Sorting Facility; Biological Waste Water Treatment; Conditioning – Cementation • Sorting of Radwaste; Plasma Facility; Grouting; Filter Press; Monitoring and Tracking

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.

Glucose diffusion in colorectal mucosa—a comparative study between normal and cancer tissues

Science.gov (United States)

Carvalho, Sónia; Gueiral, Nuno; Nogueira, Elisabete; Henrique, Rui; Oliveira, Luís; Tuchin, Valery V.

2017-09-01

Colorectal carcinoma is a major health concern worldwide and its high incidence and mortality require accurate screening methods. Following endoscopic examination, polyps must be removed for histopathological characterization. Aiming to contribute to the improvement of current endoscopy methods of colorectal carcinoma screening or even for future development of laser treatment procedures, we studied the diffusion properties of glucose and water in colorectal healthy and pathological mucosa. These parameters characterize the tissue dehydration and the refractive index matching mechanisms of optical clearing (OC). We used ex vivo tissues to measure the collimated transmittance spectra and thickness during treatments with OC solutions containing glucose in different concentrations. These time dependencies allowed for estimating the diffusion time and diffusion coefficient values of glucose and water in both types of tissues. The measured diffusion times for glucose in healthy and pathological mucosa samples were 299.2±4.7 s and 320.6±10.6 s for 40% and 35% glucose concentrations, respectively. Such a difference indicates a slower glucose diffusion in cancer tissues, which originate from their ability to trap far more glucose than healthy tissues. We have also found a higher free water content in cancerous tissue that is estimated as 64.4% instead of 59.4% for healthy mucosa.

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)

Complexon Solutions in Freon for Decontamination of Solids and SNF Treatment

International Nuclear Information System (INIS)

Kamachev, V.; Shadrin, A.; Murzin, A.

2008-01-01

Full text of publication follows: The possibility of using complexon solutions in supercritical and compressed carbon dioxide for decontamination of solid surfaces and for spent nuclear fuel (SNF) treatment was demonstrated in the works of Japanese, Russian and American researchers. The obtained data showed that the use of complexon solutions in carbon dioxide sharply decreases the volume of secondary radioactive wastes because it can be easily evaporated, purified and recycled. Moreover, high penetrability of carbon dioxide allows decontamination of surfaces with complex shape. However, one of the disadvantages of carbon dioxide is its high working pressure (10-20 MPa for supercritical CO 2 and 7 MPa for compressed CO 2 ). Moreover, in case of SNF treatment, carbon dioxide solvent will be contaminated with 14 C, which in the course of SNF dissolution in CO 2 containing TBP*HNO 3 adduct stage will be oxidized into CO 2 . These main disadvantages can be eliminated by using complexon solutions in ozone-friendly Freon HFC-134a for decontamination and SNF treatment. Our experimental data for real contaminated materials showed that the decontamination factor for complexon solutions in liquid Freon HFC-134a at 1,2 MPa and 25 deg. C is close to that attained in carbon dioxide. Moreover, the possibility of SNF treatment in Freon HFC-134a was demonstrated in trials using real SNF and its imitators. (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

Insight into the electroreduction of nitrate ions at a copper electrode, in neutral solution, after determination of their diffusion coefficient by electrochemical impedance spectroscopy

International Nuclear Information System (INIS)

Aouina, Nizar; Cachet, Hubert; Debiemme-chouvy, Catherine; Tran, Thi Tuyet Mai

2010-01-01

The electrochemical reduction of nitrate ions at a copper electrode in an unbuffered neutral aqueous solution is studied. Using a two compartment electrochemical cell, three stationary cathodic waves, noted P1, P2 and P3, were evidenced by cyclic voltammetry at -0.9, -1.2 and -1.3 V/SCE, respectively. By comparing the electrochemical response of nitrate and nitrite containing solutions, P1 was attributed to the reduction of nitrate to nitrite. In order to assign P2 and P3 features by determining the number of electrons involved at the corresponding potential, rotating disk electrode experiments at various rotation speeds, combined with linear sweep voltammetry, were performed. Current data analysis at a given potential was carried out using Koutecky-Levich treatment taking into account water reduction. Confident values of the diffusion coefficient D of nitrate ions were assessed by electrochemical impedance spectroscopy for nitrate concentrations of 10 -3 , 10 -2 and 10 -1 M. For a nitrate concentration of 10 -2 M, D was found to be 1.31 x 10 -5 cm 2 s -1 allowing the number of electrons to be determined as 6 for P2 and 8 for P3, in accordance with nitrate reduction into hydroxylamine and ammonia, respectively. The formation of hydroxylamine was confirmed by the observation of its reoxidation at a Pt microelectrode present at the Cu electrode/nitrate solution interface.

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.

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

Performance of a contact textile-based light diffuser for photodynamic therapy.

Science.gov (United States)

Khan, Tania; Unternährer, Merthan; Buchholz, Julia; Kaser-Hotz, Barbara; Selm, Bärbel; Rothmaier, Markus; Walt, Heinrich

2006-03-01

Medical textiles offer a unique contact opportunity that could provide value-added comfort, reliability, and safety for light or laser-based applications. We investigated a luminous textile diffuser for use in photodynamic therapy. Textile diffusers are produced by an embroidery process. Plastic optical fibers are bent and sewn into textile to release light by macrobending. A reflective backing is incorporated to improve surface homogeneity, intensity, and safety. Clonogenic assay (MCF-7 cells) and trypan blue exclusion (NuTu19 cells) tests were performed in vitro using 0.1μg/ml m-THPC with three textile diffusers and a standard front lens diffuser. Heating effects were studied in solution and on human skin. PDT application in vivo was performed with the textile diffuser on equine sarcoids (three animals, 50mW/cm(2), 10-20J) and eight research animals. Lastly, computer simulations were performed to see how the textile diffuser might work on a curved object. At low fluency rate, there is a trend for the textile diffuser to have lower survival rates than the front lens diffuser for both cell lines. The textile diffuser was observed to retain more heat over a long period (>1min). All animals tolerated the treatments well and showed similar initial reactions. The simulations showed a likely focusing effect in a curved geometry. The initial feasibility and application using a textile-based optical diffuser has been demonstrated. Possibilities that provide additional practical advantages of the textile diffuser are discussed.

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

Evaluation of carbon diffusion in heat treatment of H13 tool steel under different atmospheric conditions

OpenAIRE

Ramezani, Maziar; Pasang, Timotius; Chen, Zhan; Neitzert, Thomas; Au, Dominique

2015-01-01

Although the cost of the heat treatment process is only a minor portion of the total production cost, it is arguably the most important and crucial stage on the determination of material quality. In the study of the carbon diffusion in H13 steel during austenitization, a series of heat treatment experiments had been conducted under different atmospheric conditions and length of treatment. Four austenitization atmospheric conditions were studied, i.e., heat treatment without atmospheric contro...

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.

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

Study of the diffusion of iron, of silver and of carbon in beryllium using radioactive tracers; Etude de la diffusion du fer, de l'argent et du carbone dans le beryllium au moyen des traceurs radioactifs

Energy Technology Data Exchange (ETDEWEB)

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

1964-06-01

A study has been made of the diffusion of radioactive iron and silver tracers in beryllium. The following values have been found. D{sub Fe} = 0.53 exp - [51800 / RT], D{sub Ag} = 62 exp - [46100 / RT]. The values for iron are in good agreement with those found previously for chemical diffusion. A comparison of the diffusion coefficients for iron, silver and nickel shows that the diffusion rate increases with increasing solute atom radius. The existence has been shown of diffusion anisotropy for silver; it has been studied quantitatively on monocrystals. It is found that: D{sub parallel} 0.41 exp - [39100 / RT], D{sub perpendicular} = 1.98 exp - [45700 / RT]. The anisotropy decreases as the temperature increases. The silver diffuses more rapidly along the C axis than in the base plane. This result cannot be explained in terms of the model proposed for the diffusion of foreign atoms in solution in zinc. A greater number of experiments is required before a model can be put forward. An attempt has also been made to determine the diffusion coefficients of carbon in beryllium by treatment in an atmosphere of acetylene marked with C-14. Diffusion coefficients have been obtained but these should not be considered to be very significant since a chemical reaction occurs at the surface of the samples. (author) [French] On a etudie la diffusion dans le beryllium de traceurs radioactifs du fer et de l'argent. On trouve: D{sub Fe} = 0.53 exp - [51800 / RT], D{sub Ag} = 62 exp - [46100 / RT].Les valeurs trouvees pour le fer sont en bon accord avec les valeurs obtenues precedemment pour la diffusion chimique. La comparaison des coefficients de diffusion du fer, de l'argent et du nickel montre que la diffusion est d'autant plus rapide que le rayon atomique du solute est plus grand. On a mis en evidence une anisotropie de diffusion de l'argent qui a ete etudiee quantitativement sur des monocristaux. On trouve: D{sub parallele} = 0.41 exp - [39100 / RT], D{sub perpendiculaire} = 1

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.

PRESERVATIVE TREATMENT OF Mimosa scabrella BENTH. AND Eucalyptus viminalis LAB. FENCE POSTS BY DIP-DIFFUSION METHOD

Directory of Open Access Journals (Sweden)

Juarez Benigno Paes

2001-01-01

Full Text Available This work aimed to compare the diffusion of CCB preservative in bracatinga (Mimosa scabrella Benth. and Eucalyptus viminalis Lab. round fence posts when exposed to dip-diffusion method. The pieces were submitted to the concentration of 2; 3.5 and 5% of active ingredients of “Osmose CCB” commercial preservative, during 2, 5 and 8 days. The penetration was analyzed in six positions in the pieces and the retention in three positions in the disks taken in ground contact area in the fence posts fitted out. The increase of treatment time and preservative concentration provided significant gains on penetration and retention of CCB for both tree species. In the work conditions, the eucalypt fence posts showed better response to the treatment.

Neuroimaging Cerebrovascular Function and Diffuse Axonal Injury after Traumatic Brain Injury and Response to Sildenafil Treatment

Science.gov (United States)

2016-04-05

n=4, FPI+sildenafil n=3). No significant main effect of either injury or treatment was observed (data not shown). Water Maze Animals in all groups...spent in prior quadrant on trial one of test day revealed no significant main effect of either injury or treatment . 41 Figure 15. Water ...injury with sildenafil treatment (each pɘ.0001). Error bars represent SEM. 50 Analysis of mean diffusivity in grey matter ROIs

Nanofiltration Membranes with Narrow Pore Size Distribution via Contra-Diffusion-Induced Mussel-Inspired Chemistry.

Science.gov (United States)

Du, Yong; Qiu, Wen-Ze; Lv, Yan; Wu, Jian; Xu, Zhi-Kang

2016-11-02

Nanofiltration membranes (NFMs) are widely used in saline water desalination, wastewater treatment, and chemical product purification. However, conventional NFMs suffer from broad pore size distribution, which limits their applications for fine separation, especially in complete separation of molecules with slight differences in molecular size. Herein, defect-free composite NFMs with narrow pore size distribution are fabricated using a contra-diffusion method, with dopamine/polyethylenimine solution on the skin side and ammonium persulfate solution on the other side of the ultrafiltration substrate. Persulfate ions can diffuse through the ultrafiltration substrate into the other side and in situ trigger dopamine to form a codeposited coating with polyethylenimine. The codeposition is hindered on those sites completely covered by the polydopamine/polyethylenimine coating, although it is promoted at the defects or highly permeable regions because it is induced by the diffused persulfate ions. Such a "self-completion" process results in NFMs with highly uniform structures and narrow pore size distribution, as determined by their rejection of neutral solutes. These near electrically neutral NFMs show a high rejection of divalent ions with a low rejection of monovalent ions (MgCl 2 rejection = 96%, NaCl rejection = 23%), majorly based on a steric hindrance effect. The as-prepared NFMs can be applied in molecular separation such as isolating cellulose hydrogenation products.

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.

Analytical-numerical method for treatment of turbulent diffusion of particles in the air

International Nuclear Information System (INIS)

Arsov, L.J.

1976-01-01

This work deals with the problem of air pollution around a stationary punctual source. For description of air pollution from a punctual source a mathematical model is suggested, and for calculation of effluents concentration an analytical-numerical algorithm is given. In addition to the analitical treatment the mathematical model is far more flexible and complete. Eddy diffusivity is represented by an arbitrary function, and an arbitrary wind velocity profile ahs been proposed. The apsorption of the ground is introduced through a variable apsorption coefficient, and the sedimentation through the mean velocity of deposition. To determine the movement of particles a parabolic equation of diffusion is used. The method has been tested through calculation of effluents concentration for different values of physical parameters

Desorption kinetics of ciprofloxacin in municipal biosolids determined by diffusion gradient in thin films.

Science.gov (United States)

D'Angelo, E; Starnes, D

2016-12-01

Ciprofloxacin (CIP) is a commonly-prescribed antibiotic that is largely excreted by the body, and is often found at elevated concentrations in treated sewage sludge (biosolids) at municipal wastewater treatment plants. When biosolids are applied to soils, they could release CIP to surface runoff, which could adversely affect growth of aquatic organisms that inhabit receiving water bodies. The hazard risk largely depends on the amount of antibiotic in the solid phase that can be released to solution (labile CIP), its diffusion coefficient, and sorption/desorption exchange rates in biosolids particles. In this study, these processes were evaluated in a Class A Exceptional Quality Biosolids using a diffusion gradient in thin films (DGT) sampler that continuously removed CIP from solution, which induced desorption and diffusion in biosolids. Mass accumulation of antibiotic in the sampler over time was fit by a diffusion transport and exchange model available in the software tool 2D-DIFS to derive the distribution coefficient of labile CIP (K dl ) and sorption/desorption rate constants in the biosolids. The K dl was 13 mL g -1 , which equated to 16% of total CIP in the labile pool. Although the proportion of labile CIP was considerable, release rates to solution were constrained by slow desorption kinetics (desorption rate constant = 4 × 10 -6 s -1 ) and diffusion rate (effective diffusion coefficient = 6 × 10 -9  cm 2  s -1 . Studies are needed to investigate how changes in temperature, water content, pH and other physical and chemical characteristics can influence antibiotic release kinetics and availability and mobility in biosolid-amended soils. Copyright © 2016 Elsevier Ltd. All rights reserved.

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 ...

China's Scientific Investigation for Liquid Waste Treatment Solutions

International Nuclear Information System (INIS)

Liangjin, B.; Meiqiong, L.; Kelley, D.

2006-01-01

Post World War II created the nuclear age with several countries developing nuclear technology for power, defense, space and medical applications. China began its nuclear research and development programs in 1950 with the establishment of the China Institute of Atomic Energy (CIAE) located near Beijing. CIAE has been China's leader in nuclear science and technical development with its efforts to create advanced reactor technology and upgrade reprocessing technology. In addition, with China's new emphasis on environmental safety, CIAE is focusing on waste treatment options and new technologies that may provide solutions to legacy waste and newly generated waste from the full nuclear cycle. Radioactive liquid waste can pose significant challenges for clean up with various treatment options including encapsulation (cement), vitrification, solidification and incineration. Most, if not all, nuclear nations have found the treatment of liquids to be difficult, due in large part to the high economic costs associated with treatment and disposal and the failure of some methods to safely contain or eliminate the liquid. With new environmental regulations in place, Chinese nuclear institutes and waste generators are beginning to seek new technologies that can be used to treat the more complex liquid waste streams in a form that is safe for transport and for long-term storage or final disposal. [1] In 2004, CIAE and Pacific Nuclear Solutions, a division of Pacific World Trade, USA, began discussions about absorbent technology and applications for its use. Preliminary tests were conducted at CIAE's Department of Radiochemistry using generic solutions, such as lubricating oil, with absorbent polymers for solidification. Based on further discussions between both parties, it was decided to proceed with a more formal test program in April, 2005, and additional tests in October, 2005. The overall objective of the test program was to apply absorbent polymers to various waste streams

EXPERIENCE OF SEA WATER HYPERTONIC SOLUTION APPLICATION FOR TOPICAL TREATMENT OF CHRONIC TONSILLITIS

Directory of Open Access Journals (Sweden)

E.P. Karpova

2006-01-01

Full Text Available The study examined the effectiveness of sea water hypertonic solution (Aqua Maris troath and oral cavity spray, Jadran, Croatia medication to treat chronic tonsillitis of the compensated form on 84 children aged between 5 and 15. All children had their tonsil lacunae rinsed in a day № 6–8. 64 children had them rinsed with the sea water hypertonic solution (main group, while 20 children had them rinsed with the nitrofural solution (comparison group. Treatment effectiveness was determined according to dynamics of main symptoms (odynophagia, dysphagia, hyperemia and mucosa infiltration of pillars of the fauces, as well as the degree of tonsil bacterial number before and after treatment (by the 14th day. The dynamic analysis of subjective data during treatment revealed more significant and positive changes among the children of the main group if compared with patients from the comparison group. After treatment the researchers noticed reduction of tonsil bacterial number among 90,62% of children from the main group, whereas this rate made up 60% in the comparison group. Acquired data allowed recommending this medication for the multimodality therapy of infant adenoid disease.Key words: chronic tonsillitis, treatment, children, sea water hypertonic solution.

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

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

Treatment of infectious skin defects or ulcers with electrolyzed strong acid aqueous solution.

Science.gov (United States)

Sekiya, S; Ohmori, K; Harii, K

1997-01-01

A chronic ulcer with an infection such as methicillin-resistant Staphylococcus aureus is hard to heal. Plastic and reconstructive surgeons often encounter such chronic ulcers that are resistant to surgical or various conservative treatments. We applied conservative treatment using an electrolyzed strong acid aqueous solution and obtained satisfactory results. The lesion was washed with the solution or soaked in a bowl of the solution for approximately 20 min twice a day. Fresh electrolyzed strong acid aqueous solution is unstable and should be stored in a cool, dark site in a sealed bottle. It should be used within a week after it has been produced. Here we report on 15 cases of infectious ulcers that were treated by electrolyzed strong acid aqueous solution. Of these cases, 7 patients were healed, 3 were granulated, and in 5, infection subsided. In most cases the lesion became less reddish and less edematous. Discharge or foul odor from the lesion was decreased. Electrolyzed strong acid aqueous solution was especially effective for treating a chronic refractory ulcer combined with diabetes melitus or peripheral circulatory insufficiency. This clinically applied therapy of electrolyzed strong acid aqueous solution was found to be effective so that this new therapeutic technique for ulcer treatment can now be conveniently utilized.

Assessment of treatment response by total tumor volume and global apparent diffusion coefficient using diffusion-weighted MRI in patients with metastatic bone disease: a feasibility study.

Directory of Open Access Journals (Sweden)

Matthew D Blackledge

Full Text Available We describe our semi-automatic segmentation of whole-body diffusion-weighted MRI (WBDWI using a Markov random field (MRF model to derive tumor total diffusion volume (tDV and associated global apparent diffusion coefficient (gADC; and demonstrate the feasibility of using these indices for assessing tumor burden and response to treatment in patients with bone metastases. WBDWI was performed on eleven patients diagnosed with bone metastases from breast and prostate cancers before and after anti-cancer therapies. Semi-automatic segmentation incorporating a MRF model was performed in all patients below the C4 vertebra by an experienced radiologist with over eight years of clinical experience in body DWI. Changes in tDV and gADC distributions were compared with overall response determined by all imaging, tumor markers and clinical findings at serial follow up. The segmentation technique was possible in all patients although erroneous volumes of interest were generated in one patient because of poor fat suppression in the pelvis, requiring manual correction. Responding patients showed a larger increase in gADC (median change = +0.18, range = -0.07 to +0.78 × 10(-3 mm2/s after treatment compared to non-responding patients (median change = -0.02, range = -0.10 to +0.05 × 10(-3 mm2/s, p = 0.05, Mann-Whitney test, whereas non-responding patients showed a significantly larger increase in tDV (median change = +26%, range = +3 to +284% compared to responding patients (median change = -50%, range = -85 to +27%, p = 0.02, Mann-Whitney test. Semi-automatic segmentation of WBDWI is feasible for metastatic bone disease in this pilot cohort of 11 patients, and could be used to quantify tumor total diffusion volume and median global ADC for assessing response to treatment.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

Science.gov (United States)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

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

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

Observed relationships between wood density and solution uptake during pressure treatment

Science.gov (United States)

Steve Halverson; Stan Lebow

2011-01-01

A better understanding of the relationship between wood properties and solution uptake during pressure treatment could lead to improvements in treatment quality and more efficient use of preservatives. In this study several years of treatment data representing a range of wood species, charge conditions and preservative formulations were analyzed to evaluate the...

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)

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)

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.

Kinetics of dodecanoic acid adsorption from caustic solution by activated carbon.

Science.gov (United States)

Pendleton, Phillip; Wu, Sophie Hua

2003-10-15

This study examines the influences of adsorbent porosity and surface chemistry and of carbon dosage on dodecanoic acid adsorption kinetics from aqueous and 2 M NaOH solutions as batch adsorption processes. Both adsorbents are steam-activated carbons prepared from either coconut or coal precursors. Prior to use the adsorbents were washed in deionized water or 2 M NaOH. Mass transfer coefficients and effective overall diffusion coefficients indicate a minor contribution from adsorbent porosity. In contrast, high surface oxygen content impedes transport to and into the adsorbent structure. Carbon dosage shows a proportional increase in transport coefficients with increasing mass; these coefficients are constant when normalized per unit mass. Neither water nor NaOH treatment of the adsorbents has a significant influence on dodecanoic acid adsorption kinetics. Molecular and Knudsen diffusion coefficients are defined to demonstrate that the overall effective diffusion coefficient values and the diffusion process are controlled by surface diffusion.

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

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)

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

Iron doping of lithium niobate by thermal diffusion from thin film: study of the treatment effect

Energy Technology Data Exchange (ETDEWEB)

Ciampolillo, Maria Vittoria; Zaltron, Annamaria; Bazzan, Marco; Argiolas, Nicola; Sada, Cinzia [Universita di Padova (Italy); CNISM, Dipartimento di Fisica ' ' G. Galilei' ' , Padova (Italy); Mignoni, Sabrina; Fontana, Marc [Universite de Metz et Supelec, Laboratoire Materiaux Optiques, Photoniques et Systemes, UMR CNRS 7132, Metz (France)

2011-07-15

Thermal diffusion from thin film is one of the most widespread approaches to prepare iron doped regions in lithium niobate with limited size for photorefractive applications. In this work, we investigate the doping process with the aim of determining the best process conditions giving a doped region with the characteristics required for photorefractive applications. Six samples were prepared by changing the atmosphere employed in the diffusion treatment in order to obtain different combination of diffusion profiles and reduction degrees and also to check the effect of employing a wet atmosphere. The compositional, optical, and structural properties are then extensively characterized by combining Secondary ion Mass Spectrometry, UV, visible and IR spectrophotometry, High Resolution X-Rays Diffraction, and Micro-Raman Spectroscopy. Moreover, the sample topography was checked by Atomic Force Microscopy. An analysis of all our data shows that the best results are obtained performing a double step process, i.e. diffusion in oxidizing atmosphere and subsequent reduction at lower temperature in an hydrogen-containing atmosphere. (orig.)