Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Science.gov (United States)

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Directory of Open Access Journals (Sweden)

Preston Donovan

Full Text Available The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Estimating thermal diffusivity and specific heat from needle probe thermal conductivity data

Science.gov (United States)

Waite, W.F.; Gilbert, L.Y.; Winters, W.J.; Mason, D.H.

2006-01-01

Thermal diffusivity and specific heat can be estimated from thermal conductivity measurements made using a standard needle probe and a suitably high data acquisition rate. Thermal properties are calculated from the measured temperature change in a sample subjected to heating by a needle probe. Accurate thermal conductivity measurements are obtained from a linear fit to many tens or hundreds of temperature change data points. In contrast, thermal diffusivity calculations require a nonlinear fit to the measured temperature change occurring in the first few tenths of a second of the measurement, resulting in a lower accuracy than that obtained for thermal conductivity. Specific heat is calculated from the ratio of thermal conductivity to diffusivity, and thus can have an uncertainty no better than that of the diffusivity estimate. Our thermal conductivity measurements of ice Ih and of tetrahydrofuran (THF) hydrate, made using a 1.6 mm outer diameter needle probe and a data acquisition rate of 18.2 pointss, agree with published results. Our thermal diffusivity and specific heat results reproduce published results within 25% for ice Ih and 3% for THF hydrate. ?? 2006 American Institute of Physics.

Diffusion coefficients of paracetamol in aqueous solutions

International Nuclear Information System (INIS)

Ribeiro, Ana C.F.; Barros, Marisa C.F.; Veríssimo, Luís M.P.; Santos, Cecilia I.A.V.; Cabral, Ana M.T.D.P.V.; Gaspar, Gualter D.; Esteso, Miguel A.

2012-01-01

Highlights: ► Mutual diffusion coefficients of paracetamol in aqueous dilute solutions. ► Influence of the thermodynamic factors on the variation of their mutual diffusion coefficients. ► Estimation of the mutual limiting diffusion coefficients of the molecular, D m 0 , and ionized forms, D ± 0 , of this drug. - Abstract: Binary mutual diffusion coefficients measured by the Taylor dispersion method, for aqueous solutions of paracetamol (PA) at concentrations from (0.001 to 0.050) mol·dm −3 at T = 298.15 K, are reported. From the Nernst–Hartley equation and our experimental results, the limiting diffusion coefficient of this drug and its thermodynamic factors are estimated, thereby contributing in this way to a better understanding of the structure of such systems and of their thermodynamic behaviour in aqueous solution at different concentrations.

Exact analytical solutions for nonlinear reaction-diffusion equations

International Nuclear Information System (INIS)

Liu Chunping

2003-01-01

By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

Solute coupled diffusion in osmotically driven membrane processes.

Science.gov (United States)

Hancock, Nathan T; Cath, Tzahi Y

2009-09-01

Forward osmosis (FO) is an emerging water treatment technology with potential applications in desalination and wastewater reclamation. In FO, water is extracted from a feed solution using the high osmotic pressure of a hypertonic solution that flows on the opposite side of a semipermeable membrane; however, solutes diffuse simultaneously through the membrane in both directions and may jeopardize the process. In this study, we have comprehensively explored the effects of different operating conditions on the forward diffusion of solutes commonly found in brackish water and seawater, and reverse diffusion of common draw solution solutes. Results show that reverse transport of solutes through commercially available FO membranes range between 80 mg to nearly 3,000 mg per liter of water produced. Divalent feed solutes have low permeation rates (less than 1 mmol/m2-hr) while monovalent ions and uncharged solutes exhibit higher permeation. Findings have significant implications on the performance and sustainability of the FO process.

Probing the diffuse interstellar medium with diffuse interstellar bands

Science.gov (United States)

Theodorus van Loon, Jacco; Bailey, Mandy; Farhang, Amin; Javadi, Atefeh; Khosroshahi, Habib

2015-08-01

For a century already, a large number of absorption bands have been known at optical wavelengths, called the diffuse interstellar bands (DIBs). While their carriers remain unidentified, the relative strengths of these bands in various environments make them interesting new probes of the diffuse interstellar medium (ISM). We present the results from two large, dedicated campaigns to map the ISM using DIBs measured in the high signal-to-noise spectra of hundreds of early-type stars: [1] in and around the Local Bubble using ESO's New Technology Telescope and the Isaac Newton Telescope, and [2] across both Magellanic Clouds using the Very Large Telescope and the Anglo-Australian Telescope. We discuss the implications for the structure and dynamics of the ISM, as well as the constraints these maps place on the nature of the carriers of the DIBs. Partial results have appeared in the recent literature (van Loon et al. 2013; Farhang et al. 2015a,b; Bailey, PhD thesis 2014) with the remainder being prepared for publication now.

Rotational and translational diffusions of fluorescent probes during gelation process

Science.gov (United States)

Hattori, Yusuke; Panizza, Pascal; Letamendia, Louis; Ushiki, Hideharu

2006-04-01

Gelation process has been investigated by using light scattering techniques in recent years. We measured both of rotational and translational motions of fluorescent probes during gelation process. The measurements were performed after the temperature quenched at 30 °C. As the results, rotational diffusion coefficient of fluorescein was decreased after 6.0 × 10 4 s and energy transfer rate was reduced after 2.0 × 10 4 s. We sorted the gelation process into the following three parts, (I) pre-gelation, (II) reduction of translational diffusion (aging), and (III) reduction of rotational diffusion with saturating translational diffusion (post-gelation). The time scale of the process was completely different from the results of other methods.

Polymer diffusion in the interphase between surface and solution.

Science.gov (United States)

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

2018-05-22

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

Self-diffusion and solute diffusion in alloys under irradiation: Influence of ballistic jumps

International Nuclear Information System (INIS)

Roussel, Jean-Marc; Bellon, Pascal

2002-01-01

We have studied the influence of ballistic jumps on thermal and total diffusion of solvent and solute atoms in dilute fcc alloys under irradiation. For the diffusion components that result from vacancy migration, we introduce generalized five-frequency models, and show that ballistic jumps produce decorrelation effects that have a moderate impact on self-diffusion but that can enhance or suppress solute diffusion by several orders of magnitude. These could lead to new irradiation-induced transformations, especially in the case of subthreshold irradiation conditions. We also show that the mutual influence of thermal and ballistic jumps results in a nonadditivity of partial diffusion coefficients: the total diffusion coefficient under irradiation may be less than the sum of the thermal and ballistic diffusion coefficients. These predictions are confirmed by kinetic Monte Carlo simulations. Finally, it is shown that the method introduced here can be extended to take into account the effect of ballistic jumps on the diffusion of dumbbell interstitials in dilute alloys

Translational and rotational diffusion of flexible PEG and rigid dendrimer probes in sodium caseinate dispersions and acid gels

NARCIS (Netherlands)

Salami, S.; Rondeau-Mouro, C.; Barhoum, M.; Duynhoven, van J.P.M.; Mariette, F.

2014-01-01

The dynamics of rigid dendrimer and flexible PEG probes in sodium caseinate dispersions and acid gels, including both translational diffusion and rotational diffusion, were studied by NMR. Above the onset of the close-packing limit (C ~ 10 g/100 g H2O), translational diffusion of the probe depended

Can slow-diffusing solute atoms reduce vacancy diffusion in advanced high-temperature alloys?

International Nuclear Information System (INIS)

Goswami, Kamal Nayan; Mottura, Alessandro

2014-01-01

The high-temperature mechanical properties of precipitate-strengthened advanced alloys can be heavily influenced by adjusting chemical composition. The widely-accepted argument within the community is that, under certain temperature and loading conditions, plasticity occurs only in the matrix, and dislocations have to rely on thermally-activated climb mechanisms to overcome the barriers to glide posed by the hard precipitates. This is the case for γ′-strengthened Ni-based superalloys. The presence of dilute amounts of slow-diffusing solute atoms, such as Re and W, in the softer matrix phase is thought to reduce plasticity by retarding the climb of dislocations at the interface with the hard precipitate phase. One hypothesis is that the presence of these solutes must hinder the flow of vacancies, which are essential to the climb process. In this work, density functional theory calculations are used to inform two analytical models to describe the effect of solute atoms on the diffusion of vacancies. Results suggest that slow-diffusing solute atoms are not effective at reducing the diffusion of vacancies in these systems

Interferometric measurements of a dendritic growth front solutal diffusion layer

Science.gov (United States)

Hopkins, John A.; Mccay, T. D.; Mccay, Mary H.

1991-01-01

An experimental study was undertaken to measure solutal distributions in the diffusion layer produced during the vertical directional solidification (VDS) of an ammonium chloride - water (NH4Cl-H2O) solution. Interferometry was used to obtain concentration measurements in the 1-2 millimeter region defining the diffusion layer. These measurements were fitted to an exponential form to extract the characteristic diffusion parameter for various times after the start of solidification. The diffusion parameters are within the limits predicted by steady state theory and suggest that the effective solutal diffusivity is increasing as solidification progresses.

In situ composition measurements of Bunsen reaction solution by radiation probes

Energy Technology Data Exchange (ETDEWEB)

Kubo, Shinji; Nagaya, Yasunobu [Japan Atomic Energy Agency (Japan)

2010-07-01

Measuring equipments are integral to chemical process controls. A stable hydrogen production by the Iodine-Sulfur thermochemical water-splitting process is relatively difficult because of lack of existing in situ composition measurement techniques for multiple components and corrosive solution. Composition regulations of Bunsen reaction solution is particularly important, since a closed cycle system provided with this process causes that the many streams with different composition return to this section. Accordingly Bunsen solution becomes changeable composition. Radiation probes have a potential for applications to determine this multiple component solution while the non-contact approach avoids the corrosive issues. Moreover the probes have features of the promptness, contact-less and sequential use. Laboratory scale experiments to evaluate these possibilities of the measurement were conducted with use of simulated Bunsen solution, HIx solution and H{sub 2}SO{sub 4} solution, containing HI, I2, H{sub 2}SO{sub 4} and H{sub 2}O and sealed radiation sources. Radiations were counted, which were interacted with the solutions in various compositions around room temperature contained in vessels. For HIx solution, the obtained counting rates were correlated with hydrogen volume concentrations; moreover, the application of the Monte Carlo method suggests possibilities that the detector responses for HIx solution by the radiation probes are predictable. For H{sub 2}SO{sub 4} solution, iodine atoms had significant influences on the relationship between output values of two gamma-ray density meters, cesium source as higher energy and barium source as lower energy. This results suggest that the neutron ray probe, the gamma-ray probes of both lower energy and higher energy have possibilities to determine the composition of Bunsen solution of HIx and H{sub 2}SO{sub 4} solutions. (orig.)

Solution of time dependent atmospheric diffusion equation with a proposed diffusion coefficient

International Nuclear Information System (INIS)

Mayhoub, A.B.; Essa, KH.S.M.; Aly, SH.

2004-01-01

One-dimensional model for the dispersion of passive atmospheric contaminant (not included chemical reactions) in the atmospheric boundary layer is considered. On the basis of the gradient transfer theory (K-theory), the time dependent diffusion equation represents the dispersion of the pollutants is solved analytically. The solution depends on diffusion coefficient K', which is expressed in terms of the friction velocity 'u the vertical coordinate -L and the depth of the mixing layer 'h'. The solution is obtained to either the vertical coordinate 'z' is less or greater than the mixing height 'h'. The obtained solution may be applied to study the atmospheric dispersion of pollutants

Analytical solutions to matrix diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)

2014-10-06

We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.

A family of analytical solutions of a nonlinear diffusion-convection equation

Science.gov (United States)

Hayek, Mohamed

2018-01-01

Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

Radioactive diffusion gaseous probe technique for study adsorbent structure inhomogeneity

International Nuclear Information System (INIS)

Zyuzin, A.Yu.; Korobkov, V.I.; Bekman, I.N.

1990-01-01

One of the versions of the method of diffusion gaseous probe - method of longitudinal shear in combination with autoradiography (ARG) - was used for characterising sorbents and catalysts, which are considered to be promising for reprocessing of sulfur-containing natural gases. Hydrogen sulfide, labelled with 35 S was used as diffusion radioactive probe. Zeolite granules of 4A type and granulated adsorbents on the basis of CR and AM aluminium oxides, which are industrial catalysts of Clauss reaction developed at SNEA company, were used as objects under investigation. It is shown that technique for fabrication of 4A zeolite granules leads to asymmetrical pore distribution over the granule diameter. Technique for AM granule fabrication leads to occuRrence of local inhomogeneities of the structure in the form of narrow coaxial rings with decreased or increased local adsorption ability. Granules of adsorbent of CR type are characterized by rather homogeneous structure. It is recommended to use the mentioned method for industrial adsorbent diagnosis

Measurement of Solute Diffusion Behavior in Fractured Waste Glass Media

International Nuclear Information System (INIS)

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

2008-01-01

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

Measuring minority-carrier diffusion length using a Kelvin probe force microscope

International Nuclear Information System (INIS)

Shikler, R.; Fried, N.; Meoded, T.; Rosenwaks, Y.

2000-01-01

A method based on Kelvin probe force microscopy for measuring minority-carrier diffusion length in semiconductors is described. The method is based on measuring the surface photovoltage between the tip of an atomic force microscope and the surface of an illuminated semiconductor junction. The photogenerated carriers diffuse to the junction and change the contact potential difference between the tip and the sample, as a function of the distance from the junction. The diffusion length L is then obtained by fitting the measured contact potential difference using the minority-carrier continuity equation. The method was applied to measurements of electron diffusion length in GaP pn and Schottky junctions. The measured diffusion length was found to be ∼2 μm, in good agreement with electron beam induced current measurements

In situ study of radionuclide diffusion into clays with specific device: Autolab probe

International Nuclear Information System (INIS)

Porcheron, J.

1993-01-01

The aim of this shared cost contract between the French Atomic Energy Commissariat, Nuclear Safety and Protection Institute and the Commission of the European Communities was to build and use an experimental drilling probe, the AUTOLAB prob, which was designed to measure the diffusion into clay of radioactive pollutants originating from a high activity waste storage. The measurement was carried out in-situ during drilling. The probe is equipped a new operating mode which involves using the pressure of the drilling water as its source of energy. The probe is autonomous and can stay in the bore hole for an extensive period of time without requiring any monitoring and without introducing any pollution. The diffusion experiment was carried out in a bore-hole at the JRC in ISPRA (ITALY). Two diffusion experiments were carried out in identical conditions (clay, 85Sr tracer, water samples), one in Laboratory, (ISPRA JRC Radiochemistry Laboratory, ITALY), and the other in-situ. The results displayed that 85Sr diffusion was considerably faster in the in-situ experiment than in that conducted in Laboratory. The explanation for this phenomenon, which could be due to the balance of carbonates, has not yet been clearly established. This test shows the value of comparing laboratory tests with in-situ tests conducted accurately using well adapted equipment. 9 refs., 10 figs

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 ...

An effective colorimetric and ratiometric fluorescent probe for bisulfite in aqueous solution

International Nuclear Information System (INIS)

Dai, Xi; Zhang, Tao; Du, Zhi-Fang; Cao, Xiang-Jian; Chen, Ming-Yu; Hu, Sheng-Wen; Miao, Jun-Ying; Zhao, Bao-Xiang

2015-01-01

We have developed the first two-photon colorimetric and ratiometric fluorescent probe, BICO, for the detection of bisulfite (HSO 3 − ) in aqueous solution. The probe contains coumarin and benzimidazole moieties and can detect HSO 3 − based on the Michael addition reaction with a limit of detection 5.3 × 10 −8  M in phosphate-buffered saline solution. The probe was used to detect bisulfite in tap water, sugar and dry white wine. Moreover, test strips were made and used easily. We successfully applied the probe to image living cells, using one-photon fluorescence imaging. BICO overcomes the limitations in sensitivity of previously reported probes and the solvation effect of bisulfite, which demonstrates its excellent value in practical application. - Highlights: • A colorimetric and ratiometric fluorescent probe was developed. • The probe could detect bisulfite in PBS buffer solution and real samples. • Bisulfite test paper was made to naked-eye detect bisulfite. • This probe successfully used to living cell imaging in ratiometric manner

An effective colorimetric and ratiometric fluorescent probe for bisulfite in aqueous solution

Energy Technology Data Exchange (ETDEWEB)

Dai, Xi [Institute of Organic Chemistry, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 (China); Zhang, Tao [Institute of Developmental Biology, School of Life Science, Shandong University, Jinan 250100 (China); Du, Zhi-Fang; Cao, Xiang-Jian; Chen, Ming-Yu [Institute of Organic Chemistry, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 (China); Taishan College, Shandong University, Jinan 250100 (China); Hu, Sheng-Wen [Institute of Organic Chemistry, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 (China); Miao, Jun-Ying, E-mail: miaojy@sdu.edu.cn [Institute of Developmental Biology, School of Life Science, Shandong University, Jinan 250100 (China); Zhao, Bao-Xiang, E-mail: bxzhao@sdu.edu.cn [Institute of Organic Chemistry, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100 (China)

2015-08-12

We have developed the first two-photon colorimetric and ratiometric fluorescent probe, BICO, for the detection of bisulfite (HSO{sub 3}{sup −}) in aqueous solution. The probe contains coumarin and benzimidazole moieties and can detect HSO{sub 3}{sup −} based on the Michael addition reaction with a limit of detection 5.3 × 10{sup −8} M in phosphate-buffered saline solution. The probe was used to detect bisulfite in tap water, sugar and dry white wine. Moreover, test strips were made and used easily. We successfully applied the probe to image living cells, using one-photon fluorescence imaging. BICO overcomes the limitations in sensitivity of previously reported probes and the solvation effect of bisulfite, which demonstrates its excellent value in practical application. - Highlights: • A colorimetric and ratiometric fluorescent probe was developed. • The probe could detect bisulfite in PBS buffer solution and real samples. • Bisulfite test paper was made to naked-eye detect bisulfite. • This probe successfully used to living cell imaging in ratiometric manner.

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

Inference of protein diffusion probed via fluorescence correlation spectroscopy

Science.gov (United States)

Tsekouras, Konstantinos

2015-03-01

Fluctuations are an inherent part of single molecule or few particle biophysical data sets. Traditionally, ``noise'' fluctuations have been viewed as a nuisance, to be eliminated or minimized. Here we look on how statistical inference methods - that take explicit advantage of fluctuations - have allowed us to draw an unexpected picture of single molecule diffusional dynamics. Our focus is on the diffusion of proteins probed using fluorescence correlation spectroscopy (FCS). First, we discuss how - in collaboration with the Bustamante and Marqusee labs at UC Berkeley - we determined using FCS data that individual enzymes are perturbed by self-generated catalytic heat (Riedel et al, Nature, 2014). Using the tools of inference, we found how distributions of enzyme diffusion coefficients shift in the presence of substrate revealing that enzymes performing highly exothermic reactions dissipate heat by transiently accelerating their center of mass following a catalytic reaction. Next, when molecules diffuse in the cell nucleus they often appear to diffuse anomalously. We analyze FCS data - in collaboration with Rich Day at the IU Med School - to propose a simple model for transcription factor binding-unbinding in the nucleus to show that it may give rise to apparent anomalous diffusion. Here inference methods extract entire binding affinity distributions for the diffusing transcription factors, allowing us to precisely characterize their interactions with different components of the nuclear environment. From this analysis, we draw key mechanistic insight that goes beyond what is possible by simply fitting data to ``anomalous diffusion'' models.

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

Energy Technology Data Exchange (ETDEWEB)

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

1969-07-01

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

Traveling wave solutions for reaction-diffusion systems

DEFF Research Database (Denmark)

Lin, Zhigui; Pedersen, Michael; Tian, Canrong

2010-01-01

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

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

DEFF Research Database (Denmark)

Vedel, Søren

2012-01-01

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Probing the DNA Structural Requirements for Facilitated Diffusion

Science.gov (United States)

2015-01-01

DNA glycosylases perform a genome-wide search to locate damaged nucleotides among a great excess of undamaged nucleotides. Many glycosylases are capable of facilitated diffusion, whereby multiple sites along the DNA are sampled during a single binding encounter. Electrostatic interactions between positively charged amino acids and the negatively charged phosphate backbone are crucial for facilitated diffusion, but the extent to which diffusing proteins rely on the double-helical structure DNA is not known. Kinetic assays were used to probe the DNA searching mechanism of human alkyladenine DNA glycosylase (AAG) and to test the extent to which diffusion requires B-form duplex DNA. Although AAG excises εA lesions from single-stranded DNA, it is not processive on single-stranded DNA because dissociation is faster than N-glycosidic bond cleavage. However, the AAG complex with single-stranded DNA is sufficiently stable to allow for DNA annealing when a complementary strand is added. This observation provides evidence of nonspecific association of AAG with single-stranded DNA. Single-strand gaps, bubbles, and bent structures do not impede the search by AAG. Instead, these flexible or bent structures lead to the capture of a nearby site of damage that is more efficient than that of a continuous B-form duplex. The ability of AAG to negotiate these helix discontinuities is inconsistent with a sliding mode of diffusion but can be readily explained by a hopping mode that involves microscopic dissociation and reassociation. These experiments provide evidence of relatively long-range hops that allow a searching protein to navigate around DNA binding proteins that would serve as obstacles to a sliding protein. PMID:25495964

Thermal diffusivity of diamond nanowires studied by laser assisted atom probe tomography

Science.gov (United States)

Arnoldi, L.; Spies, M.; Houard, J.; Blum, I.; Etienne, A.; Ismagilov, R.; Obraztsov, A.; Vella, A.

2018-04-01

The thermal properties of single-crystal diamond nanowires (NWs) have been calculated from first principles but have never been measured experimentally. Taking advantage of the sharp geometry of samples analyzed in a laser assisted atom probe, this technique is used to measure the thermal diffusivity of a single NW at low temperature (ab-initio calculations and confirms that thermal diffusivity in nanoscale samples is lower than in bulk samples. The results impact the design and integration of diamond NWs and nanoneedles in nanoscale devices for heat dissipation.

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

A multi-probe thermophoretic soot sampling system for high-pressure diffusion flames

Energy Technology Data Exchange (ETDEWEB)

Vargas, Alex M.; Gülder, Ömer L. [Institute for Aerospace Studies, University of Toronto, Toronto, Ontario M3H 5T6 (Canada)

2016-05-15

Optical diagnostics and physical probing of the soot processes in high pressure combustion pose challenges that are not faced in atmospheric flames. One of the preferred methods of studying soot in atmospheric flames is in situ thermophoretic sampling followed by transmission electron microscopy imaging and analysis for soot sizing and morphology. The application of this method of sampling to high pressures has been held back by various operational and mechanical problems. In this work, we describe a rotating disk multi-probe thermophoretic soot sampling system, driven by a microstepping stepper motor, fitted into a high-pressure chamber capable of producing sooting laminar diffusion flames up to 100 atm. Innovative aspects of the sampling system design include an easy and precise control of the sampling time down to 2.6 ms, avoidance of the drawbacks of the pneumatic drivers used in conventional thermophoretic sampling systems, and the capability to collect ten consecutive samples in a single experimental run. Proof of principle experiments were performed using this system in a laminar diffusion flame of methane, and primary soot diameter distributions at various pressures up to 10 atm were determined. High-speed images of the flame during thermophoretic sampling were recorded to assess the influence of probe intrusion on the flow field of the flame.

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

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

A highly sensitive fluorescent probe based on BODIPY for Hg2+ in aqueous solution

Directory of Open Access Journals (Sweden)

ZHAO Junwei

2016-12-01

Full Text Available A highly sensitive fluorescent probe based on BODIPY and hydrazine for Hg2+ was designed and synthesized.This probe could detect mercury ions in aqueous solutions within 5 min.With the increase of Hg2+ mole concentration,an obvious red shift of UV-Vis absorption wavelength was observed and the fluorescence intensity significantly enhanced.It was found that the fluorescence intensity of an aqueous solution containing 0.1 μmol/L Hg2+ is much stronger than that of blank solution,which indicats that the fluorescent probe has high sensitivity.In addition,other metal ions could not cause the change of fluorescent spectra,which means this probe has good selectivity,as well.

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.

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

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{sub 2}Si{sub 2}O{sub 8}; denoted AN), albite (NaAlSi{sub 3}O{sub 8}; denoted AB), and diopside (CaMgSi{sub 2}O{sub 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{sub Ca}/D{sub Si} ~ 20 and the efficiency of isotope separation for Ca is much greater than in natural liquid experiments where D{sub Ca}/D{sub Si} ~ 1. In the AB–DI experiment, D{sub Ca}/D{sub 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{sub Mg}/D{sub 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{sub Ca}) to the diffusivity of silicon (D{sub 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{sub cation

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.

A statistical method for estimating wood thermal diffusivity and probe geometry using in situ heat response curves from sap flow measurements.

Science.gov (United States)

Chen, Xingyuan; Miller, Gretchen R; Rubin, Yoram; Baldocchi, Dennis D

2012-12-01

The heat pulse method is widely used to measure water flux through plants; it works by using the speed at which a heat pulse is propagated through the system to infer the velocity of water through a porous medium. No systematic, non-destructive calibration procedure exists to determine the site-specific parameters necessary for calculating sap velocity, e.g., wood thermal diffusivity and probe spacing. Such parameter calibration is crucial to obtain the correct transpiration flux density from the sap flow measurements at the plant scale and subsequently to upscale tree-level water fluxes to canopy and landscape scales. The purpose of this study is to present a statistical framework for sampling and simultaneously estimating the tree's thermal diffusivity and probe spacing from in situ heat response curves collected by the implanted probes of a heat ratio measurement device. Conditioned on the time traces of wood temperature following a heat pulse, the parameters are inferred using a Bayesian inversion technique, based on the Markov chain Monte Carlo sampling method. The primary advantage of the proposed methodology is that it does not require knowledge of probe spacing or any further intrusive sampling of sapwood. The Bayesian framework also enables direct quantification of uncertainty in estimated sap flow velocity. Experiments using synthetic data show that repeated tests using the same apparatus are essential for obtaining reliable and accurate solutions. When applied to field conditions, these tests can be obtained in different seasons and can be automated using the existing data logging system. Empirical factors are introduced to account for the influence of non-ideal probe geometry on the estimation of heat pulse velocity, and are estimated in this study as well. The proposed methodology may be tested for its applicability to realistic field conditions, with an ultimate goal of calibrating heat ratio sap flow systems in practical applications.

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

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.

Radionuclides in diffusion probing of inorganic materials based on chalcogenides

International Nuclear Information System (INIS)

Firsova, L.P.

1994-01-01

Migration of tellurium-125m, selenium-75, sulfur-35 radionuclides in solid solutions Pb 1-y (Se 0.08 Te 0.92 ) y and (Pb 1-x Sn x ) y Te 1-y , where x=0.1 and 0.2, has been studied, the results are presented. Data on dependence of selenium and tellurium self-diffusion coefficients on temperature in the range of 600-750 deg C are given. The results of the study of self-diffusion coefficient isothermal dependences on lead and tellurium vapour pressure in equilibrium with solid phases have been considered. It is ascertained that a change in the temperature and p-n transitions initiate the change in self-diffusion mechanisms of chalcogenide atoms. 8 refs., 3 tabs

Influence of supersaturated carbon on the diffusion of Ni in ferrite determined by atom probe tomography

KAUST Repository

Kresse, T.; Li, Yujiao; Boll, Torben; Borchers, Christine; Choi, Pyuckpa; Al-Kassab, Talaat; Raabe, Dierk; Kirchheim, Reiner

2013-01-01

In patented and cold-drawn pearlitic steel wires dissociation of cementite occurs during mechanical deformation. In this study the influence of the carbon decomposition on the diffusion of nickel in ferrite is investigated by means of atom probe tomography. In the temperature range 423-523 K we observed a much smaller activation energy of Ni diffusion than for self-diffusion in body-centered cubic iron, indicating an increased vacancy density owing to enhanced formation of vacancy-carbon complexes. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Influence of supersaturated carbon on the diffusion of Ni in ferrite determined by atom probe tomography

KAUST Repository

Kresse, T.

2013-09-01

In patented and cold-drawn pearlitic steel wires dissociation of cementite occurs during mechanical deformation. In this study the influence of the carbon decomposition on the diffusion of nickel in ferrite is investigated by means of atom probe tomography. In the temperature range 423-523 K we observed a much smaller activation energy of Ni diffusion than for self-diffusion in body-centered cubic iron, indicating an increased vacancy density owing to enhanced formation of vacancy-carbon complexes. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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

International Nuclear Information System (INIS)

Chakraverty, S.; Tapaswini, Smita

2014-01-01

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

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

International Nuclear Information System (INIS)

Leger, J.J.

1969-01-01

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

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

OpenAIRE

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

2016-01-01

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

Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

Indian Academy of Sciences (India)

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

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

Probing GFP-actin diffusion in living cells using fluorescence correlation spectroscopy

International Nuclear Information System (INIS)

Engelke, Hanna; Heinrich, Doris; Rädler, Joachim O.

2010-01-01

The cytoskeleton of eukaryotic cells is continuously remodeled by polymerization and depolymerization of actin. Consequently, the relative content of polymerized filamentous actin (F-actin) and monomeric globular actin (G-actin) is subject to temporal and spatial fluctuations. Since fluorescence correlation spectroscopy (FCS) can measure the diffusion of fluorescently labeled actin it seems likely that FCS allows us to determine the dynamics and hence indirectly the structural properties of the cytoskeleton components with high spatial resolution. To this end we investigate the FCS signal of GFP-actin in living Dictyostelium discoideum cells and explore the inherent spatial and temporal signatures of the actin cytoskeleton. Using the free green fluorescent protein (GFP) as a reference, we find that actin diffusion inside cells is dominated by G-actin and slower than diffusion in diluted cell extract. The FCS signal in the dense cortical F-actin network near the cell membrane is probed using the cytoskeleton protein LIM and is found to be slower than cytosolic G-actin diffusion. Furthermore, we show that polymerization of the cytoskeleton induced by Jasplakinolide leads to a substantial decrease of G-actin diffusion. Pronounced fluctuations in the distribution of the FCS correlation curves can be induced by latrunculin, which is known to induce actin waves. Our work suggests that the FCS signal of GFP-actin in combination with scanning or spatial correlation techniques yield valuable information about the local dynamics and concomitant cytoskeletal properties

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.

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.

Oligonucleotides as probes for studying polymerization reactions in dilute aqueous solution

Science.gov (United States)

Kolb, V.; Orgel, L. E.; Miller, S. L. (Principal Investigator)

1994-01-01

We have prepared a [32P]-labled oligonucleotide probe carrying a free primary amine at its 3'-terminus. This probe is used to initiate polymerization of aziridine (ethyleneimine) in aqueous solution. The nature of the oligomeric products and the kinetics of their formation are then monitored by gel electrophoresis. Our results are generally consistent with those obtained using conventional techniques. We have also investigated the effect of polyanionic templates on the rate of oligomerization of aziridine. We find that water-soluble polyanions generally accelerate the polymerization. The sodium salt of polymethacrylic acid is the most effective of the templates that we studied. The methods introduced in this paper should be applicable to a variety of polymerization reactions in aqueous solution. They should greatly simplify the screening of potentially prebiotic polymerization reactions.

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)

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

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

DEFF Research Database (Denmark)

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

2016-01-01

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

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

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

Differential constraints and exact solutions of nonlinear diffusion equations

International Nuclear Information System (INIS)

Kaptsov, Oleg V; Verevkin, Igor V

2003-01-01

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

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

Science.gov (United States)

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

2002-01-01

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

On Solution of a Fractional Diffusion Equation by Homotopy Transform Method

International Nuclear Information System (INIS)

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

2012-01-01

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

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

Science.gov (United States)

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

2018-01-01

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

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

International Nuclear Information System (INIS)

Jefferies, N.L.

1988-01-01

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

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

Science.gov (United States)

Shokeen, Namita; Issa, Christopher; Mukhopadhyay, Ashis

2017-12-01

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

Parallel solutions of the two-group neutron diffusion equations

International Nuclear Information System (INIS)

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

1987-01-01

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

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.

Diffusing colloidal probes of protein-carbohydrate interactions.

Science.gov (United States)

Eichmann, Shannon L; Meric, Gulsum; Swavola, Julia C; Bevan, Michael A

2013-02-19

We present diffusing colloidal probe measurements of weak, multivalent, specific protein-polysaccharide interactions mediated by a competing monosaccharide. Specifically, we used integrated evanescent wave and video microscopy methods to monitor the three-dimensional Brownian excursions of conconavilin A (ConA) decorated colloids interacting with dextran-functionalized surfaces in the presence of glucose. Particle trajectories were interpreted as binding lifetime histograms, binding isotherms, and potentials of mean force. Binding lifetimes and isotherms showed clear trends of decreasing ConA-dextran-specific binding with increasing glucose concentration, consistent with expectations. Net potentials were accurately captured by superposition of a short-range, glucose-independent ConA-dextran repulsion and a longer-range, glucose-dependent dextran bridging attraction modeled as a harmonic potential. For glucose concentrations greater than 100 mM, the net ConA-dextran potential was found to have only a nonspecific repulsion, similar to that of bovine serum albumin (BSA) decorated colloids over dextran determined in control experiments. Our results demonstrate the first use of optical microscopy methods to quantify the connections between potentials of mean force and the binding behavior of ConA-decorated colloids on dextran-functionalized surfaces.

Influence of probe pressure on diffuse reflectance spectra of human skin measured in vivo

Science.gov (United States)

Popov, Alexey P.; Bykov, Alexander V.; Meglinski, Igor V.

2017-11-01

Mechanical pressure superficially applied on the human skin surface by a fiber-optic probe influences the spatial distribution of blood within the cutaneous tissues. Upon gradual load of weight on the probe, a stepwise increase in the skin reflectance spectra is observed. The decrease in the load follows the similar inverse staircase-like tendency. The observed stepwise reflectance spectra changes are due to, respectively, sequential extrusion of blood from the topical cutaneous vascular beds and their filling afterward. The obtained results are confirmed by Monte Carlo modeling. This implies that pressure-induced influence during the human skin diffuse reflectance spectra measurements in vivo should be taken into consideration, in particular, in the rapidly developing area of wearable gadgets for real-time monitoring of various human body parameters.

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.

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.

Solute-solvent interactions and dynamics probed by THz light

Science.gov (United States)

Schwaab, Gerhard; Böhm, Fabian; Ma, Chun-Yu; Havenith, Martina

The THz range (1-12 THz, 30-400 cm-1) is especially suited to probe changes in the solvent dynamics induced by solutes of different character (hydrophobic, hydrophilic, charged, neutral). In recent years we have investigated a large variety of such solutes and found characteristic spectral fingerprints for ions, but also for uncharged solutes, such as alcohols. We will present a status report on our current understanding of the observed spectral changes and how they relate to physico-chemical parameters like hydration shell size or the lifetime of an excited intermolecular oscillation. In addition, we will show, that in some cases the spectral changes are closely related to the partition function yielding access to a microscopic understanding of macroscopic thermodynamic functions. The authors gratefully acknowledge financial support from the Cluster of Excellence RESOLV (Ruhr-Universität, EXC1069) funded by the Deutsche Forschungsgemeinschaft.

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].

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

Probing region-specific microstructure of human cortical areas using high angular and spatial resolution diffusion MRI.

Science.gov (United States)

Aggarwal, Manisha; Nauen, David W; Troncoso, Juan C; Mori, Susumu

2015-01-15

Regional heterogeneity in cortical cyto- and myeloarchitecture forms the structural basis of mapping of cortical areas in the human brain. In this study, we investigate the potential of diffusion MRI to probe the microstructure of cortical gray matter and its region-specific heterogeneity across cortical areas in the fixed human brain. High angular resolution diffusion imaging (HARDI) data at an isotropic resolution of 92-μm and 30 diffusion-encoding directions were acquired using a 3D diffusion-weighted gradient-and-spin-echo sequence, from prefrontal (Brodmann area 9), primary motor (area 4), primary somatosensory (area 3b), and primary visual (area 17) cortical specimens (n=3 each) from three human subjects. Further, the diffusion MR findings in these cortical areas were compared with histological silver impregnation of the same specimens, in order to investigate the underlying architectonic features that constitute the microstructural basis of diffusion-driven contrasts in cortical gray matter. Our data reveal distinct and region-specific diffusion MR contrasts across the studied areas, allowing delineation of intracortical bands of tangential fibers in specific layers-layer I, layer VI, and the inner and outer bands of Baillarger. The findings of this work demonstrate unique sensitivity of diffusion MRI to differentiate region-specific cortical microstructure in the human brain, and will be useful for myeloarchitectonic mapping of cortical areas as well as to achieve an understanding of the basis of diffusion NMR contrasts in cortical gray matter. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

The effect of probe choice and solution conditions on the apparent photoreactivity of dissolved organic matter.

Science.gov (United States)

Maizel, Andrew C; Remucal, Christina K

2017-08-16

Excited triplet states of dissolved organic matter ( 3 DOM) are quantified directly with the species-specific probes trans,trans-hexadienoic acid (HDA) and 2,4,6-trimethylphenol (TMP), and indirectly with the singlet oxygen ( 1 O 2 ) probe furfuryl alcohol (FFA). Although previous work suggests that these probe compounds may be sensitive to solution conditions, including dissolved organic carbon concentration ([DOC]) and pH, and may quantify different 3 DOM subpopulations, the probes have not been systematically compared. Therefore, we quantify the apparent photoreactivity of diverse environmental waters using HDA, TMP, and FFA. By conducting experiments under ambient [DOC] and pH, with standardized [DOC] and pH, and with solid phase extraction isolates, we demonstrate that much of the apparent dissimilarity in photochemical measurements is attributable to solution conditions, rather than intrinsic differences in 3 DOM production. In general, apparent quantum yields (Φ 1 O 2 ≥ Φ 3 DOM,TMP ≫ Φ 3 DOM,HDA ) and pseudo-steady state concentrations ([ 1 O 2 ] ss > [ 3 DOM] ss,TMP > [ 3 DOM] ss,HDA ) show consistent relationships in all waters under standardized conditions. However, intrinsic differences in 3 DOM photoreactivity are apparent between DOM from diverse sources, as seen in the higher Φ 1 O 2 and lower Φ 3 DOM,TMP of wastewater effluents compared with oligotrophic lakes. Additionally, while conflicting trends in photoreactivity are observed under ambient conditions, all probes observe quantum yields increasing from surface wetlands to terrestrially influenced waters to oligotrophic lakes under standardized conditions. This work elucidates how probe selection and solution conditions influence the apparent photoreactivity of environmental waters and confirms that 3 DOM or 1 O 2 probes cannot be used interchangeably in waters that vary in [DOC], pH, or DOM source.

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

Science.gov (United States)

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

2017-12-01

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

A comparison of certain variational solutions of neutron diffusion equation

International Nuclear Information System (INIS)

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

1987-01-01

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

Systematic spatial bias in DNA microarray hybridization is caused by probe spot position-dependent variability in lateral diffusion.

Science.gov (United States)

Steger, Doris; Berry, David; Haider, Susanne; Horn, Matthias; Wagner, Michael; Stocker, Roman; Loy, Alexander

2011-01-01

The hybridization of nucleic acid targets with surface-immobilized probes is a widely used assay for the parallel detection of multiple targets in medical and biological research. Despite its widespread application, DNA microarray technology still suffers from several biases and lack of reproducibility, stemming in part from an incomplete understanding of the processes governing surface hybridization. In particular, non-random spatial variations within individual microarray hybridizations are often observed, but the mechanisms underpinning this positional bias remain incompletely explained. This study identifies and rationalizes a systematic spatial bias in the intensity of surface hybridization, characterized by markedly increased signal intensity of spots located at the boundaries of the spotted areas of the microarray slide. Combining observations from a simplified single-probe block array format with predictions from a mathematical model, the mechanism responsible for this bias is found to be a position-dependent variation in lateral diffusion of target molecules. Numerical simulations reveal a strong influence of microarray well geometry on the spatial bias. Reciprocal adjustment of the size of the microarray hybridization chamber to the area of surface-bound probes is a simple and effective measure to minimize or eliminate the diffusion-based bias, resulting in increased uniformity and accuracy of quantitative DNA microarray hybridization.

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

Measurement of thermal conductivity and diffusivity in situ: Literature survey and theoretical modelling of measurements

Energy Technology Data Exchange (ETDEWEB)

Kukkonen, I.; Suppala, I. [Geological Survey of Finland, Espoo (Finland)

1999-01-01

In situ measurements of thermal conductivity and diffusivity of bedrock were investigated with the aid of a literature survey and theoretical simulations of a measurement system. According to the surveyed literature, in situ methods can be divided into `active` drill hole methods, and `passive` indirect methods utilizing other drill hole measurements together with cutting samples and petrophysical relationships. The most common active drill hole method is a cylindrical heat producing probe whose temperature is registered as a function of time. The temperature response can be calculated and interpreted with the aid of analytical solutions of the cylindrical heat conduction equation, particularly the solution for an infinite perfectly conducting cylindrical probe in a homogeneous medium, and the solution for a line source of heat in a medium. Using both forward and inverse modellings, a theoretical measurement system was analysed with an aim at finding the basic parameters for construction of a practical measurement system. The results indicate that thermal conductivity can be relatively well estimated with borehole measurements, whereas thermal diffusivity is much more sensitive to various disturbing factors, such as thermal contact resistance and variations in probe parameters. In addition, the three-dimensional conduction effects were investigated to find out the magnitude of axial `leak` of heat in long-duration experiments. The radius of influence of a drill hole measurement is mainly dependent on the duration of the experiment. Assuming typical conductivity and diffusivity values of crystalline rocks, the measurement yields information within less than a metre from the drill hole, when the experiment lasts about 24 hours. We propose the following factors to be taken as basic parameters in the construction of a practical measurement system: the probe length 1.5-2 m, heating power 5-20 Wm{sup -1}, temperature recording with 5-7 sensors placed along the probe, and

Measurement of thermal conductivity and diffusivity in situ: Literature survey and theoretical modelling of measurements

International Nuclear Information System (INIS)

Kukkonen, I.; Suppala, I.

1999-01-01

In situ measurements of thermal conductivity and diffusivity of bedrock were investigated with the aid of a literature survey and theoretical simulations of a measurement system. According to the surveyed literature, in situ methods can be divided into 'active' drill hole methods, and 'passive' indirect methods utilizing other drill hole measurements together with cutting samples and petrophysical relationships. The most common active drill hole method is a cylindrical heat producing probe whose temperature is registered as a function of time. The temperature response can be calculated and interpreted with the aid of analytical solutions of the cylindrical heat conduction equation, particularly the solution for an infinite perfectly conducting cylindrical probe in a homogeneous medium, and the solution for a line source of heat in a medium. Using both forward and inverse modellings, a theoretical measurement system was analysed with an aim at finding the basic parameters for construction of a practical measurement system. The results indicate that thermal conductivity can be relatively well estimated with borehole measurements, whereas thermal diffusivity is much more sensitive to various disturbing factors, such as thermal contact resistance and variations in probe parameters. In addition, the three-dimensional conduction effects were investigated to find out the magnitude of axial 'leak' of heat in long-duration experiments. The radius of influence of a drill hole measurement is mainly dependent on the duration of the experiment. Assuming typical conductivity and diffusivity values of crystalline rocks, the measurement yields information within less than a metre from the drill hole, when the experiment lasts about 24 hours. We propose the following factors to be taken as basic parameters in the construction of a practical measurement system: the probe length 1.5-2 m, heating power 5-20 Wm -1 , temperature recording with 5-7 sensors placed along the probe, and

Bulk Heterojunction versus Diffused Bilayer: The Role of Device Geometry in Solution p-Doped Polymer-Based Solar Cells.

Science.gov (United States)

Loiudice, Anna; Rizzo, Aurora; Biasiucci, Mariano; Gigli, Giuseppe

2012-07-19

We exploit the effect of molecular p-type doping of P3HT in diffused bilayer (DB) polymer solar cells. In this alternative device geometry, the p-doping is accomplished in solution by blending the F4-TCNQ with P3HT. The p-doping both increases the film conductivity and reduces the potential barrier at the interface with the electrode. This results in an excellent power conversion efficiency of 4.02%, which is an improvement of ∼48% over the p-doped standard bulk heterojunction (BHJ) device. Combined VOC-light intensity dependence measurements and Kelvin probe force microscopy reveal that the DB device configuration is particularly advantageous, if compared to the conventional BHJ, because it enables optimization of the donor and acceptor layers independently to minimize the effect of trapping and to fully exploit the improved transport properties.

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

International Nuclear Information System (INIS)

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

2009-01-01

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

On the solutions of fractional reaction-diffusion equations

Directory of Open Access Journals (Sweden)

Jagdev Singh

2013-05-01

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

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

Vibrational dynamics of aqueous hydroxide solutions probed using broadband 2DIR spectroscopy

International Nuclear Information System (INIS)

Mandal, Aritra; Tokmakoff, Andrei

2015-01-01

We employed ultrafast transient absorption and broadband 2DIR spectroscopy to study the vibrational dynamics of aqueous hydroxide solutions by exciting the O–H stretch vibrations of the strongly hydrogen-bonded hydroxide solvation shell water and probing the continuum absorption of the solvated ion between 1500 and 3800 cm −1 . We observe rapid vibrational relaxation processes on 150–250 fs time scales across the entire probed spectral region as well as slower vibrational dynamics on 1–2 ps time scales. Furthermore, the O–H stretch excitation loses its frequency memory in 180 fs, and vibrational energy exchange between bulk-like water vibrations and hydroxide-associated water vibrations occurs in ∼200 fs. The fast dynamics in this system originate in strong nonlinear coupling between intra- and intermolecular vibrations and are explained in terms of non-adiabatic vibrational relaxation. These measurements indicate that the vibrational dynamics of the aqueous hydroxide complex are faster than the time scales reported for long-range transport of protons in aqueous hydroxide solutions

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

Anisotropy in "isotropic diffusion" measurements due to nongaussian diffusion

DEFF Research Database (Denmark)

Jespersen, Sune Nørhøj; Olesen, Jonas Lynge; Ianuş, Andrada

2017-01-01

Designing novel diffusion-weighted NMR and MRI pulse sequences aiming to probe tissue microstructure with techniques extending beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford...... model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often...

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

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.

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

Kalman Filtering and Smoothing of the Van Allen Probes Observations to Estimate the Radial, Energy and Pitch Angle Diffusion Rates

Science.gov (United States)

Podladchikova, T.; Shprits, Y.; Kellerman, A. C.

2015-12-01

The Kalman filter technique combines the strengths of new physical models of the Earth's radiation belts with long-term spacecraft observations of electron fluxes and therefore provide an extremely useful method for the analysis of the state and evolution of the electron radiation belts. However, to get the reliable data assimilation output, the Kalman filter application is confronted with a set of fundamental problems. E.g., satellite measurements are usually limited to a single location in space, which confines the reconstruction of the global evolution of the radiation environment. The uncertainties arise from the imperfect description of the process dynamics and the presence of observation errors, which may cause the failure of data assimilation solution. The development of adaptive Kalman filter that combines the Van Allen Probes data and 3-D VERB code, its accurate customizations in the reconstruction of model describing the phase space density (PSD) evolution, extension of the possibilities to use measurement information, and the model adjustment by developing the identification techniques of model and measurement errors allowed us to reveal hidden and implicit regularities of the PSD dynamics and obtain quantitative and qualitative estimates of radial, energy and pitch angle diffusion characteristics from satellite observations. In this study we propose an approach to estimate radial, energy and pitch angle diffusion rates, as well as the direction of their propagation.

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.

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

Science.gov (United States)

Saliba, Daniel

2016-01-01

We report the synthesis of magnesium–aluminium layered double hydroxide (LDH) using a reaction–diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium–aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’. PMID:27698034

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

Science.gov (United States)

Saliba, Daniel; Al-Ghoul, Mazen

2016-11-01

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

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

Science.gov (United States)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

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

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

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

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

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

International Nuclear Information System (INIS)

1985-01-01

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

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

Directory of Open Access Journals (Sweden)

Matthew J Simpson

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-10-15

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

Diffusion studies on permeable nitroxyl spin probe through lipid bilayer membrane

International Nuclear Information System (INIS)

Benial, A. Milton Franklin; Meenakumari, V.; Ichikawa, Kazuhiro; Yamada, Ken-ichi; Utsumi, Hideo; Hyodo, Fuminori; Jawahar, A.

2014-01-01

Electron spin resonance (ESR) studies were carried out for 2mM 14 N labeled deutrated permeable 3- methoxycarbonyl-2,2,5,5-tetramethyl-pyrrolidine-1-oxyl (MC-PROXYL) in pure water, 1 mM, 2 mM, 3 mM and 4 mM concentration of MC-PROXYL in 300 mM concentration of liposomal solution by using a L-band ESR spectrometer. The ESR parameters such as linewidth, hyperfine coupling constant, g-factor, partition parameter and permeability were reported. The partition parameter and permeability values indicate the maximum spin distribution in the lipid phase at 2 mM concentration. This study illustrates that ESR can be used to differentiate between the intra and extra-membrane water by loading the liposome vesicles with a lipid-permeable nitroxyl spin probe. From the ESR results, the radical concentration was optimized as 2 mM in liposomal solution for ESR phantom studies and experiments

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)

Using solar oscillations to probe the effects of element diffusion in the solar interior

International Nuclear Information System (INIS)

Guzik, J.A.; Cox, A.N.

1993-01-01

There is growing evidence from solar oscillation and evolution studies that the Sun's convection zone helium mass fraction has decreased by about 0.03 due to element diffusion. Evolution calculations show that diffusion also produces a steep Y and Z composition gradient below the convection zone. Comparisons between calculated and observed solar p-mode frequencies of angular degrees 5 thru 60 that are sensitive to solar structure near the convection zone bottom support this steep composition gradient, rather than one smoothed significantly by turbulent mixing. Turbulent mixing induced by convective overshoot or rotation has been the favored explanation for much of the solar surface lithium depletion by a factor of 200 from its presumed primordial value. These limits on the extent of turbulent mixing imply that either most of the solar lithium destruction occurred pre-main sequence, which is not supported by observation of young star, or that some other mechanism, for example a small amount of early main-sequence mass loss, is responsible for the low observed lithium abundance. Solar models including such mass loss as well as diffusion have a slightly steeper central density gradient. Comparisons between observed and calculated low-degree p-mode frequencies that are sensitive to the Sun's central structure can be used to probe this density gradient and constrain the possible amount of mass loss

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.

Highly anisotropic mobility in solution processed TIPS-pentacene film studied by independently driven four GaIn probes

Science.gov (United States)

Yoshimoto, Shinya; Takahashi, Kohtaro; Suzuki, Mitsuharu; Yamada, Hiroko; Miyahara, Ryosuke; Mukai, Kozo; Yoshinobu, Jun

2017-08-01

We have studied in-plane anisotropy in the field-effect mobility of solution-processed organic semiconductor 6,13-bis(triisopropylsilylethynyl)pentacene by using independently driven four gallium indium (Ga-In) probes. Liquid-metal Ga-In probes are highly effective for reproducible conductivity measurements of organic thin films. We demonstrated that a high mobility anisotropy of 44 was obtained by using a square four-probe method and a feedback circuit to keep the channel potential constant. The present method minimized the influences of the contact resistance and the insensitivity of anisotropy in a linear arrangement in two-dimensional field-effect transistors.

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 .

Detection and quantification of solute clusters in a nanostructured ferritic alloy

Energy Technology Data Exchange (ETDEWEB)

Miller, M.K., E-mail: millermk@ornl.gov [Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6139 (United States); Reinhard, D., E-mail: David.Reinhard@ametek.com [CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711 (United States); Larson, D.J., E-mail: David.Larson@ametek.com [CAMECA Instruments, Inc., 5500 Nobel Drive, Madison, WI 53711 (United States)

2015-07-15

Highlights: • Simulated APT data indicate that solute clusters can be resolved at 80% detection efficiency. • Solute clusters containing 2–9 atoms were detected in a prototype ∼80% detection efficiency LEAP. • High densities, 1.8 × 10{sup 24} m{sup −3}, of solute clusters were detected in as-milled flakes of 14YWT. • Lower densities, 1.2 × 10{sup 24} m{sup −3}, were detected in the stir zone of a FSW. • Vacancies stabilize the clusters, which retard diffusion and confers excellent stability. - Abstract: A series of simulated atom probe datasets were examined with a friends-of-friends method to establish the detection efficiency required to resolve solute clusters in the ferrite phase of a 14YWT nanostructured ferritic alloy. The size and number densities of solute clusters in the ferrite of the as-milled mechanically-alloyed condition and the stir zone of a friction stir weld were estimated with a prototype high-detection-efficiency (∼80%) local electrode atom probe. High number densities, 1.8 × 10{sup 24} m{sup −3} and 1.2 × 10{sup 24} m{sup −3}, respectively of solute clusters containing between 2 and 9 solute atoms of Ti, Y and O and were detected for these two conditions. These results support first principle calculations that predicted that vacancies stabilize these Ti–Y–O– clusters, which retard diffusion and contribute to the excellent high temperature stability of the microstructure and radiation tolerance of nanostructured ferritic alloys.

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

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

Science.gov (United States)

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

2013-05-01

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

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

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

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

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

International Nuclear Information System (INIS)

Cavdar, S.

2010-01-01

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

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

International Nuclear Information System (INIS)

Esmail, S.F.H.

2011-01-01

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

Determination of the Solute Diffusion Coefficient by the Droplet Migration Method

Energy Technology Data Exchange (ETDEWEB)

Shan Liu; Jing Teng; Jeongyun Choi

2007-07-01

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

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)

NMR studies of phase behaviour in polyacrylonitrile solutions

International Nuclear Information System (INIS)

Golightly, J.A.

1998-10-01

The aim of the thesis was to study the phase behaviour of aqueous polyacrylonitrile/NaSCN solutions using a variety of nuclear magnetic resonance techniques. Polyacrylonitrile (PAN) is the basis of the acrylic fibre industry, as such fibres contain at least 85% PAN. Despite this industrial importance, the available literature describing the phase behaviour of PAN in solution is far from comprehensive. Bulk 1 H NMR relaxation measurements were carried out over a wide range of concentrations and temperatures to probe the molecular dynamics of the PAN and water molecules. The relaxation data was found to be biexponential decay for all samples, the relative amplitudes of which were shown to be equal to the ratio of PAN protons to water protons. Both species were found to be in the regime of rapid molecular motion. Bulk 1 H NMR self diffusion measurements, using the PFGSTE technique, exhibited a bi-exponential decay of the echo amplitudes. By careful selection of the observation time, Δ, it was possible to independently probe the water and PAN translational diffusion. A background gradient, resulting from inhomogeneities of the magnetic field, complicated the analysis of the data and a novel polynomial least squares fitting procedure was devised to overcome this effect. The measured attenuation of the water diffusion coefficients (D∼10 -6 -10 -5 cm 2 s -1 ) with increasing PAN volume fraction was modelled according to various theories, including free volume and scaling laws. The study of the PAN diffusion coefficient (D∼10 -7 -10 -6 cm 2 s -1 ) was limited by the experimental constraints of the NMR spectrometer. A 1 H NMR one-dimensional imaging technique was used to study the non-solvent induced phase separation (coagulation) of a PAN solution. The time dependence of the measured profiles allowed observation of the coagulation process. A diffusion model was developed to fit the experimental data using a semi-infinite diffusion framework. The fitting parameters

A new Schiff base based on vanillin and naphthalimide as a fluorescent probe for Ag+ in aqueous solution

Science.gov (United States)

Zhou, Yanmei; Zhou, Hua; Ma, Tongsen; Zhang, Junli; Niu, Jingyang

2012-03-01

A new Schiff base based on vanillin and naphthalimide was designed and synthesized as fluorescent probe. The probe showed high selectivity for Ag+ over other metal ions such as Pb2+, Na+, K+, Cd2+, Ba2+, Cr3+, Zn2+, Cu2+, Ni2+, Ca2+, Al3+ and Mg2+ in aqueous solution. A new fluorescence emission was observed at 682 nm in the presence of Ag+ ion. The fluorescence intensity quenched with increasing the concentration of Ag+ at 682 nm. The method of job's plot confirmed the 1:2 complex between Ag+ and probe, and the mechanism was proposed.

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.

Assorted interactions of amino acids prevailing in aqueous vitamin C solutions probed by physicochemical and ab-initio contrivances

Science.gov (United States)

Das, Koyeli; Roy, Milan Chandra; Rajbanshi, Biplab; Roy, Mahendra Nath

2017-11-01

Qualitative and quantitative analysis of molecular interaction prevailing in tyrosine and tryptophan in aqueous solution of vitamin C have been probed by thermophysical properties. The apparent molar volume (ϕV), viscosity B-coefficient, molal refraction (RM) of tyrosine and tryptophan have been studied in aqueous vitamin C solutions at diverse temperatures via Masson equation which deduced solute-solvent and solute-solute interactions, respectively. Spectroscopic study along with physicochemical and computational techniques provides lots of interesting and highly significant insights of the model biological systems. The overall results established strong solute-solvent interactions between studied amino acids and vitamin C mixture in the ternary solutions.

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.)

Dansyl-8-aminoquinoline as a sensitive pH fluorescent probe with dual-responsive ranges in aqueous solutions.

Science.gov (United States)

Zhang, Min; Zheng, Shuyu; Ma, Liguo; Zhao, Meili; Deng, Lengfang; Yang, Liting; Ma, Li-Jun

2014-04-24

A sensitive pH fluorescent probe based on dansyl group, dansyl-8-aminoquinoline (DAQ), has been synthesized. The probe showed dual-responsive ranges to pH changes, one range from 2.00 to 7.95 and another one from 7.95 to 10.87 in aqueous solution, as it showed pKa values of 5.73 and 8.56 under acid and basic conditions, respectively. Furthermore, the pH response mechanism of the probe was explored successfully by using NMR spectra. The results indicated that the responses of DAQ to pH changes should attribute to the protonation of the nitrogen atom in the dimethylamino group and deprotonation of sulfonamide group. Copyright © 2014. Published by Elsevier B.V.

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

Probing the hydration water diffusion of macromolecular surfaces and interfaces

International Nuclear Information System (INIS)

Ortony, Julia H; Cheng, Chi-Yuan; Franck, John M; Pavlova, Anna; Hunt, Jasmine; Han, Songi; Kausik, Ravinath

2011-01-01

We probe the translational dynamics of the hydration water surrounding the macromolecular surfaces of selected polyelectrolytes, lipid vesicles and intrinsically disordered proteins with site specificity in aqueous solutions. These measurements are made possible by the recent development of a new instrumental and methodological approach based on Overhauser dynamic nuclear polarization (DNP)-enhanced nuclear magnetic resonance (NMR) spectroscopy. This technique selectively amplifies 1 H NMR signals of hydration water around a spin label that is attached to a molecular site of interest. The selective 1 H NMR amplification within molecular length scales of a spin label is achieved by utilizing short-distance range (∼r -3 ) magnetic dipolar interactions between the 1 H spin of water and the electron spin of a nitroxide radical-based label. Key features include the fact that only minute quantities (<10 μl) and dilute (≥100 μM) sample concentrations are needed. There is no size limit on the macromolecule or molecular assembly to be analyzed. Hydration water with translational correlation times between 10 and 800 ps is measured within ∼10 A distance of the spin label, encompassing the typical thickness of a hydration layer with three water molecules across. The hydration water moving within this time scale has significant implications, as this is what is modulated whenever macromolecules or molecular assemblies undergo interactions, binding or conformational changes. We demonstrate, with the examples of polymer complexation, protein aggregation and lipid-polymer interaction, that the measurements of interfacial hydration dynamics can sensitively and site specifically probe macromolecular interactions.

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

Thermal diffusivity measurement in thin metallic filaments using the mirage method with multiple probe beams and a digital camera

Science.gov (United States)

Vargas, E.; Cifuentes, A.; Alvarado, S.; Cabrera, H.; Delgado, O.; Calderón, A.; Marín, E.

2018-02-01

Photothermal beam deflection is a well-established technique for measuring thermal diffusivity. In this technique, a pump laser beam generates temperature variations on the surface of the sample to be studied. These variations transfer heat to the surrounding medium, which may be air or any other fluid. The medium in turn experiences a change in the refractive index, which will be proportional to the temperature field on the sample surface when the distance to this surface is small. A probe laser beam will suffer a deflection due to the refractive index periodical changes, which is usually monitored by means of a quadrant photodetector or a similar device aided by lock-in amplification. A linear relationship that arises in this technique is that given by the phase lag of the thermal wave as a function of the distance to a punctual heat source when unidimensional heat diffusion can be guaranteed. This relationship is useful in the calculation of the sample's thermal diffusivity, which can be obtained straightforwardly by the so-called slope method, if the pump beam modulation frequency is well-known. The measurement procedure requires the experimenter to displace the probe beam at a given distance from the heat source, measure the phase lag at that offset, and repeat this for as many points as desired. This process can be quite lengthy in dependence of the number points. In this paper, we propose a detection scheme, which overcomes this limitation and simplifies the experimental setup using a digital camera that substitutes all detection hardware utilizing motion detection techniques and software digital signal lock-in post-processing. In this work, the method is demonstrated using thin metallic filaments as samples.

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.

Diffusion properties of NAA in human corpus callosum as studied with diffusion tensor spectroscopy.

Science.gov (United States)

Upadhyay, Jaymin; Hallock, Kevin; Erb, Kelley; Kim, Dae-Shik; Ronen, Itamar

2007-11-01

In diffusion tensor imaging (DTI) the anisotropic movement of water is exploited to characterize microstructure. One confounding issue of DTI is the presence of intra- and extracellular components contributing to the measured diffusivity. This causes an ambiguity in determining the underlying cause of diffusion properties, particularly the fractional anisotropy (FA). In this study an intracellular constituent, N-acetyl aspartate (NAA), was used to probe intracellular diffusion, while water molecules were used to probe the combined intra- and extracellular diffusion. NAA and water diffusion measurements were made in anterior and medial corpus callosum (CC) regions, which are referred to as R1 and R2, respectively. FA(NAA) was found to be greater than FA(Water) in both CC regions, thus indicating a higher degree of anisotropy within the intracellular space in comparison to the combined intra- and extracellular spaces. A decreasing trend in the FA of NAA and water was observed between R1 and R2, while the radial diffusivity (RD) for both molecules increased. The increase in RD(NAA) is particularly significant, thus explaining the more significant decrease in FA(NAA) between the two regions. It is suggested that diffusion tensor spectroscopy of NAA can potentially be used to further characterize microscopic anatomic organization in white matter. Copyright 2007 Wiley-Liss, Inc.

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.

High efficiency diffusion molecular retention tumor targeting.

Directory of Open Access Journals (Sweden)

Yanyan Guo

Full Text Available Here we introduce diffusion molecular retention (DMR tumor targeting, a technique that employs PEG-fluorochrome shielded probes that, after a peritumoral (PT injection, undergo slow vascular uptake and extensive interstitial diffusion, with tumor retention only through integrin molecular recognition. To demonstrate DMR, RGD (integrin binding and RAD (control probes were synthesized bearing DOTA (for (111 In(3+, a NIR fluorochrome, and 5 kDa PEG that endows probes with a protein-like volume of 25 kDa and decreases non-specific interactions. With a GFP-BT-20 breast carcinoma model, tumor targeting by the DMR or i.v. methods was assessed by surface fluorescence, biodistribution of [(111In] RGD and [(111In] RAD probes, and whole animal SPECT. After a PT injection, both probes rapidly diffused through the normal and tumor interstitium, with retention of the RGD probe due to integrin interactions. With PT injection and the [(111In] RGD probe, SPECT indicated a highly tumor specific uptake at 24 h post injection, with 352%ID/g tumor obtained by DMR (vs 4.14%ID/g by i.v.. The high efficiency molecular targeting of DMR employed low probe doses (e.g. 25 ng as RGD peptide, which minimizes toxicity risks and facilitates clinical translation. DMR applications include the delivery of fluorochromes for intraoperative tumor margin delineation, the delivery of radioisotopes (e.g. toxic, short range alpha emitters for radiotherapy, or the delivery of photosensitizers to tumors accessible to light.

New resin gel for uranium determination by diffusive gradient in thin films technique

International Nuclear Information System (INIS)

Gregusova, Michaela; Docekal, Bohumil

2011-01-01

A new resin gel based on Spheron-Oxin chelating ion-exchanger with anchored 8-hydroxyquinoline functional groups was tested for application in diffusive gradient in thin film technique (DGT) for determination of uranium. Selectivity of uranium uptake from model carbonate loaded solutions of natural water was studied under laboratory conditions and compared with selectivity of the conventional Chelex 100 based resin gel. The affinity of Spheron-Oxin functional groups enables determination of the overall uranium concentration in water containing carbonates up to the concentration level of 10 2 mg L -1 . The effect of uranium binding to the polyacrylamide (APA) and agarose diffusive gels (AGE) was also studied. Uranium is probably bound in both gels by a weak interaction with traces of acrylic acid groups in the structure of APA gel and with pyruvic and sulfonic acid groups in the AGE gel. These sorption effects can be eliminated to the negligible level by prolonged deployment of DGT probes or by disassembling probes after the 1-2 days post-sampling period that is sufficient for release of uranium from diffusive gel and its sorption in resin gel.

New resin gel for uranium determination by diffusive gradient in thin films technique

Energy Technology Data Exchange (ETDEWEB)

Gregusova, Michaela, E-mail: gregusova@iach.cz [Institute of Analytical Chemistry, Academy of Sciences of the Czech Republic v.v.i., Veveri 97, 602 00 Brno (Czech Republic); Docekal, Bohumil [Institute of Analytical Chemistry, Academy of Sciences of the Czech Republic v.v.i., Veveri 97, 602 00 Brno (Czech Republic)

2011-01-17

A new resin gel based on Spheron-Oxin chelating ion-exchanger with anchored 8-hydroxyquinoline functional groups was tested for application in diffusive gradient in thin film technique (DGT) for determination of uranium. Selectivity of uranium uptake from model carbonate loaded solutions of natural water was studied under laboratory conditions and compared with selectivity of the conventional Chelex 100 based resin gel. The affinity of Spheron-Oxin functional groups enables determination of the overall uranium concentration in water containing carbonates up to the concentration level of 10{sup 2} mg L{sup -1}. The effect of uranium binding to the polyacrylamide (APA) and agarose diffusive gels (AGE) was also studied. Uranium is probably bound in both gels by a weak interaction with traces of acrylic acid groups in the structure of APA gel and with pyruvic and sulfonic acid groups in the AGE gel. These sorption effects can be eliminated to the negligible level by prolonged deployment of DGT probes or by disassembling probes after the 1-2 days post-sampling period that is sufficient for release of uranium from diffusive gel and its sorption in resin gel.

Analytic solutions to linear, time-dependent fission product deposition models for isothermal laminar, slug, or multiregion flow conditions

International Nuclear Information System (INIS)

Durkee, J.W. Jr.

1983-01-01

The time-dependent convective-diffusion equation with radioactive decay is solved analytically in axisymmetric cylindrical geometry for laminar and slug velocity profiles under isothermal conditions. Concentration dependent diffusion is neglected. The laminar flow solution is derived using the method of separation of variables and Frobenius' technique for constructing a series expansion about a regular singular point. The slug flow multiregion solution is obtained using the method of separation of variables. The Davidon Variable Metric Minimization algorithm is used to compute the coupling coefficients. These solutions, which describe the transport of fission products in a flowing stream, are then used to determine the concentration of radioactive material deposited on a conduit wall using a standard mass transfer model. Fission product deposition measurements for five diffusion tubes in a Fort St. Vrain High-Temperature Gas-Cooled reactor plateout probe are analyzed. Using single region slug and laminar models, the wall mass transfer coefficients, diffusion coefficients, and inlet concentrations are determined using least squares analysis. The diffusion coefficients and inlet concentrations are consistent between tubes. The derived diffusion coefficients and wall mass transfer coefficients are in relative agreement with known literature values

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

International Nuclear Information System (INIS)

Dong Lingzhen; Chen Lansun; Shi Peilin

2007-01-01

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

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

International Nuclear Information System (INIS)

Sun Wen; Chen Shihua; Hong Zhiming; Wang Changping

2007-01-01

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

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

International Nuclear Information System (INIS)

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

2005-01-01

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

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

International Nuclear Information System (INIS)

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

1997-01-01

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

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

International Nuclear Information System (INIS)

Correia Filho, A.

1981-04-01

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

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

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

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

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

Science.gov (United States)

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

2017-07-01

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

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

Science.gov (United States)

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

2018-07-01

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

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

International Nuclear Information System (INIS)

Lane, Taylor K; McClarren, Ryan G

2013-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-12-01

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

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.

FLUORESCENCE PROBING OF THE FORMATION OF HYDROPHOBIC MICRODOMAINS BY CROSS-LINKED POLY(ALKYLMETHYLDIALLYLAMMONIUM BROMIDES) IN AQUEOUS-SOLUTION

NARCIS (Netherlands)

WANG, GJ; ENGBERTS, J B F N

Pyrene has been used as a fluorescence probe to investigate the conformational behavior of cross-linked poly(alkylmethyldiallylammonium bromides) in aqueous solutions. Binding of pyrene to hydrophobic microdomains, formed by the polysoaps, is reflected by a change in the ratio I-1/I-3 of the

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 tensor optical coherence tomography

Science.gov (United States)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Measuring Restriction Sizes Using Diffusion Weighted Magnetic Resonance Imaging: A Review

Directory of Open Access Journals (Sweden)

Melanie Martin

2013-01-01

Full Text Available This article reviews a new concept in magnetic resonance as applied to cellular and biological systems. Diffusion weighted magnetic resonance imaging can be used to infer information about restriction sizes of samples being measured. The measurements rely on the apparent diffusion coefficient changing with diffusion times as measurements move from restricted to free diffusion regimes. Pulsed gradient spin echo (PGSE measurements are limited in the ability to shorten diffusion times and thus are limited in restriction sizes which can be probed. Oscillating gradient spin echo (OGSE measurements could provide shorter diffusion times so smaller restriction sizes could be probed.

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

Effects of oversized solutes on radiation-induced segregation in austenitic stainless steels

Science.gov (United States)

Hackett, M. J.; Busby, J. T.; Miller, M. K.; Was, G. S.

2009-06-01

Zirconium or hafnium additions to austenitic stainless steels caused a reduction in grain boundary Cr depletion after proton irradiations for up to 3 dpa at 400 °C and 1 dpa at 500 °C. The predictions of a radiation-induced segregation (RIS) model were also consistent with experiments in showing greater effectiveness of Zr relative to Hf due to a larger binding energy. However, the experiments showed that the effectiveness of the solute additions disappeared above 3 dpa at 400 °C and above 1 dpa at 500 °C. The loss of solute effectiveness with increasing dose is attributed to a reduction in the amount of oversized solute from the matrix due to growth of carbide precipitates. Atom probe tomography measurements indicated a reduction in amount of oversized solute in solution as a function of irradiation dose. The observations were supported by diffusion analysis suggesting that significant solute diffusion by the vacancy flux to precipitate surfaces occurs on the time scales of proton irradiations. With a decrease in available solute in solution, improved agreement between the predictions of the RIS model and measurements were consistent with the solute-vacancy trapping process, as the mechanism for enhanced recombination and suppression of RIS.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

Multigrid solution of diffusion equations on distributed memory multiprocessor systems

International Nuclear Information System (INIS)

Finnemann, H.

1988-01-01

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

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

International Nuclear Information System (INIS)

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

1977-01-01

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

A novel “Turn-On” fluorescent probe for F− detection in aqueous solution and its application in live-cell imaging

International Nuclear Information System (INIS)

Xu, Jian; Sun, Shaobo; Li, Qian; Yue, Ying; Li, Yingdong; Shao, Shijun

2014-01-01

Highlights: • A novel BODIPY-based “Turn-On” fluorescent probe was synthesized. • Highly selective detection of fluoride ions in 100% aqueous solution. • Study of sensing mechanism using density functional theory (DFT) calculations. • Fluorescent bioimaging of F − ion in A549 and ATII cells. - Abstract: A novel probe incorporating quaternized 4-pyridinium group into a BODIPY molecule was synthesized and studied for the selective detection of fluoride ions (F − ) in aqueous solution. The design was based on a fluoride-specific desilylation reaction and the “Turn-On” fluorescent response of probe 1 to F − was ascribed to the inhibition of photoinduced electron transfer (PET) process. The probe displayed many desired properties such as high specificity, appreciable solubility, desirable response time and low toxicity to mammalian cells. There was a good linearity between the fluorescence intensity and the concentrations of F − in the range of 0.1–1 mM with a detection limit of 0.02 mM. The sensing mechanism was confirmed by the NMR, electrospray ionization mass spectrum, optical spectroscopy and the mechanism of “Turn-On” fluorescent response was also determinated by a density functional theory (DFT) calculation using Gaussian 03 program. Moreover, the probe was successfully applied for the fluorescence imaging of F − in human epithelial lung cancer (A549) cells and alveolar type II (ATII) cells under physiological conditions

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.)

Electrochemical preparation of uranium and plutonium measuring probes for alpha spectroscopy from organic solutions

International Nuclear Information System (INIS)

Gruner, W.; Beutmann, A.

1980-01-01

A method for preparation of uranium and plutonium measuring probes for α-spectrometry is described. The method is based on electrodeposition from isopropanol and especially from ethanol and methanol solution. It was shown that a definite additions of a little amount of water lead to an increase of the deposition rate. It is possible to reach a 100% deposition in ethanol after an electrolysis time of 3 minutes for uranium and 30 minutes for plutonium with voltages of 150-200 V. (author)

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.

Laser interferometric method for determining the carrier diffusion length in semiconductors

Energy Technology Data Exchange (ETDEWEB)

Manukhov, V. V. [Saint Petersburg State University (Russian Federation); Fedortsov, A. B.; Ivanov, A. S., E-mail: ivaleks58@gmail.com [Saint Petersburg Mining University (Russian Federation)

2015-09-15

A new laser interferometric method for measuring the carrier diffusion length in semiconductors is proposed. The method is based on the interference–absorption interaction of two laser radiations in a semiconductor. Injected radiation generates additional carriers in a semiconductor, which causes a change in the material’s optical constants and modulation of the probing radiation passed through the sample. When changing the distance between carrier generation and probing points, a decrease in the carrier concentration, which depends on the diffusion length, is recorded. The diffusion length is determined by comparing the experimental and theoretical dependences of the probe signal on the divergence of the injector and probe beams. The method is successfully tested on semiconductor samples with different thicknesses and surface states and can be used in scientific research and the electronics industry.

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)

Direct imaging of thermally-activated grain-boundary diffusion in Cu/Co/IrMn/Pt exchange-bias structures using atom-probe tomography

Energy Technology Data Exchange (ETDEWEB)

Letellier, F.; Lardé, R.; Le Breton, J.-M., E-mail: jean-marie.lebreton@univ-rouen.fr [Groupe de Physique des Matériaux, UMR 6634 CNRS/Université et INSA de Rouen, F-76801 Saint Etienne du Rouvray (France); Lechevallier, L. [Groupe de Physique des Matériaux, UMR 6634 CNRS/Université et INSA de Rouen, F-76801 Saint Etienne du Rouvray (France); Département de GEII, Université de Cergy-Pontoise, F-95031 Cergy-Pontoise (France); Akmaldinov, K. [SPINTEC, Univ. Grenoble-Alpes/CNRS/INAC-CEA, F-38000 Grenoble (France); CROCUS Technology, F-38025 Grenoble (France); Auffret, S.; Dieny, B.; Baltz, V., E-mail: vincent.baltz@cea.fr [SPINTEC, Univ. Grenoble-Alpes/CNRS/INAC-CEA, F-38000 Grenoble (France)

2014-11-28

Magnetic devices are often subject to thermal processing steps, such as field cooling to set exchange bias and annealing to crystallize amorphous magnetic electrodes. These processing steps may result in interdiffusion and the subsequent deterioration of magnetic properties. In this study, we investigated thermally-activated diffusion in Cu/Co/IrMn/Pt exchange biased polycrystalline thin-film structures using atom probe tomography. Images taken after annealing at 400 °C for 60 min revealed Mn diffusion into Co grains at the Co/IrMn interface and along Pt grain boundaries for the IrMn/Pt stack, i.e., a Harrison type C regime. Annealing at 500 °C showed further Mn diffusion into Co grains. At the IrMn/Pt interface, annealing at 500 °C led to a type B behavior since Mn diffusion was detected both along Pt grain boundaries and also into Pt grains. The deterioration of the films' exchange bias properties upon annealing was correlated to the observed diffusion. In particular, the topmost Pt capping layer thickness turned out to be crucial since a faster deterioration of the exchange bias properties for thicker caps was observed. This is consistent with the idea that Pt acts as a getter for Mn, drawing Mn out of the IrMn layer.

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.

Quantitative assessment of diffuse optical tomography sensitivity to the cerebral cortex using a whole-head probe

International Nuclear Information System (INIS)

Perdue, Katherine L; Diamond, Solomon G; Fang Qianqian

2012-01-01

We quantify the variability in diffuse optical tomography (DOT) sensitivity over the cortical surface in eight young adult subjects. We use the 10/5 electroencephalography system as a basis for our whole-head optical high-density probe design. The contrast-to-noise ratio (CNR) is calculated along with the percentage of the cortex that is above a CNR = 0 dB threshold. We also quantify the effect of including vasculature on the forward model and list our assumptions that allow us to estimate light penetration depth in the head. We show that using the 10/5 system for the optical probe design allows for the measurement of 37% of the cortical surface on average, with a mean CNR in the visible region of 5.5 dB. Certain anatomical regions, such as the lateral occipital cortex, had a very high percentage above the CNR threshold, while other regions such as the cingulate cortex were not measurable. Vasculature blocked optical sensitivity over 1% of the cortex. Cortical coverage was positively correlated with intracranial volume and relative cerebrospinal fluid volume, and negatively correlated with relative scalp volume and skull volume. These contributions allow experimenters to understand how anatomical variation in a subject population may impact DOT or functional near-infrared spectroscopy measurements. (paper)

Higher-order tensors in diffusion imaging

NARCIS (Netherlands)

Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.

2014-01-01

Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion

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

International Nuclear Information System (INIS)

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

1984-01-01

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

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

International Nuclear Information System (INIS)

Mello, Kelen Berra de

2005-02-01

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

Internal magnetic probe data from ZT-40

International Nuclear Information System (INIS)

Burkhardt, L.C.; Phillips, J.A.

1981-05-01

Measurements of magnetic field distribution as a function of time and radius were made in ZT-40 with its ceramic vacuum vessel. Data were obtained with a 10-station, 20-coil magnetic probe, measuring the B/sub p/ and B/sub epsilon/ orthogonal field components in deuterium plasma discharges. Sheath formation and diffusion, magnetic axis location and motion, the effect of the probe on the plasma, and the consistency of flux measurements with external probes are examined

Can disc diffusion susceptibility tests assess the antimicrobial activity of engineered nanoparticles?

Science.gov (United States)

Kourmouli, Angeliki; Valenti, Marco; van Rijn, Erwin; Beaumont, Hubertus J. E.; Kalantzi, Olga-Ioanna; Schmidt-Ott, Andreas; Biskos, George

2018-03-01

The use of disc diffusion susceptibility tests to determine the antibacterial activity of engineered nanoparticles (ENPs) is questionable because their low diffusivity practically prevents them from penetrating through the culture media. In this study, we investigate the ability of such a test, namely the Kirby-Bauer disc diffusion test, to determine the antimicrobial activity of Au and Ag ENPs having diameters from 10 to 40 nm on Escherichia coli cultures. As anticipated, the tests did not show any antibacterial effects of Au nanoparticles (NPs) as a result of their negligible diffusivity through the culture media. Ag NPs on the other hand exhibited a strong antimicrobial activity that was independent of their size. Considering that Ag, in contrast to Au, dissolves upon oxidation and dilution in aqueous solutions, the apparent antibacterial behavior of Ag NPs is attributed to the ions they release. The Kirby-Bauer method, and other similar tests, can therefore be employed to probe the antimicrobial activity of ENPs related to their ability to release ions rather than to their unique size-dependent properties. [Figure not available: see fulltext.

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

Science.gov (United States)

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

2016-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-01-15

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

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.

Static pressure recovery analysis in the vane island diffuser of a centrifugal pump

Energy Technology Data Exchange (ETDEWEB)

Si, Qiaorui [National Research Center of Pumps, Jiangsu University, Zhenjiang (China); Dupont, Patrick; Bayeul-Laine, Annie-Claude; Dazin, Antoine; Roussette, Olivier; Bois, Gerard [LML, UMR CNRS 8107 Ecole Centrale de Lille, Lille (France)

2016-02-15

The overall performance of a vane-island type diffuser of a centrifugal pump model was obtained by means of directional probe traverses. These measurements were performed in an air model of a real hydraulic pump for five volume flow rates. Directional probe traverses are performed with a classical three-hole probe to cover most of the complete inlet section of the diffuser from hub to shroud and from pressure to suction side. Existing Particle image velocimetry (PIV) measurement results are also used to compare probe measurement results between the inlet and outlet throats of vane island diffuser at mid-span. Some assistance from already existing unsteady calculation, including leakage effects, is used to evaluate the numerical approach capability and to correctly define the mean initial conditions at impeller's outlet section. Pressure recovery and the measured total pressure loss levels inside this particular vane diffuser geometry are then calculated. Detailed analysis of the flow structure at the inlet section of the vane island diffuser is presented to focus on pressure evolution inside the entire diffuser section for different flow rates. The combined effects of incidence angle and blockage distributions along hub to shroud direction are found to play an important role on loss distribution in such a diffuser.

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

Characteristics of Plasma Probes in an MHD Working Fluid

Energy Technology Data Exchange (ETDEWEB)

Whitman, A. M.; Hsuan, Yeh [Towne School of Civil and Mechanical Engineering, University of Pennsylvania (United States)

1966-10-15

In this paper an attempt is made to formulate a theory of electrostatic probes in a high-pressure plasma in which an external electrical field may be imposed. Such a situation exists in high-pressure arc discharges and in MHD channels. First, it is shown that an adequate theory must include the ionization and recombination phenomena which were ignored in almost all previous theories. Secondly, due to the preferred direction induced by the presence of the electric field, the probe problem is no longer a symmetrical one. The analysis is based on the assumption that the three-body recombination and ionization is the dominant process. In a typical MHD working fluid, say an argon gas seeded with caesium at 2000 Degree-Sign K and one atmosphere of pressure, the penetration length I of ions and electrons, i.e. the distance that an ion or electron diffuses before recombination, is of the order of 10{sup -3} cm. (It is to be noted that ambipolar diffusion prevents the electrons from travelling much faster than the ions. ) We thus have a situation where Script-Small-L /L << 1, d/ Script-Small-L << 1, {lambda}/L <<1, and {lambda}/d >> 1, where L is the characteristic dimension of the probe {lambda} is the mean free path and d the Debye length. Because of the last condition, i. e, d << {lambda}, the space charge region is contained wholly in a ''free-falling'' zone in the immediate neighbourhood of the probe. Since, also, (d/ Script-Small-L ) << 1, the region outside of the ''free-falling'' zone is in a state of ''quasi-neutrality'', i.e. the number densities of electrons and ions are approximately equal. In this latter region, the mechanisms of diffusion and recombination are both important. The two regions must of course be matched at their connecting boundaries. Furthermore, the external boundary of the ''quasi-neutrality'' region must be matched to the discharge field. Using the approximations of the classical boundary layer theory, analytic solutions are obtained in

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.

Electronically tuned sulfonamide-based probes with ultra-sensitivity for Ga"3"+ or Al"3"+ detection in aqueous solution

International Nuclear Information System (INIS)

Kumar, Ashwani; Chae, Pil Seok

2017-01-01

Three electronically tuned fluorescent probes (1–3) were synthesized by conjugating a fluorescent unit to N,N-bis-(hydroxyethyl)ethylenediamine. Probe 1 bearing an electron-deficient naphthalenedimide unit did not give a fluorescence response to the presence of various metal ions including monovalent metal ions (Na"+, K"+, and Ag"+), divalent metal ions (Ca"2"+, Cd"2"+, Co"2"+, Ni"2"+, Cu"2"+, Hg"2"+, Pb"2"+, and Zn"2"+) and trivalent metal ions (Al"3"+, Ga"3"+, Fe"3"+, and Cr"3"+) in an aqueous solution. By contrast, probes 2 and 3 possessing 1,8-naphthalimide and pyrene fluorophores, respectively, exhibited selective fluorescent “OFF-ON” behaviors as a result of Ga"3"+/Al"3"+ binding among the diverse metal ions, suggesting the importance of fluorophore electronic character with regard to metal ion sensing. The ethylenediamine analog of probe 3, corresponding to probe 4, was unable to yield a significant change in fluorescence intensity in the presence of any metal ions tested here, revealing the essential role of two hydroxyl groups for metal ion binding. A high association constant of K_a = 2.99 × 10"5 M"−"1 was obtained for probe 3 with Ga"3"+, with a limit of detection (LOD) of 10 nM. This LOD is the lowest value known for Ga"3"+ detection using chemical sensors. Along with an increase in aggregate sizes, PET suppression of probes upon metal ion binding was the primary contributor to the enhancement in fluorescence emission necessary for the sensitive detection of the target ions. The probe-metal ion complexes were fully characterized via TEM, FE-SEM, "1H NMR, fluorescence spectroscopy techniques and DFT calculations. - Highlights: • Three electronically tuned sulfonamide-based probes (probes 1, 2, and 3) were developed for metal ion-sensing. • Probes 2 and 3 exhibited AIE behavior with increasing water-content. • Probes 2 and 3 displayed a selective fluorescence “OFF-ON“ behavior for Ga"3"+ detection with the LOD of 10 nM. • PET

Absolute and direct microRNA quantification using DNA-gold nanoparticle probes.

Science.gov (United States)

Degliangeli, Federica; Kshirsagar, Prakash; Brunetti, Virgilio; Pompa, Pier Paolo; Fiammengo, Roberto

2014-02-12

DNA-gold nanoparticle probes are implemented in a simple strategy for direct microRNA (miRNA) quantification. Fluorescently labeled DNA-probe strands are immobilized on PEGylated gold nanoparticles (AuNPs). In the presence of target miRNA, DNA-RNA heteroduplexes are formed and become substrate for the endonuclease DSN (duplex-specific nuclease). Enzymatic hydrolysis of the DNA strands yields a fluorescence signal due to diffusion of the fluorophores away from the gold surface. We show that the molecular design of our DNA-AuNP probes, with the DNA strands immobilized on top of the PEG-based passivation layer, results in nearly unaltered enzymatic activity toward immobilized heteroduplexes compared to substrates free in solution. The assay, developed in a real-time format, allows absolute quantification of as little as 0.2 fmol of miR-203. We also show the application of the assay for direct quantification of cancer-related miR-203 and miR-21 in samples of extracted total RNA from cell cultures. The possibility of direct and absolute quantification may significantly advance the use of microRNAs as biomarkers in the clinical praxis.

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

Energy Technology Data Exchange (ETDEWEB)

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

2004-07-01

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

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

International Nuclear Information System (INIS)

Sato, Haruo

2001-01-01

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

A novel “Turn-On” fluorescent probe for F{sup −} detection in aqueous solution and its application in live-cell imaging

Energy Technology Data Exchange (ETDEWEB)

Xu, Jian [Key Laboratory of Chemistry of Northwestern Plant Resources and Key Laboratory for Natural Medicine of Gansu Province, Lanzhou institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); University of Chinese Academy of Sciences, Beijing 100039 (China); Sun, Shaobo [Institute of Integrated Traditional and Western Medicine, Gansu University of Chinese Medicine, Lanzhou 730000 (China); Li, Qian; Yue, Ying [Key Laboratory of Chemistry of Northwestern Plant Resources and Key Laboratory for Natural Medicine of Gansu Province, Lanzhou institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); Li, Yingdong [Institute of Integrated Traditional and Western Medicine, Gansu University of Chinese Medicine, Lanzhou 730000 (China); Shao, Shijun, E-mail: sjshao@licp.cas.cn [Key Laboratory of Chemistry of Northwestern Plant Resources and Key Laboratory for Natural Medicine of Gansu Province, Lanzhou institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)

2014-11-07

Highlights: • A novel BODIPY-based “Turn-On” fluorescent probe was synthesized. • Highly selective detection of fluoride ions in 100% aqueous solution. • Study of sensing mechanism using density functional theory (DFT) calculations. • Fluorescent bioimaging of F{sup −} ion in A549 and ATII cells. - Abstract: A novel probe incorporating quaternized 4-pyridinium group into a BODIPY molecule was synthesized and studied for the selective detection of fluoride ions (F{sup −}) in aqueous solution. The design was based on a fluoride-specific desilylation reaction and the “Turn-On” fluorescent response of probe 1 to F{sup −} was ascribed to the inhibition of photoinduced electron transfer (PET) process. The probe displayed many desired properties such as high specificity, appreciable solubility, desirable response time and low toxicity to mammalian cells. There was a good linearity between the fluorescence intensity and the concentrations of F{sup −} in the range of 0.1–1 mM with a detection limit of 0.02 mM. The sensing mechanism was confirmed by the NMR, electrospray ionization mass spectrum, optical spectroscopy and the mechanism of “Turn-On” fluorescent response was also determinated by a density functional theory (DFT) calculation using Gaussian 03 program. Moreover, the probe was successfully applied for the fluorescence imaging of F{sup −} in human epithelial lung cancer (A549) cells and alveolar type II (ATII) cells under physiological conditions.

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

A highly selective turn-on fluorescent probe for Al3+ in aqueous solution based on quinoline Schiff-base

Science.gov (United States)

Huang, Peng-Cheng; Fang, Hao; Xiong, Jing-Jing; Wu, Fang-Ying

2017-06-01

A new Al3+-specific fluorescent probe NQ was designed and synthesized from 2-hydroxy-1-naphthaldehyde and 2-aminoquinoline. Upon the addition of Al3+, the fluorescent intensity of NQ was significantly enhanced compared with other examined metal ions in aqueous solution. The result of a Job’s plot indicated the formation of a 1:1 complex between the probe and Al3+, and the possible binding mode of the system between NQ and Al3+ was clarified by IR analysis and 1H NMR titration. Moreover, other metal ions examined had little effect on the detection of Al3+. The detection limit of NQ for Al3+ detection was 1.98 μM, which is lower than the level (7.4 μM) in drinking water defined by the World Health Organization. In addition, the fluorescent probe NQ could be recyclable simply through treatment with a proper reagent such as F-, and could also be used for the detection of Al3+ in real samples.

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...

Diffusion phenomena in polycrystalline chromium near the upper homological temperature of intercrystalline diffusion manifestation

International Nuclear Information System (INIS)

Kajgorodov, V.N.; Klothman, S.M.; Kurkin, M.I.; Dyakin, V.V.; Zherebthov, D.V.

1997-01-01

A study is made into the temperature dependences of density of states in a zone of intercrystalline diffusion of atomic probes 57 Co in polycrystalline chromium as well as in the temperature dependences of isomer shift and line width in Moessbauer spectra near the upper temperature boundary of manifestation of intercrystalline diffusion. In polycrystalline chromium the release of states in the core of the crystallite conjugation region (CCR) takes place only at high temperatures due to the fact that a stationary zone of high point defect concentration in the vicinity of CCR is conserved up to high temperatures. The atomic probe escape from the core of CCR starts at the temperatures at which the equilibrium vacancy concentration in the bulk of crystallite is equal to that in a stationary zone of high defect concentration

Probing skin interaction with hydrogen peroxide using diffuse reflectance spectroscopy

International Nuclear Information System (INIS)

Zonios, George; Dimou, Aikaterini; Galaris, Dimitrios

2008-01-01

Hydrogen peroxide is an important oxidizing agent in biological systems. In dermatology, it is frequently used as topical antiseptic, it has a haemostatic function, it can cause skin blanching, and it can facilitate skin tanning. In this work, we investigated skin interaction with hydrogen peroxide, non-invasively, using diffuse reflectance spectroscopy. We observed transient changes in the oxyhaemoglobin and deoxyhaemoglobin concentrations as a result of topical application of dilute H 2 O 2 solutions to the skin, with changes in deoxyhaemoglobin concentration being more pronounced. Furthermore, we did not observe any appreciable changes in melanin absorption properties as well as in the skin scattering properties. We also found no evidence for production of oxidized haemoglobin forms. Our observations are consistent with an at least partial decomposition of hydrogen peroxide within the stratum corneum and epidermis, with the resulting oxygen and/or remaining hydrogen peroxide inducing vasoconstriction to dermal blood vessels and increasing haemoglobin oxygen saturation. An assessment of the effects of topical application of hydrogen peroxide to the skin may serve as the basis for the development of non-invasive techniques to measure skin antioxidant capacity and also may shed light onto skin related disorders such as vitiligo

Solute-solute interactions in intermetallic compounds

Energy Technology Data Exchange (ETDEWEB)

Banerjee, Debashis; Murray, Ryan; Collins, Gary S., E-mail: collins@wsu.edu [Washington State University, Department of Physics and Astronomy (United States); Zacate, Matthew O. [Northern Kentucky University, Department of Physics and Geology (United States)

2017-11-15

Experiments were carried out on highly ordered GdAl{sub 2} samples containing extremely dilute mole fractions of{sup 111}In/Cd probe-atom solutes (about 10{sup −11}), intrinsic antisite atoms Al{sub Gd} having mole fractions of order 0-10{sup −2}, and doped with Ag solutes at mole fractions of order 10{sup −2}. Three types of defect interactions were investigated. (1) Quadrupole interactions caused by Ag-solute atoms neighboring{sup 111}In/Cd solute probe atoms were detected using the method of perturbed angular correlation of gamma rays (PAC). Three complexes of pairs of In-probes and Ag-solutes occupying neighboring positions on Gd- and Al-sublattices were identified by comparing site fractions in Gd-poor and Gd-rich GdAl{sub 2}(Ag) samples and from the symmetry of the quadrupole interactions. Interaction enthalpies between solute-atom pairs were determined from temperature dependences of observed site fractions. Repulsive interactions were observed for close-neighbor complexes In{sub Gd}+Ag{sub Gd} and In{sub Gd}+Ag{sub Al} pairs, whereas a slightly attractive interaction was observed for In{sub Al}+Ag{sub Al}. Interaction enthalpies were all small, in the range ±0.15 eV. (2) Quadrupole interactions caused by intrinsic antisite atoms Al{sub Gd} neighboring In{sub Gd} probes were also detected and site fractions measured as a function of temperature, as in previous work on samples not doped with Ag-solutes [Temperature- and composition-driven changes in site occupation of solutes in Gd{sub 1+3x}Al{sub 2−3x}, Zacate and Collins (Phys. Rev. B69, 174202 (1))]. However, the effective binding enthalpy between In{sub Gd} probe and Al{sub Gd} antisite was found to change sign from -0.12 eV (attractive interaction) in undoped samples to + 0.24 eV (repulsive) in Ag-doped samples. This may be attributed to an attractive interaction between Al{sub Gd} antisite atoms and Ag-dopants that competes with the attractive interaction between In{sub Gd} and Al{sub Gd

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.

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.

Measurement of the local particle diffusion coefficient in a magnetized plasma

International Nuclear Information System (INIS)

Meyerhofer, D.D.; Levinton, F.M.

1987-02-01

Local impurity particle diffusion coefficients have been measured in a low temperature plasma by the injection of test particles at the center of the plasma. The injection is accomplished by a high voltage discharge between two small graphite electrodes on a probe. The probe can be located anywhere in the plasma. The diffusion is observed spectroscopically. An analysis of the spatial and temporal evolution of the CII radiation from the carbon discharge can determine the parallel and perpendicular diffusion of the impurity ions. Results with the diagnostic have been obtained in the Proto S-1/C spheromak. The measured value of the diffusion coefficient in the afterglow plasma is in good agreement with classical predictions

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.

Study of the Conformational State of Non-Cross-Linked and Cross-Linked Poly(alkylmethyldiallylammonium chlorides) in Aqueous Solution by Fluorescence Probing

NARCIS (Netherlands)

Wang, Guang-Jia; Engberts, Jan B.F.N.

The aggregation behaviour of novel non-cross-linked and cross-linked poly(alkylmethyldiallylammonium chlorides) in aqueous solutions has been investigated by fluorescence spectroscopy using pyrene as a probe. These copolymers were found to exhibit similar aggregate properties as the corresponding

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.)

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.

Probing ion-specific effects on aqueous acetate solutions: Ion pairing versus water structure modifications.

Science.gov (United States)

Petit, Tristan; Lange, Kathrin M; Conrad, Gerrit; Yamamoto, Kenji; Schwanke, Christoph; Hodeck, Kai F; Dantz, Marcus; Brandenburg, Tim; Suljoti, Edlira; Aziz, Emad F

2014-05-01

The effect of monovalent cations (Li(+), K(+), NH4 (+), Na(+)) on the water structure in aqueous chloride and acetate solutions was characterized by oxygen K-edge X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy, and resonant inelastic X-ray scattering (RIXS) of a liquid microjet. We show ion- and counterion dependent effects on the emission spectra of the oxygen K-edge, which we attribute to modifications of the hydrogen bond network of water. For acetates, ion pairing with carboxylates was also probed selectively by XAS and RIXS. We correlate our experimental results to speciation data and to the salting-out properties of the cations.

Probing ion-specific effects on aqueous acetate solutions: Ion pairing versus water structure modifications

Directory of Open Access Journals (Sweden)

Tristan Petit

2014-05-01

Full Text Available The effect of monovalent cations (Li+, K+, NH4+, Na+ on the water structure in aqueous chloride and acetate solutions was characterized by oxygen K-edge X-ray absorption spectroscopy (XAS, X-ray emission spectroscopy, and resonant inelastic X-ray scattering (RIXS of a liquid microjet. We show ion- and counterion dependent effects on the emission spectra of the oxygen K-edge, which we attribute to modifications of the hydrogen bond network of water. For acetates, ion pairing with carboxylates was also probed selectively by XAS and RIXS. We correlate our experimental results to speciation data and to the salting-out properties of the cations.

Mercury Amalgam Diffusion in Human Teeth Probed Using Femtosecond LIBS.

Science.gov (United States)

Bello, Liciane Toledo; da Ana, Patricia Aparecida; Santos, Dário; Krug, Francisco José; Zezell, Denise Maria; Vieira, Nilson Dias; Samad, Ricardo Elgul

2017-04-01

In this work the diffusion of mercury and other elements from amalgam tooth restorations through the surrounding dental tissue (dentin) was evaluated using femtosecond laser-induced breakdown spectroscopy (fs-LIBS). To achieve this, seven deciduous and eight permanent extracted human molar teeth with occlusal amalgam restorations were half-sectioned and analyzed using pulses from a femtosecond laser. The measurements were performed from the amalgam restoration along the amalgam/dentin interface to the apical direction. It was possible to observe the presence of metallic elements (silver, mercury, copper and tin) emission lines, as well as dental constituent ones, providing fingerprints of each material and comparable data for checking the consistence of the results. It was also shown that the elements penetration depth values in each tooth are usually similar and consistent, for both deciduous and permanent teeth, indicating that all the metals diffuse into the dentin by the same mechanism. We propose that this diffusion mechanism is mainly through liquid dragging inside the dentin tubules. The mercury diffused further in permanent teeth than in deciduous teeth, probably due to the longer diffusion times due to the age of the restorations. It was possible to conclude that the proposed femtosecond-LIBS system can detect the presence of metals in the dental tissue, among the tooth constituent elements, and map the distribution of endogenous and exogenous chemical elements, with a spatial resolution that can be brought under 100 µm.

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

Look fast: Crystallization of conjugated molecules during solution shearing probed in-situ and in real time by X-ray scattering

KAUST Repository

Smilgies, Detlef Matthias

2012-12-20

High-speed solution shearing, in which a drop of dissolved material is spread by a coating knife onto the substrate, has emerged as a versatile, yet simple coating technique to prepare high-mobility organic thin film transistors. Solution shearing and subsequent drying and crystallization of a thin film of conjugated molecules is probed in situ using microbeam grazing incidence wide-angle X-ray scattering (μGIWAXS). We demonstrate the advantages of this approach to study solution based crystal nucleation and growth, and identify casting parameter combinations to cast highly ordered and laterally aligned molecular thin films. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Look fast: Crystallization of conjugated molecules during solution shearing probed in-situ and in real time by X-ray scattering

KAUST Repository

Smilgies, Detlef Matthias; Li, Ruipeng; Giri, Gaurav; Chou, Kang Wei; Diao, Ying; Bao, Zhenan; Amassian, Aram

2012-01-01

High-speed solution shearing, in which a drop of dissolved material is spread by a coating knife onto the substrate, has emerged as a versatile, yet simple coating technique to prepare high-mobility organic thin film transistors. Solution shearing and subsequent drying and crystallization of a thin film of conjugated molecules is probed in situ using microbeam grazing incidence wide-angle X-ray scattering (μGIWAXS). We demonstrate the advantages of this approach to study solution based crystal nucleation and growth, and identify casting parameter combinations to cast highly ordered and laterally aligned molecular thin films. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

Science.gov (United States)

Ernst, Dominique; Köhler, Jürgen; Weiss, Matthias

2014-05-07

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

Differential Mobility Spectrometry-Hydrogen Deuterium Exchange (DMS-HDX) as a Probe of Protein Conformation in Solution.

Science.gov (United States)

Zhu, Shaolong; Campbell, J Larry; Chernushevich, Igor; Le Blanc, J C Yves; Wilson, Derek J

2016-06-01

Differential mobility spectrometry (DMS) is an ion mobility technique that has been adopted chiefly as a pre-filter for small- to medium-sized analytes (DMS-field asymmetric waveform ion mobility spectroscopy (FAIMS)-the application of DMS to intact biomacromolecules remains largely unexplored. In this work, we employ DMS combined with gas-phase hydrogen deuterium exchange (DMS-HDX) to probe the gas-phase conformations generated from proteins that were initially folded, partially-folded, and unfolded in solution. Our findings indicate that proteins with distinct structural features in solution exhibit unique deuterium uptake profiles as function of their optimal transmission through the DMS. Ultimately we propose that DMS-HDX can, if properly implemented, provide rapid measurements of liquid-phase protein structural stability that could be of use in biopharmaceuticals development. Graphical Abstract ᅟ.

More on Probing Branes with Branes

OpenAIRE

Brandhuber, A.; Itzhaki, N.; Sonnenschein, J.; Yankielowicz, S.

1997-01-01

We generalize the Gibbons-Wiltshire solution of four dimensional Kaluza-Klein black holes in order to describe Type IIA solutions of bound states of D6 and D0-branes. We probe the solutions with a D6-brane and a D0-brane. We also probe a system of D2+D0-branes and of a D2-brane bound to a F1-string with a D2-brane. A precise agreement between the SYM and the SUGRA calculations is found for the static force as well as for the $v^2$ force in all cases.

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.

Probing skin interaction with hydrogen peroxide using diffuse reflectance spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Zonios, George [Department of Materials Science and Engineering, University of Ioannina, 45110 Ioannina (Greece); Dimou, Aikaterini [Department of Materials Science and Engineering, University of Ioannina, 45110 Ioannina (Greece); Galaris, Dimitrios [Laboratory of Biological Chemistry, School of Medicine, University of Ioannina, 45110 Ioannina (Greece)

2008-01-07

Hydrogen peroxide is an important oxidizing agent in biological systems. In dermatology, it is frequently used as topical antiseptic, it has a haemostatic function, it can cause skin blanching, and it can facilitate skin tanning. In this work, we investigated skin interaction with hydrogen peroxide, non-invasively, using diffuse reflectance spectroscopy. We observed transient changes in the oxyhaemoglobin and deoxyhaemoglobin concentrations as a result of topical application of dilute H{sub 2}O{sub 2} solutions to the skin, with changes in deoxyhaemoglobin concentration being more pronounced. Furthermore, we did not observe any appreciable changes in melanin absorption properties as well as in the skin scattering properties. We also found no evidence for production of oxidized haemoglobin forms. Our observations are consistent with an at least partial decomposition of hydrogen peroxide within the stratum corneum and epidermis, with the resulting oxygen and/or remaining hydrogen peroxide inducing vasoconstriction to dermal blood vessels and increasing haemoglobin oxygen saturation. An assessment of the effects of topical application of hydrogen peroxide to the skin may serve as the basis for the development of non-invasive techniques to measure skin antioxidant capacity and also may shed light onto skin related disorders such as vitiligo.

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

Study on diffusion anisotropy of cerebral ischemia using diffusion weighted echo-planar MRI

International Nuclear Information System (INIS)

Kajima, Toshio

1997-01-01

Focal cerebral ischemia was produced by occlusion of the intracranial main cerebral artery with a silicone cylinder in Wistar rats. Diffusion-weighted echo-planar images (DW-EPls) using the motion-probing gradient (MPG) method were acquired at 1-3 hours and 24-48 hours after occlusion. Apparent diffusion coefficients (ADCs) were calculated from these images in ischemic lesions and in normal unoccluded regions. Results were as follows. Ischemic lesions could be detected on the DW-EPIs at 1 hour after occlusion. The ADC of water in the brain tissue was smaller than that of free water as a result of restricted diffusion. Anisotropic diffusion that probably can be attributed to the myelin sheath was observed in the normal white matter. In the ischemic lesions, the ADC decreased rapidly within 1-3 hours after occlusion and then decreased gradually after 24-48 hours. In the ischemic white matter, diffusion anisotropy disappeared at 24-48 hours after occlusion. Diffusion-weighted imaging may have applications in the examination of pathophysiological mechanisms in cerebral ischemia by means of evaluation of ADC and diffusion anisotropy. (author)

33S NMR cryogenic probe for taurine detection

Science.gov (United States)

Hobo, Fumio; Takahashi, Masato; Maeda, Hideaki

2009-03-01

With the goal of a S33 nuclear magnetic resonance (NMR) probe applicable to in vivo NMR on taurine-biological samples, we have developed the S33 NMR cryogenic probe, which is applicable to taurine solutions. The NMR sensitivity gain relative to a conventional broadband probe is as large as 3.5. This work suggests that improvements in the preamplifier could allow NMR measurements on 100 μM taurine solutions, which is the level of sensitivity necessary for biological samples.

The Effect of a Fluorophore Photo-Physics on the Lipid Vesicle Diffusion Coefficient Studied by Fluorescence Correlation Spectroscopy.

Science.gov (United States)

Drabik, Dominik; Przybyło, Magda; Sikorski, Aleksander; Langner, Marek

2016-03-01

Fluorescence Correlation Spectroscopy (FCS) is a technique, which allows determination of the diffusion coefficient and concentration of fluorescent objects suspended in the solution. The measured parameter is the fluctuation of the fluorescence signal emitted by diffusing molecules. When 100 nm DOPC vesicles labeled with various fluorescent dyes (Fluorescein-PE, NBD-PE, Atto488 DOPE or βBodipy FL) were measured, different values of diffusion coefficients have been obtained. These diffusion coefficients were different from the expected values measured using the dynamic light scattering method (DLS). The FCS was initially developed for solutions containing small fluorescent molecules therefore the observed inconsistency may result from the nature of vesicle suspension itself. The duration of the fluorescence signal may depend on the following factors: the exposure time of the labeled object to the excitation beam, the photo-physical properties (e.g., stability) of a fluorophore, the theoretical model used for the calculations of the diffusion coefficient and optical properties of the vesicle suspension. The diffusion coefficients determined for differently labeled liposomes show that its dependence on vesicle size and quantity of fluorescent probed used for labeling was significant demonstrating that the fluorescence properties of the fluorophore itself (bleaching and/or blinking) were critical factors for a correct outcome of FCS experiment. The new, based on combined FCS and DLS measurements, method for the determination of the focal volume prove itself to be useful for the evaluation of a fluorescence dye with respect to its applicability for FCS experiment.

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)

Pulsed-laser atom-probe field-ion microscopy

International Nuclear Information System (INIS)

Kellogg, G.L.; Tsong, T.T.

1980-01-01

A time-of-flight atom-probe field-ion microscope has been developed which uses nanosecond laser pulses to field evaporate surface species. The ability to operate an atom-probe without using high-voltage pulses is advantageous for several reasons. The spread in energy arising from the desorption of surface species prior to the voltage pulse attaining its maximum amplitude is eliminated, resulting in increased mass resolution. Semiconductor and insulator samples, for which the electrical resistivity is too high to transmit a short-duration voltage pulse, can be examined using pulsed-laser assisted field desorption. Since the electric field at the surface can be significantly smaller, the dissociation of molecular adsorbates by the field can be reduced or eliminated, permitting well-defined studies of surface chemical reactions. In addition to atom-probe operation, pulsed-laser heating of field emitters can be used to study surface diffusion of adatoms and vacancies over a wide range of temperatures. Examples demonstrating each of these advantages are presented, including the first pulsed-laser atom-probe (PLAP) mass spectra for both metals (W, Mo, Rh) and semiconductors (Si). Molecular hydrogen, which desorbs exclusively as atomic hydrogen in the conventional atom probe, is shown to desorb undissociatively in the PLAP. Field-ion microscope observations of the diffusion and dissociation of atomic clusters, the migration of adatoms, and the formation of vacancies resulting from heating with a 7-ns laser pulse are also presented

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.

PEGylated Red-Emitting Calcium Probe with Improved Sensing Properties for Neuroscience.

Science.gov (United States)

Ponsot, Flavien; Shen, Weida; Ashokkumar, Pichandi; Audinat, Etienne; Klymchenko, Andrey S; Collot, Mayeul

2017-11-22

Monitoring calcium concentration in the cytosol is of main importance as this ion drives many biological cascades within the cell. To this end, molecular calcium probes are widely used. Most of them, especially the red emitting probes, suffer from nonspecific interactions with inner membranes due to the hydrophobic nature of their fluorophore. To circumvent this issue, calcium probes conjugated to dextran can be used to enhance the hydrophilicity and reduce the nonspecific interaction and compartmentalization. However, dextran conjugates also feature important drawbacks including lower affinity, lower dynamic range, and slow diffusion. Herein, we combined the advantage of molecular probes and dextran conjugate without their drawbacks by designing a new red emitting turn-on calcium probe based on PET quenching, Rhod-PEG, in which the rhodamine fluorophore bears four PEG 4 units. This modification led to a high affinity calcium probe (K d = 748 nM) with reduced nonspecific interactions, enhanced photostability, two-photon absorbance, and brightness compared to the commercially available Rhod-2. After spectral characterizations, we showed that Rhod-PEG quickly and efficiently diffused through the dendrites of pyramidal neurons with an enhanced sensitivity (ΔF/F 0 ) at shorter time after patching compared to Rhod-2.

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)

Interdiffusion, Intrinsic Diffusion, Atomic Mobility, and Vacancy Wind Effect in γ(bcc) Uranium-Molybdenum Alloy

Science.gov (United States)

Huang, Ke; Keiser, Dennis D.; Sohn, Yongho

2013-02-01

U-Mo alloys are being developed as low enrichment uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. In order to understand the fundamental diffusion behavior of this system, solid-to-solid pure U vs Mo diffusion couples were assembled and annealed at 923 K, 973 K, 1073 K, 1173 K, and 1273 K (650 °C, 700 °C, 800 °C, 900 °C, and 1000 °C) for various times. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy and electron probe microanalysis, respectively. As the Mo concentration increased from 2 to 26 at. pct, the interdiffusion coefficient decreased, while the activation energy increased. A Kirkendall marker plane was clearly identified in each diffusion couple and utilized to determine intrinsic diffusion coefficients. Uranium intrinsically diffused 5-10 times faster than Mo. Molar excess Gibbs free energy of U-Mo alloy was applied to calculate the thermodynamic factor using ideal, regular, and subregular solution models. Based on the intrinsic diffusion coefficients and thermodynamic factors, Manning's formalism was used to calculate the tracer diffusion coefficients, atomic mobilities, and vacancy wind parameters of U and Mo at the marker composition. The tracer diffusion coefficients and atomic mobilities of U were about five times larger than those of Mo, and the vacancy wind effect increased the intrinsic flux of U by approximately 30 pct.

Tuning crystalline ordering by annealing and additives to study its effect on exciton diffusion in a polyalkylthiophene copolymer.

Science.gov (United States)

Chowdhury, Mithun; Sajjad, Muhammad T; Savikhin, Victoria; Hergué, Noémie; Sutija, Karina B; Oosterhout, Stefan D; Toney, Michael F; Dubois, Philippe; Ruseckas, Arvydas; Samuel, Ifor D W

2017-05-17

The influence of various processing conditions on the singlet exciton diffusion is explored in films of a conjugated random copolymer poly-(3-hexylthiophene-co-3-dodecylthiophene) (P3HT-co-P3DDT) and correlated with the degree of crystallinity probed by grazing incidence X-ray scattering and with exciton bandwidth determined from absorption spectra. The exciton diffusion coefficient is deduced from exciton-exciton annihilation measurements and is found to increase by more than a factor of three when thin films are annealed using CS 2 solvent vapour. A doubling of exciton diffusion coefficient is observed upon melt annealing at 200 °C and the corresponding films show about 50% enhancement in the degree of crystallinity. In contrast, films fabricated from polymer solutions containing a small amount of either solvent additive or nucleating agent show a decrease in exciton diffusion coefficient possibly due to formation of traps for excitons. Our results suggest that the enhancement of exciton diffusivity occurs because of increased crystallinity of alkyl-stacking and longer conjugation of aggregated chains which reduces the exciton bandwidth.

Monitoring probe for groundwater flow

Science.gov (United States)

Looney, B.B.; Ballard, S.

1994-08-23

A monitoring probe for detecting groundwater migration is disclosed. The monitor features a cylinder made of a permeable membrane carrying an array of electrical conductivity sensors on its outer surface. The cylinder is filled with a fluid that has a conductivity different than the groundwater. The probe is placed in the ground at an area of interest to be monitored. The fluid, typically saltwater, diffuses through the permeable membrane into the groundwater. The flow of groundwater passing around the permeable membrane walls of the cylinder carries the conductive fluid in the same general direction and distorts the conductivity field measured by the sensors. The degree of distortion from top to bottom and around the probe is precisely related to the vertical and horizontal flow rates, respectively. The electrical conductivities measured by the sensors about the outer surface of the probe are analyzed to determine the rate and direction of the groundwater flow. 4 figs.

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

Fiber-based hybrid probe for non-invasive cerebral monitoring in neonatology

Science.gov (United States)

Rehberger, Matthias; Giovannella, Martina; Pagliazzi, Marco; Weigel, Udo; Durduran, Turgut; Contini, Davide; Spinelli, Lorenzo; Pifferi, Antonio; Torricelli, Alessandro; Schmitt, Robert

2015-07-01

Improved cerebral monitoring systems are needed to prevent preterm infants from long-term cognitive and motor restrictions. Combining advanced near-infrared diffuse spectroscopy measurement technologies, time-resolved spectroscopy (TRS) and diffuse correlation spectroscopy (DCS) will introduce novel indicators of cerebral oxygen metabolism and blood flow for neonatology. For non-invasive sensing a fiber-optical probe is used to send and receive light from the infant head. In this study we introduce a new fiber-based hybrid probe that is designed for volume production. The probe supports TRS and DCS measurements in a cross geometry, thus both technologies gain information on the same region inside the tissue. The probe is highly miniaturized to perform cerebral measurements on heads of extreme preterm infants down to head diameters of 6cm. Considerations concerning probe production focus on a reproducible accuracy in shape and precise optical alignment. In this way deviations in measurement data within a series of probes should be minimized. In addition to that, requirements for clinical use like robustness and hygiene are considered. An additional soft-touching sleeve made of FDA compatible silicone allows for a flexible attachment with respect to the individual anatomy of each patient. We present the technical concept of the hybrid probe and corresponding manufacturing methods. A prototype of the probe is shown and tested on tissue phantoms as well as in vivo to verify its operational reliability.

Probing the photoluminescence properties of gold nanoclusters by fluorescence lifetime correlation spectroscopy

International Nuclear Information System (INIS)

Yuan, C. T.; Lin, T. N.; Shen, J. L.; Lin, C. A.; Chang, W. H.; Cheng, H. W.; Tang, J.

2013-01-01

Gold nanoclusters (Au NCs) have attracted much attention for promising applications in biological imaging owing to their tiny sizes and biocompatibility. So far, most efforts have been focused on the strategies for fabricating high-quality Au NCs and then characterized by conventional ensemble measurement. Here, a fusion single-molecule technique combining fluorescence correlation spectroscopy and time-correlated single-photon counting can be successfully applied to probe the photoluminescence (PL) properties for sparse Au NCs. In this case, the triplet-state dynamics and diffusion process can be observed simultaneously and the relevant time constants can be derived. This work provides a complementary insight into the PL mechanism at the molecular levels for Au NCs in solution

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

Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue

DEFF Research Database (Denmark)

Nielsen, Jonathan Scharff; Dyrby, Tim B; Lundell, Henrik

2018-01-01

Molecular diffusion measured with diffusion weighted MRI (DWI) offers a probe for tissue microstructure. However, inferring microstructural properties from conventional DWI data is a complex inverse problem and has to account for heterogeneity in sizes, shapes and orientations of the tissue...

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)

The Cell Probe Complexity of Succinct Data Structures

DEFF Research Database (Denmark)

Gal, Anna; Miltersen, Peter Bro

2003-01-01

In the cell probe model with word size 1 (the bit probe model), a static data structure problem is given by a map , where is a set of possible data to be stored, is a set of possible queries (for natural problems, we have ) and is the answer to question about data . A solution is given by a repre......In the cell probe model with word size 1 (the bit probe model), a static data structure problem is given by a map , where is a set of possible data to be stored, is a set of possible queries (for natural problems, we have ) and is the answer to question about data . A solution is given...

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.)

Application of Delaunay tessellation for the characterization of solute-rich clusters in atom probe tomography

International Nuclear Information System (INIS)

Lefebvre, W.; Philippe, T.; Vurpillot, F.

2011-01-01

This work presents an original method for cluster selection in Atom Probe Tomography designed to be applied to large datasets. It is based on the calculation of the Delaunay tessellation generated by the distribution of atoms of a selected element. It requires a single input parameter from the user. Furthermore, no prior knowledge of the material is needed. The sensitivity of the proposed Delaunay cluster selection is demonstrated by its application on simulated APT datasets. A strong advantage of the proposed methodology is that it is reinforced by the availability of an analytical model for the distribution of Delaunay cells circumspheres, which is used to control the accuracy of the cluster selection procedure. Another advantage of the Delaunay cluster selection is the direct calculation of a sharp envelope for each identified cluster or precipitate, which leads to the more appropriate morphology of the objects as they are reconstructed in the APT dataset. -- Research Highligthts: →Original method for cluster selection in Atom Probe Tomography. →Delaunay tessellation generated by the distribution of solute atoms. →Direct calculation of a sharp envelope for each identified cluster or precipitate. →Delaunay cluster selection demonstrated by its application on simulated APT datasets.

Sugar-influenced water diffusion, interaction, and retention in clay interlayer nanopores probed by theoretical simulations and experimental spectroscopies

Science.gov (United States)

Aristilde, Ludmilla; Galdi, Stephen M.; Kelch, Sabrina E.; Aoki, Thalia G.

2017-08-01

Understanding the hydrodynamics in clay nanopores is important for gaining insights into the trapping of water, nutrients, and contaminants in natural and engineered soils. Previous investigations have focused on the interlayer organization and molecular diffusion coefficients (D) of cations and water molecules in cation-saturated interlayer nanopores of smectite clays. Little is known, however, about how these interlayer dynamic properties are influenced by the ubiquitous presence of small organic compounds such as sugars in the soil environment. Here we probed the effects of glucose molecules on montmorillonite interlayer properties. Molecular dynamics simulations revealed re-structuring of the interlayer organization of the adsorptive species. Water-water interactions were disrupted by glucose-water H-bonding interactions. ;Dehydration; of the glucose-populated nanopore led to depletion in the Na solvation shell, which resulted in the accumulation of both Na ions (as inner-sphere complexes) and remaining hydrated water molecules at the mineral surface. This accumulation led to a decrease in both DNa and Dwater. In addition, the reduction in Dglucose as a function of increasing glucose content can be explained by the aggregation of glucose molecules into organic clusters H-bonded to the mineral surface on both walls of the nanopore. Experimental nuclear magnetic resonance and X-ray diffraction data were consistent with the theoretical predictions. Compared to clay interlayers devoid of glucose, increased intensities and new peaks in the 23Na nuclear magnetic resonance spectra confirmed increasing immobilization of Na as a function of increasing glucose content. And, the X-ray diffraction data indicated a reduced collapse of glucose-populated interlayers exposed to decreasing moisture conditions, which led to the maintenance of hydrated clay nanopores. The coupling of theoretical and experimental findings sheds light on the molecular to nanoscale mechanisms that

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

Science.gov (United States)

Ginzburg, Irina; Vikhansky, Alexander

2018-05-01

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

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

International Nuclear Information System (INIS)

Montan, D.N.

1987-02-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

Science.gov (United States)

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

2017-06-01

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

Numerical solution of multigroup diffuse equations of one-dimensional geometry

International Nuclear Information System (INIS)

Pavelesku, M.; Adam, S.

1975-01-01

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

Use of ultrafast dispersed pump-dump-probe and pump-repump-probe spectroscopies to explore the light-induced dynamics of peridinin in solution

NARCIS (Netherlands)

Papagiannakis, E.; Vengris, M.; Larsen, D.S.; van Stokkum, I.H.M.; Hiller, R.G.; van Grondelle, R.

2006-01-01

Optical pump-induced dynamics of the highly asymmetric carotenoid peridinin in methanol was studied by dispersed pump-probe, pump-dump-probe, and pump-repump-probe transient absorption spectroscopy in the visible region. Dispersed pump-probe measurements show that the decay of the initially excited

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

Demonstration of non-Gaussian restricted diffusion in tumor cells using diffusion-time dependent diffusion weighted MR contrast

Directory of Open Access Journals (Sweden)

Tuva Roaldsdatter Hope

2016-08-01

Full Text Available The diffusion weighted imaging (DWI technique enables quantification of water mobility for probing microstructural properties of biological tissue, and has become an effective tool for collecting information about the underlying pathology of cancerous tissue. Measurements using multiple b-values have indicated a bi-exponential signal attenuation, ascribed to fast (high ADC and slow (low ADC diffusion components. In this empirical study, we investigate the properties of the diffusion time (∆ - dependent components of the diffusion-weighted (DW signal in a constant b-value experiment. A Xenograft GBM mouse was imaged using ∆ = 11 ms, 20 ms, 40 ms, 60 ms and b=500-4000 s/mm2 in intervals of 500s/mm2. Data was corrected for EPI distortions and the ∆-dependence on the DW signal was measured within three regions of interest (intermediate- and high-density tumor regions and normal appearing brain tissue regions (NAB. In this empirical study we verify the assumption that the slow decaying component of the DW-signal is non-Gaussian and dependent on ∆, consistent with restricted diffusion of the intracellular space. As the DW-signal as a function of ∆ is specific to restricted diffusion, manipulating ∆ at constant b-value (cb provides a complementary and direct approach for separating the restricted from the hindered diffusion component. Our results show that only tumor tissue signal of our data demonstrate ∆-dependence, based on a bi-exponential model with a restricted diffusion component, we successfully estimated the restricted ADC, signal volume fraction and cell size within each tumor ROI.

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.

Electronically tuned sulfonamide-based probes with ultra-sensitivity for Ga{sup 3+} or Al{sup 3+} detection in aqueous solution

Energy Technology Data Exchange (ETDEWEB)

Kumar, Ashwani, E-mail: ashwanirubal@gmail.com; Chae, Pil Seok, E-mail: pchae@hanyang.ac.kr

2017-03-15

Three electronically tuned fluorescent probes (1–3) were synthesized by conjugating a fluorescent unit to N,N-bis-(hydroxyethyl)ethylenediamine. Probe 1 bearing an electron-deficient naphthalenedimide unit did not give a fluorescence response to the presence of various metal ions including monovalent metal ions (Na{sup +}, K{sup +}, and Ag{sup +}), divalent metal ions (Ca{sup 2+}, Cd{sup 2+}, Co{sup 2+}, Ni{sup 2+}, Cu{sup 2+}, Hg{sup 2+}, Pb{sup 2+}, and Zn{sup 2+}) and trivalent metal ions (Al{sup 3+}, Ga{sup 3+}, Fe{sup 3+}, and Cr{sup 3+}) in an aqueous solution. By contrast, probes 2 and 3 possessing 1,8-naphthalimide and pyrene fluorophores, respectively, exhibited selective fluorescent “OFF-ON” behaviors as a result of Ga{sup 3+}/Al{sup 3+} binding among the diverse metal ions, suggesting the importance of fluorophore electronic character with regard to metal ion sensing. The ethylenediamine analog of probe 3, corresponding to probe 4, was unable to yield a significant change in fluorescence intensity in the presence of any metal ions tested here, revealing the essential role of two hydroxyl groups for metal ion binding. A high association constant of K{sub a} = 2.99 × 10{sup 5} M{sup −1} was obtained for probe 3 with Ga{sup 3+}, with a limit of detection (LOD) of 10 nM. This LOD is the lowest value known for Ga{sup 3+} detection using chemical sensors. Along with an increase in aggregate sizes, PET suppression of probes upon metal ion binding was the primary contributor to the enhancement in fluorescence emission necessary for the sensitive detection of the target ions. The probe-metal ion complexes were fully characterized via TEM, FE-SEM, {sup 1}H NMR, fluorescence spectroscopy techniques and DFT calculations. - Highlights: • Three electronically tuned sulfonamide-based probes (probes 1, 2, and 3) were developed for metal ion-sensing. • Probes 2 and 3 exhibited AIE behavior with increasing water-content. • Probes 2 and 3 displayed a

Magnetic diffuse scattering: a theorist's perspective

International Nuclear Information System (INIS)

Long, M.W.

1996-01-01

We attempt to show that magnetic diffuse scattering is the natural probe for frustrated antiferromagnetism. Comparison between nuclear and magnetic diffuse scattering compares the range of atomic clustering with the range of the magnetic impurity. At low temperature frustration is expected to lead to large differences which are a natural signature for the relevance of such frustration effects. We provide some elementary examples in first-row transition metals which display fairly dramatic effects. (author) 11 figs., tabs., 8 refs

Review of diffusion tensor imaging and its application in children

Energy Technology Data Exchange (ETDEWEB)

Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)

2015-09-15

Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)

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

Science.gov (United States)

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

2017-05-10

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

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.

Development of high pressure conductivity probe (HPCP) for secondary shut down system (SDS-2) of 500 MWe PHWR

International Nuclear Information System (INIS)

Sapra, M.K.; Kundu, S.; Mohan, L.R.

2003-09-01

The poison solution and the moderator in Secondary Shutdown System (SDS-2) of 500 MWe PHWR, are separated by their own liquid in liquid interface. This interface moves towards the calandria because of molecular diffusion, temperature difference and physical disturbances in the moderator level. It is proposed to install two numbers of high pressure conductivity probes (HPCP) to monitor the interface movement as well as to provide the safe annunciation value for interface location. On actuation of the SDS-2 signal, high-pressure helium will inject the poison into the moderator to shutdown the reactor. During poison injection, these probes will experience high pressure of nearly 85 kg/sq.cm. Global market survey indicated that conductivity probes having built in temperature sensor are available for a maximum pressure rating of 35 kg/sq.cm. Hence in order to meet the process requirement of SDS-2, the development of HPCP suitable for a pressure of 85 kg/sq.cm. was taken up. Two numbers of such probes were successfully designed, fabricated and evaluated for their performance. The developed conductivity probes fully meet the laid design and performance criteria. The aforesaid development work was a successful endeavour towards indigenisation of high-pressure conductivity probe for future applications. This report deals with the design aspects, fabrication technique, material and performance evajuation criteria and test results of HPCP. (author)

The Measurement of Thermal Diffusivity in Conductor and Insulator by Photodeflection Technique

Science.gov (United States)

Achathongsuk, U.; Rittidach, T.; Tipmonta, P.; Kijamnajsuk, P.; Chotikaprakhan, S.

2017-09-01

The purpose of this study is to estimate thermal diffusivities of high thermal diffusivity bulk material as well as low thermal diffusivity bulk material by using many types of fluid such as Ethyl alcohol and water. This method is studied by measuring amplitude and phase of photodeflection signal in various frequency modulations. The experimental setup consists of two laser lines: 1) a pump laser beams through a modulator, varied frequency, controlled by lock-in amplifier and focused on sample surface by lens. 2) a probe laser which parallels with the sample surface and is perpendicular to the pump laser beam. The probe laser deflection signal is obtained by a position sensor which controlled by lock-in amplifier. Thermal diffusivity is calculated by measuring the amplitude and phase of the photodeflection signal and compared with the thermal diffusivity of a standard value. The thermal diffusivity of SGG agrees well with the literature but the thermal diffusivity of Cu is less than the literature value by a factor of ten. The experiment requires further improvement to measure the thermal diffusivity of Cu. However, we succeed in using ethyl alcohol as the coupling medium instead of CCl4 which is highly toxic.

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

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

Electrochemical impedance measurement of a carbon nanotube probe electrode

International Nuclear Information System (INIS)

Inaba, Akira; Takei, Yusuke; Kan, Tetsuo; Shimoyama, Isao; Matsumoto, Kiyoshi

2012-01-01

We measured and analyzed the electrochemical impedance of carbon nanotube (CNT) probe electrodes fabricated through the physical separation of insulated CNT bridges. The fabricated CNT electrodes were free-standing CNTs that were completely covered with an insulator, except for their tips. Typical dimensions of the nanoelectrodes were 1–10 nm in CNT diameter, 80–300 nm in insulator diameter, 0.5–4 μm in exposed CNT length and 1–10 μm in probe length. The electrochemical impedance at frequencies ranging from 40 Hz to 1 MHz was measured in physiological saline. The measured impedance of the CNT electrode was constant at 32 MΩ at frequencies below 1 kHz and was inversely proportional to frequency at frequencies above 10 kHz. By means of comparison with the parasitic capacitive impedance of the insulator membrane, we confirmed that the electrode was sufficiently insulated such that the measured constant impedance was given by the exposed CNT tip. Consequently, we can use the CNT electrode for highly localized electrochemical impedance measurements below 1 kHz. Considering an equivalent circuit and the nanoscopic dimensions of the CNT electrode, we demonstrated that the constant impedance was governed by diffusion impedance, whereas the solution resistance, charge-transfer resistance and double-layer capacitance were negligible. (paper)

SNOW LINES AS PROBES OF TURBULENT DIFFUSION IN PROTOPLANETARY DISKS

International Nuclear Information System (INIS)

Owen, James E.

2014-01-01

Sharp chemical discontinuities can occur in protoplanetary disks, particularly at ''snow lines'' where a gas-phase species freezes out to form ice grains. Such sharp discontinuities will diffuse out due to the turbulence suspected to drive angular momentum transport in accretion disks. We demonstrate that the concentration gradient—in the vicinity of the snow line—of a species present outside a snow line but destroyed inside is strongly sensitive to the level of turbulent diffusion (provided the chemical and transport timescales are decoupled) and provides a direct measurement of the radial ''Schmidt number'' (the ratio of the angular momentum transport to radial turbulent diffusion). Taking as an example the tracer species N 2 H + , which is expected to be destroyed inside the CO snow line (as recently observed in TW Hya) we show that ALMA observations possess significant angular resolution to constrain the Schmidt number. Since different turbulent driving mechanisms predict different Schmidt numbers, a direct measurement of the Schmidt number in accretion disks would allow inferences to be made about the nature of the turbulence

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Science.gov (United States)

Liu, Chunlei; Murphy, Nicole E.; Li, Wei

2012-01-01

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

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)

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

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)

Introducing a standard method for experimental determination of the solvent response in laser pump, x-ray probe time-resolved wide-angle x-ray scattering experiments on systems in solution

DEFF Research Database (Denmark)

Kjær, Kasper Skov; Brandt van Driel, Tim; Kehres, Jan

2013-01-01

In time-resolved laser pump, X-ray probe wide-angle X-ray scattering experiments on systems in solution the structural response of the system is accompanied by a solvent response. The solvent response is caused by reorganization of the bulk solvent following the laser pump event, and in order...... response-the solvent term-experimentally when applying laser pump, X-ray probe time-resolved wide-angle X-ray scattering. The solvent term describes difference scattering arising from the structural response of the solvent to changes in the hydrodynamic parameters: pressure, temperature and density. We...... is demonstrated to exhibit first order behaviour with respect to the amount of energy deposited in the solution. We introduce a standardized method for recording solvent responses in laser pump, X-ray probe time-resolved X-ray wide-angle scattering experiments by using dye mediated solvent heating. Furthermore...

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.

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)

Modeling dendrite density from magnetic resonance diffusion measurements

DEFF Research Database (Denmark)

Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif

2007-01-01

in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.......e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides......Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal...

Self-diffusion in single crystalline silicon nanowires

Science.gov (United States)

Südkamp, T.; Hamdana, G.; Descoins, M.; Mangelinck, D.; Wasisto, H. S.; Peiner, E.; Bracht, H.

2018-04-01

Self-diffusion experiments in single crystalline isotopically controlled silicon nanowires with diameters of 70 and 400 nm at 850 and 1000 °C are reported. The isotope structures were first epitaxially grown on top of silicon substrate wafers. Nanowires were subsequently fabricated using a nanosphere lithography process in combination with inductively coupled plasma dry reactive ion etching. Three-dimensional profiling of the nanosized structure before and after diffusion annealing was performed by means of atom probe tomography (APT). Self-diffusion profiles obtained from APT analyses are accurately described by Fick's law for self-diffusion. Data obtained for silicon self-diffusion in nanowires are equal to the results reported for bulk silicon crystals, i.e., finite size effects and high surface-to-volume ratios do not significantly affect silicon self-diffusion. This shows that the properties of native point defects determined from self-diffusion in bulk crystals also hold for nanosized silicon structures with diameters down to 70 nm.

Heat Fluxes and Evaporation Measurements by Multi-Function Heat Pulse Probe: a Laboratory Experiment

Science.gov (United States)

Sharma, V.; Ciocca, F.; Hopmans, J. W.; Kamai, T.; Lunati, I.; Parlange, M. B.

2012-04-01

Multi Functional Heat Pulse Probes (MFHPP) are multi-needles probes developed in the last years able to measure temperature, thermal properties such as thermal diffusivity and volumetric heat capacity, from which soil moisture is directly retrieved, and electric conductivity (through a Wenner array). They allow the simultaneous measurement of coupled heat, water and solute transport in porous media, then. The use of only one instrument to estimate different quantities in the same volume and almost at the same time significantly reduces the need to interpolate different measurement types in space and time, increasing the ability to study the interdependencies characterizing the coupled transports, especially of water and heat, and water and solute. A three steps laboratory experiment is realized at EPFL to investigate the effectiveness and reliability of the MFHPP responses in a loamy soil from Conthey, Switzerland. In the first step specific calibration curves of volumetric heat capacity and thermal conductivity as function of known volumetric water content are obtained placing the MFHPP in small samplers filled with the soil homogeneously packed at different saturation degrees. The results are compared with literature values. In the second stage the ability of the MFHPP to measure heat fluxes is tested within a homemade thermally insulated calibration box and results are matched with those by two self-calibrating Heatflux plates (from Huxseflux), placed in the same box. In the last step the MFHPP are used to estimate the cumulative subsurface evaporation inside a small column (30 centimeters height per 8 centimeters inner diameter), placed on a scale, filled with the same loamy soil (homogeneously packed and then saturated) and equipped with a vertical array of four MFHPP inserted close to the surface. The subsurface evaporation is calculated from the difference between the net sensible heat and the net heat storage in the volume scanned by the probes, and the

Anomalous diffusion of a probe in a bath of active granular chains

Science.gov (United States)

Jerez, Michael Jade Y.; Confesor, Mark Nolan P.; Carpio-Bernido, M. Victoria; Bernido, Christopher C.

2017-08-01

We investigate the dynamics of a passive probe particle in a bath of active granular chains (AGC). The bath and the probe are enclosed in an experimental compartment with a sinusoidal boundary to prevent AGC congestion along the boundary while connected to an electrodynamic shaker. Single AGC trajectory analysis reveals a persistent type of motion compared to a purely Brownian motion as seen in its mean squared displacement (MSD). It was found that at small concentration, Φ ≤ 0.44, the MSD exhibits two dynamical regimes characterized by two different scaling exponents. For small time scales, the dynamics is superdiffusive (1.32-1.63) with the MSD scaling exponent increasing monotonically with increasing AGC concentration. On the other hand, at long time, we recover the Brownian dynamics regime, MSD = DΔt, where the mobility D ∝ Φ. We quantify the probe dynamics at short time scale by modeling it as a fractional Brownian motion. The analytical form of the MSD agrees with experimental results.

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

Magnetic diffuse scattering: a theorist`s perspective

Energy Technology Data Exchange (ETDEWEB)

Long, M W [Birmingham Univ., School of Physics, Birmingham (United Kingdom)

1996-11-01

We attempt to show that magnetic diffuse scattering is the natural probe for frustrated antiferromagnetism. Comparison between nuclear and magnetic diffuse scattering compares the range of atomic clustering with the range of the magnetic impurity. At low temperature frustration is expected to lead to large differences which are a natural signature for the relevance of such frustration effects. We provide some elementary examples in first-row transition metals which display fairly dramatic effects. (author) 11 figs., tabs., 8 refs.

Theory of a spherical emissive probe in a low-density isotropic plasma

International Nuclear Information System (INIS)

Din, A.

2010-01-01

Emissive probes are widely being used by plasma experimentalists to determine plasma parameters. Here, a fairly general spherical-emissive-probe scenario based on trajectory integration of the Vlasov equation is formulated and specialized to the particular non-emissive situation considered by Bernstein and Rabinowitz (1959), which is monoenergetic isotropic ions and Boltzmann-distributed electrons originating from the plasma. Then, this formalism together with our newly developed analytic-numerical matching procedure is used for finding the potential profile in the entire plasma-probe transition (PPT) region, consisting of the 'inward' and 'outward' sheath solutions, and the quasineutral (plasma) solution. The analytically expanded outward sheath and plasma solutions, the quasineutral solution and the related matching procedure represent genuinely new results in the context of this particular non-emissive probe scenario, however with the underlying methodology also applicable to other probe scenarios in the future. For the emissive case we consider, in addition to the plasma ions and electrons of the Bernstein and Rabinowitz scenario, electrons emitted from the probe surface with zero tangential velocity and a 'waterbag' distribution with respect to the radial velocity. Using our newly developed numerical matching procedure, we calculate the entire potential profile also for this emissive case. Comparison of the potential profiles for the emissive and non-emissive cases shows visible differences, thus demonstrating the effect of electron emission from the probe. To our knowledge, the present work represents the first attempt at systematically developing a kinetic approach for spherical emissive probes. (author)

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

Science.gov (United States)

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

2017-07-01

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

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

Directory of Open Access Journals (Sweden)

C. Cholet

2017-07-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-07-01

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

Influence of extrinsic operational parameters on salt diffusion during ultrasound assisted meat curing.

Science.gov (United States)

Inguglia, Elena S; Zhang, Zhihang; Burgess, Catherine; Kerry, Joseph P; Tiwari, Brijesh K

2018-02-01

The present study investigated the effect of geometric parameters of the ultrasound instrument during meat salting in order to enhance salt diffusion and salt distribution in pork meat on a lab scale. The effects of probe size (∅2.5 and 1.3cm) and of different distances between the transducer and the meat sample (0.3, 0.5, and 0.8cm) on NaCl diffusion were investigated. Changes in the moisture content and NaCl gain were used to evaluate salt distribution and diffusion in the samples, parallel and perpendicular to ultrasound propagation direction. Results showed that 0.3cm was the most efficient distance between the probe and the sample to ensure a higher salt diffusion rate. A distance of 0.5cm was however considered as a trade-off distance to ensure salt diffusion and maintenance of meat quality parameters. The enhancement of salt diffusion by ultrasound was observed to decrease with increased horizontal distance from the probe. This study is of valuable importance for meat processing industries willing to apply new technologies on a larger scale and with defined operational standards. The data suggest that the geometric parameters of ultrasound systems can have strong influence on the efficiency of ultrasonic enhancement of NaCl uptake in meat and can be a crucial element in determining salt uptake during meat processing. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

Burger, Martin

2010-01-01

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

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

Science.gov (United States)

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

2018-04-01

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

On the solution of reaction-diffusion equations with double diffusivity

Directory of Open Access Journals (Sweden)

B. D. Aggarwala

1987-01-01

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

Atomistically informed solute drag in Al–Mg

International Nuclear Information System (INIS)

Zhang, F; Curtin, W A

2008-01-01

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

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

International Nuclear Information System (INIS)

Alonso-Vargas, G.

1991-01-01

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

Application of a numerical transport correction in diffusion calculations

International Nuclear Information System (INIS)

Tomatis, Daniele; Dall'Osso, Aldo

2011-01-01

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

Oxygen diffusion in bilayer polymer films

DEFF Research Database (Denmark)

Poulsen, Lars; Zebger, Ingo; Tofte, Jannik Pentti

2004-01-01

Experiments to quantify oxygen diffusion have been performed on polymer samples in which a film of poly(ethylene-co-norbornene) was cast onto a film of polystyrene which, in turn, was cast onto an oxygen-impermeable substrate. In the technique employed, the time evolution of oxygen transport...... through the film of poly(ethylene-co-norbornene) and into the polystyrene film was monitored using the phosphorescence of singlet oxygen as a spectroscopic probe. To analyze the data, it was necessary to solve Fick's second law of diffusion for both polymer films. Tractable analytical and numerical...

Evidence for Enhanced Matrix Diffusion in Geological Environment

Science.gov (United States)

Sato, Kiminori; Fujimoto, Koichiro; Nakata, Masataka; Shikazono, Naotatsu

2013-01-01

Molecular diffusion in rock matrix, called as matrix diffusion, has been appreciated as a static process for elemental migration in geological environment that has been acknowledged in the context of geological disposal of radioactive waste. However, incomprehensible enhancement of matrix diffusion has been reported at a number of field test sites. Here, the matrix diffusion of saline water at Horonobe, Hokkaido, Japan is highlighted directly probing angstrom-scale pores on a field scale up to 1 km by positron--positronium annihilation spectroscopy. The first application of positron--positronium annihilation spectroscopy to field-scale geophysical research reveals the slight variation of angstrom-scale pores influenced by saline water diffusion with complete accuracy. We found widely interconnected 3 Å pores, which offer the pathway of saline water diffusion with the highly enhanced effective matrix diffusion coefficient of 4× 10-6 cm2 s-1. The present findings provide unambiguous evidence that the angstrom-scale pores enhance effective matrix diffusion on a field scale in geological environment.

Diffusion-weighted and diffusion tensor imaging for pediatric musculoskeletal disorders

International Nuclear Information System (INIS)

MacKenzie, John D.; Gonzalez, Leonardo; Hernandez, Andrea; Ruppert, Kai; Jaramillo, Diego

2007-01-01

Diffusion-weighted imaging (DWI) is a powerful tool that has recently been applied to evaluate several pediatric musculoskeletal disorders. DWI probes abnormalities of tissue structure by detecting microscopic changes in water mobility that develop when disease alters the organization of normal tissue. DWI provides tissue characterization at a cellular level beyond what is available with other imaging techniques, and can sometimes identify pathology before gross anatomic alterations manifest. These features of early detection and tissue characterization make DWI particularly appealing for probing diseases that affect the musculoskeletal system. This article focuses on the current and future applications of DWI in the musculoskeletal system, with particular attention paid to pediatric disorders. Although most of the applications are experimental, we have emphasized the current state of knowledge and the main research questions that need to be investigated. (orig.)

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.

Connecting diffusion and entropy of bulk water at the single particle ...

Indian Academy of Sciences (India)

The relation between the dynamic (e.g., diffusion) and thermodynamic (e.g., entropy) properties of water and water-like liquids has been an active area of research for a long time. Although several studies have investigated the diffusivity and entropy for different systems, these studies have probed either the configurational ...

PROBING THE LOCAL BUBBLE WITH DIFFUSE INTERSTELLAR BANDS. II. THE DIB PROPERTIES IN THE NORTHERN HEMISPHERE

Energy Technology Data Exchange (ETDEWEB)

Farhang, Amin; Khosroshahi, Habib G.; Javadi, Atefeh; Molaeinezhad, Alireza; Tavasoli, Saeed; Habibi, Farhang; Kourkchi, Ehsan; Rezaei, Sara; Saberi, Maryam [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746 Tehran (Iran, Islamic Republic of); Van Loon, Jacco Th.; Bailey, Mandy [Astrophysics Group, Lennard-Jones Laboratories, Keele University, Staffordshire ST5 5BG (United Kingdom); Hardy, Liam, E-mail: a.farhang@ipm.ir [Isaac Newton Group, Apartado 321, E-38700 Santa Cruz de La Palma (Spain)

2015-02-10

We present a new high signal-to-noise ratio spectroscopic survey of the Northern hemisphere to probe the Local Bubble and its surroundings using the λ5780 Å and λ5797 Å diffuse interstellar bands (DIBs). We observed 432 sightlines to a distance of 200 pc over a duration of three years. In this study, we establish the λ5780 and λ5797 correlations with Na I, Ca II and E {sub B-V}, for both inside and outside the Local Bubble. The correlations show that among all neutral and ionized atoms, the correlation between Ca II and λ5780 is stronger than its correlation with λ5797, suggesting that λ5780 is more associated with regions where Ca{sup +} is more abundant. We study the λ5780 correlation with λ5797, which shows a tight correlation within and outside the Local Bubble. In addition, we investigate the DIB properties in UV irradiated and UV shielded regions. We find that, within and beyond the Local Bubble, λ5797 is located in denser parts of clouds, protected from UV irradiation, while λ5780 is located in the low-density regions of clouds.

Probing molecular dynamics of metal borohydrides on the surface of mesoporous scaffolds by multinuclear high resolution solid state NMR

Energy Technology Data Exchange (ETDEWEB)

Hwang, Son-Jong, E-mail: Sonjong@cheme.caltech.edu [Division of Chemistry and Chemical Eng., California Institute of Technology, Pasadena, CA 91125 (United States); Lee, Hyun-Sook [High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul 136-791 (Korea, Republic of); To, Magnus [Division of Chemistry and Chemical Eng., California Institute of Technology, Pasadena, CA 91125 (United States); Lee, Young-Su; Cho, Young Whan [High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul 136-791 (Korea, Republic of); Choi, Hyungkeun; Kim, Chul [Department of Chemistry, Hannam University, Daejeon 305-811 (Korea, Republic of)

2015-10-05

Graphical abstract: In situ variable temperature multinuclear solid state NMR allows to probe surface wetting, diffusivity, and confinement of metal borohydrides into nanopores. - Abstract: Understanding of surface interactions between borohydride molecules and the surfaces of porous supports have gained growing attention for successful development of nano-confinement engineering. By use of in situ variable temperature (VT) magic angle spinning (MAS) NMR, molecular mobility changes of LiBH{sub 4} crystalline solid has been investigated in the presence of silica based and carbonaceous surfaces. Spin–spin J-coupling of {sup 1}H–{sup 11}B in LiBH{sub 4} was monitored in series of VT NMR spectra to probe translational mobility of LiBH{sub 4} that appeared to be greatly enhanced upon surface contact. Such enhanced diffusivity was found to be effective in the formation of solid solution and co-confinement with other metal borohydrides. Co-confinement of LiBH{sub 4}–Ca(BH{sub 4}){sub 2} mixture was demonstrated at temperature as low as 100 °C, much lower than the reported bulk eutectic melting temperature. The discovery adds a novel property of LiBH{sub 4} that has been proven to be highly versatile in many energy related applications.

Diffusivities and atomic mobilities in Cu-rich fcc Al-Cu-Mn alloys

Energy Technology Data Exchange (ETDEWEB)

Yin, Ming; Du, Yong; Cui, Senlin; Xu, Honghui; Liu, Shuhong [Central South Univ., Changsha (China). State Key Laboratory of Powder Metallurgy; Zhang, Lijun [Bochum Univ. (DE). Interdisciplinary Centre for Advanced Materials Simulation (ICAMS)

2012-07-15

Via solid-solid diffusion couples, electron probe microanalysis and the Whittle and Green method, interdiffusivities in fcc Al-Cu-Mn alloys at 1 123 K were measured. The reliability of the obtained diffusivities is validated by comparing the computed diffusivities with literature data plus constraints among the diffusivities. Through assessments of experimentally determined diffusion coefficients by means of a diffusion-controlled transformations simulation package, the atomic mobilities of Al, Cu, and Mn in fcc Al-Cu-Mn alloys are obtained. Comprehensive comparisons between the model-predicted and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities, concentration profiles, and diffusion paths reasonably. (orig.)

Comparison of the quantitative analysis performance between pulsed voltage atom probe and pulsed laser atom probe

Energy Technology Data Exchange (ETDEWEB)

Takahashi, J., E-mail: takahashi.3ct.jun@jp.nssmc.com [Advanced Technology Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu-city, Chiba 293-8511 (Japan); Kawakami, K. [Advanced Technology Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu-city, Chiba 293-8511 (Japan); Raabe, D. [Max-Planck Institut für Eisenforschung GmbH, Department for Microstructure Physics and Alloy Design, Max-Planck-Str. 1, 40237 Düsseldorf (Germany)

2017-04-15

Highlights: • Quantitative analysis in Fe-Cu alloy was investigated in voltage and laser atom probe. • In voltage-mode, apparent Cu concentration exceeded actual concentration at 20–40 K. • In laser-mode, the concentration never exceeded the actual concentration even at 20 K. • Detection loss was prevented due to the rise in tip surface temperature in laser-mode. • Preferential evaporation of solute Cu was reduced in laser-mode. - Abstract: The difference in quantitative analysis performance between the voltage-mode and laser-mode of a local electrode atom probe (LEAP3000X HR) was investigated using a Fe-Cu binary model alloy. Solute copper atoms in ferritic iron preferentially field evaporate because of their significantly lower evaporation field than the matrix iron, and thus, the apparent concentration of solute copper tends to be lower than the actual concentration. However, in voltage-mode, the apparent concentration was higher than the actual concentration at 40 K or less due to a detection loss of matrix iron, and the concentration decreased with increasing specimen temperature due to the preferential evaporation of solute copper. On the other hand, in laser-mode, the apparent concentration never exceeded the actual concentration, even at lower temperatures (20 K), and this mode showed better quantitative performance over a wide range of specimen temperatures. These results indicate that the pulsed laser atom probe prevents both detection loss and preferential evaporation under a wide range of measurement conditions.

A Fluorescent Probe for Sensitive Detection of Hydrazine and Its Application in Red Wine and Water.

Science.gov (United States)

Wang, Jialin; Wang, Hao; Yang, Shaoxiang; Tian, Hongyu; Liu, Yongguo; Hao, Yanfeng; Zhang, Jie; Sun, Baoguo

2018-01-01

A fluorescent probe, 7-(diethylamino)-2-oxo-2H-chromene-4-carbaldehyde (probe 1), was designed and synthesized for the sensitive detection of hydrazine. The addition of N 2 H 4 caused the fluorescence intensity of probe 1 to decrease. The probe's fluorescence was turn-off after adding N 2 H 4 , which could be observed under UV light at 365 nm. Moreover, once treated with different concentrations N 2 H 4 solutions, the solution color change could be distinguished, which indicates that probe 1 could be used as a visual sensor for hydrazine. Moreover, probe 1 can be used as a signal tool to determine hydrazine levels in solutions, such as red wine and water.

Quenching methods for background reduction in luminescence-based probe-target binding assays

Energy Technology Data Exchange (ETDEWEB)

Cai, Hong [Los Alamos, NM; Goodwin, Peter M [Los Alamos, NM; Keller, Richard A [Los Alamos, NM; Nolan, Rhiannon L [Santa Fe, NM

2007-04-10

Background luminescence is reduced from a solution containing unbound luminescent probes, each having a first molecule that attaches to a target molecule and having an attached luminescent moiety, and luminescent probe/target adducts. Quenching capture reagent molecules are formed that are capable of forming an adduct with the unbound luminescent probes and having an attached quencher material effective to quench luminescence of the luminescent moiety. The quencher material of the capture reagent molecules is added to a solution of the luminescent probe/target adducts and binds in a proximity to the luminescent moiety of the unbound luminescent probes to quench luminescence from the luminescent moiety when the luminescent moiety is exposed to exciting illumination. The quencher capture reagent does not bind to probe molecules that are bound to target molecules and the probe/target adduct emission is not quenched.

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...

Proposal of experimental study on particle diffusion in superficially confined plasma by magnetic multi-dipole fields

International Nuclear Information System (INIS)

Ferreira, J.L.; Ferreira, J.G.; Sandonato, G.M.; Damasio, W.C.; Montes, A.; Ludwig, G.O.

1989-08-01

The anomalous particle diffusion in regions near to magnetic confinement walls due to ion acoustic turbulence in superficially confined quiescent plasma is studied comparing the measured diffusion coefficient with the Bohm diffusion coefficient. The plasma diagnostics are carried out using Langmuir probe, electron and ion energy analyzers, emission probes for measuring plasma potential and, mass spectrometer, the purchase of data acquisition system composed by storage unit and signal register interfaced with IBM PC computer is proposed for simultaneous measurements with several diagnostics in the quiescent plasma machine of LAP-INPE operating in pulsed regime. (M.C.K.)

Time resolved fluorescence anisotropy of basic dyes bound to poly(methacrylic acid in solution

Directory of Open Access Journals (Sweden)

Oliveira Hueder Paulo M. de

2003-01-01

Full Text Available Solutions of atactic poly(methacrylic acid, PMAA, with molecular weights in the range of (1.6 to 3.4 x 10(5 g mol-1, and labeled with the fluorescent dyes 9-aminoacridine or Nile blue were studied by photophysical measurements as a function of solvent viscosity and polarity. The conformational behavior of the PMAA chain segments around the fluorescent probe was reported by the change in the rotational diffusion of the dyes. Ethylene glycol swells the polymer chain compared with the more contracted conformation of PMAA in 50% water/ethylene glycol. The change in the rotational relaxation time of the dye bound to PMAA with the decrease of water content in the solvent mixture indicates a progressive expansion of polymer chain to a more open coil form in solution.

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)

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.

Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

International Nuclear Information System (INIS)

Keanini, R.G.

2011-01-01

Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

Light diffuseness metric, part 2 : Describing, measuring and visualizing the light flow and diffuseness in three-dimensional spaces

NARCIS (Netherlands)

Xia, L.; Pont, S.C.; Heynderickx, I.E.J.

2017-01-01

We introduce a way to simultaneously measure the light density, light vector and diffuseness of the light field using a cubic illumination meter based on the spherical harmonics representation of the light field. This approach was applied to six light probe images of natural scenes and four real

Interaction between diffusion and chemical stresses

International Nuclear Information System (INIS)

Yang Fuqian

2005-01-01

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

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

DEFF Research Database (Denmark)

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

2007-01-01

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

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

International Nuclear Information System (INIS)

LeMaster, David M.

1997-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Fournier, Andre

1944-03-30

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

Exposure to buffer solution alters tendon hydration and mechanics.

Science.gov (United States)

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

2017-08-16

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