Fractional Diffusion Limit for Collisional Kinetic Equations

KAUST Repository

Mellet, Antoine; Mischler, Sté phane; Mouhot, Clé ment

2010-01-01

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a

Inertial effects in diffusion-limited reactions

International Nuclear Information System (INIS)

Dorsaz, N; Foffi, G; De Michele, C; Piazza, F

2010-01-01

Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

Variable Eddington factors and flux-limiting diffusion coefficients

International Nuclear Information System (INIS)

Whalen, P.P.

1982-01-01

Variable Eddington factors and flux limiting diffusion coefficients arise in two common techniques of closing the moment equations of transport. The first two moment equations of the full transport equation are still frequently used to solve many problems of radiative or particle transport. An approximate analysis, developed by Levermore, exhibits the relation between the coefficients of the two different techniques. This analysis is described and then used to test the validity of several commonly used flux limiters and Eddington factors. All of the ad-hoc flux limiters have limited validity. All of the variable Eddington factors derived from some underlying description of the angular distribution function are generally valid. The use of coefficients from Minerbo's elegant maximum entropy Eddington factor analysis is suggested for use in either flux limited diffusion or variable Eddington factor equations

Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

NARCIS (Netherlands)

Arnrich, S.; Mielke, A.; Peletier, M.A.; Savaré, G.; Veneroni, M.

2012-01-01

We study a singular-limit problem arising in the modelling of chemical reactions. At finite e > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1 / e and in the limit e --> 0, the solution concentrates

Study of ODE limit problems for reaction-diffusion equations

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Jacson Simsen

2018-01-01

Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

Science.gov (United States)

Kittell, D. E.; Yarrington, C. D.; Hobbs, M. L.; Abere, M. J.; Adams, D. P.

2018-04-01

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

Science.gov (United States)

Liu, Yechi

2018-06-01

The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier-Stokes system also has the same phenomenon when Mach number is suitably small.

Investigation of detection limits for diffuse optical tomography systems: II. Analysis of slab and cup geometry for breast imaging.

Science.gov (United States)

Ziegler, Ronny; Brendel, Bernhard; Rinneberg, Herbert; Nielsen, Tim

2009-01-21

Using a statistical (chi-square) test on simulated data and a realistic noise model derived from the system's hardware we study the performance of diffuse optical tomography systems for fluorescence imaging. We compare the predicted smallest size of detectable lesions at various positions in slab and cup geometry and model how detection sensitivity depends on breast compression and lesion fluorescence contrast. Our investigation shows that lesion detection is limited by relative noise in slab geometry and by absolute noise in cup geometry.

Rethinking pattern formation in reaction-diffusion systems

Science.gov (United States)

Halatek, J.; Frey, E.

2018-05-01

The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

Shear-limited test particle diffusion in 2-dimensional plasmas

International Nuclear Information System (INIS)

Anderegg, Francois; Driscoll, C. Fred; Dubin, Daniel H.E.

2002-01-01

Measurements of test-particle diffusion in pure ion plasmas show 2D enhancements over the 3D rates, limited by shear in the plasma rotation ω E (r). The diffusion is due to 'long-range' ion-ion collisions in the quiescent, steady-state Mg + plasma. For short plasma length L p and low shear S≡r∂ω E /∂r, thermal ions bounce axially many times before shear separates them in θ, so the ions move in (r,θ) as bounce averaged 'rods' of charge (i.e. 2D point vortices). Experimentally, we vary the number of bounces over the range 0.2≤N b ≤10,000. For long plasmas with N b ≤1, we observe diffusion in quantitative agreement with the 3D theory of long-range ExB drift collisions. For shorter plasmas or lower shear, with N b >1, we measure diffusion rates enhanced by up to 100x. For exceedingly small she0ar, i.e. N b ≥1000, we observe diffusion rates consistent with the Taylor-McNamara estimates for a shear-free thermal plasma. Overall, the data shows fair agreement with Dubin's new theory of 2D diffusion in shear, which predicts an enhancement of D 2D /D 3D ≅N b up to the Taylor-McNamara limit

Contribution to the study of diffusion in poly-phase system; Contribution a l'etude de la diffusion en systeme polyphase

Energy Technology Data Exchange (ETDEWEB)

Adda, Y; Philibert, J [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires; Institut de Recherches de la Siderurgie Francaise (IRSID), 78 - Saint-Germain-en-Laye (France)

1959-07-01

After chemical diffusion between two metals, at temperatures where, according to the equilibrium diagram, several phases exist, parallel bands corresponding to these various phases can be seen in a section which is perpendicular to the diffusion front. It is known that in this case there are discontinuities in the concentration-penetration curve, corresponding to the interfaces. The concentrations at the point where the discontinuities occur give the limits of solubility in each of the present phases. During our experiments on the system uranium-zirconium, we verified that these concentrations do not vary with the diffusion time and therefore that the conditions of thermodynamical equilibrium are obeyed. It follows that an interesting method is available for determining the equilibrium diagram for the solid state. We have applied this method to the U-Zr system. Kinetic studies of poly-phase diffusion are as yet relatively scarce as a result of difficulty of experimentation. Various methods based on purely micro-graphical studies (measurement of the thickness of intermediate phases) are also proposed for evaluating the coefficient of diffusion. Our experimental results show that the hypotheses on which these methods are based are rarely valid. We have established concentration-penetration curves for the systems U-Zr (between 590 deg. C and 950 deg. C) and U-Mo (between 800 deg. C and 1050 deg. C). These curves have very often a very accentuated curvature, thus indicating variations in the diffusion coefficient, which cannot be expressed by simple relationships. Finally, we have observed certain anomalies in the neighbourhood of the interfaces between adjacent phases. Further we have studied the Kirkendall effect in poly-phase system by marking the plane of welding with tungsten wires, and compared these results to those from a previous study in the homogeneous phase. We have found that the presence of phase boundaries accentuates this effect. The interpretation of

Diffusion limited reactions in crystalline solids

International Nuclear Information System (INIS)

Fastenau, R.

1982-01-01

Diffusion limited reactions in crystal lattices are studied with diffusion and random walk theory. First the random walk on a crystal lattice is studied. These results are used in a formal study of diffusion limited reactions in which the following simplified traps are discussed: planes, cylinders, spheres, disks and rings. The traps are either present at the start of the process (annealing) or fed into the crystal at a constant rate (continuous production). For the study of trapping processes occurring in real crystals it was necessary to investigate the interaction of the reacting species on the atomic level. Using lattice relaxation calculations, several reactions were studied. These calculations result in a model for the potential energy of the crystal versus the separation of the reaction partners. This model is used in Monte Carlo simulations of the trapping process, which are made at a high trap density, since the extrapolation to the low density regime can be made using the formal part of this work. The following reactions were studied: the trapping of interstitial helium atoms by vacancies, self interstitial vacancy recombination, the trapping of vacancies by immobile, helium filled, vacancies and the capture of self interstitials and vacancies by dislocations. A part of these results is used in two models for the low temperature nucleation and growth of bubbles due to helium bombardment. The models described give the right bubble density versus helium dose, but differ widely in the fraction of helium present in the bubbles found. A mechanism of blistering based on a percolation effect is also discussed. (Auth.)

A multigrid Newton-Krylov method for flux-limited radiation diffusion

International Nuclear Information System (INIS)

Rider, W.J.; Knoll, D.A.; Olson, G.L.

1998-01-01

The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques

Contribution to the study of diffusion in poly-phase system; Contribution a l'etude de la diffusion en systeme polyphase

Energy Technology Data Exchange (ETDEWEB)

Adda, Y.; Philibert, J. [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires; Institut de Recherches de la Siderurgie Francaise (IRSID), 78 - Saint-Germain-en-Laye (France)

1959-07-01

After chemical diffusion between two metals, at temperatures where, according to the equilibrium diagram, several phases exist, parallel bands corresponding to these various phases can be seen in a section which is perpendicular to the diffusion front. It is known that in this case there are discontinuities in the concentration-penetration curve, corresponding to the interfaces. The concentrations at the point where the discontinuities occur give the limits of solubility in each of the present phases. During our experiments on the system uranium-zirconium, we verified that these concentrations do not vary with the diffusion time and therefore that the conditions of thermodynamical equilibrium are obeyed. It follows that an interesting method is available for determining the equilibrium diagram for the solid state. We have applied this method to the U-Zr system. Kinetic studies of poly-phase diffusion are as yet relatively scarce as a result of difficulty of experimentation. Various methods based on purely micro-graphical studies (measurement of the thickness of intermediate phases) are also proposed for evaluating the coefficient of diffusion. Our experimental results show that the hypotheses on which these methods are based are rarely valid. We have established concentration-penetration curves for the systems U-Zr (between 590 deg. C and 950 deg. C) and U-Mo (between 800 deg. C and 1050 deg. C). These curves have very often a very accentuated curvature, thus indicating variations in the diffusion coefficient, which cannot be expressed by simple relationships. Finally, we have observed certain anomalies in the neighbourhood of the interfaces between adjacent phases. Further we have studied the Kirkendall effect in poly-phase system by marking the plane of welding with tungsten wires, and compared these results to those from a previous study in the homogeneous phase. We have found that the presence of phase boundaries accentuates this effect. The interpretation of

Innovation-diffusion: a geographical study of the transition of family limitation practice in Taiwan.

Science.gov (United States)

Ting, T Y

1984-09-01

This paper uses map analysis to study the transition of family limitation practice in Taiwan between 1961-80. The innovation-diffusion perspective emphasizes that birth control, particularly contraception, is a recent innovation and is essentially new in human culture. The innovation-diffusion theory assumes that the decline of fertility began in a setting where there was no, or at most very limited, previous practice of birth control. The theory emphasizes the importance of the spread of information. It also assumes that innovation starts in metropolitan centers, diffuses to other urban places with some delay, and penetrates to rural areas still later. Innovation behavior also diffuses from 1 area to another which is culturally and linguistically similar. Although there was some urban to rural diffusion from the Taiwan family planning program, the government supported program provided services more evenly between urban and rural areas, thus somewhat limiting the diffusion effect from the program. For the diffusion of family practice in Taiwan, it is expected that the availability of of information about and means of family limitation practice may effect the rate of the increase of small m values -- an index of family limitation -- in an area. The case study of Pingtung county shows that the demand-side diffusion from urban to rural areas was important in the earlier decade of the transition of family plimitation practice, but distance from urban center was less important as practice became more uniform through diffusion. Ethnicity, whether or not the township was dominated by Hakka or Fukienese, also seems to have played an important role in determining the pace at which the local residents adopted family practice limitation. Hakka townships seem to have adopted family limitation practice more slowly than Fukienese townships about the same distance from the urban center. The map analysis of Pingtung county provides descriptive evidence to support the diffusion of

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

Science.gov (United States)

Gomes, S. N.; Pavliotis, G. A.

2018-06-01

In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.

Grey Box Modelling of Flow in Sewer Systems with State Dependent Diffusion

DEFF Research Database (Denmark)

Breinholt, Anders; Thordarson, Fannar Örn; Møller, Jan Kloppenborg

2011-01-01

. It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower...... flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional diffusion term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important......Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both...

Predicting the weathering of fuel and oil spills: A diffusion-limited evaporation model.

Science.gov (United States)

Kotzakoulakis, Konstantinos; George, Simon C

2018-01-01

The majority of the evaporation models currently available in the literature for the prediction of oil spill weathering do not take into account diffusion-limited mass transport and the formation of a concentration gradient in the oil phase. The altered surface concentration of the spill caused by diffusion-limited transport leads to a slower evaporation rate compared to the predictions of diffusion-agnostic evaporation models. The model presented in this study incorporates a diffusive layer in the oil phase and predicts the diffusion-limited evaporation rate. The information required is the composition of the fluid from gas chromatography or alternatively the distillation data. If the density or a single viscosity measurement is available the accuracy of the predictions is higher. Environmental conditions such as water temperature, air pressure and wind velocity are taken into account. The model was tested with synthetic mixtures, petroleum fuels and crude oils with initial viscosities ranging from 2 to 13,000 cSt. The tested temperatures varied from 0 °C to 23.4 °C and wind velocities from 0.3 to 3.8 m/s. The average absolute deviation (AAD) of the diffusion-limited model ranged between 1.62% and 24.87%. In comparison, the AAD of a diffusion-agnostic model ranged between 2.34% and 136.62% against the same tested fluids. Copyright © 2017 Elsevier Ltd. All rights reserved.

Comparing the demographic factors of patient with limited and diffuse type of alopecia areata

Directory of Open Access Journals (Sweden)

Mina Daliri

2010-09-01

Full Text Available Background: Alopecia areata is a chronic inflammatory disease that involves the hair follicle. Clinically, patients with alopecia areata may have patchy or confluent hair loss on the scalp or body so we conduct a study to compare the demographic aspects of patient with limited and diffuse type of alopecia areata.Materials and Method: We conducted a descriptive-analyzing study in which 306 patient were chosen. The patients were divided into two groups of diffuse and limited Alopecia. Demographic factors including age, gender, disease onset were compared in two groups. Results: Out of 306 patients, 58.8 % were male and 41.2 % were female. 247 patients (80.7% suffered from limited type and 59 patients (19.2% suffered from diffuse type. The mean age of the onset of involvement in limited group was 21.9±12 yr and 15.8±12 yr in diffuse group. The mean duration of involvement in limited group was 18.7 months and 71 months in diffuse group. Conclusion: Diffuse type alopecia areata starts at lower age and has longer duration. Our study results were similar to the others. Like other studies, thyroid disorders and atopic dermatitis are positively correlative to the severity of disease

Gaseous diffusion system

International Nuclear Information System (INIS)

Garrett, G.A.; Shacter, J.

1978-01-01

A gaseous diffusion system is described comprising a plurality of diffusers connected in cascade to form a series of stages, each of the diffusers having a porous partition dividing it into a high pressure chamber and a low pressure chamber, and means for combining a portion of the enriched gas from a succeeding stage with a portion of the enriched gas from the low pressure chamber of each stage and feeding it into one extremity of the high pressure chamber thereof

Limiting diffusion current at rotating disk electrode with dense particle layer.

Science.gov (United States)

Weroński, P; Nosek, M; Batys, P

2013-09-28

Exploiting the concept of diffusion permeability of multilayer gel membrane and porous multilayer we have derived a simple analytical equation for the limiting diffusion current at rotating disk electrode (RDE) covered by a thin layer with variable tortuosity and porosity, under the assumption of negligible convection in the porous film. The variation of limiting diffusion current with the porosity and tortuosity of the film can be described in terms of the equivalent thickness of stagnant solution layer, i.e., the average ratio of squared tortuosity to porosity. In case of monolayer of monodisperse spherical particles, the equivalent layer thickness is an algebraic function of the surface coverage. Thus, by means of cyclic voltammetry of RDE with a deposited particle monolayer we can determine the monolayer surface coverage. The effect of particle layer adsorbed on the surface of RDE increases non-linearly with surface coverage. We have tested our theoretical results experimentally by means of cyclic voltammetry measurements of limiting diffusion current at the glassy carbon RDE covered with a monolayer of 3 μm silica particles. The theoretical and experimental results are in a good agreement at the surface coverage higher than 0.7. This result suggests that convection in a monolayer of 3 μm monodisperse spherical particles is negligibly small, in the context of the coverage determination, in the range of very dense particle layers.

An extended fractal growth regime in the diffusion limited aggregation including edge diffusion

Directory of Open Access Journals (Sweden)

Aritra Ghosh

2016-01-01

Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.

Limiting Current of Oxygen Reduction on Gas-Diffusion Electrodes for Phosphoric Acid Fuel Cells

DEFF Research Database (Denmark)

Li, Qingfeng; Gang, Xiao; Hjuler, Hans Aage

1994-01-01

on polytetrafluorine-ethyl bonded gas-diffusion electordes in phosphoric acid with and without fluorinated additives. This provides an alternative to estimate the film thickness by combining it with the acid-adsorption measurements and the porosity analysis of the catalyst layer. It was noticed that the limiting......Various models have been devoted to the operation mechanism of porous diffusion electrodes. They are, however, suffering from the lack of accuracy concerning the acid-film thickness on which they are based. In the present paper the limiting current density has been measured for oxygen reduction...... current density can be accomplished either by gas-phase diffusion or liquid-phase diffusion, and it is the latter that can be used in the film-thickness estimation. It is also important to mention that at such a limiting condition, both the thin-film model and the filmed agglomerate model reach the same...

Amplitude equations for a sub-diffusive reaction-diffusion system

International Nuclear Information System (INIS)

Nec, Y; Nepomnyashchy, A A

2008-01-01

A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

Caring for the Patient With Limited Systemic Scleroderma.

Science.gov (United States)

Lachner, Kelly Denise

2016-01-01

Systemic scleroderma (systemic sclerosis) is a rare, autoimmune, collagen-vascular disease of unknown etiology that affects the connective tissues of the skin, internal organs, as well as the small blood vessels. There are 3 subclasses of systemic scleroderma: limited cutaneous, diffuse cutaneous, and sine scleroderma. Prognosis depends on the extent of organ involvement. Complications of systemic scleroderma can involve the cardiovascular, pulmonary, gastrointestinal, renal, integumentary, and the skeletal-muscular systems. Because systemic scleroderma is not common, many orthopaedic nurses may be unfamiliar with how to best provide care. This article provides information about the complexity of the different types of this disease and the basic nursing care of the patient with the most common subclass of systemic scleroderma, limited cutaneous systemic scleroderma.

Pattern of diffusion-limited aggregation on nonuniform substrate

CERN Document Server

Ouyang Wen Ze; Zou Xian Wu; Jin Zhun Zhi

2003-01-01

Pattern of diffusion-limited aggregation (DLA) on nonuniform substrate was investigated by computer simulations. The nonuniform substrates are represented by Leath percolations with the probability p. p stands for the degree of nonuniformity and takes values in the range p sub c<=p<=1, where p sub c is the threshold of percolation. The DLA cluster grows up on the Leath percolation substrate. The patterns of the DLA clusters appear asymmetrical and nonuniform, and the branches are relative few for the case p is close to p sub c. In addition, the pattern depends on the shape of substrate. As p increases from p sub c to 1, cluster changes to pure DLA gradually. Correspondingly, the fractal dimension increases from 1.46 to 1.68. Also, the random walks on Leath percolations through the range p sub c<=p<=1 were examined. Our simulations show the Honda-Toyoki-Matsushita relation is still reasonable for fractional dimensional systems.

Diffuse Ceiling Ventilation

DEFF Research Database (Denmark)

Zhang, Chen; Yu, Tao; Heiselberg, Per Kvols

cooling capacity, energy saving, low investment cost and low noise level; while the limitations include condensation risk and the limit on the room geometry. Furthermore, the crucial design parameters are summarized and their effects on the system performance are discussed. In addition to the stand...... is not well structured with this system. These become the motivations in developing the design guide. This design guide aims to establish a systematic understanding of diffuse ceiling ventilation and provide assistance in designing of such a system. The guide is targeted at design engineers, architects...... and manufacturers and the users of diffuse ceiling technology. The design guide introduces the principle and key characteristics of room air distribution with diffuse ceiling ventilation. It provides an overview of potential benefit and limitations of this technology. The benefits include high thermal comfort, high...

Diffusion in ordered binary solid systems

International Nuclear Information System (INIS)

Stolwijk, N.A.

1980-01-01

This thesis contains contributions to the field of diffusion in ordered binary solid systems. An extensive experimental investigation of the self diffusion in CoGa is presented. The results of these diffusion measurements strongly suggest that a substantial part of the atomic migration is caused by a new type of defect. A quantitative description of the atomic displacements via this defect is given. Finally computer simulations are presented of diffusion and ordering in binary solid systems. (Auth.)

Effect of Diffusion Limitations on Multianalyte Determination from Biased Biosensor Response

Science.gov (United States)

Baronas, Romas; Kulys, Juozas; Lančinskas, Algirdas; Žilinskas, Antanas

2014-01-01

The optimization-based quantitative determination of multianalyte concentrations from biased biosensor responses is investigated under internal and external diffusion-limited conditions. A computational model of a biocatalytic amperometric biosensor utilizing a mono-enzyme-catalyzed (nonspecific) competitive conversion of two substrates was used to generate pseudo-experimental responses to mixtures of compounds. The influence of possible perturbations of the biosensor signal, due to a white noise- and temperature-induced trend, on the precision of the concentration determination has been investigated for different configurations of the biosensor operation. The optimization method was found to be suitable and accurate enough for the quantitative determination of the concentrations of the compounds from a given biosensor transient response. The computational experiments showed a complex dependence of the precision of the concentration estimation on the relative thickness of the outer diffusion layer, as well as on whether the biosensor operates under diffusion- or kinetics-limited conditions. When the biosensor response is affected by the induced exponential trend, the duration of the biosensor action can be optimized for increasing the accuracy of the quantitative analysis. PMID:24608006

Instability induced by cross-diffusion in reaction-diffusion systems

DEFF Research Database (Denmark)

Tian, Canrong; Lin, Zhigui; Pedersen, Michael

2010-01-01

In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cros...... can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.......In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion...

Modeling persistence of motion in a crowded environment: The diffusive limit of excluding velocity-jump processes

Science.gov (United States)

Gavagnin, Enrico; Yates, Christian A.

2018-03-01

Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level. However, no diffusive limit of the ABM has been obtained from such a model. Connecting the microscopic behavior of the ABM to a diffusive macroscopic description is desirable, since it allows the exploration of a wider range of scenarios and establishes a direct connection with commonly used statistical tools of movement analysis. In order to connect the ABM at the population level to a diffusive PDE at the population level, we consider a generalization of the agent-based velocity-jump process on a two-dimensional lattice with three forms of agent interaction. This generalization allows us to take a diffusive limit and obtain a faithful population-level description. We investigate the properties of the model at both the individual and population levels and we elucidate some of the models' key characteristic features. In particular, we show an intrinsic anisotropy inherent to the models and we find evidence of a spontaneous form of aggregation at both the micro- and macroscales.

Turing instability in reaction-diffusion systems with nonlinear diffusion

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2013-10-15

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

Molecular dynamics simulations of interfacial interactions between small nanoparticles during diffusion-limited aggregation

International Nuclear Information System (INIS)

Lu, Jing; Liu, Dongmei; Yang, Xiaonan; Zhao, Ying; Liu, Haixing; Tang, Huan; Cui, Fuyi

2015-01-01

Graphical abstract: - Highlights: • Diffusion-limited aggregation is analyzed using molecular dynamic simulations. • The aggregation processand aggregate structure vary with particle size. • Particle-particle interaction and surface diffusion result in direct bonding. • Water-mediated interaction is responsible for the separation betweennanoparticles. - Abstract: Due to the limitations of experimental methods at the atomic level, research on the aggregation of small nanoparticles (D < 5 nm) in aqueous solutions is quite rare. The aggregation of small nanoparticles in aqueous solutions is very different than that of normal sized nanoparticles. The interfacial interactions play a dominant role in the aggregation of small nanoparticles. In this paper, molecular dynamics simulations, which can explore the microscopic behavior of nanoparticles during the diffusion-limited aggregation at an atomic level, were employed to reveal the aggregation mechanism of small nanoparticles in aqueous solutions. First, the aggregation processes and aggregate structure were depicted. Second, the particle–particle interaction and surface diffusion of nanoparticles during aggregation were investigated. Third, the water-mediated interactions during aggregation were ascertained. The results indicate that the aggregation of nanoparticle in aqueous solutions is affected by particle size. The strong particle–particle interaction and high surface diffusion result in the formation of particle–particle bonds of 2 nm TiO 2 nanoparticles, and the water-mediated interaction plays an important role in the aggregation process of 3 and 4 nm TiO 2 nanoparticles.

Diffuse charge dynamics in ionic thermoelectrochemical systems.

Science.gov (United States)

Stout, Robert F; Khair, Aditya S

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion

Diffuse charge dynamics in ionic thermoelectrochemical systems

Science.gov (United States)

Stout, Robert F.; Khair, Aditya S.

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion

On the transition from short-range diffusion-limited to collision-limited growth in alloy solidification

International Nuclear Information System (INIS)

Aziz, M.J.; Boettinger, W.J.

1994-01-01

Short-range diffusion-limited growth, collision-limited growth, and the transition between the two regimes are explained as natural consequences of a single model for the kinetics of alloy solidification. Analytical expressions are developed for the velocity-undercooling function of a planar interface during dilute alloy solidification, using Turnbull's collision-limited growth model and the Continuous Growth Solute Trapping Model of Aziz and Kaplan both with and without a solute drag effect. The interface mobility, -dv/dT, is shown to be very high (proportional to the speed of sound) if the alloy is sufficiently dilute or if the growth rate is sufficiently rapid for nearly complete solute trapping. The interface mobility is reduced by the three orders of magnitude (becoming proportional to the diffusive speed) at intermediate growth rates where partial solute trapping occurs. Differences in low velocity predictions of the models with and without solute drag are also discussed. Comparison of the results of the analytical expressions to numerical solutions of the non-dilute kinetic model for Al-Be alloys shows that the dilute approximation breaks down at melt compositions on the order of 10 at.%. Similar variations in the interface mobility are shown for the disorder-trapping model of Boettinger and Aziz

A tri-junction diffusion couple analysis of the Nb-Cr-Ti system at 950{degrees}C

Energy Technology Data Exchange (ETDEWEB)

Thoma, D.J. [Los Alamos National Lab., NM (United States); Perepezko, J.H. [Wisconsin Univ., Madison, WI (United States). Dept. of Materials Science and Engineering

1993-11-01

With a three-way diffusion couple consisting of a tri-junction between three elements, a whole spectrum of phase development and ternary equilibria is available within a single isothermal sample. Binary equilibria (for the three binary systems) are also available in single sample by analyzing diffusion zones at composition limits outside the field of ternary interaction. The tri-junction approach was employed to evaluate ternary phase formation, ternary solubility limits of binary phases, and diffusion paths in a candidate high-temperature structural system (Nb-Cr-Ti). Ternary phase equilibria and tie lines have been defined at 950C and results confirmed with isothermal anneals of two-phase ternary alloys. The continuous solubility in TiCr{sub 2}-NbCr{sub 2} region is broadened by at least 5 at. % from binary intermetallic phase fields. No new ternary phases were detected in the Nb-CrTi system at 950C. By examining the relative shifts in the diffusion interfaces, a qualitative ranking of interdiffusion suggests that addition of Nb restricts diffusion of Cr into Ti compared to binary (Cr/Ti) behavior.

Diffusion limit of Lévy-Lorentz gas is Brownian motion

Science.gov (United States)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

In this paper we analyze asymptotic behaviour of a stochastic process called Lévy-Lorentz gas. This process is aspecial kind of continuous-time random walk in which walker moves in the fixed environment composed of scattering points. Upon each collision the walker performs a flight to the nearest scattering point. This type of dynamics is observed in Lévy glasses or long quenched polymers. We show that the diffusion limit of Lévy-Lorentz gas with finite mean distance between scattering centers is the standard Brownian motion. Thus, for long times the behaviour of the Lévy-Lorentz gas is close to the diffusive regime.

Relativistic collective diffusion in one-dimensional systems

Science.gov (United States)

Lin, Gui-Wu; Lam, Yu-Yiu; Zheng, Dong-Qin; Zhong, Wei-Rong

2018-05-01

The relativistic collective diffusion in one-dimensional molecular system is investigated through nonequilibrium molecular dynamics with Monte Carlo methods. We have proposed the relationship among the speed, the temperature, the density distribution and the collective diffusion coefficient of particles in a relativistic moving system. It is found that the relativistic speed of the system has no effect on the temperature, but the collective diffusion coefficient decreases to zero as the velocity of the system approaches to the speed of light. The collective diffusion coefficient is modified as D‧ = D(1 ‑w2 c2 )3 2 for satisfying the relativistic circumstances. The present results may contribute to the understanding of the behavior of the particles transport diffusion in a high speed system, as well as enlighten the study of biological metabolism at relativistic high speed situation.

Excess oxygen limited diffusion and precipitation of iron in amorphous silicon dioxide

Science.gov (United States)

Leveneur, J.; Langlois, M.; Kennedy, J.; Metson, James B.

2017-10-01

In micro- and nano- electronic device fabrication, and particularly 3D designs, the diffusion of a metal into sublayers during annealing needs to be minimized as it is usually detrimental to device performance. Diffusion also causes the formation and growth of nanoprecipitates in solid matrices. In this paper, the diffusion behavior of low energy, low fluence, ion implanted iron into a thermally grown silicon oxide layer on silicon is investigated. Different ion beam analysis and imaging techniques were used. Magnetization measurements were also undertaken to provide evidence of nanocrystalline ordering. While standard vacuum furnace annealing and electron beam annealing lead to fast diffusion of the implanted species towards the Si/SiO2 interface, we show that furnace annealing in an oxygen rich atmosphere prevents the diffusion of iron that, in turn, limits the growth of the nanoparticles. The diffusion and particle growth is also greatly reduced when oxygen atoms are implanted in the SiO2 prior to Fe implantation, effectively acting as a diffusion barrier. The excess oxygen is hypothesized to trap Fe atoms and reduce their mean free path during the diffusion. Monte-Carlo simulations of the diffusion process which consider the random walk of Fe, Fick's diffusion of O atoms, Fe precipitation, and desorption of the SiO2 layer under the electron beam annealing were performed. Simulation results for the three preparation conditions are found in good agreement with the experimental data.

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

KAUST Repository

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

2009-01-01

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

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

KAUST Repository

Carrillo, J. A.

2009-10-30

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

Multifractal properties of diffusion-limited aggregates and random multiplicative processes

International Nuclear Information System (INIS)

Canessa, E.

1991-04-01

We consider the multifractal properties of irreversible diffusion-limited aggregation (DLA) from the point of view of the self-similarity of fluctuations in random multiplicative processes. In particular we analyse the breakdown of multifractal behaviour and phase transition associated with the negative moments of the growth probabilities in DLA. (author). 20 refs, 5 figs

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.

Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

Energy Technology Data Exchange (ETDEWEB)

Smedley-Stevenson, Richard P., E-mail: richard.smedley-stevenson@awe.co.uk [AWE PLC, Aldermaston, Reading, Berkshire, RG7 4PR (United Kingdom); Department of Earth Science and Engineering, Imperial College London, SW7 2AZ (United Kingdom); McClarren, Ryan G., E-mail: rmcclarren@ne.tamu.edu [Department of Nuclear Engineering, Texas A & M University, College Station, TX 77843-3133 (United States)

2015-04-01

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes.

Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

International Nuclear Information System (INIS)

Smedley-Stevenson, Richard P.; McClarren, Ryan G.

2015-01-01

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes

Diffusion and particle mobility in 1D system

International Nuclear Information System (INIS)

Borman, V.D.; Johansson, B.; Skorodumova, N.V.; Tronin, I.V.; Tronin, V.N.; Troyan, V.I.

2006-01-01

The transport properties of one-dimensional (1D) systems have been studied theoretically. Contradictory experimental results on molecular transport in quasi-1D systems, such as zeolite structures, when both diffusion transport acceleration and the existence of the diffusion mode with lower particle mobility (single-file diffusion ( 2 >∼t 1/2 )) have been reported, are consolidated in a consistent model. Transition from the single-file diffusion mode to an Einstein-like diffusion 2 >∼t with diffusion coefficient increasing with the density has been predicted to occur at large observation times

A singular perturbation limit of diffused interface energy with a fixed contact angle condition

OpenAIRE

Kagaya, Takashi; Tonegawa, Yoshihiro

2016-01-01

We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\\Omega \\subset \\mathbb{R}^n$. We show that the limit varifold derived from the diffused energy satisfies a generalized contact angle condition on the boundary under a set of assumptions.

Propagation and diffusion-limited extinction of nonadiabatic heterogeneous flame in the SHS process

International Nuclear Information System (INIS)

Makino, Atsushi

1994-01-01

Nonadiabatic heterogeneous flame propagation and extinction in self-propagating high-temperature synthesis (SHS) are analyzed based on a premixed mode of propagation for the bulk flame supported by the nonpremixed reaction of dispersed nonmetals in the liquid metal. The formulation allows for volumetric heat loss throughout the bulk flame, finite-rate Arrhenius reaction at the particle surface, and temperature-sensitive Arrhenius mass diffusion in the liquid. Results show that, subsequent to melting of the metal, the flame structure consists of a relatively thin diffusion-consumption/convection zone followed by a relatively thick convection-loss zone, that the flame propagation rate decreases with increasing heat loss, that at a critical heat-loss rate the flame extinguishes as indicated by the characteristic turning-point behavior, that the surface reaction is diffusion limited such that the nonlinear, temperature-sensitive nature of the system is actually a consequence of the Arrhenius mass diffusion, and that extinction is sensitively affected by the mixture ratio, the degree of dilution, the initial temperature of the compact, and the size of the nonmetal particles. An explicit expression is derived for the normalized mass burning rate, which exhibits the characteristic turning point and shows that extinction occurs when this value is reduced to e -1/2 , which is the same as that for the nonadiabatic gaseous premixed flame. It is further shown that the theoretical results agree well with available experimental data, indicating that the present formulation captures the essential features of the nonadiabatic heterogeneous SHS processes and its potential for extension to describe other SHS phenomena

New limit theorems for regular diffusion processes with finite speed measure

NARCIS (Netherlands)

J.H. van Zanten (Harry)

2000-01-01

textabstractWe derive limit theorems for diffusion processes that have a finite speed measure. First we prove a number of asymptotic properties of the density $rho_t = dmu_t /dmu$ of the empirical measure $mu_t$ with respect to the normalized speed measure $mu$. These results are then used to derive

Analysis of diffusivity of the oscillating reaction components in a microreactor system

Directory of Open Access Journals (Sweden)

Martina Šafranko

2017-01-01

Full Text Available When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography.

Science.gov (United States)

Leblond, Frederic; Tichauer, Kenneth M; Pogue, Brian W

2010-11-29

The spatial resolution and recovered contrast of images reconstructed from diffuse fluorescence tomography data are limited by the high scattering properties of light propagation in biological tissue. As a result, the image reconstruction process can be exceedingly vulnerable to inaccurate prior knowledge of tissue optical properties and stochastic noise. In light of these limitations, the optimal source-detector geometry for a fluorescence tomography system is non-trivial, requiring analytical methods to guide design. Analysis of the singular value decomposition of the matrix to be inverted for image reconstruction is one potential approach, providing key quantitative metrics, such as singular image mode spatial resolution and singular data mode frequency as a function of singular mode. In the present study, these metrics are used to analyze the effects of different sources of noise and model errors as related to image quality in the form of spatial resolution and contrast recovery. The image quality is demonstrated to be inherently noise-limited even when detection geometries were increased in complexity to allow maximal tissue sampling, suggesting that detection noise characteristics outweigh detection geometry for achieving optimal reconstructions.

Diffusion in Deterministic Interacting Lattice Systems

Science.gov (United States)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

Nonlinear analysis of a reaction-diffusion system: Amplitude equations

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2012-10-15

A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems

International Nuclear Information System (INIS)

Mielke, Alexander

2011-01-01

In recent years the theory of the Wasserstein metric has opened up new treatments of diffusion equations as gradient systems, where the free energy or entropy take the role of the driving functional and where the space is equipped with the Wasserstein metric. We show on the formal level that this gradient structure can be generalized to reaction–diffusion systems with reversible mass-action kinetic. The metric is constructed using the dual dissipation potential, which is a quadratic functional of all chemical potentials including the mobilities as well as the reaction kinetics. The metric structure is obtained by Legendre transform from the dual dissipation potential. The same ideas extend to systems including electrostatic interactions or a correct energy balance via coupling to the heat equation. We show this by treating the semiconductor equations involving the electron and hole densities, the electrostatic potential, and the temperature. Thus, the models in Albinus et al (2002 Nonlinearity 15 367–83), which stimulated this work, have a gradient structure

Limited diffusive fluxes of substrate facilitate coexistence of two competing bacterial strains

DEFF Research Database (Denmark)

Dechesne, Arnaud; Or, D.; Smets, Barth F.

2008-01-01

. It has been proposed, but never unambiguously experimentally tested, that a low substrate diffusive flux would impact bacterial diversity, by promoting the coexistence between slow-growing bacteria and their potentially faster-growing competitors. We used a simple experimental system, based on a Petri...... dish and a perforated Teflon((R)) membrane to control diffusive fluxes of substrate (benzoate) whilst permitting direct observation of bacterial colonies. The system was inoculated with prescribed strains of Pseudomonas, whose growth was quantified by microscopic monitoring of the fluorescent proteins...

A vanishing diffusion limit in a nonstandard system of phase field equations

Czech Academy of Sciences Publication Activity Database

Colli, P.; Gilardi, G.; Krejčí, Pavel; Sprekels, J.

2014-01-01

Roč. 3, č. 2 (2014), s. 257-275 ISSN 2163-2480 R&D Projects: GA ČR GAP201/10/2315 Institutional support: RVO:67985840 Keywords : nonstandard phase field system * nonlinear partial differential equations * asympotic limit Subject RIV: BA - General Mathematics Impact factor: 0.373, year: 2014 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=9918

Resolution-limiting factors in 2-deoxyglucose autoradiography. I. Factors other than diffusion

Energy Technology Data Exchange (ETDEWEB)

Gallistel, C.R.; Nichols, S. (Pennsylvania Univ., Philadelphia, PA (USA). Dept. of Psychology)

1983-05-16

The authors measured the extent to which factors other than the diffusion of the radioactive label during tissue preparation limits the spatial resolving power of 2-deoxyglucose (2-DG) autoradiography. Radioactive swept frequency gratings were created using microcircuit lithography. The gratings consisted of alternating equal width radioactive and non-radioactive bars in groups of narrowing bar width (effective range 500-20 ..mu..m). The vertical thickness of the gratings ranged from 2.25 to 20 ..mu..m. The isotope in the radioactive bars was either /sup 14/C or /sup 3/H. A variety of X-ray films were exposed to these gratings and the resulting images scanned with microdensitometers or video digitizers to determine the fall off in image contrast (dark-bar values minus light-bar values) as a function of the number of dark bars (lines) per millimeter. The power of the isotope was the resolution limiting factor. Grating thickness and type of film made little difference. The limit of resolution with /sup 14/C was 10 lines/mm: with /sup 3/H it was 25 lines/mm. The microdensitometer itself is apt to be a resolution limiting factor; the resolving power of those commonly used in autoradiography is unlikely to exceed 10 lines/mm. From measurements of the steepness of gray-matter to white-matter transitions in the image from a tissue section, they conclude that the resolution in the image was no worse than 1.6-3.2 lines/mm. Either the isotope or diffusion of the 2-DG during tissue preparation must be the factor that limits resolution.

Nonlinear degenerate cross-diffusion systems with nonlocal interaction

OpenAIRE

Di Francesco, M.; Esposito, A.; Fagioli, S.

2017-01-01

We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove g...

Diffusion microscopist simulator - The development and application of a Monte Carlo simulation system for diffusion MRI

International Nuclear Information System (INIS)

Yeh, C.H.

2011-09-01

Diffusion magnetic resonance imaging (dMRI) has made a significant breakthrough in neurological disorders and brain research thanks to its exquisite sensitivity to tissue cyto-architecture. However, as the water diffusion process in neuronal tissues is a complex biophysical phenomena at molecular scale, it is difficult to infer tissue microscopic characteristics on a voxel scale from dMRI data. The major methodological contribution of this thesis is the development of an integrated and generic Monte Carlo simulation framework, 'Diffusion Microscopist Simulator' (DMS), which has the capacity to create 3D biological tissue models of various shapes and properties, as well as to synthesize dMRI data for a large variety of MRI methods, pulse sequence design and parameters. DMS aims at bridging the gap between the elementary diffusion processes occurring at a micrometric scale and the resulting diffusion signal measured at millimetric scale, providing better insights into the features observed in dMRI, as well as offering ground-truth information for optimization and validation of dMRI acquisition protocols for different applications. We have verified the performance and validity of DMS through various benchmark experiments, and applied to address particular research topics in dMRI. Based on DMS, there are two major application contributions in this thesis. First, we use DMS to investigate the impact of finite diffusion gradient pulse duration (delta) on fibre orientation estimation in dMRI. We propose that current practice of using long delta, which is enforced by the hardware limitation of clinical MRI scanners, is actually beneficial for mapping fibre orientations, even though it violates the underlying assumption made in q-space theory. Second, we employ DMS to investigate the feasibility of estimating axon radius using a clinical MRI system. The results suggest that the algorithm for mapping the direct microstructures is applicable to dMRI data acquired from

Quantitative relationship between the octanol/water partition coefficient and the diffusion limitation of the exchange between adipose and blood.

Science.gov (United States)

Levitt, David G

2010-01-07

The goal of physiologically based pharmacokinetics (PBPK) is to predict drug kinetics from an understanding of the organ/blood exchange. The standard approach is to assume that the organ is "flow limited" which means that the venous blood leaving the organ equilibrates with the well-stirred tissue compartment. Although this assumption is valid for most solutes, it has been shown to be incorrect for several very highly fat soluble compounds which appear to be "diffusion limited". This paper describes the physical basis of this adipose diffusion limitation and its quantitative dependence on the blood/water (Kbld-wat) and octanol/water (Kow) partition coefficient. Experimental measurements of the time dependent rat blood and adipose concentration following either intravenous or oral input were used to estimate the "apparent" adipose perfusion rate (FA) assuming that the tissue is flow limited. It is shown that the ratio of FA to the anatomic perfusion rate (F) provides a measure of the diffusion limitation. A quantitative relationship between this diffusion limitation and Kbld-wat and Kow is derived. This analysis was applied to previously published data, including the Oberg et. al. measurements of the rat plasma and adipose tissue concentration following an oral dose of a mixture of 13 different polychlorinated biphenyls. Solutes become diffusion limited at values of log Kow greater than about 5.6, with the adipose-blood exchange rate reduced by a factor of about 30 for a solute with a log Kow of 7.36. Quantitatively, a plot of FA/F versus Kow is well described assuming an adipose permeability-surface area product (PS) of 750/min. This PS corresponds to a 0.14 micron aqueous layer separating the well-stirred blood from the adipose lipid. This is approximately equal to the thickness of the rat adipose capillary endothelium. These results can be used to quantitate the adipose-blood diffusion limitation as a function of Kow. This is especially important for the highly

Disposable glucose test strip for whole blood with integrated sensing/diffusion-limiting layer

Energy Technology Data Exchange (ETDEWEB)

Chen Zhencheng [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China); Fang Cheng, E-mail: fangpingchuan@163.co [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China); Wang Hongyan; He Jishan [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China)

2009-12-30

A disposable glucose test strip with an integrated sensing/diffusion-limiting layer was developed. A formulation containing filler, glucose oxidase and electronic mediator was screen-printed over two carbon electrodes to form an integrated sensing/diffusion-limiting layer. On rehydration, the integrated layer does not break up, but swells to form a gelled and three-dimensional meshy reaction zone on the surface of the underlying conductive elements in which reactants and mediator move freely, but interfering species such as red blood cells containing oxygenated hemoglobin are excluded. On the same time, the integrated layer maintains a rate of permeation of the analyte through it with a variation of less than 10% at temperatures ranging from 15 deg. C to 42 deg. C. This biosensor is substantially insensitive to interferents and essentially independent to relevant temperature, which provides a more reliable reading of actual blood glucose value in human whole blood.

A method to measure the diffusion coefficient by neutron wave propagation for limited samples

International Nuclear Information System (INIS)

Woznicka, U.

1986-03-01

A study has been made of the use of the neutron wave and pulse propagation method for measurement of thermal neutron diffusion parameters. Earlier works an homogenous and heterogeneous media are reviewed. A new method is sketched for the determination of the diffusion coefficient for samples of limited size. The principle is to place a relatively thin slab of the material between two blocks of a medium with known properties. The advantages and disadvantages of the method are discussed. (author)

Model of alpha particle diffusion in the outer limiter shadow of TFTR

International Nuclear Information System (INIS)

Wang, S.; Academia Sinica, Hefei, Anhui; Zweben, S.J.

1996-05-01

A new code, Monte Carlo Collisional Stochastic Orbit Retracing (MCCSOR), has been developed to model the alpha particle loss signal as measured by the outer midplane scintillator detector in TFTR. The shadowing effects due to the outer limiters and the detector itself have been included, along with a pitch angle scattering and stochastic ripple diffusion. Shadowing by the outer limiters has a strong effect on both the magnitude and pitch angle distribution of the calculated loss. There is at least qualitative agreement between the calculated results and the experimental data

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

Science.gov (United States)

Otto, Andereas; Wang, Jian; Radons, Günter

2017-11-01

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

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

Relaxation and Diffusion in Complex Systems

CERN Document Server

Ngai, K L

2011-01-01

Relaxation and Diffusion in Complex Systems comprehensively presents a variety of experimental evidences of universal relaxation and diffusion properties in complex materials and systems. The materials discussed include liquids, glasses, colloids, polymers, rubbers, plastic crystals and aqueous mixtures, as well as carbohydrates, biomolecules, bioprotectants and pharmaceuticals. Due to the abundance of experimental data, emphasis is placed on glass-formers and the glass transition problem, a still unsolved problem in condensed matter physics and chemistry. The evidence for universal properties of relaxation and diffusion dynamics suggests that a fundamental physical law is at work. The origin of the universal properties is traced to the many-body effects of the interaction, rigorous theory of which does not exist at the present time. However, using solutions of simplified models as guides, key quantities have been identified and predictions of the universal properties generated. These predictions from Ngai’...

Dynamic phase transition in diffusion-limited reactions

International Nuclear Information System (INIS)

Tauber, U.C.

2002-01-01

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d c = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues (Author)

Maxwell-Stefan diffusion coefficient estimation for ternary systems: an ideal ternary alcohol system.

Science.gov (United States)

Allie-Ebrahim, Tariq; Zhu, Qingyu; Bräuer, Pierre; Moggridge, Geoff D; D'Agostino, Carmine

2017-06-21

The Maxwell-Stefan model is a popular diffusion model originally developed to model diffusion of gases, which can be considered thermodynamically ideal mixtures, although its application has been extended to model diffusion in non-ideal liquid mixtures as well. A drawback of the model is that it requires the Maxwell-Stefan diffusion coefficients, which are not based on measurable quantities but they have to be estimated. As a result, numerous estimation methods, such as the Darken model, have been proposed to estimate these diffusion coefficients. However, the Darken model was derived, and is only well defined, for binary systems. This model has been extended to ternary systems according to two proposed forms, one by R. Krishna and J. M. van Baten, Ind. Eng. Chem. Res., 2005, 44, 6939-6947 and the other by X. Liu, T. J. H. Vlugt and A. Bardow, Ind. Eng. Chem. Res., 2011, 50, 10350-10358. In this paper, the two forms have been analysed against the ideal ternary system of methanol/butan-1-ol/propan-1-ol and using experimental values of self-diffusion coefficients. In particular, using pulsed gradient stimulated echo nuclear magnetic resonance (PGSTE-NMR) we have measured the self-diffusion coefficients in various methanol/butan-1-ol/propan-1-ol mixtures. The experimental values of self-diffusion coefficients were then used as the input data required for the Darken model. The predictions of the two proposed multicomponent forms of this model were then compared to experimental values of mutual diffusion coefficients for the ideal alcohol ternary system. This experimental-based approach showed that the Liu's model gives better predictions compared to that of Krishna and van Baten, although it was only accurate to within 26%. Nonetheless, the multicomponent Darken model in conjunction with self-diffusion measurements from PGSTE-NMR represents an attractive method for a rapid estimation of mutual diffusion in multicomponent systems, especially when compared to exhaustive

Effect of macromolecular crowding on the rate of diffusion-limited ...

Indian Academy of Sciences (India)

The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model qualitatively explains some ...

Development of an Automated Diffusion Scrubber-Conductometry System for Measuring Atmospheric Ammonia

International Nuclear Information System (INIS)

Lee, Bok Young; Lee, Chong Keun; Lee, Dong Soo

2011-01-01

A semi-continuous and automated method for quantifying atmospheric ammonia at the parts per billion level has been developed. The instrument consists of a high efficiency diffusion scrubber, an electrolytic on-line anion exchange device, and a conductivity detector. Water soluble gases in sampled air diffuse through the porous membrane and are absorbed in an absorbing solution. Interferences are eliminated by using an anion exchange devises. The electrical conductivity of the solution is measured without chromatographic separation. The collection efficiency was over 99%. Over the 0-200 ppbv concentration range, the calibration was linear with r"2 = 0.99. The lower limit of detection was 0.09 ppbv. A parallel analysis of Seoul air over several days using this method and a diffusion scrubber coupled to an ion chromatography system showed acceptable agreement, r"2 = 0.940 (n = 686). This method can be applied for ambient air monitoring of ammonia

Mathematical aspects of reacting and diffusing systems

CERN Document Server

Fife, Paul C

1979-01-01

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

Spin-diffusions and diffusive molecular dynamics

Science.gov (United States)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Plasma diffusion in systems with disrupted magnetic surfaces

International Nuclear Information System (INIS)

Morozov, D.K.; Pogutse, O.P.

1982-01-01

Plasma diffusion is analyzed in the case in which the system of magnetic surfaces is disrupted by a stochastic perturbation of the magnetic field. The diffusion coefficient is related to the statistical properties of the field. The statistical characteristics of the field are found when the magnetic surfaces near the separatrix are disrupted by an external perturbation. The diffusion coefficient is evaluated in the region in which the magnetic surfaces are disrupted. In this region the diffusion coefficient is of the Bohm form

Development of an Automated Diffusion Scrubber-Conductometry System for Measuring Atmospheric Ammonia

Energy Technology Data Exchange (ETDEWEB)

Lee, Bok Young; Lee, Chong Keun; Lee, Dong Soo [Yonsei University, Seoul (Korea, Republic of)

2011-06-15

A semi-continuous and automated method for quantifying atmospheric ammonia at the parts per billion level has been developed. The instrument consists of a high efficiency diffusion scrubber, an electrolytic on-line anion exchange device, and a conductivity detector. Water soluble gases in sampled air diffuse through the porous membrane and are absorbed in an absorbing solution. Interferences are eliminated by using an anion exchange devises. The electrical conductivity of the solution is measured without chromatographic separation. The collection efficiency was over 99%. Over the 0-200 ppbv concentration range, the calibration was linear with r{sup 2} = 0.99. The lower limit of detection was 0.09 ppbv. A parallel analysis of Seoul air over several days using this method and a diffusion scrubber coupled to an ion chromatography system showed acceptable agreement, r{sup 2} = 0.940 (n = 686). This method can be applied for ambient air monitoring of ammonia.

Entropy as a measure of diffusion

International Nuclear Information System (INIS)

Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

2013-01-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Entropy as a measure of diffusion

Energy Technology Data Exchange (ETDEWEB)

Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org

2013-10-15

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Decay to Equilibrium for Energy-Reaction-Diffusion Systems

KAUST Repository

Haskovec, Jan

2018-02-06

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

Decay to Equilibrium for Energy-Reaction-Diffusion Systems

KAUST Repository

Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander

2018-01-01

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion

Science.gov (United States)

Fukao, Takeshi; Kurima, Shunsuke; Yokota, Tomomi

2018-05-01

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as \\[ \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a growth condition for $\\beta$ even though the Stefan problem was excluded from examples of (P). This paper completely removes the growth condition for $\\beta$ by confirming Cauchy's criterion for solutions of the following approximate problem (P)$_{\\varepsilon}$ with approximate parameter $\\varepsilon>0$: \\[ \\frac{\\partial u_{\\varepsilon}}{\\partial t} + (-\\Delta+1)(\\varepsilon(-\\Delta+1)u_{\\varepsilon} + \\beta(u_{\\varepsilon}) + \\pi_{\\varepsilon}(u_{\\varepsilon})) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which is called the Cahn--Hilliard system, even if $\\Omega \\subset \\mathbb{R}^N$ ($N \\in \\mathbb{N}$) is an unbounded domain. Moreover, it can be seen that the Stefan problem is covered in the framework of this paper.

Diffusion characteristics in the Cu-Ti system

Energy Technology Data Exchange (ETDEWEB)

Laik, Arijit; Kale, Gajanan Balaji [Bhabha Atomic Reseach Centre, Mumbai (India). Materials Science Div.; Bhanumurthy, Karanam [Bhabha Atomic Reseach Centre, Mumbai (India). Scientific Information Resource Div.; Kashyap, Bhagwati Prasad [Indian Institute of Technology Bombay, Mumbai (India). Dept. of Metallurgical Engineering

2012-06-15

The formation and growth of intermetallic compounds by diffusion reaction of Cu and Ti were investigated in the temperature range 720 - 860 C using bulk diffusion couples. Only four, out of the seven stable intermediate compounds of the Cu-Ti system, were formed in the diffusion reaction zone in the sequence CuTi, Cu{sub 4}Ti, Cu{sub 4}Ti{sub 3} and CuTi{sub 2}. The activation energies required for the growth of these compounds were determined. The diffusion characteristics of Cu{sub 4}Ti, CuTi and Cu{sub 4}Ti{sub 3} and Cu(Ti) solid solution were evaluated. The activation energies for diffusion in these compounds were 192.2, 187.7 and 209.2 kJ mol{sup -1} respectively, while in Cu(Ti), the activation energy increased linearly from 201.0 kJ mol{sup -1} to 247.5 kJ mol{sup -1} with increasing concentration of Ti, in the range 0.5 - 4.0 at.%. The impurity diffusion coefficient of Ti in Cu and its temperature dependence were also estimated. A correlation between the impurity diffusion parameters for several elements in Cu matrix has been established. (orig.)

Diffusion influence on Michaelis Menten kinetics: II. The low substrate concentration limit

Science.gov (United States)

Kim, Hyojoon; Shin, Kook Joe

2007-02-01

The diffusion-influenced Michaelis-Menten kinetics in the low substrate concentration limit is studied in one and three dimensions. For the initial pair distribution of enzyme and substrate, we obtain the exact analytical results. We find that at short times the diffusion effect can make the reaction rate faster. The concentration deviations of the substrate and enzyme show t-1/2 and t-3/2 power-law behaviours in one and three dimensions, respectively, at long times. On the other hand, the average lifetime of the intermediate is independent of the initial state in one dimension, while it depends on the initial state in three dimensions. The ultimate production yield approaches unity in one dimension but it reaches a different value depending on other parameters in three dimensions. We also obtain the analytical results for the initial random distribution.

Diffusion influence on Michaelis-Menten kinetics: II. The low substrate concentration limit

International Nuclear Information System (INIS)

Kim, Hyojoon; Shin, Kook Joe

2007-01-01

The diffusion-influenced Michaelis-Menten kinetics in the low substrate concentration limit is studied in one and three dimensions. For the initial pair distribution of enzyme and substrate, we obtain the exact analytical results. We find that at short times the diffusion effect can make the reaction rate faster. The concentration deviations of the substrate and enzyme show t -1/2 and t -3/2 power-law behaviours in one and three dimensions, respectively, at long times. On the other hand, the average lifetime of the intermediate is independent of the initial state in one dimension, while it depends on the initial state in three dimensions. The ultimate production yield approaches unity in one dimension but it reaches a different value depending on other parameters in three dimensions. We also obtain the analytical results for the initial random distribution

A Weak Comparison Principle for Reaction-Diffusion Systems

Directory of Open Access Journals (Sweden)

José Valero

2012-01-01

Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.

Imaging of postthalamic visual fiber tracts by anisotropic diffusion weighted MRI and diffusion tensor imaging: principles and applications

International Nuclear Information System (INIS)

Reinges, Marcus H.T.; Schoth, Felix; Coenen, Volker A.; Krings, Timo

2004-01-01

Diffusion weighted MRI offers the possibility to study the course of the cerebral white matter tracts. In the present manuscript, the basics, the technique and the limitations of diffusion tensor imaging and anisotropic diffusion weighted MRI are presented and their applications in various neurological and neurosurgical diseases are discussed with special emphasis on the visual system. A special focus is laid on the combination of fiber tract imaging, anatomical imaging and functional MRI for presurgical planning and intraoperative neuronavigation of lesions near the visual system

Adoption of renewable heating systems: An empirical test of the diffusion of innovation theory

International Nuclear Information System (INIS)

Franceschinis, Cristiano; Thiene, Mara; Scarpa, Riccardo; Rose, John; Moretto, Michele; Cavalli, Raffaele

2017-01-01

The implementation of heating technologies based on renewable resources is an important part of Italy's energy policy. Yet, despite efforts to promote the uptake of such technologies, their diffusion is still limited while heating systems based on fossil fuels are still predominant. Theory suggests that beliefs and attitudes of individual consumers play a crucial role in the diffusion of innovative products. However, empirical studies corroborating such observations are still thin on the ground. We use a Choice Experiment and a Latent Class-Random Parameter model to analyze preferences of households in the Veneto region (North-East Italy) for key features of ambient heating systems. We evaluate the coherence of the underlying preference structure using as criteria psychological constructs from the Theory of Diffusion of Innovation by Rogers. Our results broadly support this theory by providing evidence of segmentation of the population consistent with the individuals' propensity to adopt innovations. We found that preferences for heating systems and respondents' willingness to pay for their key features vary across segments. These results enabled us to generate maps that show how willingness to pay estimates vary across the region and can guide local policy design aimed at stimulating adoption of sustainable solutions. - Highlights: • We relate preferences for wood pellet heating systems to Diffusion of Innovation theory. • We found a segmentation of the population according to individual innovativeness. • Preferences for wood pellet heating systems vary across population segments. • Public intervention seems necessary to foster adoption among late adopters.

Size dependent diffusive parameters and tensorial diffusion equations in neutronic models for optically small nuclear systems

International Nuclear Information System (INIS)

Premuda, F.

1983-01-01

Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated

Fractional Progress Toward Understanding the Fractional Diffusion Limit: The Electromagnetic Response of Spatially Correlated Geomaterials

Science.gov (United States)

Weiss, C. J.; Beskardes, G. D.; Everett, M. E.

2016-12-01

In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

Directory of Open Access Journals (Sweden)

R. Idris

2013-01-01

Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

Diffusion measurements in binary liquid mixtures by Raman spectroscopy

DEFF Research Database (Denmark)

Berg, Rolf W.; Hansen, Susanne Brunsgaard; Shapiro, Alexander

2007-01-01

It is shown that Raman spectroscopy allows determination of the molar fractions in mixtures subjected to molecular diffusion. Spectra of three binary systems, benzene/n-hexane, benzene/cyclohexane, and benzene/ acetone, were obtained during vertical (exchange) diffusion at several different heights...... in the literature were found, even in a thermostatically controlled diffusion cell, recording spectra through circulating water. For the system benzene/acetone, the determined diffusion coefficients were in good agreement with the literature data. The limitations of the Raman method are discussed...

Stress in film/substrate system due to diffusion and thermal misfit effects

International Nuclear Information System (INIS)

Shao Shanshan; Xuan Fuzhen; Wang Zhengdong; Tu Shantung

2009-01-01

The stress in film/substrate systems has been analysed taking into consideration the coupling effects of diffusion and thermal misfit within the framework of Fick's second law. The solution of diffusion-induced stress in a film/substrate system involving the thermal misfit stress feedback is developed. The effects of modulus ratios, diffusivity ratios, thickness ratios of the substrate and the film and the partial molar volume of the diffusing component on the stress distribution in the film/substrate system are then discussed with the help of the finite difference method. Results indicate that the stresses in the film/substrate system vary with diffusion time. Diffusion enhances the magnitudes of film stress when the thermal misfit stress is compressive in the film. Furthermore, the absolute values of stress in the film increase with the increasing modulus ratios of the substrate and film, while they reduce with the increasing partial molar volume of the diffusing component and the diffusivity ratio of the substrate and the film.

Diffusion archeology for diffusion progression history reconstruction.

Science.gov (United States)

Sefer, Emre; Kingsford, Carl

2016-11-01

Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring - perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.

Scanning, non-contact, hybrid broadband diffuse optical spectroscopy and diffuse correlation spectroscopy system.

Science.gov (United States)

Johansson, Johannes D; Mireles, Miguel; Morales-Dalmau, Jordi; Farzam, Parisa; Martínez-Lozano, Mar; Casanovas, Oriol; Durduran, Turgut

2016-02-01

A scanning system for small animal imaging using non-contact, hybrid broadband diffuse optical spectroscopy (ncDOS) and diffuse correlation spectroscopy (ncDCS) is presented. The ncDOS uses a two-dimensional spectrophotometer retrieving broadband (610-900 nm) spectral information from up to fifty-seven source-detector distances between 2 and 5 mm. The ncDCS data is simultaneously acquired from four source-detector pairs. The sample is scanned in two dimensions while tracking variations in height. The system has been validated with liquid phantoms, demonstrated in vivo on a human fingertip during an arm cuff occlusion and on a group of mice with xenoimplanted renal cell carcinoma.

Diffusion-weighted imaging of the musculoskeletal system in humans

International Nuclear Information System (INIS)

Baur, A.; Reiser, M.F.

2000-01-01

This article reviews the principles of diffusion-weighted imaging (DWI) and recent results in DWI of the musculoskeletal system. The potential of DWI in the diagnosis of pathology of the musculoskeletal system is discussed. DWI is a relatively new MR imaging technique that has already been established in neuroradiology, especially in the early detection of brain ischemia. The random motion of water protons on a molecular basis can be measured with DWI. To date DWI of the abdomen and of the musculoskeletal system has only been employed in scientific studies, but first results indicate that it may also be beneficial in these fields. Different diffusion characteristics have been found in normal tissues such as muscle, fat and bone marrow. Also, pathologic entities such as neoplasms, post-therapeutic soft tissue changes and inflammatory processes can be differentiated. Normal muscle shows significantly higher diffusion values than subcutaneous fat and bone marrow, due to a higher mobility of water protons within muscle. Soft tissue tumors exhibit a significantly lower diffusion value compared with post-therapeutic soft tissue changes and inflammatory processes. Necrotic tumor tissue can be distinguished from viable tumor due to significantly higher diffusion of water protons within necrotic tissue. (orig.)

Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems

OpenAIRE

Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus

2017-01-01

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...

A first-passage scheme for determination of overall rate constants for non-diffusion-limited suspensions

Science.gov (United States)

Lu, Shih-Yuan; Yen, Yi-Ming

2002-02-01

A first-passage scheme is devised to determine the overall rate constant of suspensions under the non-diffusion-limited condition. The original first-passage scheme developed for diffusion-limited processes is modified to account for the finite incorporation rate at the inclusion surface by using a concept of the nonzero survival probability of the diffusing entity at entity-inclusion encounters. This nonzero survival probability is obtained from solving a relevant boundary value problem. The new first-passage scheme is validated by an excellent agreement between overall rate constant results from the present development and from an accurate boundary collocation calculation for the three common spherical arrays [J. Chem. Phys. 109, 4985 (1998)], namely simple cubic, body-centered cubic, and face-centered cubic arrays, for a wide range of P and f. Here, P is a dimensionless quantity characterizing the relative rate of diffusion versus surface incorporation, and f is the volume fraction of the inclusion. The scheme is further applied to random spherical suspensions and to investigate the effect of inclusion coagulation on overall rate constants. It is found that randomness in inclusion arrangement tends to lower the overall rate constant for f up to the near close-packing value of the regular arrays because of the inclusion screening effect. This screening effect turns stronger for regular arrays when f is near and above the close-packing value of the regular arrays, and consequently the overall rate constant of the random array exceeds that of the regular array. Inclusion coagulation too induces the inclusion screening effect, and leads to lower overall rate constants.

Oxidative Uranium Release from Anoxic Sediments under Diffusion-Limited Conditions.

Science.gov (United States)

Bone, Sharon E; Cahill, Melanie R; Jones, Morris E; Fendorf, Scott; Davis, James; Williams, Kenneth H; Bargar, John R

2017-10-03

Uranium (U) contamination occurs as a result of mining and ore processing; often in alluvial aquifers that contain organic-rich, reduced sediments that accumulate tetravalent U, U(IV). Uranium(IV) is sparingly soluble, but may be mobilized upon exposure to nitrate (NO 3 - ) and oxygen (O 2 ), which become elevated in groundwater due to seasonal fluctuations in the water table. The extent to which oxidative U mobilization can occur depends upon the transport properties of the sediments, the rate of U(IV) oxidation, and the availability of inorganic reductants and organic electron donors that consume oxidants. We investigated the processes governing U release upon exposure of reduced sediments to artificial groundwater containing O 2 or NO 3 - under diffusion-limited conditions. Little U was mobilized during the 85-day reaction, despite rapid diffusion of groundwater within the sediments and the presence of nonuraninite U(IV) species. The production of ferrous iron and sulfide in conjunction with rapid oxidant consumption suggested that the sediments harbored large concentrations of bioavailable organic carbon that fueled anaerobic microbial respiration and stabilized U(IV). Our results suggest that seasonal influxes of O 2 and NO 3 - may cause only localized mobilization of U without leading to export of U from the reducing sediments when ample organic carbon is present.

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.

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems

Science.gov (United States)

Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A.

2018-05-01

We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.

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.

Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit

KAUST Repository

Guermond, Jean-Luc; Kanschat, Guido

2010-01-01

We revisit some results from M. L. Adams [Nu cl. Sci. Engrg., 137 (2001), pp. 298- 333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictions of the functions of this space to each mesh cell contain the linear polynomials. Furthermore, the discrete diffusion limit converges in the Sobolev space H1 to the continuous one if the boundary data is isotropic. With anisotropic boundary data, a boundary layer occurs, and convergence holds in the broken Sobolev space H with s < 1/2 only © 2010 Society for Industrial and Applied Mathematics.

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads.

Science.gov (United States)

Ha, Jiyeon; Engler, Cady R; Lee, Seung Jae

2008-07-01

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited. (c) 2007 Wiley Periodicals, Inc.

A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit

Directory of Open Access Journals (Sweden)

Jin-Han Xie

2017-01-01

Full Text Available A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: the weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed.

Protein friction limits diffusive and directed movements of kinesin motors on microtubules.

Science.gov (United States)

Bormuth, Volker; Varga, Vladimir; Howard, Jonathon; Schäffer, Erik

2009-08-14

Friction limits the operation of macroscopic engines and is critical to the performance of micromechanical devices. We report measurements of friction in a biological nanomachine. Using optical tweezers, we characterized the frictional drag force of individual kinesin-8 motor proteins interacting with their microtubule tracks. At low speeds and with no energy source, the frictional drag was related to the diffusion coefficient by the Einstein relation. At higher speeds, the frictional drag force increased nonlinearly, consistent with the motor jumping 8 nanometers between adjacent tubulin dimers along the microtubule, and was asymmetric, reflecting the structural polarity of the microtubule. We argue that these frictional forces arise from breaking bonds between the motor domains and the microtubule, and they limit the speed and efficiency of kinesin.

Diffusion-weighted imaging and the skeletal system: a literature review.

Science.gov (United States)

Yao, K; Troupis, J M

2016-11-01

Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI) sequence that has a well-established role in neuroimaging, and is increasingly being utilised in other clinical contexts, including the assessment of various skeletal disorders. It utilises the variability of Brownian motion of water molecules; the differing patterns of water molecular diffusion in various biological tissues help determine the contrast obtained in DWI. Although early research on the clinical role of DWI focused mainly on the field of neuroimaging, there are now more studies demonstrating the promising role DWI has in the diagnosis and monitoring of various osseous diseases. DWI has been shown to be useful in assessing a patient's skeletal tumour burden, monitoring the post-chemotherapy response of various bony malignancies, detecting hip ischaemia in patients with Legg-Calvé-Perthes disease, as well as determining the quality of repaired articular cartilage. Despite its relative successes, DWI has several limitations, including its limited clinical value in differentiating chondrosarcomas from benign bone lesions, as well as osteoporotic vertebral compression fractures from compression fractures due to malignancy. This literature review aims to provide an overview of the recent developments in the use of DWI in imaging the skeletal system, and to clarify the role of DWI in assessing various osseous diseases. Copyright © 2016 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.

THE MATHEMATIC MODEL OF POTENTIAL RELAXATION IN COULOSTATIC CONDITIONS FOR LIMITING DIFFUSION CURRENT CASE

Directory of Open Access Journals (Sweden)

O. H. Kapitonov

2010-05-01

Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.

Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system

DEFF Research Database (Denmark)

Brøns, Morten; Sturis, Jeppe

2001-01-01

A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong sensit...... sensitivity was introduced due to bifurcation to infinity resulting in chaotic dynamics on adding diffusion....

Parametric spatiotemporal oscillation in reaction-diffusion systems.

Science.gov (United States)

Ghosh, Shyamolina; Ray, Deb Shankar

2016-03-01

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Distribution in flowing reaction-diffusion systems

KAUST Repository

Kamimura, Atsushi; Herrmann, Hans J.; Ito, Nobuyasu

2009-01-01

A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

Distribution in flowing reaction-diffusion systems

KAUST Repository

Kamimura, Atsushi

2009-12-28

A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.

Excess Diffuse Light Absorption in Upper Mesophyll Limits CO2 Drawdown and Depresses Photosynthesis.

Science.gov (United States)

Earles, J Mason; Théroux-Rancourt, Guillaume; Gilbert, Matthew E; McElrone, Andrew J; Brodersen, Craig R

2017-06-01

In agricultural and natural systems, diffuse light can enhance plant primary productivity due to deeper penetration into and greater irradiance of the entire canopy. However, for individual sun-grown leaves from three species, photosynthesis is actually less efficient under diffuse compared with direct light. Despite its potential impact on canopy-level productivity, the mechanism for this leaf-level diffuse light photosynthetic depression effect is unknown. Here, we investigate if the spatial distribution of light absorption relative to electron transport capacity in sun- and shade-grown sunflower ( Helianthus annuus ) leaves underlies its previously observed diffuse light photosynthetic depression. Using a new one-dimensional porous medium finite element gas-exchange model parameterized with light absorption profiles, we found that weaker penetration of diffuse versus direct light into the mesophyll of sun-grown sunflower leaves led to a more heterogenous saturation of electron transport capacity and lowered its CO 2 concentration drawdown capacity in the intercellular airspace and chloroplast stroma. This decoupling of light availability from photosynthetic capacity under diffuse light is sufficient to generate an 11% decline in photosynthesis in sun-grown but not shade-grown leaves, primarily because thin shade-grown leaves similarly distribute diffuse and direct light throughout the mesophyll. Finally, we illustrate how diffuse light photosynthetic depression could overcome enhancement in canopies with low light extinction coefficients and/or leaf area, pointing toward a novel direction for future research. © 2017 American Society of Plant Biologists. All Rights Reserved.

Evaluation of glymphatic system activity with the diffusion MR technique: diffusion tensor image analysis along the perivascular space (DTI-ALPS) in Alzheimer's disease cases.

Science.gov (United States)

Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji

2017-04-01

The activity of the glymphatic system is impaired in animal models of Alzheimer's disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along the perivascular spaces as well as projection fibers and association fibers separately, to acquire an index for diffusivity along the perivascular space (ALPS-index) and correlated them with the mini mental state examinations (MMSE) score. We found a significant negative correlation between diffusivity along the projection fibers and association fibers. We also observed a significant positive correlation between diffusivity along perivascular spaces shown as ALPS-index and the MMSE score, indicating lower water diffusivity along the perivascular space in relation to AD severity. Activity of the glymphatic system may be evaluated with diffusion images. Lower diffusivity along the perivascular space on DTI-APLS seems to reflect impairment of the glymphatic system. This method may be useful for evaluating the activity of the glymphatic system.

A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method

OpenAIRE

Bondesan , Andrea; Boudin , Laurent; Grec , Bérénice

2018-01-01

In this article, we consider a multi-species kinetic model which leads to the Maxwell-Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe the as...

Turing Patterns in a Reaction-Diffusion System

International Nuclear Information System (INIS)

Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang

2006-01-01

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.

Pattern formation induced by cross-diffusion in a predator–prey system

International Nuclear Information System (INIS)

Sun Guiquan; Jin Zhen; Liu Quanxing; Li Li

2008-01-01

This paper considers the Holling–Tanner model for predator–prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator–prey system. (general)

Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

CERN Document Server

Cherniha, Roman

2017-01-01

This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception,...

Sooting limit in counterflow diffusion flames of ethylene/propane fuels and implication to threshold soot index

KAUST Repository

Joo, Peter H.

2013-01-01

Sooting limits in counterflow diffusion flames of propane/ethylene fuels have been studied experimentally using a light scattering technique, including the effects of dilution, fuel mixing, and strain rate. The results are discussed in view of the threshold soot index (TSI). In soot-formation (SF) flames, where the flame is located on the oxidizer side of the stagnation plane, the sooting limit depends critically on fuel type and subsequently on flame temperature. The sooting limit has a non-linear dependence on the fuel-mixing ratio, which is similar to the non-linear mixing rule for TSI observed experimentally in rich premixed flames, where soot oxidation is absent for both SF and rich premixed flames. In soot-formation-oxidation (SFO) flames, where the flame is located on the fuel side, the sooting limit depends critically on flame temperature, while it is relatively independent on fuel type. This result suggests a linear mixing rule for sooting limits in SFO flames, which is similar to the TSI behavior for coflow diffusion flames. Soot oxidation takes place for both types of flames. The aerodynamic strain effect on the sooting limits has also been studied and an appreciable influence has been observed. Under sooting conditions, soot volume fraction was measured using a light extinction technique. The soot loadings in SF flames of the mixture fuels demonstrated a synergistic effect, i.e., soot production increased for certain mixture fuels as compared to the respective singlecomponent fuels. © 2012 The Combustion Institute.

The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

Energy Technology Data Exchange (ETDEWEB)

Szoke, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks, E. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-07-12

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.

Experimental study of the Ca–Mg–Zn system using diffusion couples and key alloys

Directory of Open Access Journals (Sweden)

Yi-Nan Zhang, Dmytro Kevorkov, Florent Bridier and Mamoun Medraj

2011-01-01

Full Text Available Nine diffusion couples and 32 key samples were prepared to map the phase diagram of the Ca–Mg–Zn system. Phase relations and solubility limits were determined for binary and ternary compounds using scanning electron microscopy, electron probe microanalysis and x-ray diffraction (XRD. The crystal structure of the ternary compounds was studied by XRD and electron backscatter diffraction. Four ternary intermetallic (IM compounds were identified in this system: Ca3MgxZn15−x (4.6≤x≤12 at 335 °C, IM1, Ca14.5Mg15.8Zn69.7 (IM2, Ca2Mg5Zn13 (IM3 and Ca1.5Mg55.3Zn43.2 (IM4. Three binary compounds were found to have extended solid solubility into ternary systems: CaZn11, CaZn13 and Mg2Ca form substitutional solid solutions where Mg substitutes for Zn atoms in the first two compounds, and Zn substitutes for both Ca and Mg atoms in Mg2Ca. The isothermal section of the Ca–Mg–Zn phase diagram at 335 °C was constructed on the basis of the obtained experimental results. The morphologies of the diffusion couples in the Ca–Mg–Zn phase diagram at 335 °C were studied. Depending on the terminal compositions of the diffusion couples, the two-phase regions in the diffusion zone have either a tooth-like morphology or contain a matrix phase with isolated and/or dendritic precipitates.

Thermodynamics and kinetics of interstitial diffusion in a two-component system

International Nuclear Information System (INIS)

McKee, R.A.

1980-01-01

Diffusion theory is developed for a two-component system in which only the interstitial element is mobile. A thermodynamic formalism is used in direct parallel with a kinetic theory to construct a mechanism-independent relationship between tracer- and chemical-diffusion coefficients. It is found that D/sup I/=(D-italic*/f)(1+partiallnγ/partiallnC). D/sup I/ is the intrinsic- or chemical-diffusion coefficient for the interstitial, D* is the tracer-diffusion coefficient, f is the correlation factor, and γ is the activity coefficient. This expression accounts for site exclusion, correlation, and drift effects that occur as the interstitial content changes. Generalized phenomenological coefficients that are determined in this analysis can be used for standard representations of diffusion in electric fields and temperature gradients. Moreover, the forms that the phenomenological coefficients take for the interstitial system are the same as those previously derived for vacancy diffusion. A test of this predicted relationship between tracer- and chemical-diffusion coefficients is developed using a comparison between theory and experiment for carbon diffusion in fcc iron

[Novel concepts in biology of diffuse endocrine system: results and future investigations].

Science.gov (United States)

Iaglov, V V; Iaglova, N V

2012-01-01

Diffuse endocrine system is a largest part of endocrine system of vertebrates. Recend findings showed that DES-cells are not neuroectodermal but have ectodermal, mesodermal, and entodermal ontogeny. The article reviews novel concept of diffuse endocrine system anatomy and physiology, functional role of DES hormones and poorly investigated aspects like DES-cell morphology, hormones secretion in normal and pathologic conditions. Further research of diffuse endocrine system has a great significance for biochemistry, morphology, and clinical medicine.

Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system

International Nuclear Information System (INIS)

Abdusalam, H.A; Fahmy, E.S.

2003-01-01

It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional

Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system

International Nuclear Information System (INIS)

He Zhizhu; Liu, Jing

2010-01-01

This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.

Benefits of siderophore release lie in mediating diffusion limitation at low iron solubility

OpenAIRE

Leventhal, Gabriel; Schiessl, Konstanze; Ackermann, Martin

2016-01-01

Siderophores are chelators released by many bacteria to take up iron. In contrast to iron receptors located at the cell surface, released siderophores are at risk of being lost to environmental sinks. Here, we asked the question whether the release itself is essential for the function of siderophores, which could explain why such a risky strategy is widespread. We developed a reaction-diffusion model to determine the impact of siderophore release on overcoming iron limitation caused by poor s...

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

Di Francesco, M.

2008-12-08

We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

Colloid-facilitated radionuclide transport in the fractured rock: effects of decay chain and limited matrix diffusion

International Nuclear Information System (INIS)

Park, J. B.; Park, J. W.; Lee, E. Y.; Kim, C. R.

2002-01-01

Colloid-facilitated radionuclide transport in the fractured rock is studies by considering radioactive decay chain and limited matrix diffusion into surrounding porous media. Semi-analytical solution in the Laplace domain is obtained from the mass balance equation of radionuclides and colloid particles. Numerical inversion of the Laplace solution is used to get the concentration profiles both in a fracture and in rock matrix. There issues are analyzed for the radionuclide concentration in a fracture by 1) formation constant of pseudo-colloid, 2) filtration coefficient of radio-colloid and 3) effective diffusion depth into the surrounding porous rock media

Two-dimensional simulation of reactive diffusion in binary systems

Czech Academy of Sciences Publication Activity Database

Svoboda, Jiří; Stopka, J.; Fischer, F. D.

2014-01-01

Roč. 95, DEC (2014), s. 309-315 ISSN 0927-0256 R&D Projects: GA ČR(CZ) GA14-24252S Institutional support: RVO:68081723 Keywords : Phase transformation * Diffusion-controlled interface migration * Reactive diffusion * Multiphase system * Intermetallic compounds Subject RIV: BJ - Thermodynamics Impact factor: 2.131, year: 2014

Reaction-diffusion systems in intracellular molecular transport and control.

Science.gov (United States)

Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A

2010-06-07

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

Science.gov (United States)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Theoretical limit of spatial resolution in diffuse optical tomography using a perturbation model

International Nuclear Information System (INIS)

Konovalov, A B; Vlasov, V V

2014-01-01

We have assessed the limit of spatial resolution of timedomain diffuse optical tomography (DOT) based on a perturbation reconstruction model. From the viewpoint of the structure reconstruction accuracy, three different approaches to solving the inverse DOT problem are compared. The first approach involves reconstruction of diffuse tomograms from straight lines, the second – from average curvilinear trajectories of photons and the third – from total banana-shaped distributions of photon trajectories. In order to obtain estimates of resolution, we have derived analytical expressions for the point spread function and modulation transfer function, as well as have performed a numerical experiment on reconstruction of rectangular scattering objects with circular absorbing inhomogeneities. It is shown that in passing from reconstruction from straight lines to reconstruction using distributions of photon trajectories we can improve resolution by almost an order of magnitude and exceed the accuracy of reconstruction of multi-step algorithms used in DOT. (optical tomography)

Estimation and prediction of convection-diffusion-reaction systems from point measurement

NARCIS (Netherlands)

Vries, D.

2008-01-01

Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the

Pattern dynamics of the reaction-diffusion immune system.

Science.gov (United States)

Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie

2018-01-01

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.

Development of regional meteorological and atmospheric diffusion simulation system

International Nuclear Information System (INIS)

Kubota, Ryuji; Iwashige, Kengo; Kasano, Toshio

2002-01-01

Regional atmospheric diffusion online network (RADON) with atmospheric diffusion analysis code (ADAC) : a simulation program of diffusion of radioactive materials, volcanic ash, pollen, NOx and SOx was developed. This system can be executed in personal computer (PC) and note PC on Windows. Emission data consists of online, offline and default data. It uses the meteorology data sources such as meteorological forecasting mesh data, automated meteorological data acquisition system (AMeDAS) data, meteorological observation data in site and municipality observation data. The meteorological forecasting mesh data shows forecasting value of temperature, wind speed, wind direction and humidity in about two days. The nuclear environmental monitoring center retains the online data (meteorological data, emission source data, monitoring station data) in its PC server and can run forecasting or repeating calculation using these data and store and print out the calculation results. About 30 emission materials can be calculated simultaneously. This system can simulate a series of weather from the past and real time to the future. (S.Y.)

Casimir force in O(n) systems with a diffuse interface.

Science.gov (United States)

Dantchev, Daniel; Grüneberg, Daniel

2009-04-01

We study the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry infinity;{d-1}xL , where 2system. We consider a system with nearest-neighbor anisotropic interaction constants J_{ parallel} parallel to the film and J_{ perpendicular} across it. We argue that in such an anisotropic system the Casimir force, the free energy, and the helicity modulus will differ from those of the corresponding isotropic system, even at the bulk critical temperature, despite that these systems both belong to the same universality class. We suggest a relation between the scaling functions pertinent to the both systems. Explicit exact analytical results for the scaling functions, as a function of the temperature T , of the free energy density, Casimir force, and the helicity modulus are derived for the n-->infinity limit of O(n) models with antiperiodic boundary conditions applied along the finite dimension L of the film. We observe that the Casimir amplitude Delta_{Casimir}(dmid R:J_{ perpendicular},J_{ parallel}) of the anisotropic d -dimensional system is related to that of the isotropic system Delta_{Casimir}(d) via Delta_{Casimir}(dmid R:J_{ perpendicular},J_{ parallel})=(J_{ perpendicular}J_{ parallel});{(d-1)2}Delta_{Casimir}(d) . For d=3 we derive the exact Casimir amplitude Delta_{Casimir}(3,mid R:J_{ perpendicular},J_{ parallel})=[Cl_{2}(pi3)3-zeta(3)(6pi)](J_{ perpendicular}J_{ parallel}) , as well as the exact scaling functions of the Casimir force and of the helicity modulus Upsilon(T,L) . We obtain that beta_{c}Upsilon(T_{c},L)=(2pi;{2})[Cl_{2}(pi3)3+7zeta(3)(30pi)](J_{ perpendicular}J_{ parallel})L;{-1} , where T_{c} is the critical temperature of the bulk system. We find that the contributions in the excess free energy due to the existence of a diffuse interface result in a repulsive Casimir force in the whole temperature region.

Diffusion of gases in solids: rare gas diffusion in solids; tritium diffusion in fission and fusion reactor metals. Final report

International Nuclear Information System (INIS)

Abraham, P.M.; Chandra, D.; Mintz, J.M.; Elleman, T.S.; Verghese, K.

1976-01-01

Major results of tritium and rare gas diffusion research conducted under the contract are summarized. The materials studied were austenitic stainless steels, Zircaloy, and niobium. In all three of the metal systems investigated, tritium release rates were found to be inhibited by surface oxide films. The effective diffusion coefficients that control tritium release from surface films on Zircaloy and niobium were determined to be eight to ten orders of magnitude lower than the bulk diffusion coefficients. A rapid component of diffusion due to grain boundaries was identified in stainless steels. The grain boundary diffusion coefficient was determined to be about six orders of magnitude greater than the bulk diffusion coefficient for tritium in stainless steel. In Zircaloy clad fuel pins, the permeation rate of tritium through the cladding is rate-limited by the extremely slow diffusion rate in the surface films. Tritium diffusion rates through surface oxide films on niobium appear to be controlled by cracks in the surface films at temperatures up to 600 0 C. Beyond 600 0 C, the cracks appear to heal, thereby increasing the activation energy for diffusion through the oxide film. The steady-state diffusion of tritium in a fusion reactor blanket has been evaluated in order to calculate the equilibrium tritium transport rate, approximate time to equilibrium, and tritium inventory in various regions of the reactor blanket as a function of selected blanket parameters. Values for these quantities have been tabulated

Diffusion-limited reactions of hard-core particles in one dimension

Science.gov (United States)

Bares, P.-A.; Mobilia, M.

1999-02-01

We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov [Sov. Phys. JETP 64, 811 (1986)] and calculate for a single species the asymptotic long-time and/or large-distance behavior of the two-point correlation function. Based on a work by Grynberg and Stinchcombe [Phys. Rev. E 50, 957 (1994); Phys. Rev. Lett. 74, 1242 (1995); 76, 851 (1996)], which was developed to treat stochastic adsorption-desorption models, we provide in a second step the exact two-point (one- and two-time) correlation functions of Lushnikov's model. We then propose a formulation of the problem in terms of path integrals for pseudo- fermions. This formalism can be used to advantage in the multispecies case, especially when applying perturbative renormalization group techniques.

Diffusion in the plutonium zirconium system; Diffusion dans le systeme plutonium zirconium

Energy Technology Data Exchange (ETDEWEB)

Lauthier, J C [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1967-01-15

Research on the compound PuZr{sub 2}: It cannot be obtained by a direct synthesis. We suppose that its formation is due to an oxygen amount which enhances diffusion processes by a contribution of bound extrinsic vacancies. This investigation which concerned a great range of alloys (from 15 to 50 at per cent Pu) has led us to point out the nature of the isothermal transformation. It takes place at 615 deg. + 5 deg. C and is of the peritectoid type. Pu {epsilon} (bcc) + Zr {alpha} (hex) {r_reversible} Pu {delta} (f. cc) Diffusion in hexagonal phase: Diffusion coefficients have been determined from couples made of Pu Zr dilute alloys (1.15 and 0.115 at per cent Pu) and of pure zirconium; these couples have been annealed between 700 and 840 deg. C from 1000 to 3000 hours. The curves C = f(x) were plotted by X ray microanalysis and a autoradiography. They have been analysed assuming that the diffusion coefficient was constant. Our results are the following: D Zr Pu (1.15 % = 11.1 exp (-65000/RT) and D Zr Pu (0.115 %) 0.1 exp (-54000/RT). (author) [French] Recherche du compose PuZr2: II ne peut etre obtenu par synthese directe. Nous pensons que sa formation est liee a la presence d'oxygene, qui, par son apport de lacunes extrinseques accelere les processus de diffusion. Cette etude qui a porte sur toute une serie d'alliages (de 15 a 50 pour cent atomique de Pu), nous a permis de preciser la nafure de la transformation isotherme. Elle situe a 615 deg. + 5 deg. C et est du type peritectoide. Pu {epsilon} (c.c.) + Zr {alpha} (h.c.) {r_reversible} Pu {delta} (c.f.c.) Diffusion en phase {alpha} hexagonale: Les coefficients de diffusion chimique ont ete determines a partir de couples constitues d'alliages PuZr dilues (1,15 pour cent et 0,115 pour cent atomique de Pu) et de zirconium pur. Ces couples ont ete recuits entre 700 et 840 deg. C durant des temps de 1000 a 3000 heures. Les courbes C = f(x) ont ete tracees par microanalyse X et autoradiographie {alpha}. Elles ont ete

On some limitations of reaction-diffusion chemical computers in relation to Voronoi diagram and its inversion

International Nuclear Information System (INIS)

Adamatzky, Andrew; Lacy Costello, Benjamin de

2003-01-01

A reaction-diffusion chemical computer in this context is a planar uniform chemical reactor, where data and results of a computation are represented by concentration profiles of reactants and the computation itself is implemented via the spreading and interaction of diffusive and phase waves. This class of chemical computers are efficient at solving problems with a 'natural' parallelism where data sets are decomposable onto a large number of geographically neighboring domains which are then processed in parallel. Typical problems of this type include image processing, geometrical transformations and optimisation. When chemical based devices are used to solve such problems questions regarding their reproducible, efficiency and the accuracy of their computations arise. In addition to these questions what are the limitations of reaction-diffusion chemical processors--what type of problems cannot currently and are unlikely ever to be solved? To answer the questions we study how a Voronoi diagram is constructed and how it is inverted in a planar chemical processor. We demonstrate that a Voronoi diagram is computed only partially in the chemical processor. We also prove that given a specific Voronoi diagram it is impossible to reconstruct the planar set (from which diagram was computed) in the reaction-diffusion chemical processor. In the Letter we open the first ever line of enquiry into the computational inability of reaction-diffusion chemical computers

Use of perforated acoustic panels as supply air diffusers in diffuse ceiling ventilation systems

DEFF Research Database (Denmark)

Iqbal, Ahsan; Kazemi, Seyed Hossein; Ardkapan, Siamak Rahimi

Ventilation is needed for diluting and removing the contaminants, odour and excess heat from the building interior. It is important that the inhabitants perceive the ventilated spaces as comfortable. Therefore, the supply air should reach all parts of the occupied zones. Troldtekt has been...... manufacturing perforated acoustic panels for the last 13 years. The panels can be used not only in applications related to acoustics but also as low pressure drop supply air diffusers, particularly in diffuse ceiling ventilation systems. The present study verifies on a theoretically level the performance...

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Directory of Open Access Journals (Sweden)

Ervin K. Lenzi

2017-01-01

Full Text Available We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.

EPES information depth for an overlayer/substrate system with a diffuse interface

International Nuclear Information System (INIS)

Zommer, L.

2009-01-01

The information depth (ID) of elastic peak electron spectroscopy (EPES) was considered for an overlayer/substrate system with a diffuse interface. The interface was assumed to have an exponential concentration profile. The paradox previously found by Zommer and Jablonski for the Rh/Al and Al/Rh systems with sharp interfaces also occurs for these systems with diffuse interfaces. We compared IDs for diffuse and sharp interfaces. Deviations between the IDs depend on the interface width, overlayer thickness, and selected system for a given primary energy (here 2000 eV). The deviations for the Rh/Al and Al/Rh systems differ profoundly. These results are of importance when interpreting EPES measurements of layered system

CARMEN-SYSTEM, Programs System for Thermal Neutron Diffusion and Burnup with Feedback

International Nuclear Information System (INIS)

Ahnert, Carol; Aragones, Jose M.

1983-01-01

values included in the basic library, the cross sections by zone are corrected by these feedback effects and a new diffusion calculation is made with them, and the process continues until power convergence is reached between two successive diffusion calculations. Then the next burnup step starts. In one execution of CARMEN the whole burnup cycle may be calculated step by step. 3 - Restrictions on the complexity of the problem: The present version of CARMEN has the following restrictions: Number of rows, columns and planes: 210; Number of groups: 2; Number of zones: 99; Number of nuclides in a cross section set: 2; Number of coarse meshes in each direction: 150; Number of cross section sets: 99; Number of burnup steps to calculate: 15; Number of burnup steps in the basic library: 20; When CARMEN is executed without burnup option, the following restrictions apply: Number of rows: 210; Number of groups: 1000; Number of zones: 200; Number of nuclides in a cross section set: 200; Number of coarse meshes in each direction: 150; Number of cross section sets: 99; Largest nuclide number: 200. These limitations may be changed in the source program. This code system has been included in the Coordinated Research Programme (CRP) on 'Codes Adaptable to Small and Medium-Size Computers Available in Developing Countries for In-Core Fuel Management' of the International Atomic Energy Agency

Mass fractionation of noble gases in diffusion-limited hydrodynamic hydrogen escape

International Nuclear Information System (INIS)

Zahnle, K.; Pollack, J.B.; Kasting, J.F.

1990-01-01

The theory of mass fractionation by hydrogen is presently extended to atmospheres in which hydrogen is not the major constituent. This theoretical framework is applied to three different cases. In the first, it is shown that the fractionation of terrestrial atmospheric neon with respect to mantle neon is explainable as a consequence of diffusion-limited hydrogen escape from a steam atmosphere toward the end of the accretion process. In the second, the anomalously high Ar-38/Ar-36 ratio of Mars is shown to be due to hydrodynamic fractionation by a vigorously escaping and very pure hydrogen wind. In the last case, it is speculated that the currently high Martian D/H ratio emerged during the hydrodynamic escape phase which fractionated Ar. 35 refs

Exploring policy options for a transition to sustainable heating system diffusion using an agent-based simulation

International Nuclear Information System (INIS)

Maya Sopha, Bertha; Kloeckner, Christian A.; Hertwich, Edgar G.

2011-01-01

Change in home heating to more efficient and renewable systems is important for a sound climate policy. The present paper aims to identify potential interventions for the uptake of wood-pellet heating in Norway using an agent-based model (ABM). The theoretically based, empirically founded, agent-based simulation demonstrates that financial support, i.e., a stable wood-pellet price, and technical development, i.e., functional reliability improvement, have to be established all at the same time for a successful wood-pellet market to start. Furthermore, a soft intervention through persuading households to use environmentally beneficial heating system is not a promising driver for wood-pellet diffusion. Limitations and suggestions for future work are also discussed. - Research highlights: → The theoretically based, empirically founded, agent-based simulation is applied to investigate potential policy options toward diffusion of wood-pellet heating in Norway. → Relative advantages are necessary for wood-pellet heating to be adopted, consistent with Diffusion of Innovation theory (). → Simultaneous development is also required for further uptake of wood-pellet heating, supporting the existing empirical hypothesis by . → Persuading households to use environmentally friendly heating system is not a promising driver, in line with empirical finding of , who investigated psychological factors underlying the adoption of wood-pellet heating.

Exploring policy options for a transition to sustainable heating system diffusion using an agent-based simulation

Energy Technology Data Exchange (ETDEWEB)

Maya Sopha, Bertha, E-mail: bertha.sopha@ntnu.n [Industrial Ecology Programme and Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim (Norway); Kloeckner, Christian A. [Department of Psychology, Section for Risk Psychology, Environment and Safety (RIPENSA), Norwegian University of Science and Technology, NO-7491 Trondheim (Norway); Hertwich, Edgar G. [Industrial Ecology Programme and Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim (Norway)

2011-05-15

Change in home heating to more efficient and renewable systems is important for a sound climate policy. The present paper aims to identify potential interventions for the uptake of wood-pellet heating in Norway using an agent-based model (ABM). The theoretically based, empirically founded, agent-based simulation demonstrates that financial support, i.e., a stable wood-pellet price, and technical development, i.e., functional reliability improvement, have to be established all at the same time for a successful wood-pellet market to start. Furthermore, a soft intervention through persuading households to use environmentally beneficial heating system is not a promising driver for wood-pellet diffusion. Limitations and suggestions for future work are also discussed. - Research highlights: {yields} The theoretically based, empirically founded, agent-based simulation is applied to investigate potential policy options toward diffusion of wood-pellet heating in Norway. {yields} Relative advantages are necessary for wood-pellet heating to be adopted, consistent with Diffusion of Innovation theory (). {yields} Simultaneous development is also required for further uptake of wood-pellet heating, supporting the existing empirical hypothesis by . {yields} Persuading households to use environmentally friendly heating system is not a promising driver, in line with empirical finding of , who investigated psychological factors underlying the adoption of wood-pellet heating.

Innovation and creativity : Beyond diffusion

DEFF Research Database (Denmark)

Michelsen, Anders Ib

2009-01-01

of postwar systems theory and introduce Castoriadis' philosophy as an interesting option in this regard. It proceeds in four parts: (a) First, it debates the limits of the commonplace metaphor of diffusion and adoption in today's debate on innovation. (b) Second, it will present aspects of Castoriadis...

Sustained currents in coupled diffusive systems

International Nuclear Information System (INIS)

Larralde, Hernán; Sanders, David P

2014-01-01

Coupling two diffusive systems may give rise to a nonequilibrium stationary state (NESS) with a non-trivial persistent, circulating current. We study a simple example that is exactly soluble, consisting of random walkers with different biases towards a reflecting boundary, modelling, for example, Brownian particles with different charge states in an electric field. We obtain analytical expressions for the concentrations and currents in the NESS for this model, and exhibit the main features of the system by numerical simulation. (paper)

Diffusion tensor analysis with nuclear magnetic resonance in human central nervous system

International Nuclear Information System (INIS)

Nakayama, Naoki

1998-01-01

Nuclear magnetic resonance has been used to measure the diffusivity of water molecules. In central nervous system, anisotropic diffusion, which is characterized by apparent diffusion tensor D app ξ , is thought to be related to neuronal fiber tract orientation. For precise observation of anisotropic diffusion, it is needed to determine the diagonal and off-diagonal elements of D app ξ . Once D app ξ is estimated from a series of diffusion weighted images, a tissue's orthotropic principal axes and diffusivity of each direction are determined from eigenvalues and eigenvectors of D app ξ . There are several methods to represent anisotropic diffusion with D app ξ . Examples are diffusion ellipsoids constructed in each voxel depicting both these principal axes and the mean diffusion length in these directions, trace invariant values and its mapping image, largest eigenvalue, and ratio of largest eigenvalue to the other eigenvalue. In this study, the author investigated practical procedure to analyze diffusion tensor D app ξ using both of spin-echo end echo-planer diffusion weighted imagings with 3-tesla magnetic resonance machine in human brain. The ellipsoid representation provided particularly useful information about microanatomy including neuronal fiber tract orientation and molecular mobility reflective of microstructure. Furthermore, in the lesion of Wallerian degeneration, the loss of anisotropy of local apparent diffusion was observed. It is suggested that the function of axons can be observed via degree of anisotropy of apparent diffusion. Consequently, diffusion tensor analysis is expected to be a powerful, noninvasive method capable of quantitative and functional evaluation of the central nervous system. (author)

Whether diffusion in axisymmetric confinement systems is intrinsically ambipolar

International Nuclear Information System (INIS)

Kovrizhnykh, L.M.

1997-01-01

The problem of diffusion ambipolarity in axisymmetric magnetic systems is analyzed. The question is discussed of whether diffusion is intrinsically ambipolar (and if so, then in which particular cases) or the ambipolarity constraint is an additional independent condition, which does not follow from the equations of motion and, hence, contains new information. It is shown that the second assertion is correct: strictly speaking, diffusion can never be intrinsically ambipolar, and, in the presence of several different mechanisms causing electron and ion losses across the magnetic field, only the total fluxes, but not the partial ones, should satisfy the ambipolarity constraint. (UK)

An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

International Nuclear Information System (INIS)

Moore, Peter K.

2003-01-01

Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied

Ohm's law in turbulent plasmas and beta limitations by anomalous diffusion

International Nuclear Information System (INIS)

Borrass, K.

1978-01-01

For axisymmetric diffusive equilibria a condition is derived by means of a generalized Ohm's law. It relates some effective outward particle flux to the toroidal current density. An approximate version of it requires that the corresponding effective diffusion velocity Vsub(D)sup(*) must not exceed the poloidal magnetic diffusion velocity Vsub(m). The simple version of Ohm's law as used in transport calculations only applies if Vsub(D)sup(*)<< Vsub(m). A preliminary discussion is performed for the case of anomalous diffusion due to trapped particle instabilities. (author)

Universal diffusion-limited injection and the hook effect in organic thin-film transistors

Science.gov (United States)

Liu, Chuan; Huseynova, Gunel; Xu, Yong; Long, Dang Xuan; Park, Won-Tae; Liu, Xuying; Minari, Takeo; Noh, Yong-Young

2016-01-01

The general form of interfacial contact resistance was derived for organic thin-film transistors (OTFTs) covering various injection mechanisms. Devices with a broad range of materials for contacts, semiconductors, and dielectrics were investigated and the charge injections in staggered OTFTs was found to universally follow the proposed form in the diffusion-limited case, which is signified by the mobility-dependent injection at the metal-semiconductor interfaces. Hence, real ohmic contact can hardly ever be achieved in OTFTs with low carrier concentrations and mobility, and the injection mechanisms include thermionic emission, diffusion, and surface recombination. The non-ohmic injection in OTFTs is manifested by the generally observed hook shape of the output conductance as a function of the drain field. The combined theoretical and experimental results show that interfacial contact resistance generally decreases with carrier mobility, and the injection current is probably determined by the surface recombination rate, which can be promoted by bulk-doping, contact modifications with charge injection layers and dopant layers, and dielectric engineering with high-k dielectric materials. PMID:27440253

Pitfalls and Limitations of Diffusion-Weighted Magnetic Resonance Imaging in the Diagnosis of Urinary Bladder Cancer

Directory of Open Access Journals (Sweden)

Wei-Ching Lin

2015-06-01

Full Text Available Adequately selecting a therapeutic approach for bladder cancer depends on accurate grading and staging. Substantial inaccuracy of clinical staging with bimanual examination, cystoscopy, and transurethral resection of bladder tumor has facilitated the increasing utility of magnetic resonance imaging to evaluate bladder cancer. Diffusion-weighted imaging (DWI is a noninvasive functional magnetic resonance imaging technique. The high tissue contrast between cancers and surrounding tissues on DWI is derived from the difference of water molecules motion. DWI is potentially a useful tool for the detection, characterization, and staging of bladder cancers; it can also monitor posttreatment response and provide information on predicting tumor biophysical behaviors. Despite advancements in DWI techniques and the use of quantitative analysis to evaluate the apparent diffusion coefficient values, there are some inherent limitations in DWI interpretation related to relatively poor spatial resolution, lack of cancer specificity, and lack of standardized image acquisition protocols and data analysis procedures that restrict the application of DWI and reproducibility of apparent diffusion coefficient values. In addition, inadequate bladder distension, artifacts, thinness of bladder wall, cancerous mimickers of normal bladder wall and benign lesions, and variations in the manifestation of bladder cancer may interfere with diagnosis and monitoring of treatment. Recognition of these pitfalls and limitations can minimize their impact on image interpretation, and carefully applying the analyzed results and combining with pathologic grading and staging to clinical practice can contribute to the selection of an adequate treatment method to improve patient care.

Pitfalls and Limitations of Diffusion-Weighted Magnetic Resonance Imaging in the Diagnosis of Urinary Bladder Cancer

Science.gov (United States)

Lin, Wei-Ching; Chen, Jeon-Hor

2015-01-01

Adequately selecting a therapeutic approach for bladder cancer depends on accurate grading and staging. Substantial inaccuracy of clinical staging with bimanual examination, cystoscopy, and transurethral resection of bladder tumor has facilitated the increasing utility of magnetic resonance imaging to evaluate bladder cancer. Diffusion-weighted imaging (DWI) is a noninvasive functional magnetic resonance imaging technique. The high tissue contrast between cancers and surrounding tissues on DWI is derived from the difference of water molecules motion. DWI is potentially a useful tool for the detection, characterization, and staging of bladder cancers; it can also monitor posttreatment response and provide information on predicting tumor biophysical behaviors. Despite advancements in DWI techniques and the use of quantitative analysis to evaluate the apparent diffusion coefficient values, there are some inherent limitations in DWI interpretation related to relatively poor spatial resolution, lack of cancer specificity, and lack of standardized image acquisition protocols and data analysis procedures that restrict the application of DWI and reproducibility of apparent diffusion coefficient values. In addition, inadequate bladder distension, artifacts, thinness of bladder wall, cancerous mimickers of normal bladder wall and benign lesions, and variations in the manifestation of bladder cancer may interfere with diagnosis and monitoring of treatment. Recognition of these pitfalls and limitations can minimize their impact on image interpretation, and carefully applying the analyzed results and combining with pathologic grading and staging to clinical practice can contribute to the selection of an adequate treatment method to improve patient care. PMID:26055180

Diffusion archeology for diffusion progression history reconstruction

OpenAIRE

Sefer, Emre; Kingsford, Carl

2015-01-01

Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring — perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial d...

Diffusion behavior in the films of Nb-Ti systems

International Nuclear Information System (INIS)

Yoshitake, Michiko; Yoshihara, Kazuhiro

1990-01-01

The diffusion behavior of substrate element into a deposited film was investigated. The observed systems were a Nb film/Ti substrate and a Ti film/Nb substrate. When the Nb film/Ti substrate was heated in a vacuum, Ti diffused very rapidly in the Nb film. The pre-exponential factor of the diffusion constant of Ti in the Nb film was 5.6x10 -2 m 2 s -1 , and the activation energy was 220 kJmol -1 . The observed activation energy is about 60% of that of Ti in the bulk Nb. On the other hand, when the Ti film/Nb substrate was heated in a vacuum, Nb did not diffuse so rapidly. Titanium diffused through the Nb film rapidly and was concentrated on the surface of the Nb film. The chemical state of the concentrated Ti was metallic, and neither titanium oxides nor titanium carbide was observed. Therefore, the driving force of the rapid diffusion of Ti in the Nb film is considered as the reduction of the surface energy of Nb film. The difference in the diffusion behavior between Ti through the Nb film and Nb through the Ti film is explained supposing that the segregation of Ti reduces the surface energy of the Nb film but the segregation of Nb does not reduce the surface energy of the Ti film. After heating of the Nb film/Ti substrate for a long time, a new phase was formed at the interface between the Nb film and the Ti substrate. The chemical composition of the new phase is about 50% of Ti and 50% of Nb. This phase has not been reported in the phase diagram of the bulk Ti-Nb system. The surface area of the Nb film is considered to be quite large, so the contribution of surface energy to the thermodynamic state of the Nb film cannot be neglected. Therefore, the chemical potential of the film is different from that of the bulk. Then, the new phase, which does not exist in the phase diagram of the bulk system, is formed by an interaction of the films. (author)

Monitoring the development and diffusion of EHR systems in Denmark

DEFF Research Database (Denmark)

Nøhr, Christian; Andersen, Stig Kjær; Vingtoft, Søren

2003-01-01

The danish EHR Oberservatory has monitored Danish EHR projects for several years with respect to a number of parameters such as diffusion, diffusin rate, barriers and limitations, and experience gained. The results of the 2002 monitoring reveal that investment in IT is relatively low...

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

Bruna, Maria; Chapman, S. Jonathan

2013-01-01

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.

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

Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

International Nuclear Information System (INIS)

Qu Changzheng; Kang Jing

2008-01-01

In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

Particle deposition due to turbulent diffusion in the upper respiratory system

Science.gov (United States)

Hamill, P.

1979-01-01

Aerosol deposition in the upper respiratory system (trachea to segmental bronchi) is considered and the importance of turbulent diffusion as a deposition mechanism is evaluated. It is demonstrated that for large particles (diameter greater than about 5 microns), turbulent diffusion is the dominant deposition mechanism in the trachea. Conditions under which turbulent diffusion may be important in successive generations of the pulmonary system are determined. The probability of particle deposition is compared with probabilities of deposition, as determined by the equations generally used in regional deposition models. The analysis is theoretical; no new experimental data is presented.

External boundary effects on simultaneous diffusion and reaction processes

International Nuclear Information System (INIS)

Le Roux, M.N.; Wilhelmsson, H.

1989-01-01

External boundaries influence the spatial and temporal structure of evolution of dynamic systems governed by reaction-diffusion equations. Critical limits, i.e. thresholds for explosive growth or onset of diffusion dominated decay, are found to be caused by the presence of the boundary and to depend on: the position of the boundary, where the density is assumed to be zero at any instant of time: the mutual weights (coefficients) and powers of the nonlinear reaction and diffusion processes; and the initial spatial distribution. However, for particular relations between the nonlinear powers of the reaction and diffusion terms the critical limits do not depend on the initial conditions. The results are obtained by simulation experiment for one, two and three dimensions. Trends in the dynamic evolution of the system with an external boundary imposed are compared with the corresponding analytic results obtained for free boundary. Interesting applications are found in various areas, e.g. in the field of high temperature fusion plasma where the evolution of the temperature profile for the so-called H-mode (constant plasma density) is described

Structural limitations of learning in a crowd: communication vulnerability and information diffusion in MOOCs

Science.gov (United States)

Gillani, Nabeel; Yasseri, Taha; Eynon, Rebecca; Hjorth, Isis

2014-09-01

Massive Open Online Courses (MOOCs) bring together a global crowd of thousands of learners for several weeks or months. In theory, the openness and scale of MOOCs can promote iterative dialogue that facilitates group cognition and knowledge construction. Using data from two successive instances of a popular business strategy MOOC, we filter observed communication patterns to arrive at the ``significant'' interaction networks between learners and use complex network analysis to explore the vulnerability and information diffusion potential of the discussion forums. We find that different discussion topics and pedagogical practices promote varying levels of 1) ``significant'' peer-to-peer engagement, 2) participant inclusiveness in dialogue, and ultimately, 3) modularity, which impacts information diffusion to prevent a truly ``global'' exchange of knowledge and learning. These results indicate the structural limitations of large-scale crowd-based learning and highlight the different ways that learners in MOOCs leverage, and learn within, social contexts. We conclude by exploring how these insights may inspire new developments in online education.

Soil-gas diffusivity fingerprints of the dual porosity system in fractured limestone

DEFF Research Database (Denmark)

Claes, Niels; Chamindu, D.T.K.K.; Jensen, Jacob Birk

2010-01-01

processes are mostly limited to hydrogeological (water and solute) transport studies with very poor attention to the gaseous phase transport studies (Kristensen et al. 2010). This study characterizes fractured limestone soils for gas diffusion based on three different gas diffusivity fingerprints. The first...... fingerprint is a two-parameter exponential model, which mainly describes the gas diffusivity in the limestone matrix while taking both fracture connectivity and matrix pore connectivity into account. With the second fingerprint, we make a close observation of the tortuous matrix pore network by means...... of a modified Buckingham (1904) pore connectivity factor (X*). The third fingerprint of the fracture network involves the average angle of diffusion α (Moldrup et al. 2010), a parameter which characterizes the average angle at which the fractures are penetrating the sample....

Laboratory measurements of radon diffusion through multilayered cover systems for uranium tailings

International Nuclear Information System (INIS)

Nielson, K.K.; Rogers, V.C.; Rich, D.C.; Nederhand, F.A.; Sandquist, G.M.; Jensen, C.M.

1981-12-01

Laboratory measurements of radon fluxes and radon concentration profiles were conducted to characterize the effectiveness of multilayer cover systems for uranium tailings. The cover systems utilized soil and clay materials from proposed disposal sites for the Vitro, Durango, Shiprock, Grand Junction and Riverton tailings piles. Measured radon fluxes were in reasonable agreement with values predicted by multilayer diffusion theory. Results obtained by using air-filled porosities in the diffusion calculations were similar to those obtained by using total porosities. Measured diffusion coefficients were a better basis for predicting radon fluxes than were correlations of diffusion coefficient with moisture or with air porosity. Radon concentration profiles were also fitted by equations for multilayer diffusion in the air-filled space. Layer-order effects in the multilayer cover systems were examined and estimated to amount to 10 to 20 percent for the systems tested. Quality control measurements in support of the multilayer diffusion tests indicated that moisture absorption was not a significant problem in radon flux sampling with charcoal canisters, but that the geometry of the sampler was critical. The geometric design of flux-can samplers was also shown to be important. Enhanced radon diffusion along the walls of the test columns was examined and was found to be insignificant except when the columns had been physically disturbed. Additional moisture injected into two test columns decreased the radon flux, as expected, but appeared to migrate into surrounding materials or to be lost by evaporation. Control of moisture content and compaction in the test columns appeared to be the critical item affecting the accuracies of the experiments

Evaluation of glymphatic system activity with the diffusion MR technique: diffusion tensor image analysis along the perivascular space (DTI-ALPS) in Alzheimer’s disease cases

OpenAIRE

Taoka, Toshiaki; Masutani, Yoshitaka; Kawai, Hisashi; Nakane, Toshiki; Matsuoka, Kiwamu; Yasuno, Fumihiko; Kishimoto, Toshifumi; Naganawa, Shinji

2017-01-01

Purpose: The activity of the glymphatic system is impaired in animal models of Alzheimer’s disease (AD). We evaluated the activity of the human glymphatic system in cases of AD with a diffusion-based technique called diffusion tensor image analysis along the perivascular space (DTI-ALPS). Materials and methods: Diffusion tensor images were acquired to calculate diffusivities in the x, y, and z axes of the plane of the lateral ventricle body in 31 patients. We evaluated the diffusivity along t...

Diffusion models in metamorphic thermo chronology: philosophy and methods

International Nuclear Information System (INIS)

Munha, Jose Manuel; Tassinari, Colombo Celso Gaeta

1999-01-01

Understanding kinetics of diffusion is of major importance to the interpretation of isotopic ages in metamorphic rocks. This paper provides a review of concepts and methodologies involved on the various diffusion models that can be applied to radiogenic systems in cooling rocks. The central concept of closure temperature is critically discussed and quantitative estimates for the various diffusion models are evaluated, in order to illustrate the controlling factors and the limits of their practical application. (author)

Diffuse-interface model for rapid phase transformations in nonequilibrium systems.

Science.gov (United States)

Galenko, Peter; Jou, David

2005-04-01

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

Science.gov (United States)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

Operating limit study for the proposed solid waste landfill at Paducah Gaseous Diffusion Plant

Energy Technology Data Exchange (ETDEWEB)

Lee, D.W.; Wang, J.C.; Kocher, D.C.

1995-06-01

A proposed solid waste landfill at Paducah Gaseous Diffusion Plant (PGDP) would accept wastes generated during normal operations that are identified as non-radioactive. These wastes may include small amounts of radioactive material from incidental contamination during plant operations. A site-specific analysis of the new solid waste landfill is presented to determine a proposed operating limit that will allow for waste disposal operations to occur such that protection of public health and the environment from the presence of incidentally contaminated waste materials can be assured. Performance objectives for disposal were defined from existing regulatory guidance to establish reasonable dose limits for protection of public health and the environment. Waste concentration limits were determined consistent with these performance objectives for the protection of off-site individuals and inadvertent intruders who might be directly exposed to disposed wastes. Exposures of off-site individuals were estimated using a conservative, site-specific model of the groundwater transport of contamination from the wastes. Direct intrusion was analyzed using an agricultural homesteader scenario. The most limiting concentrations from direct intrusion or groundwater transport were used to establish the concentration limits for radionuclides likely to be present in PGDP wastes.

Operating limit study for the proposed solid waste landfill at Paducah Gaseous Diffusion Plant

International Nuclear Information System (INIS)

Lee, D.W.; Wang, J.C.; Kocher, D.C.

1995-06-01

A proposed solid waste landfill at Paducah Gaseous Diffusion Plant (PGDP) would accept wastes generated during normal operations that are identified as non-radioactive. These wastes may include small amounts of radioactive material from incidental contamination during plant operations. A site-specific analysis of the new solid waste landfill is presented to determine a proposed operating limit that will allow for waste disposal operations to occur such that protection of public health and the environment from the presence of incidentally contaminated waste materials can be assured. Performance objectives for disposal were defined from existing regulatory guidance to establish reasonable dose limits for protection of public health and the environment. Waste concentration limits were determined consistent with these performance objectives for the protection of off-site individuals and inadvertent intruders who might be directly exposed to disposed wastes. Exposures of off-site individuals were estimated using a conservative, site-specific model of the groundwater transport of contamination from the wastes. Direct intrusion was analyzed using an agricultural homesteader scenario. The most limiting concentrations from direct intrusion or groundwater transport were used to establish the concentration limits for radionuclides likely to be present in PGDP wastes

Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation

Science.gov (United States)

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2018-05-01

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [hC 1,hC 2] . We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits hC 1 and hC 2, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.

Plant air systems safety study: Portsmouth Gaseous Diffusion Plant

International Nuclear Information System (INIS)

1982-05-01

The Portsmouth Gaseous Diffusion Plant Air System facilities and operations are reviewed for potential safety problems not covered by standard industrial safety procedures. Information is presented under the following section headings: facility and process description (general); air plant equipment; air distribution system; safety systems; accident analysis; plant air system safety overview; and conclusion

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...

Diffusion of Finite-Size Particles in Confined Geometries

KAUST Repository

Bruna, Maria

2013-05-10

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle\\'s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.

Energy diffusion in strongly driven quantum chaotic systems: the role of correlations of the matrix elements

International Nuclear Information System (INIS)

Elyutin, P V; Rubtsov, A N

2008-01-01

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or exceeds the frequency of perturbation. For this case, the models of the Hamiltonian with random non-correlated matrix elements demonstrate that the energy evolution retains its diffusive character, but the rate of diffusion increases slower than the square of the magnitude of perturbation, thus destroying the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit ℎ → 0. The numerical calculation carried out for a model built from the first principles (the quantum analog of the Pullen-Edmonds oscillator) demonstrates that the evolving energy distribution, apart from the diffusive component, contains a ballistic one with the energy dispersion that is proportional to the square of time. This component originates from the chains of matrix elements with correlated signs and vanishes if the signs of matrix elements are randomized. The presence of the ballistic component formally extends the applicability of the FGR to the non-perturbative domain and restores the quantum-classical correspondence

Dynamics of the diffusive DM-DE interaction – Dynamical system approach

Energy Technology Data Exchange (ETDEWEB)

Haba, Zbigniew [Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204 Wrocław (Poland); Stachowski, Aleksander; Szydłowski, Marek, E-mail: zhab@ift.uni.wroc.pl, E-mail: aleksander.stachowski@uj.edu.pl, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Krakow (Poland)

2016-07-01

We discuss dynamics of a model of an energy transfer between dark energy (DE) and dark matter (DM) . The energy transfer is determined by a non-conservation law resulting from a diffusion of dark matter in an environment of dark energy. The relativistic invariance defines the diffusion in a unique way. The system can contain baryonic matter and radiation which do not interact with the dark sector. We treat the Friedman equation and the conservation laws as a closed dynamical system. The dynamics of the model is examined using the dynamical systems methods for demonstration how solutions depend on initial conditions. We also fit the model parameters using astronomical observation: SNIa, H ( z ), BAO and Alcock-Paczynski test. We show that the model with diffuse DM-DE is consistent with the data.

Analytically solvable models of reaction-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

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

2004-05-01

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

Force Limit System

Science.gov (United States)

Pawlik, Ralph; Krause, David; Bremenour, Frank

2011-01-01

The Force Limit System (FLS) was developed to protect test specimens from inadvertent overload. The load limit value is fully adjustable by the operator and works independently of the test system control as a mechanical (non-electrical) device. When a test specimen is loaded via an electromechanical or hydraulic test system, a chance of an overload condition exists. An overload applied to a specimen could result in irreparable damage to the specimen and/or fixturing. The FLS restricts the maximum load that an actuator can apply to a test specimen. When testing limited-run test articles or using very expensive fixtures, the use of such a device is highly recommended. Test setups typically use electronic peak protection, which can be the source of overload due to malfunctioning components or the inability to react quickly enough to load spikes. The FLS works independently of the electronic overload protection.

Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system

International Nuclear Information System (INIS)

Cherniha, Roman; Davydovych, Vasyl’

2013-01-01

Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)

Dynamics of a quantum two-level system under the action of phase-diffusion field

Energy Technology Data Exchange (ETDEWEB)

Sobakinskaya, E.A. [Institute for Physics of Microstructures of RAS, Nizhny Novgorod, 603950 (Russian Federation); Pankratov, A.L., E-mail: alp@ipm.sci-nnov.ru [Institute for Physics of Microstructures of RAS, Nizhny Novgorod, 603950 (Russian Federation); Vaks, V.L. [Institute for Physics of Microstructures of RAS, Nizhny Novgorod, 603950 (Russian Federation)

2012-01-09

We study a behavior of quantum two-level system, interacting with noisy phase-diffusion field. The dynamics is shown to split into two regimes, determined by the coherence time of the phase-diffusion field. For both regimes we present a model of quantum system behavior and discuss possible applications of the obtained effect for spectroscopy. In particular, the obtained analytical formula for the macroscopic polarization demonstrates that the phase-diffusion field does not affect the absorption line shape, which opens up an intriguing possibility of noisy spectroscopy, based on broadband sources with Lorentzian line shape. -- Highlights: ► We study dynamics of quantum system interacting with noisy phase-diffusion field. ► At short times the phase-diffusion field induces polarization in the quantum system. ► At long times the noise leads to polarization decay and heating of a quantum system. ► Simple model of interaction is derived. ► Application of the described effects for spectroscopy is discussed.

Qualitative analysis on a cubic predator-prey system with diffusion

Directory of Open Access Journals (Sweden)

Qunyi Bie

2011-04-01

Full Text Available In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.

Numerical Diffusion Effect in Dynamic Simulation of Thermohydraulic Systems

International Nuclear Information System (INIS)

Zanocco, Pablo; Gimenez, Marcelo; Delmastro, Dario

2003-01-01

In this work, the behavior of the explicit - up-wind method is studied in two phase natural convection circuit, near the instabilities boundaries.The effect of the numerical diffusion of the scheme upon the system stability is evaluated by means of linearization by small perturbations.The results are compared with a non-diffusive method, in the frequency domain, that solves analytically the linearized equations around a steady state condition.Moreover, a conservation equation transport model using the method of characteristics is implemented and studied.This method is compared with the explicit - up-wind scheme and it is found that it significantly reduces numerical diffusion in the equations solution. Several advantages are visualized for particular cases

Diffuse Ceiling Inlet Systems and the Room Air Distribution

DEFF Research Database (Denmark)

Nielsen, Peter V.; Jensen, Rasmus Lund; Rong, Li

2010-01-01

A diffuse ceiling inlet system is an air distribution system which is supplying the air through the whole ceiling. The system can remove a large heat load without creating draught in the room. The paper describes measurements in the case of both cooling and heating, and CFD predictions are given...

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

KAUST Repository

Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.

2009-01-01

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

KAUST Repository

Madzvamuse, Anotida

2009-08-29

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.

Diffusion coefficients of tracers in glassy polymer systems prepared by gamma radiolysis

International Nuclear Information System (INIS)

Tonge, M.P.; Gilbert, R.G.

1996-01-01

Diffusion-controlled reactions are common in free radical polymerisation reactions, especially in glassy polymer matrices. Such reactions commonly have an important influence on the polymerisation process and final polymer properties. For example, the dominant growth-stopping event (bimolecular termination) is generally diffusion-controlled. In glassy polymer systems, where molecular mobility is very low, the chain growth mechanism (propagation) may become diffusion-controlled. At present, the mechanism for propagation in glassy polymers is poorly understood, but it is expected by the Smoluchowski expression applied to propagation to depend strongly on the diffusion coefficient of monomer. The objective of this study is to measure reliable diffusion coefficients of small tracer molecules in glassy polymers, and compare these with propagation rate coefficients in similar systems, by the prediction above. Samples were initially prepared in a sealed sampled cell containing monomer, inert diluent, and tracer dye. After irradiation for several days, complete conversion of monomer to polymer can be obtained. The diffusion coefficients for two tracer dyes have been measured as a function of weight fraction polymer glassy poly(methyl methacrylate) samples

Homogenization of a thermo-diffusion system with Smoluchowski interactions

NARCIS (Netherlands)

Krehel, O.; Aiki, T.; Muntean, A.

2014-01-01

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale

Reactor limit control system

International Nuclear Information System (INIS)

Rubbel, F.E.

1982-01-01

The very extensive use of limitations in the operational field between protection system and closed-loop controls is an important feature of German understanding of operational safety. The design of limitations is based on very large activities in the computational field but mostly on the high level of the plant-wide own commissioning experience of a turnkey contractor. Limitations combine intelligence features of closed-loop controls with the high availability of protection systems. (orig.)

Multiscale integration schemes for jump-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

Givon, D.; Kevrekidis, I.G.

2008-12-09

We study a two-time-scale system of jump-diffusion stochastic differential equations. We analyze a class of multiscale integration methods for these systems, which, in the spirit of [1], consist of a hybridization between a standard solver for the slow components and short runs for the fast dynamics, which are used to estimate the effect that the fast components have on the slow ones. We obtain explicit bounds for the discrepancy between the results of the multiscale integration method and the slow components of the original system.

Film drainage and interfacial instabilities in polymeric systems with diffuse interfaces

NARCIS (Netherlands)

Zdravkov, A.N.; Peters, G.W.M.; Meijer, H.E.H.

2006-01-01

We report an experimental investigation on the effect of mutual diffusion in polymeric systems on film drainage between two captive drops. The main objective is to study the influence of diffuse interfaces on film drainage. This is done by using material combinations with different interfacial

Metric diffusion along foliations

CERN Document Server

Walczak, Szymon M

2017-01-01

Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.

A simple polarized-based diffused reflectance colour imaging system

African Journals Online (AJOL)

A simple polarized-based diffuse reflectance imaging system has been developed. The system is designed for both in vivo and in vitro imaging of agricultural specimen in the visible region. The system uses a commercial web camera and a halogen lamp that makes it relatively simple and less expensive for diagnostic ...

Signatures of a quantum diffusion limited hydrogen atom tunneling reaction.

Science.gov (United States)

Balabanoff, Morgan E; Ruzi, Mahmut; Anderson, David T

2017-12-20

We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH 2 ) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH 3 OH) isolated in solid pH 2 . Short-term irradiation of CH 3 OH at 1.8 K readily produces CH 2 O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH 3 O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH 2 OH growth. The CH 2 OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH 3 O with the pH 2 host, (ii) H atom reactions with the CH 2 O photofragment, and (iii) long-range migration of H atoms and reaction with CH 3 OH. We assign the rapid CH 2 OH growth to the following CH 3 O + H 2 → CH 3 OH + H → CH 2 OH + H 2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD 3 OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH 2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

Control of transversal instabilities in reaction-diffusion systems

Science.gov (United States)

Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

2018-05-01

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim

2012-01-01

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.

2012-05-22

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Diffuse-Illumination Systems for Growing Plants

Science.gov (United States)

May, George; Ryan, Robert

2010-01-01

Agriculture in both terrestrial and space-controlled environments relies heavily on artificial illumination for efficient photosynthesis. Plant-growth illumination systems require high photon flux in the spectral range corresponding with plant photosynthetic active radiation (PAR) (400 700 nm), high spatial uniformity to promote uniform growth, and high energy efficiency to minimize electricity usage. The proposed plant-growth system takes advantage of the highly diffuse reflective surfaces on the interior of a sphere, hemisphere, or other nearly enclosed structure that is coated with highly reflective materials. This type of surface and structure uniformly mixes discrete light sources to produce highly uniform illumination. Multiple reflections from within the domelike structures are exploited to obtain diffuse illumination, which promotes the efficient reuse of photons that have not yet been absorbed by plants. The highly reflective surfaces encourage only the plant tissue (placed inside the sphere or enclosure) to absorb the light. Discrete light sources, such as light emitting diodes (LEDs), are typically used because of their high efficiency, wavelength selection, and electronically dimmable properties. The light sources are arranged to minimize shadowing and to improve uniformity. Different wavelengths of LEDs (typically blue, green, and red) are used for photosynthesis. Wavelengths outside the PAR range can be added for plant diagnostics or for growth regulation

Diffusion Monte Carlo calculation of three-body systems

International Nuclear Information System (INIS)

Lu Mengjiao; Lin Qihu; Ren Zhongzhou

2012-01-01

The application of the diffusion Monte Carlo algorithm in three-body systems is studied. We develop a program and use it to calculate the property of various three-body systems. Regular Coulomb systems such as atoms, molecules, and ions are investigated. The calculation is then extended to exotic systems where electrons are replaced by muons. Some nuclei with neutron halos are also calculated as three-body systems consisting of a core and two external nucleons. Our results agree well with experiments and others' work. (authors)

Treatment outcome in early diffuse cutaneous systemic sclerosis

DEFF Research Database (Denmark)

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

2017-01-01

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

Systemic Sclerosis: Diffuse and Limited

Science.gov (United States)

... is the largest organ in the body. Its disadvantage is that it is spread over the surface ... blood flow to the kidneys for reasons that doctors do not understand. This then triggers the release ...

Properties of diffusive systems near a saddle point: application to a quartic double well

CERN Document Server

Battezzati, M

2003-01-01

This paper aims at the analysis of diffusive properties of unidimensional mechanical systems in the environment of maxima and minima of the potential. It begins with a study of the properties of the singular solutions of the Hamilton-Jacobi-Yasue equation in the above-mentioned environment, in both strong or very small frictional forces. For the quartic symmetrical double-well potential, approximate solutions are found for local validity and the diffusion operator is then calculated in the limits of deep wells and small temperature, the regime being supposed to be aperiodic, with high or moderate values of frictional coefficient. This equation is proved to be nonunique. This operator is then reduced to second order by imposing suitable boundary conditions. Thus an appropriate eigenvalue equation is obtained to describe stationary states in the environment of extremal points of the potential energy function. The main interest of this work relies upon the fact that transition times between wells mainly depend u...

Some reflections on the diffusion of pellet heating systems in Sweden

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Krushna; Gustavsson, Leif [1Mid Sweden University, Ecotechnology, SE-831 25 Oestersund (Sweden); Madlener, Reinhard [CEPE - Centre for Energy Policy and Economics, Swiss Federal Institute of Technology, Zurich (Switzerland)

2002-07-01

In the context of global warming and dependence on fossil fuels, modern bioenergy systems have appeared as important sustainable energy solutions with a large untapped potential in Sweden and the rest of the European Union. Small-scale pellet heating systems for space heating of small houses is one of these solutions. In Sweden, such systems have relative advantages over oil- or electricity boiler systems both in terms of greenhouse gas emission reduction and total lifetime cost of equipment and fuel. However, so far the market diffusion process of this technology has been rather slow. This paper, by employing concepts and insights from the literature of evolutionary economics and sociology, studies the factors involved in the diffusion of such systems.

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

Energy Technology Data Exchange (ETDEWEB)

Xu, Bruce S. [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Lollar, Barbara Sherwood [Earth Sciences Department, University of Toronto, 22 Russell Street, Toronto, ON M5S 3B1 (Canada); Passeport, Elodie [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Chemical Engineering and Applied Chemistry Department, University of Toronto, 200 College Street, Toronto, ON M5S 3E5 (Canada); Sleep, Brent E., E-mail: sleep@ecf.utoronto.ca [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada)

2016-04-15

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C{sub 0}), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D{sub mech}/D{sub eff}). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C{sub 0}/MDL ratios of 50 or higher. Much larger C{sub 0}/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D{sub mech}/D{sub eff} is

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

International Nuclear Information System (INIS)

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

2016-01-01

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C_0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D_m_e_c_h/D_e_f_f). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C_0/MDL ratios of 50 or higher. Much larger C_0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D_m_e_c_h/D_e_f_f is larger than 10, DRIF

Diffusion in multicomponent systems: a free energy approach

International Nuclear Information System (INIS)

Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian

2004-01-01

This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (M aa , M ab , M ba , and M bb ), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ ac and χ bc ) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested

Diffusion and phase growth in heterophase systems. 1

International Nuclear Information System (INIS)

Mchedlov-Petrosyan, P.O.

1989-01-01

The present paper gives the view of theoretical study of diffusion processes in ternary and more component solid-state systems, caused by chemical reactions and phase growth. Internal oxidation of alloys, nitridation, borating etc. are the well-known and widely investigated processes of such type. Self-consistent theoretical model of such processes must take into account both the effect of concentration macroscopic districutions on new phase precipitation growth and precipitation reaction on concentration distribution; heterophase must be explicitly allowed for. As for binary system, diffusion theory, running into the phase growth, is well developed and completely presented in monographs, the carried out theoretical investigations of ternary systems are explicitly deficient. The first part of the review presents analysis of available theoretical studies approximately up to 1980. Ratios between various analytically solved models are discussed in detail. It is shown that they don't satisfy to full extent the above-given requirements. More consistent, both numerically and analytically solvable models developed for the last years, are considered in the review second part. 119 refs

Weak rotating flow disturbances in a centrifugal compressor with a vaneless diffuser

Science.gov (United States)

Moore, F. K.

1988-01-01

A theory is presented to predict the occurrence of weak rotating waves in a centrifugal compression system with a vaneless diffuser. As in a previous study of axial systems, an undisturbed performance characteristic is assumed known. Following an inviscid analysis of the diffuser flow, conditions for a neutral rotating disturbance are found. The solution is shown to have two branches; one with fast rotation, the other with very slow rotation. The slow branch includes a dense set of resonant solutions. The resonance is a feature of the diffuser flow, and therefore such disturbances must be expected at the various resonant flow coefficients regardless of the compressor characteristic. Slow solutions seem limited to flow coefficients less than about 0.3, where third and fourth harmonics appear. Fast waves seem limited to a first harmonic. These fast and slow waves are described, and effects of diffuser-wall convergence, backward blade angles, and partial recovery of exit velocity head are assessed.

Support systems for the diffusion of renewable energy technologies-an investor perspective

International Nuclear Information System (INIS)

Dinica, Valentina

2006-01-01

Concern over climate change impacts and the projected depletion of fossil fuels has urged more governments to adopt policies that stimulate the diffusion of renewable energy technologies (RET). With an increasingly diverse suite of support instruments, the question emerges as to which instruments or combinations are able to achieve faster, more substantial diffusion results. Although various support instruments were extensively addressed in policy studies, there is still no consensus. This is partly because many policy studies take a policy-maker approach in comparing support instruments, leaving relationships between policy design and policy results as a black box. This paper proposes an investor-oriented perspective to analyze the diffusion potential of support systems for RET. The main argument is that it is not the type of support instrument but rather its risk/profitability characteristics that influence investor behavior and the rate of diffusion. The two instruments most frequently discussed and compared are the feed-in-tariff and the quota model. The analysis in this paper concludes that policy design is crucial: while often feed-in tariffs are applauded and quota system feared, feed-in tariffs may also bring about disappointing diffusion results when poorly designed while quota systems may be also conceived as attractive instruments for independent power producers

Determination of operating limits for radionuclides for a proposed landfill at Paducah Gaseous Diffusion Plant

International Nuclear Information System (INIS)

Wang, J.C.; Lee, D.W.; Ketelle, R.H.; Lee, R.R.; Kocher, D.C.

1994-01-01

The operating limits for radionuclides in sanitary and industrial wastes were determined for a proposed landfill at the Paducah Gaseous Diffusion Plant (PGDP), Kentucky. These limits, which may be very small but nonzero, are not mandated by law or regulation but are needed for rational operation. The approach was based on analyses of the potential contamination of groundwater at the plant boundary and the potential exposure to radioactivity of an intruder at the landfill after closure. The groundwater analysis includes (1) a source model describing the disposal of waste and the release of radionuclides from waste to the groundwater, (2) site-specific groundwater flow and contaminant transport calculations, and (3) calculations of operating limits from the dose limit and conversion factors. The intruder analysis includes pathways through ingestion of contaminated vegetables and soil, external exposure to contaminated soil, and inhalation of suspended activity from contaminated soil particles. In both analyses, a limit on annual effective dose equivalent of 4 mrem (0.04 mSv) was adopted. The intended application of the results is to refine the radiological monitoring standards employed by the PGDP Health Physics personnel to determine what constitutes radioactive wastes, with concurrence of the Commonwealth of Kentucky

System for diffusing light from an optical fiber or light guide

Science.gov (United States)

Maitland, Duncan J [Pleasant Hill, CA; Wilson, Thomas S [San Leandro, CA; Benett, William J [Livermore, CA; Small, IV, Ward [

2008-06-10

A system for diffusing light from an optical fiber wherein the optical fiber is coupled to a light source, comprising forming a polymer element adapted to be connected to the optical fiber and incorporating a scattering element with the polymer element wherein the scattering element diffuses the light from the polymer element. The apparatus of the present invention comprises a polymer element operatively connected to the optical fiber and a scattering element operatively connected with the shape polymer element that diffuses the light from the polymer element.

The mechanism of Turing pattern formation in a positive feedback system with cross diffusion

International Nuclear Information System (INIS)

Yang, Xiyan; Liu, Tuoqi; Zhang, Jiajun; Zhou, Tianshou

2014-01-01

In this paper, we analyze a reaction–diffusion (R–D) system with a double negative feedback loop and find cases where self diffusion alone cannot lead to Turing pattern formation but cross diffusion can. Specifically, we first derive a set of sufficient conditions for Turing instability by performing linear stability analysis, then plot two bifurcation diagrams that specifically identify Turing regions in the parameter phase plane, and finally numerically demonstrate representative Turing patterns according to the theoretical predictions. Our analysis combined with previous studies actually implies an interesting fact that Turing patterns can be generated not only in a class of monostable R–D systems where cross diffusion is not necessary but also in a class of bistable R–D systems where cross diffusion is necessary. In addition, our model would be a good candidate for experimentally testing Turing pattern formation from the viewpoint of synthetic biology. (paper)

Viscosity and viscoelasticity of two-phase systems having diffuse interfaces

Science.gov (United States)

Hopper, R. W.

1976-01-01

The equilibrium stability criterion for diffuse interfaces in a two-component solution with a miscibility gap requires that the interdiffusion flux vanish. If the system is continuously deformed, convective fluxes disrupt the equilibrium in the interface regions and induce a counter diffusive flux, which is dissipative and contributes to the apparent viscosity of the mixture. Chemical free energy is recoverably stored, causing viscoelastic phenomena. Both effects are significant.

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander

2014-09-10

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative logarithmic entropy, being based essentially on the application of the Log-Sobolev estimate and a convexification argument only, making it quite robust to model variations. An important feature of our analysis is the interaction of the two different dissipative mechanisms: pure diffusion, forcing the system asymptotically to the homogeneous state, and pure reaction, forcing the solution to the (possibly inhomogeneous) chemical equilibrium. Only the interaction of both mechanisms provides the convergence to the homogeneous equilibrium. Moreover, we introduce two generalizations of the main result: (i) vanishing diffusion constants in some chemical components and (ii) usage of different entropy functionals. We provide a few examples to highlight the usability of our approach and shortly discuss possible further applications and open questions.

Spin diffusion from an inhomogeneous quench in an integrable system.

Science.gov (United States)

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

Study on mutual diffusion and phase diagram in the Ni-Ta system

International Nuclear Information System (INIS)

Pimenov, V.N.; Ugaste, Yu.Eh.; Akkushkarova, K.A.

1977-01-01

The mutual diffusion in the Ni-Ta system has been investigated with a view of refining the constitutional diagram. The mutual diffusion factors and their effective values in the various phases and the diffusion activation energies are calculated. Given are the dependences of the phase growth constants and the mutual diffusion factors upon the temperature. The existence of five new phases Ta 2 Ni, TaNi, TaNi 2 , TaNi 3 , TaNi 8 has been discovered in the range of temperatures between 1150 and 1300 deg C. It is established that all the phases have a small concentration range of existence. It is noted that the diffusion characteristics in the phases (mutual diffusion factor and activation energy) differ widely, but fail to correlate with their melting points

Diffusion Strategy-Based Distributed Operation of Microgrids Using Multiagent System

Directory of Open Access Journals (Sweden)

Van-Hai Bui

2017-07-01

Full Text Available In distributed operation, each unit is operated by its local controller instead of using a centralized controller, which allows the action to be based on local information rather than global information. Most of the distributed solutions have implemented the consensus method, however, convergence time of the consensus method is quite long, while diffusion strategy includes a stochastic gradient term and can reach convergence much faster compared with consensus method. Therefore, in this paper, a diffusion strategy-based distributed operation of microgrids (MGs is proposed using multiagent system for both normal and emergency operation modes. In normal operation, the MG system is operated by a central controller instead of the distributed controller to minimize the operation cost. If any event (fault occurs in the system, MG system can be divided into two parts to isolate the faulty region. In this case, the MG system is changed to emergency operation mode. The normal part is rescheduled by the central controller while the isolated part schedules its resources in a distributed manner. The isolated part carries out distributed communication using diffusion between neighboring agents for optimal operation of this part. The proposed method enables peer-to-peer communication among the agents without the necessity of a centralized controller, and simultaneously performs resource optimization. Simulation results show that the system can be operated in an economic way in both normal operation and emergency operation modes.

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes.

Science.gov (United States)

Hernandez-Perez, Ruth; García-Cordero, José L; Escobar, Juan V

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes

Science.gov (United States)

Hernandez-Perez, Ruth; García-Cordero, José L.; Escobar, Juan V.

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Lévy flight with absorption: A model for diffusing diffusivity with long tails

Science.gov (United States)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

Influence of crystal structure on the CoII diffusion behavior in the Zn1-xCoxO system

International Nuclear Information System (INIS)

Peiteado, M.; Makovec, D.; Villegas, M.; Caballero, A.C.

2008-01-01

The solid state interaction of the Zn 1-x Co x O nominal system is investigated by means of diffusion couples and analysis of co-precipitated samples. The formation of a homogeneous Co:ZnO solid solution is found to be determined by the crystal structure from which Co II ions diffuse into the wurtzite lattice. No diffusion is observed whenever the CoO rock-salt structure is formed from the Co II precursor. On the contrary, the diffusion from the Co 3 O 4 spinel phase is feasible but has a limited temperature range defined by the reduction at a high temperature of Co III -Co II , since this process again leads to the formation of the rock-salt structure. However, when using a highly reactive and homogeneous co-precipitated starting powder, neither the spinel phase nor the rock-salt structure is formed, and a Co II :ZnO solid solution is obtained, which remains stable up to high temperatures. - Graphical abstract: Maximum diffusion distance for the ZnO-CoO x couple as a function of temperature. Dashed gray lines represent the temperature values at which the transformations between CoO and Co 3 O 4 compounds take place

The fractional diffusion limit of a kinetic model with biochemical pathway

Science.gov (United States)

Perthame, Benoît; Sun, Weiran; Tang, Min

2018-06-01

Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.

System-size corrections for self-diffusion coefficients calculated from molecular dynamics simulations: The case of CO{sub 2}, n-alkanes, and poly(ethylene glycol) dimethyl ethers

Energy Technology Data Exchange (ETDEWEB)

Moultos, Othonas A.; Economou, Ioannis G. [Chemical Engineering Program, Texas A& M University at Qatar, P.O. Box 23847, Doha (Qatar); Zhang, Yong; Maginn, Edward J., E-mail: ed@nd.edu [Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States); Tsimpanogiannis, Ioannis N. [Chemical Engineering Program, Texas A& M University at Qatar, P.O. Box 23847, Doha (Qatar); Environmental Research Laboratory, National Center for Scientific Research “Demokritos,” 15310 Aghia Paraskevi Attikis (Greece)

2016-08-21

Molecular dynamics simulations were carried out to study the self-diffusion coefficients of CO{sub 2}, methane, propane, n-hexane, n-hexadecane, and various poly(ethylene glycol) dimethyl ethers (glymes in short, CH{sub 3}O–(CH{sub 2}CH{sub 2}O){sub n}–CH{sub 3} with n = 1, 2, 3, and 4, labeled as G1, G2, G3, and G4, respectively) at different conditions. Various system sizes were examined. The widely used Yeh and Hummer [J. Phys. Chem. B 108, 15873 (2004)] correction for the prediction of diffusion coefficient at the thermodynamic limit was applied and shown to be accurate in all cases compared to extrapolated values at infinite system size. The magnitude of correction, in all cases examined, is significant, with the smallest systems examined giving for some cases a self-diffusion coefficient approximately 15% lower than the infinite system-size extrapolated value. The results suggest that finite size corrections to computed self-diffusivities must be used in order to obtain accurate results.

Global dynamics of a reaction-diffusion system

Directory of Open Access Journals (Sweden)

Yuncheng You

2011-02-01

Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.

Evaluation of diffusion-tensor imaging-based global search and tractography for tumor surgery close to the language system.

Directory of Open Access Journals (Sweden)

Mirco Richter

Full Text Available Pre-operative planning and intra-operative guidance in neurosurgery require detailed information about the location of functional areas and their anatomo-functional connectivity. In particular, regarding the language system, post-operative deficits such as aphasia can be avoided. By combining functional magnetic resonance imaging and diffusion tensor imaging, the connectivity between functional areas can be reconstructed by tractography techniques that need to cope with limitations such as limited resolution and low anisotropic diffusion close to functional areas. Tumors pose particular challenges because of edema, displacement effects on brain tissue and infiltration of white matter. Under these conditions, standard fiber tracking methods reconstruct pathways of insufficient quality. Therefore, robust global or probabilistic approaches are required. In this study, two commonly used standard fiber tracking algorithms, streamline propagation and tensor deflection, were compared with a previously published global search, Gibbs tracking and a connection-oriented probabilistic tractography approach. All methods were applied to reconstruct neuronal pathways of the language system of patients undergoing brain tumor surgery, and control subjects. Connections between Broca and Wernicke areas via the arcuate fasciculus (AF and the inferior fronto-occipital fasciculus (IFOF were validated by a clinical expert to ensure anatomical feasibility, and compared using distance- and diffusion-based similarity metrics to evaluate their agreement on pathway locations. For both patients and controls, a strong agreement between all methods was observed regarding the location of the AF. In case of the IFOF however, standard fiber tracking and Gibbs tracking predominantly identified the inferior longitudinal fasciculus that plays a secondary role in semantic language processing. In contrast, global search resolved connections in almost every case via the IFOF which

Understanding Whole Systems Change in Health Care: Insights into System Level Diffusion from Nursing Service Delivery Innovations--A Multiple Case Study

Science.gov (United States)

Berta, Whitney; Virani, Tazim; Bajnok, Irmajean; Edwards, Nancy; Rowan, Margo

2014-01-01

Our study responds to calls for theory-driven approaches to studying innovation diffusion processes in health care. While most research on diffusion in health care is situated at the service delivery level, we study innovations and associated processes that have diffused to the system level, and refer to work on complex adaptive systems and whole…

Classically exact surface diffusion constants at arbitrary temperature

International Nuclear Information System (INIS)

Voter, A.F.; Cohen, J.M.

1989-01-01

An expression is presented for computing the classical diffusion constant of a point defect (e.g., an adatom) in an infinite lattice of binding sites at arbitrary temperature. The transition state theory diffusion constant is simply multiplied by a dynamical correction factor that is computed from short-time classical trajectories initiated at the site boundaries. The time scale limitations of direct molecular dynamics are thus avoided in the low- and middle-temperature regimes. The expression results from taking the time derivative of the particle mean-square displacement in the lattice-discretized coordinate system. Applications are presented for surface diffusion on fcc(100) and fcc(111) Lennard-Jones crystal faces

Statistical mechanics of driven diffusive systems

CERN Document Server

Schmittmann, B

1995-01-01

Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension. Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail. Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these syst...

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.

Design of an efficient space constrained diffuser for supercritical CO2 turbines

Science.gov (United States)

Keep, Joshua A.; Head, Adam J.; Jahn, Ingo H.

2017-03-01

Radial inflow turbines are an arguably relevant architecture for energy extraction from ORC and supercritical CO 2 power cycles. At small scale, design constraints can prescribe high exit velocities for such turbines, which lead to high kinetic energy in the turbine exhaust stream. The inclusion of a suitable diffuser in a radial turbine system allows some exhaust kinetic energy to be recovered as static pressure, thereby ensuring efficient operation of the overall turbine system. In supercritical CO 2 Brayton cycles, the high turbine inlet pressure can lead to a sealing challenge if the rotor is supported from the rotor rear side, due to the seal operating at rotor inlet pressure. An alternative to this is a cantilevered layout with the rotor exit facing the bearing system. While such a layout is attractive for the sealing system, it limits the axial space claim of any diffuser. Previous studies into conical diffuser geometries for supercritical CO 2 have shown that in order to achieve optimal static pressure recovery, longer geometries of a shallower cone angle are necessitated when compared to air. A diffuser with a combined annular-radial arrangement is investigated as a means to package the aforementioned geometric characteristics into a limited space claim for a 100kW radial inflow turbine. Simulation results show that a diffuser of this design can attain static pressure rise coefficients greater than 0.88. This confirms that annular-radial diffusers are a viable design solution for supercritical CO2 radial inflow turbines, thus enabling an alternative cantilevered rotor layout.

Diffusivity measurements of volatile organics in levitated viscous aerosol particles

Directory of Open Access Journals (Sweden)

S. Bastelberger

2017-07-01

Full Text Available Field measurements indicating that atmospheric secondary organic aerosol (SOA particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low diffusivities of water in glassy aerosols. The focus of these studies is on kinetic limitations of hygroscopic growth and the plasticizing effect of water. In contrast, much less is known about diffusion limitations of organic molecules and oxidants in viscous matrices. These may affect atmospheric chemistry and gas–particle partitioning of complex mixtures with constituents of different volatility. In this study, we quantify the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and small amounts of volatile tetraethylene glycol (PEG-4 is investigated in an electrodynamic balance at controlled relative humidity (RH and temperature. The evaporative loss of PEG-4 as determined by Mie resonance spectroscopy is used in conjunction with a radially resolved diffusion model to retrieve translational diffusion coefficients of PEG-4. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes–Einstein relationship, which has often been invoked to infer diffusivity from viscosity. The evaporation of PEG-4 shows pronounced RH and temperature dependencies and is severely depressed for RH ≲ 30 %, corresponding to diffusivities < 10−14 cm2 s−1 at temperatures < 15 °C. The temperature dependence is strong, suggesting a diffusion activation energy of about 300 kJ mol−1. We conclude that atmospheric volatile organic compounds can be subject to severe diffusion limitations in viscous organic aerosol particles. This may enable an important long-range transport mechanism for organic material, including pollutant molecules such as polycyclic aromatic hydrocarbons (PAHs.

Performance of active feedforward control systems in non-ideal, synthesized diffuse sound fields.

Science.gov (United States)

Misol, Malte; Bloch, Christian; Monner, Hans Peter; Sinapius, Michael

2014-04-01

The acoustic performance of passive or active panel structures is usually tested in sound transmission loss facilities. A reverberant sending room, equipped with one or a number of independent sound sources, is used to generate a diffuse sound field excitation which acts as a disturbance source on the structure under investigation. The spatial correlation and coherence of such a synthesized non-ideal diffuse-sound-field excitation, however, might deviate significantly from the ideal case. This has consequences for the operation of an active feedforward control system which heavily relies on the acquisition of coherent disturbance source information. This work, therefore, evaluates the spatial correlation and coherence of ideal and non-ideal diffuse sound fields and considers the implications on the performance of a feedforward control system. The system under consideration is an aircraft-typical double panel system, equipped with an active sidewall panel (lining), which is realized in a transmission loss facility. Experimental results for different numbers of sound sources in the reverberation room are compared to simulation results of a comparable generic double panel system excited by an ideal diffuse sound field. It is shown that the number of statistically independent noise sources acting on the primary structure of the double panel system depends not only on the type of diffuse sound field but also on the sample lengths of the processed signals. The experimental results show that the number of reference sensors required for a defined control performance exhibits an inverse relationship to control filter length.

Diffusion coefficients of the ternary system (2-hydroxypropyl-{beta}-cyclodextrin + caffeine + water) at T = 298.15 K

Energy Technology Data Exchange (ETDEWEB)

Ribeiro, Ana C.F. [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal)], E-mail: anacfrib@ci.uc.pt; Santos, Cecilia I.A.V. [Departamento de Quimica Fisica, Facultad de Farmacia, Universidad de Alcala, 28871 Alcala de Henares, Madrid (Spain)], E-mail: cecilia.alves@uah.es; Lobo, Victor M.M. [Department of Chemistry, University of Coimbra, 3004-535 Coimbra (Portugal)], E-mail: vlobo@ci.uc.pt; Cabral, Ana M.T.D.P.V. [Faculty of Pharmacy, University of Coimbra, 3000-295 Coimbra (Portugal)], E-mail: acabral@ff.uc.pt; Veiga, Francisco J.B. [Faculty of Pharmacy, University of Coimbra, 3000-295 Coimbra (Portugal)], E-mail: fveiga@ci.uc.pt; Esteso, Miguel A. [Departamento de Quimica Fisica, Facultad de Farmacia, Universidad de Alcala, 28871 Alcala de Henares, Madrid (Spain)], E-mail: miguel.esteso@uah.es

2009-12-15

Ternary mutual diffusion coefficients measured by Taylor dispersion method (D{sub 11}, D{sub 22}, D{sub 12}, and D{sub 21}) are reported for aqueous solutions of 2-hydroxypropyl-{beta}-cyclodextrin (HP-{beta}-CD) + caffeine at T = 298.15 K at carrier concentrations from (0.000 to 0.010) mol . dm{sup -3}, for each solute, respectively. These diffusion coefficients have been measured having in mind a better understanding of the structure of these systems and thermodynamic behaviour of caffeine and 2-hydroxypropyl-{beta}-cyclodextrin in solution. For example, from these data it will be possible to estimate some parameters, such as the fraction of associated species HP-{beta}-CD (X{sub 1}) and caffeine (X{sub 2}) in this complex, the monomer and dimer fractions, X{sub 2}{sup M} and X{sub 2}{sup D}, respectively, and the limiting diffusion coefficients of the HP-{beta}-CD, D{sub HPBCD}{sup 0}, of the dimers caffeine entities, D{sub D}{sup 0}, and of those complexes (1:1), D{sub complex}{sup 0}.

Diffusion-controlled interface kinetics-inclusive system-theoretic propagation models for molecular communication systems

Science.gov (United States)

Chude-Okonkwo, Uche A. K.; Malekian, Reza; Maharaj, B. T.

2015-12-01

Inspired by biological systems, molecular communication has been proposed as a new communication paradigm that uses biochemical signals to transfer information from one nano device to another over a short distance. The biochemical nature of the information transfer process implies that for molecular communication purposes, the development of molecular channel models should take into consideration diffusion phenomenon as well as the physical/biochemical kinetic possibilities of the process. The physical and biochemical kinetics arise at the interfaces between the diffusion channel and the transmitter/receiver units. These interfaces are herein termed molecular antennas. In this paper, we present the deterministic propagation model of the molecular communication between an immobilized nanotransmitter and nanoreceiver, where the emission and reception kinetics are taken into consideration. Specifically, we derived closed-form system-theoretic models and expressions for configurations that represent different communication systems based on the type of molecular antennas used. The antennas considered are the nanopores at the transmitter and the surface receptor proteins/enzymes at the receiver. The developed models are simulated to show the influence of parameters such as the receiver radius, surface receptor protein/enzyme concentration, and various reaction rate constants. Results show that the effective receiver surface area and the rate constants are important to the system's output performance. Assuming high rate of catalysis, the analysis of the frequency behavior of the developed propagation channels in the form of transfer functions shows significant difference introduce by the inclusion of the molecular antennas into the diffusion-only model. It is also shown that for t > > 0 and with the information molecules' concentration greater than the Michaelis-Menten kinetic constant of the systems, the inclusion of surface receptors proteins and enzymes in the models

A critical comparison of constant and pulsed flow systems exploiting gas diffusion.

Science.gov (United States)

Silva, Claudineia Rodrigues; Henriquez, Camelia; Frizzarin, Rejane Mara; Zagatto, Elias Ayres Guidetti; Cerda, Victor

2016-02-01

Considering the beneficial aspects arising from the implementation of pulsed flows in flow analysis, and the relevance of in-line gas diffusion as an analyte separation/concentration step, influence of flow pattern in flow systems with in-line gas diffusion was critically investigated. To this end, constant or pulsed flows delivered by syringe or solenoid pumps were exploited. For each flow pattern, two variants involving different interaction times of the donor with the acceptor streams were studied. In the first one, both the acceptor and donor streams were continuously flowing, whereas in the second one, the acceptor was stopped during the gas diffusion step. Four different volatile species (ammonia, ethanol, carbon dioxide and hydrogen sulfide) were selected as models. For the flow patterns and variants studied, the efficiencies of mass transport in the gas diffusion process were compared, and sensitivity, repeatability, sampling frequency and recorded peak shape were evaluated. Analysis of the results revealed that sensitivity is strongly dependent on the implemented variant, and that flow pattern is an important feature in flow systems with in-line gas diffusion. Copyright © 2015 Elsevier B.V. All rights reserved.

Diffusion-controlled melting in granitic systems at 800-900degC and 100-200 MPa. Temperature and pressure dependence of the minimum diffusivity in granitic melts

International Nuclear Information System (INIS)

Yuguchi, Takashi; Yamaguchi, Takashi; Iwamoto, Manji-rou; Eguchi, Hibiki; Isobe, Hiroshi; Nishiyama, Tadao

2012-01-01

This paper presents the temperature and pressure dependence of the minimum binary diffusivity in granitic melts. The minimum diffusivities are determined by monitoring the temporal development of the diffusion-controlled melt layer(DCM) in granitic systems (albite (Ab)-quartz (Qtz)-H 2 O and orthoclase (Or)-Qtz-H 2 O) gathered during 31 melting experiments under conditions of 800-900degC and 100-200 MPa for durations of 19-72 h. The DCM is formed between single crystals (Ab or Or crystals) and powdered quartz in all runs and is characterized by a distinct concentration gradient. The maximum thickness of the DCM increases systematically with temperature, pressure, and run duration. Temporal development of the DCM obeys the parabolic growth rate law, using which the diffusivity can be estimated. Plots of concentrations along the diffusion paths in ternary diagrams (Na 2 O-Al 2 O 3 -SiO 2 diagram for the Ab-Qtz-H 2 O system and K 2 O-Al 2 O 3 -SiO 2 diagram for the Or-Qtz-H 2 O system) show linear trends rather than S-shaped trends, indicating that binary nature of diffusion occurs in these systems. Therefore, the diffusive component can be interpreted as an albite component or orthoclase and quartz components (SiO 2 ) rather than an oxide or a cation. (author)

Assessment of sorption properties and kinetic reaction of phosphorus reactive material to limit diffuse pollution

Directory of Open Access Journals (Sweden)

Bus Agnieszka

2017-09-01

Full Text Available Assessment of sorption properties and kinetic reaction of phosphorus reactive material to limit diffuse pollution. Polonite® is an effective reactive material (manufactured from opoka rock for removing phosphorus from aqueous solutions. In conducted experiments, Polonite® of grain size of 2–5 mm was used as a potential reactive material which can be used as a filter fulfillment to reduce phosphorus diffuse pollution from agriculture areas. Kinetic and equilibrium studies (performed as a batch experiment were carried out as a function of time to evaluate the sorption properties of the material. The obtained results show that Polonite® effectively removes such contamination. All tested concentrations (0.998, 5.213, 10.965 mg P-PO4·L−1 are characterized by a better fit to pseudo-second kinetic order. The Langmuir isotherm the best reflects the mechanism of adsorption process in case of Polonite® and based on the isotherm, calculated maximum adsorption capacity equals 96.58 mg P-PO4·g−1.

Diffusion and chemical activity of Zr-Sn and Zr-Ti systems

International Nuclear Information System (INIS)

Zee, R.H.; Watters, J.F.; Davidson, R.D.

1986-01-01

A modified evaporation method was used to determine the diffusion coefficients and the emission rates of Sn and Ti in Zr-Sn and Zr-Ti, respectively, at temperatures between 1605 and 1970 K. Results show that both Sn and Ti diffuse in their respective alloys via a vacancy mechanism. Comparison with data in the literature reveals that the activation energy for diffusion of Sn in Zr-Sn, with Sn content between 3 and 5 at.X is relatively constant from 1200 to 1970 K. From the measured emission rates, values of 103 and 98 kcal/mol were obtained for the enthalpies of sublimation for Sn and Ti in their alloys. With a comparison of the solute vapor pressures with those of the pure elements, partial molar free energies, entropies, and enthalpies for the two systems were determined in the temperature range investigated. The Zr-Sn system shows a very large negative heat of formation (-33 kcal/mol) whereas the Zr-Ti system behaves quite ideally, in agreement with phase-diagram predictions

Dichotomous-noise-induced pattern formation in a reaction-diffusion system

Science.gov (United States)

Das, Debojyoti; Ray, Deb Shankar

2013-06-01

We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

Di Francesco, M.; Fellner, K.; Markowich, P. A

2008-01-01

and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid

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

Science.gov (United States)

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

2018-01-01

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

Erosion of stereochemical control with increasing nucleophilicity: O-glycosylation at the diffusion limit.

Science.gov (United States)

Beaver, Matthew G; Woerpel, K A

2010-02-19

Nucleophilic substitution reactions of 2-deoxyglycosyl donors indicated that the reactivity of the oxygen nucleophile has a significant impact on stereoselectivity. Employing ethanol as the nucleophile resulted in a 1:1 (alpha:beta) ratio of diastereomers under S(N)1-like reaction conditions. Stereoselective formation of the 2-deoxy-alpha-O-glycoside was only observed when weaker nucleophiles, such as trifluoroethanol, were employed. The lack of stereoselectivity observed in reactions of common oxygen nucleophiles can be attributed to reaction rates of the stereochemistry-determining step that approach the diffusion limit. In this scenario, both faces of the prochiral oxocarbenium ion are subject to nucleophilic addition to afford a statistical mixture of diastereomeric products. Control experiments confirmed that all nucleophilic substitution reactions were performed under kinetic control.

Limit cycles in quantum systems

Energy Technology Data Exchange (ETDEWEB)

Niemann, Patrick

2015-04-27

In this thesis we investigate Limit Cycles in Quantum Systems. Limit cycles are a renormalization group (RG) topology. When degrees of freedom are integrated out, the coupling constants flow periodically in a closed curve. The presence of limit cycles is restricted by the necessary condition of discrete scale invariance. A signature of discrete scale invariance and limit cycles is log-periodic behavior. The first part of this thesis is concerned with the study of limit cycles with the similarity renormalization group (SRG). Limit cycles are mainly investigated within conventional renormalization group frameworks, where degrees of freedom, which are larger than a given cutoff, are integrated out. In contrast, in the SRG potentials are unitarily transformed and thereby obtain a band-diagonal structure. The width of the band structure can be regarded as an effective cutoff. We investigate the appearance of limit cycles in the SRG evolution. Our aim is to extract signatures as well as the scaling factor of the limit cycle. We consider the 1/R{sup 2}-potential in a two-body system and a three-body system with large scattering lengths. Both systems display a limit cycle. Besides the frequently used kinetic energy generator we apply the exponential and the inverse generator. In the second part of this thesis, Limit Cycles at Finite Density, we examine the pole structure of the scattering amplitude for distinguishable fermions at zero temperature in the medium. Unequal masses and a filled Fermi sphere for each fermion species are considered. We focus on negative scattering lengths and the unitary limit. The properties of the three-body spectrum in the medium and implications for the phase structure of ultracold Fermi gases are discussed.

Performance analysis of a new design of office diffuse ceiling ventilation system

DEFF Research Database (Denmark)

Fan, Jianhua; Hviid, Christian Anker; Yang, Honglu

2013-01-01

This paper aims to document and analyse performance of a new design of diffuse ceiling ventilation system in a typical office room. A full scale measurement is carried out in a climate chamber with an office setup at the Technical University of Denmark. Indoor air temperatures, air speeds, wall...... surface temperatures, pressure loss of the ceiling and ventilation effectiveness are measured for an air change rate of 3.5 h-1 and 5.1 h -1 respectively. A computational fluid dynamics model of the office with the diffuse ceiling ventilation system is built and validated by the full scale measurement....... The measurements of pressure loss across the ceiling show a low pressure drop between the plenum and the occupied zone. Ventilation effectiveness is measured to be close to 1 on average under the tested conditions. It is shown that the diffuse ceiling ventilation system is able to remove indoor pollutant...

The problem of birth of autowaves in parabolic systems with small diffusion

International Nuclear Information System (INIS)

Kolesov, A Yu; Rozov, N Kh; Sadovnichii, V A

2007-01-01

A parabolic reaction-diffusion system with zero Neumann boundary conditions at the end-points of a finite interval is considered under the following basic assumptions. First, the matrix diffusion coefficient in the system is proportional to a small parameter ε>0, and the system itself possesses a spatially homogeneous cycle (independent of the space variable) of amplitude of order √ε born by a zero equilibrium at an Andronov-Hopf bifurcation. Second, it is assumed that the matrix diffusion depends on an additional small parameter μ≥0, and for μ=0 there occurs in the stability problem for the homogeneous cycle the critical case of characteristic multiplier 1 of multiplicity 2 without Jordan block. Under these constraints and for independently varied parameters ε and μ the problem of the existence and the stability of spatially inhomogeneous auto-oscillations branching from the homogeneous cycle is analysed. Bibliography: 16 titles.

Observation of structural universality in disordered systems using bulk diffusion measurement

Science.gov (United States)

Papaioannou, Antonios; Novikov, Dmitry S.; Fieremans, Els; Boutis, Gregory S.

2017-12-01

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by the statistics of the placement of micrometer-thin parallel permeable barriers, and the time-dependent diffusion coefficient was measured by NMR methods over three orders of magnitude in time. The relation between the structural exponent, characterizing disorder universality class, and the dynamical exponent of the diffusion coefficient is experimentally verified. The experimentally established relation between structure and transport exemplifies the hierarchical nature of structural complexity—dynamics are mainly determined by the universality class, whereas microscopic parameters affect the nonuniversal coefficients. These results open the way for noninvasive characterization of structural correlations in porous media, complex materials, and biological tissues via a bulk diffusion measurement.

Diffusive instabilities in hyperbolic reaction-diffusion equations

Science.gov (United States)

Zemskov, Evgeny P.; Horsthemke, Werner

2016-03-01

We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.

Diffusivity measurements of volatile organics in levitated viscous aerosol particles

Science.gov (United States)

Bastelberger, Sandra; Krieger, Ulrich K.; Luo, Beiping; Peter, Thomas

2017-07-01

Field measurements indicating that atmospheric secondary organic aerosol (SOA) particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low diffusivities of water in glassy aerosols. The focus of these studies is on kinetic limitations of hygroscopic growth and the plasticizing effect of water. In contrast, much less is known about diffusion limitations of organic molecules and oxidants in viscous matrices. These may affect atmospheric chemistry and gas-particle partitioning of complex mixtures with constituents of different volatility. In this study, we quantify the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and small amounts of volatile tetraethylene glycol (PEG-4) is investigated in an electrodynamic balance at controlled relative humidity (RH) and temperature. The evaporative loss of PEG-4 as determined by Mie resonance spectroscopy is used in conjunction with a radially resolved diffusion model to retrieve translational diffusion coefficients of PEG-4. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes-Einstein relationship, which has often been invoked to infer diffusivity from viscosity. The evaporation of PEG-4 shows pronounced RH and temperature dependencies and is severely depressed for RH ≲ 30 %, corresponding to diffusivities pollutant molecules such as polycyclic aromatic hydrocarbons (PAHs).

Coupled diffusion systems with localized nonlinear reactions

DEFF Research Database (Denmark)

Pedersen, M.; Lin, Zhigui

2001-01-01

This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - δui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate...

Limits on diffuse fluxes of high energy extraterrestrial neutrinos with the AMANDA-B10 detector

International Nuclear Information System (INIS)

Ahrens, J.; Bai, X.; Barwick, S.W.; Bay, R.C.; Becka, T.; Becker, K.-H.; Bernardini, E.; Bertrand, D.; Binon, F.; Boeser, S.; Botner, O.; Bouchta, A.; Bouhali, O.; Burgess, T.; Carius, S.; Castermans, T.; Chirkin, D.; Conrad, J.; Cooley, J.; Cowen, D.F.; Davour, A.; De Clercq, C.; DeYoung, T.; Desiati, P.; Doksus, P.; Ekstrom, P.; Feser, T.; Gaisser, T.K.; Ganugapati, R.; Gaug, M.; Geenen, H.; Gerhardt, L.; Goldschmidt, A.; Hallgren, A.; Halzen, F.; Hanson, K.; Hardtke, R.; Hauschildt, T.; Hellwig, M.; Herquet, P.; Hill, G.C.; Hulth, P.O.; Hughey, B.; Hultqvist, K.; Hundertmark, S.; Jacobsen, J.; Karle, A.; Kuehn, K.; Kim, J.; Kopke, L.; Kowalski, M.; Lamoureux, J.I.; Leich, H.; Leuthold, M.; Lindahl, P.; Liubarsky, I.; Madsen, J.; Mandli, K.; Marciniewski, P.; Matis, H.S.; McParland, C.P.; Messarius, T.; Miller, T.C.; Minaeva, Y.; Miocinovic, P.; Mock, P.C.; Morse, R.; Neunhoffer, T.; Niessen, P.; Nygren, D.R.; Ogelman, H.; Olbrechts, P.; Perez de los Heros, C.; Pohl, A.C.; Porrata, R.; Price, P.B.; Przybylski, G.T.; Rawlins, K.; Resconi, E.; Rhode, W.; Ribordy, M.; Richter, S.; Rodriguez Martino, J.; Romenesko, P.; Ross, D.; Sander, H.-G.; Schlenstedt, S.; Schinarakis, K.; Schmidt, T.; Schneider, D.; Schwarz, R.; Silvestri, A.; Solarz, M.; Stamatikos, M.; Spiczak, G.M.; Spiering, C.; Steele, D.; Steffen, P.; Stokstad, R.G.; Sulanke, K.-H.; Taboada, I.; Tilav, S.; Wagner, W.; Walck, C.; Wang, Y.-R.; Wiebusch, C.H.; Wiedemann, C.; Wischnewski, R.; Wissing, H.; Woschnagg, K.; Wu, W.; Yodh, G.; Young, S.

2003-01-01

Data from the AMANDA-B10 detector taken during the austral winter of 1997 have been searched for a diffuse flux of high energy extraterrestrial muon-neutrinos, as predicted from, e.g., the sum of all active galaxies in the universe. This search yielded no excess events above those expected from the background atmospheric neutrinos, leading to upper limits on the extraterrestrial neutrino flux. For an assumed E -2 spectrum, a 90 percent classical confidence level upper limit has been placed at a level E 2 Phi(E) = 8.4 x 10 -7 GeV cm -2 s -1 1 sr -1 (for a predominant neutrino energy range 6-1000 TeV) which is the most restrictive bound placed by any neutrino detector. When specific predicted spectral forms are considered, it is found that some are excluded

Concerted diffusion of lipids in raft-like membranes

NARCIS (Netherlands)

Apajalahti, Touko; Niemela, Perttu; Govindan, Praveen Nedumpully; Miettinen, Markus S.; Salonen, Emppu; Marrink, Siewert-Jan; Vattulainen, Ilpo

2010-01-01

Currently, there is no comprehensive model for the dynamics of cellular membranes. The understanding of even the basic dynamic processes, such as lateral diffusion of lipids, is still quite limited. Recent studies of one-component membrane systems have shown that instead of single-particle motions,

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.

Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems

Science.gov (United States)

DeAngelis, Donald L.; Ming Ni, Wei; Zhang, Bo

2016-01-01

Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches. However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space. Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion. We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region. This relationship occurs in some biological populations, though not in others, so the result has ecological implications.

Planck intermediate results. XII: Diffuse Galactic components in the Gould Belt System

DEFF Research Database (Denmark)

Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

2013-01-01

We perform an analysis of the diffuse low-frequency Galactic components in the Southern part of the Gould Belt system (130^\\circ\\leq l\\leq 230^\\circ and -50^\\circ\\leq b\\leq -10^\\circ). Strong ultra-violet (UV) flux coming from the Gould Belt super-association is responsible for bright diffuse...

Diffuse radiation increases global ecosystem-level water-use efficiency

Science.gov (United States)

Moffat, A. M.; Reichstein, M.; Cescatti, A.; Knohl, A.; Zaehle, S.

2012-12-01

Current environmental changes lead not only to rising atmospheric CO2 levels and air temperature but also to changes in air pollution and thus the light quality of the solar radiation reaching the land-surface. While rising CO2 levels are thought to enhance photosynthesis and closure of stomata, thus leading to relative water savings, the effect of diffuse radiation on transpiration by plants is less clear. It has been speculated that the stimulation of photosynthesis by increased levels of diffuse light may be counteracted by higher transpiration and consequently water depletion and drought stress. Ultimately, in water co-limited systems, the overall effect of diffuse radiation will depend on the sensitivity of canopy transpiration versus photosynthesis to diffuse light, i.e. whether water-use efficiency changes with relative levels of diffuse light. Our study shows that water-use efficiency increases significantly with higher fractions of diffuse light. It uses the ecosystem-atmosphere gas-exchange observations obtained with the eddy covariance method at 29 flux tower sites. In contrast to previous global studies, the analysis is based directly on measurements of diffuse radiation. Its effect on water-use efficiency was derived by analyzing the multivariate response of carbon and water fluxes to radiation and air humidity using a purely empirical approach based on artificial neural networks. We infer that per unit change of diffuse fraction the water-use efficiency increases up to 40% depending on diffuse fraction levels and ecosystem type. Hence, in regions with increasing diffuse radiation positive effects on primary production are expected even under conditions where water is co-limiting productivity.

Classical diffusion, Anderson localization, and spectral statistics in billiard chains

International Nuclear Information System (INIS)

Dittrich, T.; Doron, E.; Smilansky, U.

1993-03-01

We study spectral properties of quasi one-dimensional extended systems that show deterministic diffusion on the classical level and Anderson localization in the quantal description. Using semiclassical arguments, we relate to universal aspects of the spectral fluctuations to features of the set of classical periodic orbits, expressed in terms of probability to perform periodic motion, that are likewise universal. This allows to derive an analytical expression for the spectral form factor which reflects the diffusive nature of the corresponding classical dynamics. It defines a novel spectral universality class which covers the transition between GOE statistics in the limit of a small ratio of the system size to the localization length, corresponding to the metallic regime of disordered systems, to Poissonian level fluctuations in the opposite limit. Our semiclassical predictions are illustrated and confirmed by a numerical investigation of aperiodic chains of chaotic billiards. (authors)

Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion

Directory of Open Access Journals (Sweden)

Shaban Aly

2016-01-01

Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

Science.gov (United States)

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

The out of equilibrium response function in sub-diffusive systems

International Nuclear Information System (INIS)

Gradenigo, G; Puglisi, A; Sarracino, A; Vulpiani, A; Villamaina, D

2012-01-01

We study the Einstein relation between spontaneous fluctuations and the response to an external perturbation for the comb model and the single file, which are examples of systems with sub-diffusive transport properties. The relevance of nonequilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down. In the case of the comb model, a general relation - appearing in the recent literature - between the response function and an unperturbed suitable correlation function allows us to explain the obtained results. This suggests that the relevant ingredient in breaking the Einstein formula, for stationary regimes, is not anomalous diffusion but the presence of currents driving the system out of equilibrium.

Self-diffusion measurements in heterogeneous systems using NMR pulsed field gradient technique

International Nuclear Information System (INIS)

Heink, W.; Kaerger, J.; Walter, A.

1978-01-01

The experimental pecularities of the NMR pulsed field gradient technique are critical surveyed in its application to zeolite adsorbate adsorbent systems. After a presentation of the different transport parameters accessible by this technique, the consequences of the existence of inner field gradients being inherent to heterogeneous systems are analyzed. Experimental conditions and consequences of an application of pulsed field gradients of high intensity which are necessary for the measurement of small intracrystalline self-diffusion coefficients, are discussed. Gradient pulses of 0.15 Tcm -1 with pulse widths of 2 ms maximum and relative deviations of less than 0.01 per mille can be realized. Since for a number of adsorbate adsorbent systems a distinct dependence of the intracrystalline self-diffusion coeffcients on adsorbate concentration is observed, determination of zeolite pore fiiling factor is of considerable importance for the interpretation of the diffusivities obtained. It is demonstrated that also this information can be obtained by NMR technique in a straightforward way with a mean error of less than 5 to 10 %. Applying this new method and using an optimum experimental device as described, pore filling factor dependences of the self-diffusion coefficients of alkanes in NaX zeolites can be followed over more than two orders of magnitude. (author)

Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity

International Nuclear Information System (INIS)

Cherstvy, Andrey G; Metzler, Ralf

2015-01-01

We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) ∼ D 0 |x| α t β depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements. (paper)

Upper limit on the diffuse flux of ultrahigh energy tau neutrinos from the Pierre Auger Observatory.

Science.gov (United States)

Abraham, J; Abreu, P; Aglietta, M; Aguirre, C; Allard, D; Allekotte, I; Allen, J; Allison, P; Alvarez-Muñiz, J; Ambrosio, M; Anchordoqui, L; Andringa, S; Anzalone, A; Aramo, C; Argirò, S; Arisaka, K; Armengaud, E; Arneodo, F; Arqueros, F; Asch, T; Asorey, H; Assis, P; Atulugama, B S; Aublin, J; Ave, M; Avila, G; Bäcker, T; Badagnani, D; Barbosa, A F; Barnhill, D; Barroso, S L C; Bauleo, P; Beatty, J J; Beau, T; Becker, B R; Becker, K H; Bellido, J A; BenZvi, S; Berat, C; Bergmann, T; Bernardini, P; Bertou, X; Biermann, P L; Billoir, P; Blanch-Bigas, O; Blanco, F; Blasi, P; Bleve, C; Blümer, H; Bohácová, M; Bonifazi, C; Bonino, R; Boratav, M; Brack, J; Brogueira, P; Brown, W C; Buchholz, P; Bueno, A; Burton, R E; Busca, N G; Caballero-Mora, K S; Cai, B; Camin, D V; Caramete, L; Caruso, R; Carvalho, W; Castellina, A; Catalano, O; Cataldi, G; Cazon, L; Cester, R; Chauvin, J; Chiavassa, A; Chinellato, J A; Chou, A; Chye, J; Clark, P D J; Clay, R W; Colombo, E; Conceição, R; Connolly, B; Contreras, F; Coppens, J; Cordier, A; Cotti, U; Coutu, S; Covault, C E; Creusot, A; Criss, A; Cronin, J; Curutiu, A; Dagoret-Campagne, S; Daumiller, K; Dawson, B R; de Almeida, R M; De Donato, C; de Jong, S J; De La Vega, G; de Mello Junior, W J M; de Mello Neto, J R T; DeMitri, I; de Souza, V; del Peral, L; Deligny, O; Della Selva, A; Delle Fratte, C; Dembinski, H; Di Giulio, C; Diaz, J C; Dobrigkeit, C; D'Olivo, J C; Dornic, D; Dorofeev, A; dos Anjos, J C; Dova, M T; D'Urso, D; Dutan, I; DuVernois, M A; Engel, R; Epele, L; Erdmann, M; Escobar, C O; Etchegoyen, A; Facal San Luis, P; Falcke, H; Farrar, G; Fauth, A C; Fazzini, N; Ferrer, F; Ferry, S; Fick, B; Filevich, A; Filipcic, A; Fleck, I; Fonte, R; Fracchiolla, C E; Fulgione, W; García, B; García Gámez, D; Garcia-Pinto, D; Garrido, X; Geenen, H; Gelmini, G; Gemmeke, H; Ghia, P L; Giller, M; Glass, H; Gold, M S; Golup, G; Gomez Albarracin, F; Gómez Berisso, M; Gómez Herrero, R; Gonçalves, P; Gonçalves do Amaral, M; Gonzalez, D; Gonzalez, J G; González, M; Góra, D; Gorgi, A; Gouffon, P; Grassi, V; Grillo, A F; Grunfeld, C; Guardincerri, Y; Guarino, F; Guedes, G P; Gutiérrez, J; Hague, J D; Hamilton, J C; Hansen, P; Harari, D; Harmsma, S; Harton, J L; Haungs, A; Hauschildt, T; Healy, M D; Hebbeker, T; Hebrero, G; Heck, D; Hojvat, C; Holmes, V C; Homola, P; Hörandel, J; Horneffer, A; Horvat, M; Hrabovský, M; Huege, T; Hussain, M; Iarlori, M; Insolia, A; Ionita, F; Italiano, A; Kaducak, M; Kampert, K H; Karova, T; Kégl, B; Keilhauer, B; Kemp, E; Kieckhafer, R M; Klages, H O; Kleifges, M; Kleinfeller, J; Knapik, R; Knapp, J; Koang, D-H; Krieger, A; Krömer, O; Kuempel, D; Kunka, N; Kusenko, A; La Rosa, G; Lachaud, C; Lago, B L; Lebrun, D; Lebrun, P; Lee, J; Leigui de Oliveira, M A; Letessier-Selvon, A; Leuthold, M; Lhenry-Yvon, I; López, R; Lopez Agüera, A; Lozano Bahilo, J; Luna García, R; Maccarone, M C; Macolino, C; Maldera, S; Mancarella, G; Manceñido, M E; Mandat, D; Mantsch, P; Mariazzi, A G; Maris, I C; Marquez Falcon, H R; Martello, D; Martínez, J; Martínez Bravo, O; Mathes, H J; Matthews, J; Matthews, J A J; Matthiae, G; Maurizio, D; Mazur, P O; McCauley, T; McEwen, M; McNeil, R R; Medina, M C; Medina-Tanco, G; Meli, A; Melo, D; Menichetti, E; Menschikov, A; Meurer, Chr; Meyhandan, R; Micheletti, M I; Miele, G; Miller, W; Mollerach, S; Monasor, M; Monnier Ragaigne, D; Montanet, F; Morales, B; Morello, C; Moreno, J C; Morris, C; Mostafá, M; Muller, M A; Mussa, R; Navarra, G; Navarro, J L; Navas, S; Necesal, P; Nellen, L; Newman-Holmes, C; Newton, D; Nguyen Thi, T; Nierstenhoefer, N; Nitz, D; Nosek, D; Nozka, L; Oehlschläger, J; Ohnuki, T; Olinto, A; Olmos-Gilbaja, V M; Ortiz, M; Ortolani, F; Ostapchenko, S; Otero, L; Pacheco, N; Pakk Selmi-Dei, D; Palatka, M; Pallotta, J; Parente, G; Parizot, E; Parlati, S; Pastor, S; Patel, M; Paul, T; Pavlidou, V; Payet, K; Pech, M; Pekala, J; Pelayo, R; Pepe, I M; Perrone, L; Petrera, S; Petrinca, P; Petrov, Y; Pham Ngoc, Diep; Pham Ngoc, Dong; Pham Thi, T N; Pichel, A; Piegaia, R; Pierog, T; Pimenta, M; Pinto, T; Pirronello, V; Pisanti, O; Platino, M; Pochon, J; Privitera, P; Prouza, M; Quel, E J; Rautenberg, J; Redondo, A; Reucroft, S; Revenu, B; Rezende, F A S; Ridky, J; Riggi, S; Risse, M; Rivière, C; Rizi, V; Roberts, M; Robledo, C; Rodriguez, G; Rodríguez Frías, D; Rodriguez Martino, J; Rodriguez Rojo, J; Rodriguez-Cabo, I; Ros, G; Rosado, J; Roth, M; Rouillé-d'Orfeuil, B; Roulet, E; Rovero, A C; Salamida, F; Salazar, H; Salina, G; Sánchez, F; Santander, M; Santo, C E; Santos, E M; Sarazin, F; Sarkar, S; Sato, R; Scherini, V; Schieler, H; Schmidt, A; Schmidt, F; Schmidt, T; Scholten, O; Schovánek, P; Schüssler, F; Sciutto, S J; Scuderi, M; Segreto, A; Semikoz, D; Settimo, M; Shellard, R C; Sidelnik, I; Siffert, B B; Sigl, G; Smetniansky De Grande, N; Smiałkowski, A; Smída, R; Smith, A G K; Smith, B E; Snow, G R; Sokolsky, P; Sommers, P; Sorokin, J; Spinka, H; Squartini, R; Strazzeri, E; Stutz, A; Suarez, F; Suomijärvi, T; Supanitsky, A D; Sutherland, M S; Swain, J; Szadkowski, Z; Takahashi, J; Tamashiro, A; Tamburro, A; Taşcău, O; Tcaciuc, R; Thomas, D; Ticona, R; Tiffenberg, J; Timmermans, C; Tkaczyk, W; Todero Peixoto, C J; Tomé, B; Tonachini, A; Torres, I; Torresi, D; Travnicek, P; Tripathi, A; Tristram, G; Tscherniakhovski, D; Tueros, M; Tunnicliffe, V; Ulrich, R; Unger, M; Urban, M; Valdés Galicia, J F; Valiño, I; Valore, L; van den Berg, A M; van Elewyck, V; Vázquez, R A; Veberic, D; Veiga, A; Velarde, A; Venters, T; Verzi, V; Videla, M; Villaseñor, L; Vorobiov, S; Voyvodic, L; Wahlberg, H; Wainberg, O; Walker, P; Warner, D; Watson, A A; Westerhoff, S; Wieczorek, G; Wiencke, L; Wilczyńska, B; Wilczyński, H; Wileman, C; Winnick, M G; Wu, H; Wundheiler, B; Yamamoto, T; Younk, P; Zas, E; Zavrtanik, D; Zavrtanik, M; Zech, A; Zepeda, A; Ziolkowski, M

2008-05-30

The surface detector array of the Pierre Auger Observatory is sensitive to Earth-skimming tau neutrinos that interact in Earth's crust. Tau leptons from nu(tau) charged-current interactions can emerge and decay in the atmosphere to produce a nearly horizontal shower with a significant electromagnetic component. The data collected between 1 January 2004 and 31 August 2007 are used to place an upper limit on the diffuse flux of nu(tau) at EeV energies. Assuming an E(nu)(-2) differential energy spectrum the limit set at 90% C.L. is E(nu)(2)dN(nu)(tau)/dE(nu)<1.3 x 10(-7) GeV cm(-2) s(-1) sr(-1) in the energy range 2 x 10(17) eV< E(nu)< 2 x 10(19) eV.

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

Science.gov (United States)

Roques, L; Walker, E; Franck, P; Soubeyrand, S; Klein, E K

2016-08-01

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems

International Nuclear Information System (INIS)

Martinez, E.; Marian, J.; Kalos, M.H.; Perlado, J.M.

2008-01-01

A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with interaction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. Our method is a controlled approximation in the sense that the error incurred by ignoring boundary conflicts can be quantified intrinsically, during the course of a simulation, and decreased arbitrarily (controlled) by modifying a few problem-dependent simulation parameters

An axisymmetric non-hydrostatic model for double-diffusive water systems

Science.gov (United States)

Hilgersom, Koen; Zijlema, Marcel; van de Giesen, Nick

2018-02-01

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems

International Nuclear Information System (INIS)

Owolabi, Kolade M.

2016-01-01

The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.

2014-01-01

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

Science.gov (United States)

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

Diffusion of interstitials in metallic systems, illustration of a complex study case: aluminum

Science.gov (United States)

David, Matthieu; Connétable, Damien

2017-11-01

While diffusion mechanisms of interstitial elements in fcc systems are generally well-known, especially in the case of H atoms, we show in this work that even in the case of a simple metallic system (aluminum), the diffusion of interstitials exhibits a wide variety of paths and mechanisms that depend on the specie. We used an approach based on first-principles calculations associated with kinetic Monte-Carlo simulations and a multi-state diffusion formalism to compute the diffusion coefficients of five interstitial elements: hydrogen, boron, carbon, nitrogen and oxygen. For instance, at the atomic scale, whilst we find that C atoms prefer to be located in octahedral sites (labeled o) rather than in tetrahedral positions (labeled t), we find one additional stable position in the lattice (M). The diffusion through these three stable positions are thus studied in detail. In the case of B atoms, for which the tetrahedral site is found unstable, the diffusion path is between o-o sites. Similarly, in the case of oxygen, t positions are found to be the only stable positions (o are unstable) and the path of migration, along t-t direction, is found through a twice degenerated asymmetric transition state. In the case of H and N atoms for which t and o sites are stable, we explain why the only path is along the t-o direction. Finally, we discuss explicit formulas to compute coefficients of diffusion of interstitials in fcc structures.

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

Science.gov (United States)

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

2014-04-11

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

Diffusion Limitation and Hyperoxic Enhancement of Oxygen Consumption in Zooxanthellate Sea Anemones, Zoanthids, and Corals.

Science.gov (United States)

Shick, J M

1990-08-01

Depending on their size and morphology, anthozoan polyps and colonies may be diffusion-limited in their oxygen consumption, even under well-stirred, air-saturated conditions. This is indicated by an enhancement of oxygen consumption under steady-state hyperoxic conditions that simulate the levels of O2 produced photosynthetically by zooxanthellae in the hosts' tissues. Such hyperoxia in the tissues of zooxanthellate species negates the effect of the diffusive boundary layer, and increases the rate of oxygen consumption; thus, in many cases, the rate of respiration measured under normoxia in the dark may not be representative of the rate during the day when the zooxanthellae are photosynthesizing and when the supply of oxygen for respiration is in the tissues themselves, not from the environment. These results have implications in respirometric methodology and in calculating the rate of gross photosynthesis in energetic studies. The activity of cytochrome c oxidase is higher in aposymbiotic than in zooxanthellate specimens of the sea anemone Aiptasia pulchella, and this may indicate a compensation for the relative hypoxia in the tissues of the former, enhancing the delivery of oxygen to the mitochondria from the environment.

The diffusion bonding of advanced material

International Nuclear Information System (INIS)

Khan, T.I.

2001-01-01

As a joining process diffusion bonding has been used since early periods, and artifacts have been found which date back to 3000 years. However, over the last 20 years this joining process has been rediscovered and research has been carried out to understand the mechanisms of the process, and the application of the technique to advanced materials. This paper will review some of the reasons to why diffusion bonding may be preferred over other more conventional welding processes to join advanced alloy systems. It also describes in brief the different types of bonding processes, namely, solid-state and liquid phase bonding techniques. The paper demonstrates the application of diffusion bonding processes to join a range of dissimilar materials for instance: oxide dispersion strengthened superalloys, titanium to duplex stainless steels and engineering ceramics such as Si/sub 3/N/sub 4/ to metal alloys. The research work highlights the success and limitations of the diffusion bonding process and is based on the experience of the author and his colleagues. (author)

A discrete model to study reaction-diffusion-mechanics systems.

Science.gov (United States)

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A discrete model to study reaction-diffusion-mechanics systems.

Directory of Open Access Journals (Sweden)

Louis D Weise

Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

NARCIS (Netherlands)

Muntean, A.

2009-01-01

Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while

Diffusion of Cardiopulmonary Resuscitation Training to Chinese Immigrants with Limited English Proficiency

Directory of Open Access Journals (Sweden)

Mei Po Yip

2011-01-01

Full Text Available Cardiopulmonary resuscitation (CPR is an effective intervention for prehospital cardiac arrest. Despite all available training opportunities for CPR, disparities exist in participation in CPR training, CPR knowledge, and receipt of bystander CPR for certain ethnic groups. We conducted five focus groups with Chinese immigrants who self-reported limited English proficiency (LEP. A bilingual facilitator conducted all the sessions. All discussions were taped, recorded, translated, and transcribed. Transcripts were analyzed by content analysis guided by the theory of diffusion. The majority of participants did not know of CPR and did not know where to get trained. Complexity of CPR procedure, advantages of calling 9-1-1, lack of confidence, and possible liability discourage LEP individuals to learn CPR. LEP individuals welcome simplified Hands-Only CPR and are willing to perform CPR with instruction from 9-1-1 operators. Expanding the current training to include Hands-Only CPR and dispatcher-assisted CPR may motivate Chinese LEP individuals to get trained for CPR.

Frozen history : limitations and possibilities of quantitative diffusion studies

NARCIS (Netherlands)

Mom, G.P.A.; Albert de la Bruhèze, A.A.; Oldenziel, R.

2009-01-01

In this contribution I have tried to show how quantitative methods can generate new questions and thus support historical research. It can be concluded that re ducing historical complexity through forcing reality into the shape of a diffusion curve does not seem to be the preferable strategy for

A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization

NARCIS (Netherlands)

Krehel, O.; Aiki, T.; Muntean, A.

2014-01-01

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale

Anomalous dimension in a two-species reaction-diffusion system

Science.gov (United States)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Real-time reactor coolant system pressure/temperature limit system

International Nuclear Information System (INIS)

Newton, D.G.; Schemmel, R.R.; Van Scooter, W.E. Jr.

1991-01-01

This patent describes an system, used in controlling the operating of a nuclear reactor coolant system, which automatically calculates and displays allowable reactor coolant system pressure/temperature limits within the nuclear reactor coolant system based upon real-time inputs. It comprises: means for producing signals representative of real-time operating parameters of the nuclear reactor cooling system; means for developing pressure and temperature limits relating the real-time operating parameters of the nuclear reactor coolant system, for normal and emergency operation thereof; means for processing the signals representative of real-time operating parameters of the nuclear reactor coolant system to perform calculations of a best estimate of signals, check manual inputs against permissible valves and test data acquisition hardware for validity and over/under range; and means for comparing the representative signals with limits for the real-time operating parameters to produce a signal for a real-time display of the pressure and temperature limits and of the real-time operating parameters use an operator in controlling the operation of the nuclear reactor coolant system

Quantifying brain microstructure with diffusion MRI

DEFF Research Database (Denmark)

Novikov, Dmitry S.; Jespersen, Sune N.; Kiselev, Valerij G.

2016-01-01

the potential to quantify the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, the degree of neuronal beading, and compartment sizes. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple non......-exchanging anisotropic Gaussian components. Here the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook...... on the future research directions which can open exciting possibilities for developing markers of pathology and development based on methods of studying mesoscopic transport in disordered systems....

Anomalous behavior of the diffusion coefficient in thin active films

International Nuclear Information System (INIS)

Basu, Abhik; Joanny, Jean-Francois; Prost, Jacques; Jülicher, Frank

2012-01-01

Inspired by recent experiments in cell biology, we elucidate the visco-elastic properties of an active gel by studying the dynamics of a small tracer particle inside it. In a stochastic hydrodynamic approach for an active gel of finite thickness L, we calculate the mean square displacement of a particle. These particle displacements are governed by fluctuations in the velocity field. We characterize the short-time behavior when the gel is a solid as well as the limit of long times when the gel becomes a fluid and the particle shows simple diffusion. Active stresses together with local polar order give rise to velocity fluctuations that lead to characteristic behaviors of the diffusion coefficient that differ fundamentally from those found in a passive system: the diffusion coefficient can depend on system size and diverges as L approaches an instability threshold. Furthermore, the diffusion coefficient becomes independent of the particle size in this case. (paper)

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

Science.gov (United States)

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

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

DIFMIG - A computer program for calculation of diffusive migration through multi-barrier systems

International Nuclear Information System (INIS)

Bo, P.; Carlsen, L.

1981-11-01

The FORTRAN IV program DIFMIG calculates one-dimensionally (i.e. column) the diffusive migration of single substances through arbitrary multibarrier systems. Time dependent changes in concentration other than dispersion/diffusion (e.g. slow dissolution of a compound from a repository, radioactive decay, and/or build up of daughter products), and possible time dependent variations in the effective dispersion into account. The diffusion equation is solved by a finite difference implicite method, the resulting trigonal matrix equation being solved by standard methods. (author)

Diffusion couple studies of the Ni-Bi-Sn system

Directory of Open Access Journals (Sweden)

Vassilev G.

2012-01-01

Full Text Available Investigations of Ni-Bi-Sn system were performed in order to inquire the phase diagram and to assess some diffusion kinetic parameters. For this purpose diffusion couples consisting of solid nickel (preliminary electroplated with tin and liquid Bi-Sn phase were annealed at 370 °C. Three compositions (0.8, 0.6 and 0.4 mole fractions Sn of the Bi-Sn melts were chosen. Annealing times from 24 to 216 h were applied. The phase and chemical compositions of the contact zone were determined by means of electron scanning microscope. It was confirmed that the diffusion layers consist mainly of Ni3Sn4 but other intermetallic phases grow as well. For the first time metastable Ni-Sn phases as NiSn and NiSn8 (NiSn9 were observed in metallurgical alloys (i.e. not in electroplated samples. The existence of a ternary compound previously reported in the literature was confirmed. More than one ternary Ni-Bi-Sn compounds might possibly be admitted. A growth coefficient of (2.29 ± 0.02 x 10-15 m2 s-1 was obtained. It was found that the apparent activation energy for diffusion layers growth (18 ± 8 kJ mol-1 is inferior to that one assessed at growth from solid state Bi-Sn mixtures (88 ± 12 kJ mol-1.

Study of the uranium-zirconium diffusion; Etude de la diffusion uranium-zirconium

Energy Technology Data Exchange (ETDEWEB)

Adda, Y; Mairy, C; Bouchet, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1957-07-01

The intermetallic diffusion of uranium fuel and zirconium used as cladding is studied. Intermetallic diffusion can occur during the cladding of uranium rods and uranium can penetrate the zirconium cladding. Different parameters are involved in this mechanism as structure and mechanical properties of the diffusion area as well as presence of impurities in the metal. The uses of different analysis techniques (micrography, Castaing electronic microprobe, microhardness and autoradiography) have permitted to determine with great accuracy the diffusion coefficient in gamma phase (body centered cubic system) and the results have given important information on the intermetallic diffusion mechanisms. The existence of the Kirkendall effect in the U-Zr diffusion is also an argument in favor of the generality of the diffusion mechanism by vacancies in body centered cubic system. (M.P.)

Diffusion paths in Ti-Zr-Nb system

International Nuclear Information System (INIS)

Omasheva, G.Sh.; Gryzunov, V.I.; Sokolovskaya, E.M.

1992-01-01

Mutual diffusion at the temperature of 1273 K was studied. Diffusional paths were plotted and matrix of mutual diffusion coefficients D ij k for 26 points of concentrational triangle was calculated. It is ascertained that all diffusion coefficients are concentration-depending values, they wary by three orders with the change in the composition, corresponding to titanium angle, to niobium one

Solar Distillation System Based on Multiple-Effect Diffusion Type Still

KAUST Repository

Huang, Bin-Juine; Chong, Tze-Ling; Chang, Hsien-Shun; Wu, Po-Hsien; Kao, Yeong-Chuan

2014-01-01

The present study intends to develop a high-performance solar-assisted desalination system (SADS) using multi-effect diffusion type still (MEDS) and the vacuum tube solar collector (VTSC). A MEDS prototype was designed and built. The measured result

Emergent structures in reaction-advection-diffusion systems on a sphere

Science.gov (United States)

Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.

2018-04-01

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

Diffusion of photovoltaic systems for rural electrification in Thailand

Energy Technology Data Exchange (ETDEWEB)

Sriwannawit, Pranpreya; Laestadius, Staffan [Department of Industrial Economics and Management, Royal Institute of Technology (KTH), Lindstedtsvagen 30, Stockholm 10044 (Sweden)

2013-07-01

This paper studies a pilot project in which photovoltaic systems were installed in thirty-six places in the remote areas of Thailand with no access to electricity. One sub-project out of thirty-six was chosen for in-depth investigation. We discuss the appropriateness of solar energy for Thailand context. The diffusion process of PV systems is analyzed on four elements: innovation, communication channel, time and social system. This project is an extreme case as the PV systems and services were provided for free of charge. Even so, there are still some challenges to get acceptance for this sustainable form of energy.

Estimating the Diffusion Coefficients of Sugars Using Diffusion Experiments in Agar-Gel and Computer Simulations.

Science.gov (United States)

Miyamoto, Shuichi; Atsuyama, Kenji; Ekino, Keisuke; Shin, Takashi

2018-01-01

The isolation of useful microbes is one of the traditional approaches for the lead generation in drug discovery. As an effective technique for microbe isolation, we recently developed a multidimensional diffusion-based gradient culture system of microbes. In order to enhance the utility of the system, it is favorable to have diffusion coefficients of nutrients such as sugars in the culture medium beforehand. We have, therefore, built a simple and convenient experimental system that uses agar-gel to observe diffusion. Next, we performed computer simulations-based on random-walk concepts-of the experimental diffusion system and derived correlation formulas that relate observable diffusion data to diffusion coefficients. Finally, we applied these correlation formulas to our experimentally-determined diffusion data to estimate the diffusion coefficients of sugars. Our values for these coefficients agree reasonably well with values published in the literature. The effectiveness of our simple technique, which has elucidated the diffusion coefficients of some molecules which are rarely reported (e.g., galactose, trehalose, and glycerol) is demonstrated by the strong correspondence between the literature values and those obtained in our experiments.

Modeling of the interplay between single-file diffusion and conversion reaction in mesoporous systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Jing [Iowa State Univ., Ames, IA (United States)

2013-01-11

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.

Diffusion and Kirkendall effect in plutonium-zirconium system; Diffusion et effet Kirkendall dans le systeme plutonium-zirconium

Energy Technology Data Exchange (ETDEWEB)

Remy, C [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-10-01

Results are reported for the chemical diffusion in {epsilon}{beta} phase (bcc) over the range 10 - 70 atomic per cent plutonium. Concentration-penetration curves, obtained by using electron microprobe, have been analysed by Hall and Matano methods. Chemical diffusion coefficients, measured from 650 to 900 deg. C., increase with plutonium concentration and follow the Arrhenius law. Activation energies range from 18000 up to 44000 cal/mole for plutonium concentrations from 60 to 20 atomic per cent plutonium. Kirkendall effect has been observed by the shift of inert markers located originally at the Zr-PuZr interface. Analysis of intrinsic diffusion coefficients variation, flux of the two species and lattice velocity has been carried out by the incremental couples technique by using Darken and Heumann equations. It was found that D{sub Pu} > D{sub Zr}; the ratio D{sub Pu}/D{sub Zr} increases from 1 to 6 over the range 15 - 60 atomic per cent Pu. Activation energies for intrinsic diffusion coefficients vary between 25 and 50 Kcal/mole. (author) [French] Nous donnons des resultats sur la diffusion chimique en phase {epsilon}{beta} (cc) de 10 a 70 pour cent atomique en plutonium. Les courbes concentration-penetration, obtenues par microanalyse X ont ete depouillees par les methodes de HALL et de MATANO. Les coefficients de diffusion chimique mesures de 650 deg. C a 900 deg. C., augmentent avec la concentration en plutonium et suivent la loi d'ARRHENIUS. Les energies d'activation passent de 18000 a 44000 calories par mole pour des concentrations de 60 a 20 pour cent atomique en plutonium. L'existence d'un effet KIRKENDALL a ete mis en evidence par le deplacement de fils inertes places initialement dans le plan de soudure. L'analyse de la variation des coefficients de diffusion intrinseques, des flux des deux especes et de la vitesse du reseau a ete faite par la technique des couples incrementaux en utilisant les equations de DARKEN et de HEUMANN. On trouve D{sub Pu} > D

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

Science.gov (United States)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

International Nuclear Information System (INIS)

Mieussens, Luc

2013-01-01

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme

Solar systems diffusion in local markets

International Nuclear Information System (INIS)

Sidiras, D.K.; Koukios, E.G.

2004-01-01

This paper reports on a study of the driving forces and barriers of the spectacular diffusion of solar energy use for domestic hot-water production in Greece. Through the various kinds of questionnaires used in this work, the main diffusion actors have been requested to grade the various diffusion factors identified by desk and preliminary field research. Households identify a number of economic (available family income), technical (new technologies), political (new incentives), and socio-cultural (sensitivity in energy matters) factors as dominant. According to the solar industry, advertising, distribution and quality control standards have to be added to the list of critical factors. Technical experts contribute with identifying, besides R and D, public awareness on energy matters. Solar collector diffusion, despite the fact that it has followed a market-driven mechanism, was revealed to be a multi-actor, multi-dimensional and multi-parametric phenomenon. Presently, the phenomenon is constrained by the available family income, with technology-related factors, i.e., research, and standardization quality control, playing increasing roles

Diffuse ceiling ventilation

DEFF Research Database (Denmark)

Zhang, Chen

Diffuse ceiling ventilation is an innovative ventilation concept where the suspended ceiling serves as air diffuser to supply fresh air into the room. Compared with conventional ventilation systems, diffuse ceiling ventilation can significantly reduce or even eliminate draught risk due to the low...

From State Dependent Diffusion to Constant Diffusion in Stochastic Differential Equations by the Lamperti Transform

DEFF Research Database (Denmark)

Møller, Jan Kloppenborg; Madsen, Henrik

the Lamperti transform. This note gives an example driven introduction to the Lamperti transform. The general applicability of the Lamperti transform is limited to univariate diffusion processes, but for a restricted class of multivariate diffusion processes Lamperti type transformations are available...

Information filtering in sparse online systems: recommendation via semi-local diffusion.

Science.gov (United States)

Zeng, Wei; Zeng, An; Shang, Ming-Sheng; Zhang, Yi-Cheng

2013-01-01

With the rapid growth of the Internet and overwhelming amount of information and choices that people are confronted with, recommender systems have been developed to effectively support users' decision-making process in the online systems. However, many recommendation algorithms suffer from the data sparsity problem, i.e. the user-object bipartite networks are so sparse that algorithms cannot accurately recommend objects for users. This data sparsity problem makes many well-known recommendation algorithms perform poorly. To solve the problem, we propose a recommendation algorithm based on the semi-local diffusion process on the user-object bipartite network. The simulation results on two sparse datasets, Amazon and Bookcross, show that our method significantly outperforms the state-of-the-art methods especially for those small-degree users. Two personalized semi-local diffusion methods are proposed which further improve the recommendation accuracy. Finally, our work indicates that sparse online systems are essentially different from the dense online systems, so it is necessary to reexamine former algorithms and conclusions based on dense data in sparse systems.

Real-space renormalization group approach to driven diffusive systems

Energy Technology Data Exchange (ETDEWEB)

Hanney, T [SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ (United Kingdom); Stinchcombe, R B [Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP (United Kingdom)

2006-11-24

We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.

Real-space renormalization group approach to driven diffusive systems

International Nuclear Information System (INIS)

Hanney, T; Stinchcombe, R B

2006-01-01

We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

Science.gov (United States)

Hibi, Yoshihiko; Kashihara, Ayumi

2018-03-01

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent

Passive Rocket Diffuser Theory: A Re-Examination of Minimum Second Throat Size

Science.gov (United States)

Jones, Daniel R.

2016-01-01

Second-throat diffusers serve to isolate rocket engines from the effects of ambient back pressure during testing without using active control systems. Among the most critical design parameters is the relative area of the diffuser throat to that of the nozzle throat. A smaller second throat is generally desirable because it decreases the stagnation-to-ambient pressure ratio the diffuser requires for nominal operation. There is a limit, however. Below a certain size, the second throat can cause pressure buildup within the diffuser and prevent it from reaching the start condition that protects the nozzle from side-load damage. This paper presents a method for improved estimation of the minimum second throat area which enables diffuser start. The new 3-zone model uses traditional quasi-one-dimensional compressible flow theory to approximate the structure of two distinct diffuser flow fields observed in Computational Fluid Dynamics (CFD) simulations and combines them to provide a less-conservative estimate of the second throat size limit. It is unique among second throat sizing methods in that it accounts for all major conical nozzle and second throat diffuser design parameters within its limits of application. The performance of the 3-zone method is compared to the historical normal shock and force balance methods, and verified against a large number of CFD simulations at specific heat ratios of 1.4 and 1.25. Validation is left as future work, and the model is currently intended to function only as a first-order design tool.

Hydrodynamic limit of a nongradient interacting particle process

International Nuclear Information System (INIS)

Wick, W.D.

1989-01-01

A simple example of a nongradient stochastic interacting particle system is analyzed. In this model, symmetric simple exclusion in one dimension in a periodic environment, the dynamical term in the Green-Kubo formula contributes to the bulk diffusion constant. The law of large numbers for the density field and the central limit theorem for the density fluctuation field are proven, and the Green-Kubo expression for the diffusion constant is computed exactly. The hydrodynamic equation for the model turns out to be linear

Diffuse alveolar hemorrhage in a young woman with systemic lupus ...

African Journals Online (AJOL)

Diffuse Alveolar Hemorrhage (DAH) is rarely reported complication of Systemic Lupus Erythematosus (SLE). A young woman diagnosed SLE, with a previously normal plain chest radiograph, developed acute onset cough, dyspnoea and hemoptysis. The repeat urgent chest radiograph revealed alveolar opacities. The triad ...

Effect of macromolecular crowding on the rate of diffusion-limited ...

Indian Academy of Sciences (India)

Enzyme kinetics; Monte Carlo; percolation; random walk; obstacle. .... enzyme E, P remains on the same site but S is converted to P with unit probability. ..... is then qualitatively understood with the help of diffusion and percolation theory.

Diffuse layer effects on the current in galvanic cells containing supporting electrolyte

Energy Technology Data Exchange (ETDEWEB)

Soestbergen, M. van, E-mail: m.vansoestbergen@tudelft.n [Materials Innovation Institute, Mekelweg 2, 2628 CD Delft (Netherlands); Department of Precision and Microsystems Engineering, University of Technology Delft, Mekelweg 2, 2628 CD Delft (Netherlands)

2010-02-01

We study the effect of an inert supporting electrolyte on the steady-state ionic current through galvanic cells by solving the full Poisson-Nernst-Planck transport equation coupled to the generalized Frumkin-Butler-Volmer boundary equation for the electrochemical charge transfer at the electrodes. Consequently, the model presented here allows for non-zero space charge densities locally at the electrodes, thus extending the frequently used models based on the local electroneutrality condition by including diffuse layer (DL) effects. This extension is necessary since the DLs determine the ion concentration and electrical field at the reaction planes, which uniquely determine the charge transfer at the electrodes. In this work we present numerical results for systems which contain added inert supporting electrolyte using finite element discretization and compare those with semi-analytical results obtained using singular perturbation theory (limit of negligibly thin DLs). In case of negligibly thin DLs the presence of supporting electrolyte will introduce a limiting current below the classical diffusion-limiting current. Just as for systems without supporting electrolyte, the supporting electrolyte induced limiting current formally does not occur for systems having non-negligibly thin double DLs. For thin, however still finite, double layers this limit can still be seen as a steepening of the polarization curve for current vs. voltage.

Diffuse layer effects on the current in galvanic cells containing supporting electrolyte

International Nuclear Information System (INIS)

Soestbergen, M. van

2010-01-01

We study the effect of an inert supporting electrolyte on the steady-state ionic current through galvanic cells by solving the full Poisson-Nernst-Planck transport equation coupled to the generalized Frumkin-Butler-Volmer boundary equation for the electrochemical charge transfer at the electrodes. Consequently, the model presented here allows for non-zero space charge densities locally at the electrodes, thus extending the frequently used models based on the local electroneutrality condition by including diffuse layer (DL) effects. This extension is necessary since the DLs determine the ion concentration and electrical field at the reaction planes, which uniquely determine the charge transfer at the electrodes. In this work we present numerical results for systems which contain added inert supporting electrolyte using finite element discretization and compare those with semi-analytical results obtained using singular perturbation theory (limit of negligibly thin DLs). In case of negligibly thin DLs the presence of supporting electrolyte will introduce a limiting current below the classical diffusion-limiting current. Just as for systems without supporting electrolyte, the supporting electrolyte induced limiting current formally does not occur for systems having non-negligibly thin double DLs. For thin, however still finite, double layers this limit can still be seen as a steepening of the polarization curve for current vs. voltage.

Applications of a general random-walk theory for confined diffusion.

Science.gov (United States)

Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi

2011-01-01

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

Pattern formation in reaction diffusion systems with finite geometry

International Nuclear Information System (INIS)

Borzi, C.; Wio, H.

1990-04-01

We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs

Externally controlled anisotropy in pattern-forming reaction-diffusion systems.

Science.gov (United States)

Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P

2015-06-01

The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.

Stimulating the diffusion of photovoltaic systems: A behavioural perspective

International Nuclear Information System (INIS)

Jager, Wander

2006-01-01

This paper first discusses consumer motives for adopting photovoltaic systems (PV systems) from a behavioural-theoretical perspective. Different motives are discussed within a framework of underlying needs and the time sensitivity of various outcomes. Next, empirical data are presented concerning the motives of buyers of PV systems after a promotional and support campaign in the city of Groningen (the Netherlands). Financial support and general problem awareness are found to be critical motives, but the (strong) positive effects of information meetings, technical support meetings and social networks are also identified. Conclusions focus on the critical motives for adopting a PV system, and suggestions are presented concerning policy measures to stimulate the further diffusion of PV systems

A Diffusion Model for Two-sided Service Systems

Science.gov (United States)

Homma, Koichi; Yano, Koujin; Funabashi, Motohisa

A diffusion model is proposed for two-sided service systems. ‘Two-sided’ refers to the existence of an economic network effect between two different and interrelated groups, e.g., card holders and merchants in an electronic money service. The service benefit for a member of one side depends on the number and quality of the members on the other side. A mathematical model by J. H. Rohlfs explains the network (or bandwagon) effect of communications services. In Rohlfs' model, only the users' group exists and the model is one-sided. This paper extends Rohlfs' model to a two-sided model. We propose, first, a micro model that explains individual behavior in regard to service subscription of both sides and a computational method that drives the proposed model. Second, we develop macro models with two diffusion-rate variables by simplifying the micro model. As a case study, we apply the models to an electronic money service and discuss the simulation results and actual statistics.

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D; Keesman, K.J.; Zwart, Heiko J.

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space

Linear regressive model structures for estimation and prediction of compartmental diffusive systems

NARCIS (Netherlands)

Vries, D.; Keesman, K.J.; Zwart, H.

2006-01-01

Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

Science.gov (United States)

Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

2009-06-01

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

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

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

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction 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 of nonlinear conjugate gradient is studied together with 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 solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Solid state reaction studies in Fe3O4–TiO2 system by diffusion couple method

International Nuclear Information System (INIS)

Ren, Zhongshan; Hu, Xiaojun; Xue, Xiangxin; Chou, Kuochih

2013-01-01

Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe 3 O 4 –TiO 2 system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO 2 gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe 3 O 4 phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe 3 O 4 –TiO 2 system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol −1

Diffusion of innovative domestic heating systems and multi-storey wood-framed buildings in Sweden

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Krushna

2007-10-15

The diffusion of innovations that promote sustainable use of forest resources and energy efficiency is important for reducing greenhouse gas emission and dependency on oil. In this thesis the 'systems of innovation' (SI) approach is used to analyse the diffusion of multi-storey wood-framed buildings and wood pellet heating systems in Sweden. The diffusion of an innovative heating system (IHS) is influenced by the diffusion of other types of IHSs, making it complex to analyse the diffusion of all these systems simultaneously using the SI approach. Hence, an 'adopter-centric' approach was used, as homeowners make the decision to adopt an IHS, which affects the rate of adoption of that system. The SI analyses showed that several sources of path dependency, resulting from the establishment and growth of the concrete-based construction system over the past 100 years, hinder the expansion of a wood-based multi-storey construction system. However, development of the wood construction system was possible due to government policies and funding, the wood industry's interest in expanding the market for value-added wood products, and the involvement of the wood research community. The growth of the pellet market was supported by national energy policy, the abundance of raw material and broad dissemination of district heating systems. However, a lack of co-ordination between the pellet and equipment suppliers in the early phase of market development, high annual operating cost, lack of information, dissatisfaction among early adopters and technology lock-in contributed to its relatively slow growth. The adopter-centric approach included household questionnaire surveys: one covering the whole of Sweden in 2004 involving 1500 randomly selected homeowners with any type of heating system, and another in the city of Oestersund in 2005 of 700 homeowners who had resistance heaters. The same homeowners in Oestersund were re-surveyed in 2006 to analyse the

Fractional diffusion equations and anomalous diffusion

CERN Document Server

Evangelista, Luiz Roberto

2018-01-01

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

Investigating the Eddy Diffusivity Concept in the Coastal Ocean

Science.gov (United States)

Rypina, I.; Kirincich, A.; Lentz, S. J.; Sundermeyer, M. A.

2016-12-01

We test the validity, utility, and limitations of the lateral eddy diffusivity concept in a coastal environment through analyzing data from coupled drifter and dye releases within the footprint of a high-resolution (800 m) high-frequency radar south of Martha's Vineyard, Massachusetts. Specifically, we investigate how well a combination of radar-based velocities and drifter-derived diffusivities can reproduce observed dye spreading over an 8-h time interval. A drifter-based estimate of an anisotropic diffusivity tensor is used to parameterize small-scale motions that are unresolved and under-resolved by the radar system. This leads to a significant improvement in the ability of the radar to reproduce the observed dye spreading. Our drifter-derived diffusivity estimates are O(10 m2/s), are consistent with the diffusivity inferred from aerial images of the dye taken using the quadcopter-mounted digital camera during the dye release, and are roughly an order of magnitude larger than diffusivity estimates of Okubo (O(1 m2/s)) for similar spatial scales ( 1 km). Despite the fact that the drifter-based diffusivity approach was successful in improving the ability of the radar to reproduce the observed dye spreading, the dispersion of drifters was, for the most part, not consistent with the diffusive spreading regime.

Lung function study and diffusion capacity in anorexia nervosa.

Science.gov (United States)

Pieters, T; Boland, B; Beguin, C; Veriter, C; Stanescu, D; Frans, A; Lambert, M

2000-08-01

In humans, malnutrition alters the respiratory system in different ways. It impairs the ventilatory drive, decreases respiratory muscle strength and reduces immune competence. In addition, typical emphysema-like changes were demonstrated in starved animals. The presence of emphysema has never been demonstrated in starved humans. Our objective was to investigate whether pulmonary emphysema occurs in anorexia nervosa by means of a pulmonary function study. We examined 24 women aged between 14 and 38 years (nine smokers). We studied the lung function including lung volumes, ventilatory capacity, maximal respiratory pressures and transfer factor, as well as PaO2. All respiratory tests were within normal limits with the exception of decreased maximal inspiratory (59% of predicted values) and expiratory pressures (35%), and increased residual volume (162%). Diffusion capacity (98.1 +/- 16.2%) and transfer coefficient (98.4 +/- 16.2%) were also normal. The diffusion coefficient was lower in current smokers than in those who had never smoked (P anorexia nervosa, pulmonary function tests are within normal limits with the exception of maximal pressures and residual volume. Diffusion capacity is not decreased. The present results within the limitations of the used method are not compatible with the hypothesis of starvation-induced pulmonary emphysema.

Eddy diffusion coefficients and their upper limits based on application of the similarity theory

Directory of Open Access Journals (Sweden)

M. N. Vlasov

2015-07-01

Full Text Available The equation for the diffusion velocity in the mesosphere and the lower thermosphere (MLT includes the terms for molecular and eddy diffusion. These terms are very similar. For the first time, we show that, by using the similarity theory, the same formula can be obtained for the eddy diffusion coefficient as the commonly used formula derived by Weinstock (1981. The latter was obtained by taking, as a basis, the integral function for diffusion derived by Taylor (1921 and the three-dimensional Kolmogorov kinetic energy spectrum. The exact identity of both formulas means that the eddy diffusion and heat transport coefficients used in the equations, both for diffusion and thermal conductivity, must meet a criterion that restricts the outer eddy scale to being much less than the scale height of the atmosphere. This requirement is the same as the requirement that the free path of molecules must be much smaller than the scale height of the atmosphere. A further result of this criterion is that the eddy diffusion coefficients Ked, inferred from measurements of energy dissipation rates, cannot exceed the maximum value of 3.2 × 106 cm2 s−1 for the maximum value of the energy dissipation rate of 2 W kg−1 measured in the mesosphere and the lower thermosphere (MLT. This means that eddy diffusion coefficients larger than the maximum value correspond to eddies with outer scales so large that it is impossible to use these coefficients in eddy diffusion and eddy heat transport equations. The application of this criterion to the different experimental data shows that some reported eddy diffusion coefficients do not meet this criterion. For example, the large values of these coefficients (1 × 107 cm2 s−1 estimated in the Turbulent Oxygen Mixing Experiment (TOMEX do not correspond to this criterion. The Ked values inferred at high latitudes by Lübken (1997 meet this criterion for summer and winter polar data, but the Ked values for summer at low latitudes

Portable, Fiber-Based, Diffuse Reflection Spectroscopy (DRS) Systems for Estimating Tissue Optical Properties.

Science.gov (United States)

Vishwanath, Karthik; Chang, Kevin; Klein, Daniel; Deng, Yu Feng; Chang, Vivide; Phelps, Janelle E; Ramanujam, Nimmi

2011-02-01

Steady-state diffuse reflection spectroscopy is a well-studied optical technique that can provide a noninvasive and quantitative method for characterizing the absorption and scattering properties of biological tissues. Here, we compare three fiber-based diffuse reflection spectroscopy systems that were assembled to create a light-weight, portable, and robust optical spectrometer that could be easily translated for repeated and reliable use in mobile settings. The three systems were built using a broadband light source and a compact, commercially available spectrograph. We tested two different light sources and two spectrographs (manufactured by two different vendors). The assembled systems were characterized by their signal-to-noise ratios, the source-intensity drifts, and detector linearity. We quantified the performance of these instruments in extracting optical properties from diffuse reflectance spectra in tissue-mimicking liquid phantoms with well-controlled optical absorption and scattering coefficients. We show that all assembled systems were able to extract the optical absorption and scattering properties with errors less than 10%, while providing greater than ten-fold decrease in footprint and cost (relative to a previously well-characterized and widely used commercial system). Finally, we demonstrate the use of these small systems to measure optical biomarkers in vivo in a small-animal model cancer therapy study. We show that optical measurements from the simple portable system provide estimates of tumor oxygen saturation similar to those detected using the commercial system in murine tumor models of head and neck cancer.

Characterization of adsorption uptake curves for both intraparticle diffusion and liquid film mass transfer controlling systems

International Nuclear Information System (INIS)

Sonetaka, Noriyoshi; Fan, Huan-Jung; Kobayashi, Seiji; Su, Yang-Chih; Furuya, Eiji

2009-01-01

In general, the adsorption uptake curve (AUC) can be easily determined in either intraparticle diffusion or liquid film mass transfer dominating systems. However, for both intraparticle diffusion and liquid film mass transfer controlling systems, the characterization of AUC is much more complicated, for example, when relatively small adsorbent particles are employed. In addition, there is no analytical solution available for both intraparticle diffusion and liquid film mass transfer controlling systems. Therefore, this paper is trying to characterize AUC for both intraparticle diffusion and liquid film mass transfer controlling adsorption systems using the shallow bed reactor technique. Typical parameters influencing AUC include liquid film mass transfer coefficient (k F ), effective intraparticle diffusivity (D S ), influent concentration (c 0 ) and equilibrium parameters (such as Freundlich isotherm constants k and 1/n). These parameters were investigated in this research and the simulated results indicated that the ratio of k F /D S and Freundlich constant 1/n had impact on AUC. Biot number (Bi) was used to replace the ratio of k F /D S in this study. Bi represents the ratio of the rate of transport across the liquid layer to the rate of intraparticle diffusion. Furthermore, Bi is much more significant than that of 1/n for AUC. Therefore, AUC can be characterized by Bi. In addition, the obtained Bi could be used to determine D S and k F simultaneously. Both parameters (D S and k F ) are important for designing and operating fixed bed reactors.

Diffusion of Wilson loops

International Nuclear Information System (INIS)

Brzoska, A.M.; Lenz, F.; Thies, M.; Negele, J.W.

2005-01-01

A phenomenological analysis of the distribution of Wilson loops in SU(2) Yang-Mills theory is presented in which Wilson loop distributions are described as the result of a diffusion process on the group manifold. It is shown that, in the absence of forces, diffusion implies Casimir scaling and, conversely, exact Casimir scaling implies free diffusion. Screening processes occur if diffusion takes place in a potential. The crucial distinction between screening of fundamental and adjoint loops is formulated as a symmetry property related to the center symmetry of the underlying gauge theory. The results are expressed in terms of an effective Wilson loop action and compared with various limits of SU(2) Yang-Mills theory

Numerical Analysis of Characteristics of Cellular Counterflow Diffusion Flames near Radiative Extinction Limit

Energy Technology Data Exchange (ETDEWEB)

Lee, Su Ryong [Seoul National University of Technology, Seoul (Korea, Republic of)

2014-06-15

Nonlinear characteristics of cellular counterflow diffusion flame near the radiative extinction limit at large Damköhler number are numerically investigated. Lewis number is assumed to be 0.5 and flame evolution is calculated by imposing an infinitesimal disturbance to a one-dimensional(1-D) steady state flame. The early stage of nonlinear development is very similar to that predicted in a linear stability analysis. The disturbance with the wavenumber of the fastest growing mode emerges and grows gradually. Eventual, an alternating pattern of reacting and quenching stripes is developed. The cellular flame temperature is higher than that of 1-D flame because of the gain of the total enthalpy. As the Damköhler number is further increased, the shape of the cell becomes circular to increase the surface area per unit reacting volume. The cellular flames do not extinguish but survive even above the 1-D steady state extinction condition.

Diffusion and Perfusion MR Imaging in Acute Stroke: Clinical Utility and Potential Limitations for Treatment Selection

DEFF Research Database (Denmark)

Bateman, Mathew; Slater, Lee-Anne; Leslie-Mazwi, Thabele M

2017-01-01

Magnetic resonance (MR) diffusion-weighted imaging (DWI) and perfusion-weighted imaging (PWI) offer unique insight into acute ischemic stroke pathophysiology. These techniques may offer the ability to apply pathophysiology to accurately individualize acute stroke reperfusion treatment, including ...... to be investigated in ongoing randomized controlled trials, and continued research into these techniques will help achieve the goal of tissue-based decision making and individualized acute stroke treatment....... extending the opportunity of reperfusion treatment to well beyond the current time-based treatment windows. This review examines the use of DWI and PWI in the major stroke trials, their current clinical utility, and potential limitations for reperfusion treatment selection. DWI and PWI continue...

Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

CERN Document Server

Ódor, G

2003-01-01

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.

Effect of Ion Streaming on Diffusion of Dust Grains in Dissipative System

Science.gov (United States)

Begum, M.; Das, N.

2018-01-01

The presence of strong electric fields in the sheath region of laboratory complex plasma induces an ion drift and perturbs the field around dust grains. The downstream focusing of ions leads to the formation of oscillatory kind of attractive wake potential which superimpose with the normal Debye-Hückel (DH) potential. The structural properties of complex plasma and diffusion coefficient of dust grains in the presence of such a wake potential have been investigated using Langevin dynamics simulation in the subsonic regime of ion flow. The study reveals that the diffusion of dust grains is strongly affected by the ion flow, so that the diffusion changes its character in the wake potential to the DH potential dominant regimes. The dependence of the diffusion coefficient on the parameters, such as the neutral pressure, dust grain size, ion flow velocity, and Coulomb coupling parameter, have been calculated for the subsonic regime by using the Green-Kubo expression, which is based on the integrated velocity autocorrelation function. It is found that the diffusion and the structural property of the system is intimately connected with the interaction potential and significantly get affected in the presence of ion flow in the subsonic regime.

Lacute evy diffusion and classes of universal parametric correlations

International Nuclear Information System (INIS)

Kusnezov, D.; Lewenkopf, C.H.

1996-01-01

A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be labeled by a parameter α element-of(0,2), in a manner analogous to Lacute evy diffusion. Universality is obtained after scaling by the (anomalous) diffusion constant D α (the usual scaling is divergent for α<2). For each α, correlation functions are universal, and distinct. The previous results in the literature correspond to the limiting case of superdiffusion, α=2. copyright 1996 The American Physical Society

The Trouble with Diffusion

Directory of Open Access Journals (Sweden)

R.T. DeHoff

2002-09-01

Full Text Available The phenomenological formalism, which yields Fick's Laws for diffusion in single phase multicomponent systems, is widely accepted as the basis for the mathematical description of diffusion. This paper focuses on problems associated with this formalism. This mode of description of the process is cumbersome, defining as it does matrices of interdiffusion coefficients (the central material properties that require a large experimental investment for their evaluation in three component systems, and, indeed cannot be evaluated for systems with more than three components. It is also argued that the physical meaning of the numerical values of these properties with respect to the atom motions in the system remains unknown. The attempt to understand the physical content of the diffusion coefficients in the phenomenological formalism has been the central fundamental problem in the theory of diffusion in crystalline alloys. The observation by Kirkendall that the crystal lattice moves during diffusion led Darken to develop the concept of intrinsic diffusion, i.e., atom motion relative to the crystal lattice. Darken and his successors sought to relate the diffusion coefficients computed for intrinsic fluxes to those obtained from the motion of radioactive tracers in chemically homogeneous samples which directly report the jump frequencies of the atoms as a function of composition and temperature. This theoretical connection between tracer, intrinsic and interdiffusion behavior would provide the basis for understanding the physical content of interdiffusion coefficients. Definitive tests of the resulting theoretical connection have been carried out for a number of binary systems for which all three kinds of observations are available. In a number of systems predictions of intrinsic coefficients from tracer data do not agree with measured values although predictions of interdiffusion coefficients appear to give reasonable agreement. Thus, the complete

Pulsed neutron method for diffusion, slowing down, and reactivity measurements

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1985-01-01

An outline is given on the principles of the pulsed neutron method for the determination of thermal neutron diffusion parameters, for slowing-down time measurements, and for reactivity determinations. The historical development is sketched from the breakthrough in the middle of the nineteen fifties and the usefulness and limitations of the method are discussed. The importance for the present understanding of neutron slowing-down, thermalization and diffusion are point out. Examples are given of its recent use for e.g. absorption cross section measurements and for the study of the properties of heterogeneous systems

Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source

Energy Technology Data Exchange (ETDEWEB)

Vanacore, G. M.; Zani, M.; Tagliaferri, A., E-mail: alberto.tagliaferri@polimi.it [CNISM-Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Nicotra, G. [IMM-CNR, Stradale Primosole 50, I-95121 Catania (Italy); Bollani, M. [CNR-IFN, LNESS, Via Anzani 42, I-22100 Como (Italy); Bonera, E.; Montalenti, F.; Picco, A.; Boioli, F. [Dipartimento di Scienza dei Materiali and L-NESS, Università Milano-Bicocca, via Cozzi 53, I-20125 Milano (Italy); Capellini, G. [Department of Sciences at the Università Roma Tre, Via Vasca Navale 79, 00146 Roma (Italy); Isella, G. [CNISM, LNESS, Dipartimento di Fisica, Politecnico di Milano (Polo di Como), Via Anzani 42, I-22100 Como (Italy); Osmond, J. [ICFO–The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, 3, E-08860 Castelldefels (Barcelona) (Spain)

2015-03-14

The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.

Distortion-free diffusion MRI using an MRI-guided Tri-Cobalt 60 radiotherapy system: Sequence verification and preliminary clinical experience.

Science.gov (United States)

Gao, Yu; Han, Fei; Zhou, Ziwu; Cao, Minsong; Kaprealian, Tania; Kamrava, Mitchell; Wang, Chenyang; Neylon, John; Low, Daniel A; Yang, Yingli; Hu, Peng

2017-10-01

Monitoring tumor response during the course of treatment and adaptively modifying treatment plan based on tumor biological feedback may represent a new paradigm for radiotherapy. Diffusion MRI has shown great promises in assessing and predicting tumor response to radiotherapy. However, the conventional diffusion-weighted single-shot echo-planar-imaging (DW-ssEPI) technique suffers from limited resolution, severe distortion, and possibly inaccurate ADC at low field strength. The purpose of this work was to develop a reliable, accurate and distortion-free diffusion MRI technique that is practicable for longitudinal tumor response evaluation and adaptive radiotherapy on a 0.35 T MRI-guided radiotherapy system. A diffusion-prepared turbo spin echo readout (DP-TSE) sequence was developed and compared with the conventional diffusion-weighted single-shot echo-planar-imaging sequence on a 0.35 T MRI-guided radiotherapy system (ViewRay). A spatial integrity phantom was used to quantitate and compare the geometric accuracy of the two diffusion sequences for three orthogonal orientations. The apparent diffusion coefficient (ADC) accuracy was evaluated on a diffusion phantom under both 0 °C and room temperature to cover a diffusivity range between 0.40 × 10 -3 and 2.10 × 10 -3 mm 2 /s. Ten room temperature measurements repeated on five different days were conducted to assess the ADC reproducibility of DP-TSE. Two glioblastoma (GBM) and six sarcoma patients were included to examine the in vivo feasibility. The target registration error (TRE) was calculated to quantitate the geometric accuracy where structural CT or MR images were co-registered to the diffusion images as references. ADC maps from DP-TSE and DW-ssEPI were calculated and compared. A tube phantom was placed next to patients not treated on ViewRay, and ADCs of this reference tube were also compared. The proposed DP-TSE passed the spatial integrity test (< 1 mm within 100 mm radius and < 2 mm within 175 mm radius

Diffusion of protein through the human cornea.

Science.gov (United States)

Charalel, Resmi A; Engberg, Kristin; Noolandi, Jaan; Cochran, Jennifer R; Frank, Curtis; Ta, Christopher N

2012-01-01

To determine the rate of diffusion of myoglobin and bovine serum albumin (BSA) through the human cornea. These small proteins have hydrodynamic diameters of approximately 4.4 and 7.2 nm, and molecular weights of 16.7 and 66 kDa, for myoglobin and BSA, respectively. Diffusion coefficients were measured using a diffusion chamber where the protein of interest and balanced salt solution were in different chambers separated by an ex vivo human cornea. Protein concentrations in the balanced salt solution chamber were measured over time. Diffusion coefficients were calculated using equations derived from Fick's law and conservation of mass in a closed system. Our experiments demonstrate that the diffusion coefficient of myoglobin is 5.5 ± 0.9 × 10(-8) cm(2)/s (n = 8; SD = 1.3 × 10(-8) cm(2)/s; 95% CI: 4.6 × 10(-8) to 6.4 × 10(-8) cm(2)/s) and the diffusion coefficient of BSA is 3.1 ± 1.0 × 10(-8) cm(2)/s (n = 8; SD = 1.4 × 10(-8) cm(2)/s; 95% CI: 2.1 × 10(-8) to 4.1 × 10(-8) cm(2)/s). Our study suggests that molecules as large as 7.2 nm may be able to passively diffuse through the human cornea. With applications in pharmacotherapy and the development of an artificial cornea, further experiments are warranted to fully understand the limits of human corneal diffusion and its clinical relevance. Copyright © 2012 S. Karger AG, Basel.

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

Strong Stationary Duality for Diffusion Processes

OpenAIRE

Fill, James Allen; Lyzinski, Vince

2014-01-01

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well ch...

Reaction diffusion in chromium-zircaloy-2 system

International Nuclear Information System (INIS)

Xiang Wenxin; Ying Shihao

2001-01-01

Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound

Turbulent eddy diffusion models in exposure assessment - Determination of the eddy diffusion coefficient.

Science.gov (United States)

Shao, Yuan; Ramachandran, Sandhya; Arnold, Susan; Ramachandran, Gurumurthy

2017-03-01

The use of the turbulent eddy diffusion model and its variants in exposure assessment is limited due to the lack of knowledge regarding the isotropic eddy diffusion coefficient, D T . But some studies have suggested a possible relationship between D T and the air changes per hour (ACH) through a room. The main goal of this study was to accurately estimate D T for a range of ACH values by minimizing the difference between the concentrations measured and predicted by eddy diffusion model. We constructed an experimental chamber with a spatial concentration gradient away from the contaminant source, and conducted 27 3-hr long experiments using toluene and acetone under different air flow conditions (0.43-2.89 ACHs). An eddy diffusion model accounting for chamber boundary, general ventilation, and advection was developed. A mathematical expression for the slope based on the geometrical parameters of the ventilation system was also derived. There is a strong linear relationship between D T and ACH, providing a surrogate parameter for estimating D T in real-life settings. For the first time, a mathematical expression for the relationship between D T and ACH has been derived that also corrects for non-ideal conditions, and the calculated value of the slope between these two parameters is very close to the experimentally determined value. The values of D T obtained from the experiments are generally consistent with values reported in the literature. They are also independent of averaging time of measurements, allowing for comparison of values obtained from different measurement settings. These findings make the use of turbulent eddy diffusion models for exposure assessment in workplace/indoor environments more practical.

A system for the obtention and analysis of diffuse reflection spectra from biological tissue

International Nuclear Information System (INIS)

La Cadena, A. de; La Rosa, J. de; Stolik, S.

2012-01-01

The diffuse reflection spectroscopy is a technique with is possible to study biological tissue. In the field of the biomedical applications is useful for diagnostic purposes, since is possible to analyze biological tissue in a non invasive way. also, can be used with therapeutical purposes, for example in photodynamic therapy or laser surgery because with this technique it can be determined the biological effects produced by these treatments. In this paper is shown the development of a system to obtain and analyze diffuse reflection spectra of biological tissues, using a LED as a light source, that emits light between 400-700nm. The system has an interface for the regulation of the emittance of the LED. For diffuse reflectance spectra analysis, we use an HR4000CG-UV-NIR spectrometer. (Author)

Systemic diffuse large B-cell lymphoma masquerading as neovascular glaucoma.

Science.gov (United States)

Bawankar, Pritam; Das, Dipankar; Bhattacharjee, Harsha; Tayab, Shahinur; Deori, Nilutparna; Paulbuddhe, Vivek; Dhar, Shriya; Deka, Apurba

2018-02-01

We describe a case of spontaneous hyphema associated with anterior uveitis presents in a 69-year old female as the prominent sign of the intraocular spread of systemic diffuse large B-cell lymphoma (DLBCL). She had a history of diabetes and initially misdiagnosed as neovascular glaucoma. Clinical history of systemic lymphoma, characteristic findings on B-scan ultrasonography and magnetic resonance imaging scan, and identification of atypical lymphoid cells in aqueous sample established the diagnosis of intraocular metastasis of systemic DLBCL. Therefore, this report highlights that life-threatening malignant systemic lymphoma may masquerade as anterior segment ocular inflammation or neovascular glaucoma.

On the limit dynamics of systems with infinite multiple degrees of freedom

Energy Technology Data Exchange (ETDEWEB)

Braun, W A

1977-01-01

By using N/sup -2/ phi (g sub i - g sub j) regular pair interactions, it is shown that, for n approaching infinity, the Vlasovdynamics is the omega meson resonances -limit of the classical canonical N-particle-dynamics. Propagation of molecular chaos holds in this limit and the fluctuations converge to a Gaussian stochastic process, which is, however, non-Markovian. A model of a nerve membrane is studied in the limit of singular interaction with Fermion reservoirs. The resulting axon equations have the same structure as the Hodgkin Huxley equations. Recently proven theorems are used on nonlinear diffusion equations to show the existance of a propagating pulse solution.

Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems

International Nuclear Information System (INIS)

Cherniha, Roman

2010-01-01

New definitions of Q-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear reaction-diffusion systems is examined to demonstrate the applicability of the definitions proposed and it is shown when different definitions of Q-conditional symmetry lead to the same operators.

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.

Exact substitute processes for diffusion-reaction systems with local complete exclusion rules

International Nuclear Information System (INIS)

Schulz, Michael; Reineker, Peter

2005-01-01

Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically starting from the usual master equations with discrete variables and their corresponding representation in a Fock space. On this basis, a formulation of the transition probability as a Grassmann path integral is derived in a straightforward manner. It will be demonstrated that this Grassmann path integral is equivalent to a set of Ito stochastic differential equations. Averages of arbitrary variables and correlation functions of the underlying diffusion-reaction system can be expressed as weighted averages over all solutions of the system of stochastic differential equations. Furthermore, these differential equations are equivalent to a Fokker-Planck equation describing the probability distribution of the actual Ito solutions. This probability distribution depends on continuous variables in contrast to the original master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to the corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well-known substitute process for the same system without exclusion rules, there exists a set of remarkable differences. The given approach is not only valid for the discussed single-species processes. We give sufficient arguments to show that arbitrary combinations of unimolecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach

Diffusion between evolving interfaces

International Nuclear Information System (INIS)

Juntunen, Janne; Merikoski, Juha

2010-01-01

Diffusion in an evolving environment is studied by continuous-time Monte Carlo simulations. Diffusion is modeled by continuous-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.

Neutron scattering for investigation into the connection between phonons and diffusion in metallic systems

International Nuclear Information System (INIS)

Herzig, C.

1995-01-01

For examining the connection between the diffusion systematics and the lattice dynamics of the body-centered cubic metals, the temperature dependence of the self-diffusion (radiotracer technique) and the phonon dispersion (neutron scattering) have been measured in selected systems. In continuation of previous studies, the goal of the examinations reported was to put the earlier developed phonon-related diffusion model on a broader experimental basis, in order to perform verifying analyses. The phonon dispersion of the group 5 metal Nb has been measured up to high temperatures. In contrast to the values measured for the group 4 (β-Zr) and group 6 (Cr) metals, the dispersion in Nb revealed an only very weak temperature dependence. The exceptional case of the bcc β-Tl has been examined by measuring the diffusion and the dispersion in the β-T 83 In 17 alloy. Significant deviations from the conditions in the bcc transition metals have been found. Self-diffusion has been measured for the first time in Ba and β-Sc. Their diffusion systematics correlate with electron configuration. The influence of the d-electron concentration on the diffusion systematics has been measured in Ti-Mo and Hf-Nb alloys, the results backing the predictions of the phonon-related diffusion model. (orig.) [de

Longitudinal diffusion MRI for treatment response assessment: Preliminary experience using an MRI-guided tri-cobalt 60 radiotherapy system.

Science.gov (United States)

Yang, Yingli; Cao, Minsong; Sheng, Ke; Gao, Yu; Chen, Allen; Kamrava, Mitch; Lee, Percy; Agazaryan, Nzhde; Lamb, James; Thomas, David; Low, Daniel; Hu, Peng

2016-03-01

To demonstrate the preliminary feasibility of a longitudinal diffusion magnetic resonance imaging (MRI) strategy for assessing patient response to radiotherapy at 0.35 T using an MRI-guided radiotherapy system (ViewRay). Six patients (three head and neck cancer, three sarcoma) who underwent fractionated radiotherapy were enrolled in this study. A 2D multislice spin echo single-shot echo planar imaging diffusion pulse sequence was implemented on the ViewRay system and tested in phantom studies. The same pulse sequence was used to acquire longitudinal diffusion data (every 2-5 fractions) on the six patients throughout the entire course of radiotherapy. The reproducibility of the apparent diffusion coefficient (ADC) measurements was assessed using reference regions and the temporal variations of the tumor ADC values were evaluated. In diffusion phantom studies, the ADC values measured on the ViewRay system matched well with reference ADC values with ViewRay MRI. Larger patient cohort studies are warranted to correlate the longitudinal diffusion measurements to patient outcomes. Such an approach may enable response-guided adaptive radiotherapy.

Jump locations of jump-diffusion processes with state-dependent rates

International Nuclear Information System (INIS)

Miles, Christopher E; Keener, James P

2017-01-01

We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’. However, the state-dependence of the jump rate provides direct coupling between the diffusion and jump components, making it difficult to disentangle the two to study individually. In this work, we provide an iterative map formulation of the sequence of distributions of jump locations. The distributions computed by this map can be used to elucidate other interesting quantities about the process, including statistics of the interjump times. Ultimately, the limit of the map reveals that knowledge of the stationary distribution of the full process is sufficient to recover (but not necessarily equal to) the distribution of jump locations. We propose two biophysical examples to illustrate the use of this framework to provide insight about a system. We find that a sharp threshold voltage emerges robustly in a simple stochastic integrate-and-fire neuronal model. The interplay between the two sources of noise is also investigated in a stepping model of molecular motor in intracellular transport pulling a diffusive cargo. (paper)

Formation of multiple stoichiometric phases in binary systems by combined bulk and grain boundary diffusion: Experiments and model

International Nuclear Information System (INIS)

Svoboda, J.; Fischer, F.D.; Schillinger, W.

2013-01-01

The thermodynamic extremal principle has been used by the authors to treat the evolution of binary and multicomponent systems under the assumption that all phases are nearly stoichiometric. Up to now only bulk diffusion has been taken into account. The concept is now extended to combined bulk and grain boundary diffusion possible in each newly formed phase. The grains are approximated by cylinders allowing interface diffusion along the top and bottom of the grains and grain boundary diffusion along the mantle with different interface/grain boundary diffusion coefficients. A consistent analysis yields an effective diffusion coefficient taking into account the combined interface/grain boundary and bulk diffusion of each individual component. The current concept is applied to the Cu–Sn couple which has been studied by a number of researchers. The results of simulations are compared with experiments at 200 °C on solid systems reported in the literature as well as with our experiments at 250 °C with liquid Sn.

Comparative study of silver nanoparticle permeation using Side-Bi-Side and Franz diffusion cells

Science.gov (United States)

Trbojevich, Raul A.; Fernandez, Avelina; Watanabe, Fumiya; Mustafa, Thikra; Bryant, Matthew S.

2016-03-01

Better understanding the mechanisms of nanoparticle permeation through membranes and packaging polymers has important implications for the evaluation of drug transdermal uptake, in food safety and the environmental implications of nanotechnology. In this study, permeation of 21 nm diameter silver nanoparticles (AgNPs) was tested using Side-Bi-Side and Franz static diffusion cells through hydrophilic 0.1 and 0.05 µm pore diameter 125 µm thick synthetic cellulose membranes, and 16 and 120 µm thick low-density polyethylene (LDPE) films. Experiments performed with LDPE films discarded permeation of AgNPs or Ag ions over the investigated time-frame in both diffusion systems. But controlled release of AgNPs has been quantified using semipermeable hydrophilic membranes. The permeation followed a quasi-linear time-dependent model during the experimental time-frame, which represents surface reaction-limited permeation. Diffusive flux, diffusion coefficients, and membrane permeability were determined as a function of pore size and diffusion model. Concentration gradient and pore size were key to understand mass transfer phenomena in the diffusion systems.

Comparative study of silver nanoparticle permeation using Side-Bi-Side and Franz diffusion cells

International Nuclear Information System (INIS)

Trbojevich, Raul A.; Fernandez, Avelina; Watanabe, Fumiya; Mustafa, Thikra; Bryant, Matthew S.

2016-01-01

Better understanding the mechanisms of nanoparticle permeation through membranes and packaging polymers has important implications for the evaluation of drug transdermal uptake, in food safety and the environmental implications of nanotechnology. In this study, permeation of 21 nm diameter silver nanoparticles (AgNPs) was tested using Side-Bi-Side and Franz static diffusion cells through hydrophilic 0.1 and 0.05 µm pore diameter 125 µm thick synthetic cellulose membranes, and 16 and 120 µm thick low-density polyethylene (LDPE) films. Experiments performed with LDPE films discarded permeation of AgNPs or Ag ions over the investigated time-frame in both diffusion systems. But controlled release of AgNPs has been quantified using semipermeable hydrophilic membranes. The permeation followed a quasi-linear time-dependent model during the experimental time-frame, which represents surface reaction-limited permeation. Diffusive flux, diffusion coefficients, and membrane permeability were determined as a function of pore size and diffusion model. Concentration gradient and pore size were key to understand mass transfer phenomena in the diffusion systems.Graphical Abstract

Comparative study of silver nanoparticle permeation using Side-Bi-Side and Franz diffusion cells

Energy Technology Data Exchange (ETDEWEB)

Trbojevich, Raul A. [U.S. Food and Drug Administration, Division of Biochemical Toxicology, National Center for Toxicological Research (United States); Fernandez, Avelina, E-mail: velifdez@ific.uv.es [Consejo Superior de Investigaciones Científicas-Universitat de València, Parc Científic, Instituto de Física Corpuscular (Spain); Watanabe, Fumiya; Mustafa, Thikra [University Arkansas at Little Rock, Center for Integrative Nanotechnology Sciences (United States); Bryant, Matthew S. [U.S. Food and Drug Administration, Division of Biochemical Toxicology, National Center for Toxicological Research (United States)

2016-03-15

Better understanding the mechanisms of nanoparticle permeation through membranes and packaging polymers has important implications for the evaluation of drug transdermal uptake, in food safety and the environmental implications of nanotechnology. In this study, permeation of 21 nm diameter silver nanoparticles (AgNPs) was tested using Side-Bi-Side and Franz static diffusion cells through hydrophilic 0.1 and 0.05 µm pore diameter 125 µm thick synthetic cellulose membranes, and 16 and 120 µm thick low-density polyethylene (LDPE) films. Experiments performed with LDPE films discarded permeation of AgNPs or Ag ions over the investigated time-frame in both diffusion systems. But controlled release of AgNPs has been quantified using semipermeable hydrophilic membranes. The permeation followed a quasi-linear time-dependent model during the experimental time-frame, which represents surface reaction-limited permeation. Diffusive flux, diffusion coefficients, and membrane permeability were determined as a function of pore size and diffusion model. Concentration gradient and pore size were key to understand mass transfer phenomena in the diffusion systems.Graphical Abstract.

Separation of Kr-Xe system by thermal diffusion method

International Nuclear Information System (INIS)

Yoshida, Hiroshi; Numata, Kazuyoshi; Matsuda, Yuji; Ouchi, Misao; Naruse, Yuji

1979-11-01

Separation experiments of Kr-Xe system were carried out to study the possibility of adapting thermal diffusion method for concentration of krypton in a fuel reprocessing off-gas treatment process. The results are as follows. (1) A batchwise thermal diffusion column of hot tube diameter 21 mm, cold tube diameter 32 mm, effective hight 1000 mm and volume -- 500 CC is the best in separation characteristics and in ease of operation under the different conditions. (2) The overall separation factor increases with increase of the operating temperature in the column with and without reservoir. (3) The optimum operating pressure (about 400 Torr) is independent of the operating conditions such as temperature, reservoir volume and feed gas content. (4) A preliminary design of the Kr-Xe separating plant for a reprocessing plant (1500 ton-U/yr) shows the required number of columns and the total electric power. (author)

Modular pump limiter systems for large tokamaks

International Nuclear Information System (INIS)

Uckan, T.; Klepper, C.C.; Mioduszewski, P.K.; McGrath, R.T.

1987-09-01

Long-pulse (>10-s) operation of large tokamaks with high-power (>10-MW) heating and extensive external fueling will require correspondingly efficient particle exhaust for density control. A pump limiter can provide the needed exhaust capability by removing a small percentage of the particles, which would otherwise be recycled. Single pump limiter modules have been operated successfully on ISX-B, PDX, TEXTOR, and PLT. An axisymmetric pump limiter is now being installed and will be studied in TEXTOR. A third type of pump limiter is a system that consists of several modules and exhibits performance different from that of a single module. To take advantage of the flexibility of a modular pump limiter system in a high-power, long-pulse device, the power load must be distributed among a number of modules. Because each added module changes the performance of all the others, a set of design criteria must be defined for the overall limiter system. The design parameters for the modules are then determined from the system requirements for particle and power removal. Design criteria and parameters are presented, and the impact on module design of the state of the art in engineering technology is discussed. The relationship between modules are considered from the standpoint of flux coverage and shadowing effects. The results are applied to the Tore Supra tokamak. A preliminary conceptual design for the Tore Supra pump limiter system is discussed, and the design parameters of the limiter modules are presented. 21 refs., 12 figs

Ignition in Convective-Diffusive Systems

National Research Council Canada - National Science Library

Law, Chung

1999-01-01

... efficiency as well as the knock and emission characteristics. The ignition event is clearly controlled by the chemical reactions of fuel oxidation and the fluid mechanics of convective and diffusive transport...

Diffusive Silicon Nanopore Membranes for Hemodialysis Applications.

Directory of Open Access Journals (Sweden)

Steven Kim

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

Diffusive Silicon Nanopore Membranes for Hemodialysis Applications

Science.gov (United States)

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

2016-01-01

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

Diffusivity database (DDB) system for major rocks and buffer materials (Released on 2007/specification)

International Nuclear Information System (INIS)

Tochigi, Yoshikatsu; Shibata, Masahiro; Sato, Haruo; Kitamura, Akira

2007-03-01

The Diffusivity Database (DDB) System developed on early 2006 was upgraded to apply the data of effective diffusion coefficient of the nuclides in the rock matrix for the 'H12: Project to Establish the Scientific and Technical Basis for HLW Disposal in Japan', and the data in the buffer materials from literature survey was newly added. Some functions of data search and selection were reformed to improve the level of convenience. This DDB system (work on MS-Access TM ) is released to the public through Web server managed by JAEA. (author)

Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates

Science.gov (United States)

Wu, Yixiang; Zou, Xingfu

2018-04-01

In this paper, we investigate a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts. We first prove that the solution of the model exists globally and the model system possesses a global attractor. We then identify the basic reproduction number R0 for the model and prove its threshold role: if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable; if R0 > 1, the solution of the model is uniformly persistent and there exists a positive (pathogen persistent) steady state. Finally, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen's most favoured sites when the mobility of the infected host is limited.

Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks

Science.gov (United States)

Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.

2012-01-01

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

International Nuclear Information System (INIS)

Mittal, R.C.; Rohila, Rajni

2016-01-01

In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.

Reaction phases and diffusion paths in SiC/metal systems

Energy Technology Data Exchange (ETDEWEB)

Naka, M.; Fukai, T. [Osaka Univ., Osaka (Japan); Schuster, J.C. [Vienna Univ., Vienna (Austria)

2004-07-01

The interface structures between SiC and metal are reviewed at SiC/metal systems. Metal groups are divided to carbide forming metals and non-carbide forming metals. Carbide forming metals form metal carbide granular or zone at metal side, and metal silicide zone at SiC side. The further diffusion of Si and C from SiC causes the formation of T ternary phase depending metal. Non-carbide forming metals form silicide zone containing graphite or the layered structure of metal silicide and metal silicide containing graphite. The diffusion path between SiC and metal are formed along tie-lines connecting SiC and metal on the corresponding ternary Si-C-M system. The reactivity of metals is dominated by the forming ability of carbide or silicide. Te reactivity tendency of elements are discussed on the periodical table of elements, and Ti among elements shows the highest reactivity among carbide forming metals. For non-carbide forming metals the reactivity sequence of metals is Fe>Ni>Co. (orig.)

Uniqueness for cross-diffusion systems issuing from seawater intrusion problems

Directory of Open Access Journals (Sweden)

Catherine Choquet

2017-10-01

Full Text Available We consider a model mixing sharp and diffuse interface approaches for seawater intrusion phenomenons in confined and unconfined aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic and elliptic type describing the evolution of the depth of the interface between salt- and freshwater and the evolution of the freshwater hydraulic head. Assuming a low hydraulic conductivity inside the aquifer, we prove the uniqueness of a weak solution for the model completed with initial and boundary conditions. Thanks to a generalization of a Meyer's regularity result, we establish that the gradient of the solution belongs to the space $L^r$, r>2. This additional regularity combined with the Gagliardo-Nirenberg inequality for r=4 allows to handle the nonlinearity of the system in the proof of uniqueness.

Prediction and validation of diffusion coefficients in a model drug delivery system using microsecond atomistic molecular dynamics simulation and vapour sorption analysis.

Science.gov (United States)

Forrey, Christopher; Saylor, David M; Silverstein, Joshua S; Douglas, Jack F; Davis, Eric M; Elabd, Yossef A

2014-10-14

Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.

Energy and exergy analyses of the diffusion absorption refrigeration system

International Nuclear Information System (INIS)

Yıldız, Abdullah; Ersöz, Mustafa Ali

2013-01-01

This paper describes the thermodynamic analyses of a DAR (diffusion absorption refrigeration) cycle. The experimental apparatus is set up to an ammonia–water DAR cycle with helium as the auxiliary inert gas. A thermodynamic model including mass, energy and exergy balance equations are presented for each component of the DAR cycle and this model is then validated by comparison with experimental data. In the thermodynamic analyses, energy and exergy losses for each component of the system are quantified and illustrated. The systems' energy and exergy losses and efficiencies are investigated. The highest energy and exergy losses occur in the solution heat exchanger. The highest energy losses in the experimental and theoretical analyses are found 25.7090 W and 25.4788 W respectively, whereas those losses as to exergy are calculated 13.7933 W and 13.9976 W. Although the values of energy efficiencies obtained from both the model and experimental studies are calculated as 0.1858, those values, in terms of exergy efficiencies are found 0.0260 and 0.0356. - Highlights: • The diffusion absorption refrigerator system is designed manufactured and tested. • The energy and exergy analyses of the system are presented theoretically and experimentally. • The energy and exergy losses are investigated for each component of the system. • The highest energy and exergy losses occur in the solution heat exchanger. • The energy and the exergy performances are also calculated

Spreading speeds for a two-species competition-diffusion system

Science.gov (United States)

Carrère, Cécile

2018-02-01

In this paper, spreading properties of a competition-diffusion system of two equations are studied. This system models the invasion of an empty favorable habitat, by two competing species, each obeying a logistic growth equation, such that any coexistence state is unstable. If the two species are initially absent from the right half-line x > 0, and the slowest one dominates the fastest one on x < 0, then the latter will invade the right space at its Fisher-KPP speed, and will be replaced by or will invade the former, depending on the parameters, at a slower speed. Thus, the system forms a propagating terrace, linking an unstable state to two consecutive stable states.

Spectrometer system for diffuse extreme ultraviolet radiation

Science.gov (United States)

Labov, Simon E.

1989-01-01

A unique grazing incidence spectrometer system has been designed to study diffuse line emission between 80 and 650 A with 10-30 A resolution. The minimum detectable emission line strength during a 5-min observation ranges from 100-2000 ph/sq cm sec str. The instrument uses mechanically ruled reflection gratings placed in front of a linear array of mirrors. These mirrors focus the spectral image on microchannel plate detectors located behind thin filters. The field of view is 40 min of arc by 15 deg, and there is no spatial imaging. This instrument has been fabricated, calibrated, and successfully flown on a sounding rocket to observe the astronomical background radiation.

Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems

International Nuclear Information System (INIS)

Borysiewicz, M.; Mika, J.; Spiga, G.

1982-01-01

Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived

Diffusion in the Muscovite 40K Decay System (Invited)

Science.gov (United States)

Harrison, T. M.

2010-12-01

The considerable potential of muscovite for thermochronological applications is beginning to be fully exploited following the belated publication of Ar kinetic data. Muscovite’s high potassium content, low solubility for excess 40Ar*, and ubiquitous presence in regionally metamorphosed terranes make it an important phase for 40Ar/39Ar thermochronometry, particularly in light of recognition that both age spectra and vacuum-step-heating-derived 39Ar Arrhenius plots reflect Ar release via the same volume diffusion mechanism. Thus instead of assuming a nominal closure temperature to estimate a single T-t datum, continuous and accurate thermal histories can be inferred in a similar fashion to that well-documented for K-feldspar using the multi-diffusion domain (MDD) model. The Arrhenius parameters for Ar diffusion in muscovite (E=64 kcal/mol, Do=4 cm2/s) correspond to an effective intragrain closure temperature range of ~500 to 300oC for ca. 100 μm grains cooling at ~10oC/Ma at 5 kbar. However, even greater exploitation of the 40K decay system remains possible as only one of every ten 40K atoms decay to 40Ar. The other 90% decay to 40Ca giving the 40K-40Ca branch, in principle, greater sensitivity for dating high K/Ca minerals such as muscovite. The advent of the ‘double-plus’ SIMS 40K++-40Ca++ dating method, which permits analysis of Ca isotopes at an MRP of ~4k rather than the ~25k required for full separation of 40K+ from 40Ca+, opens up the prospect of directly revealing 40K-40Ca closure profiles in muscovite (as opposed to their indirect inference from inversion of 40Ar/39Ar data through the MDD model) at a gain of enhanced precision and accuracy in thermal history reconstruction. We have used SIMS to observe K-Ca age variations in natural muscovites pressed into In. Translating this data into thermal history information, however, requires knowledge of the Arrhenius parameters for Ca tracer diffusion in muscovite. We are undertaking hydrothermal piston

Permanganate diffusion and reaction in sedimentary rocks.

Science.gov (United States)

Huang, Qiuyuan; Dong, Hailiang; Towne, Rachael M; Fischer, Timothy B; Schaefer, Charles E

2014-04-01

In situ chemical oxidation using permanganate has frequently been used to treat chlorinated solvents in fractured bedrock aquifers. However, in systems where matrix back-diffusion is an important process, the ability of the oxidant to migrate and treat target contaminants within the rock matrix will likely determine the overall effectiveness of this remedial approach. In this study, a series of diffusion experiments were performed to measure the permanganate diffusion and reaction in four different types of sedimentary rocks (dark gray mudstone, light gray mudstone, red sandstone, and tan sandstone). Results showed that, within the experimental time frame (~2 months), oxidant migration into the rock was limited to distances less than 500 μm. The observed diffusivities for permanganate into the rock matrices ranged from 5.3 × 10(-13) to 1.3 × 10(-11) cm(2)/s. These values were reasonably predicted by accounting for both the rock oxidant demand and the effective diffusivity of the rock. Various Mn minerals formed as surface coatings from reduction of permanganate coupled with oxidation of total organic carbon (TOC), and the nature of the formed Mn minerals was dependent upon the rock type. Post-treatment tracer testing showed that these Mn mineral coatings had a negligible impact on diffusion through the rock. Overall, our results showed that the extent of permanganate diffusion and reaction depended on rock properties, including porosity, mineralogy, and organic carbon. These results have important implications for our understanding of long-term organic contaminant remediation in sedimentary rocks using permanganate. Copyright © 2014 Elsevier B.V. All rights reserved.

Production of a table of diffusion of light at small angles

International Nuclear Information System (INIS)

Desert, Sylvain

2001-01-01

This thesis reports the development of an optical table for the analysis, in absolute unit, of the light diffused by samples in air within an angle range from 1 to 25 degrees, by using a 16 bit Ccd camera. In this installation, a sample is located in a parallelepiped vessel where it is illuminated by a laser beam, and the power of this laser is controlled by means of a polarizer system. A lens is placed behind the sample, and the sensor (a Ccd camera) behind its focal point. After some generalities about light diffusion (Van de Huist criterion, Rayleigh diffusion, Mie theory), the author presents the different components of the experimental set-up, reports its calibration and the measurement of its performance (linearity, dynamics and detectability, angular range and resolution). He describes how a diffusion measurement is performed: experimental protocol, data processing, experimental limitations. He reports the application to light diffusion by latexes [fr

FLAMMABLE GAS DIFFUSION THROUGH SINGLE SHELL TANK (SST) DOMES

Energy Technology Data Exchange (ETDEWEB)

MEACHAM, J.E.

2003-11-10

This report quantified potential hydrogen diffusion through Hanford Site Single-Shell tank (SST) domes if the SSTs were hypothetically sealed airtight. Results showed that diffusion would keep headspace flammable gas concentrations below the lower flammability limit in the 241-AX and 241-SX SST. The purpose of this document is to quantify the amount of hydrogen that could diffuse through the domes of the SSTs if they were hypothetically sealed airtight. Diffusion is assumed to be the only mechanism available to reduce flammable gas concentrations. The scope of this report is limited to the 149 SSTs.

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

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.

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

Energy Technology Data Exchange (ETDEWEB)

Vasques, R. [Department of Mathematics, Center for Computational Engineering Science, RWTH Aachen University, Schinkel Strasse 2, D-52062 Aachen (Germany)

2013-07-01

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

International Nuclear Information System (INIS)

Vasques, R.

2013-01-01

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

DIFFUSIVE PROPAGATION OF ENERGY IN A NON-ACOUSTIC CHAIN

OpenAIRE

Komorowski , Tomasz; Olla , Stefano

2017-01-01

International audience; We consider a non acoustic chain of harmonic oscil-lators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy a system of evolution equations. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped Euler-Bernoulli beam eq...

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

Temperature jump boundary conditions in radiation diffusion

International Nuclear Information System (INIS)

Alonso, C.T.

1976-12-01

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

Prognosis of localized diffuse large B-cell lymphoma in younger patients

DEFF Research Database (Denmark)

Møller, Michael B; Christensen, Bjarne E; Pedersen, Niels T

2003-01-01

BACKGROUND: The International Prognostic Index (IPI) is widely used as a predictive model in diffuse large B-cell lymphoma (DLBCL) patients of all ages and stages. To determine the optimal IPI-based prognostic system at the time of diagnosis in younger patients with limited-stage DLBCL, the authors...

Study of uranium-titanium diffusion; Etude de la diffusion uranium-titane

Energy Technology Data Exchange (ETDEWEB)

Adda, Y; Philibert, J [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires; Institut de Recherches de la Siderurgie Francaise (IRSID), 78 - Saint-Germain-en-Laye (France)

1959-07-01

In the overall scheme of research on the chemical diffusion of uranium and the transition metals we have studied the uranium-titanium system. The diffusion couples are prepared by welding together small plates of uranium and titanium under pressure, using a technique already described by us. After diffusion under vacuum, polished sections of the samples were micro-graphically examined. This inspection showed that intergranular diffusion occurred at temperatures below 650 deg. C. At higher temperatures, the diffusion occurred uniquely throughout the volume of the metal, and the diffusion zone appeared as a succession of micro-graphically distinguishable bands. Study of the rate of increase of these corresponding 'penetration coefficients'. In addition, we have observed important variations in microhardness within the diffusion zone, we have tried to relate these variations to the variation of concentration. This is measured with the Castaing microprobe. We have thus accurately established the concentration-penetration curves for temperatures between 950 and 1075 deg. C. From these curves, we have calculated the diffusion coefficient D as a function of the concentration using Matano's method. At all temperatures, D(c) curve has a U form as for the U-Zr system. The activation energy has a maximum value of 42 kcal/g atom at an atomic concentration of 0,5. Even though we have rarely seen pores in the diffusion zone, we have nevertheless observed an important Kirkendall-effect by studying the displacements x{sub i} of the interface using tungsten wires as markers. These displacements can be expressed as a function of time and temperature by the equation: x{sub i} = 0,9 t {sup 1/2} exp ( - 14600/(RT)). Finally, using Darken's equations we calculated the intrinsic diffusion coefficients Du and Dti as well as the corresponding activation energies. These energies are similar (QU = 38,5 and QTi = 40 kcal/at. g) and also almost the same as those found for the U-Zr system

Excess diffuse light absorption in upper mesophyll limits CO2 drawdown and depresses photosynthesis

Science.gov (United States)

Sun-grown and shade-grown leaves of some species absorb direct and diffuse light differently. Sun-grown leaves can photosynthesize ~10-15% less under diffuse compared to direct irradiance, while shade-grown leaves do not exhibit this sensitivity. In this study, we investigate if the spatial differen...

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

Simulation Studies of Diffusion-Release and Effusive-Flow of Short-Lived Radioactive Isotopes

CERN Document Server

Zhang, Yan; Kawai, Yoko

2005-01-01

Delay times associated with diffusion release from targets and effusive-flow transport of radioactive isotopes to ion sources are principal intensity limiters at ISOL-based radioactive ion beam facilities, and simulation studies with computer models are cost effective methods for designing targets and vapor transport systems with minimum delay times to avoid excessive decay losses of short lived ion species. A finite difference code, Diffuse II, was recently developed at the Oak Ridge National Laboratory to study diffusion-release of short-lived species from three principal target geometries. Simulation results are in close agreement with analytical solutions to Fick’s second equation. Complementary to the development of Diffuse II, the Monte-Carlo code, Effusion, was developed to address issues related to the design of fast vapor transport systems. Results, derived by using Effusion, are also found to closely agree with experimental measurements. In this presentation, the codes will be used in conc...

Anomalous diffusion of fermions in superlattices

International Nuclear Information System (INIS)

Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.

1996-03-01

Diffusion of fermions in the periodic two-dimensional lattice of fermions is studied. It is shown that effects connected with antisymmetrization of the wave function increase chaoticness of motion. Various types of anomalous diffusion, characterized by a power spectral analysis are found. The nonlocality of the Pauli potential destroys cantori in the phase space. Consequently, the diffusion process is dominated by long free paths and the power spectrum is logarithmic at small frequency limit. (author)

Radon diffusion through multilayer earthen covers: models and simulations

International Nuclear Information System (INIS)

Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.

1981-09-01

A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained. The study has been conducted using a four-phase approach. The first phase develops the solution to the steady-state radon-diffusion equation in one-dimensieered barriers; disposal charge analysis; analysis of spent fuel policy implementation; spent f water. Field measurements and observations are reported for each site. Analytical data and field measurements are presented in tables and maps. Uranium concentrations in the sediments which were above detection limits ranged from 0.10 t 51.2 ppM. The mean of the logarithms of the uranium concentrations was 0.53. A group of high uranium concentrations occurs near the junctions of quadrangles AB, AC, BB, a 200 mK. In case 2), x-ray studies of isotopic phase separation in 3 He-- 4 He bcc solids were carried out by B. A. Fraass

On-line vibration and analysis system at the Paducah Gaseous Diffusion Plant

International Nuclear Information System (INIS)

Herricks, D.M.; Strunk, W.D.

1987-11-01

The enrichment facility in Paducah, KY uses a unique hard-wired vibration monitoring and analysis system for gaseous diffusion equipment. The axial flow and centrifugal flow compressors used in uranium enrichment range in size from 6 feet in diameter to less than one foot in diameter. These compressors must operate smoothly and safely, without breech of containment, since the working fluid of gaseous diffusion is gaseous UF 6 . The condition of 1925 compressors is monitored by use of the 2500 point vibration analysis system. Since the failure mechanisms of the compressors are well known and documented, only one accelerometer per machine is needed for most machines. The system is completely automated and can generate spectra or broadband levels in either acceleration or velocity units. Levels are stored for historical review. The analyst can, via a custom telecommunications link, view and analyze data from all monitored points with an office PC. 4 figs

DIFFUSION - WRS system module number 7539 for solving a set of multigroup diffusion equations in one dimension

International Nuclear Information System (INIS)

Grimstone, M.J.

1978-06-01

The WRS Modular Programming System has been developed as a means by which programmes may be more efficiently constructed, maintained and modified. In this system a module is a self-contained unit typically composed of one or more Fortran routines, and a programme is constructed from a number of such modules. This report describes one WRS module, the function of which is to solve a set of multigroup diffusion equations for a system represented in one-dimensional plane, cylindrical or spherical geometry. The information given in this manual is of use both to the programmer wishing to incorporate the module in a programme, and to the user of such a programme. (author)

Diffusion in liquids a theoretical and experimental study

CERN Document Server

Tyrrell, H J V

1984-01-01

Diffusion in Liquids: A Theoretical and Experimental Study aims to discuss the principles, applications, and advances in the field of diffusion, thermal diffusion, and thermal conduction in liquid systems. The book covers topics such as the principles of non-equilibrium thermodynamics; diffusion in binary and multicompetent systems; and experimental methods of studying diffusion processes in liquids. Also covered in the book are topics such as the theoretical interpretations of diffusion coefficients; hydrodynamic and kinetic theories; and diffusion in electrolyte systems. The text is recommen

Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model

International Nuclear Information System (INIS)

Kutner, R.; Sosnowska, I.

1977-01-01

A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al (J. Phys. Chem. Solids; 32:41 (1971)) model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbHsub(x) system. (author)

Mutual diffusion coefficient models for polymer-solvent systems based on the Chapman-Enskog theory

Directory of Open Access Journals (Sweden)

R. A. Reis

2004-12-01

Full Text Available There are numerous examples of the importance of small molecule migration in polymeric materials, such as in drying polymeric packing, controlled drug delivery, formation of films, and membrane separation, etc. The Chapman-Enskog kinetic theory of hard-sphere fluids with the Weeks-Chandler-Andersen effective hard-sphere diameter (Enskog-WCA has been the most fruitful in diffusion studies of simple fluids and mixtures. In this work, the ability of the Enskog-WCA model to describe the temperature and concentration dependence of the mutual diffusion coefficient, D, for a polystyrene-toluene system was evaluated. Using experimental diffusion data, two polymer model approaches and three mixing rules for the effective hard-sphere diameter were tested. Some procedures tested resulted in models that are capable of correlating the experimental data with the refereed system well for a solvent mass fraction greater than 0.3.

Effects of a finite melt on the thickness and composition of liquid phase epitaxial InGaAsP and InGaAs layers grown by the diffusion-limited step-cooling technique

International Nuclear Information System (INIS)

Cook, L.W.; Tashima, M.M.; Stillman, G.E.

1980-01-01

The thickness of InGaAsP (lambda/sub g/=1.15 μm) and InGaAs (lambda/sub g/=1.68 μm) liquid phase epitaxial layers grown on (100) InP substrates by the step-cooling technique has been measured as a function of growth time. (lambda/sub g/ is defined as the wavelength corresponding to the energy gap of the epitaxial layer.) For growth times much less than the shortest diffusion time tau/sub i/=l 2 /D/sub i/ of the melt constituents, where l is the melt height and D/sub i/ is the diffusivity of each component in the melt, the thickness is consistent with diffusion-limited theory, and the composition is constant. The time at which the growth rate deviates sharply from diffusion-limited theory and beyond which constant composition growth can no longer be maintained has been determined for the melt size used in our experiments and can be estimated for any melt size

ALPS - advanced limiter-divertor plasma-facing systems

International Nuclear Information System (INIS)

Allain, J. P.; Bastasz, R.; Brooks, J. N.; Evans, T.; Hassanein, A.; Luckhardt, S.; Maingi, R.; Mattas, R. F.; McCarthy, K.; Mioduszewski, P.; Mogahed, E.; Moir, R.; Molokov, S.; Morely, N.; Nygren, R.; Reed, C.; Rognlien, T.; Ruzic, D.; Sviatoslavsky, I.; Sze, D.; Tillack, M.; Ulrickson, M.; Wade, P. M.; Wong, C.; Wooley, R.

1999-01-01

The Advanced Limiter-divertor Plasma-facing Systems (ALPS) program was initiated in order to evaluate the potential for improved performance and lifetime for plasma-facing systems. The main goal of the program is to demonstrate the advantages of advanced limiter/divertor systems over conventional systems in terms of power density capability, component lifetime, and power conversion efficiency, while providing for safe operation and minimizing impurity concerns for the plasma. Most of the work to date has been applied to free surface liquids. A multi-disciplinary team from several institutions has been organized to address the key issues associated with these systems. The main performance goals for advanced limiters and diverters are a peak heat flux of >50 MW/m 2 ,elimination of a lifetime limit for erosion, and the ability to extract useful heat at high power conversion efficiency (approximately40%). The evaluation of various options is being conducted through a combination of laboratory experiments, modeling of key processes, and conceptual design studies. The current emphasis for the work is on the effects of free surface liquids on plasma edge performance

Organization-wide adoption of computerized provider order entry systems: a study based on diffusion of innovations theory

Directory of Open Access Journals (Sweden)

Timpka Toomas

2009-12-01

Full Text Available Abstract Background Computerized provider order entry (CPOE systems have been introduced to reduce medication errors, increase safety, improve work-flow efficiency, and increase medical service quality at the moment of prescription. Making the impact of CPOE systems more observable may facilitate their adoption by users. We set out to examine factors associated with the adoption of a CPOE system for inter-organizational and intra-organizational care. Methods The diffusion of innovation theory was used to understand physicians' and nurses' attitudes and thoughts about implementation and use of the CPOE system. Two online survey questionnaires were distributed to all physicians and nurses using a CPOE system in county-wide healthcare organizations. The number of complete questionnaires analyzed was 134 from 200 nurses (67.0% and 176 from 741 physicians (23.8%. Data were analyzed using descriptive-analytical statistical methods. Results More nurses (56.7% than physicians (31.3% stated that the CPOE system introduction had worked well in their clinical setting (P P = P = 0.041. We found that in particular the received relative advantages of the CPOE system were estimated to be significantly (P P Conclusions Qualifications for CPOE adoption as defined by three attributes of diffusion of innovation theory were not satisfied in the study setting. CPOE systems are introduced as a response to the present limitations in paper-based systems. In consequence, user expectations are often high on their relative advantages as well as on a low level of complexity. Building CPOE systems therefore requires designs that can provide rather important additional advantages, e.g. by preventing prescription errors and ultimately improving patient safety and safety of clinical work. The decision-making process leading to the implementation and use of CPOE systems in healthcare therefore has to be improved. As any change in health service settings usually faces resistance

Releasing cation diffusion in self-limited nanocrystalline defective ceria thin films

DEFF Research Database (Denmark)

Esposito, Vincenzo; Ni, D. W.; Gualandris, Fabrizio

2017-01-01

Acceptor-doped nanocrystalline cerium oxide thin films are mechanically constrained nano-domains, with film/substrate interfacial strain and chemical doping deadlock mass diffusion. In contrast, in this paper we show that chemical elements result in highly unstable thin films under chemical...

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)

Diffusion of Antimicrobials Across Silicone Hydrogel Contact Lenses.

Science.gov (United States)

Zambelli, Alison M; Brothers, Kimberly M; Hunt, Kristin M; Romanowski, Eric G; Nau, Amy C; Dhaliwal, Deepinder K; Shanks, Robert M Q

2015-09-01

To measure the diffusion of topical preparations of moxifloxacin, amphotericin B (AmB), and polyhexamethylene biguanide (PHMB) through silicone hydrogel (SH) contact lenses (CLs) in vitro. Using an in vitro model, the diffusion of three antimicrobials through SH CLs was measured. Diffused compounds were measured using a spectrophotometer at set time points over a period of 4 hr. The amount of each diffused antimicrobial was determined by comparing the experimental value with a standard curve. A biological assay was performed to validate the CL diffusion assay by testing antimicrobial activity of diffused material against lawns of susceptible bacteria (Staphylococcus epidermidis) and yeast (Saccharomyces cerevisiae). Experiments were repeated at least two times with a total of at least four independent replicates. Our data show detectable moxifloxacin and PHMB diffusion through SH CLs at 30 min, whereas AmB diffusion remained below the limit of detection within the 4-hr experimental period. In the biological assay, diffused moxifloxacin demonstrated microbial killing starting at 20 min on bacterial lawns, whereas PHMB and AmB failed to demonstrate killing on microbial lawns over the course of the 60-min experiment. In vitro diffusion assays demonstrate limited penetration of certain anti-infective agents through SH CLs. Further studies regarding the clinical benefit of using these agents along with bandage CL for corneal pathologic condition are warranted.