Hiraishi, Noriko; Sadek, Fernanda T.; King, Nigel M.; Ferrari, Marco; Pashley, David H.; Tay, Franklin R
2013-01-01
Purpose Cholesterol esterase is both a component of salivary hydrolases as well as an inflammatory cell-derived enzyme and has been shown to cause biodegradation of methacrylate-based resin composites. This study examined whether Resilon, a polycaprolactone-based thermoplastic root filling material is susceptible to biodegradation by cholesterol esterase using agar-well diffusion assay of serially-diluted aqueous Resilon emulsions that were dispersed in agar. Materials and methods Emulsions of Resilon and polycaprolactone were prepared and dispersed in agar on culture plates. Two different concentrations of a cholesterol esterase (0.3 and 1.2 U/mL) were prepared and fed to wells prepared in the agar plates using an agar-well diffusion assay for examination the degradation of polymeric materials. Results Degradation of the emulsified Resilon was manifested as the formation of clear zones of different sizes around the agar wells. No clear zones were observed in agar wells that contain sterile distilled water as the negative control. Clinical significance Although dispersion Resilon into an emulsion is not the way in which this material is employed as a root filling material, the potential for Resilon to be degraded by cholesterol esterase is of potential concern as one cannot limit the degradation of extruded Resilon from a root apex by monocyte-derived macrophages to just the anatomical root apex. As the present study employed a high concentration of cholesterol esterase, further studies should be directed to examining the degradation of Resilon using macrophage cell cultures. PMID:18578181
Mathematical Methods for Diffusion MRI Processing
Lenglet, C.; Campbell, J.S.W.; Descoteaux, M.; Haro, G.; Savadjiev, P.; Wassermann, D.; Anwander, A.; Deriche, R.; Pike, G.B.; Sapiro, G.; Siddiqi, K.; Thompson, P.
2009-01-01
In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI). PMID:19063977
Diffusion method of seperating gaseous mixtures
Pontius, Rex B.
1976-01-01
A method of effecting a relatively large change in the relative concentrations of the components of a gaseous mixture by diffusion which comprises separating the mixture into heavier and lighter portions according to major fraction mass recycle procedure, further separating the heavier portions into still heavier subportions according to a major fraction mass recycle procedure, and further separating the lighter portions into still lighter subportions according to a major fraction equilibrium recycle procedure.
Diffusion in Condensed Matter: Methods, Materials, Models
NASA Astrophysics Data System (ADS)
Heitjans, Paul; Kärger, Jög
This comprehensive, handbook-style survey of diffusion in condensed matter gives detailed insight into diffusion as the process of particle transport due to stochastic movement. It is understood and presented as a phenomenon of crucial relevance for a large variety of processes and materials. In this book, all aspects of the theoretical fundamentals, experimental techniques, highlights of current developments and results for solids, liquids and interfaces are presented.
New method to measure liquid diffusivity by analyzing an instantaneous diffusion image.
Sun, Licun; Meng, Weidong; Pu, Xiaoyun
2015-09-01
A novel optical method was applied to measure the binary liquid diffusion coefficient (D) quickly. Equipped with an asymmetric liquid-core cylindrical lens (ALCL), the spatially resolving ability of the ALCL in measuring refractive index of liquid was utilized to obtain the gradient distribution of the liquid concentration along diffusive direction. Based on Fick's second law, the D value was then calculated by analyzing diffusion images. It was worth mentioning that only one instantaneous diffusive image was required to measure D value by the method, reducing the measurement time greatly from several hours in traditional methods to a few seconds. The diffusion coefficients of ethylene glycol diffusing in pure water, at temperatures from 288.15 to 308.15 K, were measured by analyzing instantaneous diffusion images, the results were consistent well with the values measured by using holographic interferometry and Taylor dispersion methods. The method is characterized by faster measurement, direct observation of diffusive process, and easy operation, which provides a new method in measuring diffusion coefficient of liquids rapidly. PMID:26368418
Diffuse-Interface Methods in Fluid Mechanics
NASA Technical Reports Server (NTRS)
Anderson, D. M.; McFadden, G. B.; Wheeler, A. A.
1997-01-01
The authors review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. The authors discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, the authors address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, related computational approaches to describe interfacial phenomena, and related approaches describing fully-miscible fluids.
A vertical diffusion method for the microbiological assay of isoniazid
Lloyd, Janet; Mitchison, D. A.
1964-01-01
A method is described for the assay of isoniazid in serum and other fluids by diffusion along slopes of Löwenstein-Jensen medium inoculated with tubercle bacilli. The method is convenient, rapid and robust, but is less accurate than diffusion systems for the assay of some other substances. PMID:14227431
Fokas method for a multi-domain linear reaction-diffusion equation with discontinuous diffusivity
NASA Astrophysics Data System (ADS)
Asvestas, M.; Sifalakis, A. G.; Papadopoulou, E. P.; Saridakis, Y. G.
2014-03-01
Motivated by proliferation-diffusion mathematical models for studying highly diffusive brain tumors, that also take into account the heterogeneity of the brain tissue, in the present work we consider a multi-domain linear reaction-diffusion equation with a discontinuous diffusion coefficient. For the solution of the problem at hand we implement Fokas transform method by directly following, and extending in this way, our recent work for a white-gray-white matter brain model pertaining to high grade gliomas. Fokas's novel approach for the solution of linear PDE problems, yields novel integral representations of the solution in the complex plane that, for appropriately chosen integration contours, decay exponentially fast and converge uniformly at the boundaries. Combining these method-inherent advantages with simple numerical quadrature rules, we produce an efficient method, with fast decaying error properties, for the solution of the discontinuous reaction-diffusion problem.
Kalwarf, D.R.; Nielson, K.K.; Rich, D.C.; Rogers, V.C.
1982-11-01
A method was developed and used to determine radon diffusion coefficients in compacted soils by transient-diffusion measurements. A relative standard deviation of 12% was observed in repeated measurements with a dry soil by the transient-diffusion method, and a 40% uncertainty was determined for moistures exceeding 50% of saturation. Excellent agreement was also obtained between values of the diffusion coefficient for radon in air, as measured by the transient-diffusion method, and those in the published literature. Good agreement was also obtained with diffusion coefficients measured by a steady-state method on the same soils. The agreement was best at low moistures, averaging less than ten percent difference, but differences of up to a factor of two were observed at high moistures. The comparison of the transient-diffusion and steady-state methods at low moistures provides an excellent verification of the theoretical validity and technical accuracy of these approaches, which are based on completely independent experimental conditions, measurement methods and mathematical interpretations.
Capturing correlations in chaotic diffusion by approximation methods.
Knight, Georgie; Klages, Rainer
2011-10-01
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line that contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher-order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, while the third method approximates Markov partitions and transition matrices by using a slight variation of the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence, and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in the case of dynamics where exact results for the diffusion coefficient are not available. PMID:22181115
Lattice Boltzmann method for the fractional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering. PMID:27176431
The method for detecting diffusion ring diameter in Hemagglutinin measuring
NASA Astrophysics Data System (ADS)
Jing, Wenbo; Liu, Xue; Duan, Jin; Wang, Xiao-man
2014-11-01
The diffuser ring diameter measurement is the most critical in hemagglutinin Measuring. The traditional methods, such as a vernier caliper or high-definition scanned images are subjective and low for the measurement data reliability. Propose high-resolution diffusion ring image for drop-resolution processing, adaptive Canny operator and local detection method to extract complete and clear diffusion ring boundaries, and finally make use of polynomial interpolation algorithm to make diffusion ring outer boundary pixel coordinates achieve sub-pixel accuracy and the least-squares fitting circle algorithm to calculate the precise center of the circle and the diameter of the diffuser ring. Experimental results show that the method detection time is only 63.61ms, which is a faster speed; diffuser ring diameter estimation error can achieve 0.55 pixel, high stability in experimental data. This method is adapted to the various types of influenza vaccine hemagglutinin content measurements, and has important value in the influenza vaccine quality detection.
A novel method to evaluate spin diffusion length of Pt
NASA Astrophysics Data System (ADS)
Zhang, Yan-qing; Sun, Niu-yi; Che, Wen-ru; Shan, Rong; Zhu, Zhen-gang
2016-05-01
Spin diffusion length of Pt is evaluated via proximity effect of spin orbit coupling (SOC) and anomalous Hall effect (AHE) in Pt/Co2FeAl bilayers. By varying the thicknesses of Pt and Co2FeAl layer, the thickness dependences of AHE parameters can be obtained, which are theoretically predicted to be proportional to the square of the SOC strength. According to the physical image of the SOC proximity effect, the spin diffusion length of Pt can easily be identified from these thickness dependences. This work provides a novel method to evaluate spin diffusion length in a material with a small value.
Adaptive domain decomposition methods for advection-diffusion problems
Carlenzoli, C.; Quarteroni, A.
1995-12-31
Domain decomposition methods can perform poorly on advection-diffusion equations if diffusion is dominated by advection. Indeed, the hyperpolic part of the equations could affect the behavior of iterative schemes among subdomains slowing down dramatically their rate of convergence. Taking into account the direction of the characteristic lines we introduce suitable adaptive algorithms which are stable with respect to the magnitude of the convective field in the equations and very effective on bear boundary value problems.
Practical method for diffusion welding of steel plate in air.
NASA Technical Reports Server (NTRS)
Moore, T. J.; Holko, K. H.
1972-01-01
Description of a simple and easily applied method of diffusion welding steel plate in air which does not require a vacuum furnace or hot press. The novel feature of the proposed welding method is that diffusion welds are made in air with deadweight loading. In addition, the use of an autogenous (self-generated) surface-cleaning principle (termed 'auto-vac cleaning') to reduce the effects of surface oxides that normally hinder diffusion welding is examined. A series of nine butt joints were diffusion welded in thick sections of AISI 1020 steel plate. Diffusion welds were attempted at three welding temperatures (1200, 1090, and 980 C) using a deadweight pressure of 34,500 N/sq m (5 psi) and a two-hour hold time at temperature. Auto-vac cleaning operations prior to welding were also studied for the same three temperatures. Results indicate that sound welds were produced at the two higher temperatures when the joints were previously fusion seal welded completely around the periphery. Also, auto-vac cleaning at 1200 C for 2-1/2 hours prior to diffusion welding was highly beneficial, particularly when subsequent welding was accomplished at 1090 C.
Efficient stochastic Galerkin methods for random diffusion equations
Xiu Dongbin Shen Jie
2009-02-01
We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.
A method for thermal diffusivity measurement in fluids.
Marín, E; Hernández-Rosales, E; Mansanares, A M; Ivanov, R; Rojas-Trigos, J B; Calderón, A
2013-10-01
A technique is proposed for thermal diffusivity measurement in fluids. It is based on the Angstrom method, but with excitation of thermal waves by electromagnetic energy absorption and pyroelectric detection. The good agreement between measured thermal diffusivity of air and some test liquids with literature values shows the validity of the method. It is free of some limitations of conventional photopyroelectric technique with length scanning because it is free of moving parts inside the sample and because it avoids problems associated with the non-parallelism between thermal wave generator surface and sensor. It does not require any data normalization procedure or special sample preparation. PMID:24182147
A method for thermal diffusivity measurement in fluids
NASA Astrophysics Data System (ADS)
Marín, E.; Hernández-Rosales, E.; Mansanares, A. M.; Ivanov, R.; Rojas-Trigos, J. B.; Calderón, A.
2013-10-01
A technique is proposed for thermal diffusivity measurement in fluids. It is based on the Angstrom method, but with excitation of thermal waves by electromagnetic energy absorption and pyroelectric detection. The good agreement between measured thermal diffusivity of air and some test liquids with literature values shows the validity of the method. It is free of some limitations of conventional photopyroelectric technique with length scanning because it is free of moving parts inside the sample and because it avoids problems associated with the non-parallelism between thermal wave generator surface and sensor. It does not require any data normalization procedure or special sample preparation.
Comparison of thermal diffusivity and thermal conductivity methods
Sheffield, G.S.; Schorr, J.R. )
1991-01-01
This paper reports on applications involving ceramics which require that this diverse group of materials act as either thermal insulators or thermal conductors. Values of thermal conductivity can range over more than 4 orders of magnitude from 0.1 W/(m {center dot} K) (0.7 BTU {center dot} in./(h {center dot} ft{sup 2} {center dot} {degrees}F)) for fiberboard insulation to 1300 W/(M {center dot} K) (9013 BTU {center dot} in./(h {center dot} {degrees}F)) for boron nitride. The magnitude of temperature gradients in materials is governed by thermal diffusivity and thermal conductivity. In ceramic materials, gradients can create significant thermal stresses, cause heat flow (causing furnaces to heat but also causing usually undesirable heat losses) and be a controlling factor in reaction rates. In general, no single method is dominant because of the wide range of temperatures involved, the large variations in diffusivity and conductivity encountered, the differences in sampling requirements (homogeneity), and the duration of measurement time. Five thermal diffusivity and conductivity methods, all of which have been successfully applied to ceramic materials are reviewed. The methods covered are dynamic radial heat flow, laser flash, hot wire, calorimeter, and guarded hot plate. The dynamic radial heat flow and laser flash methods are diffusivity methods, whereas the remaining three are representative of conductivity methods.
Stochastic operator-splitting method for reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Choi, TaiJung; Maurya, Mano Ram; Tartakovsky, Daniel M.; Subramaniam, Shankar
2012-11-01
Many biochemical processes at the sub-cellular level involve a small number of molecules. The local numbers of these molecules vary in space and time, and exhibit random fluctuations that can only be captured with stochastic simulations. We present a novel stochastic operator-splitting algorithm to model such reaction-diffusion phenomena. The reaction and diffusion steps employ stochastic simulation algorithms and Brownian dynamics, respectively. Through theoretical analysis, we have developed an algorithm to identify if the system is reaction-controlled, diffusion-controlled or is in an intermediate regime. The time-step size is chosen accordingly at each step of the simulation. We have used three examples to demonstrate the accuracy and robustness of the proposed algorithm. The first example deals with diffusion of two chemical species undergoing an irreversible bimolecular reaction. It is used to validate our algorithm by comparing its results with the solution obtained from a corresponding deterministic partial differential equation at low and high number of molecules. In this example, we also compare the results from our method to those obtained using a Gillespie multi-particle (GMP) method. The second example, which models simplified RNA synthesis, is used to study the performance of our algorithm in reaction- and diffusion-controlled regimes and to investigate the effects of local inhomogeneity. The third example models reaction-diffusion of CheY molecules through the cytoplasm of Escherichia coli during chemotaxis. It is used to compare the algorithm's performance against the GMP method. Our analysis demonstrates that the proposed algorithm enables accurate simulation of the kinetics of complex and spatially heterogeneous systems. It is also computationally more efficient than commonly used alternatives, such as the GMP method.
The Flux-integral Method for Multidimensional Convection and Diffusion
NASA Technical Reports Server (NTRS)
Leonard, B. P.; Macvean, M. K.; Lock, A. P.
1994-01-01
The flux-integral method is a procedure for constructing an explicit, single-step, forward-in-time, conservative, control volume update of the unsteady, multidimensional convection-diffusion equation. The convective plus diffusive flux at each face of a control-volume cell is estimated by integrating the transported variable and its face-normal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cell-average data. Cellwise constant behavior results in a (very artificially diffusive) first-order convection scheme. Second-order convection-diffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convection-diffusion scheme with excellent phase accuracy. Under constant-coefficient conditions, this is a uniformly third-order polynomial interpolation algorithm (UTOPIA).
Methods for diffusive relaxation in the Pn equation
Hauck, Cory D; Mcclarren, Ryan G; Lowrie, Robert B
2008-01-01
We present recent progress in the development of two substantially different approaches for simulating the so-called of P{sub N} equations. These are linear hyperbolic systems of PDEs that are used to model particle transport in a material medium, that in highly collisional regimes, are accurately approximated by a simple diffusion equation. This limit is based on a balance between function values and gradients of certain variables in the P{sub N} system. Conventional reconstruction methods based on upwinding approximate such gradients with an error that is dependent on the size of the computational mesh. Thus in order to capture the diffusion limit, a given mesh must resolve the dynamics of the continuum equation at the level of the mean-free-path, which tends to zero in the diffusion limit. The two methods analyzed here produce accurate solutions in both collisional and non-collisional regimes; in particular, they do not require resolution of the mean-free-path in order to properly capture the diffusion limit. The first method is a straight-forward application of the discrete Galerkin (DG) methodology, which uses additional variables in each computational cell to capture the balance between function values and gradients, which are computed locally. The second method uses a temporal splitting of the fast and slow dynamics in the P{sub N} system to derive so-called regularized equations for which the diffusion limit is built-in. We focus specifically on the P{sub N} equations for one-dimensional, slab geometries. Preliminary results for several benchmark problems are presented which highlight the advantages and disadvantages of each method. Further improvements and extensions are also discussed.
Modeling the flow in diffuse interface methods of solidification
NASA Astrophysics Data System (ADS)
Subhedar, A.; Steinbach, I.; Varnik, F.
2015-08-01
Fluid dynamical equations in the presence of a diffuse solid-liquid interface are investigated via a volume averaging approach. The resulting equations exhibit the same structure as the standard Navier-Stokes equation for a Newtonian fluid with a constant viscosity, the effect of the solid phase fraction appearing in the drag force only. This considerably simplifies the use of the lattice Boltzmann method as a fluid dynamics solver in solidification simulations. Galilean invariance is also satisfied within this approach. Further, we investigate deviations between the diffuse and sharp interface flow profiles via both quasiexact numerical integration and lattice Boltzmann simulations. It emerges from these studies that the freedom in choosing the solid-liquid coupling parameter h provides a flexible way of optimizing the diffuse interface-flow simulations. Once h is adapted for a given spatial resolution, the simulated flow profiles reach an accuracy comparable to quasiexact numerical simulations.
Modeling the flow in diffuse interface methods of solidification.
Subhedar, A; Steinbach, I; Varnik, F
2015-08-01
Fluid dynamical equations in the presence of a diffuse solid-liquid interface are investigated via a volume averaging approach. The resulting equations exhibit the same structure as the standard Navier-Stokes equation for a Newtonian fluid with a constant viscosity, the effect of the solid phase fraction appearing in the drag force only. This considerably simplifies the use of the lattice Boltzmann method as a fluid dynamics solver in solidification simulations. Galilean invariance is also satisfied within this approach. Further, we investigate deviations between the diffuse and sharp interface flow profiles via both quasiexact numerical integration and lattice Boltzmann simulations. It emerges from these studies that the freedom in choosing the solid-liquid coupling parameter h provides a flexible way of optimizing the diffuse interface-flow simulations. Once h is adapted for a given spatial resolution, the simulated flow profiles reach an accuracy comparable to quasiexact numerical simulations. PMID:26382542
Analytical method to estimate resin cement diffusion into dentin
NASA Astrophysics Data System (ADS)
de Oliveira Ferraz, Larissa Cristina; Ubaldini, Adriana Lemos Mori; de Oliveira, Bruna Medeiros Bertol; Neto, Antonio Medina; Sato, Fracielle; Baesso, Mauro Luciano; Pascotto, Renata Corrêa
2016-05-01
This study analyzed the diffusion of two resin luting agents (resin cements) into dentin, with the aim of presenting an analytical method for estimating the thickness of the diffusion zone. Class V cavities were prepared in the buccal and lingual surfaces of molars (n=9). Indirect composite inlays were luted into the cavities with either a self-adhesive or a self-etch resin cement. The teeth were sectioned bucco-lingually and the cement-dentin interface was analyzed by using micro-Raman spectroscopy (MRS) and scanning electron microscopy. Evolution of peak intensities of the Raman bands, collected from the functional groups corresponding to the resin monomer (C–O–C, 1113 cm-1) present in the cements, and the mineral content (P–O, 961 cm-1) in dentin were sigmoid shaped functions. A Boltzmann function (BF) was then fitted to the peaks encountered at 1113 cm-1 to estimate the resin cement diffusion into dentin. The BF identified a resin cement-dentin diffusion zone of 1.8±0.4 μm for the self-adhesive cement and 2.5±0.3 μm for the self-etch cement. This analysis allowed the authors to estimate the diffusion of the resin cements into the dentin. Fitting the MRS data to the BF contributed to and is relevant for future studies of the adhesive interface.
Thermal diffusivity of nonflat plates using the flash method
Salazar, Agustin; Fuente, Raquel; Apinaniz, Estibaliz; Mendioroz, Arantza
2011-01-15
The flash method is the standard technique to measure the thermal diffusivity of solid samples. It consists of heating the front surface of an opaque sample by a brief light pulse and detecting the temperature evolution at its rear surface. The thermal diffusivity is obtained by measuring the time corresponding to the half maximum of the temperature rise, which only depends on the sample thickness and thermal diffusivity through a simple formula. Up to now, the flash method has been restricted to flat samples. In this work, we extend the flash method to measure the thermal diffusivity of nonflat samples. In particular, we focus on plates with cylindrical and spherical shapes. The theoretical model indicates that the same expression for flat samples can also be applied to cylindrical and spherical plates, except for extremely curved samples. Accordingly, a curvature limit for the application of the expression for flat samples is established. Flash measurements on lead foils of cylindrical shape confirm the validity of the model.
Method of making gas diffusion layers for electrochemical cells
Frisk, Joseph William; Boand, Wayne Meredith; Larson, James Michael
2002-01-01
A method is provided for making a gas diffusion layer for an electrochemical cell comprising the steps of: a) combining carbon particles and one or more surfactants in a typically aqueous vehicle to make a preliminary composition, typically by high shear mixing; b) adding one or more highly fluorinated polymers to said preliminary composition by low shear mixing to make a coating composition; and c) applying the coating composition to an electrically conductive porous substrate, typically by a low shear coating method.
NASA Astrophysics Data System (ADS)
Lin, Guoxing
2015-10-01
Pulsed field gradient (PFG) diffusion measurement has a lot of applications in NMR and MRI. Its analysis relies on the ability to obtain the signal attenuation expressions, which can be obtained by averaging over the accumulating phase shift distribution (APSD). However, current theoretical models are not robust or require approximations to get the APSD. Here, a new formalism, an effective phase shift diffusion (EPSD) equation method is presented to calculate the APSD directly. This is based on the idea that the gradient pulse effect on the change of the APSD can be viewed as a diffusion process in the virtual phase space (VPS). The EPSD has a diffusion coefficient, Kβ(t)D radβ/sα, where α is time derivative order and β is a space derivative order, respectively. The EPSD equations of VPS are built based on the diffusion equations of real space by replacing the diffusion coefficients and the coordinate system (from real space coordinate to virtual phase coordinate). Two different models, the fractal derivative model and the fractional derivative model from the literature were used to build the EPSD fractional diffusion equations. The APSD obtained from solving these EPSD equations were used to calculate the PFG signal attenuation. From the fractal derivative model the attenuation is exp(-γβgβδβDf1 tα), a stretched exponential function (SEF) attenuation, while from the fractional derivative model the attenuation is Eα,1(-γβgβδβDf2 tα), a Mittag-Leffler function (MLF) attenuation. The MLF attenuation can be reduced to SEF attenuation when α = 1, and can be approximated as a SEF attenuation when the attenuation is small. Additionally, the effect of finite gradient pulse widths (FGPW) is calculated. From the fractal derivative model, the signal attenuation including FGPW effect is exp[ -Df1 ∫0τ Kβ (t)dtα ] . The results obtained in this study are in good agreement with the results in literature. Several expressions that describe signal
Lin, Guoxing
2015-10-01
Pulsed field gradient (PFG) diffusion measurement has a lot of applications in NMR and MRI. Its analysis relies on the ability to obtain the signal attenuation expressions, which can be obtained by averaging over the accumulating phase shift distribution (APSD). However, current theoretical models are not robust or require approximations to get the APSD. Here, a new formalism, an effective phase shift diffusion (EPSD) equation method is presented to calculate the APSD directly. This is based on the idea that the gradient pulse effect on the change of the APSD can be viewed as a diffusion process in the virtual phase space (VPS). The EPSD has a diffusion coefficient, K(β)(t)D rad(β)/s(α), where α is time derivative order and β is a space derivative order, respectively. The EPSD equations of VPS are built based on the diffusion equations of real space by replacing the diffusion coefficients and the coordinate system (from real space coordinate to virtual phase coordinate). Two different models, the fractal derivative model and the fractional derivative model from the literature were used to build the EPSD fractional diffusion equations. The APSD obtained from solving these EPSD equations were used to calculate the PFG signal attenuation. From the fractal derivative model the attenuation is exp(-γ(β)g(β)δ(β)Df1t(α)), a stretched exponential function (SEF) attenuation, while from the fractional derivative model the attenuation is Eα,1(-γ(β)g(β)δ(β)Df2t(α)), a Mittag-Leffler function (MLF) attenuation. The MLF attenuation can be reduced to SEF attenuation when α=1, and can be approximated as a SEF attenuation when the attenuation is small. Additionally, the effect of finite gradient pulse widths (FGPW) is calculated. From the fractal derivative model, the signal attenuation including FGPW effect is exp[ -Df1∫0(τ) K(β)(t)dt(α)]. The results obtained in this study are in good agreement with the results in literature. Several expressions that
Instantaneous signal attenuation method for analysis of PFG fractional diffusions.
Lin, Guoxing
2016-08-01
An instantaneous signal attenuation (ISA) method for analyzing pulsed field gradient (PFG) fractional diffusion (FD) has been developed, which is modified from the propagator approach developed in 2001 by Lin et al. for analyzing PFG normal diffusion. Both, the current ISA method and the propagator method have the same fundamental basis that the total signal attenuation (SA) is the accumulation of all the ISA, and the ISA is the average SA of the whole diffusion system at each moment. However, the manner of calculating ISA is different. Unlike the use of the instantaneous propagator in the propagator method, the current method directly calculates ISA as A(K(t'),t'+dt')/A(K(t'),t'), where A(K(t'),t'+dt') and A(K(t'),t') are the SA. This modification makes the current method applicable to PFG FD as the instantaneous propagator may not be obtainable in FD. The ISA method was applied to study PFG SA including the effect of finite gradient pulse widths (FGPW) for free FD, restricted FD and the FD affected by a non-homogeneous gradient field. The SA expressions were successfully obtained for all three types of free FDs while other current methods still have difficulty in obtaining all of them. The results from this method agree with reported results such as that obtained by the effective phase shift diffusion equation (EPSDE) method. The M-Wright phase distribution approximation was also used to derive an SA expression for time FD as a comparison, which agrees with ISA method. Additionally, the continuous-time random walk (CTRW) simulation was performed to simulate the SA of PFG FD, and the simulation results agree with the analytical results. Particularly, the CTRW simulation results give good support to the analytical results including FGPW effect for free FD and restricted time FD based on a fractional derivative model where there have been no corresponding theoretical reports to date. The theoretical SA expressions including FGPW obtained here such as [Formula: see
Instantaneous signal attenuation method for analysis of PFG fractional diffusions
NASA Astrophysics Data System (ADS)
Lin, Guoxing
2016-08-01
An instantaneous signal attenuation (ISA) method for analyzing pulsed field gradient (PFG) fractional diffusion (FD) has been developed, which is modified from the propagator approach developed in 2001 by Lin et al. for analyzing PFG normal diffusion. Both, the current ISA method and the propagator method have the same fundamental basis that the total signal attenuation (SA) is the accumulation of all the ISA, and the ISA is the average SA of the whole diffusion system at each moment. However, the manner of calculating ISA is different. Unlike the use of the instantaneous propagator in the propagator method, the current method directly calculates ISA as A(K(t‧), t‧ + dt‧)/A(K(t‧), t‧), where A(K(t‧), t‧ + dt‧) and A(K(t‧), t‧) are the SA. This modification makes the current method applicable to PFG FD as the instantaneous propagator may not be obtainable in FD. The ISA method was applied to study PFG SA including the effect of finite gradient pulse widths (FGPW) for free FD, restricted FD and the FD affected by a non-homogeneous gradient field. The SA expressions were successfully obtained for all three types of free FDs while other current methods still have difficulty in obtaining all of them. The results from this method agree with reported results such as that obtained by the effective phase shift diffusion equation (EPSDE) method. The M-Wright phase distribution approximation was also used to derive an SA expression for time FD as a comparison, which agrees with ISA method. Additionally, the continuous-time random walk (CTRW) simulation was performed to simulate the SA of PFG FD, and the simulation results agree with the analytical results. Particularly, the CTRW simulation results give good support to the analytical results including FGPW effect for free FD and restricted time FD based on a fractional derivative model where there have been no corresponding theoretical reports to date. The theoretical SA expressions including FGPW obtained
Measurement of gas diffusion through soils: comparison of laboratory methods.
Allaire, Suzanne E; Lafond, Jonathan A; Cabral, Alexandre R; Lange, Sébastien F
2008-11-01
Gas movement through soils is important for ecosystems and engineering in many ways such as for microbial and plant respiration, passive methane oxidation in landfill covers and oxidation of mine residues. Diffusion is one of the most important gas movement processes and the determination of the diffusion coefficient is a crucial step in any study. Five laboratory methods used for measuring the relative gas diffusion coefficient (D(s)/D(o)) were compared using a loamy sand, a porous media commonly found in agricultural fields and in several engineered structures, such as in landfill final covers. In the absence of macropores, all methods gave rather similar values of D(s)/D(o). Methods allowing the study of microscale variability indicated that the presence of macropores highly influenced gas movement, thus the value of D(s)/D(o), which, near a macropore may be one order of magnitude higher than in regions without macropores. Repacked columns do not allow the study of heterogeneity in D(s)/D(o). Natural spatial variability in D(s)/D(o) due to water distribution and preferential pathways can only be studied in large systems, but these systems are difficult to handle. Advantages and disadvantages of each method are discussed. PMID:18974902
Some basic mathematical methods of diffusion theory. [emphasis on atmospheric applications
NASA Technical Reports Server (NTRS)
Giere, A. C.
1977-01-01
An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.
A Numerical Method for Determining Diffusivity from Annealing Experiments
NASA Astrophysics Data System (ADS)
Harris-Kuhlman, K. R.; Kulcinski, G. L.
1998-12-01
Terrestrial analogs of lunar ilmenite (FeTiO3) have been implanted with solar-wind energy 4He at 4 keV and 3He at 3 keV using Plasma Source Ion Implantation (PSII). Isochronal annealing of the samples revealed thermally induced 4He evolution similar to the helium release of the Apollo 11 regoliths reported by Pepin, et. al., [1970]. These annealing experiments are analyzed with a three dimensional numerical method based on Fick's law for diffusion. An iterative method is used to calculate the diffusivity. The code uses an assumed diffusivity to calculate the amount of gas released during a temperature step. The initial depth profile of the implanted species is generated using the TRIM electronic stopping code [Ziegler, 1996]. The calculated value is compared to the measured value and a linear regression is used to calculate a new diffusivity until there is convergence within a specified tolerance level. The diffusivity as a function of temperature is then fitted to an Arrhenius equation. Analysis of results for 4 keV 4He on ilmenite shows two distinct regions of Arrehnius behavior with activation energies of 0.5 +/- 0.1 eV at emperatures below 800 deg C and 1.5 +/- 0.2 eV at temperatures from 800 deg C to 1100 deg C. Pepin, R. O., L. E. Nyquist, D. Phinney, and D. C. Black (1970) "Rare Gases in Apollo 11 Lunar Material," Proceedings of the Apollo 11 Lunar Science Conference, 2, pp. 1435-1454. Ziegler, J. P. (1996) SRIM Instruction Manual: The Stopping and Range of Ions in Matter, (Yorktown, New York: IBM - Research); based on Ziegler, J. P., J. P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids, (New York: Pergamon Press, 1985).
Linear method of fluorescent source reconstruction in a diffusion medium.
Janunts, Edgar; Pöschinger, Thomas; Brünner, Holger; Langenbucher, Achim
2008-01-01
A new method is described for obtaining a 2D reconstruction of a fluorescent source distribution inside a diffusion medium from planar measurements of the emission light at the surface after excitation by a plane wave. Point sources are implanted at known locations of a rectangular phantom. The forward model of the photon transport is based on the diffusion approximation of the radiative transport equation (RTE) for homogeneous media. This can be described by a hierarchical system of two time-independent RTE's, one for the excitation plane wave originating from the external light source to the medium and another one for the fluorescence emission originating from the fluorophore marker to the detector. A linear inverse source problem was solved for image reconstruction. The applicability of the theoretical method is demonstrated in some representative working examples. For an optimization of the problem we used least squares minimization technique. PMID:18826162
Support Operators Method for the Diffusion Equation in Multiple Materials
Winters, Andrew R.; Shashkov, Mikhail J.
2012-08-14
A second-order finite difference scheme for the solution of the diffusion equation on non-uniform meshes is implemented. The method allows the heat conductivity to be discontinuous. The algorithm is formulated on a one dimensional mesh and is derived using the support operators method. A key component of the derivation is that the discrete analog of the flux operator is constructed to be the negative adjoint of the discrete divergence, in an inner product that is a discrete analog of the continuum inner product. The resultant discrete operators in the fully discretized diffusion equation are symmetric and positive definite. The algorithm is generalized to operate on meshes with cells which have mixed material properties. A mechanism to recover intermediate temperature values in mixed cells using a limited linear reconstruction is introduced. The implementation of the algorithm is verified and the linear reconstruction mechanism is compared to previous results for obtaining new material temperatures.
A localized meshless method for diffusion on folded surfaces
NASA Astrophysics Data System (ADS)
Cheung, Ka Chun; Ling, Leevan; Ruuth, Steven J.
2015-09-01
Partial differential equations (PDEs) on surfaces arise in a variety of application areas including biological systems, medical imaging, fluid dynamics, mathematical physics, image processing and computer graphics. In this paper, we propose a radial basis function (RBF) discretization of the closest point method. The corresponding localized meshless method may be used to approximate diffusion on smooth or folded surfaces. Our method has the benefit of having an a priori error bound in terms of percentage of the norm of the solution. A stable solver is used to avoid the ill-conditioning that arises when the radial basis functions (RBFs) become flat.
A radial basis function Galerkin method for inhomogeneous nonlocal diffusion
Lehoucq, Richard B.; Rowe, Stephen T.
2016-02-01
We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.
Minutes to Millennia: Diffusion Methods in Subduction-Related Volcanism
NASA Astrophysics Data System (ADS)
Morgan, D. J.; Allan, A.; Wilson, C. J. N.; Charlier, B. L.; Davidson, J.
2014-12-01
Diffusion methods have several advantages as relative geochronometers in volcano-related magmatic processes: diffusion stops on eruption, locking in short timescale information; methods are relatively easy to implement; and suitable material is generally abundant. Such methods also pose significant, accompanying challenges: the need for accurate melt palaeothermometry, uncertainties in diffusion parameters, and sometimes even a cryptic connection between mineral zonation and timescale. As all timescales are relative to an event, timing is not absolute, and care must be taken in interpretation. Yet for all the difficulties, diffusion tools are seeing more widespread usage. This has come about because of the potential of diffusion methods to interrogate certain pre-eruptive processes operating over timescales of relevance to human timescales and responses, having direct bearing on hazard mitigation procedures. In studying subduction zone systems we have a wide range of minerals to choose from but will, in subduction-related, andesitic-to-rhyolitic systems, usually be operating away from the relatively well-constrained system of olivine, and instead be dealing with mineral phases that offer different challenges, such as plagioclase, quartz, sanidine, amphibole, orthopyroxene, Fe-Ti oxides and mica. Timescales here span a wide range across different mineral-element combinations, from minutes for Li in plagioclase and quartz to days by Fe-Ti oxides, years by orthopyroxene Fe-Mg and decades to millennia with plagioclase, sanidine and quartz. This contribution will focus on the interpretation of diffusion signals in minerals found in subduction-related volcanic systems. To understand what any modelled timescale means, the process which formed the relevant zonation pattern is absolutely key, yet often elusive. Variations in P, T, X conditions really drive the crystallisation process yet certain zonation patterns are non-unique. This ambiguity necessitates painstaking
Diffusely reflecting paints including polytetrafluoroethylene and method of manufacture
NASA Technical Reports Server (NTRS)
Schutt, J. B.; Shai, M. C. (Inventor)
1985-01-01
The invention pertains to a high diffuse, reflective paint comprising an alcohol soluble binder, polytetrafluoroethylene (TFE) and an alcohol for coating a substrate and forming an optical reference with a superior Lambertian characteristic. A method for making the paint by first mixing the biner and alcohol, and thereafter by mixing in outgassed TFE is described. A wetting agent may be employed to aid the mixing process.
Effective Thermal Diffusivity Study of Powder Biocomposites via Photoacoustic Method
NASA Astrophysics Data System (ADS)
Mariucci, V. V. G.; da Cruz, J. A.; Bonadio, T. G. M.; Picolloto, A. M.; Weinand, W. R.; Lima, W. M.; Medina, A. N.; Bento, A. C.
2015-10-01
The effective thermal diffusivity for biocomposites of hydroxyapatite (HAp), and niobium pentoxide (Nb2O5) on powder form was studied via photoacoustic method adapted for porous materials. The concentration of each element was accompanied with the results of X-ray diffractometer (XRD) and scanning electron microscopy (SEM). A theoretical model for the thermal coupling of a three layered sample, designed to contain the powder material is proposed. The method for mixtures obeyed the formula [(1 - x) H A p + ( x) N b 2O5] for 0.0 ≤ x ≤ 1.0. Experimental results for effective thermal diffusivity ranged between (6.4 ± 0.3) × 10-6 m2 s-1 and (9.8 ± 0.4) × 10-6 m2 s-1 for x ≤ 0.7. Values of the effective thermal diffusivity have decreased sharply to (0.7 ± 0.03) ×10-6 m2 s-1 for x > 0.7. SEM micrographs showed a coating of HAp over the particles of Nb2O5 for some mixtures.
A diffusive information preservation method for small Knudsen number flows
NASA Astrophysics Data System (ADS)
Fei, Fei; Fan, Jing
2013-06-01
The direct simulation Monte Carlo (DSMC) method is a powerful particle-based method for modeling gas flows. It works well for relatively large Knudsen (Kn) numbers, typically larger than 0.01, but quickly becomes computationally intensive as Kn decreases due to its time step and cell size limitations. An alternative approach was proposed to relax or remove these limitations, based on replacing pairwise collisions with a stochastic model corresponding to the Fokker-Planck equation [J. Comput. Phys., 229, 1077 (2010); J. Fluid Mech., 680, 574 (2011)]. Similar to the DSMC method, the downside of that approach suffers from computationally statistical noise. To solve the problem, a diffusion-based information preservation (D-IP) method has been developed. The main idea is to track the motion of a simulated molecule from the diffusive standpoint, and obtain the flow velocity and temperature through sampling and averaging the IP quantities. To validate the idea and the corresponding model, several benchmark problems with Kn ˜ 10-3-10-4 have been investigated. It is shown that the IP calculations are not only accurate, but also efficient because they make possible using a time step and cell size over an order of magnitude larger than the mean collision time and mean free path, respectively.
A diffusive information preservation method for small Knudsen number flows
Fei, Fei; Fan, Jing
2013-06-15
The direct simulation Monte Carlo (DSMC) method is a powerful particle-based method for modeling gas flows. It works well for relatively large Knudsen (Kn) numbers, typically larger than 0.01, but quickly becomes computationally intensive as Kn decreases due to its time step and cell size limitations. An alternative approach was proposed to relax or remove these limitations, based on replacing pairwise collisions with a stochastic model corresponding to the Fokker–Planck equation [J. Comput. Phys., 229, 1077 (2010); J. Fluid Mech., 680, 574 (2011)]. Similar to the DSMC method, the downside of that approach suffers from computationally statistical noise. To solve the problem, a diffusion-based information preservation (D-IP) method has been developed. The main idea is to track the motion of a simulated molecule from the diffusive standpoint, and obtain the flow velocity and temperature through sampling and averaging the IP quantities. To validate the idea and the corresponding model, several benchmark problems with Kn ∼ 10{sup −3}–10{sup −4} have been investigated. It is shown that the IP calculations are not only accurate, but also efficient because they make possible using a time step and cell size over an order of magnitude larger than the mean collision time and mean free path, respectively.
Newton-Krylov methods applied to nonequilibrium radiation diffusion
Knoll, D.A.; Rider, W.J.; Olsen, G.L.
1998-03-10
The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step.
On matrix diffusion: formulations, solution methods and qualitative effects
NASA Astrophysics Data System (ADS)
Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme
On matrix diffusion: formulations, solution methods and qualitative effects
NASA Astrophysics Data System (ADS)
Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme
Diffuse optical methods for assessing breast cancer chemotherapy
NASA Astrophysics Data System (ADS)
Tromberg, Bruce J.
2014-03-01
In his talk, "Diffuse Optical Methods for Assessing Breast Cancer Chemotherapy," SPIE Fellow Bruce Tromberg (Beckman Laser Institute and Medical Clinic) describes a method combining frequency domain photon migration, essentially a method of tracking photon motion in tissue, with a NIR spectroscopy technique using 850nm LEDs. The result is a scatter corrected absorption spectra. The technique takes advantage of elevated blood and water levels and decreased lipid levels in the presence of tumors to provide a more accurate mapping of the breast, allowing more effective treatment. Tromberg's team recently completed their first full mapping of the breast and have taken the instrument from a standalone unit to a portable one suitable for travel. In addition to providing feedback to enhance breast cancer treatment, Tromberg expects that this technique will be applicable in treating other forms of cancer as well.
Compact finite volume methods for the diffusion equation
NASA Technical Reports Server (NTRS)
Rose, Milton E.
1989-01-01
The paper describes an approach to treating initial-boundary-value problems by finite volume methods in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second-order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and ADI methods.
Extrapolation techniques applied to matrix methods in neutron diffusion problems
NASA Technical Reports Server (NTRS)
Mccready, Robert R
1956-01-01
A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.
Compact finite volume methods for the diffusion equation
NASA Technical Reports Server (NTRS)
Rose, Milton E.
1989-01-01
An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.
A method for quantitatively estimating diffuse and discrete hydrothermal discharge
NASA Astrophysics Data System (ADS)
Baker, Edward T.; Massoth, Gary J.; Walker, Sharon L.; Embley, Robert W.
1993-07-01
Submarine hydrothermal fluids discharge as undiluted, high-temperature jets and as diffuse, highly diluted, low-temperature percolation. Estimates of the relative contribution of each discharge type, which are important for the accurate determination of local and global hydrothermal budgets, are difficult to obtain directly. In this paper we describe a new method of using measurements of hydrothermal tracers such as Fe/Mn, Fe/heat, and Mn/heat in high-temperature fluids, low-temperature fluids, and the neutrally buoyant plume to deduce the relative contribution of each discharge type. We sampled vent fluids from the north Cleft vent field on the Juan de Fuca Ridge in 1988, 1989 and 1991, and plume samples every year from 1986 to 1991. The tracers were, on average, 3 to 90 times greater in high-temperature than in low-temperature fluids, with plume values intermediate. A mixing model calculates that high-temperature fluids contribute only ˜ 3% of the fluid mass flux but > 90% of the hydrothermal Fe and > 60% of the hydrothermal Mn to the overlying plume. Three years of extensive camera-CTD sled tows through the vent field show that diffuse venting is restricted to a narrow fissure zone extending for 18 km along the axial strike. Linear plume theory applied to the temperature plumes detected when the sled crossed this zone yields a maximum likelihood estimate for the diffuse heat flux of8.9 × 10 4 W/m, for a total flux of 534 MW, considering that diffuse venting is active along only one-third of the fissure system. For mean low- and high-temperature discharge of 25°C and 319°C, respectively, the discrete heat flux must be 266 MW to satisfy the mass flux partitioning. If the north Cleft vent field is globally representative, the assumption that high-temperature discharge dominates the mass flux in axial vent fields leads to an overestimation of the flux of many non-conservative hydrothermal species by about an order of magnitude.
An efficient method for model refinement in diffuse optical tomography
NASA Astrophysics Data System (ADS)
Zirak, A. R.; Khademi, M.
2007-11-01
Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.
A Critical Study of Agglomerated Multigrid Methods for Diffusion
NASA Technical Reports Server (NTRS)
Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.
2011-01-01
Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.
A Critical Study of Agglomerated Multigrid Methods for Diffusion
NASA Technical Reports Server (NTRS)
Thomas, James L.; Nishikawa, Hiroaki; Diskin, Boris
2009-01-01
Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.
NASA Astrophysics Data System (ADS)
Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-05-01
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.
Evaluation of Hamaker coefficients using Diffusion Monte Carlo method
NASA Astrophysics Data System (ADS)
Maezono, Ryo; Hongo, Kenta
We evaluated the Hamaker's constant for Cyclohexasilane to investigate its wettability, which is used as an ink of 'liquid silicon' in 'printed electronics'. Taking three representative geometries of the dimer coalescence (parallel, lined, and T-shaped), we evaluated these binding curves using diffusion Monte Carlo method. The parallel geometry gave the most long-ranged exponent, ~ 1 /r6 , in its asymptotic behavior. Evaluated binding lengths are fairly consistent with the experimental density of the molecule. The fitting of the asymptotic curve gave an estimation of Hamaker's constant being around 100 [zJ]. We also performed a CCSD(T) evaluation and got almost similar result. To check its justification, we applied the same scheme to Benzene and compared the estimation with those by other established methods, Lifshitz theory and SAPT (Symmetry-adopted perturbation theory). The result by the fitting scheme turned to be twice larger than those by Lifshitz and SAPT, both of which coincide with each other. It is hence implied that the present evaluation for Cyclohexasilane would be overestimated.
NASA Astrophysics Data System (ADS)
Wang, Fei; Kobayashi, Yasukazu; Muhammad, Usman; Wang, Dezheng; Wang, Yao
2016-03-01
The use of numerical analysis to solve the diffusion equation in the uptake method allowed the measurement of molecular diffusivity in a zeolite with a variable pressure around it. The diffusivity was obtained from the data in the measurement of the adsorption isotherm, which means that the diffusivity measurement now needs neither a special instrument nor procedure. The diffusivities of all the gases are readily available from the measurement of their adsorption isotherms and these data include how the diffusivity changes versus adsorbed concentration. The modeling introduced can also be used for a zeolite with a surface barrier.
Method for applying a diffusion barrier interlayer for high temperature components
Wei, Ronghua; Cheruvu, Narayana S.
2016-03-08
A coated substrate and a method of forming a diffusion barrier coating system between a substrate and a MCrAl coating, including a diffusion barrier coating deposited onto at least a portion of a substrate surface, wherein the diffusion barrier coating comprises a nitride, oxide or carbide of one or more transition metals and/or metalloids and a MCrAl coating, wherein M includes a transition metal or a metalloid, deposited on at least a portion of the diffusion barrier coating, wherein the diffusion barrier coating restricts the inward diffusion of aluminum of the MCrAl coating into the substrate.
NASA Astrophysics Data System (ADS)
Ringermacher, Harry I.
2013-04-01
We describe an analysis of a flash thermographic method to measure thermal diffusivity that is particularly insensitive to heat loss mechanisms near thermal boundaries. This approach is an alternative to the "Parker method" which requires that a plate-like region subject to a uniform energy flux must reach a maximum constant temperature in order to obtain an accurate measurement of thermal diffusivity at the half-temperature point in time. The present approach relies on evaluating another unique point, the inflection point, of the same back-side thermal response curve as Parker's or, from the front side, using a contrast versus time curve in the sample region of interest. This inflection point occurs so early in the response history that little heat loss, for example, near heat-sink boundaries or surface convection, is expressed. Since the method is insensitive to the achieved temperature, it is also insensitive to surface emissivity variations.
Improved agar diffusion method for detecting residual antimicrobial agents.
Tsai, C E; Kondo, F
2001-03-01
The improved agar diffusion method for determination of residual antimicrobial agents was investigated, and the sensitivities of various combinations of test organisms and assay media were determined using 7 organisms, 5 media, and 31 antimicrobial agents. Bacillus stearothermophilus and synthetic assay medium (SAM) showed the greatest sensitivity for screening penicillins (penicillin G and ampicillin). The combination of Bacillus subtilis and minimum medium (MM) was the most sensitive for tetracyclines (oxytetracycline and chlortetracycline), B. stearothermophilus and SAM or Micrococcus luteus and Mueller-Hinton agar (MHA) for detecting tylosin and erythromycin, B. subtilis and MHA for aminoglycosides (streptomycin, kanamycin, gentamicin, and dihydrostreptomycin), B. stearothermophilus and SAM for polyethers (salinomycin and lasalocid), and B. subtilis and MM or Clostridium perfringens and GAM for polypeptides (thiopeptin, enramycin, virginiamycin, and bacitracin). However, gram-negative bacterium Escherichia coli ATCC 27166 and MM were better for screening for colistin and polymixin-B. For detecting the synthetic drugs tested, the best combination was B. subtilis and MM for sulfonamides, E. coli 27166 and MM for quinolones (oxolinic acid and nalidixic acid), B. subtilis and MM for furans (furazolidone), and the bioluminescent bacterium Photobacterium phosphoreum and luminescence assay medium for chloramphenicol and oxolinic acid. The results showed that the use of four assay plates, B. stearothermophilus and SAM, B. subtilis and MM, M. luteus and MHA, and E. coli 27166 and MM, was superior to the currently available techniques for screening for residual antimicrobial agents in edible animal tissues. PMID:11252480
Lessing, Paul A.
2008-07-22
An electrochemically active hydrogen diffusion barrier which comprises an anode layer, a cathode layer, and an intermediate electrolyte layer, which is conductive to protons and substantially impermeable to hydrogen. A catalytic metal present in or adjacent to the anode layer catalyzes an electrochemical reaction that converts any hydrogen that diffuses through the electrolyte layer to protons and electrons. The protons and electrons are transported to the cathode layer and reacted to form hydrogen. The hydrogen diffusion barrier is applied to a polymeric substrate used in a storage tank to store hydrogen under high pressure. A storage tank equipped with the electrochemically active hydrogen diffusion barrier, a method of fabricating the storage tank, and a method of preventing hydrogen from diffusing out of a storage tank are also disclosed.
Lessing, Paul A.
2004-09-07
An electrochemically active hydrogen diffusion barrier which comprises an anode layer, a cathode layer, and an intermediate electrolyte layer, which is conductive to protons and substantially impermeable to hydrogen. A catalytic metal present in or adjacent to the anode layer catalyzes an electrochemical reaction that converts any hydrogen that diffuses through the electrolyte layer to protons and electrons. The protons and electrons are transported to the cathode layer and reacted to form hydrogen. The hydrogen diffusion barrier is applied to a polymeric substrate used in a storage tank to store hydrogen under high pressure. A storage tank equipped with the electrochemically active hydrogen diffusion barrier, a method of fabricating the storage tank, and a method of preventing hydrogen from diffusing out of a storage tank are also disclosed.
An integration factor method for stochastic and stiff reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Ta, Catherine; Wang, Dongyong; Nie, Qing
2015-08-01
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction-diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction-diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction-diffusion equations arising from models in biology and physical sciences.
An integration factor method for stochastic and stiff reaction–diffusion systems
Ta, Catherine; Wang, Dongyong; Nie, Qing
2015-08-15
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction–diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction–diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction–diffusion equations arising from models in biology and physical sciences.
AEROSOL SIZE MEASUREMENT BY ELECTRICAL MOBILITY AND DIFFUSION ANALYSIS - A COMPARISON OF METHODS
The principle of the electrical aerosol analyzer method is reviewed and the diffusion battery method is described in detail. An appendix explains the basis of the calculations used. The diffusion battery method is complicated by counting losses of very small particles, inherent t...
A method for distinguishing between propagons, diffusions, and locons
NASA Astrophysics Data System (ADS)
Seyf, Hamid Reza; Henry, Asegun
2016-07-01
The majority of intuition on phonon transport has been derived from studies of homogenous crystalline solids, where the atomic composition and structure are periodic. For this specific class of materials, the solutions to the equations of motions for the atoms (in the harmonic limit) result in plane wave modulated velocity fields for the normal modes of vibration. However, it has been known for several decades that whenever a system lacks periodicity, either compositional or structural, the normal modes of vibration can still be determined (in the harmonic limit), but the solutions take on different characteristics and many modes may not be plane wave modulated. Previous work has classified the types of vibrations into three primary categories, namely, propagons, diffusions, and locons. One can use the participation ratio to distinguish locons, from propagons and diffusons, which measures the extent to which a mode is localized. However, distinguishing between propagons and diffusons has remained a challenge, since both are spatially delocalized. Here, we present a new method that quantifies the extent to which a mode's character corresponds to a propagating mode, e.g., exhibits plane wave modulation. This then allows for clear and quantitative distinctions between propagons and diffusons. By resolving this issue quantitatively, one can now automate the classification of modes for any arbitrary material or structure, subject to a single constraint that the atoms must vibrate stably around their respective equilibrium sites. Several example test cases are studied including crystalline silicon and germanium, crystalline silicon with different defect concentrations, as well as amorphous silicon, germanium, and silica.
A Multiresolution Method for Parameter Estimation of Diffusion Processes
Kou, S. C.; Olding, Benjamin P.; Lysy, Martin; Liu, Jun S.
2014-01-01
Diffusion process models are widely used in science, engineering and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data is typically only observed at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation, and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems – one in biophysics and two in finance – one of which features a multivariate diffusion model with an entirely unobserved component. PMID:25328259
NASA Astrophysics Data System (ADS)
Bultinck, E.; Mahieu, S.; Depla, D.; Bogaerts, A.
2010-07-01
'Bohm diffusion' causes the electrons to diffuse perpendicularly to the magnetic field lines. However, its origin is not yet completely understood: low and high frequency electric field fluctuations are both named to cause Bohm diffusion. The importance of including this process in a Monte Carlo (MC) model is demonstrated by comparing calculated ionization rates with particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. A good agreement is found with a Bohm diffusion parameter of 0.05, which corresponds well to experiments. Since the PIC/MCC method accounts for fast electric field fluctuations, we conclude that Bohm diffusion is caused by fast electric field phenomena.
A new gauge-invariant method for diagnosing eddy diffusivities
NASA Astrophysics Data System (ADS)
Mak, J.; Maddison, J. R.; Marshall, D. P.
2016-08-01
Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke mixing of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from unfiltered fluxes are thus contaminated by the presence of these rotational components. Here a new methodology is applied whereby eddy diffusivities are diagnosed directly from the eddy force function. The eddy force function depends only upon flux divergences, is independent of any rotational flux components, and is inherently non-local and smooth. A one-shot inversion procedure is applied, minimising the mis-match between parameterised force functions and force functions derived from eddy resolving calculations. This enables diffusivities associated with the eddy potential vorticity and Gent-McWilliams coefficients associated with eddy buoyancy fluxes to be diagnosed. This methodology is applied to multi-layer quasi-geostrophic ocean gyre simulations. It is found that: (i) a strictly down-gradient scheme for mixing potential vorticity and quasi-geostrophic buoyancy has limited success in reducing the mis-match compared to one with no sign constraint on the eddy diffusivity or Gent--McWilliams coefficient, with prevalent negative signals around the time-mean jet; (ii) the diagnostic is successful away from the jet region and wind-forced top layer; (iii) the locations of closed mean stream lines correlate with signals of positive eddy potential vorticity diffusivity; (iv) there is indication that the magnitude of the eddy potential vorticity diffusivity correlates well with the eddy energy. Implications for parameterisation are discussed in light of these diagnostic results.
Multilevel methods for transport equations in diffusive regimes
NASA Technical Reports Server (NTRS)
Manteuffel, Thomas A.; Ressel, Klaus
1993-01-01
We consider the numerical solution of the single-group, steady state, isotropic transport equation. An analysis by means of the moment equations shows that a discrete ordinate S(sub N) discretization in direction (angle) with a least squares finite element discretization in space does not behave properly in the diffusion limit. A scaling of the S(sub N) equations is introduced so that the least squares discretization has the correct diffusion limit. For the resulting discrete system a full multigrid algorithm was developed.
Thermal diffusivity measurement by lock-in photothermal shadowgraph method
NASA Astrophysics Data System (ADS)
Cifuentes, A.; Alvarado, S.; Cabrera, H.; Calderón, A.; Marín, E.
2016-04-01
Here, we present a novel application of the shadowgraph technique for obtaining the thermal diffusivity of an opaque solid sample, inspired by the orthogonal skimming photothermal beam deflection technique. This new variant utilizes the shadow projected by the sample when put against a collimated light source. The sample is then heated periodically by another light beam, giving rise to thermal waves, which propagate across it and through its surroundings. Changes in the refractive index of the surrounding media due to the heating distort the shadow. This phenomenon is recorded and lock-in amplified in order to determine the sample's thermal diffusivity.
Diffusion NMR methods applied to xenon gas for materials study.
Mair, R W; Rosen, M S; Wang, R; Cory, D G; Walsworth, R L
2002-12-01
We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. PMID:12807139
Diffusion NMR methods applied to xenon gas for materials study
NASA Technical Reports Server (NTRS)
Mair, R. W.; Rosen, M. S.; Wang, R.; Cory, D. G.; Walsworth, R. L.
2002-01-01
We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. c2002 John Wiley & Sons, Ltd.
Method of independently operating a group of stages within a diffusion cascade
Benedict, Manson; Fruit, Allen J.; Levey, Horace B.
1976-06-08
1. A method of operating a group of the diffusion stages of a productive diffusion cascade with countercurrent flow, said group comprising a top and a bottom stage, which comprises isolating said group from said cascade, circulating the diffused gas produced in said top stage to the feed of said bottom stage while at the same time circulating the undiffused gas from said bottom stage to the feed of said top stage whereby major changes in
Kernel weights optimization for error diffusion halftoning method
NASA Astrophysics Data System (ADS)
Fedoseev, Victor
2015-02-01
This paper describes a study to find the best error diffusion kernel for digital halftoning under various restrictions on the number of non-zero kernel coefficients and their set of values. As an objective measure of quality, WSNR was used. The problem of multidimensional optimization was solved numerically using several well-known algorithms: Nelder- Mead, BFGS, and others. The study found a kernel function that provides a quality gain of about 5% in comparison with the best of the commonly used kernel introduced by Floyd and Steinberg. Other kernels obtained allow to significantly reduce the computational complexity of the halftoning process without reducing its quality.
Volume imaging with diffuse light: method, device, and clinical application
NASA Astrophysics Data System (ADS)
Hampel, Uwe; Schleicher, Eckhard; Freyer, Richard
2000-11-01
Diffuse optical imaging and tomography is of some interest in the diagnosis of testicular pathologies. For a clinical evaluation of 3D optical tomography a special laser scanning device as well as dedicated tomography algorithms have been developed. With the device we are able to obtain continuous- wave tomographic scans from an object under investigation using different laser wavelengths. Tomographic image reconstruction is based on the solution of the linearized inverse problem of optical absorption imaging for a three- dimensional volume. Priority is given to a spatial resolution adapted volume discretization and an efficient matrix solution algorithm based on singular value decomposition.
Cosmic-ray diffusion modeling: Solutions using variational methods
NASA Astrophysics Data System (ADS)
Tautz, R. C.; Lerche, I.
2013-05-01
The diffusion of energetic particles in turbulent magnetic fields is usually described via the two-point, two-time velocity correlation function. A variational principle is used to determine the characteristic function that results from the Fourier-transformed correlation function. Both for a linear approximation and for the wave vector set to zero, explicit solutions are derived that depend on the Fokker-Planck coefficient of pitch-angle scattering. It is shown that, for an isotropic form of the Fokker-Planck coefficient, the characteristic function is divergent, which can be remedied only by using a Fokker-Planck coefficient that is finite at all pitch angles.
A Review of Diffusion Tensor Magnetic Resonance Imaging Computational Methods and Software Tools
Hasan, Khader M.; Walimuni, Indika S.; Abid, Humaira; Hahn, Klaus R.
2010-01-01
In this work we provide an up-to-date short review of computational magnetic resonance imaging (MRI) and software tools that are widely used to process and analyze diffusion-weighted MRI data. A review of different methods used to acquire, model and analyze diffusion-weighted imaging data (DWI) is first provided with focus on diffusion tensor imaging (DTI). The major preprocessing, processing and post-processing procedures applied to DTI data are discussed. A list of freely available software packages to analyze diffusion MRI data is also provided. PMID:21087766
A review of diffusion tensor magnetic resonance imaging computational methods and software tools.
Hasan, Khader M; Walimuni, Indika S; Abid, Humaira; Hahn, Klaus R
2011-12-01
In this work we provide an up-to-date short review of computational magnetic resonance imaging (MRI) and software tools that are widely used to process and analyze diffusion-weighted MRI data. A review of different methods used to acquire, model and analyze diffusion-weighted imaging data (DWI) is first provided with focus on diffusion tensor imaging (DTI). The major preprocessing, processing and post-processing procedures applied to DTI data are discussed. A list of freely available software packages to analyze diffusion MRI data is also provided. PMID:21087766
A multigrid Newton-Krylov method for flux-limited radiation diffusion
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-09-01
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.
Validation of the diffusion-barrier charcoal canister method
Martz, D.E.; George, J.L.; Mamich, S.T.; Langner, G.H. Jr.
1989-05-01
A six-month study was conducted by the Technical Measurements Center, US Department of Energy Grand Junction Projects Office, to evaluate the accuracy and reliability of indoor radon measurements using an intermittent diffusion-barrier charcoal canister sampling protocol. Diffusion-barrier charcoal canisters (DBCC) were exposed for seven days in sixteen occupied residences each week during the 26-week study. The radon concentrations measured by the DBCCs were compared to radon concentrations measured by triplicate sets of four different types of alpha-track monitors and integrated hourly radon concentrations measured by a Pylon Model AB-5 continuous radon monitor. The results were also compared with radon-daughter concentrations measured in these same residences by an Eberline WLM-1 working level monitor. Excellent agreement was observed between the integrated mean radon concentrations measured by the DBCCs compared with the six-month alpha-track results, and between the weekly DBCC readings and average weekly radon concentrations measured by the Pylon radon monitors. An intermittent sampling protocol employing six weekly DBCC measurements spaced approximately every two months throughout the year should provide estimates of the average annual indoor radon concentrations that meet the criteria established for the Grand Junction Remedial Action Program. 9 refs., 17 figs., 9 tabs.
A fully implicit method for 3D quasi-steady state magnetic advection-diffusion.
Siefert, Christopher; Robinson, Allen Conrad
2009-09-01
We describe the implementation of a prototype fully implicit method for solving three-dimensional quasi-steady state magnetic advection-diffusion problems. This method allows us to solve the magnetic advection diffusion equations in an Eulerian frame with a fixed, user-prescribed velocity field. We have verified the correctness of method and implementation on two standard verification problems, the Solberg-White magnetic shear problem and the Perry-Jones-White rotating cylinder problem.
Experimental Verification to Obtain Intrinsic Thermal Diffusivity by Laser-Flash Method
NASA Astrophysics Data System (ADS)
Akoshima, M.; Hay, B.; Neda, M.; Grelard, M.
2013-05-01
There is a need to obtain highly reliable values of thermophysical properties. The thermal conductivity of solids is often calculated from the thermal diffusivity, specific heat, and density, respectively, measured by the laser-flash method, differential scanning calorimetry, and Archimedes' method. The laser-flash method is one of the most well-known methods for measuring the thermal diffusivity of solids above room temperature. This method is very convenient to measure the thermal diffusivity without contact in a short time. On the other hand, it is considered as an absolute reference measurement method, in particular, because only measurements of basic quantities such as time, temperature, length, and electrical quantities are required, and because the uncertainty of measurement can be analytically evaluated. However, it could be difficult in some cases to obtain reliable thermal-diffusivity values. The measurement results can indeed depend on experimental conditions; in particular, the pulse heating energy. A procedure to obtain the intrinsic thermal-diffusivity value was proposed by National Metrology Institute of Japan (NMIJ). Here, "intrinsic" means unique for the material, independent of measurement conditions. In this method, apparent thermal-diffusivity values are first measured by changing the pulse heating energy at the same test temperature. Then, the intrinsic thermal diffusivity is determined by extrapolating these apparent thermal diffusivities to a zero energy pulse. In order to verify and examine the applicability of the procedure for intrinsic thermal-diffusivity measurements, we have measured the thermal diffusivity of some materials (metals, ceramics) using the laser-flash method with this extrapolation procedure. NMIJ and Laboratoire National de Metrologie et d'essais (LNE) have laser-flash thermal-diffusivity measurement systems that are traceable to SI units. The thermal diffusivity measured by NMIJ and LNE on four materials shows good
Lou, Shishu; Zhu, Huishi; Hu, Shaoxu; Zhao, Chunhua; Han, Peide
2015-01-01
Characterization of the diffusion length of solar cells in space has been widely studied using various methods, but few studies have focused on a fast, simple way to obtain the quantified diffusion length distribution on a silicon wafer. In this work, we present two different facile methods of doing this by fitting photoluminescence images taken in two different wavelength ranges or from different sides. These methods, which are based on measuring the ratio of two photoluminescence images, yield absolute values of the diffusion length and are less sensitive to the inhomogeneity of the incident laser beam. A theoretical simulation and experimental demonstration of this method are presented. The diffusion length distributions on a polycrystalline silicon wafer obtained by the two methods show good agreement. PMID:26364565
Lou, Shishu; Zhu, Huishi; Hu, Shaoxu; Zhao, Chunhua; Han, Peide
2015-01-01
Characterization of the diffusion length of solar cells in space has been widely studied using various methods, but few studies have focused on a fast, simple way to obtain the quantified diffusion length distribution on a silicon wafer. In this work, we present two different facile methods of doing this by fitting photoluminescence images taken in two different wavelength ranges or from different sides. These methods, which are based on measuring the ratio of two photoluminescence images, yield absolute values of the diffusion length and are less sensitive to the inhomogeneity of the incident laser beam. A theoretical simulation and experimental demonstration of this method are presented. The diffusion length distributions on a polycrystalline silicon wafer obtained by the two methods show good agreement. PMID:26364565
Maki, Yasuyuki; Furusawa, Kazuya; Yasuraoka, Sho; Okamura, Hideki; Hosoya, Natsuki; Sunaga, Mari; Dobashi, Toshiaki; Sugimoto, Yasunobu; Wakabayashi, Katsuzo
2014-08-01
Molecular orientation in anisotropic gels of chitosan, Curdlan and DNA obtained by dialysis of those aqueous solutions in gelation-inducing solutions was investigated. In this diffusion method (or dialysis method), the gel formation was induced by letting small molecules diffuse in or out of the polymer solutions through the surface. For the gels of DNA and chitosan, the polymer chains aligned perpendicular to the diffusion direction. The same direction of molecular orientation was observed for the Curdlan gel prepared in the dialysis cell. On the other hand, a peculiar nature was observed for the Curdlan gel prepared in the dialysis tube: the molecular orientation was perpendicular to the diffusion direction in the outermost layer of the gel, while the orientation was parallel to the diffusion direction in the inner translucent layer. The orientation parallel to the diffusion direction is attributed to a small deformation of the inner translucent layer caused by a slight shrinkage of the central region after the gel formation. At least near the surface of the gel, the molecular orientation perpendicular to the diffusion direction is a universal characteristic for the gels prepared by the diffusion method. PMID:24751255
NASA Technical Reports Server (NTRS)
Miller, Teresa Y.; He, Xiao-Min; Carter, Daniel C.
1992-01-01
Crystals of human serum albumin have been successfully grown in a variety of gels using crystallization conditions otherwise equivalent to those utilized in the popular hanging-drop vapor-equilibrium method. Preliminary comparisons of gel grown crystals with crystals grown by the vapor diffusion method via both ground-based and microgravity methods indicate that crystals superior in size and quality may be grown by limiting solutal convection. Preliminary X-ray diffraction statistics are presented.
Diffusion Rate Tomography for Time Domain Electromagnetic Induction Methods
NASA Astrophysics Data System (ADS)
Kazlauskas, E. M.; Weiss, C. J.
2010-12-01
Although it is now routine to invert near-surface electromagnetic induction data in terms of ground conductivity, geoelectromagnetic inversion remains an open research problem because of its intrinsic non-uniqueness and the need to balance computational efficiency with recovering models bearing some resemblance to real geologic structure. The most popular approach for fitting electromagnetic data is analogous to seismic full-waveform inversion. Whether the data are in the time- or frequency-domain, a model is sought which recovers either the amplitude and phase, or the transient response of some measured waveform. However, imperfect knowledge of the source waveform has the potential to erroneously introduce unwarranted geologic structure in the final recovered earth model. Hence, we explore here an alternative approach that mitigates these effects in highly attenuated electromagnetic data. Rather than inverting for the full waveform response, Diffusion Rate Tomography (DiRT) is based on inverting for the arrival time of some key, diagnostic feature in the measured data. This procedure eliminates any error introduced by incomplete knowledge of the source amplitude due to miscalibration, instrument drift, or battery drainage. Time-domain electromagnetic sounding experiments conducted with a horizontal loop transmitter and offset receiver coil provide a useful test of the concept. As induced eddy currents from the transmitter diffuse beneath the receiver, a polarity change occurs in the vertical component of the observed magnetic field. This polarity change (or zero crossing) is our invertible diagnostic, and given a range of offsets between the transmitter and receiver antennae, the zero-crossing moveout curve constitutes the data we invert. Examples of DiRT for a range of geologic settings will be presented and compared against results from smooth, full-waveform inversion. Interestingly, although DiRT works on fewer data than the full-waveform inversion, there is
Diffusion limitations of the lung - comparison of different measurement methods.
Preisser, A M; Seeber, M; Harth, V
2015-01-01
Pulmonary fibrosis leads to a decrease of oxygen diffusion, in particular during exercise. Bronchial obstruction also could decrease the partial pressure of oxygen (P(a)O(2)). In this study we investigated the validity of blood gas content, especially P(a)O(2) and P(a)O(2) affected by hyperventilation (P(a)O(2corr)) and alveolo-arterial oxygen gradient (P(A-a)O(2)) in comparison with the CO diffusion capacity (DLCO) in different lung diseases. A total of 250 subjects were studied (52.3 ± 12.5 year; F/M 40/210), among which there were 162 subjects with different lung disorders and 88 healthy controls. Pearson's correlation coefficients (r) of DLCO with P(a)O(2), P(a)O(2corr), and PA-aO(2) were analyzed in each group. The results show that the diagnostic power of P(A-a)O(2) against P(a)O(2corr) was equivalent, especially during exercise (r = -0.89 and -0.92, respectively). DLCO showed only weak correlations with P(a)O(2corr) and P(A-a)O(2) (r = 0.17 and -0.19, respectively). In conclusion, DLCO shows a better match with blood gas content during exercise than at rest during which it is routinely tested. Thus, the exercise test is advisable. The P(A-a)O(2) takes into account the level of ventilation, which makes it correlate better with DLCO rather than with blood gas content. The most significant problems in clinical evaluation of blood gas parameters during exercise are the insufficiently defined limits of normal-to-pathological range. PMID:25381558
Comparative study of methods used to estimate ionic diffusion coefficients using migration tests
Narsilio, G.A. Li, R. Pivonka, P. Smith, D.W.
2007-08-15
Ionic diffusion coefficients are estimated rapidly using electromigration tests. In this paper, electromigration tests are accurately simulated by numerically solving the Nernst-Planck (NP) equation (coupled with the electroneutrality condition (EN)) using the finite element method. Numerical simulations are validated against experimental data obtained elsewhere [E. Samson, J. Marchand, K.A. Snyder, Calculation of ionic diffusion coefficients on the basis of migration test results, Materials and Structures/Materiaux et Constructions 36 (257) (2003) 156-165., H. Friedmann, O. Amiri, A. Ait-Mokhtar, A direct method for determining chloride diffusion coefficient by using migration test, Cement and Concrete Research 34 (11) (2004) 1967-1973.]. It is shown that migration due to the non-linear electric potential completely overwhelms diffusion due to concentration gradients. The effects of different applied voltage differences and chloride source concentrations on estimations of chloride diffusion coefficients are explored. We show that the pore fluid within concrete and mortar specimens generally differs from the curing solution, lowering the apparent diffusion coefficient, primarily due to interactions of chloride ions with other ions in the pore fluid. We show that the variation of source chloride concentration strongly affects the estimation of diffusion coefficients in non-steady-state tests; however this effect vanishes under steady-state conditions. Most importantly, a comparison of diffusion coefficients obtained from sophisticated analyses (i.e., NP-EN) and a variety of commonly used simplifying methods to estimate chloride diffusion coefficients allows us to identify those methods and experimental conditions where both approaches deliver good estimates for chloride diffusion coefficients. Finally, we demonstrate why simultaneous use and monitoring of current density and fluxes are recommended for both the non-steady and steady-state migration tests.
A method for optimizing the cosine response of solar UV diffusers
NASA Astrophysics Data System (ADS)
Pulli, Tomi; Kärhä, Petri; Ikonen, Erkki
2013-07-01
Instruments measuring global solar ultraviolet (UV) irradiance at the surface of the Earth need to collect radiation from the entire hemisphere. Entrance optics with angular response as close as possible to the ideal cosine response are necessary to perform these measurements accurately. Typically, the cosine response is obtained using a transmitting diffuser. We have developed an efficient method based on a Monte Carlo algorithm to simulate radiation transport in the solar UV diffuser assembly. The algorithm takes into account propagation, absorption, and scattering of the radiation inside the diffuser material. The effects of the inner sidewalls of the diffuser housing, the shadow ring, and the protective weather dome are also accounted for. The software implementation of the algorithm is highly optimized: a simulation of 109 photons takes approximately 10 to 15 min to complete on a typical high-end PC. The results of the simulations agree well with the measured angular responses, indicating that the algorithm can be used to guide the diffuser design process. Cost savings can be obtained when simulations are carried out before diffuser fabrication as compared to a purely trial-and-error-based diffuser optimization. The algorithm was used to optimize two types of detectors, one with a planar diffuser and the other with a spherically shaped diffuser. The integrated cosine errors—which indicate the relative measurement error caused by the nonideal angular response under isotropic sky radiance—of these two detectors were calculated to be f2=1.4% and 0.66%, respectively.
Efficacy of capsicum oleoresin nanocapsules formulation by the modified emulsion-diffusion method.
Surassmo, Suvimol; Min, Sang-Gi; Bejrapha, Piyawan; Choi, Mi-Jung
2011-01-01
In this study, we investigated the effect of high pressure homogenizer on the physico-chemical properties of capsicum oleoresin loaded nanoemulsion (NE) or nanocapsules (NCs) based on the emulsion-diffusion method. According to the application stage of high pressure process at principle emulsion-diffusion method, NCs was prepared by conventional-emulsion-diffusion method (CED), modified-emulsion-microfluidization-diffusion method (MEMD) and modified-emulsion-diffusion-microfluidization method (MEDM). The nanocapsules of MEMD showed homogeneous and the smallest particle size as compared with CED. In addition, MEMD presented the surface tension at the value 36.5 mN/m. The encapsulated capsicum oleoresin was generated the bright color and suppressed the dark red color. Furthermore, MEMD gave the high encapsulation efficiency of capsicum oleoresin around 95% and showed the slow release rate. On the other hand, MEDM presented the non-homogeneous and agglomerate of the particle, low percentage of encapsulation efficiency and the high initial release rate when compared with CED and MEMD methods. According these results, it was supposed that the microfluidization was interesting technique to ameliorate the physical properties and efficiency of NCs. However, it was depending on the appropriate combination of microfluidization based on the emulsion-diffusion method. PMID:21446515
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing
2012-01-01
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849
Parameters estimation using the first passage times method in a jump-diffusion model
NASA Astrophysics Data System (ADS)
Khaldi, K.; Meddahi, S.
2016-06-01
The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.
An efficient wavelet analysis method to film-pore diffusion model arising in mathematical chemistry.
Hariharan, G
2014-04-01
In this paper, we have established an efficient Legendre wavelet based approximation method to solve film-pore diffusion model arising in engineering. Film-pore diffusion model is widely used to determine study the kinetics of adsorption systems. The use of Legendre wavelet based approximation method is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. It is shown that film-pore diffusion model satisfactorily describe kinetics of methylene blue adsorption onto the three low-cost adsorbents, Guava, teak and gulmohar plant leaf powders, used in this study. PMID:24562792
A fast finite volume method for conservative space-fractional diffusion equations in convex domains
NASA Astrophysics Data System (ADS)
Jia, Jinhong; Wang, Hong
2016-04-01
We develop a fast finite volume method for variable-coefficient, conservative space-fractional diffusion equations in convex domains via a volume-penalization approach. The method has an optimal storage and an almost linear computational complexity. The method retains second-order accuracy without requiring a Richardson extrapolation. Numerical results are presented to show the utility of the method.
Accurate determination of specific heat at high temperatures using the flash diffusivity method
NASA Technical Reports Server (NTRS)
Vandersande, J. W.; Zoltan, A.; Wood, C.
1989-01-01
The flash diffusivity method of Parker et al. (1961) was used to measure accurately the specific heat of test samples simultaneously with thermal diffusivity, thus obtaining the thermal conductivity of these materials directly. The accuracy of data obtained on two types of materials (n-type silicon-germanium alloys and niobium), was + or - 3 percent. It is shown that the method is applicable up to at least 1300 K.
Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations
Zhou Tao; Tang Tao
2010-11-01
In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.
Diffuse interface method for a compressible binary fluid.
Liu, Jiewei; Amberg, Gustav; Do-Quang, Minh
2016-01-01
Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO_{2} + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO_{2} + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO_{2} the smaller the surface tension and the easier the drop deforms. PMID:26871168
Diffuse interface method for a compressible binary fluid
NASA Astrophysics Data System (ADS)
Liu, Jiewei; Amberg, Gustav; Do-Quang, Minh
2016-01-01
Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO2 + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO2 + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO2 the smaller the surface tension and the easier the drop deforms.
A combined reconstruction-classification method for diffuse optical tomography.
Hiltunen, P; Prince, S J D; Arridge, S
2009-11-01
We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels. PMID:19820265
NASA Astrophysics Data System (ADS)
Kang, Hyesung; Jones, T. W.
1995-07-01
Direct comparisons of diffusive particle acceleration numerical simulations have been made against Monte Carlo and hybrid plasma simulations by Ellison et al. (1993) and against observations at the Earth's bow shock presented by Ellison et al. (1990). Toward this end we have introduced a new numerical scheme for injection of cosmic-ray particles out of the thermal plasma, modeled by way of the diffusive scattering process itself; that is, the diffusion and acceleration across the shock front of particles out of the suprathermal tail of the Maxwellian distribution. Our simulations take two forms. First, we have solved numerically the timedependent diffusion-advection equation for the high-energy (cosmic-ray) protons in one-dimensional quasiparallel shocks. Dynamical feedback between the particles and thermal plasma is included. The proton fluxes on both sides of the shock derived from our method are consistent with those calculated by Ellison et al. (1993). A similar test has compared our methods to published measurements at the Earth's bow shock when the interplanetary magnetic field was almost parallel to the solar wind velocity (Ellison et al. 1990). Again our results are in good agreement. Second, the same shock conditions have been simulated with the two-fluid version of diffusive shock acceleration theory by adopting injection rates and the closure parameters inferred from the diffusion-advection equation calculations. The acceleration efficiency and the shock structure calculated with the two-fluid method are in good agreement with those computed with the diffusion-advection method. Thus, we find that all of these computational methods (diffusion-advection, two-fluid, Monte Carlo, and hybrid) are in substantial agreement on the issues they can simultaneously address, so that the essential physics of diffusive particle acceleration is adequately contained within each. This is despite the fact that each makes what appear to be very different assumptions or
Development of a numerical method for the prediction of turbulent flows in dump diffusers
NASA Astrophysics Data System (ADS)
Ando, Yasunori; Kawai, Masafumi; Sato, Yukinori; Toh, Hidemi
1987-01-01
In order to obtain an effective tool to design dump diffusers for gas turbine combustors, a finite-volume numerical calculation method has been developed for the solution of two-dimensional/axisymmetric incompressible steady Navier-Stokes equation in general curvilinear coordinate system. This method was applied to the calculations of turbulent flows in a two-dimensional dump diffuser with uniform and distorted inlet velocity profiles as well as an annular dump diffuser with uniform inlet velocity profile, and the calculated results were compared with experimental data. The numerical results showed a good agreement with experimental data in case of both inlet velocity profiles; eventually, the numerical method was confirmed to be an effective tool for the development of dump diffusers which can predict the flow pattern, velocity distribution and the pressure loss.
NASA Astrophysics Data System (ADS)
Sweilam, N. H.; Abou Hasan, M. M.
2016-08-01
This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.
Convergence of the binomial tree method for Asian options in jump-diffusion models
NASA Astrophysics Data System (ADS)
Kim, Kwang Ik; Qian, Xiao-Song
2007-06-01
The binomial tree methods (BTM), first proposed by Cox, Ross and Rubinstein [J. Cox, S. Ross, M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ. 7 (1979) 229-264] in diffusion models and extended by Amin [K.I. Amin, Jump diffusion option valuation in discrete time, J. Finance 48 (1993) 1833-1863] to jump-diffusion models, is one of the most popular approaches to pricing options. In this paper, we present a binomial tree method for Asian options in jump-diffusion models and show its equivalence to certain explicit difference scheme. Employing numerical analysis and the notion of viscosity solution, we prove the uniform convergence of the binomial tree method for European-style and American-style Asian options.
Data on the verification and validation of segmentation and registration methods for diffusion MRI.
Esteban, Oscar; Zosso, Dominique; Daducci, Alessandro; Bach-Cuadra, Meritxell; Ledesma-Carbayo, María J; Thiran, Jean-Philippe; Santos, Andres
2016-09-01
The verification and validation of segmentation and registration methods is a necessary assessment in the development of new processing methods. However, verification and validation of diffusion MRI (dMRI) processing methods is challenging for the lack of gold-standard data. The data described here are related to the research article entitled "Surface-driven registration method for the structure-informed segmentation of diffusion MR images" [1], in which publicly available data are used to derive golden-standard reference-data to validate and evaluate segmentation and registration methods in dMRI. PMID:27508235
A comparison of the Monte Carlo and the flux gradient method for atmospheric diffusion
Lange, R.
1990-05-01
In order to model the dispersal of atmospheric pollutants in the planetary boundary layer, various methods of parameterizing turbulent diffusion have been employed. The purpose of this paper is to use a three-dimensional particle-in-cell transport and diffusion model to compare the Markov chain (Monte Carlo) method of statistical particle diffusion with the deterministic flux gradient (K-theory) method. The two methods are heavily used in the study of atmospheric diffusion under complex conditions, with the Monte Carlo method gaining in popularity partly because of its more direct application of turbulence parameters. The basis of comparison is a data set from night-time drainage flow tracer experiments performed by the US Department of Energy Atmospheric Studies in Complex Terrain (ASCOT) program at the Geysers geothermal region in northern California. The Atmospheric Diffusion Particle-In-Cell (ADPIC) model used is the main model in the Lawrence Livermore National Laboratory emergency response program: Atmospheric Release Advisory Capability (ARAC). As a particle model, it can simulate diffusion in both the flux gradient and Monte Carlo modes. 9 refs., 6 figs.
Study of acid diffusion behaves form PAG by using top coat method
NASA Astrophysics Data System (ADS)
Sekiguchi, Atsushi; Matsumoto, Yoko
2014-03-01
Our past research on measurements of simulation parameters for ArF resists focused on establishing methods for measuring the following parameters:[1]-[4] • Development parameters[1] • PEB parameters[2] • Dill's ABC parameters[3] • Quencher parameter[4] We entered these parameters into a lithography simulator and performed ArF resist simulations.We then explored ways to optimize the ArF resist material and process. This paper reports on our study of methods for measuring the diffusion length of acid generated from PAG during exposures. In our experiment, we applied a PAG-containing top coat (TC) material (second layer) to a PAG-free ArF resist (first layer), then performed the exposure and PEB processes. The acid generated in the TC during the exposure diffused into the ArF resist in the lower layer (first layer) when PEB was performed. The process of developing this sample removed the TC in the second layer and the parts of the first layer into which the acid had diffused.We obtained the acid diffusion length based on the quantity of film removed by the development. We calculated the acid diffusion coefficient after varying the exposure value and repeating the measurement. For this report, we also performed measurements to determine how differences in PAG anion size, amount of quencher additive, and PEB temperature affected the acid diffusion coefficient.We entered the measurements obtained into the PROLITH simulator and explored the effects of acid diffusion on pattern profile.
Method of applying a cerium diffusion coating to a metallic alloy
Jablonski, Paul D.; Alman, David E.
2009-06-30
A method of applying a cerium diffusion coating to a preferred nickel base alloy substrate has been discovered. A cerium oxide paste containing a halide activator is applied to the polished substrate and then dried. The workpiece is heated in a non-oxidizing atmosphere to diffuse cerium into the substrate. After cooling, any remaining cerium oxide is removed. The resulting cerium diffusion coating on the nickel base substrate demonstrates improved resistance to oxidation. Cerium coated alloys are particularly useful as components in a solid oxide fuel cell (SOFC).
A New Method for the Calculation of Diffusion Coefficients with Monte Carlo
NASA Astrophysics Data System (ADS)
Dorval, Eric
2014-06-01
This paper presents a new Monte Carlo-based method for the calculation of diffusion coefficients. One distinctive feature of this method is that it does not resort to the computation of transport cross sections directly, although their functional form is retained. Instead, a special type of tally derived from a deterministic estimate of Fick's Law is used for tallying the total cross section, which is then combined with a set of other standard Monte Carlo tallies. Some properties of this method are presented by means of numerical examples for a multi-group 1-D implementation. Calculated diffusion coefficients are in general good agreement with values obtained by other methods.
Practical method of diffusion-welding steel plate in air
NASA Technical Reports Server (NTRS)
Holko, K. H.; Moore, T. J.
1971-01-01
Method is ideal for critical service requirements where parent metal properties are equaled in notch toughness, stress rupture and other characteristics. Welding technique variations may be used on a variety of materials, such as carbon steels, alloy steels, stainless steels, ceramics, and reactive and refractory materials.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Joo, H.; Nichols, W.R.
1994-05-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.
NASA Astrophysics Data System (ADS)
Bouffard, M.; Labrosse, M.; Choblet, M.; Fournier, M.; Aubert, M.; Tackley, M.
2015-10-01
Convection in the liquid layers of planetary interiors is usually driven by a combination of thermal and compositional sources of buoyancy. The low molecular diffusivity of composition causes troubles in the description of this field on the Eulerian grids typically employed in current codes of geodynamo because numerical diffusion on these grids is potentially larger than the real diffusivity. We developed a Lagrangian description of composition based on a method of tracers. The absence of numerical diffusion inherent to this method allows modeling of thermo-chemical convection with infinite Lewis number. The validation of this new tool on benchmark cases will be presented at EPSC as well as its first applications to the ocean of Ganymede with consistently coupled boundary condi- tions for temperature and composition.
NASA Astrophysics Data System (ADS)
Ziemys, A.; Kojic, M.; Milosevic, M.; Kojic, N.; Hussain, F.; Ferrari, M.; Grattoni, A.
2011-06-01
We present a successful hierarchical modeling approach which accounts for interface effects on diffusivity, ignored in classical continuum theories. A molecular dynamics derived diffusivity scaling scheme is incorporated into a finite element method to model transport through a nanochannel. In a 5 nm nanochannel, the approach predicts 2.2 times slower mass release than predicted by Fick's law by comparing time spent to release 90% of mass. The scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. We show robustness of our discrete continuum model in addressing complex diffusion phenomena in biomedical and engineering applications by providing flexible hierarchical coupling of molecular scale effects and preserving computational finite element method speed.
A new method of optimal design for a two-dimensional diffuser by using dynamic programming
NASA Technical Reports Server (NTRS)
Gu, Chuangang; Zhang, Moujin; Chen, XI; Miao, Yongmiao
1991-01-01
A new method for predicting the optimal velocity distribution on the wall of a two dimensional diffuser is presented. The method uses dynamic programming to solve the optimal control problem with inequality constraints of state variables. The physical model of optimization is designed to prevent the separation of the boundary layer while approaching the maximum pressure ratio in a diffuser of a specified length. The computational results are in fair agreement with the experimental ones. Optimal velocity distribution on a diffuser wall is said to occur when the flow decelerates quickly at first and then smoothly, while the flow is near separation, but always protected from it. The optimal velocity distribution can be used to design the contour of the diffuser.
First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2014-01-01
A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.
Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.
2012-08-15
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.
The arbitrary order mixed mimetic finite difference method for the diffusion equation
Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco
2016-05-01
Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less
NASA Astrophysics Data System (ADS)
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Kotilainen, Pirkko; Puukka, Pauli; Nakari, Ulla-Maija; Siitonen, Anja; Eerola, Erkki; Huovinen, Pentti; Hakanen, Antti J.
2012-01-01
The agar dilution method has been standardized by the CLSI for the susceptibility testing of Campylobacter species, and according to these standards, the disk diffusion method should be used only in screening for macrolide and ciprofloxacin resistance. Nevertheless, the disk diffusion test is currently widely used, since it is easy to perform in clinical microbiology laboratories. In this study, the disk diffusion method was compared to the agar dilution method by analyzing the in vitro activities of seven antimicrobial agents against 174 Campylobacter strains collected in Finland between 2003 and 2008. Recommendations of the CLSI were followed using Mueller-Hinton agar plates with 5% of sheep blood. For each strain, the disk diffusion tests were performed two to four times. Of the 33 erythromycin-resistant strains (MIC, ≥16 μg/ml), 24 (73%) constantly showed a 6-mm erythromycin inhibition zone (i.e., no inhibition), while for seven strains the inhibition zone varied from 6 to 44 mm in repeated measurements. Among the 141 erythromycin-susceptible strains (MIC, <16 μg/ml), erythromycin inhibition zones varied between 6 and 61 mm. Of the 87 ciprofloxacin-resistant strains, 47 (54%) showed 6-mm inhibition zones, while 40 strains showed inhibition zones between 6 and 60 mm. Significant differences between the repetitions were observed in the disk diffusion for all antimicrobial agents and all strains except for the macrolide-resistant strains regarding the macrolides. For 17 (10%) strains, the variation in repeated measurements was substantial. These results show that the disk diffusion method may not be a reliable tool for the susceptibility testing of Campylobacter spp. Further studies are needed to assess whether the disk diffusion test could be improved or whether all susceptibilities of campylobacters should be tested using an MIC-based method. PMID:22075583
Method of fluxless brazing and diffusion bonding of aluminum containing components
NASA Technical Reports Server (NTRS)
Featherston, A. B.; Okelly, K. P. (Inventor)
1976-01-01
A method of diffusion bonding and fluxless brazing of aluminum containing components is reported. The aluminum surfaces are freed of any aluminum oxide coating and are coated with a polymeric sealer which can be thermally removed leaving essentially no residue. The polymeric sealer is being removed in a substantially oxygen free environment, and the aluminum components are then being brazed or diffusion bonded without the use of a flux to remove oxide coating.
Martelli, Fabrizio; Zaccanti, Giovanni
2007-01-22
In spite of many progresses achieved both with theories and with experiments in studying light propagation through diffusive media, a reliable method for accurate measurements of the optical properties of diffusive media at NIR wavelengths is, in our opinion, still missing. It is therefore difficult to create a diffusive medium with well known optical properties to be used as a reference. In this paper we describe a method to calibrate the reduced scattering coefficient, mu'(s) , of a liquid diffusive medium and the absorption coefficient, mu(a), of an absorbing medium with a standard error smaller than 2% both on mu'(s) and on mu(a). The method is based on multidistance measurements of fluence into an infinite medium illuminated by a CW source. The optical properties are retrieved with simple inversion procedures (linear fits) exploiting the knowledge of the absorption coefficient of the liquid into which the diffuser and the absorber are dispersed. In this study Intralipid diluted in water has been used as diffusive medium and Indian ink as absorber. For a full characterization of these media measurements of collimated transmittance have also been carried out, from which the asymmetry factor of the scattering function of Intralipid and the single scattering albedo of Indian ink have been determined. PMID:19532267
An adaptive pseudo-spectral method for reaction diffusion problems
NASA Technical Reports Server (NTRS)
Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.
1987-01-01
The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.
Accelerated molecular dynamics and equation-free methods for simulating diffusion in solids.
Deng, Jie; Zimmerman, Jonathan A.; Thompson, Aidan Patrick; Brown, William Michael; Plimpton, Steven James; Zhou, Xiao Wang; Wagner, Gregory John; Erickson, Lindsay Crowl
2011-09-01
Many of the most important and hardest-to-solve problems related to the synthesis, performance, and aging of materials involve diffusion through the material or along surfaces and interfaces. These diffusion processes are driven by motions at the atomic scale, but traditional atomistic simulation methods such as molecular dynamics are limited to very short timescales on the order of the atomic vibration period (less than a picosecond), while macroscale diffusion takes place over timescales many orders of magnitude larger. We have completed an LDRD project with the goal of developing and implementing new simulation tools to overcome this timescale problem. In particular, we have focused on two main classes of methods: accelerated molecular dynamics methods that seek to extend the timescale attainable in atomistic simulations, and so-called 'equation-free' methods that combine a fine scale atomistic description of a system with a slower, coarse scale description in order to project the system forward over long times.
Advanced computational methods for nodal diffusion, Monte Carlo, and S[sub N] problems
Martin, W.R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
Advanced computational methods for nodal diffusion, Monte Carlo, and S(sub N) problems
NASA Astrophysics Data System (ADS)
Martin, W. R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. An alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
Method of fabricating reflection-mode EUV diffusers
Anderson, Erik; Naulleau, Patrick P.
2005-03-01
Techniques for fabricating well-controlled, random relief, engineered surfaces that serve as substrates for EUV optical devices are accomplished with grayscale exposure. The method of fabricating a multilevel EUV optical element includes: (a) providing a substrate; (b) depositing a layer of curable material on a surface of the substrate; (c) creating a relief profile in a layer of cured material from the layer of curable material wherein the relief profile comprises multiple levels of cured material that has a defined contour; and (d) depositing a multilayer reflection film over the relief profile wherein the film has an outer contour that substantially matches that of the relief profile. The curable material can comprise photoresist or a low dielectric constant material.
A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes
Mauro, Ava J.; Sigurdsson, Jon Karl; Shrake, Justin; Atzberger, Paul J.; Isaacson, Samuel A.
2014-02-15
Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.
NASA Astrophysics Data System (ADS)
Punegov, V. I.; Sivkov, D. V.
2015-03-01
Two independent approaches to calculate the angular distribution of X-ray diffusion scattering from a crystalline medium with spheroidal quantum dots (QDs) have been proposed. The first method is based on the analytical solution involving the multipole expansion of elastic strain fields beyond QDs. The second approach is based on calculations of atomic displacements near QDs by the Green's function method. An analysis of the diffuse scattering intensity distribution in the reciprocal space within these two approaches shows that both methods yield similar results for the chosen models of QD spatial distribution.
Gentile, N A
2000-10-01
We present a method for accelerating time dependent Monte Carlo radiative transfer calculations by using a discretization of the diffusion equation to calculate probabilities that are used to advance particles in regions with small mean free path. The method is demonstrated on problems with on 1 and 2 dimensional orthogonal grids. It results in decreases in run time of more than an order of magnitude on these problems, while producing answers with accuracy comparable to pure IMC simulations. We call the method Implicit Monte Carlo Diffusion, which we abbreviate IMD.
Punegov, V. I. Sivkov, D. V.
2015-03-15
Two independent approaches to calculate the angular distribution of X-ray diffusion scattering from a crystalline medium with spheroidal quantum dots (QDs) have been proposed. The first method is based on the analytical solution involving the multipole expansion of elastic strain fields beyond QDs. The second approach is based on calculations of atomic displacements near QDs by the Green’s function method. An analysis of the diffuse scattering intensity distribution in the reciprocal space within these two approaches shows that both methods yield similar results for the chosen models of QD spatial distribution.
Yang, J; Köhler, K; Davis, D M; Burroughs, N J
2010-06-01
Fluorescence recovery after photobleaching is a widely established method for the estimation of diffusion coefficients, strip bleaching with an associated recovery curve analysis being one of the simplest techniques. However, its implementation requires near 100% bleaching in the region of interest with negligible fluorescence loss outside, both constraints being hard to achieve concomitantly for fast diffusing molecules. We demonstrate that when these requirements are not met there is an error in the estimation of the diffusion coefficient D, either an under- or overestimation depending on which assumption is violated the most. We propose a simple modification to the recovery curve analysis incorporating the concept of the relative bleached mass m giving a revised recovery time parametrization tau=m(2)w(2)/4piD for a strip of width w. This modified model removes the requirement of 100% bleaching in the region of interest and allows for limited diffusion of the fluorophore during bleaching. We validate our method by estimating the (volume) diffusion coefficient of FITC-labelled IgG in 60% glycerol solution, D= 4.09 +/- 0.21 microm(2) s(-1), and the (surface) diffusion coefficient of a green-fluorescent protein-tagged class I MHC protein expressed at the surface of a human B cell line, D= 0.32 +/- 0.03 microm(2) s(-1) for a population of cells. PMID:20579262
A new Sumudu transform iterative method for time-fractional Cauchy reaction-diffusion equation.
Wang, Kangle; Liu, Sanyang
2016-01-01
In this paper, a new Sumudu transform iterative method is established and successfully applied to find the approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations. The approach is easy to implement and understand. The numerical results show that the proposed method is very simple and efficient. PMID:27386314
Method of hepatitis diagnostics of changes in human skin diffuse reflectivity
NASA Astrophysics Data System (ADS)
Kirsh, M. L.; Sokol, A. M.; Lomanets, V. S.; Gayka, O. R.
1999-11-01
The results on the study of influence of bilirubinum concentration in a human blood on the spectrum of a diffuse reflectivity of his skin are represented. On this basis, the method for hepatitis diagnostics has been developed, and the laboratory device implementing this method has been designed.
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
NASA Technical Reports Server (NTRS)
Cockburn, Bernardo; Shu, Chi-Wang
1997-01-01
In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.
Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods
Mamonov, Artem B.; Kurnikova, Maria G.; Coalson, Rob D.
2007-01-01
The local diffusion constant of K+ inside the Gramicidin A (GA) channel has been calculated using four computational methods based on molecular dynamics (MD) simulations, specifically: Mean Square Displacement (MSD), Velocity Autocorrelation Function (VACF), Second Fluctuation Dissipation Theorem (SFDT) and analysis of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were first tested and compared for K+ in bulk water—all predicted the correct diffusion constant. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the membrane-channel system on the ion. SFDT and GLE-HO techniques properly unbias the influence of the systematic force on the diffusion properties and predicted a similar diffusion constant of K+ inside GA, namely, ca. 10 times smaller than in the bulk. It was found that both SFDT and GLE-HO methods require extensive MD sampling on the order of tens of nanoseconds to predict a reliable diffusion constant of K+ inside GA. PMID:16797116
Diffused interface ghost fluid method for incompressible multiphase, phase change simulations
NASA Astrophysics Data System (ADS)
Lee, Moon Soo; Riaz, Amir
2013-11-01
Sharp interface methods for simulating multiphase flow often suffer from unstable pressure and velocity fluctuations for problems involving mass transfer. An improved sharp interface method is developed for multiphase flow with phase change using both sharp and diffused interfacial properties. The approach is based on defining continuous, phase averaged velocity and density fields within a diffused interfacial region while using the sharp treatment for the implementation of the jumps in the pressure and the temperature gradient. The method implements interface advection with diffused and stable velocity field but can represent accurate movement of the sharp interface. Two-dimensional film boiling problems are solved on a horizontal surface to demonstrate the performance of the new approach.
Laser interferometric method for determining the carrier diffusion length in semiconductors
Manukhov, V. V.; Fedortsov, A. B.; Ivanov, A. S.
2015-09-15
A new laser interferometric method for measuring the carrier diffusion length in semiconductors is proposed. The method is based on the interference–absorption interaction of two laser radiations in a semiconductor. Injected radiation generates additional carriers in a semiconductor, which causes a change in the material’s optical constants and modulation of the probing radiation passed through the sample. When changing the distance between carrier generation and probing points, a decrease in the carrier concentration, which depends on the diffusion length, is recorded. The diffusion length is determined by comparing the experimental and theoretical dependences of the probe signal on the divergence of the injector and probe beams. The method is successfully tested on semiconductor samples with different thicknesses and surface states and can be used in scientific research and the electronics industry.
Individual Differences and Fitting Methods for the Two-Choice Diffusion Model of Decision Making
Ratcliff, Roger; Childers, Russ
2015-01-01
Methods of fitting the diffusion model were examined with a focus on what the model can tell us about individual differences. Diffusion model parameters were obtained from the fits to data from two experiments and consistency of parameter values, individual differences, and practice effects were examined using different numbers of observations from each subject. Two issues were examined, first, what sizes of differences between groups can be obtained to distinguish between groups and second, what sizes of differences would be needed to find individual subjects that had a deficit relative to a control group. The parameter values from the experiments provided ranges that were used in a simulation study to examine recovery of individual differences. This study used several diffusion model fitting programs, fitting methods, and published packages. In a second simulation study, 64 sets of simulated data from each of 48 sets of parameter values (spanning the range of typical values obtained from fits to data) were fit with the different methods and biases and standard deviations in recovered model parameters were compared across methods. Finally, in a third simulation study, a comparison between a standard chi-square method and a hierarchical Bayesian method was performed. The results from these studies can be used as a starting point for selecting fitting methods and as a basis for understanding the strengths and weaknesses of using diffusion model analyses to examine individual differences in clinical, neuropsychological, and educational testing. PMID:26236754
NASA Astrophysics Data System (ADS)
Jia, Jinhong; Wang, Hong
2015-07-01
Numerical methods for space-fractional diffusion equations often generate dense or even full stiffness matrices. Traditionally, these methods were solved via Gaussian type direct solvers, which requires O (N3) of computational work per time step and O (N2) of memory to store where N is the number of spatial grid points in the discretization. In this paper we develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite difference methods (both steady-state and time-dependent) space-fractional diffusion equations with fractional derivative boundary conditions in one space dimension. The method requires O (N) of memory and O (Nlog N) of operations per iteration. Due to the application of effective preconditioners, significantly reduced numbers of iterations were achieved that further reduces the computational cost of the fast method. Numerical results are presented to show the utility of the method.
Albertson, B J; Blue, T E; Niemkiewicz, J
2001-09-01
This paper outlines a method for determining proper removal-diffusion parameters to be used in removal-diffusion theory calculations for the purpose of BNCT treatment planning. Additionally, this paper demonstrates that, given the proper choice of removal-diffusion parameters, removal-diffusion theory may provide an accurate calculation technique for determining absorbed dose distributions for the purpose of BNCT treatment planning. For a four-group, one-dimensional calculation in water, this method was used to determine values for the neutron scattering cross sections, neutron removal cross sections, neutron diffusion coefficients, and extrapolation distances. These values were then used in a one-dimensional DIF3D calculation. The results of the DIF3D calculation showed a maximum deviation of 2.5% from a MCNP calculation performed for the same geometry. PMID:11585220
NASA Technical Reports Server (NTRS)
Penner, Reginald M.; Vandyke, Leon S.; Martin, Charles R.
1987-01-01
The current pulse E sub oc relaxation method and its application to the determination of diffusion coefficients in electrochemically synthesized polypyrrole thin films is described. Diffusion coefficients for such films in Et4NBF4 and MeCN are determined for a series of submicron film thicknesses. Measurement of the double-layer capacitance, C sub dl, and the resistance, R sub u, of polypyrrole thin films as a function of potential obtained with the galvanostatic pulse method is reported. Measurements of the electrolyte concentration in reduced polypyrrole films are also presented to aid in the interpretation of the data.
Calculation of the neutron diffusion equation by using Homotopy Perturbation Method
NASA Astrophysics Data System (ADS)
Koklu, H.; Ersoy, A.; Gulecyuz, M. C.; Ozer, O.
2016-03-01
The distribution of the neutrons in a nuclear fuel element in the nuclear reactor core can be calculated by the neutron diffusion theory. It is the basic and the simplest approximation for the neutron flux function in the reactor core. In this study, the neutron flux function is obtained by the Homotopy Perturbation Method (HPM) that is a new and convenient method in recent years. One-group time-independent neutron diffusion equation is examined for the most solved geometrical reactor core of spherical, cubic and cylindrical shapes, in the frame of the HPM. It is observed that the HPM produces excellent results consistent with the existing literature.
An asymptotic induced numerical method for the convection-diffusion-reaction equation
NASA Technical Reports Server (NTRS)
Scroggs, Jeffrey S.; Sorensen, Danny C.
1988-01-01
A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.
NASA Astrophysics Data System (ADS)
Bodammer, N. C.; Kaufmann, J.; Kanowski, M.; Tempelmann, C.
2009-02-01
Diffusion tensor tractography (DTT) allows one to explore axonal connectivity patterns in neuronal tissue by linking local predominant diffusion directions determined by diffusion tensor imaging (DTI). The majority of existing tractography approaches use continuous coordinates for calculating single trajectories through the diffusion tensor field. The tractography algorithm we propose is characterized by (1) a trajectory propagation rule that uses voxel centres as vertices and (2) orientation probabilities for the calculated steps in a trajectory that are obtained from the diffusion tensors of either two or three voxels. These voxels include the last voxel of each previous step and one or two candidate successor voxels. The precision and the accuracy of the suggested method are explored with synthetic data. Results clearly favour probabilities based on two consecutive successor voxels. Evidence is also provided that in any voxel-centre-based tractography approach, there is a need for a probability correction that takes into account the geometry of the acquisition grid. Finally, we provide examples in which the proposed fibre-tracking method is applied to the human optical radiation, the cortico-spinal tracts and to connections between Broca's and Wernicke's area to demonstrate the performance of the proposed method on measured data.
Development of Reference Materials for Thermal-Diffusivity Measurements by the Flash Method
NASA Astrophysics Data System (ADS)
Akoshima, M.; Abe, H.; Baba, T.
2015-12-01
The thermal conductivity of solid materials used for thermal simulations and thermal designs can be obtained as the product of thermal diffusivity, specific heat capacity, and bulk density in many cases. The thermal diffusivity is usually measured by the flash method, and the specific heat capacity is usually measured by differential scanning calorimetry. In order to obtain reliable thermal conductivities for strict thermal design, it is necessary to measure the thermal diffusivity using the flash method, a well-validated apparatus. Reference materials are an effective means for validation of most practical measurement apparatus. For the flash method, isotropic graphite was selected as a candidate reference material. A batch of isotropic graphite samples was prepared and characterized in detail in order to be a certified reference material for thermal-diffusivity measurement. The detailed characterization ensures the traceability of the measurement results to the international system of units (SI). A convenient reference material for thermal conductivity was also obtained by using the known thermal-diffusivity measurements, specific heat capacity, and density of the material.
A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations
Densmore, Jeffery D. . E-mail: jdd@lanl.gov; Urbatsch, Todd J. . E-mail: tmonster@lanl.gov; Evans, Thomas M. . E-mail: tme@lanl.gov; Buksas, Michael W. . E-mail: mwbuksas@lanl.gov
2007-03-20
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo particle-transport simulations in diffusive media. If standard Monte Carlo is used in such media, particle histories will consist of many small steps, resulting in a computationally expensive calculation. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many small Monte Carlo steps, thus increasing the efficiency of the simulation. In addition, given that DDMC is based on a diffusion equation, it should produce accurate solutions if used judiciously. In practice, DDMC is combined with standard Monte Carlo to form a hybrid transport-diffusion method that can accurately simulate problems with both diffusive and non-diffusive regions. In this paper, we extend previously developed DDMC techniques in several ways that improve the accuracy and utility of DDMC for nonlinear, time-dependent, radiative-transfer calculations. The use of DDMC in these types of problems is advantageous since, due to the underlying linearizations, optically thick regions appear to be diffusive. First, we employ a diffusion equation that is discretized in space but is continuous in time. Not only is this methodology theoretically more accurate than temporally discretized DDMC techniques, but it also has the benefit that a particle's time is always known. Thus, there is no ambiguity regarding what time to assign a particle that leaves an optically thick region (where DDMC is used) and begins transporting by standard Monte Carlo in an optically thin region. Also, we treat the interface between optically thick and optically thin regions with an improved method, based on the asymptotic diffusion-limit boundary condition, that can produce accurate results regardless of the angular distribution of the incident Monte Carlo particles. Finally, we develop a technique for estimating radiation momentum deposition during the
Ryabov, Yaroslav E; Geraghty, Charles; Varshney, Amitabh; Fushman, David
2006-12-01
We propose a new computational method for predicting rotational diffusion properties of proteins in solution. The method is based on the idea of representing protein surface as an ellipsoid shell. In contrast to other existing approaches this method uses principal component analysis of protein surface coordinates, which results in a substantial increase in the computational efficiency of the method. Direct comparison with the experimental data as well as with the recent computational approach (Garcia de la Torre; et al. J. Magn. Reson. 2000, B147, 138-146), based on representation of protein surface as a set of small spherical friction elements, shows that the method proposed here reproduces experimental data with at least the same level of accuracy and precision as the other approach, while being approximately 500 times faster. Using the new method we investigated the effect of hydration layer and protein surface topography on the rotational diffusion properties of a protein. We found that a hydration layer constructed of approximately one monolayer of water molecules smoothens the protein surface and effectively doubles the overall tumbling time. We also calculated the rotational diffusion tensors for a set of 841 protein structures representing the known protein folds. Our analysis suggests that an anisotropic rotational diffusion model is generally required for NMR relaxation data analysis in single-domain proteins, and that the axially symmetric model could be sufficient for these purposes in approximately half of the proteins. PMID:17132010
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method.
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-20
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability. PMID:24351275
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method
NASA Astrophysics Data System (ADS)
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-01
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.
Development of advanced methods for analysis of experimental data in diffusion
NASA Astrophysics Data System (ADS)
Jaques, Alonso V.
There are numerous experimental configurations and data analysis techniques for the characterization of diffusion phenomena. However, the mathematical methods for estimating diffusivities traditionally do not take into account the effects of experimental errors in the data, and often require smooth, noiseless data sets to perform the necessary analysis steps. The current methods used for data smoothing require strong assumptions which can introduce numerical "artifacts" into the data, affecting confidence in the estimated parameters. The Boltzmann-Matano method is used extensively in the determination of concentration - dependent diffusivities, D(C), in alloys. In the course of analyzing experimental data, numerical integrations and differentiations of the concentration profile are performed. These methods require smoothing of the data prior to analysis. We present here an approach to the Boltzmann-Matano method that is based on a regularization method to estimate a differentiation operation on the data, i.e., estimate the concentration gradient term, which is important in the analysis process for determining the diffusivity. This approach, therefore, has the potential to be less subjective, and in numerical simulations shows an increased accuracy in the estimated diffusion coefficients. We present a regression approach to estimate linear multicomponent diffusion coefficients that eliminates the need pre-treat or pre-condition the concentration profile. This approach fits the data to a functional form of the mathematical expression for the concentration profile, and allows us to determine the diffusivity matrix directly from the fitted parameters. Reformulation of the equation for the analytical solution is done in order to reduce the size of the problem and accelerate the convergence. The objective function for the regression can incorporate point estimations for error in the concentration, improving the statistical confidence in the estimated diffusivity matrix
Spectral approximation to advection-diffusion problems by the fictitious interface method
NASA Astrophysics Data System (ADS)
Frati, A.; Pasquarelli, F.; Quarteroni, A.
1993-08-01
The algorithmic aspects of the 'fictitious interface' method used in numerical approximations of convection-dominated flows are discussed. The solution algorithm presented alternates the advection-equation solution with that of the advection-diffusion equation within complementary subdomains. For the problems presently considered, spatial discretization is obtained by the spectral collocation method via Legendre-Gaussian modes. Attention is given to the the fictitious interface method's application to the Burgers equation.
Group iterative methods for the solution of two-dimensional time-fractional diffusion equation
NASA Astrophysics Data System (ADS)
Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.
2016-06-01
Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.
A deterministic Lagrangian particle separation-based method for advective-diffusion problems
NASA Astrophysics Data System (ADS)
Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.
2008-12-01
A simple and robust Lagrangian particle scheme is proposed to solve the advective-diffusion transport problem. The scheme is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general scheme is mass conservative and is free from numerical diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, numerical stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.
Multiscale numerical methods for passive advection-diffusion in incompressible turbulent flow fields
NASA Astrophysics Data System (ADS)
Lee, Yoonsang; Engquist, Bjorn
2016-07-01
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the velocity fields in the Fourier space, which are similar to the decomposition in large eddy simulations. It also uses a hierarchy of local domains with different resolutions as in multigrid methods. The effective diffusivity from finer scale is used for the next coarser level computation and this process is repeated up to the coarsest scale of interest. The grids are only in local domains whose sizes decrease depending on the resolution level so that the overall computational complexity increases linearly as the number of different resolution grids increases. The method captures interactions between finer and coarser scales but has to sacrifice some of interactions between different scales. The proposed method is numerically tested with 2D examples including a successful approximation to a continuous spectrum flow.
New contactless method for thermal diffusivity measurements using modulated photothermal radiometry.
Pham Tu Quoc, S; Cheymol, G; Semerok, A
2014-05-01
Modulated photothermal radiometry is a non-destructive and contactless technique for the characterization of materials. It has two major advantages: a good signal-to-noise ratio through a synchronous detection and a low dependence on the heating power and the optical properties of the sample surface. This paper presents a new method for characterizing the thermal diffusivity of a material when the phase shift between a modulated laser power signal and the thermal signal of a plate sample is known at different frequencies. The method is based on a three-dimensional analytical model which is used to determine the temperature amplitude and the phase in the laser heating of the plate. A new simple formula was developed through multi-parametric analysis to determine the thermal diffusivity of the plate with knowledge of the frequency at the minimum phase shift, the laser beam radius r0 and the sample thickness L. This method was developed to control the variation of the thermal diffusivity of nuclear components and it was first applied to determine the thermal diffusivity of different metals: 304 L stainless steel, nickel, titanium, tungsten, molybdenum, zinc, and iron. The experimental results were obtained with 5%-10% accuracy and corresponded well with the reference values. The present paper also demonstrates the limit of application of this method for plate with thickness r0/100 ≤ L ≤ r0/2. The technique is deemed interesting for the characterization of barely accessible components that require a contactless measurement. PMID:24880399
A moving mesh finite difference method for equilibrium radiation diffusion equations
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A moving mesh finite difference method for equilibrium radiation diffusion equations
NASA Astrophysics Data System (ADS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
New contactless method for thermal diffusivity measurements using modulated photothermal radiometry
NASA Astrophysics Data System (ADS)
Pham Tu Quoc, S.; Cheymol, G.; Semerok, A.
2014-05-01
Modulated photothermal radiometry is a non-destructive and contactless technique for the characterization of materials. It has two major advantages: a good signal-to-noise ratio through a synchronous detection and a low dependence on the heating power and the optical properties of the sample surface. This paper presents a new method for characterizing the thermal diffusivity of a material when the phase shift between a modulated laser power signal and the thermal signal of a plate sample is known at different frequencies. The method is based on a three-dimensional analytical model which is used to determine the temperature amplitude and the phase in the laser heating of the plate. A new simple formula was developed through multi-parametric analysis to determine the thermal diffusivity of the plate with knowledge of the frequency at the minimum phase shift, the laser beam radius r0 and the sample thickness L. This method was developed to control the variation of the thermal diffusivity of nuclear components and it was first applied to determine the thermal diffusivity of different metals: 304 L stainless steel, nickel, titanium, tungsten, molybdenum, zinc, and iron. The experimental results were obtained with 5%-10% accuracy and corresponded well with the reference values. The present paper also demonstrates the limit of application of this method for plate with thickness r0/100 ≤ L ≤ r0/2. The technique is deemed interesting for the characterization of barely accessible components that require a contactless measurement.
DEVELOPMENT OF LOW-DIFFUSION FLUX-SPLITTING METHODS FOR DENSE GAS-SOLID FLOWS
The development of a class of low-diffusion upwinding methods for computing dense gas-solid flows is presented in this work. An artificial compressibility/low-Mach preconditioning strategy is developed for a hyperbolic two-phase flow equation system consisting of separate solids ...
Liquid-phase thermal diffusion isotope separation apparatus and method having tapered column
Rutherford, William M.
1988-05-24
A thermal diffusion counterflow method and apparatus for separating isotopes in solution in which the solution is confined in a long, narrow, vertical slit which tapers from bottom to top. The variation in the width of the slit permits maintenance of a stable concentration distribution with relatively long columns, thus permitting isotopic separation superior to that obtainable in the prior art.
Liquid-phase thermal diffusion isotope separation apparatus and method having tapered column
Rutherford, W.M.
1985-12-04
A thermal diffusion counterflow method and apparatus for separating isotopes in solution in which the solution is confined in a long, narrow, vertical slit which tapers from bottom to top. The variation in the width of the slit permits maintenance of a stable concentration distribution with relatively long columns, thus permitting isotopic separation superior to that obtained in the prior art.
Anti-diffusion method for interface steepening in two-phase incompressible flow
NASA Astrophysics Data System (ADS)
So, K. K.; Hu, X. Y.; Adams, N. A.
2011-06-01
In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.
A new in-situ method to determine the apparent gas diffusion coefficient of soils
NASA Astrophysics Data System (ADS)
Laemmel, Thomas; Paulus, Sinikka; Schack-Kirchner, Helmer; Maier, Martin
2015-04-01
Soil aeration is an important factor for the biological activity in the soil and soil respiration. Generally, gas exchange between soil and atmosphere is assumed to be governed by diffusion and Fick's Law is used to describe the fluxes in the soil. The "apparent soil gas diffusion coefficient" represents the proportional factor between the flux and the gas concentration gradient in the soil and reflects the ability of the soil to "transport passively" gases through the soil. One common way to determine this coefficient is to take core samples in the field and determine it in the lab. Unfortunately this method is destructive and needs laborious field work and can only reflect a small fraction of the whole soil. As a consequence insecurity about the resulting effective diffusivity on the profile scale must remain. We developed a new in-situ method using new gas sampling device, tracer gas and inverse soil gas modelling. The gas sampling device contains several sampling depths and can be easily installed into vertical holes of an auger, which allows for fast installation of the system. At the lower end of the device inert tracer gas is injected continuously. The tracer gas diffuses into the surrounding soil. The resulting distribution of the tracer gas concentrations is used to deduce the diffusivity profile of the soil. For Finite Element Modeling of the gas sampling device/soil system the program COMSOL is used. We will present the results of a field campaign comparing the new in-situ method with lab measurements on soil cores. The new sampling pole has several interesting advantages: it can be used in-situ and over a long time; so it allows following modifications of diffusion coefficients in interaction with rain but also vegetation cycle and wind.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665
Kempka, S.N.; Strickland, J.H.
1993-08-01
A numerical method to simulate viscous diffusion of vorticity using vortex blobs (i.e., without a grid) is presented. The method consists of casting the effects of viscous diffusion into an effective ``diffusion velocity`` at which vortex blobs convect. The diffusion velocity was proposed previously by Ogami and Akamatsu, but they did not consider the effects of the divergence of the diffusion velocity. In fact, the diffusion velocity is highly non-solenoidal, which significantly affects the area over which a vortex blob diffuses. A formulation is presented that relates the area expansion to the diffusion velocity divergence. By taking into account the area expansion, more accurate simulations of diffusion are obtained, as demonstrated by a comparison of numerical and analytical diffusion solutions. Results from simulations show that vortex areas expand significantly in regions of large vorticity gradients. As a result of the area expansion, adjacent vortices remain overlapped, thereby maintaining smooth solution fields. The non-solenoidal diffusion velocity method is easily implemented in vortex blob algorithms, thus facilitating the development of vortex methods to simulate flows with finite Reynolds numbers.
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
NASA Astrophysics Data System (ADS)
Burger, Martin; Løseth Elvetun, Ole; Schlottbom, Matthias
2015-12-01
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to perturbed or not well resolved domains, and which allow for efficient discretizations not resolving any fine detail of those geometries. For forward problems in partial differential equations methods based on diffuse interface representations have gained strong attention in the last years, but so far they have not been considered systematically for inverse problems. In this work we introduce a diffuse domain method as a tool for the solution of variational inverse problems. As a particular example we study ECG inversion in further detail. ECG inversion is a linear inverse source problem with boundary measurements governed by an anisotropic diffusion equation, which naturally cries for solutions under changing geometries, namely the beating heart. We formulate a regularization strategy using Tikhonov regularization and, using standard source conditions, we prove convergence rates. A special property of our approach is that not only operator perturbations are introduced by the diffuse domain method, but more important we have to deal with topologies which depend on a parameter \\varepsilon in the diffuse domain method, i.e. we have to deal with \\varepsilon -dependent forward operators and \\varepsilon -dependent norms. In particular the appropriate function spaces for the unknown and the data depend on \\varepsilon . This prevents the application of some standard convergence techniques for inverse problems, in particular interpreting the perturbations as data errors in the original problem does not yield suitable results. We consequently develop a novel approach based on saddle-point problems. The numerical solution of the problem is discussed as well and results for several computational experiments are reported. In
An efficient and positivity-preserving layer method for modeling radiation belt diffusion processes
NASA Astrophysics Data System (ADS)
Tao, X.; Zhang, L.; Wang, C.; Li, X.; Albert, J. M.; Chan, A. A.
2016-01-01
An efficient and positivity-preserving layer method is introduced to solve the radiation belt diffusion equation and is applied to study the bounce resonance interaction between relativistic electrons and magnetosonic waves. The layer method with linear interpolation, denoted by LM-L (layer method-linear), requires the use of a large number of grid points to ensure accurate solutions. We introduce a monotonicity- and positivity-preserving cubic interpolation method to be used with the Milstein-Tretyakov layer method. The resulting method, called LM-MC (layer method-monotone cubic), can be used to solve the radiation belt diffusion equation with a much smaller number of grid points than LM-L while still being able to preserve the positivity of the solution. We suggest that LM-MC can be used to study long-term dynamics of radiation belts. We then develop a 2-D LM-MC code and use it to investigate the bounce resonance diffusion of radiation belt electrons by magnetosonic waves. Using a previously published magnetosonic wave model, we demonstrate that bounce resonance with magnetosonic waves is as important as gyroresonance; both can cause several orders of magnitude increase of MeV electron fluxes within 1 day. We conclude that bounce resonance with magnetosonic waves should be taken into consideration together with gyroresonance.
Novel front-surface thermal-diffusivity measurement method based on phase analysis
NASA Astrophysics Data System (ADS)
Braggiotti, Alberto; Marinetti, Sergio
2000-05-01
The technique described in this paper is for one-side thermal diffusivity measurement. A single stripe-shaped pulse provided by a flash lamp is used to heat the front surface of a specimen slab. Classical methods for estimating a parameter out of a distribution involve fitting the temperature distribution with its theoretical model. With the technique described in this paper the evolution of the temperature distribution along a line perpendicular to the heated stripe is analyzed in the frequency domain. An estimate of the thermal diffusivity is then obtained from comparison of the phase component behavior with an abacus similarly built from the theoretical model. This technique is valid for any shape of flash lamp pulse (i.e. laser spot), and can be used also for estimating the thermal diffusivity of anisotropic materials. The choice of the stripe shape is due to the limitations of the simulation environment used.
Zheng, Y.P.; Zhang, T.Y.
1998-12-31
In order to verify the results predicted by the model in Part 1 of this work, permeation experiments were conducted at room and high temperatures on fully-annealed-commercially-pure iron with two kinds of surface treatment, one group with plasma cleaning and presputtering and the other without it. The experimental results show that the diffusivity evaluated by the new model is independent of sample thickness and surface treatment, while the diffusivity evaluated by the time-lag model varies two orders of magnitude. The experimental results confirm that a fine surface treatment yields a low energy barrier for desorption. The energy barrier for either group is higher than the activation energy of diffusion. Consequently, the ratio of drift velocity through surface to that in bulk increases with increasing temperature and makes the time-lag method appropriate at elevated temperatures.
NASA Technical Reports Server (NTRS)
Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)
2005-01-01
Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.
NASA Technical Reports Server (NTRS)
Atkins, H. L.; Shu, Chi-Wang
2001-01-01
The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.
COMPARISON OF THE COMPLETE FOURIER DIRECT MRI WITH EXISTING DIFFUSION WEIGHTED MRI METHODS
Özcan, Alpay
2011-01-01
The Complete Fourier Direct (CFD) MRI method introduced in earlier work for modeling the diffusion weighted MRI signal is compared with the existing methods. The preservation of Hermitian symmetry in the diffusion weighted MRI signal without affecting its energy is the key point that differentiates CFD–MRI from the existing methods. By keeping the correct Fourier relationship intact, the joint distribution function is represented ‘as it is’, without any constraints, e.g. being symmetric. The necessity to model or assume models for spin motion and try to fit the model to the samples of the Fourier transform as in case of model matching methods is not required because the Discrete Fourier Transform applied to correctly processed signal in CFD–MRI gives more accurate results. PMID:21918715
Preconditioned time-difference methods for advection-diffusion-reaction equations
Aro, C.; Rodrigue, G.; Wolitzer, D.
1994-12-31
Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions placed on stepsize due to stability. Stability bounds for explicit time differencing methods on advection-diffusion-reaction problems are generally quite severe and implicit methods are used instead. The linear systems arising from these implicit methods are large and sparse so that iterative methods must be used to solve them. In this paper the authors develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods.
METHOD FOR REMOVAL OF LIGHT ISOTOPE PRODUCT FROM LIQUID THERMAL DIFFUSION UNITS
Hoffman, J.D.; Ballou, J.K.
1957-11-19
A method and apparatus are described for removing the lighter isotope of a gaseous-liquid product from a number of diffusion columns of a liquid thermal diffusion system in two stages by the use of freeze valves. The subject liquid flows from the diffusion columns into a heated sloping capsule where the liquid is vaporized by the action of steam in a heated jacket surrounding the capsule. When the capsule is filled the gas flows into a collector. Flow between the various stages is controlled by freeze valves which are opened and closed by the passage of gas and cool water respectively through coils surrounding portions of the pipes through which the process liquid is passed. The use of the dual stage remover-collector and the freeze valves is an improvement on the thermal diffusion separation process whereby the fraction containing the lighter isotope many be removed from the tops of the diffusion columns without intercolumn flow, or prior stage flow while the contents of the capsule is removed to the final receiver.
Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI.
Daducci, Alessandro; Canales-Rodríguez, Erick Jorge; Descoteaux, Maxime; Garyfallidis, Eleftherios; Gur, Yaniv; Lin, Ying-Chia; Mani, Merry; Merlet, Sylvain; Paquette, Michael; Ramirez-Manzanares, Alonso; Reisert, Marco; Reis Rodrigues, Paulo; Sepehrband, Farshid; Caruyer, Emmanuel; Choupan, Jeiran; Deriche, Rachid; Jacob, Mathews; Menegaz, Gloria; Prčkovska, Vesna; Rivera, Mariano; Wiaux, Yves; Thiran, Jean-Philippe
2014-02-01
Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies. PMID:24132007
A quantitative radioluminographic imaging method for evaluating lateral diffusion rates in skin.
Rush, Allison K; Miller, Matthew A; Smith, Edward D; Kasting, Gerald B
2015-10-28
A method is presented for measuring the lateral diffusion coefficients of exogenously applied compounds on excised skin. The method involves sequential high resolution imaging of the spatial distribution of β-radiation associated with [(14)C]-labeled compounds to monitor the development of the concentration profile on the skin surface. It is exemplified by measurements made on three radiolabeled test compounds--caffeine, testosterone, and zinc pyrithione (ZnPT)--administered as solutions. Lateral diffusivity is expected to be an important determinant of the topical bioavailability of ZnPT, which is characteristically administered as a fine suspension and must reach microorganisms in molecular form to exert biocidal activity. Application of the test compounds at levels below and above their estimated saturation doses in the upper stratum corneum allows one to distinguish between diffusion-limited and dissolution rate-limited kinetics. The effective lateral diffusivities of the two chemically stable reference compounds, caffeine and testosterone, were (1-4) × 10(-9) cm(2)/s and (3-9) × 10(-9) cm(2)/s, respectively. Lateral transport of [(14)C] associated with ZnPT was formulation-dependent, with effective diffusivities of (1-2) × 10(-9) cm(2)/s in water and (3-9) × 10(-9) cm(2)/s in a 1% body wash solution. These differences are thought to be related to molecular speciation and/or the presence of a residual surfactant phase on the skin surface. All values were greater than those estimated for the transverse diffusivities of these compounds in stratum corneum by factors ranging from 250 to over 2000. Facile lateral transport on skin, combined with a low transdermal permeation rate, may thus be seen to be a key factor in the safe and effective use of ZnPT as a topical antimicrobial agent. PMID:26241749
Data Assimilation Using a Variational Method for a 1D Radiation Belt Diffusion Model
NASA Astrophysics Data System (ADS)
Marchand, R.; Degeling, A. W.; O'Donnell, S.; Rankin, R.; Kabin, K.
2009-12-01
A variational data assimilation algorithm has been developed to incorporate electron flux time-series data from satellites into a simple one dimensional diffusion model for the radial transport of radiation belt electrons. The model developed assumes a power law scaling for the radial diffusion coefficient with L shell. The effectiveness of this method is investigated by means of a series of identical twin numerical experiments. This involves using the diffusion model to produce synthetic observations along various satellite trajectories. These observations are in turn used to estimate time-dependent parameters input to the diffusion model, which are compared against the values initially used. The data assimilation algorithm considers the time dependent source located at the outer boundary as a function to be determined. Using synthetic satellite electron flux observations, the algorithm computes a source function that, when used as an input to the diffusion model, most closely reproduces the synthetic observations in a least-squares sense. Observational errors are taken into account, and an estimate of the uncertainty in the output source function is also produced. This uncertainty is found to consistently reflect the quality of the source function estimation during identical twin numerical experiments. Initial tests indicate that the quality of the outer boundary source estimation is strongly dependent on the satellite location, indicating that the outer boundary source estimation becomes poor as information relating to the outer boundary contained in the observations is reduced. The potential of using this data assimilation method to estimate one or more parameters that determine the radial diffusion coefficient, and the possibility of determining whether physical processes affecting the observations are missing in the dynamical model will be discussed.
An in situ method for real-time monitoring of soil gas diffusivity
NASA Astrophysics Data System (ADS)
Laemmel, Thomas; Maier, Martin; Schack-Kirchner, Helmer; Lang, Friederike
2016-04-01
Soil aeration is an important factor for the biogeochemistry of soils. Generally, gas exchange between soil and atmosphere is assumed to be governed by molecular diffusion and by this way fluxes can be calculated using by Fick's Law. The soil gas diffusion coefficient DS represents the proportional factor between the gas flux and the gas concentration gradient in the soil and reflects the ability of the soil to "transport passively" gas through the soil. One common way to determine DS is taking core samples in the field and measuring DS in the lab. Unfortunately this method is destructive and laborious and it can only reflect a small fraction of the whole soil. As a consequence, uncertainty about the resulting effective diffusivity on the profile scale, i.e. the real aeration status remains. We developed a method to measure and monitor DS in situ. The set-up consists of a custom made gas sampling device, the continuous injection of an inert tracer gas and inverse gas transport modelling in the soil. The gas sampling device has seven sampling depths (from 0 to -43 cm of depth) and can be easily installed into vertical holes drilled by an auger, which allows for fast installation of the system. Helium (He) as inert tracer gas was injected continuously at the lower end of the device. The resulting steady state distribution of He was used to deduce the DS depth distribution of the soil. For Finite Element Modeling of the gas-sampling-device/soil system the program COMSOL was used. We tested our new method both in the lab and in a field study and compared the results with a reference lab method using soil cores. DS profiles obtained by our in-situ method were consistent with DS profiles determined based on soil core analyses. Soil gas profiles could be measured with a temporal resolution of 30 minutes. During the field study, there was an important rain event and we could monitor the decrease in soil gas diffusivity in the top soil due to water infiltration. The effect
GPU-accelerated 3D neutron diffusion code based on finite difference method
Xu, Q.; Yu, G.; Wang, K.
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
NASA Astrophysics Data System (ADS)
Lu, Yao; Chan, Heang-Ping; Wei, Jun; Hadjiiski, Lubomir M.
2013-02-01
Digital breast tomosynthesis (DBT) has strong promise to improve sensitivity for detecting breast cancer. DBT reconstruction estimates the breast tissue attenuation using projection views (PVs) acquired in a limited angular range. Because of the limited field of view (FOV) of the detector, the PVs may not completely cover the breast in the x-ray source motion direction at large projection angles. The voxels in the imaged volume cannot be updated when they are outside the FOV, thus causing a discontinuity in intensity across the FOV boundaries in the reconstructed slices, which we refer to as the truncated projection artifact (TPA). Most existing TPA reduction methods were developed for the filtered backprojection method in the context of computed tomography. In this study, we developed a new diffusion-based method to reduce TPAs during DBT reconstruction using the simultaneous algebraic reconstruction technique (SART). Our TPA reduction method compensates for the discontinuity in background intensity outside the FOV of the current PV after each PV updating in SART. The difference in voxel values across the FOV boundary is smoothly diffused to the region beyond the FOV of the current PV. Diffusion-based background intensity estimation is performed iteratively to avoid structured artifacts. The method is applicable to TPA in both the forward and backward directions of the PVs and for any number of iterations during reconstruction. The effectiveness of the new method was evaluated by comparing the visual quality of the reconstructed slices and the measured discontinuities across the TPA with and without artifact correction at various iterations. The results demonstrated that the diffusion-based intensity compensation method reduced the TPA while preserving the detailed tissue structures. The visibility of breast lesions obscured by the TPA was improved after artifact reduction.
Lu, Yao; Chan, Heang-Ping; Wei, Jun; Hadjiiski, Lubomir M
2013-02-01
Digital breast tomosynthesis (DBT) has strong promise to improve sensitivity for detecting breast cancer. DBT reconstruction estimates the breast tissue attenuation using projection views (PVs) acquired in a limited angular range. Because of the limited field of view (FOV) of the detector, the PVs may not completely cover the breast in the x-ray source motion direction at large projection angles. The voxels in the imaged volume cannot be updated when they are outside the FOV, thus causing a discontinuity in intensity across the FOV boundaries in the reconstructed slices, which we refer to as the truncated projection artifact (TPA). Most existing TPA reduction methods were developed for the filtered backprojection method in the context of computed tomography. In this study, we developed a new diffusion-based method to reduce TPAs during DBT reconstruction using the simultaneous algebraic reconstruction technique (SART). Our TPA reduction method compensates for the discontinuity in background intensity outside the FOV of the current PV after each PV updating in SART. The difference in voxel values across the FOV boundary is smoothly diffused to the region beyond the FOV of the current PV. Diffusion-based background intensity estimation is performed iteratively to avoid structured artifacts. The method is applicable to TPA in both the forward and backward directions of the PVs and for any number of iterations during reconstruction. The effectiveness of the new method was evaluated by comparing the visual quality of the reconstructed slices and the measured discontinuities across the TPA with and without artifact correction at various iterations. The results demonstrated that the diffusion-based intensity compensation method reduced the TPA while preserving the detailed tissue structures. The visibility of breast lesions obscured by the TPA was improved after artifact reduction. PMID:23318346
Application of Electrode Methods in Studies of Nitric Oxide Metabolism and Diffusion Kinetics
Liu, Xiaoping; Zweier, Jay L.
2012-01-01
Nitric oxide (NO) has many important physiological roles in the body. Since NO electrodes can directly measure NO concentration in the nM range and in real time, NO electrode methods have been generally used in laboratories for measuring NO concentration in vivo and in vitro. This review focuses on the application of electrode methods in studies of NO diffusion and metabolic kinetics. We have described the physical and chemical properties that need to be considered in the preparation of NO stock solution, discussed the effect of several interfering factors on the measured curves of NO concentration that need to be eliminated in the experimental setup for NO measurements, and provided an overview of the application of NO electrode methods in measuring NO diffusion and metabolic kinetics in solution and in biological systems. This overview covers NO metabolism by oxygen (O2), superoxide, heme proteins, cells and tissues. Important conclusions and physiological implication of these studies are discussed. PMID:23730264
Application of numerical methods for diffusion-based modeling of skin permeation.
Frasch, H Frederick; Barbero, Ana M
2013-02-01
The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions. PMID:22261307
Preconditioned iterative methods for space-time fractional advection-diffusion equations
NASA Astrophysics Data System (ADS)
Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.
2016-08-01
In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.
A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation
Evans, Thomas M.; Mosher, Scott W.; Slattery, Stuart R.; Hamilton, Steven P.
2014-02-01
We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
Ku, Bon Ki; Kulkarni, Pramod
2015-01-01
We compare different approaches to measure surface area of aerosol agglomerates. The objective was to compare field methods, such as mobility and diffusion charging based approaches, with laboratory approach, such as Brunauer, Emmett, Teller (BET) method used for bulk powder samples. To allow intercomparison of various surface area measurements, we defined ‘geometric surface area’ of agglomerates (assuming agglomerates are made up of ideal spheres), and compared various surface area measurements to the geometric surface area. Four different approaches for measuring surface area of agglomerate particles in the size range of 60–350 nm were compared using (i) diffusion charging-based sensors from three different manufacturers, (ii) mobility diameter of an agglomerate, (iii) mobility diameter of an agglomerate assuming a linear chain morphology with uniform primary particle size, and (iv) surface area estimation based on tandem mobility–mass measurement and microscopy. Our results indicate that the tandem mobility–mass measurement, which can be applied directly to airborne particles unlike the BET method, agrees well with the BET method. It was also shown that the three diffusion charging-based surface area measurements of silver agglomerates were similar within a factor of 2 and were lower than those obtained from the tandem mobility–mass and microscopy method by a factor of 3–10 in the size range studied. Surface area estimated using the mobility diameter depended on the structure or morphology of the agglomerate with significant underestimation at high fractal dimensions approaching 3. PMID:26692585
Tchitchekova, Deyana S.; Morthomas, Julien; Perez, Michel; Ribeiro, Fabienne; Ducher, Roland
2014-07-21
A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.
Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel
2014-07-21
A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress. PMID:25053312
NASA Astrophysics Data System (ADS)
Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel
2014-07-01
A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.
Theoretical principles of experimental methods for determining the thermal diffusivity of soils
NASA Astrophysics Data System (ADS)
Mikayilov, F. D.; Shein, E. V.
2010-05-01
Mathematical models for predicting the heat transfer in soils are used for the management of the soil thermal conditions; the development of different soil constructions; the analysis of the thermal effects related to the loosening or compaction of the surface soil layers, the sanding of peat, and the application of friable mulching materials; and the description of many other phenomena and processes. The experimental support of the development and functioning of these models is provided by the function of thermal diffusivity, which describes the thermal diffusivity as a function of the water content and can be derived using the methods based on the solution of direct and inverse problems of heat transfer. On the basis of the different boundary conditions and sine-shaped daily and annual temperature cycles, a number of equations were proposed for calculating the thermal diffusivity that contained logarithms, arctangents of amplitudes, and the phase shift between the daily temperatures at two depths. A mean-integral solution was obtained for the estimation of the average temperature in a specific soil layer. A number of methods were developed starting from the analysis of the temperature dynamics on the basis of four daily observations at the same depth with 6-hour intervals, and nomograms were given for the rapid and simple calculation of the soil thermal diffusivity at a specific depth. The developed methods can be used for assessing the soil thermal diffusivity under natural conditions, which should improve the reliability, accuracy, and adequacy and expand the application range of predictive mathematical models for the thermal regime of soils.
NASA Astrophysics Data System (ADS)
Jiang, Tian; Zhang, Yong-Tao
2016-04-01
Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods were combined with weighted essentially non-oscillatory (WENO) schemes in Jiang and Zhang (2013) [19] to efficiently solve stiff nonlinear advection-diffusion-reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the non-stiff hyperbolic part of the system. To efficiently calculate large matrix exponentials, Krylov subspace approximation is directly applied to the implicit integration factor (IIF) methods. So far, the IIF methods developed in the literature are multistep methods. In this paper, we develop Krylov single-step IIF-WENO methods for solving stiff advection-diffusion-reaction equations. The methods are designed carefully to avoid generating positive exponentials in the matrix exponentials, which is necessary for the stability of the schemes. We analyze the stability and truncation errors of the single-step IIF schemes. Numerical examples of both scalar equations and systems are shown to demonstrate the accuracy, efficiency and robustness of the new methods.
Farzad Rahnema; Dingkang Zhang; Abderrafi Ougouag; Frederick Gleicher
2011-04-04
The main objective of this research is to develop an integrated diffusion/transport (IDT) method to substantially improve the accuracy of nodal diffusion methods for the design and analysis of Very High Temperature Reactors (VHTR). Because of the presence of control rods in the reflector regions in the Pebble Bed Reactor (PBR-VHTR), traditional nodal diffusion methods do not accurately model these regions, within which diffusion theory breaks down in the vicinity of high neutron absorption and steep flux gradients. The IDT method uses a local transport solver based on a new incident flux response expansion method in the controlled nodes. Diffusion theory is used in the rest of the core. This approach improves the accuracy of the core solution by generating transport solutions of controlled nodes while maintaining computational efficiency by using diffusion solutions in nodes where such a treatment is sufficient. The transport method is initially developed and coupled to the reformulated 3-D nodal diffusion model in the CYNOD code for PBR core design and fuel cycle analysis. This method is also extended to the prismatic VHTR. The new method accurately captures transport effects in highly heterogeneous regions with steep flux gradients. The calculations of these nodes with transport theory avoid errors associated with spatial homogenization commonly used in diffusion methods in reactor core simulators
Klancnik, Anja; Piskernik, Sasa; Jersek, Barbara; Mozina, Sonja Smole
2010-05-01
The aim of this study was to evaluate diffusion and dilution methods for determining the antibacterial activity of plant extracts and their mixtures. Several methods for measurement of the minimal inhibitory concentration (MIC) of a plant extract are available, but there is no standard procedure as there is for antibiotics. We tested different plant extracts, their mixtures and phenolic acids on selected gram-positive (Staphylococcus aureus, Bacillus cereus, and Listeria monocytogenes) and gram-negative bacteria (Escherichia coli O157:H7, Salmonella Infantis, Campylobacter jejuni, Campylobacter coli) with the disk diffusion, agar dilution, broth microdilution and macrodilution methods. The disk diffusion method was appropriate only as a preliminary screening test prior to quantitative MIC determination with dilution methods. A comparison of the results for MIC obtained by agar dilution and broth microdilution was possible only for gram-positive bacteria, and indicated the latter as the most accurate way of assessing the antimicrobial effect. The microdilution method with TTC (2,3,5-triphenyl tetrazolium chloride) or INT (2-p-iodophenyl-3-p-nitrophenyl-5-phenyl tetrazolium chloride) to indicate the viability of aerobic bacteria was found to be the best alternative approach, while only ATP determination was appropriate for microaerophilic Campylobacter spp. Using survival curves the kinetics of bacterial inactivation on plant extract exposure was followed for 24h and in this way the MIC values determined by the microdilution method were confirmed as the concentrations of extracts that inhibited bacterial growth. We suggest evaluation of the antibacterial activity of plant extracts using the broth microdilution method as a fast screening method for MIC determination and the macrodilution method at selected MIC values to confirm bacterial inactivation. Campylobacter spp. showed a similar sensitivity to plant extracts as the tested gram-positive bacteria, but S
A simple method for the determination of resistance to gas diffusion in plant organs.
Cameron, A C; Yang, S F
1982-07-01
A simple method was developed for the determination of resistance coefficients for ethylene diffusion in plant tissues based on the kinetic analysis of the efflux of preloaded ethane gas. Efflux curves were analyzed to obtain first-order rate constants and resistance coefficients. Resistance coefficients determined by the ethane efflux and steady-state methods were found to agree well. Employing the ethane efflux method, it was shown that over 97% of gas exchange of tomato (Lycopersicum esculentum Mill., cv. ;Ace') fruits occurs through the stem scar. The resistances to diffusion of tomato skin and stem scar were found to be 280,000 and 300 seconds per centimeter, respectively; the combined resistance of intact tomato fruits was approximately 7,800 seconds per centimeter. The ethane efflux method was employed to show that plastic shrink-wrapping of English cucumbers (Cucumis sativus L. var anglicus Bailey) increased the resistance to ethane diffusion from 1.1 x 10(3) to 23 x 10(3) seconds per centimeter. PMID:16662447
A novel model for diffusion based release kinetics using an inverse numerical method.
Mohammadi, Hadi; Herzog, Walter
2011-10-01
We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important. PMID:21382735
Non-invasive measurements of tissue hemodynamics with hybrid diffuse optical methods
NASA Astrophysics Data System (ADS)
Durduran, Turgut
Diffuse optical techniques were used to measure hemodynamics of tissues non-invasively. Spectroscopy and tomography of the brain, muscle and implanted tumors were carried out in animal models and humans. Two qualitatively different methods, diffuse optical tomography and diffuse correlation tomography, were hybridized permitting simultaneous measurement of total hemoglobin concentration, blood oxygen saturation and blood flow. This combination of information was processed further to derive estimates of oxygen metabolism (e.g. CMRO 2) in tissue. The diffuse correlation measurements of blood flow were demonstrated in human tissues, for the first time, demonstrating continous, non-invasive imaging of oxygen metabolism in large tissue volumes several centimeters below the tissue surface. The bulk of these investigations focussed on cerebral hemodynamics. Extensive validation of this methodology was carried out in in vivo rat brain models. Three dimensional images of deep tissue hemodynamics in middle cerebral artery occlusion and cortical spreading depression (CSD) were obtained. CSD hemodynamics were found to depend strongly on partial pressure of carbon dioxide. The technique was then adapted for measurement of human brain. All optical spectroscopic measurements of CMRO2 during functional activation were obtained through intact human skull non-invasively. Finally, a high spatio-temporal resolution measurement of cerebral blood flow due to somatosensory cortex activation following electrical forepaw stimulation in rats was carried out with laser speckle flowmetry. New analysis methods were introduced for laser speckle flowmetry. In other organs, deep tissue hemodynamics were measured on human calf muscle during exercise and cuff-ischemia and were shown to have some clinical utility for peripheral vascular disease. In mice tumor models, the measured hemodynamics were shown to be predictive of photodynamic therapy efficacy, again suggesting promise of clinical utility
NASA Astrophysics Data System (ADS)
Kang, Q.; Chen, L.
2014-12-01
Although short-term production of unconventional gas depends on the area of contact created by hydraulic fracturing and connections with pre-existing natural fracture networks, sustainable recovery is limited by transfer of gas from nanoporous matrix into the fractures, because the permeability of hydraulic fractures is orders of magnitude higher than that of the shale matrix. Therefore, a fundamental understanding of hydrocarbon mobility in shale matrix is urgently needed for improving recovery efficiencies. Shale transport properties (diffusivity, permeability, and electronic conductivity), which are critical for understanding the fundamental transport mechanisms, are still poorly understood. There have been some studies using experimental techniques such as scanning electron microscopy (SEM) to visualize the nanoscale structures of shale. Due to the ultra-low porosity and permeability, it is difficult to experimentally investigate the fundamental transport processes inside the shale or accurately measure the transport properties. Advanced pore-scale numerical methods, e.g., the lattice Boltzman method (LBM) may provide an alternative approach. In the present study, three-dimensional nanoscale porous structures of shale are reconstructed based on SEM images of shale samples. Characterization analysis of the nanoscale reconstructed shale is performed, including determination of porosity, pore size distribution, specific surface area, and pore connectivity. The LBM flow model and diffusion model are adopted to simulate fluid flow and Knudsen diffusion in the reconstructed shale, respectively. Tortuosity, intrinsic permeability, and effective Knudsen diffusivity are numerically predicted. The tortuosity is much higher than what is commonly employed in Bruggeman equation. Correction of the intrinsic permeability by taking into consideration the contribution of Knudsen diffusion, which leads to the apparent permeability, is performed. The correction factor under
Cu diffusion as an alternative method for nanopatterned CuTCNQ film growth
NASA Astrophysics Data System (ADS)
Capitán, M. J.; Álvarez, J.; Navío, C.; Miranda, R.
2016-05-01
In this paper we show by means of ‘in situ’ x-ray diffraction studies that CuTCNQ formation from Cu(solid)–TCNQ(solid tetracyanoquinodimethane) goes through Cu diffusion at room temperature. The film quality depends on the TCNQ evaporation rate. At low evaporation rate we get a single phase-I CuTCNQ film very well crystallized and well oriented. The film has a CuTCNQ(0 2 0) orientation. The film is formed by CuTCNQ nanorods of a very homogeneous size. The film homogeneity has also been seen by atomic force microscopy (AFM). The electronic properties of the film have been measured by x-ray photoelectron spectroscopy (XPS) and ultra-violet photoelectron spectroscopy (UPS). Thus, the Cu-diffusion method has arisen as a very simple, clean and efficient method to grow localized CuTCNQ nanorods on Cu, opening up new insights for technological applications.
Does diffusion MRI tell us anything about the white matter? An overview of methods and pitfalls
O’Donnell, Lauren J.; Pasternak, Ofer
2014-01-01
One key pitfall in diffusion magnetic resonance imaging (dMRI) clinical neuroimaging research is the challenge of understanding and interpreting the results of a complex analysis pipeline. The sophisticated algorithms employed by the analysis software, combined with the relatively non-specific nature of many diffusion measurements, lead to challenges in interpretation of the results. This paper is aimed at an intended audience of clinical researchers who are learning about dMRI or trying to interpret dMRI results, and who may be wondering “Does dMRI tell us anything about the white matter?” We present a critical review of dMRI methods and measures used in clinical neuroimaging research, focusing on the most commonly used analysis methods and the most commonly reported measures. We describe important pitfalls in every section, and provide extensive references for the reader interested in more detail. PMID:25278106
Errors associated with standard nodal diffusion methods as applied to mixed oxide fuel problems
Brantley, P. S., LLNL
1998-07-24
The evaluation of the disposition of plutonium using light water reactors is receiving increased attention. However, mixed-oxide (MOX) fuel assemblies possess much higher absorption and fission cross- sections when compared to standard UO2 assemblies. Those properties yield very high thermal flux gradients at the interfaces between MOX and UO2 assemblies. It has already been reported that standard flux reconstruction methods (that recover the homogeneous intranodal flux shape using the converged nodal solution) yield large errors in the presence of MOX assemblies. In an accompanying paper, we compare diffusion and simplified PN calculations of a mixed-oxide benchmark problem to a reference transport calculation. In this paper, we examine the errors associated with standard nodal diffusion methods when applied to the same benchmark problem. Our results show that a large portion of the error is associated with the quadratic leakage approximation (QLA) that is commonly used in the standard nodal codes.
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Padgett, Jill M. A.; Ilie, Silvana
2016-03-01
Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.
NASA Astrophysics Data System (ADS)
Trochet, Mickaël; Béland, Laurent Karim; Joly, Jean-François; Brommer, Peter; Mousseau, Normand
2015-06-01
We study point-defect diffusion in crystalline silicon using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities based on the activation-relaxation technique (ART nouveau), coupled to the standard Stillinger-Weber potential. We focus more particularly on the evolution of crystalline cells with one to four vacancies and one to four interstitials in order to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics. We show formation energies, activation barriers for the ground state of all eight systems, and migration barriers for those systems that diffuse. Additionally, we characterize diffusion paths and special configurations such as dumbbell complex, di-interstitial (IV-pair+2I) superdiffuser, tetrahedral vacancy complex, and more. This study points to an unsuspected dynamical richness even for this apparently simple system that can only be uncovered by exhaustive and systematic approaches such as the kinetic activation-relaxation technique.
Method for the measurement of the diffusion coefficient of benzalkonium chloride.
Smith, M J; Flowers, T H; Cowling, M J; Duncan, H J
2002-03-01
Biofilm formation on the optical ports of cameras and underwater sensors is the primary cause of their reduced useful deployment time. The use of a transparent hydrogel coating containing the cationic surfactant benzalkonium chloride has been shown to extend the deployment times for up to 12 weeks for these instruments. In order to predict the effective lifetime of these coatings it was necessary to obtain the diffusion coefficient of the benzalkonium chloride used in the coatings. Benzalkonium chloride can have different alkyl chain lengths ranging from C8H17 to C18H37 with chain length greatly affecting its chemical properties. The benzalkonium chloride materials investigated here were mixtures of C12H25 and C14H29 as well as C14H29 on its own. These materials were selected for their proven biofilm resistant qualities. The diaphragm diffusion cell technique was investigated for its applicability to the measurement of diffusion coefficients of molecules with surfactant properties and the ability to form micelles. The method was found to be satisfactory for the cationic surfactant benzalkonium chloride. The average value of the membrane cell integral diffusion coefficient D was 7.78 x 10(-6) cm2 s(-1) at 25 degrees C and there was no significant effect of alkyl chain length on the measured value of D. PMID:11996332
A Proposal for a Novel Method to Measure the Diffusivity of Species in Slag
NASA Astrophysics Data System (ADS)
Muhmood, Luckman; Viswanathan, Nurni Neelakantan; Seetharaman, Seshadri
2011-04-01
The rate of reactions involved in steel-refining operations largely depend on the transport of species through the slag or metal phase at steel refining temperatures; the intrinsic reaction rates are expected to be high. Therefore, the study of diffusivity of species in slag is of great importance. The present work proposes a new methodology, in which experiments can be designed to determine the diffusivity of species in liquid slag. In this article, a mathematical description for the methodology is formulated and subsequently solved using numerical methods. This exercise will help in identifying appropriate bounds for experimental parameters for a desired accuracy. The proposed methodology is generic for any species in the liquid slag phase. However, diffusion of sulfur through slag has been illustrated as a case study. The order of magnitude for the diffusion coefficient for sulfur was taken from the classic works of Saito and Kawai, the sulfide capacity and sulfur partition ratio were retrieved from the works of Taniguchi et al., and the slag density was retrieved from earlier experimental results of the present authors. The slag density was obtained from earlier experimental results from the present group. The Henrian activity coefficients were retrieved from literature. Subsequent to the present work, the design of experiments and measurements carried out using the proposed methodology and the results obtained are presented as the second article on this subject.
A hybrid method for efficient and accurate simulations of diffusion compartment imaging signals
NASA Astrophysics Data System (ADS)
Rensonnet, Gaëtan; Jacobs, Damien; Macq, Benoît; Taquet, Maxime
2015-12-01
Diffusion-weighted imaging is sensitive to the movement of water molecules through the tissue microstructure and can therefore be used to gain insight into the tissue cellular architecture. While the diffusion signal arising from simple geometrical microstructure is known analytically, it remains unclear what diffusion signal arises from complex microstructural configurations. Such knowledge is important to design optimal acquisition sequences, to understand the limitations of diffusion-weighted imaging and to validate novel models of the brain microstructure. We present a novel framework for the efficient simulation of high-quality DW-MRI signals based on the hybrid combination of exact analytic expressions in simple geometric compartments such as cylinders and spheres and Monte Carlo simulations in more complex geometries. We validate our approach on synthetic arrangements of parallel cylinders representing the geometry of white matter fascicles, by comparing it to complete, all-out Monte Carlo simulations commonly used in the literature. For typical configurations, equal levels of accuracy are obtained with our hybrid method in less than one fifth of the computational time required for Monte Carlo simulations.
A novel grating-imaging method to measure carrier diffusion coefficient in graphene
NASA Astrophysics Data System (ADS)
Chen, Ke; Wang, Yaguo; Akinwande, Deji; Bank, Seth; Lin, Jung-Fu
Similar to carrier mobility, carrier diffusion coefficient in graphene determines the response rate of future graphene-based electronics. Here we present a simple, sensitive and non-destructive technique integrated with ultrafast pump-probe spectroscopy to measure carrier diffusion in CVD-grown graphene. In the method, the pump and the probe beams pass through the same area of a photomask with metal strips i.e. a transmission amplitude grating, and get diffracted. The diffracted light is collected by an objective lens and focused onto the sample to generate carrier density grating. Relaxation of this carrier density grating is governed by both carrier recombination and carrier diffusion in the sample. Transient transmission change of the probe beams, which reflects this relaxation process, is recorded. The measured diffusion coefficients of multilayer and monolayer CVD-grown graphene are 2000cm2/s and 10000cm2/s, respectively, comparable with the reported values of epitaxial graphene and reduced graphene. This transmission grating technique can be used to measure carrier dynamics in versatile 2D materials.
New contactless method for thermal diffusivity measurements using modulated photothermal radiometry
Pham Tu Quoc, S. Cheymol, G.; Semerok, A.
2014-05-15
Modulated photothermal radiometry is a non-destructive and contactless technique for the characterization of materials. It has two major advantages: a good signal-to-noise ratio through a synchronous detection and a low dependence on the heating power and the optical properties of the sample surface. This paper presents a new method for characterizing the thermal diffusivity of a material when the phase shift between a modulated laser power signal and the thermal signal of a plate sample is known at different frequencies. The method is based on a three-dimensional analytical model which is used to determine the temperature amplitude and the phase in the laser heating of the plate. A new simple formula was developed through multi-parametric analysis to determine the thermal diffusivity of the plate with knowledge of the frequency at the minimum phase shift, the laser beam radius r{sub 0} and the sample thickness L. This method was developed to control the variation of the thermal diffusivity of nuclear components and it was first applied to determine the thermal diffusivity of different metals: 304 L stainless steel, nickel, titanium, tungsten, molybdenum, zinc, and iron. The experimental results were obtained with 5%–10% accuracy and corresponded well with the reference values. The present paper also demonstrates the limit of application of this method for plate with thickness r{sub 0}/100 ≤ L ≤ r{sub 0}/2. The technique is deemed interesting for the characterization of barely accessible components that require a contactless measurement.
Cytotoxicity of ferrite particles by MTT and agar diffusion methods for hyperthermic application
NASA Astrophysics Data System (ADS)
Kim, Dong-Hyun; Lee, Se-Ho; Kim, Kyoung-Nam; Kim, Kwang-Mahn; Shim, In-Bo; Lee, Yong-Keun
2005-05-01
We investigated the cytotoxicity of the prepared various ferrites (Fe-, Li-, Ni/Zn/Cu-, Ba-, Sr-, Co-, Co/Ni-ferrites) using MTT assay as well as agar diffusion method. Their cytotoxicity was compared with that of alginate-encapsulated ferrites. In the MTT assay, Fe 3O 4 and SrFe 12O 19 ferrite showed the highest cell viability of 90%. Alginate-encapsulated Ba-ferrite was ranked mildly cytotoxic, whereas their ferrite particles were ranked cytotoxic.
Bowen, Constance Mary; Stanton, Marietta; Manno, Martin
2012-01-01
Routine screening of mechanically ventilated patients for delirium is essential for prompt recognition and management; however, this represents a change in practice. Rogers' Diffusion of Innovations Theory can be useful as a strategy to facilitate adoption of a practice change. This case study describes the effectiveness of identifying barriers to a change in practice and developing strategies, specific to Rogers' innovation decision process, for implementing the Confusion Assessment Method for the intensive care unit. PMID:22367153
NASA Astrophysics Data System (ADS)
Lai, Yongzeng; Zeng, Yan; Xi, Xiaojing
2011-11-01
In this paper, we discuss control variate methods for Asian option pricing under exponential jump diffusion model for the underlying asset prices. Numerical results show that the new control variate XNCV is much more efficient than the classical control variate XCCV when used in pricing Asian options. For example, the variance reduction ratios by XCCV are no more than 120 whereas those by XNCV vary from 15797 to 49171 on average over sample sizes 1024, 2048, 4096, 8192, 16384 and 32768.
NASA Astrophysics Data System (ADS)
Liu, Quan; Ramanujam, Nirmala
2007-04-01
A scaling Monte Carlo method has been developed to calculate diffuse reflectance from multilayered media with a wide range of optical properties in the ultraviolet-visible wavelength range. This multilayered scaling method employs the photon trajectory information generated from a single baseline Monte Carlo simulation of a homogeneous medium to scale the exit distance and exit weight of photons for a new set of optical properties in the multilayered medium. The scaling method is particularly suited to simulating diffuse reflectance spectra or creating a Monte Carlo database to extract optical properties of layered media, both of which are demonstrated in this paper. Particularly, it was found that the root-mean-square error (RMSE) between scaled diffuse reflectance, for which the anisotropy factor and refractive index in the baseline simulation were, respectively, 0.9 and 1.338, and independently simulated diffuse reflectance was less than or equal to 5% for source-detector separations from 200 to 1500 μm when the anisotropy factor of the top layer in a two-layered epithelial tissue model was varied from 0.8 to 0.99; in contrast, the RMSE was always less than 5% for all separations (from 0 to 1500 μm) when the anisotropy factor of the bottom layer was varied from 0.7 to 0.99. When the refractive index of either layer in the two-layered tissue model was varied from 1.3 to 1.4, the RMSE was less than 10%. The scaling method can reduce computation time by more than 2 orders of magnitude compared with independent Monte Carlo simulations.
Impact of the emulsification-diffusion method on the development of pharmaceutical nanoparticles.
Quintanar-Guerrero, David; Zambrano-Zaragoza, María de la Luz; Gutierrez-Cortez, Elsa; Mendoza-Munoz, Nestor
2012-12-01
Nanotechnology is having a profound impact in many scientific fields and it has become one of the most important and exciting discipline. Like all technological advances, nanotechnology has its own scientific basis with a broad interdisciplinary effect. Perhaps, we are witnessing an exponential growth of nanotechnology, reflection of this is the important increase in the number of patents, scientific papers and specialized "nano" meetings and journals. The impact in the pharmaceutical area is related to the use of colloidal drug delivery systems as carriers for bioactive agents, in particular, the nanoparticle technology. The term nanoparticles designates solid submicronic particles formed of acceptable materials (e.g. polymers, lipids, etc.) containing an active substance. It includes both nanospheres (matricial systems) and nanocapsules (membrane systems). The knowledge of the nanoparticle preparation methods is a key issue for the formulator involved with drug-delivery research and development. In general, the methods based on preformed polymers, in particular biodegradable polymers, are preferred due to their easy implementation and lower potential toxicity. One of the most widely used methods to prepare polymeric nanoparticles is emulsification-diffusion. This method has been discussed in some reviews that compile research works but has a small number of patents. In this review, the emulsification-diffusion method is discussed from a technological point of view in order to show the operating conditions and formulation variables from data extracted of recent patents and experimental works. The main idea is to provide the reader with a general guide for formulators to make decisions about the usefulness of this method to develop specific nanoparticulate systems. The first part of this review provides an overview of the emulsification-diffusion method to prepare polymeric nanoparticles, while the second part evaluates the influence of preparative variables on the
A modified evaluation method to reduce finite pulse time effects in flash diffusivity measurement
NASA Astrophysics Data System (ADS)
Tao, Ye; Yang, Liping; Zhong, Qiu; Xu, Zijun; Luo, Caiyun
2015-12-01
A modified evaluation method for laser flash is proposed. In this method, the moment of laser-heating cutoff time is considered as zero point. The penetration depth and formula equation of the sample temperature distribution are obtained with the approximate analytical solution before time zero (during laser heating) for the physical model of a continuously heated half-infinite, well-distributed sample. The weighted-average and approximate-equation methods are then used to quantitatively determine the laser effect depth, which leads to the formulation of a modified evaluation method in flash thermal diffusivity measurement. Results of the simulation calculations and experiments confirm the correctness of the modified method, which remarkably increases flash method applications. The modified method is applicable only to cases in which δ(x) does not exceed the sample thickness ( √{ 12 α τ 0 } ≤ L ) during laser heating.
A modified evaluation method to reduce finite pulse time effects in flash diffusivity measurement.
Tao, Ye; Yang, Liping; Zhong, Qiu; Xu, Zijun; Luo, Caiyun
2015-12-01
A modified evaluation method for laser flash is proposed. In this method, the moment of laser-heating cutoff time is considered as zero point. The penetration depth and formula equation of the sample temperature distribution are obtained with the approximate analytical solution before time zero (during laser heating) for the physical model of a continuously heated half-infinite, well-distributed sample. The weighted-average and approximate-equation methods are then used to quantitatively determine the laser effect depth, which leads to the formulation of a modified evaluation method in flash thermal diffusivity measurement. Results of the simulation calculations and experiments confirm the correctness of the modified method, which remarkably increases flash method applications. The modified method is applicable only to cases in which δ(x) does not exceed the sample thickness (√(12ατ0)≤L) during laser heating. PMID:26724057
Contribution to an effective design method for stationary reaction-diffusion patterns.
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences. PMID:26117122
Contribution to an effective design method for stationary reaction-diffusion patterns
NASA Astrophysics Data System (ADS)
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Method for Calculating the Optical Diffuse Reflection Coefficient for the Ocular Fundus
NASA Astrophysics Data System (ADS)
Lisenko, S. A.; Kugeiko, M. M.
2016-07-01
We have developed a method for calculating the optical diffuse reflection coefficient for the ocular fundus, taking into account multiple scattering of light in its layers (retina, epithelium, choroid) and multiple refl ection of light between layers. The method is based on the formulas for optical "combination" of the layers of the medium, in which the optical parameters of the layers (absorption and scattering coefficients) are replaced by some effective values, different for cases of directional and diffuse illumination of the layer. Coefficients relating the effective optical parameters of the layers and the actual values were established based on the results of a Monte Carlo numerical simulation of radiation transport in the medium. We estimate the uncertainties in retrieval of the structural and morphological parameters for the fundus from its diffuse reflectance spectrum using our method. We show that the simulated spectra correspond to the experimental data and that the estimates of the fundus parameters obtained as a result of solving the inverse problem are reasonable.
Song, Yun S.; Steinrücken, Matthias
2012-01-01
The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899
Computing quasi-linear diffusion coefficients using the delta-f particle-in-cell method
Austin, T. M.; Smithe, D. N.; Ranjbar, V.
2009-11-26
Linear wave codes AORSA and TORIC couple to the bounce-averaged nonlinear Fokker-Planck code CQL3D through quasi-linear diffusion coefficients. Both linear wave codes rely on the quasi-local approximation that includes only first-order parallel and perpendicular gradient variations of cyclotron frequency and ignores field line curvature along with temperature and density gradient effects. The delta-f particle-in-cell (DFPIC) method has been successfully used for simulating ion-cyclotron fast wave behavior. This method also permits particle behavior such as multiple pass resonance, banana orbits, and superadiabaticity. We present new work on generating quasi-linear diffusion coefficients using the DFPIC method that will permit the electromagnetic particle-in-cell (EMPIC) code, VORPAL, to couple to CQL3D and to compare to AORSA and TORIC. A new multiple weight delta-f approach will be presented that converts velocity derivatives to action derivatives and yields a full tensor quasi-linear diffusion coefficient.
The diffuse-scattering method for investigating locally ordered binary solid solutions
Epperson, J.E. ); Anderson, J.P. ); Chen, H. . Materials Science and Engineering Dept.)
1994-01-01
Diffuse-scattering investigations comprise a series of maturing methods for detailed characterization of the local-order structure and atomic displacements of binary alloy systems. The distribution of coherent diffuse scattering is determined by the local atomic ordering, and analytical techniques are available for extracting the relevant structural information. An extension of such structural investigations, for locally ordered alloys at equilibrium, allows one to obtain pairwise interaction energies. Having experimental pairwise interaction energies for the various coordination shells offers one the potential for more realistic kinetic Ising modeling of alloy systems as they relax toward equilibrium. Although the modeling of atomic displacements in conjunction with more conventional studies of chemical ordering is in its infancy, the method appears to offer considerable promise for revealing additional information about the strain fields in locally ordered and clustered alloys. The diffuse-scattering methods for structural characterization and for the recovery of interaction energies are reviewed, and some preliminary results are used to demonstrate the potential of the kinetic Ising modeling technique to follow the evolution of ordering or phase separation in an alloy system.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-15
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Method and apparatus for determining minority carrier diffusion length in semiconductors
Goldstein, Bernard; Dresner, Joseph; Szostak, Daniel J.
1983-07-12
Method and apparatus are provided for determining the diffusion length of minority carriers in semiconductor material, particularly amorphous silicon which has a significantly small minority carrier diffusion length using the constant-magnitude surface-photovoltage (SPV) method. An unmodulated illumination provides the light excitation on the surface of the material to generate the SPV. A manually controlled or automatic servo system maintains a constant predetermined value of the SPV. A vibrating Kelvin method-type probe electrode couples the SPV to a measurement system. The operating optical wavelength of an adjustable monochromator to compensate for the wavelength dependent sensitivity of a photodetector is selected to measure the illumination intensity (photon flux) on the silicon. Measurements of the relative photon flux for a plurality of wavelengths are plotted against the reciprocal of the optical absorption coefficient of the material. A linear plot of the data points is extrapolated to zero intensity. The negative intercept value on the reciprocal optical coefficient axis of the extrapolated linear plot is the diffusion length of the minority carriers.
Fabrication of graded-index plastic optical fiber by the diffusion-assisted coextrusion method
NASA Astrophysics Data System (ADS)
Sohn, In-Sung
Recently, plastic optical fibers (POFs) have drawn significant attention as high-speed transmission media due to their advantages over conventional glass optical fibers such as flexibility and durability. In addition, Grade-Index (GRIN) POFs with smoothly varying refractive indices provide increased data transmission speeds suitable for the short-distance communications such as local area networking or home networking. In this research, the diffusion-assisted coextrusion process is introduced as a method to fabricate GRIN POFs. In this process, two or more polymeric materials containing additives for refractive index modification are fed separately into a coextrusion die where a concentric multi-layer structure is formed. Subsequently, the diffusion of additives take places in a diffusion zone creating a non-equilibrium concentration profile, hence the refractive index profile. A theoretical analysis for the prediction of the refractive index profile obtainable by this process indicates that it is difficult to obtain a near-parabolic refractive index profile with the tubular flow design unless a very large residence time in the diffusion zone is provided. However, significant changes in the refractive index profile can be induced by adopting a multi-layer approach and an annulus flow design. Furthermore, the bandwidth estimated by the ray analysis indicates that even a small variation of the refractive index profile created by the additive diffusion can result in a significant increase in the bandwidth. To verify the findings from theoretical analysis, poly(methyl methacrylate)-base GRIN POFs with diphenyl sulfide and diphenyl sulfoxide as refractive index-modifying dopants were prepared and the effects of various operating conditions such as melt temperatures, flow rates and core-cladding interface positions were investigated. The dopant concentration profile, thus the refractive index profile, characterized by FT-IR spectroscopy, has been shown to be controllable
A deterministic particle method for one-dimensional reaction-diffusion equations
NASA Technical Reports Server (NTRS)
Mascagni, Michael
1995-01-01
We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.
Li, Xiaofan; Nie, Qing
2015-01-01
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated. PMID:26487788
NASA Astrophysics Data System (ADS)
Zhang, Xiaofeng
2012-03-01
Image formation in fluorescence diffuse optical tomography is critically dependent on construction of the Jacobian matrix. For clinical and preclinical applications, because of the highly heterogeneous characteristics of the medium, Monte Carlo methods are frequently adopted to construct the Jacobian. Conventional adjoint Monte Carlo method typically compute the Jacobian by multiplying the photon density fields radiated from the source at the excitation wavelength and from the detector at the emission wavelength. Nonetheless, this approach assumes that the source and the detector in Green's function are reciprocal, which is invalid in general. This assumption is particularly questionable in small animal imaging, where the mean free path length of photons is typically only one order of magnitude smaller than the representative dimension of the medium. We propose a new method that does not rely on the reciprocity of the source and the detector by tracing photon propagation entirely from the source to the detector. This method relies on the perturbation Monte Carlo theory to account for the differences in optical properties of the medium at the excitation and the emission wavelengths. Compared to the adjoint methods, the proposed method is more valid in reflecting the physical process of photon transport in diffusive media and is more efficient in constructing the Jacobian matrix for densely sampled configurations.
NASA Astrophysics Data System (ADS)
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-28
Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less
Fixed and pulsed gradient diffusion methods in low-field core analysis.
Leu, Gabriela; Fordham, Edmund J; Hürlimann, Martin D; Frulla, Phil
2005-02-01
We review diffusion-weighted relaxation protocols for two-dimensional diffusion/relaxation time (D, T(2)) distributions and their application to fluid-saturated sedimentary rocks at low fields typical of oil-well logging tools (< or = 2 MHz for 1H). Fixed field gradient (FFG) protocols may be implemented in logging tools and in the laboratory; there, pulsed field gradient (PFG) protocols are also available. In either category, direct or stimulated echoes may be used for the diffusion evolution periods. We compare the results of several variant FFG and PFG protocols obtained on liquids and two contrasting sedimentary rocks. For liquids and rocks of negligible internal gradients (g(int)), results are comparable, as expected, for all the studied protocols. For rocks of strong g(int), protocol-dependent artifacts are seen in the joint (D, T2) distributions, consistent with the effects of the internal fields. For laboratory petrophysics, the PFG methods offer several advantages: (a) significantly improved signal-to-noise ratio and acquisition times for repetitions over many samples; (b) freedom from heteronuclear contamination when fluorinated liquids are used in core holders; and (c) a palette of variants--one comparable with the FFG--for the study of rocks of significant g(int). Given suitable hardware, both PFG and FFG methods can be implemented in the same bench-top apparatus, providing a versatile test bed for application in a petrophysical laboratory. PMID:15833632
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-28
Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247
Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S; Yao, Jun; Tao, Wenquan
2015-01-01
Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247
NASA Astrophysics Data System (ADS)
Zhu, Jianting; Ogden, Fred L.; Lai, Wencong; Chen, Xiangfeng; Talbot, Cary A.
2016-04-01
Vadose zone flow problems are usually solved from the Richards equation. Solution to the Richards equation is generally challenging because the hydraulic conductivity and diffusivity in the equation are strongly non-linear functions of water content. The finite water-content method was proposed as an alternative general solution method of the vadose zone flow problem for infiltration, falling slugs, and vadose zone response to water table dynamics based on discretizing the water content domain into numerous bins instead of the traditional spatial discretization. In this study, we develop an improved approach to the original finite water-content method (referred to as TO method hereinafter) that better simulates diffusive effects but retains the robustness of the TO method. The approach treats advection and diffusion separately and considers diffusion on a bin by bin basis. After discretizing into water content bins, we treat the conductivity and diffusivity in individual bins as water content dependent constant evaluated at given water content corresponding to each bin. For each bin, we can solve the flow equations analytically since the hydraulic conductivity and diffusivity can be treated as a constant. We then develop solutions for each bin to determine the diffusive water amounts at each time step. The water amount ahead of the convective front for each bin is redistributed among water content bins to account for diffusive effects. The application of developed solution is straightforward only involving algebraic manipulations at each time step. The method can mainly improve water content profiles, but has no significant difference for the total infiltration rate and cumulative infiltration compared to the TO method. Although the method separately deals with advection and diffusion, it can account for the coupling effects of advection and diffusion reasonably well.
Absorption spectroscopy of powdered materials using time-resolved diffuse optical methods.
D'Andrea, Cosimo; Obraztsova, Ekaterina A; Farina, Andrea; Taroni, Paola; Lanzani, Guglielmo; Pifferi, Antonio
2012-11-10
In this paper a novel method, based on time-resolved diffuse optical spectroscopy, is proposed to measure the absorption of small amounts of nanostructured powder materials independent of scattering. Experimental validation, in the visible and near-infrared spectral range, has been carried out on India Ink^{particles. The effectiveness of the technique to measure scattering-free absorption is demonstrated on carbon nanotubes. The comparison between the absorption spectra acquired by the proposed method and conventional measurements performed with a commercial spectrophotometer is discussed. PMID:23142900}
Properties of alloy steel powders produced by the method of diffusion impregnation (review)
Napara-Volgina, S.G.
1985-06-01
In their review of research on the properties of alloy steel powders produced by the method of diffusion impregnation, the authors systematize their data into three charts, one on the characteristics of charges and the recommended areas of use of powders, one on the chemical and particle size compositions and technological properties of the powders, and one on the fine crystalline structure of alloy powders of different compositions. The authors recommend the use of such powders, especially powder metallurgy constructional steels, produced by hot stamping and other methods providing high density.
Diffusive Plasma Dechucking Method for Wafers to Reduce Falling Dust Particles
NASA Astrophysics Data System (ADS)
Jun, Hyun-Su
2013-06-01
A plasma dechucking method capable of effectively eliminating dust particles created during the plasma process was developed. Referred to as diffusive plasma dechucking (DPD), the method reduces the plasma potential and includes an argon gas purge to remove dust particles floating on top of the sheath after the main process. Experimental results indicate that DPD reduces the amount of falling dust particles after the process by approximately 50-80%. To analyze these results quantitatively, the Coulomb force and the neutral drag force exerted on the dust particles were considered. In addition, dust particle exhaust conditions were proposed with respect to dust particle size, plasma potential, and spatial electric field.
A balancing domain decomposition method by constraints for advection-diffusion problems
Tu, Xuemin; Li, Jing
2008-12-10
The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.
NASA Astrophysics Data System (ADS)
Kaźmierczak-Bałata, Anna; Bodzenta, Jerzy; Trefon-Radziejewska, Dominika
2010-01-01
The use of a typical measuring cryostat with a standard temperature controller was proposed for investigation of the temperature dependence of the thermal diffusivity of transparent samples. The basic idea is to use the cryostat heater to control the mean sample temperature and to generate the thermal wave in it, simultaneously. Because of the relatively high thermal inertia of the system, the measurements are carried out at frequencies not exceeding 50 mHz. The periodic temperature disturbance in the sample was detected optically by the use of the mirage effect. The proposed method was used for determination of the thermal diffusivity of yttrium aluminum garnet single crystals in a temperature range from 20 °C to 200 °C.
Engle, Mark A.; Olea, Ricardo A.; O'Keefe, Jennifer M. K.; Hower, James C.; Geboy, Nicholas J.
2013-01-01
Coal fires occur in nature spontaneously, contribute to increases in greenhouse gases, and emit atmospheric toxicants. Increasing interest in quantifying coal fire emissions has resulted in the adaptation and development of specialized approaches and adoption of numerical modeling techniques. Overview of these methods for direct estimation of diffuse gas emissions from coal fires is presented in this paper. Here we take advantage of stochastic Gaussian simulation to interpolate CO2 fluxes measured using a dynamic closed chamber at the Ruth Mullins coal fire in Perry County, Kentucky. This approach allows for preparing a map of diffuse gas emissions, one of the two primary ways that gases emanate from coal fires, and establishing the reliability of the study both locally and for the entire fire. Future research directions include continuous and automated sampling to improve quantification of gaseous coal fire emissions.
GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography
Schweiger, Martin
2011-01-01
We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media. The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. We present solutions for both time-domain and frequency-domain problems. A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations, and factors beyond 20 for single-precision computations. The gains are also shown to be dependent on the mesh complexity, where the largest gains are achieved for high mesh resolutions. PMID:22013431
NASA Astrophysics Data System (ADS)
Hirao, Akiko; Nishizawa, Hideyuki; Tsukamoto, Takayuki; Matsumoto, Kazuki
1999-10-01
A new easy method for obtaining a drift mobility and a diffusion coefficient from a nondispersive time-of-flight transient has been developed. Nondispersive transients are described well in the theoretical photocurrent equation (PTE) based on the fact that a carrier packet drifts at a constant velocity and is spread by diffusion, the top electrode acts as a reflecting and partially absorbing wall, and the counter electrode acts as an absorbing wall. The fitting of the PTE to photocurrent transients gives the mobility and the diffusion coefficient (D) simultaneously. These are suitable characteristic values for descriptions of carriers transport because they do not show the thickness dependence and the negative field dependence in a low electric field. The mobility that sometimes shows the thickness dependence and the negative field dependence in a low electric field, however, has usually been measured from the time of the intersection of the asymptotes to the plateau and trailing edge of the transients. In order to obtain (mu) a from photocurrent transients by a simple method, we have tried to describe t0 and tail-broadening parameter W as functions of (mu) a and D, where W is defined as (t1/2 - t0)/t1/2 and t1/2 is the time at which the current is a half of that in the plateau region. The dependences of calculated (mu) k and W on the electric field and the sample thickness agreed well with those of the experimental data. These results verify the PTE and suggest that (mu) a and D can be calculated from t0 and W. We also report that the diffusion coefficient is proportional to the power of 2 of the mobility. This result agrees with a theory based on the Langevin equation which describes motions of carriers in a fluctuated field.
Social diffusion of novel foraging methods in brown capuchin monkeys (Cebus apella)
Dindo, Marietta; Thierry, Bernard; Whiten, Andrew
2007-01-01
It has been reported that wild capuchin monkeys exhibit several group-specific behavioural traditions. By contrast, experiments have found little evidence for the social learning assumed necessary to support such traditions. The present study used a diffusion chain paradigm to investigate whether a novel foraging task could be observationally learned by capuchins (Cebus apella) and then transmitted along a chain of individuals. We used a two-action paradigm to control for independent learning. Either of two methods (lift or slide) could be used to open the door of a foraging apparatus to retrieve food. Two chains were tested (N1=4; N2=5), each beginning with an experimenter-trained model who demonstrated to a partner its group-specific method for opening the foraging apparatus. After the demonstration, if the observer was able to open the apparatus 20 times by either method, then it became the demonstrator for a new subject, thus simulating the spread of a foraging tradition among ‘generations’ of group members. Each method was transmitted along these respective chains with high fidelity, echoing similar results presently available only for chimpanzees and children. These results provide the first clear evidence for faithful diffusion of alternative foraging methods in monkeys, consistent with claims for capuchin traditions in the wild. PMID:17971322
NASA Astrophysics Data System (ADS)
Bodzenta, J.; Kaźmierczak-Bałata, A.; Łukasiewicz, T.; Pyka, M.
2008-01-01
Thermal diffusivities of pure YVO{4} single crystal and single crystals doped with Nd, Tm and Ca ions are measured using a modified Ångström's method. Measurements were carried out for main crystallographic directions ([100], [010] and [001]). Obtained results show that the thermal diffusivity in [001] direction is considerably higher than in (001) plane. Decrease of the thermal diffusivity is observed with growing concentration of dopants. For the heavier doped sample (5% at. of Tm + 0.4% at. of Ca) a drop of the thermal diffusivity is about 35%. The current investigation is a part of research project 3 T08A 035 29.
Özarslan, Evren; Westin, Carl-Fredrik; Mareci, Thomas H.
2016-01-01
The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the b-value and b-matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen. PMID:27182208
Studies on Aspirin Crystals Generated by a Modified Vapor Diffusion Method.
Mittal, Amit; Malhotra, Deepak; Jain, Preeti; Kalia, Anupama; Shunmugaperumal, Tamilvanan
2016-08-01
The objectives of the current investigation were (1) to study the influence of selected two different non-solvents (diethylether and dichloromethane) on the drug crystal formation of a model drug, aspirin (ASP-I) by the modified vapor diffusion method and (2) to characterize and compare the generated crystals (ASP-II and ASP-III) using different analytical techniques with that of unprocessed ASP-I. When compared to the classical vapor diffusion method which consumes about 15 days to generate drug crystals, the modified method needs only 12 h to get the same. Fourier transform-infrared spectroscopy (FT-IR) reveals that the internal structures of ASP-II and ASP-III crystals were identical when compared with ASP-I. Although the drug crystals showed a close similarity in X-ray diffraction patterns, the difference in the relative intensities of some of the diffraction peaks (especially at 2θ values of around 7.7 and 15.5) could be attributed to the crystal habit or crystal size modification. Similarly, the differential scanning calorimetry (DSC) study speculates that only the crystal habit modifications might occur but without involving any change in internal structure of the generated drug polymorphic form I. This is further substantiated from the scanning electron microscopy (SEM) pictures that indicated the formation of platy shape for the ASP-II crystals and needle shape for the ASP-III crystals. In addition, the observed slow dissolution of ASP crystals should indicate polymorph form I formation. Thus, the modified vapor diffusion method could routinely be used to screen and legally secure all possible forms of other drug entities too. PMID:26729528
NASA Astrophysics Data System (ADS)
Price, H. C.; Murray, B. J.; Mattsson, J.; O'Sullivan, D.; Wilson, T. W.; Baustian, K. J.; Benning, L. G.
2014-04-01
Recent research suggests that under certain temperature and relative humidity conditions atmospheric aerosol may be present in the form of a glassy solid. In order to understand the impacts that this may have on aerosol-cloud interactions and atmospheric chemistry, knowledge of water diffusion within such aerosol particles is required. Here, a method is described in which Raman spectroscopy is used to observe D2O diffusion in high-viscosity aqueous solutions, enabling a quantitative assessment of water diffusion coefficients, Dwater, as a function of relative humidity. Results for sucrose solutions compare well with literature data at 23.5 ± 0.3 °C, and demonstrate that water diffusion is slow (Dwater ~5 × 10-17 m2 s-1), but not arrested, just below the glass transition at a water activity of 0.2. Room temperature water diffusion coefficients are also presented for aqueous levoglucosan and an aqueous mixture of raffinose, dicarboxylic acids and ammonium sulphate: at low humidity, diffusion is retarded but still occurs on millisecond to second timescales in atmospherically relevant-sized particles. The effect of gel formation on diffusion in magnesium sulfate solutions is shown to be markedly different from the gradual decrease in diffusion coefficients of highly viscous liquids. We show that using the Stokes-Einstein equation to determine diffusion timescales from viscosity leads to values which are more than 5 orders of magnitude too big, which emphasises the need to make measurements of diffusion coefficients. In addition, comparison of bounce fraction data for levoglucosan with measured diffusion data reveals that even when particles bounce the diffusion timescales for water are a fraction of a second for a 100 nm particle. This suggests a high bounce fraction does not necessarily indicate retarded water diffusion.
Lattice simulation method to model diffusion and NMR spectra in porous materials.
Merlet, Céline; Forse, Alexander C; Griffin, John M; Frenkel, Daan; Grey, Clare P
2015-03-01
A coarse-grained simulation method to predict nuclear magnetic resonance (NMR) spectra of ions diffusing in porous carbons is proposed. The coarse-grained model uses input from molecular dynamics simulations such as the free-energy profile for ionic adsorption, and density-functional theory calculations are used to predict the NMR chemical shift of the diffusing ions. The approach is used to compute NMR spectra of ions in slit pores with pore widths ranging from 2 to 10 nm. As diffusion inside pores is fast, the NMR spectrum of an ion trapped in a single mesopore will be a sharp peak with a pore size dependent chemical shift. To account for the experimentally observed NMR line shapes, our simulations must model the relatively slow exchange between different pores. We show that the computed NMR line shapes depend on both the pore size distribution and the spatial arrangement of the pores. The technique presented in this work provides a tool to extract information about the spatial distribution of pore sizes from NMR spectra. Such information is difficult to obtain from other characterisation techniques. PMID:25747093
Diffusivity and porosity in rock matrix-laboratory methods using artificial and natural tracers
Valkiainen, M.; Olin, M.; Uusheimo, K.; Kumpulainen, H.; Lehikoinene, J.; Muurinen, A.
1993-12-31
The nature of diffusivity and porosity in crystalline rock was studied by electrical conductivity measurements, steady-state diffusion experiments, saturation-leaching of tracers with cylindrical rock samples and analysis of the concentrations of different elements from core samples or pore water near fractures. The phenomena of main interest were dead-end porosity, ion-exclusion, sorption, and the continuity of pore networks. The modelling of experimental results was based on a modified Fick`s second law for diffusion, which was solved either by analytical or numerical methods. The measured D{sub e} and {epsilon} were found to statistically follow an exponential presentation: Archie`s law. The existence of ion-exclusion for anions was confirmed. The connectivity of the pore network extended in the laboratory experiments at least six centimetres, in coarse of the pore network extended in the laboratory experiments at least six centimetres, in coarse-grained granite in nature several metres but in fine-grained rock samples of a uranium deposit the element mobilization effects could be seen only to the depth of 2-3 centimetres.