Simple supersymmetric methods in neutron diffusion
1996-01-01
We present the supersymmetric Witten and double Darboux (strictly isospectral) constructions as applied to the diffusion of thermal neutrons from an infinitely long line source. While the Witten construction is just a mathematical scheme, the double Darboux method introduces a one-parameter family of diffusion solutions which are strictly isospectral to the stationary solution. They correspond to a Darboux-transformed diffusion length which is flux dependent
Image Magnification Method Using Joint Diffusion
Zhong-Xuan Liu; Hong-Jian Wang; Si-Long Peng
2004-01-01
In this paper a new algorithm for image magnification is presented. Because linear magnification/interpolation techniques diminish the contrast and produce sawtooth effects, in recent years, many nonlinear interpolation methods, especially nonlinear diffusion based approaches, have been proposed to solve these problems. Two recently proposed techniques for interpolation by diffusion, forward and backward diffusion (FAB) and level-set reconstruction (LSR), cannot enhance the contrast and smooth edges simultaneously. In this article, a novel Partial Differential Equations (PDE) based approach is presented. The contributions of the paper include:firstly, a unified form of diffusion joining FAB and LSR is constructed to have all of their virtues; secondly, to eliminate artifacts of the joint diffusion, soft constraint takes the place of hard constraint presented by LSR;thirdly, the determination of joint coefficients, criterion for stopping time and color image processing are also discussed. The results demonstrate that the method is visually and quantitatively better than Bicubic, FAB and LSR.
Direct methods of analyzing diffuse scattering
Georgopoulos, P.; Cohen, J.B.
1979-07-01
Methods of analysis of diffuse scattering have now reached the stage where thee are well tested and documented standard procedures for a variety of materials, and software, for both x-rays and neutrons. These methods and their meaning Are briefly reviewed.
Entropy methods for diffusive partial differential equations
Jüngel, Ansgar
2016-01-01
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.
A Mapping method for mixing with diffusion
Schlick, Conor P.; Christov, Ivan C.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2012-11-01
We present an accurate and efficient computational method for solving the advection-diffusion equation in time-periodic chaotic flows. The method uses operator splitting which allows advection and diffusion steps to be treated independently. Taking advantage of flow periodicity, the advection step is solved with a mapping method, and diffusion is added discretely after each iteration of the advection map. This approach allows for a ``composite'' mapping matrix to be constructed for an entire period of a chaotic advection-diffusion process, which provides a natural approach to the spectral analysis of mixing. To test the approach, we consider the two-dimensional time-periodic sine flow. When compared to the exact solution for this simple velocity field, the operator splitting method exhibits qualitative agreement (overall concentration structure) for large time steps and is quantitatively accurate (average and maximum error) for small time steps. We extend the operator splitting approach to three-dimensional chaotic flows. Funded by NSF Grant CMMI-1000469. Present affiliation: Princeton University. Supported by NSF Grant DMS-1104047.
Diffusion in Solids Fundamentals, Methods, Materials, Diffusion-Controlled Processes
Mehrer, Helmut
2007-01-01
Diffusion is a vital topic in solid-state physics and chemistry, physical metallurgy and materials science. Diffusion processes are ubiquitous in solids at elevated temperatures. A thorough understanding of diffusion in materials is crucial for materials development and engineering. This book first gives an account of the central aspects of diffusion in solids, for which the necessary background is a course in solid state physics. It then provides easy access to important information about diffuson in metals, alloys, semiconductors, ion-conducting materials, glasses and nanomaterials. Several diffusion-controlled phenomena, including ionic conduction, grain-boundary and dislocation pipe diffusion, are considered as well. Graduate students in solid-state physics, physical metallurgy, materials science, physical and inorganic chemistry or geophysics will benefit from this book as will physicists, chemists, metallurgists, materials engineers in academic and industrial research laboratories.
Matrix methods for reflective inverse diffusion
Burgi, Kenneth W.; Marciniak, Michael A.; Nauyoks, Stephen E.; Oxley, Mark E.
2016-09-01
Reflective inverse diffusion is a method of refocusing light scattered by a rough surface. An SLM is used to shape the wavefront of a HeNe laser at 632.8-nm wavelength to produce a converging phase front after reflection. Iterative methods previously demonstrated intensity enhancements of the focused spot over 100 times greater than the surrounding background speckle. This proof-of-concept method was very time consuming and the algorithm started over each time the desired location of the focus spot in the observation plane was moved. Transmission matrices have been developed to control light scattered by transmission through a turbid media. Time varying phase maps are applied to an SLM and used to interrogate the phase scattering properties of the material. For each phase map, the resultant speckle intensity pattern is recorded less than 1 mm from the material surface and represents an observation plane of less than 0.02 mm2. Fourier transforms are used to extract the phase scattering properties of the material from the intensity measurements. We investigate the effectiveness this method for constructing the reflection matrix (RM) of a diffuse reflecting medium where the propagation distances and observation plane are almost 1,000 times greater than the previous work based on transmissive scatter. The RM performance is based on its ability to refocus reflectively scattered light to a single focused spot or multiple foci in the observation plane. Diffraction-based simulations are used to corroborate experimental results.
Design Method for Channel Diffusers of Centrifugal Compressors
Mykola Kalinkevych
2013-01-01
Full Text Available The design method for channel diffusers of centrifugal compressors, which is based on the solving of the inverse problem of gas dynamics, is presented in the paper. The concept of the design is to provide high pressure recovery of the diffuser by assuming the preseparation condition of the boundary layer along one of the channel surfaces. The channel diffuser was designed with the use of developed method to replace the vaned diffuser of the centrifugal compressor model stage. The numerical simulation of the diffusers was implemented by means of CFD software. Obtained gas dynamic characteristics of the designed diffuser were compared to the base vaned diffuser of the compressor stage.
Simulation of anisotropic diffusion by means of a diffusion velocity method
Beaudoin, A; Rivoalen, E
2003-01-01
An alternative method to the Particle Strength Exchange method for solving the advection-diffusion equation in the general case of a non-isotropic and non-uniform diffusion is proposed. This method is an extension of the diffusion velocity method. It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity. This approach is used to simulate pollutant transport in groundwater and the results are compared to those of the PSE method presented in an earlier study by Zimmermann et al.
Adiabatic optimization versus diffusion Monte Carlo methods
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
Diffusion in condensed matter methods, materials, models
Kärger, Jörg
2005-01-01
Diffusion as the process of particle transport due to stochastic movement is a phenomenon of crucial relevance for a large variety of processes and materials. 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. Leading experts in the field describe in 23 chapters the different aspects of diffusion, covering microscopic and macroscopic experimental techniques and exemplary results for various classes of solids, liquids and interfaces as well as several theoretical concepts and models. Students and scientists in physics, chemistry, materials science, and biology will benefit from this detailed compilation.
Fluctuating lattice Boltzmann method for the diffusion equation.
Wagner, Alexander J; Strand, Kyle
2016-09-01
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.
A Fluctuating Lattice Boltzmann Method for the Diffusion Equation
Wagner, Alexander J
2016-01-01
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.
Methods for measuring diffusion coefficients of radon in building materials
Cozmuta, [No Value; van der Graaf, ER
2001-01-01
Two methods for determining the Rn-222 diffusion coefficient in concrete are presented. Experimentally, the flush and adsorption technique to measure radon release rates underlines both methods. Theoretically, the first method was developed fur samples of cubical geometry. The radon diffusion
The finite element method solution of variable diffusion coefficient convection-diffusion equations
Aydin, Selçuk Han; ćiftçi, Canan
2012-08-01
Mathematical modeling of many physical and engineering problems is defined with convection-diffusion equation. Therefore, there are many analytic and numeric studies about convection-diffusion equation in literature. The finite element method is the most preferred numerical method in these studies since it can be applied to many problems easily. But, most of the studies in literature are about constant coefficient case of the convection-diffusion equation. In this study, the finite element formulation of the variable coefficient case of the convection-diffusion equation is given in both one and two dimensional cases. Accuracy of the obtained formulations are tested on some problems in one and two dimensions.
Qualitative methods for the study of policy diffusion
Starke, Peter
2013-01-01
This article deals with the question whether and how processes of policy diffusion can be examined with qualitative methods. More specifically, how can qualitative methods address the “twin challenge of interdependence,” namely the challenge to identify diffusion, on the one hand, and the challenge...... can be adapted to the study of policy diffusion. Second, a combination of these methods is the best practice, since they are largely complementary in terms of the twin challenge of diffusion. The discussion draws on numerous illustrations from recent qualitative policy diffusion studies. The article...... closes with some suggestions for further methodological development in the study of policy diffusion, including the combination of quantitative and qualitative methods....
Diffuse-Interface Methods in Fluid Mechanics
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.
Eigenmode analysis of advective-diffusive transport in micromixers by the diffusive mapping method
Anderson, Patrick; Speetjens, Michel; Gorodetskyi, Oleksandr; Giona, Max; Mixing Collaboration
2013-11-01
Advective-diffusive transport in microflows is studied by means of the diffusive map- ping method, a recent extension of the mapping method by Gorodetskyi et al. (Phys. Fluids 24, 2012) that includes molecular diffusion. This greatly expands the application area of the mapping technique and makes the powerful concepts of eigenmode decompo- sition and spectral analysis of scalar transport accessible to an important class of flows: inline micromixers with diffusion. The staggered herringbone micro-mixer is adopted as a prototypical three-dimensional micro mixer. Simulations with the diffusive mapping method are in close agreement with experimental observations in literature and expose a strong impact of diffusion on the transport. Diffusion enables crossing of Lagrangian trans- port barriers and thus smoothens concentration gradients and accelerates homogenization. Spectral analysis of the mapping matrix reveals this already occurs on a modal level in that individual eigenmodes progressively smoothen and spread out across transport bar- riers with stronger diffusion. Concurrently, the corresponding eigenvalues diminish and thus fundamentally alter the mixing process by invariably causing homogenization, irre- spective of the Lagrangian flow structure. This happens faster and exhibits an earlier emergence of the dominant eigenmode the stronger the diffusion. Lagrangian structures may still affect the spectral properties in that flows comprising both islands and chaotic seas typically result in a richer set of eigenmodes compared to cases with global chaos.
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.
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.
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.
New complex variable meshless method for advection-diffusion problems
Wang Jian-Fei; Cheng Yu-Min
2013-01-01
In this paper,an improved complex variable meshless method (ICVMM) for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square (ICVMLS) approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for two-point boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.
Monotone method for initial value problem for fractional diffusion equation
ZHANG Shuqin
2006-01-01
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
Qualitative methods for the study of policy diffusion
Starke, Peter
2013-01-01
This article deals with the question whether and how processes of policy diffusion can be examined with qualitative methods. More specifically, how can qualitative methods address the “twin challenge of interdependence,” namely the challenge to identify diffusion, on the one hand, and the challen...... closes with some suggestions for further methodological development in the study of policy diffusion, including the combination of quantitative and qualitative methods.......This article deals with the question whether and how processes of policy diffusion can be examined with qualitative methods. More specifically, how can qualitative methods address the “twin challenge of interdependence,” namely the challenge to identify diffusion, on the one hand, and the challenge...... to discriminate between mechanisms of diffusion, on the other? I argue, first, that there are three distinct qualitative techniques that can be used, namely cross-case analysis (often based on systematic case selection), within-case process tracing, and counterfactual reasoning. I demonstrate how these techniques...
A novel method to evaluate spin diffusion length of Pt
Zhang, Yan-qing; Sun, Niu-yi; Che, Wen-ru [Shanghai Key Laboratory of Special Artificial Microstructure and Pohl Institute of Solid State Physics and School of Physics Science and Engineering, Tongji University, Shanghai 200092 (China); Shan, Rong, E-mail: shan.rong@hotmail.com [Shanghai Key Laboratory of Special Artificial Microstructure and Pohl Institute of Solid State Physics and School of Physics Science and Engineering, Tongji University, Shanghai 200092 (China); Zhu, Zhen-gang, E-mail: zgzhu@ucas.ac.cn [School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049 (China)
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/Co{sub 2}FeAl bilayers. By varying the thicknesses of Pt and Co{sub 2}FeAl 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.
Diffusion method in random matrix theory
Grela, Jacek
2016-01-01
We introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson’s Brownian motion and Grassmann/complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the β =2 Girko-Ginibre ensembles.
Solutions of fractional diffusion equations by variation of parameters method
Mohyud-Din Syed Tauseef
2015-01-01
Full Text Available This article is devoted to establish a novel analytical solution scheme for the fractional diffusion equations. Caputo’s formulation followed by the variation of parameters method has been employed to obtain the analytical solutions. Following the derived analytical scheme, solution of the fractional diffusion equation for several initial functions has been obtained. Graphs are plotted to see the physical behavior of obtained solutions.
An explicit high order method for fractional advection diffusion equations
Sousa, Ercília
2014-12-01
We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS
Abdellatif Agouzal
2000-01-01
A discontinuous finite element method for convection-diffusion equations is proposed and analyzed. This scheme is designed to produce an approximate solution which is completely discontinuous. Optimal order of convergence is obtained for model problem. This is the same convergence rate known for the classical methods.
Diffusion-equation method for crystallographic figure of merits.
Markvardsen, Anders J; David, William I F
2010-09-01
Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem. 93, 3339-3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data.
Interleaving Gradient Magnetic Field Method for Diffusion Weighted Spectroscopy
GAO Song; ZU Zhong-Liang; BAO Shang-Lian
2008-01-01
Diffusion-weighted magnetic resonance spectroscopy(DWS)has considerable potential in clinical and research applications.However.it is seldom implemented in conventional magnetic resonance imaging(MRI)scanners due to the strict hardware requirements.We propose an interleaving gradient magnetic field(IGMF)method based on point resolved spectroscopy(PRESS).Four interlaced powerful diffusion sensitive gradient magnetic fields are positioned around the two πrefocusing rf pulses in the PRESS sequence.This method utilizes the interval time in the PRESS pulse sequence,doubles the duration time of the diffusion sensitive gradient magnetic field and decreases the detrimental effect of the induced eddy current.The results of theoretical analysis and experimental observation demonstrate that the IGMF method is suitable for conventional MRI scanners.
Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn
2015-12-15
Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
Samuel Livingstone
2014-06-01
Full Text Available Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.
Quantifying Diffuse Contamination: Method and Application to Pb in Soil.
Fabian, Karl; Reimann, Clemens; de Caritat, Patrice
2017-06-20
A new method for detecting and quantifying diffuse contamination at the continental to regional scale is based on the analysis of cumulative distribution functions (CDFs). It uses cumulative probability (CP) plots for spatially representative data sets, preferably containing >1000 determinations. Simulations demonstrate how different types of contamination influence elemental CDFs of different sample media. It is found that diffuse contamination is characterized by a distinctive shift of the low-concentration end of the distribution of the studied element in its CP plot. Diffuse contamination can be detected and quantified via either (1) comparing the distribution of the contaminating element to that of an element with a geochemically comparable behavior but no contamination source (e.g., Pb vs Rb), or (2) comparing the top soil distribution of an element to the distribution of the same element in subsoil samples from the same area, taking soil forming processes into consideration. Both procedures are demonstrated for geochemical soil data sets from Europe, Australia, and the U.S.A. Several different data sets from Europe deliver comparable results at different scales. Diffuse Pb contamination in surface soil is estimated to be contamination sources and can be used to efficiently monitor diffuse contamination at the continental to regional scale.
Mixed Anti-diffusion Method for High Resolution Schemes
李荣华; 张威威
2004-01-01
In this paper we study a kied of mixed anti-diffusion method for partial differntial equations. Firstly, we use the method to construct some difference schemes for the conservation laws. The schemes are of second order accuracy and are total variation decreasing (TVD). In particular, there are only three knots involved in the schemes. Secondly, we extend the method to construct a few high accuracy difference schemes for elliptic and parabolic equations. Numerical experiments are carried out to illustrate the efficiency of the method.
A Numerical Method for Determining Diffusivity from Annealing Experiments
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).
An atmospheric electrical method to determine the eddy diffusion coefficient
M N Kulkarni; A K Kamra
2010-02-01
The ion–aerosol balance equations are solved to get the profiles of atmospheric electric parameters over the ground surface in an aerosol-rich environment under the conditions of surface radioactivity. Combining the earlier results for low aerosol concentrations and the present results for high aerosol concentrations, a relation is obtained between the average value of atmospheric electric space charge in the lowest ∼2m, the surface electric field and eddy diffusivity/aerosol concentration. The values of eddy diffusivity estimated from this method using some earlier measurements of space charge and surface electric field are in reasonably good agreement with those calculated from other standard methods using meteorological or electrical variables.
Support Operators Method for the Diffusion Equation in Multiple Materials
Winters, Andrew R. [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory
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.
Background and Mathematical Analysis of Diffusion MRI Methods.
Ozcan, Alpay; Wong, Kenneth H; Larson-Prior, Linda; Cho, Zang-Hee; Mun, Seong K
2012-03-01
The addition of a pair of magnetic field gradient pulses had initially provided the measurement of spin motion with nuclear magnetic resonance (NMR) techniques. In the adaptation of DW-NMR techniques to magnetic resonance imaging (MRI), the taxonomy of mathematical models is divided in two categories: model matching and spectral methods. In this review, the methods are summarized starting from early diffusion weighted (DW) NMR models followed up with their adaptation to DW MRI. Finally, a newly introduced Fourier analysis based unifying theory, so-called Complete Fourier Direct MRI, is included to explain the mechanisms of existing methods.
A localized meshless method for diffusion on folded surfaces
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.
Maxwell iteration for the lattice Boltzmann method with diffusive scaling.
Zhao, Weifeng; Yong, Wen-An
2017-03-01
In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
The Method of Lines for Ternary Diffusion Problems
Henryk Leszczyński
2014-01-01
Full Text Available The method of lines (MOL for diffusion equations with Neumann boundary conditions is considered. These equations are transformed by a discretization in space variables into systems of ordinary differential equations. The proposed ODEs satisfy the mass conservation law. The stability of solutions of these ODEs with respect to discrete L2 norms and discrete W1,∞ norms is investigated. Numerical examples confirm the parabolic behaviour of this model and very regular dynamics.
Thermal Diffusivity of Sweet Potato Flour Measured Using Dickerson Method
I.K. Tastra
2006-08-01
Full Text Available Sweet potato (Ipmoea batatas I. is one the carbohydrate sources in indonesia that can be used both for food and industry purposes. To support the utilization of sweet potato as flour, it is imperative to develop a drying system that can improve its quality. A preliminary study using an improved variety, namely Sari, was conducted to determine its floure thermal diffusivity ( , an imprortant parameter in developing drying process. The experiment was run according to Dickerson method using sweet potato flour at different levels of moisture content (5.05-5.97% wet basis and temperatures (23.7 -40.9 oC this method used an apparatus based on transient heat transfer condition requiring only a time- temperature data. At the levels of moisture and temperature studied, the thermal diffusivity of sweet potato flour could be expressed using a linear regression model, = 10-9 M.T + 9X 10-9( R2=0.9779. the average value of the thermal diffusivity sweet potato flour was 1.72 x 10-7 m2/s at a moisture level of 5.51 % wet basis and temperature of 29.58 oC. Similar studies are needed for different varieties or cultivars of sweet potato as well at a wide range of moisture content and temperature content and temperature levels.
Effective thermal diffusivity study of powder biocomposites via photoacoustic method
Mariucci, V.V.G.; Cruz, J.A. da; Bonadio, T.G.M.; Picolloto, A.M.; Weinand, W.R.; Lima, W.M.; Medina, A.N.; Bento, A.C., E-mail: vgmariucci@hotmail.com, E-mail: pg51508@uem.br [Universidade Estadual de Maringa (UEM), PR (Brazil). Departamento de Fisica
2015-10-15
The effective thermal diffusivity for biocomposites of hydroxyapatite (HAp), and niobium pentoxide (Nb{sub 2}O{sub 5}) 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)HAp + (x)Nb{sub 2}O{sub 5}] for 0.0 ≤ x ≤ 1.0. Experimental results for effective thermal diffusivity ranged between (6.4 ± 0.3) x 10{sup -6} m{sup 2} s{sup -1} and (9.8 ± 0.4) x 10{sup -6} m{sup 2} s{sup -1} for x ≤ 0.7. Values of the effective thermal diffusivity have decreased sharply to (0.70 ± 0.03) x 10{sup -6} m{sup 2} s{sup -1} for x > 0.7. SEM micrographs showed a coating of HAp over the particles of Nb{sub 2}O{sub 5} for some mixtures. (author)
Gradient-Diffusion Methods for Simulating Decoherence by NMR Spectroscopy
Havel, T F; Viola, L; Cory, D G; Havel, Timothy F.; Sharf, Yehuda; Viola, Lorenza; Cory, David G.
2001-01-01
Theoretical techniques are developed for designing nuclear magnetic resonance (NMR) experiments to simulate a variety of adiabatic decoherence (aka T_2 relaxation) processes, using sequences of pulsed field gradients and diffusion periods. To this end an efficient Hadamard product formalism is introduced and used to derive Lindblad master equations from NMR pulse sequences for both collective and independent phase damping on any number of spins. The Kraus operator sum form is shown to be related to the Hadamard form by diagonalization, and explicit Lindblad and Kraus operators given for arbitrary correlations between two spins. Finally, gradient-diffusion methods are outlined for more complex forms of decoherence, including the three-axis collective model.
Variational methods applied to problems of diffusion and reaction
Strieder, William
1973-01-01
This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free ...
On matrix diffusion: formulations, solution methods and qualitative effects
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
A granular computing method for nonlinear convection-diffusion equation
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
Prediction of Chloride Diffusion in Concrete Structure Using Meshless Methods
Ling Yao
2016-01-01
Full Text Available Degradation of RC structures due to chloride penetration followed by reinforcement corrosion is a serious problem in civil engineering. The numerical simulation methods at present mainly involve finite element methods (FEM, which are based on mesh generation. In this study, element-free Galerkin (EFG and meshless weighted least squares (MWLS methods are used to solve the problem of simulation of chloride diffusion in concrete. The range of a scaling parameter is presented using numerical examples based on meshless methods. One- and two-dimensional numerical examples validated the effectiveness and accuracy of the two meshless methods by comparing results obtained by MWLS with results computed by EFG and FEM and results calculated by an analytical method. A good agreement is obtained among MWLS and EFG numerical simulations and the experimental data obtained from an existing marine concrete structure. These results indicate that MWLS and EFG are reliable meshless methods that can be used for the prediction of chloride ingress in concrete structures.
Nonlinear diffusion methods based on robust statistics for noise removal
JIA Di-ye; HUANG Feng-gang; SU Han
2007-01-01
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M[1] model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering,which is more effective than normal bilateral filter.
Introduction to the variational and diffusion Monte Carlo methods
Toulouse, Julien; Umrigar, C J
2015-01-01
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.
PERTURBATION FINITE VOLUME METHOD FOR CONVECTIVE-DIFFUSION INTEGRAL EQUATION
GAO Zhi; YANG Guowei
2004-01-01
A perturbation finite volume (PFV) method for the convective-diffusion integral equation is developed in this paper. The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations, with the least nodes similar to the standard three-point schemes, that is, the number of the nodes needed is equal to unity plus the face-number of the control volume. For instance, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D linear and nonlinear problems, 2-D and 3-D flow model equations. Comparing with other standard three-point schemes, the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme (UDS). Its numerical accuracies are also higher than the second-order central scheme (CDS), the power-law scheme (PLS) and QUICK scheme.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Systematic study of exciton diffusion length in organic semiconductors by six experimental methods
Lin, Jason D. A.; Mikhnenko, Oleksandr V.; Chen, Jingrun; Masri, Zarifi; Ruseckas, Arvydas; Mikhailovsky, Alexander; Raab, Reilly P.; Liu, Jianhua; Blom, Paul W. M.; Loi, Maria Antonietta; Garcia-Cervera, Carlos J.; Samuel, Ifor D. W.; Thuc-Quyen Nguyen, [No Value
Six experimental methods have been used to investigate the exciton diffusion length in materials with systematic chemical modifications. We find that exciton diffusion length correlates with molecular ordering. We discuss situations in which certain experimental techniques are more appropriate.
Yolcu, Cem; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-01-01
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 multi-dimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike for the case of traditional methods that employ a diffusion tensor, aniso...
A Critical Study of Agglomerated Multigrid Methods for Diffusion
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.
Multitracer and filter-separated half-cell method for measuring solute diffusion in undisturbed soil
Lægdsmand, Mette; Møldrup, Per; Schjønning, Per
2010-01-01
Solute diffusion controls important processes in soils: plant uptake of nutrients, sorption-desorption processes, degradation of organic matter, and leaching of radionuclides through clay barriers. We developed a new method for measuring the solute diffusivity (solute diffusion coefficient...... in the soil relative to water) in intact soil samples (the Multiple Tracer, Filter Separated half-cell method using a Dynamic Model for parameter estimation [MT-FS-DM]). The MT-FS-DM method consists of half-cell diffusion of two pairs of counterdiffusing anionic tracers and a parameter estimation scheme...... that the MT-FS-DM method provided reliable results. We compared diffusivities measured on a sandy loam soil using the MT-FS-DM method with diffusivities from six sandy loam test soils from the literature. The new method can be used to estimate solute diffusivity in intact structured soil and provides a more...
Estimating the diffuseness of sound fields: A wavenumber analysis method
Nolan, Melanie; Davy, John L.; Brunskog, Jonas
2017-01-01
The concept of a diffuse sound field is widely used in the analysis of sound in enclosures. The diffuse sound field is generally described as composed of plane waves with random phases, which wave number vectors are uniformly distributed over all angles of incidence. In this study......, an interpretation in the spatial frequency domain is discussed, with the prospect of evaluating the diffuse field conditions in non-anechoic enclosures. This work examines how theoretical considerations compare with experimental results obtained in rooms with various diffuse field conditions. In addition, the paper...
Computational Methods for Multi-dimensional Neutron Diffusion Problems
Song Han
2009-10-15
Lead-cooled fast reactor (LFR) has potential for becoming one of the advanced reactor types in the future. Innovative computational tools for system design and safety analysis on such NPP systems are needed. One of the most popular trends is coupling multi-dimensional neutron kinetics (NK) with thermal-hydraulic (T-H) to enhance the capability of simulation of the NPP systems under abnormal conditions or during rare severe accidents. Therefore, various numerical methods applied in the NK module should be reevaluated to adapt the scheme of coupled code system. In the author's present work a neutronic module for the solution of two dimensional steady-state multigroup diffusion problems in nuclear reactor cores is developed. The module can produce both direct fluxes as well as adjoints, i.e. neutron importances. Different numerical schemes are employed. A standard finite-difference (FD) approach is firstly implemented, mainly to serve as a reference for less computationally challenging schemes, such as transverse-integrated nodal methods (TINM) and boundary element methods (BEM), which are considered in the second part of the work. The validation of the methods proposed is carried out by comparisons of the results for some reference structures. In particular a critical problem for a homogeneous reactor for which an analytical solution exists is considered as a benchmark. The computational module is then applied to a fast spectrum system, having physical characteristics similar to the proposed European Lead-cooled System (ELSY) project. The results show the effectiveness of the numerical techniques presented. The flexibility and the possibility to obtain neutron importances allow the use of the module for parametric studies, design assessments and integral parameter evaluations, as well as for future sensitivity and perturbation analyses and as a shape solver for time-dependent procedures
Sumit Gupta
2015-09-01
Full Text Available The aim of this paper was to present a user friendly numerical algorithm based on homotopy perturbation transform method for solving various linear and nonlinear convection-diffusion problems arising in physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. The homotopy perturbation transform method is a combined form of the homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He’s polynomials. The technique presents an accurate methodology to solve many types of partial differential equations The approximate solutions obtained by proposed scheme in a wide range of the problem’s domain were compared with those results obtained from the actual solutions. The comparison shows a precise agreement between the results.
Mucoadhesive microspheres prepared by interpolymer complexation and solvent diffusion method.
Chun, Myung-Kwan; Cho, Chong-Su; Choi, Hoo-Kyun
2005-01-20
Mucoadhesive microspheres were prepared to increase gastric residence time using an interpolymer complexation of poly(acrylic acid) (PAA) with poly(vinyl pyrrolidone) (PVP) and a solvent diffusion method. The complexation between poly(acrylic acid) and poly(vinyl pyrrolidone) as a result of hydrogen bonding was confirmed by the shift in the carbonyl absorption bands of poly(acrylic acid) using FT-IR. A mixture of ethanol/water was used as the internal phase, corn oil was used as the external phase of emulsion, and span 80 was used as the surfactant. Spherical microspheres were prepared and the inside of the microspheres was completely filled. The optimum solvent ratio of the internal phase (ethanol/water) was 8/2 and 7/3, and the particle size increased as the content of water was increased. The mean particle size increased with the increase in polymer concentration. The adhesive force of microspheres was equivalent to that of Carbopol. The release rate of acetaminophen from the complex microspheres was slower than the PVP microspheres at pH 2.0 and 6.8.
Diffusion Monte Carlo methods applied to Hamaker Constant evaluations
Hongo, Kenta
2016-01-01
We applied diffusion Monte Carlo (DMC) methods to evaluate Hamaker constants of liquids for wettabilities, with practical size of a liquid molecule, Si$_6$H$_{12}$ (cyclohexasilane). The evaluated constant would be justified in the sense that it lies within the expected dependence on molecular weights among similar kinds of molecules, though there is no reference experimental values available for this molecule. Comparing the DMC with vdW-DFT evaluations, we clarified that some of the vdW-DFT evaluations could not describe correct asymptotic decays and hence Hamaker constants even though they gave reasonable binding lengths and energies, and vice versa for the rest of vdW-DFTs. We also found the advantage of DMC for this practical purpose over CCSD(T) because of the large amount of BSSE/CBS corrections required for the latter under the limitation of basis set size applicable to the practical size of a liquid molecule, while the former is free from such limitations to the extent that only the nodal structure of...
Anisotropic phantom to calibrate high-q diffusion MRI methods
Komlosh, M. E.; Benjamini, D.; Barnett, A. S.; Schram, V.; Horkay, F.; Avram, A. V.; Basser, P. J.
2017-02-01
A silicon oil-filled glass capillary array is proposed as an anisotropic diffusion MRI phantom. Together with a computational/theoretical pipeline these provide a gold standard for calibrating and validating high-q diffusion MRI experiments. The phantom was used to test high angular resolution diffusion imaging (HARDI) and double pulsed-field gradient (d-PFG) MRI acquisition schemes. MRI-based predictions of microcapillary diameter using both acquisition schemes were compared with results from optical microscopy. This phantom design can be used for quality control and quality assurance purposes and for testing and validating proposed microstructure imaging experiments and the processing pipelines used to analyze them.
Marion, Bill
2017-05-01
A numerical method is provided for solving the integral equation for the angle-of-incidence (AOI) correction factor for diffuse radiation incident photovoltaic (PV) modules. The types of diffuse radiation considered include sky, circumsolar, horizon, and ground-reflected. The method permits PV module AOI characteristics to be addressed when calculating AOI losses associated with diffuse radiation. Pseudo code is provided to aid users in the implementation, and results are shown for PV modules with tilt angles from 0 degrees to 90 degrees. Diffuse AOI losses are greatest for small PV module tilt angles. Including AOI losses associated with the diffuse irradiance will improve predictions of PV system performance.
Lessing, Paul A [Idaho Falls, ID
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.
A new gauge-invariant method for diagnosing eddy diffusivities
Mak, Julian; Marshall, David P
2015-01-01
Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke down-gradient mixing, or diffusion, 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 buo...
An Analytical Method for Relationship Between Hydraulic Diffusivity and Soil Sorptivity
WANG Quan-Jiu; ZHANG Jiang-Hui; FAN Jun
2006-01-01
A simple method was developed to relate soil sorptivity to hydraulic diffusivity and water absorption experiments were conducted utilizing one-dimensional horizontal soil columns to validate the relationship. In addition, an estimation method for hydraulic diffusivity with disc infiltrometer was developed. The results indicated a favorable fit of the theoretical relation to the experimental data. Also, the experiment with disc infiltrometer for estimating the diffusivity showed that the new method was feasible.
An integration factor method for stochastic and stiff reaction–diffusion systems
Ta, Catherine; Wang, Dongyong; Nie, Qing, E-mail: qnie@uci.edu
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.
López-Oviedo, E.; Aller, A. I.; Martín, C.; Castro, C.; Ramirez, M.; Pemán, J. M.; Cantón, E.; Almeida, C.; Martín-Mazuelos, E.
2006-01-01
The disk diffusion method was evaluated for determining posaconazole susceptibility against 78 strains of molds using two culture media in comparison with the CLSI (Clinical Laboratory Standards Institute) broth microdilution method (M38-A). A significant correlation between disk diffusion and microdilution methods was observed with both culture media. PMID:16495281
Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods
Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.
2010-01-01
In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed t...
Development of agar diffusion method for dosage of gramicidin
Ana Gabriela Reis Solano
2011-09-01
Full Text Available Gramicidin, an antimicrobial peptide active against Gram positive bacteria, is commonly used in pharmaceutical preparations for topical use. Considering that only the turbidimetric method has been described in the literature, the present study sought to develop and validate an agar diffusion method for the dosage of gramicidin. The method was developed and validated using the Kocuria rhizophila ATCC 9341 as a test microorganism. Two designs were used: a 3x3 parallel-line model, and a 5x1 standard curve. The validation demonstrated that the method follows the linear model (r²= 0.994, presenting a significant regression between the zone diameter of growth inhibition and the logarithm of the concentration within the range of 5 to 25.3 µg/mL. The results obtained for both designs were precise, having a relative standard deviation (R.S.D. for intra-day precision of 0.81 for the 3x3 assay and 1.90 for the 5x1 assay. For the inter-day precision, the R.S.D. was 1.35 for the 3x3 and 2.64 for the 5x1. The accuracy was verified and results confirmed to be accurate, having a tolerance interval of 95%, which lay within permitted limits and appropriate trueness. In addition, the method was considered selective, with limit of detection and upper and lower limits of quantification of 2.00, 5.00 and 25.3 µg/mL, respectively. No difference in precision between the designs used in the agar diffusion method was evident (p>0.05. The method proved to be appropriate for the microbiological dosage of the raw material gramicidin.A gramicidina, um peptídeo antimicrobiano ativo contra bactérias Gram positivo, é utilizada em preparações farmacêuticas de uso tópico. Neste trabalho procurou-se desenvolver e validar outro método para o doseamento de gramicidina tendo em vista que somente o método turbidimétrico é descrito. O método de difusão em ágar foi desenvolvido e validado utilizando como microrganismo teste Kocuria rhizophila ATCC 9341. Foram utilizados
Blumenthal, Adrian
2015-01-01
Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equations driven by jump-diffusion processes. In addition, there are situations, where a stochastic model is based on stochastic differential equations with multiple scales. Such stochastic problems are called stiff and lead for classical ex...
A Multiresolution Method for Parameter Estimation of Diffusion Processes.
Kou, S C; Olding, Benjamin P; Lysy, Martin; Liu, Jun S
2012-12-01
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.
Modelling and simulation of diffusive processes methods and applications
Basu, SK
2014-01-01
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport
Thermal diffusivity measurement by lock-in photothermal shadowgraph method
Cifuentes, A. [Instituto Politécnico Nacional, Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Unidad Legaria, Ciudad de México 11500 (Mexico); Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería, Universidad del País Vasco UPV/EHU, Alameda Urquijo s/n, 48013 Bilbao (Spain); Alvarado, S. [Instituto Politécnico Nacional, Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Unidad Legaria, Ciudad de México 11500 (Mexico); Laboratory for Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, Heverlee B-3001 (Belgium); Cabrera, H. [Centro Multidisciplinario de Ciencias, Instituto Venezolano de Investigaciones Científicas, IVIC, Mérida 5101, Venezuela and SPIE-ICTP Anchor Research in Optics Program Lab, International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste (Italy); Calderón, A.; Marín, E., E-mail: emarinm@ipn.mx [Instituto Politécnico Nacional, Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Unidad Legaria, Ciudad de México 11500 (Mexico)
2016-04-28
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.
Application of the Clustering Method in Molecular Dynamics Simulation of the Diffusion Coefficient
无
2008-01-01
Using molecular dynamics (MD) simulation, the diffusion of oxygen, methane, ammonia and carbon dioxide in water was simulated in the canonical NVT ensemble, and the diffusion coefficient was analyzed by the clustering method. By comparing to the conventional method (using the Einstein model) and the differentiation-interval variation method, we found that the results obtained by the clustering method used in this study are more close to the experimental values. This method proved to be more reasonable than the other two methods.
Determining Diffuser Augmented Wind Turbine performance using a combined CFD/BEM method
Kesby, JE; Bradney, D. R.; Clausen, PD
2016-09-01
The optimisation of a Diffuser Augmented Wind Turbine has traditionally focused on maximising its power output. Optimising the design of the blade and the shape of the diffuser for maximum turbine power over a range of wind velocities is a complex process, as each will influence the others flow regime. In this paper we propose a method that combines the predictions of flow through a diffuser, using computational fluid dynamics, and the flow from a turbine blade using a modified blade element theory to predict the power output of a diffuser augmented wind turbine. Good agreement was found between the predictions from this new method and experimental data from the literature.
Diffusion NMR methods applied to xenon gas for materials study
Mair, R. W.; Rosen, M. S.; Wang, R.; Cory, D. G.; Walsworth, R. L.
2002-01-01
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.
无
2003-01-01
Objective To performance susceptibility testing of antifungal agents. Due to the increasing number of resistant strains, susceptibility testing of antifungal agents is gaining importance. Methods We compared the results of standard macrotube dilution reference method with two different microdilution methods, as well as the disc diffusion method in order to test the susceptibility of 150 Candida strains to fluconazole. Results Overall correlation between microdilution and macrodilution methods was 86%. It was 91% between the Minimal Inhibitory Concentrations obtained from macrodilution and disc diffusion zone diameters. Conclusion The disc diffusion test was evaluated as a low-cost, reproducible, and efficient way of assessing the in vitro susceptibility of Candida strains to fluconazole.
Johnson, Philip; Johnsen, Eric
2016-11-01
The Discontinuous Galerkin (DG) numerical method, while well-suited for hyperbolic PDE systems such as the Euler equations, is not naturally competitive for convection-diffusion systems, such as the Navier-Stokes equations. Where the DG weak form of the Euler equations depends only on the field variables for calculation of numerical fluxes, the traditional form of the Navier-Stokes equations requires calculation of the gradients of field variables for flux calculations. It is this latter task for which the standard DG discretization is ill-suited, and several approaches have been proposed to treat the issue. The most popular strategy for handling diffusion is the "mixed" approach, where the solution gradient is constructed from the primal as an auxiliary. We designed a new mixed approach, called Gradient-Recovery DG; it uses the Recovery concept of Van Leer & Nomura with the mixed approach to produce a scheme with excellent stability, high accuracy, and unambiguous implementation when compared to typical mixed approach concepts. In addition to describing the scheme, we will perform analysis with comparison to other DG approaches for diffusion. Gas dynamics examples will be presented to demonstrate the scheme's capabilities.
Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method
Abdelraheem M Aly; Zehba A.S. Raizah
2016-01-01
The double-diffusive natural convection in an enclosure filled with nanofluid is studied using ISPH method. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. In ISPH algorithm, a semi implicit velocity correction procedure is utilized and the pressure is implicitly evaluated by solving pressure Poisson equation. The results are presented with flow config...
Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids
2006-12-01
H. A.; Wilkes, J. O. Applied Numerical Methods ; Wiley: New York, 1969. Chapra , S. C.; Canale, R. P. Numerical Methods for Engineers with... Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids by John D. Clayton, Peter W. Chung, Michael A. Greenfield...Proving Ground, MD 21005-5066 ARL-TR-4002 December 2006 Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids
Bretscher, M.M.
1984-01-01
Simple diffusion theory cannot be used to evaluate control rod worths in thermal neutron reactors because of the strongly absorbing character of the control material. However, reliable control rod worths can be obtained within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters. For thin slab absorbers the effective diffusion parameters can be expressed as functions of a suitably-defined pair of blackness coefficients. Methods for calculating these blackness coefficients in the P/sub 1/, P/sub 3/, and P/sub 5/ approximations, with and without scattering, are presented. For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is discussed.
Proposal of novel measurement method for thermal diffusivity from infrared thermal movie
Okamoto, Yoichi; Watanabe, Shin; Ogata, Kento; Hiramatsu, Koji; Miyazaki, Hisashi; Morimoto, Jun
2017-05-01
A brand new thermal diffusivity measurement method was developed. In this new noncontact and absolute measurement method, thermal diffusivity was measured from infrared movie data. The model of one-dimensional thermal conduction was constructed by taking into account the thermal flow other than one-dimensional thermal conduction in the sample. On the basis of this thermal conduction model, the analytical equation for calculating thermal diffusivity was derived. A single-crystal sapphire plate was used as a test specimen for the new method. The test specimen was arranged to cause one-dimensional heat conduction. Infrared movies were taken by using an infrared camera at room temperature. Then, thermal diffusivity was numerically calculated from the acquired movie data using the analytical equation. It was experimentally demonstrated that thermal diffusivity was measured with an accuracy of around 10% error, from an infrared movie of a single-crystal sapphire sample.
Real-time convolution method for generating light diffusion profiles of layered turbid media.
Kim, Hoe-Min; Ko, Kwang Hee; Lee, Kwan H
2011-06-01
In this paper we present a technique to obtain a diffusion profile of layered turbid media in real time by using the quasi fast Hankel transform (QFHT) and the latest graphics processing unit technique. We apply the QFHT to convolve the diffusion profiles of each layer so as to dramatically reduce the time for the convolution step while maintaining the accuracy. In addition, we also introduce an accelerated technique to generate individual discrete diffusion profiles for each layer through parallel processing. The proposed method is 2 orders of magnitude faster than the existing method, and we validate its efficiency by comparing it with Monte Carlo simulation and another relevant methods.
LIANG Hui; ZHAO Wei; DAI Dejun; ZHANG Jun
2014-01-01
Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography. It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.
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
A method for optimizing the cosine response of solar UV diffusers
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.
The First Integral Method to Study a Class of Reaction-Diffusion Equations
KE Yun-Quan; YU Jun
2005-01-01
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.
Parameters estimation using the first passage times method in a jump-diffusion model
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.
Accurate determination of specific heat at high temperatures using the flash diffusivity method
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.
Antimicrobial potentials of Mentha longifolia by disc diffusion method.
Bakht, Jehan; Shaheen, Salma; Shafi, Mohammad
2014-07-01
This study was conducted for the assessment of the antimicrobial activities of different solvents extracted samples from the aerial parts of Mentha longifolia against ten microbial species through the disc diffusion assay using two different concentrations of 1 and 2 mg disc1. All extracts from Mentha longifolia showed different ranges of antimicrobial activities. Butanol and ethyl acetate fractions showed inhibitory activities against all microbial species. Methanol fraction showed inhibitory effects against all the tested microbial species except Salmonella typhi. Salmonella typhi was also not controlled by methanol, petroleum ether and dichloromethane extracted samples. The most susceptible gram positive bacteria was Bacillus atropheus and Bacillus subtilis and were inhibited by all extracts and Staphylococus aureus was least susceptible among gram positive bacteria. Klebsiella pneumoniae was the most susceptible gram negative bacterium and Salmonella typhi was highly resistant among the gram negative bacteria. Erwinia carotovora and Agrobacterium tumefaciene were susceptible to all fractions. All fractions showed antifungal activities against Candida albicans except water extracted samples.
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 (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.
The Study of Thermal Diffusivity Measurement of Composite Materials by Unsteady Probe Method
Saiki, Yukihiro; Yamada, Etsuro; Ikeda, Hiroshi
The object of this study is to research the possibility of in-line measurement of the thermal diffusivity on composite materials, such as suspension and emulsion, by previously developed apparatus for the dynamic viscosity. The calibration curve between the thermal diffusivity and any physical quantity that can be measured by this apparatus is proposed by the numerical analysis. The experimental results were obtained by using the dispersed materials composed agargel cooking oil (as matrix) and Ti02 particle. Nondimensional effective thermal diffusivity that is the ratio of the effective thermal diffusivity of dispersed materials to the one of the matrix are compared with previous results obtained by periodic heating method. These data of nondimensional values show good agreement with each other. From these results, this measurement apparatus may be applicable for the thermal diffusivity measurement of dispersed materals.
A modified orthogonal collocation method for reaction diffusion problems
M. Soliman
2014-12-01
Full Text Available A low-order collocation method is often useful in revealing the main features such as concentration and temperature profiles and the effectiveness factor for porous catalyst particles. Two modifications are introduced in this paper to make the method more efficient. The first modification is to add an extra collocation point at the center of the particle. It is shown that such extra point introduces a single variable non-linear equation to be solved after obtaining the standard collocation method solution. In the second modification, the polynomial solution obtained from the application of the orthogonal collocation method is transformed to a rational function form. These two modifications are applied to specific examples and it is shown that they can improve the performance of collocation methods in general and the one-point collocation method in particular.
Finite volume element method for analysis of unsteady reaction-diffusion problems
Sutthisak Phongthanapanich; Pramote Dechaumphai
2009-01-01
A finite volume element method is developed for analyzing unsteady scalar reaction--diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction--diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the highgradient boundary layers.
A Lagrangian particle method for reaction-diffusion systems on deforming surfaces.
Bergdorf, Michael; Sbalzarini, Ivo F; Koumoutsakos, Petros
2010-11-01
Reaction-diffusion processes on complex deforming surfaces are fundamental to a number of biological processes ranging from embryonic development to cancer tumor growth and angiogenesis. The simulation of these processes using continuum reaction-diffusion models requires computational methods capable of accurately tracking the geometric deformations and discretizing on them the governing equations. We employ a Lagrangian level-set formulation to capture the deformation of the geometry and use an embedding formulation and an adaptive particle method to discretize both the level-set equations and the corresponding reaction-diffusion. We validate the proposed method and discuss its advantages and drawbacks through simulations of reaction-diffusion equations on complex and deforming geometries.
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.
Thermal Diffusivity of Sintered Steels with Flash Method at Ambient Temperature
Bocchini, G. F.; Bovesecchi, G.; Coppa, P.; Corasaniti, S.; Montanari, R.; Varone, A.
2016-04-01
Due to lack of reliable thermal diffusivity data of sintered steels in literature, experimental investigations were conducted on samples made of different powder types (based on prealloyed, or diffusion-bonded, or admixed powders) and under different process conditions. So the influence of pressing pressure and sintering temperature on thermal diffusivity was established. Thermal diffusivity was measured using the "flash method": a sample in the shape of a slab is irradiated with a light pulse on one of the two surfaces, and temperature of the other surface is detected by an ambient temperature pyrometer. The value of the thermal diffusivity is obtained by a least squares regression on the entire trend of the temperature vs. time using the analytical solution of the heat conduction as regression model. Results show the increase of the thermal diffusivity with increasing density. This outcome can be explained from the mutual effect of thermal conductivity and density on thermal diffusivity in porous media. The experimental results have also permitted to verify the influence of the composition of the sintered materials and carbon contents on thermal diffusivity.
Data on the verification and validation of segmentation and registration methods for diffusion MRI
Oscar Esteban
2016-09-01
Full Text Available 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.
Numerical study of water diffusion in biological tissues using an improved finite difference method.
Xu, Junzhong; Does, Mark D; Gore, John C
2007-04-07
An improved finite difference (FD) method has been developed in order to calculate the behaviour of the nuclear magnetic resonance signal variations caused by water diffusion in biological tissues more accurately and efficiently. The algorithm converts the conventional image-based finite difference method into a convenient matrix-based approach and includes a revised periodic boundary condition which eliminates the edge effects caused by artificial boundaries in conventional FD methods. Simulated results for some modelled tissues are consistent with analytical solutions for commonly used diffusion-weighted pulse sequences, whereas the improved FD method shows improved efficiency and accuracy. A tightly coupled parallel computing approach was also developed to implement the FD methods to enable large-scale simulations of realistic biological tissues. The potential applications of the improved FD method for understanding diffusion in tissues are also discussed.
Measurement of the Ar diffusion coefficient in graphite at high temperature by the ISOL method
Eleon, C. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Jardin, P. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France)], E-mail: Jardin@ganil.fr; Thomas, J.C.; Saint-Laurent, M.-G.; Huet-Equilbec, C.; Alves Conde, R. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Angelique, J.C. [Laboratoire de Physique Subatomique et de Cosmologie, 38026 Grenoble (France); Laboratoire de Physique Corpusculaire, ISMRA, 14050 Caen (France); Boilley, D.; Cornell, J.; Dubois, M. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Franberg, H. [Paul Scherrer Institute, 5232 Villigen PSI (Switzerland); ISOLDE, CERN, 1211 Geneve 23 (Switzerland); Gaubert, G.; Jacquot, B. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Koester, U. [ISOLDE, CERN, 1211 Geneve 23 (Switzerland); Institut Laue Langevin, 38042 Grenoble (France); Leroy, R. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France); Maunoury, L. [Centre Interdisciplinaire de Recherche Ion Laser, 14070 Caen (France); Orr, N. [Laboratoire de Physique Corpusculaire, ISMRA, 14050 Caen (France); Pacquet, J.Y.; Pellemoine, F.; Stodel, C. [Grand Accelerateur National d' Ions Lourds, CEA/DSM CNRS/IN2P3, 14076 Caen (France)] (and others)
2008-10-15
This work has been carried out at GANIL within the ambit of the TARGISOL European collaboration which aims to study the relevant variables governing the release of radioactive elements from targets in an ISOL system. This work shows how it has been possible to extract diffusion coefficients for {sup 35}Ar atoms diffusing out of graphite targets from release time measurements by using an analytic description of the release times. The diffusion coefficients and efficiencies are presented and compared with results obtained using a 'continuous' method.
Yan Sheng-Ping
2015-01-01
Full Text Available In this article, we first propose the local fractional Laplace series expansion method, which is a coupling method of series expansion method and Laplace transform via local fractional differential operator. An illustrative example for handling the diffusion equation arising in fractal heat transfer is given.
MapReduce based computation of the diffusion method in recommender systems
彭飞
2016-01-01
The performance of existing diffusion-based algorithms in recommender systems is still limited by the processing ability of a single computer .In order to conduct the diffusion computation on large data sets, a parallel implementation of the classic diffusion method on the MapReduce framework is proposed.At first, the diffusion computation is transformed from a summation format to a cascade matrix multiplication format , and then , a parallel matrix multiplication algorithm based on dynamic vector is proposed to reduce the CPU and I/O cost on the MapReduce framework , which can also be applied to other parallel matrix multiplication scenarios .Then, block partitioning is used to further improve the performance , while the order of matrix multiplication is also taken into consideration . Experiments on different kinds of data sets have verified the efficiency of the proposed method .
Low temperature thermal diffusivity of LiKSO4 obtained using the photoacoustic phase lag method
Jorge M.P.P.M.
1999-01-01
Full Text Available This paper describes the determination of the thermal diffusivity of LiKSO4 crystals using the photoacoustic phase lag method, in the 77 K to 300 K temperature interval. This method is quite simple and fast and when it is coupled to a specially designed apparatus, that includes a resonant photoacoustic cell, allows for the determination of the thermal diffusivity at low temperatures. The thermal diffusivity is an important parameter that depends on the temperature, and no values of this parameter for LiKSO4, at low temperature, have yet been reported. The LiKSO4 is a crystal with many phase transitions which can be detected via the anomalies in the variation of the thermal diffusivity as a function of the temperature.
Baoshan Zhu; Kyoji Kamemoto
2005-01-01
In this study, an advanced Lagrangian vortexboundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present.Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field.The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.
On the Diffusion Coefficient of Two-step Method for LWR analysis
Lee, Deokjung; Choi, Sooyoung [UNIST, Ulsan (Korea, Republic of); Smith, Kord S. [Massachusetts Institute of Technology, Cambridge (United States)
2015-10-15
The few-group constants including diffusion coefficients are generated from the assembly calculation results. Once the assembly calculation is done, the cross sections (XSs) are spatially homogenized, and a critical spectrum calculation is performed in order to take into account the neutron leakages of the lattice. The diffusion coefficient is also generated through the critical spectrum calculation. Three different methods of the critical spectrum calculation such as B1 method, P1 method, and fundamental mode (FM) calculation method are considered in this paper. The diffusion coefficients can also be affected by transport approximations for the transport XS calculation which is used in the assembly transport lattice calculation in order to account for the anisotropic scattering effects. The outflow transport approximation and the inflow transport approximation are investigated in this paper. The accuracy of the few group data especially the diffusion coefficients has been studied to optimize the combination of the transport correction methods and the critical spectrum calculation methods using the UNIST lattice physics code STREAM. The combination of the inflow transport approximation and the FM method is shown to provide the highest accuracy in the LWR core calculations. The methodologies to calculate the diffusion coefficients have been reviewed, and the performances of them have been investigated with a LWR core problem. The combination of the inflow transport approximation and the fundamental mode critical spectrum calculation shows the smallest errors in terms of assembly power distribution.
Incremental Unknowns Method for Solving Three-Dimensional Convection-Diffusion Equations
Lunji Song; Yujiang Wu
2007-01-01
We use the incremental unknowns method in conjunction with the iterative methods to approximate the solution of the nonsymmetric and positive-definite linear systems generated from a multilevel discretization of three-dimensional convection-diffusion equations. The condition numbers of incremental unknowns matrices associated with the convection-diffusion equations and the number of iterations needed to attain an acceptable accuracy are estimated. Numerical results are presented with two-level approximations,which demonstrate that the incremental unknowns method when combined with some iterative methods is very efficient.
Investigation of Three-Dimensional Flow Structure in a Transonic Diffuser by the LIF Method
小野, 大輔; 半田, 太郎; 青木, 俊之; 益田, 光治
2007-01-01
The three-dimensional flow structure induced by normal shock-wave/boundary-layer interaction in a transonic diffuser is investigated by a laser-induced fluorescence (LIF) method. This diagnostic system uses an argon-ion laser as a light source, and target gas is dry nitrogen with iodine seeded as a fluorescence material. The Mach-number distributions in the diffuser are obtained from the measured fluorescence intensity, and the three-dimensional shape of the boundary layers is obtained immedi...
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.
Diffusion-based method for producing density equalizing maps
Gastner, M T; Gastner, Michael T.
2004-01-01
Map makers have long searched for a way to construct cartograms -- maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, in order to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here we present a new technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the metho...
Diffusion coefficients for LMFBR cells calculated with MOC and Monte Carlo methods
Rooijen, W.F.G. van, E-mail: rooijen@u-fukui.ac.j [Research Institute of Nuclear Energy, University of Fukui, Bunkyo 3-9-1, Fukui-shi, Fukui-ken 910-8507 (Japan); Chiba, G., E-mail: chiba.go@jaea.go.j [Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195 (Japan)
2011-01-15
The present work discusses the calculation of the diffusion coefficient of a lattice of hexagonal cells, with both 'sodium present' and 'sodium absent' conditions. Calculations are performed in the framework of lattice theory (also known as fundamental mode approximation). Unlike the classical approaches, our heterogeneous leakage model allows the calculation of diffusion coefficients under all conditions, even if planar voids are present in the lattice. Equations resulting from this model are solved using the method of characteristics (MOC). Independent confirmation of the MOC result comes from Monte Carlo calculations, in which the diffusion coefficient is obtained without any of the assumptions of lattice theory. It is shown by comparison to the Monte Carlo results that the MOC solution yields correct values of the diffusion coefficient under all conditions, even in cases where the classic calculation of the diffusion coefficient fails. This work is a first step in the development of a robust method to calculate the diffusion coefficient of lattice cells. Adoption into production codes will require more development and validation of the method.
Wu, Wen; Wu, Zhouhu; Song, Zhiwen
2017-07-01
Prediction of the pollutant mixing zone (PMZ) near the discharge outfall in Huangshaxi shows large error when using the methods based on the constant lateral diffusion assumption. The discrepancy is due to the lack of consideration of the diffusion coefficient variation. The variable lateral diffusion coefficient is proposed to be a function of the longitudinal distance from the outfall. Analytical solution of the two-dimensional advection-diffusion equation of a pollutant is derived and discussed. Formulas to characterize the geometry of the PMZ are derived based on this solution, and a standard curve describing the boundary of the PMZ is obtained by proper choices of the normalization scales. The change of PMZ topology due to the variable diffusion coefficient is then discussed using these formulas. The criterion of assuming the lateral diffusion coefficient to be constant without large error in PMZ geometry is found. It is also demonstrated how to use these analytical formulas in the inverse problems including estimating the lateral diffusion coefficient in rivers by convenient measurements, and determining the maximum allowable discharge load based on the limitations of the geometrical scales of the PMZ. Finally, applications of the obtained formulas to onsite PMZ measurements in Huangshaxi present excellent agreement.
Kucza, Witold, E-mail: witek@agh.edu.pl
2013-07-25
Graphical abstract: -- Highlights: •Former random walk approach for FIA simulations has been improved. •Random walk and uniform dispersion models have been used for FIA simulations. •Diffusivities have been optimized by genetic and the Levenberg–Marquardt methods. •Both approaches have given similar results in agreement with experimental ones. -- Abstract: Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg–Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches.
Two regularization methods for solving a Riesz-Feller space-fractional backward diffusion problem
Zheng, G. H.; Wei, T.
2010-11-01
In this paper, a backward diffusion problem for a space-fractional diffusion equation (SFDE) in a strip is investigated. Such a problem is obtained from the classical diffusion equation in which the second-order space derivative is replaced with a Riesz-Feller derivative of order β in (0, 2]. We show that such a problem is severely ill-posed and further propose a new regularization method and apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical methods are effective.
Accelerated molecular dynamics and equation-free methods for simulating diffusion in solids.
Deng, Jie; Zimmerman, Jonathan A.; Thompson, Aidan Patrick; Brown, William Michael (Oak Ridge National Laboratories, Oak Ridge, TN); 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.
Sample Duplication Method for Monte Carlo Simulation of Large Reaction-Diffusion System
张红东; 陆建明; 杨玉良
1994-01-01
The sample duplication method for the Monte Carlo simulation of large reaction-diffusion system is proposed in this paper. It is proved that the sample duplication method will effectively raise the efficiency and statistical precision of the simulation without changing the kinetic behaviour of the reaction-diffusion system and the critical condition for the bifurcation of the steady-states. The method has been applied to the simulation of spatial and time dissipative structure of Brusselator under the Dirichlet boundary condition. The results presented in this paper definitely show that the sample duplication method provides a very efficient way to sol-’e the master equation of large reaction-diffusion system. For the case of two-dimensional system, it is found that the computation time is reduced at least by a factor of two orders of magnitude compared to the algorithm reported in literature.
Rapid Inverse Method to Measure Thermal Diffusivity of Low-Moisture Foods.
Muramatsu, Yoshiki; Greiby, Ibrahim; Mishra, Dharmendra K; Dolan, Kirk D
2017-02-01
Thermal diffusivity is an important transport property needed in modeling and computations of transient heat transfer in basic food processing operations. In addition, the prediction of nutritional and microbial changes occurring in food during thermal processing requires knowledge of thermal diffusivity of foods. The objectives of this study were to develop a new nonisothermal and nonlinear determination method of thermal diffusivity and to measure the thermal diffusivity of low-moisture foods using that new method. Thermal diffusivities of 5 kinds of low-moisture foods (almond meal, corn meal, wheat flour, chocolate fudge, and peanut butter) were estimated using an inverse technique. Samples were canned and heated at the surface in a water bath at about 70 °C. The 1-dimensional transient heat conduction problem for radial coordinates was solved with a finite-difference model. The thermal diffusivity of each of the 5 samples was determined by the ordinary least squares and sequential estimation methods, respectively. Predicted and observed temperature matched well, with maximum residuals of 0.9 °C. The thermal diffusivity values of the samples ranged from 9.8 × 10(-8) to 1.3 × 10(-7) m(2) /s. The advantages of this method are that the device and the estimation method are simple, inexpensive, rapid, and can handle large spatial temperature gradients, such as those experienced during heating of low-moisture foods. The results obtained in this study will be useful in the design of equipment and in calculations for the thermal processing of low-moisture foods. © 2017 Institute of Food Technologists®.
Chen, Li; Kang, Qinjun; Yao, Jun; Tao, Wenquan
2014-01-01
Porous structures of shales are reconstructed based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analyzes of the nanoscale reconstructed shales are performed, including porosity, pore size distribution, specific surface area and pore connectivity. The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) fluid flow model and single-relaxation-time (SRT) LBM diffusion model are adopted to simulate the fluid flow and Knudsen diffusion process within the reconstructed shales, respectively. Tortuosity, intrinsic permeability and effective Knudsen diffusivity are numerically predicted. The tortuosity is much higher than that 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 different Knudsen number and pressure are estimated and compared with existing corrections re...
Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method
Abdelraheem M. Aly
2016-12-01
Full Text Available The double-diffusive natural convection in an enclosure filled with nanofluid is studied using ISPH method. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. In ISPH algorithm, a semi implicit velocity correction procedure is utilized and the pressure is implicitly evaluated by solving pressure Poisson equation. The results are presented with flow configurations, isotherms, concentration and nanoparticle volume fraction contours and average Nusselt and Sherwood numbers for different cases. The results from this investigation are well validated and have favorable comparisons with previously published results. It is found that, among all cases, a good natural convection can be obtained by considering the double diffusive case. An increase in Soret number accompanied by a decrease in Dufour number results in an increase in average Nusselt number and a decrease in average Sherwood number.
Variational iteration method for solving the time-fractional diffusion equations in porous medium
Wu Guo-Cheng
2012-01-01
The variational iteration method is successfully extended to the case of solving fractional differential equations,and the Lagrange multiplier of the method is identified in a more accurate way.Some diffusion models with fractional derivatives are investigated analytically,and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Anandh, K R; Sujatha, C M; Ramakrishnan, S
2014-01-01
Ventricle enlargement is a useful structural biomarker for the diagnosis of Alzheimers Disease (AD). This devastating neurodegenerative disorder results in progression of dementia. Although AD results in the passive increment of ventricle volume, there exists a large overlap in the volume measurements of AD and normal subjects. Hence, shape based analysis of ventricle dilation is appropriate to detect the subtle morphological changes among these two groups. In this work, segmentation of ventricle in Alzheimer MR images is employed using level set method and anisotropic based diffusion filtering. Images considered for this study are preprocessed using filters. Anisotropic based diffusion filtering is employed to extract the edge map. This filtering performs region specific smoothing process using the diffusion coefficient as a function of image gradient. Filtered images are subjected to level set method which employs an improved diffusion rate equation for the level set evolution. Geometric features are extracted from the segmented ventricles. Results show that the diffusion filter could extract edge map with sharp region boundaries. The modified level set method is able to extract the morphological changes in ventricles. The observed morphological changes are distinct for normal and AD subjects (p < 0.0001). It is also observed that the sizes of ventricle in the AD subjects are noticeably enlarged when compared to normal subjects. Features obtained from the segmented ventricles are also clearly distinct and demonstrate the differences in the AD subjects. As ventricle volume and its morphometry are significant biomarkers, this study seems to be clinically relevant.
Study of the diffusion of points defects in crystalline silicon using the kinetic ART method
Trochet, Mickael; Brommer, Peter; Beland, Laurent-Karim; Joly, Jean-Francois; Mousseau, Normand
2013-03-01
Because of the long-time scale involved, the activated diffusion of point defects is often studied in standard molecular dynamics at high temperatures only, making it more difficult to characterize complex diffusion mechanisms. Here, we turn to the study of point defect diffusion in crystalline silicon using kinetic ART (kART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building based on the activation-relaxation technique (ART nouveau). By generating catalogs of diffusion mechanisms and fully incorporating elastic and off-lattice effects, kART is a unique tool for characterizing this problem. More precisely, using kART with the standard Stillinger-Weber potential we consider the evolution of crystalline cells with 1 to 4 vacancies and 1 to 4 interstitials at various temperatures and to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics in addition to identifying special configurations such as a 2-interstitial super-diffuser.
A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation
Chunye Gong
2014-01-01
Full Text Available The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M compared with O(NM for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.
A semi-analytical finite element method for a class of time-fractional diffusion equations
Sun, HongGuang; Sze, K Y
2011-01-01
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related mathematical descriptions. These models usually involve long-time range computation, which is a critical obstacle for its application, improvement of the computational efficiency is of great significance. In this paper, a semi-analytical method is presented for solving a class of time-fractional diffusion equations which overcomes the critical long-time range computation problem of time fractional differential equations. In the procedure, the spatial domain is discretized by the finite element method which reduces the fractional diffusion equations into approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time range computation can effectively be minimized. To illustrate its efficiency and simplicity, four...
Thermal Diffusivity of Film/Substrate Structures Characterized by Transient Thermal Grating Method
XU Xiao-Dong; MA Di; ZHANG Shu-Yi; LUO Ai-Hua; KIYOTAKA Wasa
2008-01-01
Transient thermal grating method is used to measure the thermal diffusivity of absorbing films deposited on transparent substrates.According to periodically modulated dielectric constant variations and thermoelastic deformations of the thin films caused by the transient thermal gratings,an improved optical diffraction theory is presented.In the experiment,the probing laser beam reflectively diffracted by the thermal grating is measured by a photomultipliar at different grating fringe spaces.The thermal diffusivity of the film can be evaluated by fitting the theoretical calculations of diffraction signals to the experimental measured data.The validity of the method is tested by measuring the thermal diffusivities of absorbing ZnO films deposited on glass substrates.
Development of advanced methods for analysis of experimental data in diffusion
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
王文洽
2003-01-01
A new discrete approximation to the convection term of the covection-diffusionequation was constructed in Saul' yev type difference scheme, then the alternating segmentCrank-Nicolson( ASC-N) method for solving the convection-diffusion equation with variablecoefficient was developed. The ASC-N method is unconditionally stable. Numericalexperiment shows that this method has the obvious property of parallelism and accuracy. Themethod can be used directly on parallel computers.
Xiang-Chao Shi
2016-02-01
Full Text Available The fractional reaction diffusion equation is one of the popularly used fractional partial differential equations in recent years. The fast Adomian decomposition method is used to obtain the solution of the Cauchy problem. Also, the analytical scheme is extended to the fractional one where the Taylor series is employed. In comparison with the classical Adomian decomposition method, the ratio of the convergence is increased. The method is more reliable for the fractional partial differential equations.
Mixed time discontinuous space-time finite element method for convection diffusion equations
无
2008-01-01
A mixed time discontinuous space-time finite element scheme for second-order convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 This test method provides procedures for measuring the leach rates of elements from a solidified matrix material, determining if the releases are controlled by mass diffusion, computing values of diffusion constants based on models, and verifying projected long-term diffusive releases. This test method is applicable to any material that does not degrade or deform during the test. 1.1.1 If mass diffusion is the dominant step in the leaching mechanism, then the results of this test can be used to calculate diffusion coefficients using mathematical diffusion models. A computer program developed for that purpose is available as a companion to this test method (Note 1). 1.1.2 It should be verified that leaching is controlled by diffusion by a means other than analysis of the leach test solution data. Analysis of concentration profiles of species of interest near the surface of the solid waste form after the test is recommended for this purpose. 1.1.3 Potential effects of partitioning on the test results can...
Merks, R.M.H.; Hoekstra, A.G.; Sloot, P.M.A.
2002-01-01
We numerically validate the moment propagation method for advection-diffusion in a Lattice Boltzmann simulation against the analytic Taylor-Aris prediction for dispeion in a three dimensional Poiseuille flow. Good agreement between simulation and teh tehory is found, with relative errors smaller tha
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
A semi-analytical method for simulating matrix diffusion in numerical transport models
Falta, Ronald W.; Wang, Wenwen
2017-02-01
A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.
The Induced Dimension Reduction method applied to convection-diffusion-reaction problems
Astudillo, R.; Van Gijzen, M.B.
2016-01-01
Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b. (1) In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) [10], with other short-recurrences Krylov met
Zegers, Ben J.M.; Poen, H.; Stoop, J.W.; Ballieux, R.E.
1968-01-01
A comparative study was made of the results of immunoglobulin determination in sera using immunoelectrophoresis and the radial diffusion method of Mancini. The results indicated that, except for certain ranges of immunoglobulin concentration (low, normal or slightly increased) the data obtained by i
A new computational method for fractal heat-diffusion via local fractional derivative
Liu Geng-Yuan
2016-01-01
Full Text Available The fractal heat-conduction problem via local fractional derivative is investigated in this paper. The solution of the fractal heat-diffusion equation is obtained. The characteristic equation method is proposed to find the analytical solution of the partial differential equation in fractal heat-conduction problem.
Strang-type preconditioners for solving fractional diffusion equations by boundary value methods
Gu, Xian-Ming; Huang, Ting-Zhu; Zhao, Xi-Le; Li, Hou-Biao; Li, Liang
2015-01-01
The finite difference scheme with the shifted Grünwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with initial values. Recently, boundary value method (BVM) was develop
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Ranjit Kumar; R S Kaushal; Awadhesh Prasad
2010-10-01
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)
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 new in-situ method to determine the apparent gas diffusion coefficient of soils
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.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
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
Bording, Thue Sylvester; Nielsen, Søren Bom; Balling, Niels
2016-01-01
Accurate information on thermal conductivity and thermal diffusivity of materials is of central importance in relation to geoscience and engineering problems involving the transfer of heat. Within the geosciences, this applies to all aspects regarding the determination of terrestrial heat flow...... and volumetric heat capacity, and thereby also thermal diffusivity, are measured simultaneously. As the density of samples is easily determined independently, specific heat capacity may also be determined. Finite element formulation provides a flexible forward solution for heat transfer across the bar...... and subsurface temperature modelling. Several methods, including the classical divided-bar technique, are available for laboratory measurements of thermal conductivity, and much fewer for thermal diffusivity. We have generalized the divided-bar technique to the transient case, in which thermal conductivity...
Calculations of Self-diffusion Activation Energies for Alkaline Metals With Embedded Atom Method
欧阳义芳; 张邦维; 廖树帜
1994-01-01
Calculations were performed for the self-diffusion activation energies of monovacancy and both formation and binding energies of divacancies for alkaline metals Li, Na, K, Rb, Cs using the embedded atom method (EAM) model for bcc transition metals developed by the authors recently. The aim of the paper is to extend the application of the new model, to compare the calculated values for self-diffusion with the experimental data and those of previous calculations, and to discuss the intrinsic characteristic of self-diffusion in alkaline metals. The calculated monovacancy migration energies and activation energies are in excellent agreement with experimental data, and the calculated divacancy migration and activation energies are in good agreement with the experimental values available.
Thermal diffusivity measurement of glass at high temperature by using flash method
Kabayabaya, Thomas; Yu, Fan; Zhang, Xinxin
2004-02-01
A measurement of the thermal diffusivity of a semi-transparent material (glass) by means of the “Flash Method” is investigated in the present work. By taking into account the heat losses on the two faces of the sample, and using a new experimental technique design, an improvement of the determination of the thermal diffusivity of the semi-transparent material (glass) at high temperature is realized. The experimental design presented here is an original technical concept that enables a significant reduction in heat loss during the experiments. A very simple model based on the quadrupole method is used to theoretically determine the thermal diffusivity of the semitransparent material by taking into account both conduction and radiation. Theoretical results clarify the effect of the absorption coefficient and the thickness of the sample on the heat transfer in the semi-transparent medium.
Bording, Thue Sylvester; Nielsen, Søren Bom; Balling, Niels
2016-01-01
Accurate information on thermal conductivity and thermal diffusivity of materials is of central importance in relation to geoscience and engineering problems involving the transfer of heat. Within the geosciences, this applies to all aspects regarding the determination of terrestrial heat flow...... and subsurface temperature modelling. Several methods, including the classical divided-bar technique, are available for laboratory measurements of thermal conductivity, and much fewer for thermal diffusivity. We have generalized the divided-bar technique to the transient case, in which thermal conductivity...... and volumetric heat capacity, and thereby also thermal diffusivity, are measured simultaneously. As the density of samples is easily determined independently, specific heat capacity may also be determined. Finite element formulation provides a flexible forward solution for heat transfer across the bar...
MODELING OF SUPERCRITICAL FLUID EXTRACTION KINETIC OF FLAXSEED OIL BY DIFFUSION CONTROL METHOD
Emir Zafer HOŞGÜN
2013-06-01
Full Text Available In this study, Flaxseed oil was extracted by Supercritical Carbondioxide Extraction, and extractionkinetics was modelled using diffusion controlled method.The effect of process parameters, such as pressure (20, 35, 55 MPa, temperature (323 and 343 K, and CO2 flow rate (1 and 3 L CO2 /min on the extraction yield and effective diffusivity (De was investigated. The effective diffusion coefficient varied between 2.4 x10-12 and 10.8 x10-12 m2s-1 for the entire range of experiments and increased with the pressure and flow rate. The model fitted well theexperimental data (ADD varied between 2.35 and 7.48%.
Aleš Mráček
2010-02-01
Full Text Available The amorphous polymer film swelling in a liquid solvent below the glass transition temperature was characterized by a few kinetic parameters (especially the mutual diffusion coefficient of swelling and its mean value obtained by interference of monochromatic light in the wedge arrangement. This interferometric method allows one to determine the concentration field in the swollen surface layer and consequently to compute the concentration-dependent diffusion coefficient. A software system developed at the Department of Physics and Material Engineering at TBU in Zlin has been used for the evaluation of the main kinetic parameters of the swelling process. The software can be used for the on-line analyses of interferograms during the swelling process. The main application outputs are the computation of the concentration profile, the concentration gradient, the mutual diffusion coefficient of the swelling by the solvent and its mean value.
Axisymmetric vortex method for low-Mach number, diffusion-controlled combustion
Lakkis, I
2003-01-01
A grid-free, Lagrangian method for the accurate simulation of low-Mach number, variable-density, diffusion-controlled reacting flow is presented. A fast-chemistry model in which the conversion rate of reactants to products is limited by the local mixing rate is assumed in order to reduce the combustion problem to the solution of a convection-diffusion-generation equation with volumetric expansion and vorticity generation at the reaction fronts. The solutions of the continuity and vorticity equations, and the equations governing the transport of species and energy, are obtained using a formulation in which particles transport conserved quantities by convection and diffusion. The dynamic impact of exothermic combustion is captured through accurate integration of source terms in the vorticity transport equations at the location of the particles, and the extra velocity field associated with volumetric expansion at low Mach number computed to enforced mass conservation. The formulation is obtained for an axisymmet...
Li, Xianping
2010-01-01
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral ...
Exciton diffusion length in some thermocleavable polythiophenes by the surface photovoltage method
Tousek, J.; Touskova, J.; Remes, Z.
2012-01-01
Poly-3-(2-methylhexyloxycarbonyl) dithiophene (P3MHOCT), poly-3-carboxydithiophene (P3CT) and polythiophene (PT) polymers were studied by optical and optoelectronic methods to find diffusion length as one of the important parameters characterizing them as candidates for solar cells. Their important...... be ascribed to the increase of the crystalline fraction. The highest diffusion length was found in P3CT polymer but its large resistivity represents a disadvantage in application in solar cells. Taking into account just these parameters, relatively low resistivity together with quite high diffusion length (13...... ± 2 nm) predetermine the native polythiophene among the polymers studied in the present work as the best candidate for construction of solar cells....
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
Thermal diffusivity of aligned multi-walled carbon nanotubes measured by the flash method
Maeklin, Jani; Halonen, Niina; Toth, Geza; Jantunen, Heli [Microelectronics and Materials Physics Laboratories, University of Oulu (Finland); Sapi, Andras; Kukovecz, Akos; Konya, Zoltan [Department of Applied and Environmental Chemistry, University of Szeged (Hungary); Mikkola, Jyri-Pekka [Department of Chemistry, Technical Chemistry, Umeaa University (Sweden); Kordas, Krisztian [Microelectronics and Materials Physics Laboratories, University of Oulu (Finland); Department of Chemistry, Technical Chemistry, Umeaa University (Sweden)
2011-11-15
Thermal diffusivity of freestanding catalytic chemical vapor deposition (CCVD) grown multi-walled carbon nanotube (MWCNT) forests (height of 1.5 and 1.9 mm) was characterized in the temperature range between 25 and 200 C. Copper and Al-alloy metal blocks were used as references for validation of the experimental setup. The measurements were carried out along the MWCNT alignment direction with a thermal property analyzer that uses the flash method. The thermal diffusivities measured at room temperature for as-grown and post-annealed (2 h at 480 C in open air) samples were found to be {proportional_to}0.45 and {proportional_to}0.23 cm{sup 2}/s, respectively. In both cases, the thermal diffusivity values were slightly decreasing with increasing temperature. The observed decrease in diffusivity after annealing is most probably due to the loss of amorphous carbon in the specimens and also because of the increased defect density in the nanotube walls resulting in a more pronounced phonon scattering in the lattice. The measured thermal diffusivities for as-grown samples agree with data reported elsewhere for similar MWCNT materials [W. Yi et al., Rev. B 59, 9015 (1999) and T. Borca-Tasciuc et al., J. Appl. Phys. 98, 054309 (2005)]. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Gjesdal, Thor
1997-12-31
This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.
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.
Preconditioned time-difference methods for advection-diffusion-reaction equations
Aro, C.; Rodrigue, G. [Lawrence Livermore National Lab., CA (United States); Wolitzer, D. [California State Univ., Hayward, CA (United States)
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.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Shumanova M.V.
2015-03-01
Full Text Available The process fish salting has been studied by the method of photon correlation spectroscopy; the distribution of salt concentration in the solution and herring flesh with skin has been found, diffusion coefficients and salt concentrations used for creating a mathematical model of the salting technology have been worked out; the possibility of determination by this method the coefficient of dynamic viscosity of solutions and different media (minced meat etc. has been considered
An in situ method for real-time monitoring of soil gas diffusivity
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. [Dept. of Engineering Physics, Tsinghua Univ. (China)
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)
Studies of the accuracy of time integration methods for reaction-diffusion equations
Ropp, David L.; Shadid, John N.; Ober, Curtis C.
2004-03-01
In this study we present numerical experiments of time integration methods applied to systems of reaction-diffusion equations. Our main interest is in evaluating the relative accuracy and asymptotic order of accuracy of the methods on problems which exhibit an approximate balance between the competing component time scales. Nearly balanced systems can produce a significant coupling of the physical mechanisms and introduce a slow dynamical time scale of interest. These problems provide a challenging test for this evaluation and tend to reveal subtle differences between the various methods. The methods we consider include first- and second-order semi-implicit, fully implicit, and operator-splitting techniques. The test problems include a prototype propagating nonlinear reaction-diffusion wave, a non-equilibrium radiation-diffusion system, a Brusselator chemical dynamics system and a blow-up example. In this evaluation we demonstrate a "split personality" for the operator-splitting methods that we consider. While operator-splitting methods often obtain very good accuracy, they can also manifest a serious degradation in accuracy due to stability problems.
CMOS-compatible method for doping of buried vertical polysilicon structures by solid phase diffusion
Turkulets, Yury; Silber, Amir; Ripp, Alexander; Sokolovsky, Mark; Shalish, Ilan
2016-03-01
Polysilicon receives attention nowadays as a means to incorporate 3D-structured photonic devices into silicon processes. However, doping of buried layers of a typical 3D structure has been a challenge. We present a method for doping of buried polysilicon layers by solid phase diffusion. Using an underlying silicon oxide layer as a dopant source facilitates diffusion of dopants into the bottom side of the polysilicon layer. The polysilicon is grown on top of the oxide layer, after the latter has been doped by ion implantation. Post-growth heat treatment drives in the dopant from the oxide into the polysilicon. To model the process, we studied the diffusion of the two most common silicon dopants, boron (B) and phosphorus (P), using secondary ion mass spectroscopy profiles. Our results show that shallow concentration profiles can be achieved in a buried polysilicon layer using the proposed technique. We present a quantitative 3D model for the diffusion of B and P in polysilicon, which turns the proposed method into an engineerable technique.
A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems
Yang Liu
2013-01-01
Full Text Available A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇·(a(x,t∇u is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div;Ω space and the hyperbolic part d(x(∂u/∂t+c(x,t·∇u is handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2- and H1-norms for the scalar unknown u and a priori error estimates in (L22-norm for its gradient λ and its flux σ (the coefficients times the negative gradient are derived. Finally, a numerical example is provided to verify our theoretical results.
Tchitchekova, Deyana S. [IRSN, PSN, SEMIA, LPTM, Saint-Paul-Lez-Durance (France); Univ. Lyon, INSA Lyon, MATEIS, UMR CNRS 5510, Villeurbanne (France); Morthomas, Julien; Perez, Michel [Univ. Lyon, INSA Lyon, MATEIS, UMR CNRS 5510, Villeurbanne (France); Ribeiro, Fabienne [IRSN, PSN, SEMIA, LPTM, Saint-Paul-Lez-Durance (France); Ducher, Roland [IRSN, PSN, SAG, LETR, Saint-Paul-Lez-Durance (France)
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
2014-07-01
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.
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.
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.
A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation
Evans, Thomas M., E-mail: evanstm@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States); Mosher, Scott W., E-mail: moshersw@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States); Slattery, Stuart R., E-mail: sslattery@wisc.edu [University of Wisconsin–Madison, 1500 Engineering Dr., Madison, WI 53716 (United States); Hamilton, Steven P., E-mail: hamiltonsp@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States)
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.
Theoretical study of some nodal methods for the solution of the diffusion equation. Numerical tests
Fedon-Magnaud, C.
1983-08-01
The nodal methods used in the solution of the neutron multigroup diffusion equation are described. A new formulation of this methods is obtained in order to have a comparison with the finite element methods. After a brief review of nonconforming finite element theory, we use a Radau formula to establish the equivalence with nodal schemes. Convergence theorems and error estimations are then obtained. In the last part, numerical calculations are performed for two reactor test configurations. Comparisons are done between nodal or nonconforming schemes and more classical methods (F.D., conforming F.E.) wich are used in reactor analysis.
Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J
2006-09-01
A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (
Takeuchi, Akito; Takigawa, Tomoko; Kawasumi, Yaeko; Yasugi, Tomojiro; Endo, Yoko; Wang, Da-Hong; Takaki, Jiro; Sakurai, Haruhiko; Ogino, Keiki
2007-11-01
Monitoring of the workplace concentration of 3-methoxybutyl acetate (MBA), which is used in printer's ink and thinner for screen-printing and as an organic solvent to dissolve various resins, is important for health reasons. An active and a diffusive sampling method, using a gas chromatograph equipped with a flame ionization detector, were developed for the determination of MBA in workplace air. For the active sampling method using an activated charcoal tube, the overall desorption efficiency was 101%, the overall recovery was 104%, and the recovery after 8 days of storage in a refrigerator was more than 90%. For the diffusive sampling method using the 3M 3500 organic vapor monitor, the MBA sampling rate was 19.89 cm(3) min(-1). The linear range was from 0.01 to 96.00 microg ml(-1), with a correlation coefficient of 0.999, and the detection limits of the active and diffusive samplers were 0.04 and 0.07 microg sample(-1), respectively. The geometric mean of stationary sampling and personal sampling in a screen-printing factory were 12.61 and 16.52 ppm, respectively, indicating that both methods can be used to measure MBA in workplace air.
Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas
1999-10-01
We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)
A Proposal for a Novel Method to Measure the Diffusivity of Species in Slag
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.
Diffusion behavior of Cr diluted in bcc and fcc Fe: Classical and quantum simulation methods
Ramunni, Viviana P., E-mail: vpram@cnea.gov.ar [CONICET, Avda. Rivadavia 1917, Cdad. de Buenos Aires C.P. 1033 (Argentina); Comisión Nacional de Energía Atómica, Gerencia Materiales, Av. Del Libertador 8250, C1429BNP Ciudad de Buenos Aires (Argentina); Rivas, Alejandro M.F. [CONICET, Avda. Rivadavia 1917, Cdad. de Buenos Aires C.P. 1033 (Argentina); Comisión Nacional de Energía Atómica, Departamento de Física Teórica, Tandar, Av. Del Libertador 8250, C1429BNP Ciudad de Buenos Aires (Argentina)
2015-07-15
We characterize the atomic mobility behavior driven by vacancies, in bcc and fcc Fe−Cr diluted alloys, using a multi-frequency model. We calculate the full set of the Onsager coefficients and the tracer self and solute diffusion coefficients in terms of the mean jump frequencies. The involved jump frequencies are calculated using a classical molecular static (CMS) technique. For the bcc case, we also perform quantum calculations based on the density functional theory (DFT). There, we show that, in accordance with Bohr's correspondence principle, as the size of the atomic cell (total number of atoms) is increased, quantum results with DFT recover the classical ones obtained with CMS calculations. This last ones, are in perfect agreement with available experimental data for both, solute and solvent diffusion coefficients. For high temperatures, in the fcc phase where no experimental data are yet available, our CMS calculations predict the expected solute and solvent diffusion coefficients. - Graphical abstract: Display Omitted - Highlights: • Comparison of diffusion coefficients obtained from classical and quantum methods. • We perform our calculations in diluted bcc/fcc Fe–Cr alloy. • Magnetic and phonon effects must be taken into account. • Classical calculations are in perfect agreement with experimental data.
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.
A hybrid method for efficient and accurate simulations of diffusion compartment imaging signals
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.
Graphene nanoplatelets: Thermal diffusivity and thermal conductivity by the flash method
Potenza, M.; Cataldo, A.; Bovesecchi, G.; Corasaniti, S.; Coppa, P.; Bellucci, S.
2017-07-01
The present work deals with the measurement of thermo-physical properties of a freestanding sheet of graphene (thermal diffusivity and thermal conductivity), and their dependence on sample density as result of uniform mechanical compression. Thermal diffusivity of graphene nano-platelets (thin slabs) was measured by the pulse flash method. Obtained response data were processed with a specifically developed least square data processing algorithm. GNP specific heat was assumed from literature and thermal conductivity derived from thermal diffusivity, specific heat and density. Obtained results show a significant difference with respect to other porous media: the thermal diffusivity decreases as the density increases, while thermal conductivity increases for low and high densities, and remain fairly constant for the intermediate range. This can be explained by the very high thermal conductivity values reached by the nano-layers of graphene and the peculiar arrangement of platelets during the compression applied to the samples to get the desired density. Due to very high thermal conductivity of graphene layers, the obtained results show that thermal conductivity of conglomerates increases when there is an air reduction due to compression, and consequent density increases, with the number of contact points between platelets also increased. In the intermediate range (250 ≤ ρ ≤ 700 kg.m-3) the folding of platelets reduces density, without increasing the contact points of platelets, so thermal conductivity can slightly decrease.
Sasaki, Nobuhiko; Horinouchi, Hirohisa; Ushiyama, Akira; Minamitani, Haruyuki
2012-01-01
Oxygen transport is believed to primarily occur via capillaries and depends on the oxygen tension gradient between the vessels and tissues. As blood flows along branching arterioles, the O(2) saturation drops, indicating either consumption or diffusion. The blood flow rate, the O(2) concentration gradient, and Krogh's O(2) diffusion constant (K) of the vessel wall are parameters affecting O(2)delivery. We devised a method for evaluating K of arteriolar wall in vivo using phosphorescence quenching microscopy to measure the partial pressure of oxygen in two areas almost simultaneously. The K value of arteriolar wall (inner diameter, 63.5 ± 11.9 μm; wall thickness, 18.0 ± 1.2 μm) was found to be 6.0 ± 1.2 × 10(-11) (cm(2)/s)(ml O(2)·cm(-3) tissue·mmHg(-1)). The arteriolar wall O(2) consumption rate (M) was 1.5 ± 0.1 (ml O(2)·100 cm(-3) tissue·min(-1)), as calculated using Krogh's diffusion equation. These results suggest that the arteriolar wall consumes a considerable proportion of the O(2) that diffuses through it.
Thermal diffusivity study of aged Li-ion batteries using flash method
Nagpure, Shrikant C. [Center for Automotive Research (CAR), The Ohio State University, 930 Kinnear Rd., Columbus, OH 43212 (United States); Nanoprobe Laboratory for Bio- and Nanotechnology and Biomimetics (NLBB), The Ohio State University, 201 W. 19th Ave., Columbus, OH 43210 (United States); Dinwiddie, Ralph [Oak Ridge National Lab (ORNL), One Bethel Valley Road, Bldg 4515, Oak Ridge, TN 37831 (United States); Babu, S.S. [Integrated Systems Engineering, The Ohio State University, 1248 Arthur E Adams Drive, Columbus, OH 43210 (United States); Rizzoni, Giorgio [Center for Automotive Research (CAR), The Ohio State University, 930 Kinnear Rd., Columbus, OH 43212 (United States); Bhushan, Bharat [Nanoprobe Laboratory for Bio- and Nanotechnology and Biomimetics (NLBB), The Ohio State University, 201 W. 19th Ave., Columbus, OH 43210 (United States); Frech, Tim [Edison Welding Institute (EWI), 1250 Arthur E Adams Drive, Columbus, OH 43221 (United States)
2010-02-01
Advanced Li-ion batteries with high energy and power density are fast approaching compatibility with automotive demands. While the mechanism of operation of these batteries is well understood, the aging mechanisms are still under investigation. Investigation of aging mechanisms in Li-ion batteries becomes very challenging, as aging does not occur due to a single process, but because of multiple physical processes occurring at the same time in a cascading manner. As the current characterization techniques such as Raman spectroscopy, X-ray diffraction, and atomic force microscopy are used independent of each other they do not provide a comprehensive understanding of material degradation at different length (nm{sup 2} to m{sup 2}) scales. Thus to relate the damage mechanisms of the cathode at mm length scale to micro/nanoscale, data at an intermediate length scale is needed. As such, we demonstrate here the use of thermal diffusivity analysis by flash method to bridge the gap between different length scales. In this paper we present the thermal diffusivity analysis of an unaged and aged cell. Thermal diffusivity analysis maps the damage to the cathode samples at millimeter scale lengths. Based on these maps we also propose a mechanism leading to the increase of the thermal diffusivity as the cells are aged. (author)
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
Padgett, Jill M. A.; Ilie, Silvana, E-mail: silvana@ryerson.ca [Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3 (Canada)
2016-03-15
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.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent
2008-01-01
In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
PREDRAG POLIC
2001-09-01
Full Text Available A selective and sensitive procedure for the fast and indirect determination of chloride by the gas-diffusion FIA method has been optimized and applied for the determination of chloride in water samples which contained different amounts of the analyte. The examined samples were: seawater, tap water and very pure water from the water-steam system of the power plant Nikola Tesla B in Obrenovac. Application of an amperometric detector (model LC-17A; BAS, West Lafayette, USA enables the detection limit to be decreased down to 0.05 mmol/dm3 of chloride, which corresponds to 35.5 pg, and adjustment of the acceptor flow rate and direction inside the gas-diffusion unit. In this way the optimized FIA system has excellent repeatability. For 5 mmol/dm3 it was found to be 1.11 % (n = 5. The throughput of this method is 60 samples per hour.
Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)
2017-05-15
In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.
Bashar Zogheib
2017-01-01
Full Text Available A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients. By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points, equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the efficiency and spectral (exponential accuracy of the proposed method.
Zhang, Hong-yan; Ding, Dong; Song, Li-qiang; Gu, Lin-na; Yang, Peng; Tang, Yu-guo
2005-06-01
The noninvasive measurement of human blood glucose was achieved with NIR diffusion reflectance spectrum method. The thumb fingertip NIR diffusion reflectance spectra of six different age healthy volunteers were collected using Nexus-870 and its NIR fiber port smart accessory. The test was implemented with changing the blood glucose concentration for the limosis and satiation of every volunteer. The calibration model was set up using PLS method with the smoothing, baseline correction and first derivatives pretreatment spectrum in the 7500-8500 cm(-1) region for single volunteer, the same age combination and that of different age. When the spectrum was obtained, the actual blood glucose value of every spectrun sample was demarcated using ultraviolet spectrophotometer. The correlation between the calibration value and true value for single volunteer is better than that for the combination of volunteers, the correlative coefficients are all over 0.90471, RMSECs are all less than 0.171.
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
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.
Aydin, E. D.; Katsimichas, S.; de Oliveira, C. R. E.
2005-10-01
In this paper, the finite-element-spherical harmonics (FE-PN) method is applied to the solution of transient Boltzmann transport equation. Firstly, transport and diffusion calculations are obtained for homogeneous and inhomogeneous circular regions. Results are compared in order to show the effects of different absorption coefficient values on the propagation of photons. Significant differences between two theories are shown to occur especially in cases when the absorption is increased. Secondly, to validate the FE-PN method, results from this method are compared with Monte Carlo calculations for different cases. Comparisons show good agreements between FE-transport and Monte Carlo solutions and demonstrate the correctness of the results obtained.
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Free and forced convective-diffusion solutions by finite element methods
Gartling, D.K.; Nickell, R.E.
1976-01-01
Several free and forced convective-diffusion examples are solved and compared to either laboratory experiment or closed-form analysis. The problems solved illustrate the application of finite element methods to both strongly-coupled and weakly-coupled velocity and temperature fields governed by the steady-state momentum and energy equations. Special attention is given to internal forced convection with temperature-dependent viscosity and free convection within an enclosure.
Can, Ahmet [Department of Mechanical Engineering, University of Trakya, 22030 Edirne (Turkey)
2007-02-15
This paper presents an analytical method, which determines the moisture diffusion coefficients for the natural and forced convection hot air drying of pumpkin seeds and their temperature dependence. In order to obtain scientific data, the pumpkin seed drying process was investigated under both natural and forced hot air convection regimes. This paper presents the experimental results in which the drying air was heated by solar energy. (author)
New contactless method for thermal diffusivity measurements using modulated photothermal radiometry
Pham Tu Quoc, S., E-mail: sang.phamtuquoc@cea.fr; Cheymol, G.; Semerok, A. [French Alternative Energies and Atomic Energy Commission, Division of Nuclear Energy, DEN/DANS/DPC/SEARS/LISL, 91191 Gif/Yvette (France)
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.
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
Vladimir V. Lyubimov
2007-01-01
Full Text Available The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT. The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a 27% gain in spatial resolution can be obtained.
Method for Calculating the Optical Diffuse Reflection Coefficient for the Ocular Fundus
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.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)
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.
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.
Song, Yun S; Steinrücken, Matthias
2012-03-01
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.
An On-Line Method for Thermal Diffusivity Detection of Thin Films Using Infrared Video
Dong Huilong
2016-03-01
Full Text Available A novel method for thermal diffusivity evolution of thin-film materials with pulsed Gaussian beam and infrared video is reported. Compared with common pulse methods performed in specialized labs, the proposed method implements a rapid on-line measurement without producing the off-centre detection error. Through mathematical deduction of the original heat conduction model, it is discovered that the area s, which is encircled by the maximum temperature curve rTMAX(θ, increases linearly over elapsed time. The thermal diffusivity is acquired from the growth rate of the area s. In this study, the off-centre detection error is avoided by performing the distance regularized level set evolution formulation. The area s was extracted from the binary images of temperature variation rate, without inducing errors from determination of the heat source centre. Thermal diffusivities of three materials, 304 stainless steel, titanium, and zirconium have been measured with the established on-line detection system, and the measurement errors are: −2.26%, −1.07%, and 1.61% respectively.
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.
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
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
Generalized monotone method and numerical approach for coupled reaction diffusion systems
Sowmya, M.; Vatsala, Aghalaya S.
2017-01-01
Study of coupled reaction diffusion systems are very useful in various branches of science and engineering. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to the unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical methodology.
Improved diffusion methods for nitrogen and 15nitrogen analysis of Kjeldahl digests.
Stevens, W B; Mulvaney, R L; Khan, S A; Hoeft, R G
2000-01-01
Simple methods are described that permit the use of either H3BO3 indicator solution or acidified filter disks to collect NH3 liberated by treatment of Kjeldahl digests with NaOH. These methods incorporate modifications to improve reliability, analytical capacity, and convenience. A semimicro digest was diluted to 25 mL with deionized water, and a 10 mL aliquot, containing up to 4 mg N (150 microg N for diffusions into acidified disks), was transferred to a shell vial, which was placed inside a 473 mL (1 pint) Mason jar containing 10 mL 10N NaOH. The NH3 liberated by overturning the vial was collected after 12 to 48 h at ambient temperature, or after 4 h at 45 to 50 degrees C on a hotplate, for quantitative and/or isotope-ratio analyses. With either H3BO3 indicator solution or acidified filter disks, recovery of diffused N was quantitative. Isotope-ratio analyses of diffused N from 15N-labeled chemical, plant, and soil samples were within 3% of analyses using steam distillation.
Extension of the low diffusion particle method for near-continuum two-phase flow simulations
Su Wei; He Xiaoying; Cai Guobiao
2013-01-01
The low diffusion (LD) particle method,proposed by Burt and Boyd,is modified for the near-continuum two-phase flow simulations.The LD method has the advantages of easily coupling with the direct simulation Monte Carlo (DSMC) method for multi-scale flow simulations and dramatically reducing the numerical diffusion error and statistical scatter of the equilibrium particle methods.Liquid-or solid-phase particles are introduced in the LD method.Their velocity and temperature updating are respectively,calculated from the motion equation and the temperature equation according to the local gas properties.Coupling effects from condensed phase to gas phase are modeled as momentum and energy sources,which are respectively,equal to the negative values of the total momentum and energy increase in liquid or solid phase.The modified method is compared with theoretical results for unsteady flows,and good agreements are obtained to indicate the reliability of the one-way gas-to-particle coupling models.Hybrid LD-DSMC algorithm is implemented and performed for nozzle discharging gas-liquid flow to show the prospect of the LDDSMC scheme for multi-scale two-phase flow simulations.
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.
Sunahara, Y.; Kojima, F.
1988-01-01
The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.
Grejs, Anders Morten; Gjedsted, Jakob; Pedersen, Michael;
2016-01-01
The aim of this randomized porcine study was to compare surface targeted temperature management (TTM) to endovascular TTM evaluated by cerebral diffusion-weighted magnetic resonance imaging (MRI): apparent diffusion coefficient (ADC), and by intracerebral/intramuscular microdialysis. It is well...... known that alteration in the temperature affects ADC, but the relationship between cerebral ADC values and the cooling method per se has not been established. Eighteen anesthetized 60-kg female swine were hemodynamically and intracerebrally monitored and subsequently subjected to a baseline MRI...... a significantly lower median ADC than endovascular cooling: 714 (634; 804) × 10(-6) mm(2)/s versus 866 (828; 927) × 10(-6) mm(2)/s, (p edema and these low values could not be explained solely by the temperature effect per se...
Gurhan Gurarslan
2013-01-01
Full Text Available This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for Pe≤5. For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.
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.
Beltrán-Prieto Juan Carlos
2016-01-01
Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Determining the performance of a Diffuser Augmented Wind Turbine using a combined CFD/BEM method
Kesby Joss E.
2017-01-01
Full Text Available Traditionally, the optimisation of a Diffuser Augmented Wind Turbine has focused on maximising power output. However, due to the often less than ideal location of small-scale turbines, cut-in speed and starting time are of equal importance in maximising Annual Energy Production, which is the ultimate goal of any wind turbine design. This paper proposes a method of determining power output, cut-in speed and starting time using a combination of Computational Fluid Dynamics and Blade Element Momentum theory. The proposed method has been validated against published experimental data.
Numerical method for solving the three-dimensional time-dependent neutron diffusion equation
Khaled, S.M. [Institute of Nuclear Techniques, Budapest University of Technology and Economics, Budapest (Hungary)]. E-mail: K_S_MAHMOUD@hotmail.com; Szatmary, Z. [Institute of Nuclear Techniques, Budapest University of Technology and Economics, Budapest (Hungary)]. E-mail: szatmary@reak.bme.hu
2005-07-01
A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.
1976-09-01
The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem.
Bording, Thue S.; Nielsen, Søren B.; Balling, Niels
2016-04-01
Accurate information on thermal conductivity and thermal diffusivity of materials is of central importance in relation to geoscience and engineering problems involving the transfer of heat. Within the geosciences, this applies to all aspects regarding the determination of terrestrial heat flow and subsurface temperature modelling. Several methods, including the classical divided-bar technique, are available for laboratory measurements of thermal conductivity, and much fewer for thermal diffusivity. We have generalized the divided-bar technique to the transient case, in which thermal conductivity and volumetric heat capacity, and thereby also thermal diffusivity, are measured simultaneously. As the density of samples is easily determined independently, specific heat capacity may also be determined. Finite element formulation provides a flexible forward solution for heat transfer across the bar and thermal properties are estimated by inverse Monte Carlo modelling. This methodology enables a proper quantification of experimental uncertainties on measured thermal properties. The developed methodology was applied to laboratory measurements of various materials, including a standard ceramic material and different rock samples, and measuring results were compared with results applying traditional steady-state divided-bar and an independent line-source method. All measurements show highly consistent results and with excellent reproducibility and high accuracy. For conductivity, uncertainty is typically 1-3 %, and for diffusivity uncertainty may be reduced to about 3-5 %. The main uncertainty originates from the presence of thermal contact resistance associated with the internal interfaces of the bar. They are not resolved during inversion, and it is highly important that they are minimized by careful sample preparation.
A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection
Bachman, S. D.; Fox-Kemper, B.; Bryan, F. O.
2015-02-01
A diagnosis method is presented which inverts a set of tracer flux statistics into an eddy-induced transport intended to apply for all tracers. The underlying assumption is that a linear flux-gradient relationship describes eddy-induced tracer transport, but a full tensor coefficient is assumed rather than a scalar coefficient which allows for down-gradient and skew transports. Thus, Lagrangian advection and anisotropic diffusion not necessarily aligned with the tracer gradient can be diagnosed. In this method, multiple passive tracers are initialized in an eddy-resolving flow simulation. Their spatially-averaged gradients form a matrix, where the gradient of each tracer is assumed to satisfy an identical flux-gradient relationship. The resulting linear system, which is overdetermined when using more than three tracers, is then solved to obtain an eddy transport tensor R which describes the eddy advection (antisymmetric part of R) and potentially anisotropic diffusion (symmetric part of R) in terms of coarse-grained variables. The mathematical basis for this inversion method is presented here, along with practical guidelines for its implementation. We present recommendations for initialization of the passive tracers, maintaining the required misalignment of the tracer gradients, correcting for nonconservative effects, and quantifying the error in the diagnosed transport tensor. A method is proposed to find unique, tracer-independent, distinct rotational and divergent Lagrangian transport operators, but the results indicate that these operators are not meaningfully relatable to tracer-independent eddy advection or diffusion. With the optimal method of diagnosis, the diagnosed transport tensor is capable of predicting the fluxes of other tracers that are withheld from the diagnosis, including even active tracers such as buoyancy, such that relative errors of 14% or less are found.
REN Zhongqi; FEI Weiyang; Hans-Joerg Bart
2005-01-01
The Taylor dispersion method was used to measure diffusion coefficients of three-component liquid systems. An improved constrained nonlinear least-square method was used to evaluate the ternary diffusion coefficients directly by fitting the mathematical solutions of the dispersion equation to eluted solute peaks detected using a differential refractometer. Diffusion coefficients of the three-component system of acetone-benzene-CCl4, determined at 25℃, were used to test the procedure. The measured diffusion coefficients were compared with values obtained by optical interferometry and the diaphragm cell method. Ternary diffusion coefficients are also determinated for solutions of 1-hexanol-hexane-toluene and 1-propanol-water-ethylene glycol at 25℃, with an accuracy of approximately 0.05 m2·s-1.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
Radial point collocation method (RPCM) for solving convection-diffusion problems
LIU Xin
2006-01-01
In this paper, Radial point collocation method (RPCM), a kind ofmeshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the present method is very attractive in solving computational fluid problems.
Peppelenbos, H.W.; Jeksrud, W.K.
1998-01-01
To measure the relationship between gas exchange rates and diffusion resistance, and their changes in time, both should be measured on the same fruit or vegetable, because diffusion resistance shows large variations between individuals of the same species and cultivar. The method described enables
Zistler, M.; Wachter, P.; Gores, H.J. [Institut fuer Physikalische und Theoretische Chemie der Universitaet Regensburg, Regensburg (Germany); Wasserscheid, P.; Gerhard, D. [Institut fuer Chemische Reaktionstechnik, Friedrich-Alexander-Universitaet, Erlangen-Nuernberg (Germany); Hinsch, A. [Fraunhofer Institute for Solar Energy Systems ISE, Freiburg (Germany). Department of Materials Research and Applied Optics; Sastrawan, R. [Freiburg Materials Research Center, Freiburg (Germany)
2006-10-05
Results of diffusion coefficient measurements of triiodide in a mixture of two ionic liquids (1-methyl-3-propylimidazolium iodide and 1-butyl-3-methylimidazolium tetrafluoroborate) at 25{sup o}C are described in this paper. Four electrochemical methods for measuring diffusion coefficients of triiodide were evaluated for their reliability and performance, including impedance spectroscopy and polarization measurements at thin layer cells as well as cyclic voltammetry and chronoamperometry at microelectrodes of different radii. Viscosities of the blends were measured to investigate the transport behaviour of triiodide ions used in Gratzel-type dye-sensitized solar cells. (author)
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.
Na An
2016-01-01
Full Text Available We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences. The two-dimensional system is discretized by the local discontinuous Galerkin (LDG method on unstructured triangular meshes associated with the piecewise linear finite element spaces, which can derive not only numerical solutions but also approximations for fluxes at the same time comparing with most of study work up to now which has derived numerical solutions only. Considering the stability requirement for the explicit scheme with strict time step restriction (Δt=O(hmin2, the implicit integration factor (IIF method is employed for the temporal discretization so that the time step can be relaxed as Δt=O(hmin. Moreover, the method allows us to compute element by element and avoids solving a global system of nonlinear algebraic equations as the standard implicit schemes do, which can reduce the computational cost greatly. Numerical simulations about the system with exact solution and the Brusselator model, which is a theoretical model for a type of autocatalytic chemical reaction, are conducted to confirm the expected accuracy, efficiency, and advantages of the proposed schemes.
Ping Zhang
2016-01-01
Full Text Available Variational multiscale element free Galerkin (VMEFG method is applied to Burgers’ equation. It can be found that, for the very small diffusivity coefficients, VMEFG method still suffers from instability in the presence of boundary or interior layers. In order to overcome this problem, the high order low-pass filter is used to smooth the solution. Three test examples with very small diffusion are presented and the solutions obtained are compared with exact solutions and some other numerical methods. The numerical results are found in which the VMEFG coupled with low-pass filter works very well for Burgers’ equation with very small diffusivity coefficients.
Hellriegel, Christian; Kirstein, Johanna; Braeuchle, Christoph [Dept. Chemie und Biochemie and CeNS, Ludwig-Maximilians-Universitaet Muenchen Butenandtstr. 11, D-81377 Munich (Germany)
2005-01-01
The diffusion of individual fluorescent molecules can be observed by single-molecule tracking techniques and characterized by the analysis of their diffusional trajectory. Heterogeneities in the diffusivity that would pass undetected by conventional ensemble methods or fluorescence correlation spectroscopy are resolved by this method. This is demonstrated using four different examples in which we analyse the diffusion of single organic dye molecules in mesoporous materials. We show that this method can be used to obtain structural information from the inner structure of nanoporous materials with a resolution better than the optical diffraction limit.
Venter, J P; Müller, D G; du Plessis, J; Goosen, C
2001-05-01
In order to determine whether a drug shows the potential for percutaneous absorption, both in situ and in vitro studies are used. In vitro studies are good indicators of transdermal drug delivery, but the possibility exists that anatomical changes in excised skin can influence drug delivery. The aim of this study was to compare the in vitro Franz diffusion cell method with an in situ adapted diffusion cell method. A saturated aqueous solution of doxylamine succinate was used as model drug and the receptor phase was an isotonic Sörensen buffered solution. The in vitro permeation studies were conducted using vertical Franz diffusion cells with nude mice skin. For in situ studies, a diffusion cell was implanted under the dorsal skin of a nude mouse, simulating the in vitro method. Both in situ and in vitro experiments were conducted over a period of 12 h during which samples were collected every 90 min. The mean steady-state flux from Franz diffusion cells was 0.164+/-0.045 microg/cm2/h and flux determined by the in situ method was 0.113+/-0.034 microg/cm2/h. A statistical significant difference existed between the permeation results of the in vitro and in situ experimental methods. A subjective, semi-quantitative assessment of histological changes to excised nude mouse skin was done using light microscopy. This showed that excised skin undergoes sub-lethal injury (necrosis) during in vitro experiments, which may lead to increased permeability of the drug. It was noticed that in vitro and in situ permeation results showed very close correlation until approximately 4.5 h after commencement of experiments, after which, the permeation through excised skin increased. It was assumed that cell necrosis occurred to such an extent after approximately 4.5 h, that the barrier function of the stratum corneum decreased and permeation of the drug increased.
Marta C de Castillo
1998-07-01
Full Text Available At present, most Neisseria gonorrhoeae testing is done with ß-lactamase and agar dilution tests with common therapeutic agents. Generally, in bacteriological diagnosis laboratories in Argentina, study of antibiotic susceptibility of N.gonorrhoeae is based on ß-lactamase determination and agar dilution method with common therapeutic agents. The National Committee for Clinical Laboratory Standards (NCCLS has recently described a disk diffusion test that produces results comparable to the reference agar dilution method for antibiotic susceptibility of N.gonorrhoeae, using a dispersion diagram for analyzing the correlation between both techniques. We obtained 57 gonococcal isolates from patients attending a clinic for sexually transmitted diseases in Tucumán, Argentina. Antibiotic susceptibility tests using agar dilution and disk diffusion techniques were compared. The established NCCLS interpretive criteria for both susceptibility methods appeared to be applicable to domestic gonococcal strains. The correlation between the MIC's and the zones of inhibition was studied for penicillin, ampicillin, cefoxitin, spectinomycin, cefotaxime, cephaloridine, cephalexin, tetracycline, norfloxacin and kanamycin. Dispersion diagrams showed a high correlation between both methods.
A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations
Reboux, Sylvain; Schrader, Birte; Sbalzarini, Ivo F.
2012-05-01
We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.
A fast collocation method for a variable-coefficient nonlocal diffusion model
Wang, Che; Wang, Hong
2017-02-01
We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N3) required by a commonly used direct solver to O (Nlog N) per iteration and the memory requirement from O (N2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N2) to O (N). Numerical results are presented to show the utility of the fast method.
Pestiaux, A.; Kärnä, T.; Melchior, S.; Lambrechts, J.; Remacle, J. F.; Deleersnijder, E.; Fichefet, T.
2012-04-01
The discretization of the Gent-McWilliams velocity and isopycnal diffusion with a discontinuous Galerkin finite element method is presented. Both processes are implemented in an ocean model thanks to a tensor related to the mesoscale eddies. The antisymmetric part of this tensor is computed from the Gent-McWilliams velocity and is subsequently included in the tracer advection equation. This velocity can be constructed to be divergence-free. The symmetric part that describes the diapycnal and isopycnal diffusions requires a special treatment. A stable and physically sound isopycnal tracer diffusion scheme is needed. Here, an interior penalty method is chosen that enables to build stable diffusion terms. However, due to the strong anisotropy of the diffusion, the common-usual penalty factor by Ern et al. (2008) is not sufficient. A novel method for computing the penalty term of Ern is then proposed for diffusion equations when both the diffusivity and the mesh are strongly anisotropic. Two test cases are resorted to validate the methodology and two more realistic applications illustrate the diapycnal and isopycnal diffusions, as well as the Gent-McWilliams velocity.
Frassinetti, L.; Olofsson, K. E. J.; Fridström, R.; Setiadi, A. C.; Brunsell, P. R.; Volpe, F. A.; Drake, J.
2013-08-01
A new method for the estimate of the wall diffusion time of non-axisymmetric fields is developed. The method based on rotating external fields and on the measurement of the wall frequency response is developed and tested in EXTRAP T2R. The method allows the experimental estimate of the wall diffusion time for each Fourier harmonic and the estimate of the wall diffusion toroidal asymmetries. The method intrinsically considers the effects of three-dimensional structures and of the shell gaps. Far from the gaps, experimental results are in good agreement with the diffusion time estimated with a simple cylindrical model that assumes a homogeneous wall. The method is also applied with non-standard configurations of the coil array, in order to mimic tokamak-relevant settings with a partial wall coverage and active coils of large toroidal extent. The comparison with the full coverage results shows good agreement if the effects of the relevant sidebands are considered.
Improved Quasi-Static Method: IQS Method Implementation for CFEM Diffusion in Rattlesnake
Prince, Zachary M. [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Ragusa, Jean C. [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Wang, Yaqi [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
2016-02-29
The improved quasi-static (IQS) method is a transient spatial kinetics method that involves factorizing flux into space- and time-dependent components. These components include the flux’s power and shape. Power is time-dependent, while the shape is both space- and time-dependent. However, the impetus of the method is the assumption that the shape is only weakly dependent on time; therefore, the shape may not require computation at every time step, invoking the quasi-static nature. This paper describes the implementation and testing of IQS as an alternative kinetics solver within Rattlesnake to provide improved time performance with minimal reduction in accuracy.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
cAMP diffusion in Dictyostelium discoideum: A Green's function method
Calovi, Daniel S.; Brunnet, Leonardo G.; de Almeida, Rita M. C.
2010-07-01
A Green’s function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed.
The modeling method of diffusion of radio activated materials in clay waste disposals
Saberi, Reza; Sepanloo, Kamran [NSTRI, Tehran (Iran, Islamic Republic of); Alinejad, Majid [Engineering Research Institute of Natural Hazard, Isfahan (Iran, Islamic Republic of); Mozaffari, Ali [KNT Univ. of Technology, Tehran (Iran, Islamic Republic of)
2017-02-15
New nuclear power plants are necessary to meet today's and future challenges of energy supply. Nuclear power is the only large-scale energy source that takes full responsibility for all its wastes. Nuclear wastes are particularly hazardous and hard to manage relative to different toxic industrial wastes. Three methods are presented and analysed to model the diffusion of the waste from the waste disposal to the bottom surface. For this purpose three software programmes such as ABAQUS, Matlab coding, Geostudio and ArcGIS have been applied.
Liu, Cong; Kolarik, Barbara; Gunnarsen, Lars; Zhang, Yinping
2015-10-20
Polychlorinated biphenyls (PCBs) have been found to be persistent in the environment and possibly harmful. Many buildings are characterized with high PCB concentrations. Knowledge about partitioning between primary sources and building materials is critical for exposure assessment and practical remediation of PCB contamination. This study develops a C-depth method to determine diffusion coefficient (D) and partition coefficient (K), two key parameters governing the partitioning process. For concrete, a primary material studied here, relative standard deviations of results among five data sets are 5%-22% for K and 42-66% for D. Compared with existing methods, C-depth method overcomes the inability to obtain unique estimation for nonlinear regression and does not require assumed correlations for D and K among congeners. Comparison with a more sophisticated two-term approach implies significant uncertainty for D, and smaller uncertainty for K. However, considering uncertainties associated with sampling and chemical analysis, and impact of environmental factors, the results are acceptable for engineering applications. This was supported by good agreement between model prediction and measurement. Sensitivity analysis indicated that effective diffusion distance, contacting time of materials with primary sources, and depth of measured concentrations are critical for determining D, and PCB concentration in primary sources is critical for K.
Synthesis of metal-organic framework films by pore diffusion method
Murayama, Naohiro; Nishimura, Yuki; Kajiro, Hiroshi; Kishida, Satoru; Kinoshita, Kentaro; Tottori Univ Team; Nippon Steel; Sumitomo Metal Co. Collaboration; Tottori Integrated Frontier Resaerch Center (Tifrec) Collaboration; Tottori University Electronic Display Resaerch Center (Tedrec) Collaboration
Metal-organic frameworks (MOFs) presents high controllability in designing the nano-scale pore, and this enable molecular storages, catalysts, gas sensors, gas separation membranes, and electronic devices for next-generation. Therefore, a simple method for film synthesis of MOFs compared with conventional methods [1] is strongly required. In this paper, we provide pore diffusion method, in which a substrate containing constituent metals of MOF is inserted in solution that includes only linker molecules of MOF. As a result, 2D growth of MOF was effectively enhanced, and the formation of flat and dense MOF films was attained. The growth time, t, dependence of film thickness, d, can be expressed by the relation of d = Aln(t + 1) + B, where A and B are constants. It means that ionized coppers diffuse through the pores of MOFs and the synthesis reaction proceeds at the MOF/solvent interface. We demonstrated the fabrication of a HKUST-1/Cu-TPA hetero structure by synthesizing a Cu-TPA film continuously after the growth of a HKUST-1 film on the CuOx substrate.
Diffuse reflectance startigraphy - a new method in the study of loess (?)
József, Szeberényi; Balázs, Bradák; Klaudia, Kiss; József, Kovács; György, Varga; Réka, Balázs; Viczián, István
2017-04-01
The different varieties of loess (and intercalated paleosol layers) together constitute one of the most widespread terrestrial sediments, which was deposited, altered, and redeposited in the course of the changing climatic conditions of the Pleistocene. To reveal more information about Pleistocene climate cycles and/or environments the detailed lithostratigraphical subdivision and classification of the loess variations and paleosols are necessary. Beside the numerous method such as various field measurements, semi-quantitative tests and laboratory investigations, diffuse reflectance spectroscopy (DRS) is one of the well applied method on loess/paleosol sequences. Generally, DRS has been used to separate the detrital and pedogenic mineral component of the loess sections by the hematite/goethite ratio. DRS also has been applied as a joint method of various environmental magnetic investigations such as magnetic susceptibility- and isothermal remanent magnetization measurements. In our study the so-called "diffuse reflectance stratigraphy method" were developed. At First, complex mathematical method was applied to compare the results of the spectral reflectance measurements. One of the most preferred multivariate methods is cluster analysis. Its scope is to group and compare the loess variations and paleosol based on the similarity and common properties of their reflectance curves. In the Second, beside the basic subdivision of the profiles by the different reflectance curves of the layers, the most characteristic wavelength section of the reflectance curve was determined. This sections played the most important role during the classification of the different materials of the section. The reflectance value of individual samples, belonged to the characteristic wavelength were depicted in the function of depth and well correlated with other proxies like grain size distribution and magnetic susceptibility data. The results of the correlation showed the significance of the
A comparison between the fission matrix method, the diffusion model and the transport model
Dehaye, B.; Hugot, F. X.; Diop, C. M. [Commissariat a l' Energie Atomique et aux Energies Alternatives, Direction de l' Energie Nucleaire, Departement de Modelisation des Systemes et Structures, CEA DEN/DM2S, PC 57, F-91191 Gif-sur-Yvette cedex (France)
2013-07-01
The fission matrix method may be used to solve the critical eigenvalue problem in a Monte Carlo simulation. This method gives us access to the different eigenvalues and eigenvectors of the transport or fission operator. We propose to compare the results obtained via the fission matrix method with those of the diffusion model, and an approximated transport model. To do so, we choose to analyse the mono-kinetic and continuous energy cases for a Godiva-inspired critical sphere. The first five eigenvalues are computed with TRIPOLI-4{sup R} and compared to the theoretical ones. An extension of the notion of the extrapolation distance is proposed for the modes other than the fundamental one. (authors)
Fast Drift and Diffusion in a Class of Isochronous Systems with the Windows Method
Fortunati, Alessandro, E-mail: alessandro.fortunati@bristol.ac.uk [University of Bristol, School of Mathematics (United Kingdom)
2017-06-15
The aim of the paper is to deal with some peculiar difficulties arising from the use of the geometrical tool known as windows method in the context of the well known problem of Arnold’s diffusion for isochronous nearly-integrable Hamiltonian systems. Despite the simple features of the class of systems at hand, it is possible to show how the absence of an anisochrony term leads to several substantial differences in the application of the method, requiring some additional devices, such as non-equally spaced transition chains and variable windows. As a consequence, we show the existence of a set of unstable orbits, whose drifting time matches, up to a constant, the one obtained via variational methods.
A high-order discontinuous Galerkin method for unsteady advection-diffusion problems
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017-03-01
A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection-diffusion problems in the high Péclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential-algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Péclet number constant-coefficient model flow problems.
Nagy, Elisabeth; Justesen, Ulrik Stenz; Eitel, Zsuzsa
2015-01-01
-clavulanic acid, cefoxitin, clindamycin, imipenem, metronidazole, moxifloxacin, piperacillin/tazobactam, tigecycline by agar dilution method previously. The inhibition zones of the same antibiotics including meropenem disc were determined by the disc diffusion on Brucella blood agar supplemented with haemin...
D. Spivakovskaya
2007-12-01
Full Text Available Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000. The latter is best suited to the problems under consideration. It is then applied to two test cases with discontinuous diffusivity, highlighting the advantages of this method.
E. Deleersnijder
2007-07-01
Full Text Available Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000. The latter is best suited to the problems under consideration. It is then applied for two test cases with discontinuous diffusivity, highlighting the advantages of this method.
Makarenkov, A. M.; Seregina, E. V.; Stepovich, M. A.
2017-05-01
Using the diffusion equation as an example, results of applying the projection Galerkin method for solving time-independent heat and mass transfer equations in a semi-infinite domain are presented. The convergence of the residual corresponding to the approximate solution of the timeindependent diffusion equation obtained by the projection method using the modified Laguerre functions is proved. Computational results for a two-dimensional toy problem are presented.
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
A sparse representation based method to classify pulmonary patterns of diffuse lung diseases.
Zhao, Wei; Xu, Rui; Hirano, Yasushi; Tachibana, Rie; Kido, Shoji
2015-01-01
We applied and optimized the sparse representation (SR) approaches in the computer-aided diagnosis (CAD) to classify normal tissues and five kinds of diffuse lung disease (DLD) patterns: consolidation, ground-glass opacity, honeycombing, emphysema, and nodule. By using the K-SVD which is based on the singular value decomposition (SVD) and orthogonal matching pursuit (OMP), it can achieve a satisfied recognition rate, but too much time was spent in the experiment. To reduce the runtime of the method, the K-Means algorithm was substituted for the K-SVD, and the OMP was simplified by searching the desired atoms at one time (OMP1). We proposed three SR based methods for evaluation: SR1 (K-SVD+OMP), SR2 (K-Means+OMP), and SR3 (K-Means+OMP1). 1161 volumes of interest (VOIs) were used to optimize the parameters and train each method, and 1049 VOIs were adopted to evaluate the performances of the methods. The SR based methods were powerful to recognize the DLD patterns (SR1: 96.1%, SR2: 95.6%, SR3: 96.4%) and significantly better than the baseline methods. Furthermore, when the K-Means and OMP1 were applied, the runtime of the SR based methods can be reduced by 98.2% and 55.2%, respectively. Therefore, we thought that the method using the K-Means and OMP1 (SR3) was efficient for the CAD of the DLDs.
Blood species identification using Near-Infrared diffuse transmitted spectra and PLS-DA method
Zhang, Linna; Zhang, Shengzhao; Sun, Meixiu; Wang, Zhennan; Li, Hongxiao; Li, Yingxin; Li, Gang; Lin, Ling
2016-05-01
Blood species identification is of great significance for blood supervision and wildlife investigations. The current methods used to identify the blood species are destructive. Near-Infrared spectroscopy method is known for its non-invasive properties. In this research, we combined Near-Infrared diffuse transmitted spectra and Partial Least Square Discrimination Analysis (PLS-DA) to identify three blood species, including macaque, human and mouse. Blind test and external test were used to assess the PLS-DA model. The model performed 100% accuracy in its identification between three blood species. This approach does not require a specific knowledge of biochemical features for each individual class but relies on a spectroscopic statistical differentiation of the whole components. This is the first time to demonstrate Near-Infrared diffuse transmitted spectra have the ability to identify the species of origin of blood samples. The results also support a good potential of absorption and scattering spectroscopy for species identification in practical applications for real-time detection.
A Simple and Efficient Diffuse Interface Method for Compressible Two-Phase Flows
Ray A. Berry; Richard Saurel; Fabien Petitpas
2009-05-01
In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. For many reasons, to be discussed, there is growing interest in the application of two-phase flow models to provide diffuse, but nevertheless resolved, simulation of interfaces between two immiscible compressible fluids – diffuse interface method (DIM). Because of its ability to dynamically create interfaces and to solve interfaces separating pure media and mixtures for DNS-like (Direct Numerical Simulation) simulations of interfacial flows, we examine the construction of a simple, robust, fast, and accurate numerical formulation for the 5-equation Kapila et al. [1] reduced two-phase model. Though apparently simple, the Kapila et al. model contains a volume fraction differential transport equation containing a nonlinear, non-conservative term which poses serious computational challenges. To circumvent the difficulties encountered with the single velocity and single pressure Kapila et al. [1] multiphase flow model, a 6-equation relaxation hyperbolic model is built to solve interface problems with compressible fluids. In this approach, pressure non-equilibrium is first restored, followed by a relaxation to an asymptotic solution which is convergent to the solutions of the Kapila et al. reduced model. The apparent complexity introduced with this extended hyperbolic model actually leads to considerable simplifications regarding numerical resolution, and the various ingredients used by this method are general enough to consider future extensions to problems involving complex physics.
Sierakowski, Adam J.; Lukassen, Laura J.
2016-11-01
In the shear flow of non-Brownian particles, we describe the long-time diffusive processes stochastically using a Fokker-Planck equation. Previous work has indicated that a Fokker-Planck equation coupling the probability densities of position and velocity spaces may be appropriate for describing this phenomenon. The stochastic description, integrated over velocity space to obtain a reduced position-space Fokker-Planck equation, contains unknown space diffusion coefficients. In this work, we use the Physalis method for simulating disperse particle flows to verify the colored-noise velocity space model (an Ornstein-Uhlenbeck process) by comparing the simulated long-time diffusion rate with the diffusion rate proposed by the theory. We then use the simulated data to calculate the unknown space diffusion coefficients that appear in the reduced position-space Fokker-Planck equation and summarize the results. This study was partially supported by US NSF Grant CBET1335965.
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
Bodor, Sándor; Zook, Justin M; Lindner, Erno; Tóth, Klára; Gyurcsányi, Róbert E
2008-05-01
The diffusion coefficients of active components in ion-selective membranes have a decisive influence on the life-time and detection limit of the respective ion-selective electrodes, as well as influencing the rate of polarization and relaxation processes of electrically perturbed ion sensors. Therefore, the rational design of mass transport controlled ion-selective electrodes with sub-nanomolar detection limits requires reliable data on the diffusion coefficients. We have implemented electrochemical methods for the quantitative assessment of both the diffusion coefficients of free ionophores and ion-ionophore complexes. The diffusion coefficients of the pH-sensitive chromoionophore ETH 5294 and the calcium-selective ionophore ETH 5234 were determined in plasticized PVC membranes with different PVC to plasticizer ratios. The diffusion coefficient of the free chromoionophore determined by a chronoamperometric method was validated with optical methods for a variety of membrane compositions. The calcium-selective ionophore ETH 5234 was used as a model compound to assess the diffusion coefficient of the ion-ionophore complex calculated from the time required for the complexes to cross a freshly prepared membrane during potentiometric ion-breakthrough experiments. The difference between the diffusion coefficients of the free ionophore ETH 5234 and the ion-ionophore complex was found to be significant and correlated well with the geometry of the respective species.
Xie, Wenhao; Deng, Yong; Lian, Lichao; Yan, Dongmei; Yang, Xiaoquan; Luo, Qingming
2016-01-01
The functional information, the absorption and diffusion coefficients, as well as the structural information of biological tissues can be provided by the DOT(Diffuse Optical Tomograph)/MicroCT. In this paper, we use boundary element method to calculate the forward problem of DOT based on the structure prior given by the MicroCT, and then we reconstruct the absorption and diffusion coefficients of different biological tissues by the Levenberg-Marquardt algorithm. The method only needs surface meshing, reducing the complexity of calculation; in addition, it reconstructs a single value within an organ, which reduces the ill-posedness of the inverse problem to make reconstruction results have good noise stability. This indicates that the boundary element method-based reconstruction can serve as an new scheme for getting absorption and diffusion coefficients in DOT/MicroCT multimodality imaging.
MULTIGRID METHOD FOR A MODIFIED CURVATURE DRIVEN DIFFUSION MODEL FOR IMAGE INPAINTING
Carlos Brito-Loeza; Ke Chen
2008-01-01
Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation (TV) model [11] designed for local inpainting and its improved version for large scale inpainting: the Curvature-Driven Diffusion (CDD) model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear par-tial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immedi-ate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 (2005), pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the orig-inal CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.
2014-05-30
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Muhammad Abbas
Full Text Available In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Abbas, Muhammad; Majid, Ahmad Abd; Md Ismail, Ahmad Izani; Rashid, Abdur
2014-01-01
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Oka, Chiemi; Ushimaru, Kazunori; Horiishi, Nanao; Tsuge, Takeharu; Kitamoto, Yoshitaka
2016-02-01
The present paper describes optimization of preparation conditions of a core-shell composite particle, and its heat generation by alternating magnetic fields. The composite particles are prepared with a modified emulsion solvent diffusion method, which is combined with Pickering emulsion stabilized by magnetic nanoparticles. In this method, the magnetic nanoparticles act as an emulsifier, and its amount and size are crucial to morphology of the composite particles. The magnetic nanoparticles of 8-9 nm would be strongly adsorbed at a liquid-liquid interface rather than the larger nanoparticles. At the optimized concentration of the magnetic nanoparticle’s suspension for the preparation, small and uniform composite particles are obtained since the amount of the nanoparticles is enough to prevent coalescence of droplets during the formation of the composites. The heat generation by alternating magnetic fields emerged certainly. This result suggests the composite particles have a property as a heat-generating carrier for hyperthermia treatment.
Wang, Wei-Ming; Dong, Da-Ming; Zheng, Wen-Gang; Zhao, Xian-De; Jiao, Lei-Zi; Wang, Ming-Fei
2013-02-01
The content of sugar is an important quality index for pears. However, the traditional sugar measurement methods are time-consuming and destructive. In the present study, the authors measured the sugar content of pears using visible and near infrared diffuse reflection spectroscopy. The pretreatment methods of multiplicative scatter correction (MSC), baseline correction, standard normal variate (SNV) transformation, and moving average algorithms were used on the original absorbance spectrum. Results indicate that the absorbance spectra after pretreatment are better than the original absorbance spectra for prediction. Partial least squares (PLS) regression was also used on the original absorbance spectrum and the absorbance spectrum after moving average and baseline correction. It follows that the forecast accuracy of the absorbance spectra after moving average is higher than that of the original absorbance spectra. The models gave good predictions of the sugar content of pears, with corresponding r values of 0.990 8, and standard errors of predictions of 0.019 0.
Bucur, R.V.
1985-01-01
Influences of electrical parameters, surface roughness, controlled surface contamination and concentration of the electrolyte (NaOH- and H/sub 2/SO/sub 4/-solutions) upon the permeation rate of hydrogen through a palladium membrane (thickness: 5x10/sup -3/ cm) are reported. Diffusion measurements were carried out with an electrochemical permeation cell under transient conditions. The cathodic side of the membrane was subjected either to a constant hydrogen-concentration or hydrogen-flux, while the anodic side was permanently kept at negligibly low hydrogen-concentration. The diffusion coefficient was calculated from the charging and stripping current vs. time curves, by semi-log plots. Reliable and reproducible diffusion coefficient values were obtained both from the charging and stripping curves, under galvanostatic charging conditions. By contrast, reliable values were obtained only from the stripping curves, under potentiostatic charging conditions. Within the temperature range from 5 to 50/sup 0/C the following values have been calculated for hydrogen and deuterium: Dsub(H)/sup 0/=(2.48+-0.40)x10/sup -3/ cm/sup 2/s/sup -1/; Dsub(H)/sup 298/=3.8 . 10/sup -7/ cm/sup 2/s/sup -1/; Esub(H)=5210+-70 cal/mol; Dsub(D)/sup 0/=(1.67+-0.28)x10/sup -3/ cm/sup 2/s/sup -1/; Dsub(D)/sup 298/=4.8 . 10/sup -7/ cm/sup 2/s/sup -1/; Esub(D)=4830+-70 cal/mol. These values agree well with those obtained by non-electrolytical methods.
Convergence of methods for coupling of microscopic and mesoscopic reaction–diffusion simulations
Flegg, Mark B.
2015-05-01
© 2015 Elsevier Inc. In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a "ghost cell" in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step δ. t (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered:. (i)δt→0 and h is fixed;(ii)δt→0 and h→0 such that δt/h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model.
Testing the U-Th/4He dating method on carbonates I. Helium diffusion
Pinti, D. L.; Ghaleb, B. G.; Sano, Y.; Blanchette, S.; Mathouchanh, E.; Takahata, N.
2012-12-01
Corals and other carbonates, such as speleothems, are important climatic-change proxies which need to be precisely dated for paleoclimatic reconstructions. Yet, U-Th disequilibrium method is applicable up to ca. 500 ka old carbonates. Calcite is difficult to date precisely by U-Pb method because of the low U amounts often found and difficulties in correcting for the common lead. Radiogenic 4He produced by decay of 238U and 235U incorporated into carbonates is a potential chronometer of Quaternary, and possibly Tertiary, corals and speleothems. However, several limitations exist for this method, related to the few data on the He diffusion [1] and on the alpha recoil effect in carbonate minerals. We decided to measure 4He by step heating in carbonate samples dated previously by U-Th disequilibrium: a coral (Scleractinia) from Cape Verde dated at 125 ka; a stalagmite from Patagonia dated at 128 ka; and two hydrothermal travertines from the Ziz Valley in Morocco with ages ≥ 500 ka. A one cm3 of each sample was cut by saw, crushed, washed and sieved to 80-100μm and 100-125μm fractions. Crushed samples (0.5 to 1 gram) were loaded in a vacuum crucible and 4He extracted by step heating. Previous step heating experiments on a sub-Arctic flowstone suggested that 4He is mainly released between 400 and 600°C [2]. However, the first coral sample heated at 100°C steps, showed a release pattern profile with 4He mainly released between 200 and 400°C. Measured 4He amount of 2.05 x 10-8 (±0.03% 1σ) ccSTP/g and U content of 2.7 ppm yield a U-4He age of 62.5 ka, lower than that obtained by U-Th disequilibrium. Data were not precise enough to calculate diffusion parameters using the Arrhenius diagram. The second step-heating pyrolysis of the coral using 50°C-steps indicated that all 4He is released between 250 and 350°C. The measured 4He amount was 2.27 x 10-8 (±0.04% 1σ) ccSTP/g, yielding an age of 83 ka, again lower compared to that obtained by U-Th disequilibrium. The
Jackson, Bob; Silgram, Martyn; Quinton, John
2010-05-01
Recent UK government-funded research has shown that compacted, unvegetated tramlines wheelings can represent an important source and transport pathway, which can account for 80% of surface runoff, sediment and phosphorus losses to edge-of-field from cereals on moderate slopes. For example, recent research found 5.5-15.8% of rainfall lost as runoff, and losses of 0.8-2.9 kg TP/ha and 0.3-4.8 T/ha sediment from tramline wheelings. When compaction was released by shallow cultivation, runoff was reduced to 0.2-1.7% of rainfall with losses of 0.0-0.2 kg TP/ha and 0.003-0.3 T/ha sediment respectively i.e. close to reference losses from control areas without tramlines. Recent independent assessments using novel tracer techniques have also shown that tramline wheelings can represent important sediment sources at river catchment scale. In response to these latest findings, a new project is now underway investigating the most cost-effective and practical ways of operationalising methods for managing tramline wheelings in autumn-sown cereal systems to reduce the risk of soil compaction from the autumn spray operation and the associated risk of surface runoff and diffuse pollution loss of sediment, phosphorus and nitrogen to edge of field. Research is focusing on the over-winter period when soils are close to field capacity and the physical protection of the soil surface granted by growing crop is limited. This paper outlines this new multi-disciplinary project and associated methodologies, which include hillslope-scale event-based evaluations of the effectiveness of novel mitigation methods on surface runoff and diffuse pollution losses to edge of field, assessments of the economic and practical viability of mitigation methods, and modelling the impact on water quality of implementation of the most promising techniques at both farm and catchment scale. The study involves a large consortium with 20 partners, including many industrial organisations representing tractor, crop
Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions
Hu, Zexi; Huang, Juntao; Yong, Wen-An
2016-04-01
In this work, we propose an interfacial scheme accompanying the lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, including conjugate conditions with or without jumps in heat and mass transfer, continuity of macroscopic variables and normal fluxes in ion diffusion in porous media with different porosity, and the Kapitza resistance in heat transfer. The construction of this scheme is based on our boundary schemes [Huang and Yong, J. Comput. Phys. 300, 70 (2015), 10.1016/j.jcp.2015.07.045] for Robin boundary conditions on straight or curved boundaries. It gives second-order accuracy for straight interfaces and first-order accuracy for curved ones. In addition, the new scheme inherits the advantage of the boundary schemes in which only the current lattice nodes are involved. Such an interfacial scheme is highly desirable for problems with complex geometries or in porous media. The interfacial scheme is numerically validated with several examples. The results show the utility of the constructed scheme and very well support our theoretical predications.
Rejmstad, Peter; Johansson, Johannes D; Haj-Hosseini, Neda; Wårdell, Karin
2017-03-01
Continuous measurement of local brain oxygen saturation (SO2 ) can be used to monitor the status of brain trauma patients in the neurocritical care unit. Currently, micro-oxygen-electrodes are considered as the "gold standard" in measuring cerebral oxygen pressure (pO2 ), which is closely related to SO2 through the oxygen dissociation curve (ODC) of hemoglobin, but with the drawback of slow in response time. The present study suggests estimation of SO2 in brain tissue using diffuse reflectance spectroscopy (DRS) for finding an analytical relation between measured spectra and the SO2 for different blood concentrations. The P3 diffusion approximation is used to generate a set of spectra simulating brain tissue for various levels of blood concentrations in order to estimate SO2 . The algorithm is evaluated on optical phantoms mimicking white brain matter (blood volume of 0.5-2%) where pO2 and temperature is controlled and on clinical data collected during brain surgery. The suggested method is capable of estimating the blood fraction and oxygen saturation changes from the spectroscopic signal and the hemoglobin absorption profile.
Impact of post-processing methods on apparent diffusion coefficient values.
Zeilinger, Martin Georg; Lell, Michael; Baltzer, Pascal Andreas Thomas; Dörfler, Arnd; Uder, Michael; Dietzel, Matthias
2017-03-01
The apparent diffusion coefficient (ADC) is increasingly used as a quantitative biomarker in oncological imaging. ADC calculation is based on raw diffusion-weighted imaging (DWI) data, and multiple post-processing methods (PPMs) have been proposed for this purpose. We investigated whether PPM has an impact on final ADC values. Sixty-five lesions scanned with a standardized whole-body DWI-protocol at 3 T served as input data (EPI-DWI, b-values: 50, 400 and 800 s/mm(2)). Using exactly the same ROI coordinates, four different PPM (ADC_1-ADC_4) were executed to calculate corresponding ADC values, given as [10(-3) mm(2)/s] of each lesion. Statistical analysis was performed to intra-individually compare ADC values stratified by PPM (Wilcoxon signed-rank tests: α = 1 %; descriptive statistics; relative difference/∆; coefficient of variation/CV). Stratified by PPM, mean ADCs ranged from 1.136-1.206 *10(-3) mm(2)/s (∆ = 7.0 %). Variances between PPM were pronounced in the upper range of ADC values (maximum: 2.540-2.763 10(-3) mm(2)/s, ∆ = 8 %). Pairwise comparisons identified significant differences between all PPM (P ≤ 0.003; mean CV = 7.2 %) and reached 0.137 *10(-3) mm(2)/s within the 25th-75th percentile. Altering the PPM had a significant impact on the ADC value. This should be considered if ADC values from different post-processing methods are compared in patient studies. • Post-processing methods significantly influenced ADC values. • The mean coefficient of ADC variation due to PPM was 7.2 %. • To achieve reproducible ADC values, standardization of post-processing is recommended.
R Dinarvand
2008-09-01
Full Text Available Background: The inherent shortcomings of conventional drug delivery systems containing estrogens and the potential of nanoparticles (NPs have offered tremendous scope for investigation. Although polymeric NPs have been used as drug carriers for many active agents, the use of appropriate polymer and method of NP preparation to overcome different challenges is very important. Materials and methods: Poly lactide-co-glycolide (PLGA NPs containing estradiol valerate were prepared by the modified spontaneous emulsification solvent diffusion method. Several parameters including the drug/polymer ratios in range of 2.5-10%, poly vinyl alcohol (PVA in concentration of 0-4% as stabilizer and internal phase volume and composition were examined to optimize formulation. The size distribution and morphology of the NPs, encapsulation efficacy and in vitro release profile in phosphate buffer medium (pH 7.4 during 12 hrs were then investigated. Results: The NPs prepared in this study were spherical with a relatively mono-dispersed size distribution. By adjustment of the process parameters, the size and the drug encapsulation efficacy as well as the drug release kinetics can be optimally controlled. The mean particle size of the best formula with encapsulation efficiency of 100% was 175 ± 19, in which release profile was best fitted to Higuchi's model of release which showed that release mechanism was mainly controlled by diffusion of the drug to the release medium. Conclusion: According to the size and surface properties of the prepared particles, it may be concluded that they are a good formulation for non-parenteral routes of administration.
Johannesson, Björn
2010-01-01
There exist, mainly, two different continuum approaches to calculate transient multi species ionic diffusion. One of them is based on explicitly assuming a zero current in the diffusing mixture together with an introduction of a streaming electrical potential in the constitutive equations...... are compared with existing results from the solutions of the Gauss’ law method. For the studied case the calculated concentrations of the ionic species, using the two different methods, differed very little....
Jie－MinZHAN; Yao－SongCHEN
1996-01-01
An operator splitting method combining finite difference method and finite element method is proposed in this paper by using boundary-fitted coordinate system.The governing equation is split into advection and diffusion equations and solved by finit difference method using boundary-fitted coordinate system and finite element method respectively.An example for which analytic solution is available is used to verified the proposed methods and the agreement is very good.Numerical results show that it is very efficient.
Solution verification, goal-oriented adaptive methods for stochastic advection–diffusion problems
Almeida, Regina C.
2010-08-01
A goal-oriented analysis of linear, stochastic advection-diffusion models is presented which provides both a method for solution verification as well as a basis for improving results through adaptation of both the mesh and the way random variables are approximated. A class of model problems with random coefficients and source terms is cast in a variational setting. Specific quantities of interest are specified which are also random variables. A stochastic adjoint problem associated with the quantities of interest is formulated and a posteriori error estimates are derived. These are used to guide an adaptive algorithm which adjusts the sparse probabilistic grid so as to control the approximation error. Numerical examples are given to demonstrate the methodology for a specific model problem. © 2010 Elsevier B.V.
Method of measuring blood oxygenation based on spectroscopy of diffusely scattered light
Kleshnin, M. S.; Orlova, A. G.; Kirillin, M. Yu.; Golubyatnikov, G. Yu.; Turchin, I. V.
2017-05-01
A new approach to the measurement of blood oxygenation is developed and implemented, based on an original two-step algorithm reconstructing the relative concentration of biological chromophores (haemoglobin, water, lipids) from the measured spectra of diffusely scattered light at different distances from the radiation source. The numerical experiments and approbation of the proposed approach using a biological phantom have shown the high accuracy of the reconstruction of optical properties of the object in question, as well as the possibility of correct calculation of the haemoglobin oxygenation in the presence of additive noises without calibration of the measuring device. The results of the experimental studies in animals agree with the previously published results obtained by other research groups and demonstrate the possibility of applying the developed method to the monitoring of blood oxygenation in tumour tissues.
Akash Yadav
2010-01-01
Full Text Available Microballoons floatable on JPXIII No.1 solution were developed as a dosage form capable of floating in the stomach. Microballoons were prepared by the emulsion solvent diffusion method using enteric acrylic and other polymers with drug in a mixture of dichloromethane and ethanol. It was found that preparation temperature determined the formation of cavity inside the microsphere and the surface smoothness, determining the floatability and the drug release rate of the microballoons. The correlation between the buoyancy of microballoons and their physical properties, e.g. apparent density and roundness of microballoons were elucidated. The drug loading efficiency of microballoons was also determined. The optimum loading amount of metformin in the microballoons was found to impart ideal floatable properties to the microballoons. By fitting the data into zero order, first order and Highuchi model it was concluded that the release followed zero order release.
Yadav, Akash; Jain, Dinesh Kumar
2010-01-01
Microballoons floatable on JPXIII No.1 solution were developed as a dosage form capable of floating in the stomach. Microballoons were prepared by the emulsion solvent diffusion method using enteric acrylic and other polymers with drug in a mixture of dichloromethane and ethanol. It was found that preparation temperature determined the formation of cavity inside the microsphere and the surface smoothness, determining the floatability and the drug release rate of the microballoons. The correlation between the buoyancy of microballoons and their physical properties, e.g. apparent density and roundness of microballoons were elucidated. The drug loading efficiency of microballoons was also determined. The optimum loading amount of metformin in the microballoons was found to impart ideal floatable properties to the microballoons. By fitting the data into zero order, first order and Highuchi model it was concluded that the release followed zero order release.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
Veronese, S.V.; Othmer, H.G. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.
Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media
XU You-Sheng; ZHONG Yi-Jun; HUANG Guo-Xiang
2004-01-01
Based on the lattice Boltzmann method and general theory of fluids flowing in porous media, a numerical model is presented for the diffusion-reaction-transport (DRT) processes in porous media. As a test, we simulate a DRT process in a two-dimensional horizontal heterogeneous porous medium. The influence of gravitation in this case can be neglected, and the DRT process can be described by a strongly heterogeneous diagnostic test strip or a thin confined piece of soil with stochastically distributing property in horizontal directions. The results obtained for the relations between reduced fluid saturation S, concentration c1, and concentration c2 are shown by using the visualization computing technique. The computational efficiency and stability of the model are satisfactory.
Impact of post-processing methods on apparent diffusion coefficient values
Zeilinger, Martin Georg; Lell, Michael; Uder, Michael [University of Erlangen-Nuremberg, Institute of Diagnostic Radiology, Erlangen (Germany); Baltzer, Pascal Andreas Thomas [Medical University Vienna, Department of Radiology and Nuclear Medicine, Vienna (Austria); Doerfler, Arnd; Dietzel, Matthias [University of Erlangen-Nuremberg, Department of Neuroradiology, Erlangen (Germany)
2017-03-15
The apparent diffusion coefficient (ADC) is increasingly used as a quantitative biomarker in oncological imaging. ADC calculation is based on raw diffusion-weighted imaging (DWI) data, and multiple post-processing methods (PPMs) have been proposed for this purpose. We investigated whether PPM has an impact on final ADC values. Sixty-five lesions scanned with a standardized whole-body DWI-protocol at 3 T served as input data (EPI-DWI, b-values: 50, 400 and 800 s/mm{sup 2}). Using exactly the same ROI coordinates, four different PPM (ADC{sub 1}-ADC{sub 4}) were executed to calculate corresponding ADC values, given as [10{sup -3} mm{sup 2}/s] of each lesion. Statistical analysis was performed to intra-individually compare ADC values stratified by PPM (Wilcoxon signed-rank tests: α = 1 %; descriptive statistics; relative difference/∇; coefficient of variation/CV). Stratified by PPM, mean ADCs ranged from 1.136-1.206 *10{sup -3} mm{sup 2}/s (∇ = 7.0 %). Variances between PPM were pronounced in the upper range of ADC values (maximum: 2.540-2.763 10{sup -3} mm{sup 2}/s, ∇ = 8 %). Pairwise comparisons identified significant differences between all PPM (P ≤ 0.003; mean CV = 7.2 %) and reached 0.137 *10{sup -3} mm{sup 2}/s within the 25th-75th percentile. Altering the PPM had a significant impact on the ADC value. This should be considered if ADC values from different post-processing methods are compared in patient studies. (orig.)
A method of precise profile analysis of diffuse scattering for the KENS pulsed neutrons
Todate, Y. [Department of Physics, Ochanomizu Univ., Tokyo (Japan); Fukumura, T. [Department of Applied Physics, Hokkaido Univ., Sapporo, Hokkaido (Japan); Fukazawa, H. [High Energy Accelerator Research Organization, Tsukuba, Ibaraki (Japan)
2001-03-01
An outline of our profile analysis method, which is now of practical use for the asymmetric KENS pulsed thermal neutrons, are presented. The analysis of the diffuse scattering from a single crystal of D{sub 2}O is shown as an example. The pulse shape function is based on the Ikeda-Carpenter function adjusted for the KENS neutron pulses. The convoluted intensity is calculated by a Monte-Carlo method and the precision of the calculation is controlled. Fitting parameters in the model cross section can be determined by the built-in nonlinear least square fitting procedure. Because this method is the natural extension of the procedure conventionally used for the triple-axis data, it is easy to apply with generality and versatility. Most importantly, furthermore, this method has capability of precise correction of the time shift of the observed peak position which is inevitably caused in the case of highly asymmetric pulses and broad scattering function. It will be pointed out that the accurate determination of true time-of-flight is important especially in the single crystal inelastic experiments. (author)
Roskop, Luke; Fedorov, Dmitri G.; Gordon, Mark S.
2013-07-01
The fragment molecular orbital (FMO) method is used to model truncated portions of mesoporous silica nanoparticle (MSN) pores. The application of the FMO/RHF (restricted Hartree-Fock) method to MCM-41 type MSNs is discussed and an error analysis is given. The FMO/RHF method is shown to reliably approximate the RHF energy (error ∼0.2 kcal/mol), dipole moment (error ∼0.2 debye) and energy gradient (root mean square [RMS] error ∼0.2 × 10-3 a.u./bohr). Several FMO fragmentation schemes are employed to provide guidance for future applications to MSN models. An MSN pore model is functionalised with (phenyl)propyl substituents and the diffusion barrier for benzene passing through the pore is computed by the FMO/RHF-D method with the Grimme dispersion correction (RHF-D). For the reaction coordinates examined here, the maximum FMO/RHF-D interaction energies range from -0.3 to -5.8 kcal/mol.
Tian, Xin; Li, Hua; Jiang, Xiaoyu; Xie, Jingping; Gore, John C.; Xu, Junzhong
2017-02-01
Two diffusion-based approaches, CG (constant gradient) and FEXI (filtered exchange imaging) methods, have been previously proposed for measuring transcytolemmal water exchange rate constant kin, but their accuracy and feasibility have not been comprehensively evaluated and compared. In this work, both computer simulations and cell experiments in vitro were performed to evaluate these two methods. Simulations were done with different cell diameters (5, 10, 20 μm), a broad range of kin values (0.02-30 s-1) and different SNR's, and simulated kin's were directly compared with the ground truth values. Human leukemia K562 cells were cultured and treated with saponin to selectively change cell transmembrane permeability. The agreement between measured kin's of both methods was also evaluated. The results suggest that, without noise, the CG method provides reasonably accurate estimation of kin especially when it is smaller than 10 s-1, which is in the typical physiological range of many biological tissues. However, although the FEXI method overestimates kin even with corrections for the effects of extracellular water fraction, it provides reasonable estimates with practical SNR's and more importantly, the fitted apparent exchange rate AXR showed approximately linear dependence on the ground truth kin. In conclusion, either CG or FEXI method provides a sensitive means to characterize the variations in transcytolemmal water exchange rate constant kin, although the accuracy and specificity is usually compromised. The non-imaging CG method provides more accurate estimation of kin, but limited to large volume-of-interest. Although the accuracy of FEXI is compromised with extracellular volume fraction, it is capable of spatially mapping kin in practice.
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
Potemki, Valeri G. [Moscow State Engineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Automatics and Electronics; Borisevich, Valentine D.; Yupatov, Sergei V. [Moscow State Enineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Technical Physics
1996-12-31
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner`s basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker`s form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author) 7 refs., 10 figs.
Baker, K. L.; Curtin, W. A.
2016-07-01
In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the extended defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.
A reaction-diffusion model of the Darien Gap Sterile Insect Release Method
Alford, John G.
2015-05-01
The Sterile Insect Release Method (SIRM) is used as a biological control for invasive insect species. SIRM involves introducing large quantities of sterilized male insects into a wild population of invading insects. A fertile/sterile mating produces offspring that are not viable and the wild insect population will eventually be eradicated. A U.S. government program maintains a permanent sterile fly barrier zone in the Darien Gap between Panama and Columbia to control the screwworm fly (Cochliomyia Hominivorax), an insect that feeds off of living tissue in mammals and has devastating effects on livestock. This barrier zone is maintained by regular releases of massive quantities of sterilized male screwworm flies from aircraft. We analyze a reaction-diffusion model of the Darien Gap barrier zone. Simulations of the model equations yield two types of spatially inhomogeneous steady-state solutions representing a sterile fly barrier that does not prevent invasion and a barrier that does prevent invasion. We investigate steady-state solutions using both phase plane methods and monotone iteration methods and describe how barrier width and the sterile fly release rate affects steady-state behavior.
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
Flegga, Mark B.; Hellander, Stefan; Erban, Radek
2015-01-01
In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a “ghost cell” in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step Δt (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: (i) Δt → 0 and h is fixed; (ii) Δt → 0 and h → 0 such that √Δt/h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model. PMID:26568640
Ahmed Nawaz Khan
2016-01-01
Full Text Available Objective: The aim of present study was to establish near infrared-chemometric methods that could be effectively used for quality profiling through identification and quantification of amoxicillin (AMOX in formulated capsule which were similar to commercial products. In order to evaluate a large number of market products easily and quickly, these methods were modeled. Materials and Methods: Thermo Scientific Antaris II near infrared analyzer with TQ Analyst Chemometric Software were used for the development and validation of the identification and quantification models. Several AMOX formulations were composed with four excipients microcrystalline cellulose, magnesium stearate, croscarmellose sodium and colloidal silicon dioxide. Development includes quadratic mixture formulation design, near infrared spectrum acquisition, spectral pretreatment and outlier detection. According to prescribed guidelines by International Conference on Harmonization (ICH and European Medicine Agency (EMA developed methods were validated in terms of specificity, accuracy, precision, linearity, and robustness. Results: On diffuse reflectance mode, an identification model based on discriminant analysis was successfully processed with 76 formulations; and same samples were also used for quantitative analysis using partial least square algorithm with four latent variables and 0.9937 correlation of coefficient followed by 2.17% root mean square error of calibration (RMSEC, 2.38% root mean square error of prediction (RMSEP, 2.43% root mean square error of cross-validation (RMSECV. Conclusion: Proposed model established a good relationship between the spectral information and AMOX identity as well as content. Resulted values show the performance of the proposed models which offers alternate choice for AMOX capsule evaluation, relative to that of well-established high-performance liquid chromatography method. Ultimately three commercial products were successfully evaluated
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
Danilo ePezo
2014-11-01
Full Text Available To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie’s method for Markov Chains (MC simulation is highly accurate, yet it becomes computationally intensive in the regime of high channel numbers. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA. Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties – such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Dangerfield et al., 2012; Linaro et al., 2011; Huang et al., 2013a; Orio and Soudry, 2012; Schmandt and Galán, 2012; Goldwyn et al., 2011; Güler, 2013, comparing all of them in a set of numerical simulations that asses numerical accuracy and computational efficiency on three different models: the original Hodgkin and Huxley model, a model with faster sodium channels, and a multi-compartmental model inspired in granular cells. We conclude that for low channel numbers (usually below 1000 per simulated compartment one should use MC – which is both the most accurate and fastest method. For higher channel numbers, we recommend using the method by Orio and Soudry (2012, possibly combined with the method by Schmandt and Galán (2012 for increased speed and slightly reduced accuracy. Consequently, MC modelling may be the best method for detailed multicompartment neuron models – in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
Pezo, Danilo; Soudry, Daniel; Orio, Patricio
2014-01-01
To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties—such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC—which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models—in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels. PMID:25404914
Accelerated stochastic and hybrid methods for spatial simulations of reaction-diffusion systems
Rossinelli, D; Bayati, B; Koumoutsakos, P.
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial т-Leaping (Sт -Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid т-Leaping (Hт-Leaping), combining a deterministic diffusion approximation with a т-Leaping acceleration of the stochastic reactions. The algorithms are v...
Zhong, Xinxin; Zhao, Yi; Cao, Jianshu
2014-04-01
The time-dependent wavepacket diffusion method for carrier quantum dynamics (Zhong and Zhao 2013 J. Chem. Phys. 138 014111), a truncated version of the stochastic Schrödinger equation/wavefunction approach that approximately satisfies the detailed balance principle and scales well with the size of the system, is applied to investigate the carrier transport in one-dimensional systems including both the static and dynamic disorders on site energies. The predicted diffusion coefficients with respect to temperature successfully bridge from band-like to hopping-type transport. As demonstrated in paper I (Moix et al 2013 New J. Phys. 15 085010), the static disorder tends to localize the carrier, whereas the dynamic disorder induces carrier dynamics. For the weak dynamic disorder, the diffusion coefficients are temperature-independent (band-like property) at low temperatures, which is consistent with the prediction from the Redfield equation, and a linear dependence of the coefficient on temperature (hopping-type property) only appears at high temperatures. In the intermediate regime of dynamic disorder, the transition from band-like to hopping-type transport can be easily observed at relatively low temperatures as the static disorder increases. When the dynamic disorder becomes strong, the carrier motion can follow the hopping-type mechanism even without static disorder. Furthermore, it is found that the memory time of dynamic disorder is an important factor in controlling the transition from the band-like to hopping-type motions.
Gaspari, Roberto; Rapallo, Arnaldo
2008-06-28
In this work a new method is proposed for the choice of basis functions in diffusion theory (DT) calculations. This method, named hybrid basis approach (HBA), combines the two previously adopted long time sorting procedure (LTSP) and maximum correlation approximation (MCA) techniques; the first emphasizing contributions from the long time dynamics, the latter being based on the local correlations along the chain. In order to fulfill this task, the HBA procedure employs a first order basis set corresponding to a high order MCA one and generates upper order approximations according to LTSP. A test of the method is made first on a melt of cis-1,4-polyisoprene decamers where HBA and LTSP are compared in terms of efficiency. Both convergence properties and numerical stability are improved by the use of the HBA basis set whose performance is evaluated on local dynamics, by computing the correlation times of selected bond vectors along the chain, and on global ones, through the eigenvalues of the diffusion operator L. Further use of the DT with a HBA basis set has been made on a 71-mer of syndiotactic trans-1,2-polypentadiene in toluene solution, whose dynamical properties have been computed with a high order calculation and compared to the "numerical experiment" provided by the molecular dynamics (MD) simulation in explicit solvent. The necessary equilibrium averages have been obtained by a vacuum trajectory of the chain where solvent effects on conformational properties have been reproduced with a proper screening of the nonbonded interactions, corresponding to a definite value of the mean radius of gyration of the polymer in vacuum. Results show a very good agreement between DT calculations and the MD numerical experiment. This suggests a further use of DT methods with the necessary input quantities obtained by the only knowledge of some experimental values, i.e., the mean radius of gyration of the chain and the viscosity of the solution, and by a suitable vacuum
Zhang, Yun; Cai, Chen; Pang, Shu-Feng; Reid, Jonathan P; Zhang, Yun-Hong
2017-09-25
We report a new method to investigate water transport kinetics in aerosol particles by using rapid scan FTIR spectroscopy combined with a custom-built pulse relative humidity (RH) control system. From real time in situ measurements of RH and composition using high time resolution infrared spectroscopy (0.12 s for one spectrum), and through achieving a high rate of RH change (as fast as 60% per second), we are able to investigate the competition between the gas and condensed phase diffusive transport limits of water for particles with mean diameter ∼3 μm and varying phase and viscosity. The characteristic time (τ) for equilibration in particle composition following a step change in RH is measured to quantify dissolution timescales for crystalline particles and to probe the kinetics of water evaporation and condensation in amorphous particles. We show that the dissolution kinetics are prompt for crystalline inorganic salt particles following an increase in RH from below to above the deliquescence RH, occurring on a timescale comparable to the timescale of the RH change (particles, we show that the timescales for both the drying and condensation processes can be delayed by many orders of magnitude, depending on the viscosity of the particles in the range 10(1) to 10(9) Pa s considered here. For amorphous particles, these kinetics are shown to be consistent with previous measurements of mass transfer rates in larger single particles. More specifically, the consistency suggests that fully understanding and modelling the complex microphysical processes and heterogeneities that form in viscous particles may not be necessary for estimating timescales for particle equilibration. A comparison of the kinetics for crystalline and amorphous particles illustrates the interplay of the rates of gas and condensed phase diffusion in determining the mass transport rates of water in aerosols.
Shahnam Javadi
2013-07-01
Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.
Boyanova, Lyudmila; Ilieva, Juliana; Gergova, Galina; Mitov, Ivan
2016-01-01
We compared levofloxacin (1 μg/disk) disk diffusion method to E test against 212 Helicobacter pylori strains. Using diameter breakpoints for susceptibility (≥15 mm) and resistance (≤9 mm), very major error, major error rate, and categoric agreement were 0.0%, 0.6%, and 93.9%, respectively. The method may be useful in low-resource laboratories.
Stephansen, A.F
2007-12-15
In this thesis we analyse a discontinuous Galerkin (DG) method and two computable a posteriori error estimators for the linear and stationary advection-diffusion-reaction equation with heterogeneous diffusion. The DG method considered, the SWIP method, is a variation of the Symmetric Interior Penalty Galerkin method. The difference is that the SWIP method uses weighted averages with weights that depend on the diffusion. The a priori analysis shows optimal convergence with respect to mesh-size and robustness with respect to heterogeneous diffusion, which is confirmed by numerical tests. Both a posteriori error estimators are of the residual type and control the energy (semi-)norm of the error. Local lower bounds are obtained showing that almost all indicators are independent of heterogeneities. The exception is for the non-conforming part of the error, which has been evaluated using the Oswald interpolator. The second error estimator is sharper in its estimate with respect to the first one, but it is slightly more costly. This estimator is based on the construction of an H(div)-conforming Raviart-Thomas-Nedelec flux using the conservativeness of DG methods. Numerical results show that both estimators can be used for mesh-adaptation. (author)
Agglomeration of Celecoxib by Quasi Emulsion Solvent Diffusion Method: Effect of Stabilizer
Maryam Maghsoodi
2016-12-01
Full Text Available Purpose: The quasi-emulsion solvent diffusion (QESD has evolved into an effective technique to manufacture agglomerates of API crystals. Although, the proposed technique showed benefits, such as cost effectiveness, that is considerably sensitive to the choice of a stabilizer, which agonizes from a absence of systemic understanding in this field. In the present study, the combination of different solvents and stabilizers were compared to investigate any connections between the solvents and stabilizers. Methods: Agglomerates of celecoxib were prepared by QESD method using four different stabilizers (Tween 80, HPMC, PVP and SLS and three different solvents (methyl acetate, ethyl acetate and isopropyl acetate. The solid state of obtained particles was investigated by differential scanning calorimetry (DSC and Fourier transform infrared (FT-IR spectroscopy. The agglomerated were also evaluated in term of production yield, distribution of particles and dissolution behavior. Results: The results showed that the effectiveness of stabilizer in terms of particle size and particle size distribution is specific to each solvent candidate. A stabilizer with a lower HLB value is preferred which actually increased its effectiveness with the solvent candidates with higher lipophilicity. HPMC appeared to be the most versatile stabilizer because it showed a better stabilizing effect compared to other stabilizers in all solvents used. Conclusion: This study demonstrated that the efficiency of stabilizers in forming the celecoxib agglomerates by QESD was influenced by the HLB of the stabilizer and lipophilicity of the solvents.
张立国; 欧阳霄雯; 倪力军; 史万忠
2014-01-01
Microcapsules of volatile oil containing Herba Schizonepetae (VOHS) were prepared by emulsion solvent diffusion method to improve the drug loading and reduce the amount of pharmaceutical excipients. Orthogonal assay was applied to optimize the preparation condition of microcapsulation, and the results illustrated that the ratio of ethyl cellulose (EC) to VOHS influenced the property of VOHS microcapsule significantly. GC-MS analysis indicated that some volatile components with low concentration in VOHS were lost after microencapsulation. The microcapsules prepared with optimum condition had good fluidity, and the holes on the surface of the microcapsules contributed to the release of VOHS. The particles of the microcapsule conformed to a normal distribution with the diameter of 45-220 µm. In the simulated intestinal fluid containing 0.2% sodium dodecyl sulfate, pulegone in VOHS microcapsule showed a certain degree of slow release. Compared withβ-cyclodextrin method, the microencapsulation used in the present work could reduce the amount of excipients and increase the drug loading. It was beneficial to reduce the dose of Chinese medicines containing volatile oils.
Xu, Jing; Wu, Jian; Feng, Daming; Cui, Zhiming
Serious types of vascular diseases such as carotid stenosis, aneurysm and vascular malformation may lead to brain stroke, which are the third leading cause of death and the number one cause of disability. In the clinical practice of diagnosis and treatment of cerebral vascular diseases, how to do effective detection and description of the vascular structure of two-dimensional angiography sequence image that is blood vessel skeleton extraction has been a difficult study for a long time. This paper mainly discussed two-dimensional image of blood vessel skeleton extraction based on the level set method, first do the preprocessing to the DSA image, namely uses anti-concentration diffusion model for the effective enhancement and uses improved Otsu local threshold segmentation technology based on regional division for the image binarization, then vascular skeleton extraction based on GMM (Group marching method) with fast sweeping theory was actualized. Experiments show that our approach not only improved the time complexity, but also make a good extraction results.
Spectral decomposition in advection-diffusion analysis by finite element methods
Nickell, R.E.; Gartling, D.K.
1979-03-01
A spectral decomposition method based upon finite element modeling is compared to a Crank-Nicolson direct integration solution scheme and the exact solution for the one-dimensional, nonlinear system defined by Burger's equation. Results from this study are applicable to both fluid mechanics and combined conduction-convection heat transfer. The parameter ..cap alpha.., which governs the importance of diffusive transport, was varied over a sufficiently wide range such that comments on the comparisons are general. The mode superposition method proved to be very attractive in comparison to the second-order accurate Crank-Nicolson approach, generally allowing an order of magnitude larger time step for equivalent convergence to the exact solution. The modal shapes themselves tend to provide useful information about the ability of a given mesh to produce accurate results, much in the same way that modal information is used in nonlinear structural dynamics. For this class of problems, in contrast to structural dynamics, system nonlinearities did not manifest themselves in dramatic changes in the eigenspectrum.
Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings.
Strand, Kyle T; Feickert, Aaron J; Wagner, Alexander J
2017-06-01
We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally.
Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem
Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul; Lee, Deokjung
2015-12-01
In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.
Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem
Jeong, Yongjin; Park, Jinsu [Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798 (Korea, Republic of); Lee, Hyun Chul [Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 beon-gil, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Lee, Deokjung, E-mail: deokjung@unist.ac.kr [Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798 (Korea, Republic of)
2015-12-01
In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.
Preparation of PLA and PLGA nanoparticles by binary organic solvent diffusion method
蒋新宇; 周春山; 唐课文
2003-01-01
The nanoparticles of polylactide (PLA) and poly(lactide-co-glycolide) (PLGA) were prepared by the bi-nary organic solvent diffusion method. The yield, particle size and size distribution of these nanoparticles wereevaluated. The yield of nanoparticles prepared by this method is over 90%, and the average size of the nanoparticlesis between 130-180 nm. In order to clarify the effect of the organic solvent used in the system on nanoparticle yieldand size, the cloud points of PLA and PLGA were examined by cloud point titration. The results indicate that theyields of nanoparticles increase with the increase of ethanol in the acetone solution and attain the maximum at thecloud point of ethanol, while the size of nanoparticles decreases with the increase of ethanol in the acetone solutionand attains the minimum at the cloud point of ethanol. The optimal composition ratio of binary organic solvents coin-cides to that near the cloud point and the optimal condition of binary organic solvents can be predicted.
A novel method for computing effective diffusivity: Application to helium implanted α-Fe thin films
Dunn, Aaron [George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, UMI 2958 Georgia Tech CNRS, 57070 Metz (France); Agudo-Merida, Laura; Martin-Bragado, Ignacio [IMDEA Materials Institute, C/ Eric Kandel, 2, Tecnogetafe, 28906 Getafe, Madrid (Spain); McPhie, Mathieu; Cherkaoui, Mohammed [George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, UMI 2958 Georgia Tech CNRS, 57070 Metz (France); Capolungo, Laurent, E-mail: laurent.capolungo@me.gatech.edu [George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, UMI 2958 Georgia Tech CNRS, 57070 Metz (France)
2014-05-01
The effective diffusivity of helium in thin iron films is quantified using spatially resolved stochastic cluster dynamics and object kinetic Monte Carlo simulations. The roles of total displacement dose (in DPA), damage rate, helium to DPA ratio, layer thickness, and damage type (cascade damage vs Frenkel pair implantation) on effective He diffusivity are investigated. Helium diffusivity is found to decrease with increasing total damage and decreasing damage rate. Arrhenius plots show strongly increased helium diffusivity at high temperatures, high total implantation, and low implantation rates due to decreased vacancy and vacancy cluster concentrations. At low temperatures, effective diffusivity is weakly dependent on foil thickness while at high temperatures, narrower foils prevent defect accumulation by releasing all defects at the free surfaces. Helium to DPA ratio is not shown to strongly change helium diffusivity in the range of irradiation conditions simulated. Frenkel pair implantation is shown to cause higher effective diffusivity and more complex diffusion mechanisms than cascade implantation. The results of these simulations indicate that the differences in damage rates between implantation experiments and fission or fusion environments may result in differences in the final microstructure.
Wazwaz, Abdul-Majid
2017-07-01
In this work we address the Lane-Emden boundary value problems which appear in chemical applications, biochemical applications, and scientific disciplines. We apply the variational iteration method to solve two specific models. The first problem models reaction-diffusion equation in a spherical catalyst, while the second problem models the reaction-diffusion process in a spherical biocatalyst. We obtain reliable analytical expressions of the concentrations and the effectiveness factors. Proper graphs will be used to illustrate the obtained results. The proposed analysis demonstrates reliability and efficiency applicability of the employed method.
Ryu, Meguya; Morikawa, Junko
2016-11-01
Simultaneous measurements of anisotropic thermal diffusivity and thermal effusivity in the phase transition of the liquid crystal 4‧-(pentyloxy)-4-biphenyl carbonitrile (5OCB), Cry-53-N-68-Iso, are demonstrated using the temperature wave analysis method. A detailed calibration procedure for determining thermal diffusivity (α), thermal effusivity (e), thermal conductivity (λ), and heat capacity per unit volume (Cp ρ) is proposed utilizing hexaethylene glycol monododecyl ether (C12E6) as a calibration material, the heat capacity of which is precisely determined using a calorimetric method.
Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume
2017-09-01
The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.
Jayawardena, Asitha; Boardman, Allison; Cook, Thomas; Oprescu, Florin; Morcuende, Jose A
2011-01-01
This ethnographic study evaluated the use of low-bandwidth web-conferencing to enhance diffusion of a specific best practice, the Ponseti method to treat clubfoot, in three economically diverse countries in Latin America. A "Ponseti Virtual Forum" (PVF) was organized in Guatemala, Peru and Chile to examine the influences of economic level and telecommunication infrastructure on the effectiveness of tins approach. Across the three countries, a total of 14 different sites participated in the PVFs. Thirty-three Ponseti-trained practitioners were interviewed before and after each PVF, which included interactions with a Spanish-speaking Ponseti method expert. Semi-structured interviews, observations, and IP address data were triangulated and analyzed. The results demonstrated that 100% of the practitioners rated the sessions as very useful and that they would use this approach again. The largest obstacles to using PVFs were financial (7 out of 9 practitioners) in Guatemala; a lack of equipment and network access (6 out of 11) in Peru; and the organization and implementation of the conferences themselves (7 out of 9) in Chile. This study illustrates the usefulness of Ponseti Virtual Forums in Latin America. Health officials in Peru are currently developing a large-scale information session for traumatologists about the Ponseti method, while practitioners in Guatemala and Chile are organizing monthly scholarly meetings for physicians in remote areas. This initial feedback suggests that low-bandwidth web-conferencing can be an important vehicle for the dissemination of best practices, such as the Ponseti method, in developing countries.
Modelling Gas Diffusion from Breaking Coal Samples with the Discrete Element Method
Dan-Ling Lin
2015-01-01
Full Text Available Particle scale diffusion is implemented in the discrete element code, Esys-Particle. We focus on the question of how to calibrate the particle scale diffusion coefficient. For the regular 2D packing, theoretical relation between micro- and macrodiffusion coefficients is derived. This relation is then verified in several numerical tests where the macroscopic diffusion coefficient is determined numerically based on the half-time of a desorption scheme. To further test the coupled model, we simulate the diffusion and desorption in the circular sample. The numerical results match the analytical solution very well. An example of gas diffusion and desorption during sample crushing and fragmenting is given at the last. The current approach is the first step towards a realistic and comprehensive modelling of coal and gas outbursts.
Mey, Paula; Varges, Priscilla R.; Mendes, Paulo R. de Souza [Dept. of Mechanical Engineering. Pontificia Universidade Catolica do RJ (PUC-Rio), RJ (Brazil)], e-mails: prvarges@puc-rio.br, pmendes@puc-rio.br
2010-07-01
This research looked for a method to determine the binary diffusion coefficient D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water.D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water. (author)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)
2017-04-01
In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.
Barrier heights of hydrogen-transfer reactions with diffusion quantum monte carlo method.
Zhou, Xiaojun; Wang, Fan
2017-04-30
Hydrogen-transfer reactions are an important class of reactions in many chemical and biological processes. Barrier heights of H-transfer reactions are underestimated significantly by popular exchange-correlation functional with density functional theory (DFT), while coupled-cluster (CC) method is quite expensive and can be applied only to rather small systems. Quantum Monte-Carlo method can usually provide reliable results for large systems. Performance of fixed-node diffusion quantum Monte-Carlo method (FN-DMC) on barrier heights of the 19 H-transfer reactions in the HTBH38/08 database is investigated in this study with the trial wavefunctions of the single-Slater-Jastrow form and orbitals from DFT using local density approximation. Our results show that barrier heights of these reactions can be calculated rather accurately using FN-DMC and the mean absolute error is 1.0 kcal/mol in all-electron calculations. Introduction of pseudopotentials (PP) in FN-DMC calculations improves efficiency pronouncedly. According to our results, error of the employed PPs is smaller than that of the present CCSD(T) and FN-DMC calculations. FN-DMC using PPs can thus be applied to investigate H-transfer reactions involving larger molecules reliably. In addition, bond dissociation energies of the involved molecules using FN-DMC are in excellent agreement with reference values and they are even better than results of the employed CCSD(T) calculations using the aug-cc-pVQZ basis set. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Xu, Xiao Quan; Hu, Hao Hu; Su, Guo Yi; Liu, Hu; Shi, Hai Bin; Wu, Fei Yun [First Affiliated Hospital of Nanjing Medical University, Nanjing (China)
2016-09-15
To evaluate the differences in the apparent diffusion coefficient (ADC) measurements based on three different region of interest (ROI) selection methods, and compare their diagnostic performance in differentiating benign from malignant orbital tumors. Diffusion-weighted imaging data of sixty-four patients with orbital tumors (33 benign and 31 malignant) were retrospectively analyzed. Two readers independently measured the ADC values using three different ROIs selection methods including whole-tumor (WT), single-slice (SS), and reader-defined small sample (RDSS). The differences of ADC values (ADC-ROI{sub WT}, ADC-ROI{sub SS}, and ADC-ROI{sub RDSS}) between benign and malignant group were compared using unpaired t test. Receiver operating characteristic curve was used to determine and compare their diagnostic ability. The ADC measurement time was compared using ANOVA analysis and the measurement reproducibility was assessed using Bland-Altman method and intra-class correlation coefficient (ICC). Malignant group showed significantly lower ADC-ROI{sub WT}, ADC-ROI{sub SS}, and ADC-ROI{sub RDSS} than benign group (all p < 0.05). The areas under the curve showed no significant difference when using ADC-ROI{sub WT}, ADC-ROI{sub SS}, and ADC-ROI{sub RDSS} as differentiating index, respectively (all p > 0.05). The ROI{sub SS} and ROI{sub RDSS} required comparable measurement time (p > 0.05), while significantly shorter than ROI{sub WT} (p < 0.05). The ROI{sub SS} showed the best reproducibility (mean difference ± limits of agreement between two readers were 0.022 [-0.080–0.123] × 10{sup -3} mm{sup 2}/s; ICC, 0.997) among three ROI method. Apparent diffusion coefficient values based on the three different ROI selection methods can help to differentiate benign from malignant orbital tumors. The results of measurement time, reproducibility and diagnostic ability suggest that the ROI{sub SS} method are potentially useful for clinical practice.
Nguyen, Dang Van [INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex (France); Li, Jing-Rebecca, E-mail: jingrebecca.li@inria.fr [INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex (France); Grebenkov, Denis [Laboratoire de Physique de la Matiere Condensee, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex (France); Le Bihan, Denis [NeuroSpin, Bat145, Point Courrier 156, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex (France)
2014-04-15
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.
Wicaksono, Hendro; Zhang, Xing; Fujii, Motoo
2001-01-01
In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural con...
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
Fluconazole susceptibility of Brazilian Candida isolates assessed by a disk diffusion method
Arnaldo L. Colombo
Full Text Available The increasing magnitude of antifungal resistance as well as the advent of new antifungal drugs has generated a renewed interest in fungal susceptibility testing. We used a previously described disk diffusion method to evaluate the susceptibility profile of a large collection of recent clinical Candida spp. isolates against fluconazole. A total of 1,784 yeast isolates were tested, including the following species: Candida albicans (1,036, C. tropicalis (279, C. parapsilosis (202, C. glabrata (119, C. guilliermondii (90, C. krusei (32, C. lusitaniae (7, Candida spp. (14 and other yeasts (5. Susceptibility ranking to fluconazole obtained with all yeasts tested was: C. parapsilosis @ C. tropicalis @ C. guilliermondii > C. glabrata > C. krusei. The majority (94% of all yeast isolates tested were susceptible to fluconazole. Isolates of C. glabrata and C. krusei exhibited the highest rate of DDS/resistance among all isolates tested but they represented only 9% of all yeasts routinely sent to our lab. Careful periodical surveillance is needed in order to identify any changes in the susceptibility patterns of fluconazole with the increased use of this antifungal agent in Brazilian tertiary care hospitals.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Optimal Analysis Method for Dynamic Contrast-Enhanced Diffuse Optical Tomography
Michael Ghijsen
2011-01-01
Full Text Available Diffuse Optical Tomography (DOT is an optical imaging modality that has various clinical applications. However, the spatial resolution and quantitative accuracy of DOT is poor due to strong photon scatting in biological tissue. Structural a priori information from another high spatial resolution imaging modality such as Magnetic Resonance Imaging (MRI has been demonstrated to significantly improve DOT accuracy. In addition, a contrast agent can be used to obtain differential absorption images of the lesion by using dynamic contrast enhanced DOT (DCE-DOT. This produces a relative absorption map that consists of subtracting a reconstructed baseline image from reconstructed images in which optical contrast is included. In this study, we investigated and compared different reconstruction methods and analysis approaches for regular endogenous DOT and DCE-DOT with and without MR anatomical a priori information for arbitrarily-shaped objects. Our phantom and animal studies have shown that superior image quality and higher accuracy can be achieved using DCE-DOT together with MR structural a priori information. Hence, implementation of a combined MRI-DOT system to image ICG enhancement can potentially be a promising tool for breast cancer imaging.
Giese-Bogdan, Stefan It; Levine, Steven P
1996-08-01
International cooperation and diffusion of environmental technologies is a central goal of the U.S. EPA Environmental Technology Initiative, and is of great interest to many countries. One objective is to exchange knowledge and skills concerning new monitoring technologies. In this case, the technology was open path Fourier Transform Infrared Spectrometry (op-FTIR). Taiwan is a high-technology, newly industrialized country. Because of air pollution problems, it is interested in obtaining skills, knowledge, and instrumentation for monitoring air pollutants. In April 1994, the Industrial Technology Research Institute, Center for Industrial Safety and Health Technology (ITRI/CISH) in Hsinchu, Taiwan, requested intensive training in op-FTIR. Training was held between September 30,1994 and October 29,1994. During the stay, the instructor provided intensive training on op-FTIR theory as well as an introduction to available instrumentation and software. The training concluded with a field demonstration of the instrumentation in a manufacturing facility. This report gives an overview of the training methods, structure, and materials in the op-FTIR training course. It will also address various problems encountered while teaching this course. In addition, the potential use for this technology in industry as well as by the Taiwanese government will be explained.
Weres, Jerzy; Kujawa, Sebastian; Olek, Wiesław; Czajkowski, Łukasz
2016-04-01
Knowledge of physical properties of biomaterials is important in understanding and designing agri-food and wood processing industries. In the study presented in this paper computational methods were developed and combined with experiments to enhance identification of agri-food and forest product properties, and to predict heat and water transport in such products. They were based on the finite element model of heat and water transport and supplemented with experimental data. Algorithms were proposed for image processing, geometry meshing, and inverse/direct finite element modelling. The resulting software system was composed of integrated subsystems for 3D geometry data acquisition and mesh generation, for 3D geometry modelling and visualization, and for inverse/direct problem computations for the heat and water transport processes. Auxiliary packages were developed to assess performance, accuracy and unification of data access. The software was validated by identifying selected properties and using the estimated values to predict the examined processes, and then comparing predictions to experimental data. The geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer were analysed. The estimated values, used as an input for simulation of the examined processes, enabled reduction in the uncertainty associated with predictions.
Production method of raw material dispersion liquid for reaction layer of gas diffusion electrode
Furuya, Choichi; Motoo, Satoshi
1987-10-13
Heretofore, in order to make a raw material dispersion liquid of a reaction layer of a gas diffusion electrode, water repellent carbon, polytetrafluoroethylene, water and a surface active agent are mixed, then a cake is made by filtering this mixed liquid and afterwards the cake is heated and dried before being crushed. Since this crushing is done mechanically, homogeneous fine raw material powders cannot be obtained. Accordingly, even when a reaction layer is made by sintering a mixture of this powder, hydrophilic carbon black or hydrophilic carbon black carrying catalyst, and polytetrafluoroethylene, the hydrophilic part and the water repellent part are not distributed homogeneously and the catalytic performance of the reaction layer declines. In order to solve this, this invention proposes a production method that water repellent carbon black, polyterafluoroethylene, water and a surface active agent are mixed, then this mixture is frozen so that the surface active agent may not become active and homogeneous condensed cores of water repellent carbon black and polytetrafluoroethylene powders may be formed, and afterwards a homogeneous fine raw material dispersion liquid is made from thawing the condensed cores without change by thawing the above frozen mixture.
A modified method to estimate eddy diffusivity in the North Pacific using altimeter eddy statistics
ZHANG Zhiwei; LI Yaru; TIAN Jiwei
2013-01-01
The method proposed by Stammer (1998) is modified using eddy statistics from altimeter observation to obtain more realistic eddy diffusivity (K) for the North Pacific.Compared with original estimates,the modified K has remarkably reduced values in the Kuroshio Extension (KE) and North Equatorial Counter Current (NECC) regions,but slightly enhanced values in the Subtropical Counter Current (STCC) region.In strong eastward flow areas like the KE and NECC,owing to a large difference between mean flow velocity and propagation velocity of mesoscale eddies,tracers inside the mesoscale eddies are transported outside rapidly by advection,and mixing length L is hence strongly suppressed.The low eddy probability (P) is also responsible for the reduced K in the NECC area.In the STCC region,however,L is mildly suppressed and P is very high,so K there is enhanced.The zonally-averaged K has two peaks with comparable magnitudes,in the latitude bands of the STCC and KE.In the core of KE,because of the reduced values of P and L,the zonally-averaged K is a minimum.Zonally-integrated eddy heat transport in the KE band,calculated based on the modified K,is much closer to the results of previous independent research,indicating the robustness of our modified K.The map of modified K provides useful information for modeling studies in the North Pacific.
DEVELOPMENT OF AN ITERATIVE METHOD TO SOLVE THE DIFFUSION PROBLEM IN THE PREDESIGN STEP
Abouali Sanchez, Said
2014-01-01
One of the most important and difficult steps in the design process is the predesign. In this step, the main goal is to obtain the geometry characteristics and some other features to solve the problem we want to solve. Thus, reducing the duration of this phase is one of the challenging objectives in the actual engineering design process. As regards our study, following the energy deposition calculations with the means of the FLUKA code, a heat diffusion code is usually needed to calculate the evolution in time of the temperature distributions as well the associated stresses on the object under study. As a preliminary optimization step in the object design process, in this project we are proposing thedevelopment of a new method implemented in a code which allows us to obtain the solution for this equation in a complex geometry by using the information given by the FLUKA code for a simple geometry. By this way, we will be able to reduce the predesign phase duration.
Ishii, Hiroyuki; Kobayashi, Nobuhiko; Hirose, Kenji
2012-02-01
Organic materials form crystals by relatively weak Van der Waals attraction between molecules, and thus differ fundamentally from covalently bonded semiconductors. Carriers in the organic semiconductors induce the drastic lattice deformation, which is called as polaron state. The polaron effect on the transport is a serious problem. Exactly what conduction mechanism applies to organic semiconductors has not been established. Therefore, we have investigated the transport properties using the Time-Dependent Wave-Packet Diffusion (TD-WPD) method [1]. To consider the polaron effect on the transport, in the methodology, we combine the wave-packet dynamics based on the quantum mechanics theory with the molecular dynamics. As the results, we can describe the electron motion modified by (electron-phonon mediated) time-dependent structural change. We investigate the transport property from an atomistic viewpoint and evaluate the mobility of organic semiconductors. We clarify the temperature dependence of mobility from the thermal activated behavior to the power law behavior. I will talk about these results in my presentation. [1] H. Ishii, N. Kobayashi, K. Hirose, Phys. Rev. B, 82 085435 (2010).
ANTI-DIFFUSIVE FINITE DIFFERENCE WENO METHODS FOR SHALLOW WATER WITH TRANSPORT OF POLLUTANT
Zhengfu Xu; Chi-Wang Shu
2006-01-01
In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18]to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENOscheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution.The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution
Han, Xu; Suo, Shiteng; Sun, Yawen; Zu, Jinyan; Qu, Jianxun; Zhou, Yan; Chen, Zengai; Xu, Jianrong
2017-03-01
To compare four methods of region-of-interest (ROI) placement for apparent diffusion coefficient (ADC) measurements in distinguishing low-grade gliomas (LGGs) from high-grade gliomas (HGGs). Two independent readers measured ADC parameters using four ROI methods (single-slice [single-round, five-round and freehand] and whole-volume) on 43 patients (20 LGGs, 23 HGGs) who had undergone 3.0 Tesla diffusion-weighted imaging and time required for each method of ADC measurements was recorded. Intraclass correlation coefficients (ICCs) were used to assess interobserver variability of ADC measurements. Mean and minimum ADC values and time required were compared using paired Student's t-tests. All ADC parameters (mean/minimum ADC values of three single-slice methods, mean/minimum/standard deviation/skewness/kurtosis/the10(th) and 25(th) percentiles/median/maximum of whole-volume method) were correlated with tumor grade (low versus high) by unpaired Student's t-tests. Discriminative ability was determined by receiver operating characteristic curves. All ADC measurements except minimum, skewness, and kurtosis of whole-volume ROI differed significantly between LGGs and HGGs (all P value of single-round ROI had the highest effect size (0.72) and the greatest areas under the curve (0.872). Three single-slice methods had good to excellent ICCs (0.67-0.89) and the whole-volume method fair to excellent ICCs (0.32-0.96). Minimum ADC values differed significantly between whole-volume and single-round ROI (P = 0.003) and, between whole-volume and five-round ROI (P = 0.001). The whole-volume method took significantly longer than all single-slice methods (all P measurements are influenced by ROI determination methods. Whole-volume histogram analysis did not yield better results than single-slice methods and took longer. Mean ADC value derived from single-round ROI is the most optimal parameter for differentiating LGGs from HGGs. 3 J. Magn. Reson. Imaging 2017;45:722-730.
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs.
QIN Xin-qiang; MA Yi-chen; ZHANG Yin
2005-01-01
For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.
Accelerated stochastic and hybrid methods for spatial simulations of reaction diffusion systems
Rossinelli, Diego; Bayati, Basil; Koumoutsakos, Petros
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial τ-Leaping ( Sτ-Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid τ-Leaping ( Hτ-Leaping), combining a deterministic diffusion approximation with a τ-Leaping acceleration of the stochastic reactions. The algorithms are validated by solving Fisher's equation and used to explore the role of the number of particles in pattern formation. The results indicate that the present algorithms have a nearly constant time complexity with respect to the number of events (reaction and diffusion), unlike the exact stochastic simulation algorithm which scales linearly.
Spivakovskaya, D.; Heemink, A.W.; Deleersnijder, E.
2007-01-01
Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but
The solid-phase diffusion coefficient (Dm) and material-air partition coefficient (Kma) are key parameters for characterizing the sources and transport of semivolatile organic compounds (SVOCs) in the indoor environment. In this work, a new experimental method was developed to es...
Thermal conductivity and thermal diffusivity are two important physical properties essential for designing any food engineering processes. Recently a new transient plane-source method was developed to measure a variety of materials, but its application in foods has not been documented. Therefore, ...
Artun, Huseyin; Costu, Bayram
2013-01-01
The aim of this study was to explore a group of prospective primary teachers' conceptual understanding of diffusion and osmosis as they implemented a 5E constructivist model and related materials in a science methods course. Fifty prospective primary teachers' ideas were elicited using a pre- and post-test and delayed post-test survey consisting…
Pregosin, Paul S
2017-05-01
This mini-review provides a brief overview of the use of NMR diffusion methods in connection with estimating molecular weights in solution, recognizing hydrogen bonding and encapsulation processes and, primarily, identifying and estimating the varying degrees of ion pairing. Copyright © 2016 John Wiley & Sons, Ltd.
Pratibha Joshi
2014-12-01
Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.
Spivakovskaya, D.; Heemink, A.W.; Deleersnijder, E.
2007-01-01
Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continu
Titanium diffusion coatings on austenitic steel obtained by the pack cementation method
MIRELA BRITCHI
2009-02-01
Full Text Available The surface of specimens made of 316L austenitic steel was modified by titanium diffusion. The diffusion coatings were obtained by packing in a powder mixture consisting of titanium powder, NH4Cl and Al2O3 powder. The procedure required high temperatures, over 900 °C, and long durations. Atomic titanium was formed in the muffle during the process. Titanium atoms from the metallic part surfaces diffuse towards the interior and a diffusion layer is formed as a function of the steel composition. Titanium diffusion into the surface of 316L austenitic steel determines the formation of a complex coating: a thin layer of TiN at the exterior and a layer consisting of compounds containing Ti, Ni and Fe in the interior of the coating. The obtained coatings were continuous, adherent and had a hardness higher than that of the substrate material. The diffusion coatings were investigated by optical and electron microscopy, X-ray diffraction and Vickers microhardness tests.
Role of Cl on Diffusion of Cu in In2S3 Layers Prepared by Ion Layer Gas Reaction Method
Henry Wafula; Musembi Robinson; Albert Juma; Thomas Sakwa; Manasse Kitui; Rodrigo Araoz; Christian-H. Fischer
2015-01-01
Ion layer gas reaction ILGAR method allows for deposition of Cl containing and Cl free In2S3 layers from InCl3 and In OCCH3CHOCCH3 3 precursor salts, respectively. A comparative study was performed to investigate the role of Cl on the diffusion of Cu from CuSCN source layer into ILGAR deposited In2S3 layers. The Cl concentration was varied between 7 and 14 at. by varying deposition parameters. The activation energies and exponential pre factors for Cu diffusion in Cl containing samples we...
Tsang, P W M; Poon, T-C
2013-10-01
We report a novel and fast method for converting a digital, complex Fresnel hologram into a phase-only hologram. Briefly, the pixels in the complex hologram are scanned sequentially in a row by row manner. The odd and even rows are scanned from opposite directions, constituting to a bidirectional error diffusion process. The magnitude of each visited pixel is forced to be a constant value, while preserving the exact phase value. The resulting error is diffused to the neighboring pixels that have not been visited before. The resulting novel phase-only hologram is called the bidirectional error diffusion (BERD) hologram. The reconstructed image from the BERD hologram exhibits high fidelity as compared with those obtained with the original complex hologram.
Van Hecke, Wim; Sijbers, Jan; De Backer, Steve; Poot, Dirk; Parizel, Paul M; Leemans, Alexander
2009-07-01
Although many studies are starting to use voxel-based analysis (VBA) methods to compare diffusion tensor images between healthy and diseased subjects, it has been demonstrated that VBA results depend heavily on parameter settings and implementation strategies, such as the applied coregistration technique, smoothing kernel width, statistical analysis, etc. In order to investigate the effect of different parameter settings and implementations on the accuracy and precision of the VBA results quantitatively, ground truth knowledge regarding the underlying microstructural alterations is required. To address the lack of such a gold standard, simulated diffusion tensor data sets are developed, which can model an array of anomalies in the diffusion properties of a predefined location. These data sets can be employed to evaluate the numerous parameters that characterize the pipeline of a VBA algorithm and to compare the accuracy, precision, and reproducibility of different post-processing approaches quantitatively. We are convinced that the use of these simulated data sets can improve the understanding of how different diffusion tensor image post-processing techniques affect the outcome of VBA. In turn, this may possibly lead to a more standardized and reliable evaluation of diffusion tensor data sets of large study groups with a wide range of white matter altering pathologies. The simulated DTI data sets will be made available online (http://www.dti.ua.ac.be).
Marek Danielewski
2015-01-01
Full Text Available The problem of Kirkendall’s trajectories in finite, three- and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: (i multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, (ii multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and (iii a Kirkendall plane that coincides with the interphase interface. The details of the deformation (material trajectories in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.
Ricieri, Reinaldo Prandini; Escobedo, Joao Francisco; Almeida Frisina, Valeria de [UNESP, Botucatu, SP (Brazil). Faculdade de Ciencias Agronomicas. Dept. de Ciencias Ambientais
1998-07-01
The evaluation results from measuring methods of the diffuse solar radiation, disc and shadow ring are described compared to the method by difference between the global radiation and the direct radiation projected in a horizontal plane. The disc method is dependent on the diffuse radiation anisotropy, with an average relative deviation around 7.1% with percentages according to the sky cover; 11.56% for open sky days; 4.8% for partly cloudy days and 2.43% for cloudy days. The shadow ring method is also sky cover dependent with an average relative deviation 8.0% ranging from 8.99% for open sky days; 7.70% for partly cloudy and 2.5% for cloudy days. (author)
Niphon Wansophark; Pramote Dechaumphai
2008-01-01
A streamline upwind finite element method using 6-node triangular element is presented.The method is applied to the convection term of the governing transport equation directly along local streamlines.Several convective-diffusion examples are used to evaluate efficiency of the method.Results show that the method is monotonic and does not produce any oscillation.In addition,an adaptive meshing technique is combined with the method to further increase accuracy of the solution,and at the same time,to minimize computational time and computer memory requirement.
Guerin, P
2007-12-15
The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)
Russell, Greg; Harkins, Kevin D; Secomb, Timothy W; Galons, Jean-Philippe; Trouard, Theodore P
2012-02-21
A new finite difference (FD) method for calculating the time evolution of complex transverse magnetization in diffusion-weighted magnetic resonance imaging and spectroscopy experiments is described that incorporates periodic boundary conditions. The new FD method relaxes restrictions on the allowable time step size employed in modeling which can significantly reduce computation time for simulations of large physical extent and allow for more complex, physiologically relevant, geometries to be simulated.
Barajas-Solano, David A.; Tartakovsky, A. M.
2016-10-13
We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\\Omega^{hs}$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $\\Omega^{hs}$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.
Kuusimäki, Leea; Peltonen, Kimmo; Vainiotalo, Sinikka
A previously introduced method for monitoring environmental tobacco smoke (ETS) was further validated. The method is based on diffusive sampling of a vapour-phase marker, 3-ethenylpyridine (3-EP), with 3 M passive monitors (type 3500). Experiments were done in a dynamic chamber to assess diffusive sampling in comparison with active sampling in charcoal tubes or XAD-4 tubes. The sampling rate for 3-EP collected on the diffusive sampler was 23.1±0.6 mL min -1. The relative standard deviation for parallel samples ( n=6) ranged from 4% to 14% among experiments ( n=9). No marked reverse diffusion of 3-EP was detected nor any significant effect of relative humidity at 20%, 50% or 80%. The diffusive sampling of 3-EP was validated in field measurements in 15 restaurants in comparison with 3-EP and nicotine measurements using active sampling. The 3-EP concentration in restaurants ranged from 0.01 to 9.8 μg m -3, and the uptake rate for 3-EP based on 92 parallel samples was 24.0±0.4 mL min -1. A linear correlation ( r=0.98) was observed between 3-EP and nicotine concentrations, the average ratio of 3-EP to nicotine being 1:8. Active sampling of 3-EP and nicotine in charcoal tubes provided more reliable results than sampling in XAD-4 tubes. All samples were analysed using gas chromatography-mass spectrometry after elution with a 15% solution of pyridine in toluene. For nicotine, the limit of quantification of the charcoal tube method was 4 ng per sample, corresponding to 0.04 μg m -3 for an air sample of 96 L. For 3-EP, the limit of quantification of the diffusive method was 0.5-1.0 ng per sample, corresponding to 0.04-0.09 μg m -3 for 8 h sampling. The diffusive method proved suitable for ETS monitoring, even at low levels of ETS.
Duerigen, Susan
2013-05-15
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
Holden, Helge; Karlsen, Kenneth Hvistendal; Lie, Knut Andreas
1999-12-01
We present an accurate numerical method for a large class of scalar, strongly degenerate convection-diffusion equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. The method is based on splitting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion part is solved by an implicit-explicit finite difference scheme. In addition, one version of the implemented operator splitting method has a mechanism built in for detecting and correcting unphysical entropy loss, which may occur when the time step is large. This mechanism helps us gain a large time step ability for practical computations. A detailed convergence analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling secondary oil recovery and sedimentation-consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use large time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient. (author)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Cangiani, Andrea [University of Leicester, Leicester (United Kingdom); Sutton, Oliver [University of Leicester, Leicester (United Kingdom)
2014-10-02
This document describes the conforming formulations for virtual element approximation of the convection-reaction-diffusion equation with variable coefficients. Emphasis is given to construction of the projection operators onto polynomial spaces of appropriate order. These projections make it possible the virtual formulation to achieve any order of accuracy. We present the construction of the internal and the external formulation. The difference between the two is in the way the projection operators act on the derivatives (laplacian, gradient) of the partial differential equation. For the diffusive regime we prove the well-posedness of the external formulation and we derive an estimate of the approximation error in the H^{1}-norm. For the convection-dominated case, the streamline diffusion stabilization (aka SUPG) is also discussed.
Raefat, Saad; Garoum, Mohammed; Laaroussi, Najma; Thiam, Macodou; Amarray, Khaoula
2017-07-01
In this work experimental investigation of apparent thermal diffusivity and adiabatic limit temperature of expanded granular perlite mixes has been made using the flash technic. Perlite granulates were sieved to produce essentially three characteristic grain sizes. The consolidated samples were manufactured by mixing controlled proportions of the plaster and water. The effect of the particle size on the diffusivity was examined. The inverse estimation of the diffusivity and the adiabatic limit temperature at the rear face as well as the heat losses coefficients were performed using several numerical global minimization procedures. The function to be minimized is the quadratic distance between the experimental temperature rise at the rear face and the analytical model derived from the one dimension heat conduction. It is shown that, for all granulometry tested, the estimated parameters lead to a good agreement between the mathematical model and experimental data.
Alqasemi, Umar; Salehi, Hassan S.; Zhu, Quing
2016-01-01
This paper reports a method of estimating an approximate closed-form solution to the light diffusion equation for any type of geometry involving Dirichlet’s boundary condition with known source location. It is based on estimating the optimum locations of multiple imaginary point sources to cancel the fluence at the extrapolated boundary by constrained optimization using a genetic algorithm. The mathematical derivation of the problem to approach the optimum solution for the direct-current type of diffuse optical systems is described in detail. Our method is first applied to slab geometry and compared with a truncated series solution. After that, it is applied to hemispherical geometry and compared with Monte Carlo simulation results. The method provides a fast and sufficiently accurate fluence distribution for optical reconstruction. PMID:26831771
Extension of Newman's method to electrochemical reaction-diffusion in a fuel cell catalyst layer
Duan, Tianping; Weidner, John W.; White, Ralph E.
A numerical technique is developed for solving coupled electrochemical reaction-diffusion equations. Through analyzing the nonlinearity of the problem, a trial and error iterating procedure is constructed. The coefficient matrix is arranged as a tridiagonal form with elements of block matrix and is decomposed to LU form. A compact forward and backward substitution algorithm based on the shift of inversing block matrix by Gauss-Jordan full pivoting is developed. A large number of node points is required to converge the calculation. Computation experiences show that the iteration converges very quickly. The effects of inner diffusion on the electrochemical reaction are analyzed by numerical solutions.
Ramadan, Yousof [Department of Physical Chemistry II, Faculty of Pharmacy, Complutense University of Madrid, 28040 Madrid (Spain); González-Sánchez, M. Isabel [Department of Physical Chemistry, School of Industrial Engineering, Castilla-La Mancha University, 02071 Albacete (Spain); Hawkins, Karl [Centre of Nanohealth, Institute of Life Sciences, College of Medicine, Swansea University, Singleton Park, Swansea SA2 8PP, Wales (United Kingdom); Rubio-Retama, Jorge [Department of Physical Chemistry II, Faculty of Pharmacy, Complutense University of Madrid, 28040 Madrid (Spain); Valero, Edelmira [Department of Physical Chemistry, School of Industrial Engineering, Castilla-La Mancha University, 02071 Albacete (Spain); Perni, Stefano [School of Pharmacy and Pharmaceutical Sciences, Cardiff University, Cardiff CF103NB (United Kingdom); Department of Biological Engineering, MA Institute of Technology, Cambridge (United States); Prokopovich, Polina [School of Pharmacy and Pharmaceutical Sciences, Cardiff University, Cardiff CF103NB (United Kingdom); Institute of Medical Engineering and Medical Physics, School of Engineering, Cardiff University, Cardiff (United Kingdom); Department of Biological Engineering, MA Institute of Technology, Cambridge (United States); López-Cabarcos, Enrique, E-mail: cabarcos@farm.ucm.es [Department of Physical Chemistry II, Faculty of Pharmacy, Complutense University of Madrid, 28040 Madrid (Spain)
2014-09-01
The present paper describes the synthesis and characterization of a new polymeric biomaterial mineralized with calcium phosphate using the reaction–diffusion method. The scaffold of this biomaterial was a hydrogel constituted by biocompatible polyethylene glycol methyl ether methacrylate (PEGMEM) and 2-(dimethylamino)ethyl methacrylate (DMAEM), which were cross-linked with N-N’-methylenebisacrylamide (BIS). The cross-linking content of the hydrogels was varied from 0.25% to 15% (w/w). The gels were used as matrix where two reactants (Na{sub 2}HPO{sub 4} and CaCl{sub 2}) diffused from both ends of the gel and upon encountering produced calcium phosphate crystals that precipitated within the polymer matrix forming bands. The shape of the crystals was tuned by modifying the matrix porosity in such a way that when the polymer matrix was slightly reticulated the diffusion reaction produced round calcium phosphate microcrystals, whilst when the polymer matrix was highly reticulated the reaction yielded flat calcium phosphate crystals. Selected area electron diffraction performed on the nanocrystals that constitute the microcrystals showed that they were formed by Brushite (CaHPO{sub 4}.2H{sub 2}O). This new composite material could be useful in medical and dentistry applications such as bone regeneration, bone repair or tissue engineering. - Highlights: • New polymeric biomaterial mineralized with calcium phosphate using the reaction-diffusion method.-Growing of brushite nanocrystals within a polymeric matrix. • Mineralization by reaction diffusion method controls the crystal growth within gels.
Hart, Vern P; Doyle, Timothy E
2013-09-01
A Monte Carlo method was derived from the optical scattering properties of spheroidal particles and used for modeling diffuse photon migration in biological tissue. The spheroidal scattering solution used a separation of variables approach and numerical calculation of the light intensity as a function of the scattering angle. A Monte Carlo algorithm was then developed which utilized the scattering solution to determine successive photon trajectories in a three-dimensional simulation of optical diffusion and resultant scattering intensities in virtual tissue. Monte Carlo simulations using isotropic randomization, Henyey-Greenstein phase functions, and spherical Mie scattering were additionally developed and used for comparison to the spheroidal method. Intensity profiles extracted from diffusion simulations showed that the four models differed significantly. The depth of scattering extinction varied widely among the four models, with the isotropic, spherical, spheroidal, and phase function models displaying total extinction at depths of 3.62, 2.83, 3.28, and 1.95 cm, respectively. The results suggest that advanced scattering simulations could be used as a diagnostic tool by distinguishing specific cellular structures in the diffused signal. For example, simulations could be used to detect large concentrations of deformed cell nuclei indicative of early stage cancer. The presented technique is proposed to be a more physical description of photon migration than existing phase function methods. This is attributed to the spheroidal structure of highly scattering mitochondria and elongation of the cell nucleus, which occurs in the initial phases of certain cancers. The potential applications of the model and its importance to diffusive imaging techniques are discussed.
Baoyan Li
2003-09-01
Full Text Available We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE methods for the numerical solution of advection-diffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems. Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory.
Ahmad, So'bah; Shamsul Anuar, Mohd; Saleena Taip, Farah; Shamsudin, Rosnah; M, Siti Roha A.
2017-05-01
The effects of two drying methods, oven and microwave drying on the effective moisture diffusivity and activation energy of rambutan seed were studied. Effective moisture diffusivity and activation energy are the main indicators used for moisture movement within the material. Hence, it is beneficial to determine an appropriate drying method to attain a final moisture content of rambutan seed that potentially could be used as secondary sources in the industry. An appropriate final moisture content will provide better storage stability that can extend the lifespan of the rambutan seed. The rambutan seeds were dried with two drying methods (oven and microwave) at two level of the process variables (oven temperature; 40°C and 60°C and microwave power; 250W and 1000W) at constant initial moisture contents. The result showed that a higher value of effective moisture diffusivity and less activation energy were observed in microwave drying compared to oven drying. This finding portrays microwave drying expedites the moisture removal to achieve the required final moisture content and the most appropriate drying method for longer storage stability for rambutan seed. With respect to the process variables; higher oven temperatures and lower microwave powers also exhibit similar trends. Hopefully, this study would provide a baseline data to determine an appropriate drying method for longer storage period for turning waste to by-products.
Thermitus, M.A.; Laurent, M. [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)
1997-12-31
Using a logarithmic transformation, the thermogram of a flash experiment can be interpreted as the sum of the adiabatic model solution with a term representative of the losses. Two methods based on this transformation are proposed in this study. They are based on the identification of a parameter that depends on the thickness of the sample and on its diffusivity and not on the experimental conditions. They allow to identify the diffusivity with a high precision even for materials with a low conductivity at high temperatures. (J.S.) 12 refs.
Non-parametric Estimation of Diffusion-Paths Using Wavelet Scaling Methods
Høg, Esben
In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean-reverting process) has been used to model non-speculative price processes. We discuss non--parametric estimation of these processes...
Hareesh, K.; Deore, Avinash V.; Dahiwale, S. S.; Sanjeev, Ganesh; Kanjilal, D.; Ojha, Sunil; Dhole, N. A.; Kodam, K. M.; Bhoraskar, V. N.; Dhole, S. D.
2015-07-01
Gold (Au)-Polycarbonate (PC) matrix was prepared by gamma radiation assisted diffusion of Au nanoparticles in PC matrix. UV-Visible spectroscopy showed the surface plasmon resonance around 550 nm which corresponds to Au and this peak shift towards lower wavelength i.e. blue shift indicating the decrease in particle size of Au. Rutherford Backscattering (RBS) experiment confirmed the diffusion of Au in PC and depth of diffusion is found to be around 0.85 μm. X-ray Diffractogram (XRD) results also revealed the diffusion of Au in PC where the peak observed at 2θ∼38.29° which correspond to the FCC structure. Scanning Electron Microscope (SEM) images showed the hexagonal shaped Au nanoparticles and average particle size is found to be around 110 nm. These samples also showed anti-bacterial properties with both gram positive and gram negative bacteria's and revealed the inhibition of the overall growth of the bacteria with gamma dose.
Comparison of the antibacterial activity of chelating agents using the agar diffusion method
The agar diffusion assay was used to examine antibacterial activity of 2 metal chelators. Concentrations of 0 to 40 mM of ethylenediaminetetraacetic acid (EDTA) and ethylenediamine-N,N’-disuccinic acid (EDDS) were prepared in 1.0 M potassium hydroxide (KOH). The pH of the solutions was adjusted to 1...
Non-Parametric Estimation of Diffusion-Paths Using Wavelet Scaling Methods
Høg, Esben
2003-01-01
In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean--reverting process) has been used to model non-speculative price processes. We discuss non--parametric estimation of these processes...
Varandani, Deepak; Agarwal, Khushboo; Brugger, Juergen; Mehta, Bodh Raj
2016-08-01
A commercial scanning thermal microscope has been upgraded to facilitate its use in estimating the radial thermal diffusivity of thin films close to room temperature. The modified setup includes a microcontroller driven microhotplate coupled with a Bluetooth module for wireless control. The microcontroller board (Arduino Leonardo) is used to generate a bias of suitable voltage amplitude and pulse duration which is applied across the microhotplate contact pads. A corresponding heat pulse from the Pt heating element (1 mm(2)) embedded within the microhotplate is delivered to the lower surface of the thin film (25 mm(2)) deposited over it. The large difference in the dimensions of the heating source and the thin film surface causes heat to flow radially outwards on the top surface of the latter. The decay of this radial heat wave as it flows outwards is recorded by the scanning thermal microscope in terms of temperature-time (T-t) profiles at varying positions around the central heating zone. A fitting procedure is suggested to extract the thermal diffusivity value from the array of T-t profiles. The efficacy of the above setup has been established by evaluating the thermal diffusivities of Bi2Te3 and Bi2Te3:Si thin film samples. Further, with only minor alterations in design the capabilities of the above setup can be extended to estimate the axial thermal diffusivity and specific heat of thin films, as a function of temperature.
Varandani, Deepak; Agarwal, Khushboo; Brugger, Juergen; Mehta, Bodh Raj
2016-08-01
A commercial scanning thermal microscope has been upgraded to facilitate its use in estimating the radial thermal diffusivity of thin films close to room temperature. The modified setup includes a microcontroller driven microhotplate coupled with a Bluetooth module for wireless control. The microcontroller board (Arduino Leonardo) is used to generate a bias of suitable voltage amplitude and pulse duration which is applied across the microhotplate contact pads. A corresponding heat pulse from the Pt heating element (1 mm2) embedded within the microhotplate is delivered to the lower surface of the thin film (25 mm2) deposited over it. The large difference in the dimensions of the heating source and the thin film surface causes heat to flow radially outwards on the top surface of the latter. The decay of this radial heat wave as it flows outwards is recorded by the scanning thermal microscope in terms of temperature-time (T-t) profiles at varying positions around the central heating zone. A fitting procedure is suggested to extract the thermal diffusivity value from the array of T-t profiles. The efficacy of the above setup has been established by evaluating the thermal diffusivities of Bi2Te3 and Bi2Te3:Si thin film samples. Further, with only minor alterations in design the capabilities of the above setup can be extended to estimate the axial thermal diffusivity and specific heat of thin films, as a function of temperature.
Non-Parametric Estimation of Diffusion-Paths Using Wavelet Scaling Methods
Høg, Esben
2003-01-01
In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean--reverting process) has been used to model non-speculative price processes. We discuss non--parametric estimation of these processes...
Non-parametric Estimation of Diffusion-Paths Using Wavelet Scaling Methods
Høg, Esben
In continuous time, diffusion processes have been used for modelling financial dynamics for a long time. For example the Ornstein-Uhlenbeck process (the simplest mean-reverting process) has been used to model non-speculative price processes. We discuss non--parametric estimation of these processes...
Fujiwara, Seiji; Maki, Syou; Tanaka, Seiichi; Maekawa, Ryunosuke; Masuda, Tomoki; Hagiwara, Masayuki
2017-07-01
Thermal conductivity and thermal diffusivity of hen egg-white lysozyme (HEWL) crystals were examined by using the transient short hot wire method. This method is based on the conventional hot wire method, but improved by using a wire that is much shorter than conventional ones. The magneto-Archimedes levitation technique was utilized to attach the HEWL crystals onto the wire. Owing to the upward magnetic force, the HEWL crystals were deposited at the air-liquid interface of the protein buffer solution where the short hot wire was preliminarily fixed. In situ observation clarified that the wire was completely buried into the HEWL crystals. By means of these techniques, the measurement of thermal conductivity and thermal diffusivity of HEWL crystals was realized for the first time. Gadolinium chloride (a paramagnetic subject) was used as a precipitant agent of crystallization. Crystal growth was carried out over 20 h at 17.2 °C. The applied magnetic field was 4 T. Measurements were conducted during the crystal growth at two different times. The thermal conductivity and diffusivity of the HEWL crystals were determined to be 0.410 W/(m.K) and 3.77×10-8 m2/s at 14 h after, and 0.438 W/(m.K) and 5.18×10-8 m2/s at 20 h after, respectively. We emphasize that this method is versatile and applicable for other protein crystals.
Zhu, Caigang; Liu, Quan
2012-01-01
We present a hybrid method that combines a multilayered scaling method and a perturbation method to speed up the Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with finite-size tumor-like heterogeneities. The proposed method consists of two steps. In the first step, a set of photon trajectory information generated from a baseline Monte Carlo simulation is utilized to scale the exit weight and exit distance of survival photons for the multilayered tissue model. In the second step, another set of photon trajectory information, including the locations of all collision events from the baseline simulation and the scaling result obtained from the first step, is employed by the perturbation Monte Carlo method to estimate diffuse reflectance from the multilayered tissue model with tumor-like heterogeneities. Our method is demonstrated to shorten simulation time by several orders of magnitude. Moreover, this hybrid method works for a larger range of probe configurations and tumor models than the scaling method or the perturbation method alone.
Makuch, Karol; Heinen, Marco; Abade, Gustavo Coelho; Nägele, Gerhard
2015-07-14
We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.
S. X. Yao
2017-08-01
Full Text Available In this research, theoretical CO2 diffusivity coefficients in amorphous polymers were calculated from dielectric constant changes during CO2 desorption. These values showed agreement with experimental diffusivity coefficients from a gravimetric method. Three amorphous polymer films made from Polystyrene (PS, Polycarbonate (PC, and Cyclic Olefin Polymer (COP resins were saturated with supercritical CO2 at 5.5 MPa and 25 °C for 24 hours in a pressure chamber. The CO2 infused films were removed from the chamber for gas desorption experiments. The capacitance of the samples were recorded with an Inductance, Capacitance and Resistance (LCR meter. These values were used to calculate the change in dielectric constants. CO2 weight percentages measured by a scale was used to calculate experimental diffusivity and solubility coefficients. It was found that the trend of dielectric constant changes was similar to that of the CO2 weight percentage changes during gas desorption. A mathematical model was built to predict the CO2 weight percentages during desorption from the measured dielectric constants. Theoretical diffusivity coefficients from this work agree well with literature data.
Kojima, Shinsuke; Endo, Hiroshi; Seki, Mitsuo
We developed a compact snow crystal formation apparatus based on a diffusion method using a Peltier device. This apparatus does not need an assemblage and is small enough to be operated on a desk. Anyone can easily observe snow crystal formation in a normal temperature room. We adopted a diffusion method because the shape enable that several people can simultaneously observe the snow crystal formation from above. To estimate a performance of the apparatus, we investigated temperature profiles in the apparatus by measurement and simulations with (Case 1) and without (Case 2) natural convection. As results of the simulations, Case 1 and Case 2 reached a steady state. In each case, temperature stratification condition was formed in lower part of the apparatus. From the comparison of the results of measurement and simulations, finally, it is concluded that there is a natural convection, but the air current is not so strong as disturbing the temperature stratification condition in the apparatus.
Liu, Qing; Wang, Hai-Shui; Zeng, Qiang
2016-09-01
The polymorph control of calcium carbonate by the vapor diffusion method is still a challenging issue because the resultant crystal polymorphs and morphologies highly depend on the experimental setup. In this communication, we demonstrated that the concentration gradients accompanied by the vapor diffusion method (ammonia concentration, pH and the ratio of CO32- to Ca2+ are changed with the solution depth and with time) are probably the main reasons to significantly affect the formation of crystal polymorphs. Raman, SEM and XRD data showed that calcite and vaterite crystals were preferred to nucleate and grow in the upper or the lower areas of aqueous solution respectively. The above results can be explained by the gradient effect.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Makuch, Karol; Heinen, Marco; Abade, Gustavo Coelho; Nägele, Gerhard
To the present day, the Beenakker-Mazur (BM) method is the most comprehensive statistical physics approach to the calculation of short-time transport properties of colloidal suspensions. A revised version of the BM method with an improved treatment of hydrodynamic interactions is presented and evaluated regarding the rotational short-time self-diffusion coefficient, $D^r$ , of suspensions of charged particles interacting by a hard-sphere plus screened Coulomb (Yukawa) pair potential. To assess the accuracy of the method, elaborate simulations of $D^r$ have been performed, covering a broad range of interaction parameters and particle concentrations. The revised BM method is compared in addition with results by a simplifying pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a two-body level. The static pair correlation functions re- quired as input to both theoretical methods are calculated using the Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it systematically and significantly underestimates the rotational diffusion coefficient. The PA method agrees well with the simulation data at lower volume fractions, but at higher concentrations $D^r$ is likewise underestimated. For a fixed value of the pair potential at mean particle distance comparable to the thermal energy, $D^r$ increases strongly with increasing Yukawa potential screening parameter.
Arbogast, Todd
2010-05-01
Tracer transport is governed by a convection-diffusion problem modeling mass conservation of both tracer and ambient fluids. Numerical methods should be fully conservative, enforcing both conservation principles on the discrete level. Locally conservative characteristics methods conserve the mass of tracer, but may not conserve the mass of the ambient fluid. In a recent paper by the authors [T. Arbogast, C. Huang, A fully mass and volume conserving implementation of a characteristic method for transport problems, SIAM J. Sci. Comput. 28 (2006) 2001-2022], a fully conservative characteristic method, the Volume Corrected Characteristics Mixed Method (VCCMM), was introduced for potential flows. Here we extend and apply the method to problems with a solenoidal (i.e., divergence-free) flow field. The modification is a computationally inexpensive simplification of the original VCCMM, requiring a simple adjustment of trace-back regions in an element-by-element traversal of the domain. Our numerical results show that the method works well in practice, is less numerically diffuse than uncorrected characteristic methods, and can use up to at least about eight times the CFL limited time step. © 2010 Elsevier Inc.
A one-level FETI method for the drift–diffusion-Poisson system with discontinuities at an interface
Baumgartner, Stefan
2013-06-01
A 3d feti method for the drift-diffusion-Poisson system including discontinuities at a 2d interface is developed. The motivation for this work is to provide a parallel numerical algorithm for a system of PDEs that are the basic model equations for the simulation of semiconductor devices such as transistors and sensors. Moreover, discontinuities or jumps in the potential and its normal derivative at a 2d surface are included for the simulation of nanowire sensors based on a homogenized model. Using the feti method, these jump conditions can be included with the usual numerical properties and the original Farhat-Roux feti method is extended to the drift-diffusion-Poisson equations including discontinuities. We show two numerical examples. The first example verifies the correct implementation including the discontinuities on a 2d grid divided into eight subdomains. The second example is 3d and shows the application of the algorithm to the simulation of nanowire sensors with high aspect ratios. The Poisson-Boltzmann equation and the drift-diffusion-Poisson system with jump conditions are solved on a 3d grid with real-world boundary conditions. © 2013 Elsevier Inc..
Fan, Yue; Yip, Sidney; Yildiz, Bilge
2014-09-01
This paper presents an extension of the autonomous basin climbing (ABC) method, an atomistic activation-relaxation technique for sampling transition-state pathways. The extended algorithm (ABC-E) allows the sampling of multiple transition pathways from a given minimum, with the additional feature of identifying the pathways in the order of increasing activation barriers, thereby prioritizing them according to their importance in the kinetics. Combined with on-the-fly kinetic Monte Carlo calculations, the method is applied to simulate the anisotropic diffusion of point defects in hcp Zr. Multiple migration mechanisms are identified for both the interstitials and vacancies, and benchmarked against results from other methods in the literature. The self-interstitial atom (SIA) diffusion kinetics shows a maximum anisotropy at intermediate temperatures (400~700 K), a non-monotonic behavior that we explain to originate from the stabilities and migration mechanisms associated with different SIA sites. The accuracy of the ABC-E calculations is validated, in part, by the existing results in the literature for point defect diffusion in hcp Zr, and by benchmarking against analytical results on a hypothetical rough-energy landscape. Lastly, sampling prioritization and computational efficiency are demonstrated through a direct comparison between the ABC-E and the activation relaxation technique.
Measurements of diffusion coefficients of hydrogen in palladium by a galvanostatic permeation method
Bucur, R.V.
1985-01-01
A study by the galvanostatic permeation technique is reported which has derived reliable and repro ducible measurements of diffusion coefficients for hydrogen in palladium. A description is given o the thermostated electrochemical permeation cell. Hydrogen permeation rates have been determined on the detection side of a palladium membrane electrode (geometrical surface area 7.2 cm/sup 2/; thickness 5 x 10/sup -3/ cm) by measuring the anodic current I /SUB o/ under potentiostatic conditions. Measurements have been made of rising and decaying I /SUB o/ when the hydrogen entrance side of the membrane has been subjected to constant cathodic currents I/iota/ whic were subsequently interrupted after establishments of steady-state conditions. Semi-log plots of I..cap alpha.. against time have yielded reliable determinations of the hydrogen and deuterium diffusion coefficients D..mu.. and D /SUB D/ . Studies have been made of the influence on measurement of D /SUB H/ by alterations of I/iota/, surface roughness of the membrane, variations of electrolyte solution, surface contamination and temperature. Over the temperature range 5-50/sup 0/C equations representing the temperature dependence of the diffusion coefficients have been determined.
Study on diffusion and recombination of minority carriers by the method of photoconductive decay
Chow, R. H.
1984-09-01
This paper describes an experiment relating to the diffusion of charge carriers in homogeneous semiconductor material. Diffusion theory, as outlined in this paper, is applied to deduce from measurements a quantity called the bulk lifetime of excess minority carriers: a quantity which is independent of the size, shape, and surface condition of the semiconductor sample. Because of this independence, the bulk lifetime is used as one of the characterizing quantities of semiconductor material. In performing this experiment, the student will gain a working knowledge of diffusion theory as applied to semiconductor carriers, and at the same time become acquainted with an important technique for the characterization of semiconductor material. The actual duration of involvement will depend upon the amount of setting up of equipment, sample preparation, etc., that is expected of the student. An oscilloscope of fast rise time (200-MHz bandwidth), and a xenon flash tube with pulse duration of a few microseconds (General Radio 1542-B electronic stroboscope is a proven possibility), are the major items of equipment needed.
Chayjan, Reza Amiri; Salari, Kamran; Barikloo, Hossein
2012-04-02
Modelling moisture diffusivity of pomegranate cultivars is considered to be a major aspect of the drying process optimization. Its goal is mainly to apply the optimum drying method and conditions in which the final product meets the required standards. Temperature is the major parameter which affects the moisture diffusivity. This parameter is not equal for different cultivars of pomegranate. So modelling of moisture diffusivity is important in designing, optimizing and adjusting the dryer system. This research studied thin layer drying of three cultivars of pomegranate seeds (Alak, Siah and Malas) under fixed, semi fluidized and fluidized bed conditions. Drying process of samples was implemented at 50, 60, 70 and 80°C air temperature levels. Second law of Fick in diffusion was utilized to compute the effective moisture diffusivity (D(eff)) of the seeds. Linear and artificial neural networks (ANNs) also were used to model D(eff) of seeds. Maximum and minimum values of the D(eff) were related to Malas and Alak cultivars, respectively. Three linear models were found to fit the experimental data with average R2 = 0.9350, 0.9320 and 0.9400 for Alak, Siah and Malas cultivars, respectively. The best results for neural network were related to feed forward neural network with training algorithm of Levenberg-Marquardt was appertained to the topology of 3-4-3-1 and threshold function of LOGSIG. By the use of this structure, R2 = 0.9972 was determined. A direct relationship was found between D(eff) and thickness of fleshy section of the seeds. The Siah cultivar has the highest value of D(eff). This is due to higher volume of fleshy section of the Siah cultivar. Cultivar type and air velocity have the highest and the least effect on D(eff), respectively.
Diffusion archeology for diffusion progression history reconstruction.
Sefer, Emre; Kingsford, Carl
2016-11-01
Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring - perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.
Zhaoyuan Liu; Kord Smith; Benoit Forget; Javier Ortensi
2016-05-01
A new method for computing homogenized assembly neutron transport cross sections and dif- fusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations per- formed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section ap- proximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.
Szymkiewicz, Romuald; Gasiorowski, Dariusz
2012-09-01
SummaryWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference method are its particular cases. Time integration is performed using a two-stage difference scheme with another weighting parameter. The resulting systems of nonlinear algebraic equations are solved using the Picard and Newton iterative methods. It is shown that the two weighting parameters determine the accuracy and stability of the numerical solution as well as the convergence of iterative process. Accuracy analysis using the modified equation approach carried out for linear version of the governing equation allowed to evaluate the numerical diffusion and dispersion generated by the method as well as to explain its properties. As the finite element method accounts for the Neumann type of boundary conditions in a natural way, no special treatment of the boundary is needed. Consequently the problem of moving grid point, which must follow the shoreline, in the proposed approach is overcome automatically. The current position of moving boundary is obtained as a result of solution of the governing equation at fixed grid point.
Sunahara, Y.; Kojima, F.
1987-01-01
The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Hasibun Naher
2012-01-01
Full Text Available We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.
Haijing Niu; Ping Guo; Xiaodong Song; Tianzi Jiang
2008-01-01
The sensitivity of diffuse optical tomography (DOT) imaging exponentially decreases with the increase of photon penetration depth, which leads to a poor depth resolution for DOT. In this letter, an exponential adjustment method (EAM) based on maximum singular value of layered sensitivity is proposed. Optimal depth resolution can be achieved by compensating the reduced sensitivity in the deep medium. Simulations are performed using a semi-infinite model and the simulation results show that the EAM method can substantially improve the depth resolution of deeply embedded objects in the medium. Consequently, the image quality and the reconstruction accuracy for these objects have been largely improved.
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
Bhat, Kishore G; Sogi, Suma
2016-01-01
Aims The aim of this study was to determine the relative antimicrobial effectiveness of these endodontic medicaments and various vehicles using an agar well diffusion assay. Materials and methods Double Antibiotic Paste(DAP), modified DAP, 2% Chlorhexidine gluconate and their combination with four vehicles namely Polyethylene glycol 400 (PEG), Propylene glycol (PG), combinations of PG with PEG and lastly Glycerine were tested using agar well diffusion assay. The minimum bactericidal concentration was noted against four standard strains of organisms ie Streptococcus mutans ATCC( American Type Culture Collection) 25175, Staphylococcus aureus ATCC 12598, Enterococcus faecalis ATCC 35550 and Eschericia coli ATCC 25922. Successful endodontic therapy depends upon thorough disinfection of root canals. In some refractory cases, routine endodontic therapy is not sufficient, so intracanal medicaments are used for proper disinfection of canals. Issues of resistance, limited spectrum of activity and lack of antifungal properties, the hunt for the ideal intracanal medicament continues. In this regard, the vehicles used to form the pastes play a supportive role by forming the appropriate consistency for placement and may dramatically influence their chemical characteristics like their solubility and diffusion. Thus, inorder to use safer and equally effective intracanal medicaments, Chlorhexidine gluconate is being unveiled in this study. Results The difference between the four vehicles when combined with the same endodontic medicament studied above is nonsignificant (NS) except against Porphyromonas gingivalis. Propylene glycol is significantly effective than Glycerine when used with DAP ie C+M medicament combination. (p = 0.029) Conclusion 2% chlorhexidine gluconate and modified DAP can definitely replace DAP and triple antibiotic paste as end-odontic medicaments with chlorhexidine having an added advantage of bactericidal action, substantivity, biocompatibility, low toxicity
New method for the determination of diffusion constants from partially narrowed NMR lines
Wolf, D.
1980-01-01
The effect of atomic and molecular motions on the NMR free-induction decay (FID) and lineshape is investigated theoretically in the intermediate temperature range in which the NMR line is only partially narrowed. It is shown that the FID may be decomposed into the weighted sum of a rigid-lattice (background) contribution and an exponentially decaying part containing all the information on the diffusive or reorientational motions in the crystal in terms of the spin-spin relaxation time T/sub 2/.
Thamlikitkul, Visanu; Tiengrim, Surapee
2014-03-01
To determine a correlation of minimum inhibitory concentration (MIC) of sitafloxacin determined by agar dilution method with inhibition zone diameter of sitafloxacin determined by disk diffusion method, and to determine inhibition zone, diameter breakpoints of sitafloxacin against resistant gram-negative bacilli isolated from Thai patients. The study bacteria were 332 clinical isolates of gram-negative bacilli including ESBL-producing E. coli, ESBL-producing K. pneumoniae, P. aeruginosa andA. baumannii. Each isolate of the present study bacteria was tested for minimum inhibitory concentration (MIC) of sitafloxacin by agar dilution method and inhibition zone diameter of sitafloxacin by disk diffusion method. The MICs and inhibition zone diameters of sitafloxacin against gram-negative bacilli were well correlated (correlation coefficient -0.926, p-value or = 15 mm had the least total error for determining susceptibility to sitafloxacin based on MIC value of sitafloxacin but the inhibition zone diameter > or = 16 mm had less false susceptibility than that of > or = 15 mm when compared with sitafloxacin MIC or = 19 mm had the least total error for determining susceptibility to sitafloxacin based on MIC value of sitafloxacin but the inhibition zone diameter > or = 18 mm had less false susceptibility than that of > or = 19 mm when compared with sitafloxacin MIC gram-negative bacilli by disk diffusion method, the inhibition zone diameter > or = 16 mm and > or = 18 mm seem to be the appropriate breakpoints for susceptibility for resistant gram-negative bacilli isolated from urine and blood, respectively, since the serum concentration of sitafloxacin is rather low whereas the urinary concentration of sitafloxacin is much higher.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Inoue, Chie; Fujii, Shinya; Kaneda, Sachi; Fukunaga, Takeru; Kaminou, Toshio; Kigawa, Junzo; Harada, Tasuku; Ogawa, Toshihide
2014-07-01
To investigate the influence of different-shaped regions of interest (ROIs) on tumor apparent diffusion coefficient (ADC) measurements and interobserver variability in endometrial carcinoma. Sixty-nine patients (age range, 32-92 years; mean, 61 years) were evaluated in this retrospective study. Patients had undergone magnetic resonance (MR) examinations including diffusion-weighted imaging (DWI) using a 3.0-T MR system. Two readers measured tumor ADCs using four ROI methods: freehand ROI; square ROI; round ROI; and five small, round ROIs. Minimum and mean ADCs were obtained. The interclass correlation coefficient (ICC) was statistically analyzed to assess measurement reliability. Repeated-measures analysis of variance was used for comparisons of ADCs measured with each ROI method. ICCs were 0.93 (minimum ADC) / 0.93 (mean ADC) for freehand ROIs, 0.94/0.95 for square ROIs, 0.94/0.95 for round ROIs, and 0.95/0.96 for five small, round ROIs. All ROI methods indicated excellent correlations. Each minimum ADC was significantly different except between square ROI and round ROI (P < 0.001). Mean ADCs showed significant differences only between freehand ROI and the other ROI methods (P < 0.001). ROI shape has no marked influence on ICC in endometrial carcinoma. Compared with minimum ADCs, mean ADCs are suggested to provide more stable results regardless of the ROI method. © 2013 Wiley Periodicals, Inc.
Thomsen, E.L. (Aerosol Lab., Risoe, Denmark); Lovelock, J.E.
1976-01-01
In many atmospheric diffusion experiments using tracer gases continuous tracer recording is of decisive importance. The main obstacle to continuous electron capture detection of tracer gases in the atmosphere is presented by the oxygen, which is an electron capturer. A method for removing this difficulty is described. Its practical use in an airborne atmospheric plume diffusion experiment is demonstrated.
Solid state reaction studies in Fe{sub 3}O{sub 4}–TiO{sub 2} system by diffusion couple method
Ren, Zhongshan [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Hu, Xiaojun, E-mail: huxiaojun@ustb.edu.cn [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Xue, Xiangxin [School of Materials and Metallurgy, Northeastern University, Shenyang 110006 (China); Chou, Kuochih [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China)
2013-12-15
Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe{sub 3}O{sub 4}–TiO{sub 2} system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO{sub 2} gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe{sub 3}O{sub 4} phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe{sub 3}O{sub 4}–TiO{sub 2} system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol{sup −1}.
Tang, Min; Wang, Yihong
2017-02-01
In magnetized plasma, the magnetic field confines the particles around the field lines. The anisotropy intensity in the viscosity and heat conduction may reach the order of 1012. When the boundary conditions are periodic or Neumann, the strong diffusion leads to an ill-posed limiting problem. To remove the ill-conditionedness in the highly anisotropic diffusion equations, we introduce a simple but very efficient asymptotic preserving reformulation in this paper. The key idea is that, instead of discretizing the Neumann boundary conditions locally, we replace one of the Neumann boundary condition by the integration of the original problem along the field line, the singular 1 / ɛ terms can be replaced by O (1) terms after the integration, which yields a well-posed problem. Small modifications to the original code are required and no change of coordinates nor mesh adaptation are needed. Uniform convergence with respect to the anisotropy strength 1 / ɛ can be observed numerically and the condition number does not scale with the anisotropy.
Perez Sanchez-Canete, Enrique; Scott, Russell L.; Barron-Gafford, Greg; van Haren, Joost
2016-04-01
Soil CO2 fluxes represent a major source of CO2 emissions, where small changes in their estimation provoke large changes in the quantification of the global carbon cycle. Recently, the gradient method that employs soil CO2 probes at multiple depths has been offered as a way to inexpensively and continuously measure soil CO2 flux. However, the use of the gradient method can yield inappropriate flux estimates due to the uncertainties mainly associated with the inappropriate determination of the soil diffusion coefficient. Therefore, in-situ methods to determine diffusion coefficient are necessary to obtain accurate CO2 fluxes. Here the data obtained during one year with two automatic soil CO2 chambers along with CO2 molar fraction data from 4 probes at 10 cm depth, were used to determine a model of soil diffusion coefficient (Ds), which was applied later to obtain the soil CO2 fluxes by the gradient method. Another Ds model was obtained by injection and sampling of SF6 during several campaigns with different soil water content levels. Both Ds models obtained in situ were compared with another 13 Ds models published. We addressed three questions: 1) Can we use a previously published model, or do we need to determine Ds in situ? 2) How accurate are the CO2 fluxes estimates obtained by the gradient method for different Ds models, compared with chamber-measured CO2 fluxes? 3) Can we take a limited number of chamber measurements to obtain a good Ds model, or we need longer calibration periods? Comparing the cumulative soil respiration for the different diffusion models, we found that the model with empirical calibration to the soil chambers had the best agreement with the chamber fluxes (SF6 model underestimated by chamber fluxes by 23% and the published models ranged from an underestimate of 78% to an overestimate of 14%. Most importantly, we found that a few days of measurements with a soil respiration chamber (with widely varying soil water content) are enough to build
Role of Cl on Diffusion of Cu in In2S3 Layers Prepared by Ion Layer Gas Reaction Method
Henry Wafula
2015-02-01
Full Text Available Ion layer gas reaction (ILGAR method allows for deposition of Cl-containing and Cl-free In2S3 layers from InCl3 and In(OCCH3CHOCCH33 precursor salts, respectively. A comparative study was performed to investigate the role of Cl on the diffusion of Cu from CuSCN source layer into ILGAR deposited In2S3 layers. The Cl concentration was varied between 7 and 14 at.% by varying deposition parameters. The activation energies and exponential pre-factors for Cu diffusion in Cl-containing samples were between 0.70 to 0.78 eV and between 6.0 × 10−6 and 3.2 × 10−5 cm2/s. The activation energy in Cl-free ILGAR In2S3 layers was about three times less compared to the Cl-containing In2S3, and the pre-exponential constant six orders of magnitude lower. These values were comparable to those obtained from thermally evaporated In2S3 layers. The residual Cl-occupies S sites in the In2S3 structure leading to non-stoichiometry and hence different diffusion mechanism for Cu compared to stoichiometric Cl-free layers.
Kinosada, Yasutomi; Okuda, Yasuyuki (Mie Univ., Tsu (Japan). School of Medicine); Ono, Mototsugu (and others)
1993-02-01
We developed a new noninvasive technique to visualize the anatomical structure of the nerve fiber system in vivo, and named this technique magnetic resonance (MR) tractography and the acquired image an MR tractogram. MR tractography has two steps. One is to obtain diffusion-weighted images sensitized along axes appropriate for depicting the intended nerve fibers with anisotropic water diffusion MR imaging. The other is to extract the anatomical structure of the nerve fiber system from a series of diffusion-weighted images by the maximum intensity projection method. To examine the clinical usefulness of the proposed technique, many contiguous, thin (3 mm) coronal two-dimensional sections of the brain were acquired sequentially in normal volunteers and selected patients with paralyses, on a 1.5 Tesla MR system (Signa, GE) with an ECG-gated Stejskal-Tanner pulse sequence. The structure of the nerve fiber system of normal volunteers was almost the same as the anatomy. The tractograms of patients with paralyses clearly showed the degeneration of nerve fibers and were correlated with clinical symptoms. MR tractography showed great promise for the study of neuroanatomy and neuroradiology. (author).
Hsu, Po Jen; Lai, S K; Rapallo, Arnaldo
2014-03-14
Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit
Alman, David E.; Wilson, Rick D.; Davis, Daniel L.
2011-03-08
This invention relates to a method for producing components with internal architectures, and more particularly, this invention relates to a method for producing structures with microchannels via the use of diffusion bonding of stacked laminates. Specifically, the method involves weakly bonding a stack of laminates forming internal voids and channels with a first generally low uniaxial pressure and first temperature such that bonding at least between the asperites of opposing laminates occurs and pores are isolated in interfacial contact areas, followed by a second generally higher isostatic pressure and second temperature for final bonding. The method thereby allows fabrication of micro-channel devices such as heat exchangers, recuperators, heat-pumps, chemical separators, chemical reactors, fuel processing units, and combustors without limitation on the fin aspect ratio.
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
Weitao Li; Zhiyu Qian; Ting Li
2009-01-01
In order to improve the performance of reflectance diffuse optical imaging(rDOI),a novel polynomial geometry(PG)of optical fibers arrangement is proposed.Polynomial geometry is based on the hexagonal geometry(HG)and multicentered double-density(MD)mode.The overlapping sensitivity matrix,area ratio(AR),reconstruction image,two-absorber model,arid contrast-to-noise ratio(CNR)in different depths are used to evaluate the performance of PG.The other three geometries including HG,rectangular geometry(RG),and MD mode are also compared with PG.The deformation of the reconstruction images is evaluted by circular ratio(CR).The results prove that the proposed PG has high performance and minimum deformation in quality of reconstruction image in rDOI.
A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs.
Rosenbaum, Robert
2016-01-01
Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public.
Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach
Brannick, J; Qian, T; Sun, H
2014-01-01
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with the Onsager principle of least energy dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been car...
Electron microscopy observations of MgB 2 wire prepared by an internal Mg diffusion method
Shimada, Y.; Kubota, Y.; Hata, S.; Ikeda, K.; Nakashima, H.; Matsumoto, A.; Togano, K.; Kumakura, H.
2011-11-01
Microstructure in a high-density MgB2 wire fabricated by an internal Mg diffusion (IMD) process has been investigated by electron microscopy imaging and analysis at different scales. In the IMD process, a pure Mg rod was used as Mg source, and nanosized SiC powders were mixed with amorphous B powders. In the case of a heat treatment at 640 °C for 1 h carried out after rolling and drawing processes, the wire has two microstructural features that degrade critical current density: uncrystallized zones composed mainly of unreacted B and SiC powders, and cracks partly filled with course Mg2Si crystals. Those cracks were formed in the uncrystallized zones as well as in crystallized MgB2 zones. It indicate that the cracks formed by the mechanical milling and drawing remain after the heat treatment.
Zheng, Weisen; Ågren, John; Lu, Xiao-Gang; He, Yanlin; Li, Lin
2017-01-01
In order to simulate the diffusional phase transformations involving the fcc and bcc phases for microalloyed steels, the diffusion mobilities for fcc and bcc Fe-Mo and Fe-Mn-Mo alloys were experimentally investigated and critically assessed. The diffusion-couple technique was employed to extract the interdiffusion coefficients in Fe-Mo and Fe-Mn-Mo alloys with the Sauer-Freise and Whittle-Green methods. Based on the present experimental interdiffsivities, the mobility parameters for the fcc and bcc phases in the Fe-Mo and Fe-Mn-Mo systems were optimized using the traditional method. Simultaneously, a direct method was developed and utilized to directly fit mobilities to the diffusion profiles rather than the diffusivities in the present work. The satisfactory description of the diffusion behavior in the Fe-Mo and Fe-Mn-Mo systems has confirmed the reliability of the direct method. Particularly, the two sets of diffusion mobilities obtained with both methods could simulate the diffusion phenomenon between the fcc and bcc phases in the Fe-Mo and Fe-Mn-Mo systems successfully.
An efficient method for the analysis of the space-charge region of diffused junctions
Eltoukhy, A. A.; Roulston, D. J.
1982-08-01
An efficient numerical method is presented which gives the solution for electrostatic potential, carrier density and space charge density distribution of an asymetrical junction. This method is based on the numerical solution of Poisson's equation assuming a zero-current approximation. A comparison between the present method and two different methods is made.
Welland, M. J.; Tenuta, E.; Prudil, A. A.
2017-06-01
This article describes a phase-field model for an isothermal multicomponent, multiphase system which avoids implicit interfacial energy contributions by starting from a grand potential formulation. A method is developed for incorporating arbitrary forms of the equilibrium thermodynamic potentials in all phases to determine an explicit relationship between chemical potentials and species concentrations. The model incorporates variable densities between adjacent phases, defect migration, and dependence of internal pressure on object dimensions ranging from the macro- to nanoscale. A demonstrative simulation of an overpressurized nanoscopic intragranular bubble in nuclear fuel migrating to a grain boundary under kinetically limited vacancy diffusion is shown.
Numerical method for a 2D drift diffusion model arising in strained n-type MOSFET device
BENSEGUENI RACHIDA; LATRECHE SAIDA
2016-06-01
This paper reports the calculation of electron transport in metal oxide semiconductor field effects transistors (MOSFETs) with biaxially tensile strained silicon channel. The calculation is formulated based on two-dimensional drift diffusion model (DDM) including strain effects. The carrier mobility dependence on the lateral and vertical electric field model is especially consideredin the formulation. By using the model presented here, numerical method based on finite difference approach is performed. The obtained results show that the presence of biaxially tensile strain enhances the current in the devices.
Joe Harris
2017-07-01
Full Text Available Employing the widely used ammonium carbonate diffusion method, we demonstrate that altering an extrinsic parameter—desiccator size—which is rarely detailed in publications, can alter the route of crystallization. Hexagonally packed assemblies of spherical magnesium-calcium carbonate particles or spherulitic aragonitic particles can be selectively prepared from the same initial reaction solution by simply changing the internal volume of the desiccator, thereby changing the rate of carbonate addition and consequently precursor formation. This demonstrates that it is not merely the quantity of an additive which can control particle morphogenesis and phase selectivity, but control of other often ignored parameters are vital to ensure adequate reproducibility.
Yesim Cekin
2014-03-01
Full Text Available Aim: Acinetobacter species are amoung the most common two cause of infections isolated from patients of intensive care unit in our hospital. Doripenem which acts by inhibiting cell wall synthesis is resently introduced for use in our country is broad spectrum antibiotic belonging to carbapenems. There are many studies investigating the susceptibility of doripenem of Acinetobacter baumannii which is isolated as a cause of ventilatory associated pneumonia in the literature. We aimed to compare e-test and disc diffusion methods for doripenem susceptibility of acinetobacter baumannii strains as nosocomial infections Acinetobacter baumanni isolates detected as nosocomial infection. Material and Method:. Between January to December, 2009 a total of 94 Acinetobacter baumanni strains isolated from different clinical specimens from intensive care units have been studied for doripenem susceptibility by disc diffusion and E-test methods. Minimal inhibitory consantrations (MIC were accepted as; sensitive %u22641 %u03BCg/ml, intermadiate 2-4 %u03BCg/ml, resistant >4 %u03BCg/ml and diameters of inhibition zone with 10 µg disc; sensitive
Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2017-02-15
The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.
da Silva, Wilton Pereira; E Silva, Cleide M D P S
2014-09-01
Cooling of fruits and vegetables, immediately after the harvest, has been a widely used method for maximizing post-harvest life. In this paper, an optimization algorithm and a numerical solution are used to determine simultaneously the convective heat transfer coefficient, hH, and the thermal diffusivity, α, for an individual solid with cylindrical shape, using experimental data obtained during its cooling. To this end, the one-dimensional diffusion equation in cylindrical coordinates is discretized and numerically solved through the finite volume method, with a fully implicit formulation. This solution is coupled to an optimizer based on the inverse method, in which the chi-square referring to the fit of the numerical simulation to the experimental data is used as objective function. The optimizer coupled to the numerical solution was applied to experimental data relative to the cooling of a cucumber. The obtained results for α and hH were coherent with the values available in the literature. With the results obtained in the optimization process, the cooling kinetics of cucumbers was described in details.
An, Xue-Song; Song, Chun-Feng; Yuan, Hong-Fu; Xie, Jin-Chun; Li, Xiao-Yu
2013-11-01
A rapid nondestructive method for identifying intact foods containing trans fatty acids (TFA) using diffuse near infrared spectroscopy (NIR) was proposed in the present paper. The diffuse Fourier transform near infrared (FT-NIR) spectra of intact samples were collected by fiber probe, and the reference data of TFA content were determined by Chinese standard method GB/T 22110-2008 (gas chromatography (GC) method). In this work, all the samples were classified into two categories: foods with TFA and foods without TFA according to the TFA content of the foods. The identification models were established by different supervised pattern recognition algorithms including partial least square discriminant analysis (PLSDA), support vector machine (SVM), soft independent modeling of class analogy (SIMCA) and K-nearest neighbor method (KNN) etc. The performances of the established models employing different algorithms, data pretreatments and wavelength bands were compared. The results show that PLSDA and SVM algorithms have the ability of identifying intact foods with TFA, and the performance of identification models established by PLSDA is better than that of SVM. The PLSDA models established by the wavelength bands of 4 138-4 428, 5 507-5 963 and 7 794-8 960 cm(-1) which were pretreated with pretreatment methods of auto scaling and second derivative have the best performance. The correct classification percentages of its calibration and validation set are 96.4% and 88%, respectively, which indicates that this method is feasible for the identification of foods with TFA. This NIR method above mentioned has the characteristics of rapidness, non-destruction and easy operation due to the elimination of sample pretreatment such as oil extraction and grinding, therefore it is very suitable for on-line and in-site detection application.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
Q. Li
2013-02-01
Full Text Available The predictive analysis of natural disasters and their consequences is challenging because of uncertainties and incomplete data. The present article studies the use of variable fuzzy sets (VFS and improved information diffusion method (IIDM to construct a composite method. The proposed method aims to integrate multiple factors and quantification of uncertainties within a consistent system for catastrophic risk assessment. The fuzzy methodology is proposed in the area of flood disaster risk assessment to improve probability estimation. The purpose of the current study is to establish a fuzzy model to evaluate flood risk with incomplete data sets. The results of the example indicate that the methodology is effective and practical; thus, it has the potential to forecast the flood risk in flood risk management.
Evaluation of policy measures and methods to reduce diffuse water pollution
Lange, Ute; Doehler, Helmut; Eurich-Menden, Brigitte; Goemann, Horst; Jaeger, Peter; Kreins, Peter; Moeller, Christine; Prigge, Achim; Ristenpart, Erik; Schultheiss, Ute
2006-11-15
After considerable improvements of wastewater treatment, the loads of nutrients and plant protection agents, deriving from agriculture and heavy metals from urban drainages effluents as well as from erosion of agricultural soils are the main sources of nutrients and harmful substances in the loads of water bodies. The targets of the project were on the one hand the analysis of the political and legislative framework of both policy fields and on the other hand the evaluation of several, selected water protection measures with regard to their contribution to reduce water pollution, their economical effects as well as their political enforceability. The focus was laid on diffuse water pollution caused by agriculture. As main reasons for the diffuse water pollution stagnating at high level, the analysis of the political framework identified a lack of implementation discipline of water law, followed by the fragmented and insufficient water protection legislation itself and the previous design of the common agricultural policy slanted towards increasing productivity. For the future co-operation of agricultural and water authorities in implementation of their reforms and better definition of 'Good Farming Practice' are recommended. The second investigation level focuses on the analysis and assessment of selected measures to reduce the input of nutrients and plant protection agents. This part was done with help of calculation models focussing on the specific cost/benefit ratios for water protection. In detail the following measures have been analysed: decoupling of direct payments, coupling of livestock farming to areas, tax on mineral nitrogen, pesticide levy, buffer stripes alongside of watercourses, all season crop cover on arable land, soil cultivation procedures, changing the use of arable land, optimisation of animal nutrition, optimisation of manure storage and application, co-operative agreements, education and training. Co-operations and water protection
Gillet, Y.; Bissieux, Ch. [Reims Univ. - 51 (France). Laboratoire d`Energetique et d`Optique, Unite de Thermique et analyse Physique, UFR, Sciences Exactes et Naturelles
1999-06-01
The thermal behaviour of a sample submitted to a sinusoidal optical irradiation is modelled in axisymmetrical two-dimensional geometry. The solution by integral transforms and by Green`s functions or harmonic responses points out characteristic heat diffusion behaviours, according to the ratio between the thermal diffusion length and the dimensions of the beam or of the sample. With a view to parameter identification, these particular behaviours provide model reduction opportunities. The spherical behaviour, mainly involved with a micrometric excitation, contributes to the spatial resolution of the photothermal techniques. (authors) 20 refs.
Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Tokyo (Japan); Aoki, Shigeki [University of Tokyo, Department of Radiology, Tokyo (Japan); Sato, Noriko [National Center of Neurology and Psychiatry, Department of Radiology, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Nemoto, Kiyotaka [Ibaraki Prefectural Tomobe Hospital, Department of Psychiatry, Ibaraki (Japan); Arima, Kunimasa; Furuta, Nobuo [National Center of Neurology and Psychiatry, Department of Psychiatry, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Uno, Masatake [Yoshioka Rehabilitation Clinic, Department of Psychiatry, Tokyo (Japan); Hirai, Shigeo [Iruma Hirai Clinic, Department of Psychiatry, Saitama (Japan)
2008-04-15
Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P < 0.0001) in the UF of patients with AD than of controls. There was no significant difference in MD along the UF between the two groups. Intraobserver reliability (intraclass correlation coefficient) for the first and second measurement was r > 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)
A new, coupled transport-diffusion method for radiative transfer calculations
Wollaber, A. B.; Warsa, J. S. [Los Alamos National Laboratory, MS D409, P.O. Box 1663, Los Alamos NM, 87545 (United States)
2013-07-01
We derive and present a new frequency- and angle-integrated low-order system of equations designed to enhance the accuracy of a coupled, high-order (transport) solution of the thermal radiative transfer equations. In particular, our new low-order system is designed to use intensity-weighted opacities and anisotropic diffusion coefficients generated by a solution of the Implicit Monte Carlo (IMC) equations in order to predict the spatial dependence of the material temperature and radiation energies in the ensuing time cycle. The predicted temperature solution can then be exploited to generate appropriately time-centered opacities, specific heats, and Planck emission spectra for the upcoming IMC solution. Additionally, the relatively inexpensive solution of the low-order system can be iteratively solved to recommend an adaptive time step size before the IMC solution is computed. A test implementation has been implemented using existing software available from the Jayenne and Capsaicin projects at Los Alamos National Laboratory. We present initial results from a new driver code that has integrated these stochastic and deterministic software packages. (authors)
Tauriello, Gerardo; Koumoutsakos, Petros
2015-02-01
We present a comparative study of penalization and phase field methods for the solution of the diffusion equation in complex geometries embedded using simple Cartesian meshes. The two methods have been widely employed to solve partial differential equations in complex and moving geometries for applications ranging from solid and fluid mechanics to biology and geophysics. Their popularity is largely due to their discretization on Cartesian meshes thus avoiding the need to create body-fitted grids. At the same time, there are questions regarding their accuracy and it appears that the use of each one is confined by disciplinary boundaries. Here, we compare penalization and phase field methods to handle problems with Neumann and Robin boundary conditions. We discuss extensions for Dirichlet boundary conditions and in turn compare with methods that have been explicitly designed to handle Dirichlet boundary conditions. The accuracy of all methods is analyzed using one and two dimensional benchmark problems such as the flow induced by an oscillating wall and by a cylinder performing rotary oscillations. This comparative study provides information to decide which methods to consider for a given application and their incorporation in broader computational frameworks. We demonstrate that phase field methods are more accurate than penalization methods on problems with Neumann boundary conditions and we present an error analysis explaining this result.
Bernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equation
Jani, Mostafa; Babolian, Esmail
2016-01-01
In this paper, we develop a dual-Petrov-Galerkin method using Bernstein polynomials. The method is then implemented for the numerical simulation of the two-dimensional subdiffusion equation. The method is based on a finite difference discretization in time and a spectral method in space utilizing a suitable compact combinations of dual Bernstein basis as the test functions and the Bernstein polynomials as the trial ones. We derive the exact sparse operational matrix of differentiation for the dual Bernstein basis which provides a matrix-based approach for spatial discretization of the problem. It is also shown that the proposed method leads to banded linear systems. Finally some numerical examples are provided to show the efficiency and accuracy of the method.
Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions
Jianming Liu; Zhizhong Sun
2007-01-01
In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.
A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation
Evans, Thomas M [ORNL; Mosher, Scott W [ORNL; Slattery, Stuart [University of Wisconsin, Madison
2014-01-01
We present a novel synthetic-acceleration based Monte Carlo method for solving the equilibrium thermal radiation diusion equation in three 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 not only can our Monte Carlo method be an eective solver for sparse matrix systems, but also that it performs competitively with deterministic methods including preconditioned Conjugate Gradient while producing numerically identical results. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation
Jiang Wei
2016-01-01
Full Text Available The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewise polynomials that can not be used to solve differential equations directly because of lack of the smoothness. Moreover, new bases of reproducing kernel spaces are constructed. On the other hand, the existence of any ε-approximate solution is proved and an effective method for obtaining the ε-approximate solution is established. A numerical example is given to show the accuracy and effectiveness of theoretical results.
Rundle-Thiele, Dayle [Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia); Day, Bryan; Stringer, Brett [Brain Cancer Research Unit, Queensland Institute of Medical Research, Brisbane, Queensland (Australia); Fay, Michael [Department of Radiation Oncology, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Martin, Jennifer [Discipline of Clinical Pharmacology, School of Medicine and Public Health, University of Newcastle, Newcastle, New South Wales (Australia); Jeffree, Rosalind L [Department of Neurosurgery, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Thomas, Paul [Queensland PET Service, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Bell, Christopher [Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia); Salvado, Olivier [CSIRO Digital Productivity Flagship, CSIRO, Herston, Queensland (Australia); Gal, Yaniv [Centre for Medical Diagnostic Technologies in Queensland, University of Queensland, Brisbane, Queensland (Australia); Coulthard, Alan [Discipline of Medical Imaging, University of Queensland, St Lucia, Queensland (Australia); Department of Medical Imaging, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Crozier, Stuart [Centre for Medical Diagnostic Technologies in Queensland, University of Queensland, Brisbane, Queensland (Australia); Rose, Stephen, E-mail: stephen.rose@csiro.au [CSIRO Digital Productivity Flagship, CSIRO, Herston, Queensland (Australia); Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia)
2015-06-15
Accurate knowledge of O{sup 6}-methylguanine methyltransferase (MGMT) gene promoter subtype in patients with glioblastoma (GBM) is important for treatment. However, this test is not always available. Pre-operative diffusion MRI (dMRI) can be used to probe tumour biology using the apparent diffusion coefficient (ADC); however, its ability to act as a surrogate to predict MGMT status has shown mixed results. We investigated whether this was due to variations in the method used to analyse ADC. We undertook a retrospective study of 32 patients with GBM who had MGMT status measured. Matching pre-operative MRI data were used to calculate the ADC within contrast enhancing regions of tumour. The relationship between ADC and MGMT was examined using two published ADC methods. A strong trend between a measure of ‘minimum ADC’ and methylation status was seen. An elevated minimum ADC was more likely in the methylated compared to the unmethylated MGMT group (U = 56, P = 0.0561). In contrast, utilising a two-mixture model histogram approach, a significant reduction in mean measure of the ‘low ADC’ component within the histogram was associated with an MGMT promoter methylation subtype (P < 0.0246). This study shows that within the same patient cohort, the method selected to analyse ADC measures has a significant bearing on the use of that metric as a surrogate marker of MGMT status. Thus for dMRI data to be clinically useful, consistent methods of data analysis need to be established prior to establishing any relationship with genetic or epigenetic profiling.
Accary, A. [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires; Centre d' Etudes de Chimie Metallurgique du CNRS (France)
1959-07-01
Diffusion in {alpha} brasses has been investigated using methods involving the evaporation and the condensation of zinc. Having shown that at sufficiently high temperatures intergranular diffusion has no effect, it was then proved that the rate of evaporation or of condensation can only be defined if the mechanical treatment of the test piece before diffusion, the direction of the diffusion and the nature of the impurities present are also defined. The coefficient of diffusion D is then given by the equation D ({pi}/4t){rho}{sup 2}{sub 0} where t is the duration of the diffusion; {rho}{sub 0} is the extrapolated value of {rho} = ({delta}m)/({delta}C) for a zero value of the variation of concentration ({delta}m in is the change in weight of the test piece per unit surface; {delta}C is the difference between the concentration at the surface and the initial concentration of the test piece). This method has been used to study the effect of the direction of the diffusion on the coefficient of diffusion. The coefficient for diffusion which decreases the concentration of zinc is 5 times greater than that for diffusion which increases the quantity of zinc in the metal; an interpretation of this phenomena based on the mechanism of diffusion vacancies in the structure has been proposed. By means of micrographic investigation and by weighing it has been shown that the presence of certain impurities, such as phosphorous, arsenic, antimony, silicon, and aluminium can result in a marked increase of the rate of diffusion: the effect of these impurities on the coefficient of diffusion has been related to their valency and atomic weight. (author) [French] La diffusion dans les laitons {alpha} a ete etudiee au moyen des methodes d'evaporation et de condensafion du zinc. Apres avoir montre qu'aux temperatures suffisamment elevees, la diffusion intergranulaire ne jouait aucun role, l'auteur a prouve que la vitesse d'evaporation ou de condensation n'est definie
Chen, Qing; Zhang, Xiaobing; Zhang, Junfeng
2013-09-01
In spite of the increasing applications of the lattice Boltzmann method (LBM) in simulating various flow and transport systems in recent years, complex boundary conditions for the convection-diffusion and heat transfer processes in LBM have not been well addressed. In this paper, we propose an improved bounce-back method by using the midpoint concentration value to modify the bounced-back density distribution for LBM simulations of the concentration field. An accurate finite-difference scheme in the normal boundary direction has also been introduced for gradient boundary conditions. Compared with existing boundary methods, our method has a simple algorithm and can easily deal with boundaries with general geometries, motions, and surface conditions (the Dirichlet, Neumann, and mixed conditions). Carefully designed simulations are performed to examine the capacity and accuracy of this proposed boundary method. Simulation results are compared with those from theory and a representative boundary method, and an improved performance is observed. We have also simulated the effect of reference velocity on global accuracy to examine the performance of our model in preserving the fundamental Galilean invariance. These boundary treatments for concentration boundary conditions can be readily applied to other processes such as heat transfer systems.
Chen, Qing; Zhang, Xiaobing; Zhang, Junfeng
2013-09-01
In spite of the increasing applications of the lattice Boltzmann method (LBM) in simulating various flow and transport systems in recent years, complex boundary conditions for the convection-diffusion and heat transfer processes in LBM have not been well addressed. In this paper, we propose an improved bounce-back method by using the midpoint concentration value to modify the bounced-back density distribution for LBM simulations of the concentration field. An accurate finite-difference scheme in the normal boundary direction has also been introduced for gradient boundary conditions. Compared with existing boundary methods, our method has a simple algorithm and can easily deal with boundaries with general geometries, motions, and surface conditions (the Dirichlet, Neumann, and mixed conditions). Carefully designed simulations are performed to examine the capacity and accuracy of this proposed boundary method. Simulation results are compared with those from theory and a representative boundary method, and an improved performance is observed. We have also simulated the effect of reference velocity on global accuracy to examine the performance of our model in preserving the fundamental Galilean invariance. These boundary treatments for concentration boundary conditions can be readily applied to other processes such as heat transfer systems.
First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems
2014-03-01
fully-implicit steady solver with exact linearization , i.e., Newton’s method, for a second-order upwind scheme. The strategy taken here may be thought...second-order accuracy is achieved within a compact stencil, thus allowing the exact linearization with a sparse Jacobian matrix. The same is true for...a much larger num- ber of outer iterations as well if the exact linearization is not possible and Newton’s method cannot be constructed. Hence, the
Koshu, K; Hirota, S; Sonobe, M; Takahashi, S; Takaku, A; Saito, T; Ushijima, T
1987-11-01
The thermal diffusion method is known to be effective for making quantitative measurements of blood flow, but cannot be easily applied to problems concerning quantitative changes in blood flow. Carter et al. found that the thermal diffusion technique using a Peltier stack as the probe produced extremely stable recordings and was suitable for quantitative work. We made a more stable probe containing an air space and having a stainless cap that added weight. A stable recording of blood flow was then possible. For calibration of the probe, we used blood flow values measured by means of an electrolytic technique and the equation proposed by Carter et al. In the present study, we have shown that it is theoretically possible to perform the calibration even without obtaining data on blood flow after cardiac arrest. Experimentally, the validity of such calibration was confirmed. This technique for measuring blood flow should be applicable in various fields and its use in a clinical setting, particularly in the monitoring of blood flow during neurosurgical operations, can be expected.
Bucur, R.V.; Mecea, V.
1986-07-15
The diffusion and permeation rates of hydrogen through a metallized polymer membrane were measured by a non-equilibrium stripping potentiostatic method. A description of the gas membrane electrolyte permeation cell is given. The membrane was made of commercial polyethylene terephthalate (PET) (thickness, 7.3 x 10/sup -3/ cm) coated on the detection side with a thin palladium film (thickness, 800-1400 A). The membrane was first charged with hydrogen under a constant pressure at the entrance side until a linear concentration gradient was established across its thickness. Meanwhile, currents (stationary anodic current) were recorded corresponding to anodic removal of hydrogen from the detection side, while a constant anodic potential E/sub a/ was applied to the detection side. The E/sub a/ value corresponded to the potential of the palladium film free of hydrogen and was in the range 880 - 890 mV versus the reference hydrogen electrode in the same solution. Subsequently, hydrogen charging was ceased by replacing hydrogen with argon or air at the entrance side and the current corresponding to the stripping of hydrogen held within the membrane was recorded. The diffusion coefficient D was estimated from the stripping current-time curves, while the permeation coefficient P was estimated from the stationary anodic current within the range 283-333 K. The solubility coefficient S was calculated from the relation P=DS. Data on similar measurements carried out when hydrogen was electrolytically generated on Pd/PET/Pd membranes are also reported.
Wen-Zheng Wang
2015-01-01
Full Text Available Coal dust seriously threatens the safety and occupational health of coal mines. Numerical simulation research on the infrared radiation characteristics of diffused coal dust is carried out in fully mechanized working faces based on the optical monitoring problem of dust particles in mine atmospheric environments. The CFD method is applied to obtain the law of dust transport and distribution. Combined with Mie scattering model, the infrared radiation change characteristics and spectral selection of diffused coal dust particles are simulated and analyzed along the working face. The comparison results show the following: the attenuation and scattering characteristics of mine dust particles system are first enhanced, and then they weaken as the distance from dust source increases. The infrared attenuation of mine dust at the center of the vertical cross-section is generally greater than that at the roof and floor in the same location. The dispersion of mine dust directly determines the attenuation contribution of respirable dust to total dust. Moreover, the infrared absorption effect of functional groups in coal causes the infrared attenuation effect of coal dust to have obvious optical selectivity along the roadway, the existing optical “window.”
Nachabé, Rami; Evers, Daniel J.; Hendriks, Benno H. W.; Lucassen, Gerald W.; van der Voort, Marjolein; Rutgers, Emiel J.; Peeters, Marie-Jeanne Vrancken; van der Hage, Jos A.; Oldenburg, Hester S.; Wesseling, Jelle; Ruers, Theo J. M.
2011-08-01
We report on the use of diffuse optical spectroscopy analysis of breast spectra acquired in the wavelength range from 500 to 1600 nm with a fiber optic probe. A total of 102 ex vivo samples of five different breast tissue types, namely adipose, glandular, fibroadenoma, invasive carcinoma, and ductal carcinoma in situ from 52 patients were measured. A model deriving from the diffusion theory was applied to the measured spectra in order to extract clinically relevant parameters such as blood, water, lipid, and collagen volume fractions, β-carotene concentration, average vessels radius, reduced scattering amplitude, Mie slope, and Mie-to-total scattering fraction. Based on a classification and regression tree algorithm applied to the derived parameters, a sensitivity-specificity of 98%-99%, 84%-95%, 81%-98%, 91%-95%, and 83%-99% were obtained for discrimination of adipose, glandular, fibroadenoma, invasive carcinoma, and ductal carcinoma in situ, respectively; and a multiple classes overall diagnostic performance of 94%. Sensitivity-specificity values obtained for discriminating malignant from nonmalignant tissue were compared to existing reported studies by applying the different classification methods that were used in each of these studies. Furthermore, in these reported studies, either lipid or β-carotene was considered as adipose tissue precursors. We estimate both chromophore concentrations and demonstrate that lipid is a better discriminator for adipose tissue than β-carotene.
Saha, S; Saha, S K; Hossain, M A; Paul, S K; Gomes, R R; Imtiaz, M; Islam, M M; Nahar, H; Begum, S A; Mirza, T T
2016-01-01
The study was performed to determine the antibacterial effect of aqueous extract of garlic (Allium sativum) against standard strain of Escherichia coli ATCC 25922. An interventional study was conducted in Department of Pharmacology and Therapeutics in collaboration with Department of Microbiology, Mymensingh Medical College, Mymensingh. Antibacterial effect of AGE was determined by disc diffusion method. Sensitivity of AGE determined in disc diffusion and the zone of inhibition (ZOI) was 4 mm, 10 mm and 20 mm at 25 μg/10 μl, 50 μg/10 μl and 100 μg/10 μl concentrations respectively. From the findings it is clearly determined the extract has definite antibacterial effect upon Escherichia coli. Further studies are required to detect and isolate the active ingredients present in the Garlic extract as well as detail steps of mechanism responsible for antibacterial effect. Then their effects against the studied organism should be studied in vivo separately and its toxicity profile should also be taken into account.
Nadano, D; Yasuda, T; Kishi, K
1993-03-01
In the single radial enzyme-diffusion (SRED) method for assay of deoxyribonuclease I, a precisely measured volume of the enzyme solution is dispensed into a circular well in an agarose gel layer in which DNA and ethidium bromide are uniformly distributed. A circular dark zone is formed as the enzyme diffuses from the well radially into the gel and digests substrate DNA. The diameter of the dark circle of hydrolyzed DNA increases in size with time and correlates linearly with the amount of enzyme applied to the well. Thus, the SRED can be used for quantitation of deoxyribonuclease I with a limit of detection of 2 x 10(-6) unit. This corresponds to 1 pg of purified urine deoxyribonuclease I. We measured the deoxyribonuclease I activity of 17 different human tissues and body fluids from healthy donors. Urine samples showed the greatest activity, 6.0 +/- 2.2 kilo-units/g protein (mean +/- SD). Serum deoxyribonuclease I activity was 4.4 +/- 1.8 units/L.
Pfaffmann, Lukas; Birkenmaier, Claudia; Müller, Marcus; Bauer, Werner; Mitsch, Tim; Feinauer, Julian; Krämer, Yvonne; Scheiba, Frieder; Hintennach, Andreas; Schleid, Thomas; Schmidt, Volker; Ehrenberg, Helmut
2016-03-01
Negative electrodes of lithium-ion batteries generally consist of graphite-based active materials. In order to realize batteries with a high current density and therefore accelerated charging processes, the intercalation of lithium and the diffusion processes of these carbonaceous materials must be understood. In this paper, we visualized the electrochemical active surface area for three different anode materials using a novel OsO4 staining method in combination with scanning electron microscopy techniques. The diffusion behavior of these three anode materials is investigated by potentiostatic intermittent titration technique measurements. From those we determine the diffusion coefficient with and without consideration of the electrochemical active surface area.
Mason, Harris E. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Walsh, Stuart D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); DuFrane, Wyatt L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carroll, Susan A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2014-06-17
The development of accurate, predictive models for use in determining wellbore integrity requires detailed information about the chemical and mechanical changes occurring in hardened Portland cements. X-ray computed tomography (XRCT) provides a method that can nondestructively probe these changes in three dimensions. Here, we describe a method for extracting subvoxel mineralogical and chemical information from synchrotron XRCT images by combining advanced image segmentation with geochemical models of cement alteration. The method relies on determining “effective linear activity coefficients” (ELAC) for the white light source to generate calibration curves that relate the image grayscales to material composition. The resulting data set supports the modeling of cement alteration by CO_{2}-rich brine with discrete increases in calcium concentration at reaction boundaries. The results of these XRCT analyses can be used to further improve coupled geochemical and mechanical models of cement alteration in the wellbore environment.
Mirjalili, Shahab; Ivey, Christopher Blake; Mani, Ali
2016-11-01
The diffuse interface(DI) and volume of fluid(VOF) methods are mass conserving front capturing schemes which can handle large interfacial topology changes in realistic two phase flows. The DI method is a conservative phase field method that tracks an interface with finite thickness spread over a few cells and does not require reinitialization. In addition to having the desirable properties of level set methods for naturally capturing curvature and surface tension forces, the model conserves mass continuously and discretely. The VOF method, which tracks the fractional tagged volume in a cell, is discretely conservative by requiring costly geometric reconstructions of the interface and the fluxes. Both methods however, suffer from inaccuracies in calculation of curvature and surface tension forces. We present a quantitative comparison of these methods in terms of their accuracy, convergence rate, memory, and computational cost using canonical 2D two-phase test cases: damped surface wave, oscillating drop, equilibrium static drop, and dense moving drop. We further compared the models in their ability to handle thin films by looking at the impact of a water drop onto a deep water pool. Considering these results, we suggest qualitative guidelines for using the DI and VOF methods. Supported by ONR.
Jianyin Xiong
Full Text Available The diffusion coefficient (D(m and material/air partition coefficient (K are two key parameters characterizing the formaldehyde and volatile organic compounds (VOC sorption behavior in building materials. By virtue of the sorption process in airtight chamber, this paper proposes a novel method to measure the two key parameters, as well as the convective mass transfer coefficient (h(m. Compared to traditional methods, it has the following merits: (1 the K, D(m and h(m can be simultaneously obtained, thus is convenient to use; (2 it is time-saving, just one sorption process in airtight chamber is required; (3 the determination of h(m is based on the formaldehyde and VOC concentration data in the test chamber rather than the generally used empirical correlations obtained from the heat and mass transfer analogy, thus is more accurate and can be regarded as a significant improvement. The present method is applied to measure the three parameters by treating the experimental data in the literature, and good results are obtained, which validates the effectiveness of the method. Our new method also provides a potential pathway for measuring h(m of semi-volatile organic compounds (SVOC by using that of VOC.
A method to evaluate the diffusion rate of drugs from a microdialysis probe through brain tissue
Westerink, B.H.C.; de Vries, J.B
2001-01-01
For interpretation of microdialysis experiments in which compounds are applied retrodialysis, it is important to have information about the migration rate of the infused compounds. Here we describe a dual-probe microdialysis method that can be used to evaluate the penetration rate of the infused dru
A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation
2013-05-01
examples of nonstan- dard discretizations include higher order continuity basis functions (splines and NURBS [34]), and discontinuous functions (DG...analysis: CAD, finite elements, NURBS , exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39–41):4135
A method for polycrystalline silicon delineation applicable to a double-diffused MOS transistor
Halsor, J. L.; Lin, H. C.
1974-01-01
Method is simple and eliminates requirement for unreliable special etchants. Structure is graded in resistivity to prevent punch-through and has very narrow channel length to increase frequency response. Contacts are on top to permit planar integrated circuit structure. Polycrystalline shield will prevent creation of inversion layer in isolated region.
1983-02-01
Anthony Ralston and Herbert S. Wilf. New York: John Wiley and Sons, Inc., 95-115, 1967. 15. Patankar, Suhas V.. Numerical Heat Transfer and Fluid Flow...Series in Computational Methods in Mechanics and Thermal Sciences. New York: McGraw- Hill Book Company, 1980. 16. Patankar, Suhas V. and B. R
D. Spivakovskaya; A. W. Heemink; Deleersnijder, Eric
2007-01-01
Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward (I) over cap to calculus can be used for these problems. This model was proposed by LaBolle ...
Lee, Eun Gyung; Magrm, Rana; Kusti, Mohannad; Kashon, Michael L; Guffey, Steven; Costas, Michelle M; Boykin, Carie J; Harper, Martin
2017-01-01
This study was to determine occupational exposures to formaldehyde and to compare concentrations of formaldehyde obtained by active and passive sampling methods. In one pathology and one histology laboratories, exposure measurements were collected with sets of active air samplers (Supelco LpDNPH tubes) and passive badges (ChemDisk Aldehyde Monitor 571). Sixty-six sample pairs (49 personal and 17 area) were collected and analyzed by NIOSH NMAM 2016 for active samples and OSHA Method 1007 (using the manufacturer's updated uptake rate) for passive samples. All active and passive 8-hr time-weighted average (TWA) measurements showed compliance with the OSHA permissible exposure limit (PEL-0.75 ppm) except for one passive measurement, whereas 78% for the active and 88% for the passive samples exceeded the NIOSH recommended exposure limit (REL-0.016 ppm). Overall, 73% of the passive samples showed higher concentrations than the active samples and a statistical test indicated disagreement between two methods for all data and for data without outliers. The OSHA Method cautions that passive samplers should not be used for sampling situations involving formalin solutions because of low concentration estimates in the presence of reaction products of formaldehyde and methanol (a formalin additive). However, this situation was not observed, perhaps because the formalin solutions used in these laboratories included much less methanol (3%) than those tested in the OSHA Method (up to 15%). The passive samplers in general overestimated concentrations compared to the active method, which is prudent for demonstrating compliance with an occupational exposure limit, but occasional large differences may be a result of collecting aerosolized droplets or splashes on the face of the samplers. In the situations examined in this study the passive sampler generally produces higher results than the active sampler so that a body of results from passive samplers demonstrating compliance with the
Cui, Fude; Yang, Mingshi; Jiang, Yanyan
2003-01-01
To improve the bioavailability of nitrendipine microspheres, a sustained-release microspheres having solid dispersion structure were prepared in one step. Two types of polymer, i.e. solid dispersing and sustained-release polymers, were employed to prepare the microspheres by the spherical...... crystallization technique, i.e. quasi-emulsion solvent diffusion method. The factors of effect on micromeritic properties and release profiles of the resultant microspheres were investigated. And the bioavailability of nitrendipine microspheres was evaluated in six healthy dogs. The results showed...... that the particle size of microspheres was determined mainly by the agitation speed. The dissolution rate of nitrendipine from microspheres was enhanced significantly with increasing the amount of dispersing agents, and sustained by adding retarding agents. The release rate of microspheres could be controlled...
Risk assessment of failure modes of gas diffuser liner of V94.2 siemens gas turbine by FMEA method
Mirzaei Rafsanjani, H.; Rezaei Nasab, A.
2012-05-01
Failure of welding connection of gas diffuser liner and exhaust casing is one of the failure modes of V94.2 gas turbines which are happened in some power plants. This defect is one of the uncertainties of customers when they want to accept the final commissioning of this product. According to this, the risk priority of this failure evaluated by failure modes and effect analysis (FMEA) method to find out whether this failure is catastrophic for turbine performance and is harmful for humans. By using history of 110 gas turbines of this model which are used in some power plants, the severity number, occurrence number and detection number of failure determined and consequently the Risk Priority Number (RPN) of failure determined. Finally, critically matrix of potential failures is created and illustrated that failure modes are located in safe zone.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
Global/Local iterative homogenization methods for neutron diffusion nodal theory
Kim, Hark Rho
1994-02-15
The objective of this research is to develop efficient spatial homogenization methods for coarse-mesh nodal analysis of the light water reactors in which the reference solutions are not known. The methods developed are the global/local iterative procedures, including procedures based on variational principles. The nodal expansion method (NEM) with generalized equivalence theory is employed in coarse-mesh nodal analysis. The finite difference method (FDM) is used in fine-mesh local assembly calculation. To achieve fast and stable convergence in local assembly calculation, the mixed boundary condition is imposed at the assembly surface, where the surface flux is modulated. The assembly wise fundamental mode eigenfunction is used as the modulating function. Two direct methods are developed for the global/local iterative homogenization : G{sub 1} and G{sub 2}·G{sub 1} procedure is based on the rigorous definition of the flux-weighted constants (FWCs) and G{sub 2} procedure preserves the reaction rate ratio. Three variational principles are also proposed for the assembly homogenization. The basic form is inferred from the Pomraning's variational principle. Since the two variational methods, F{sub 0} and F{sub 2}, are based on the ratio of reaction rates, these are insensitive to the amplitude of the flux and hence they are of the Lagrangian form. On the while, the other variational principle F{sub 1} is based on the reaction rate and this requires a normalization due to its property that is sensitive to the amplitude of the flux. Thus the resulting form of F{sub 1} becomes the Swinger type. The homogenization methods developed were applied to the LWR problems. In the PWR problems we treated, there is no strong need for a global/local iterative homogenization procedure, since the heterogeneity between the fuel assemblies is relatively weak. Using the assembly discontinuity factor(ADF), the nodal analysis was improved with reasonable accuracy, while no significant
Hansen, Carl L.; Skordalakes, Emmanuel; Berger, James M.; Quake, Stephen R.
2002-01-01
Producing robust and scalable fluid metering in a microfluidic device is a challenging problem. We developed a scheme for metering fluids on the picoliter scale that is scalable to highly integrated parallel architectures and is independent of the properties of the working fluid. We demonstrated the power of this method by fabricating and testing a microfluidic chip for rapid screening of protein crystallization conditions, a major hurdle in structural biology efforts. The chip has 480 active...
Szałapak Jerzy
2015-12-01
Full Text Available The Low Temperature Joining Technique (LTJT using silver compounds enables to significantly increase the thermal conductivity between joined elements, which is much higher than for soldered joints. However, it also makes difficult to measure the thermal conductivity of the joint. The Laser Flash Analysis (LFA is a non-intrusive method of measuring the temperature rise of one surface of a specimen after excitation with a laser pulse of its other surface. The main limitation of the LFA method is its standard computer software, which assumes the dimensions of a bonded component to be similar to those of the substrate, because it uses the standard Parker’s formula dedicated for one-dimensional heat flow. In the paper a special design of measured specimen was proposed, consisting of two copper plates of different size joined with the sintered silver layer. It was shown that heat properties of these specimens can also be measured after modifying the LFA method. The authors adapted these specimens by masking the false heat signal sourced from the uncovered plate area. Another adaptation was introducing a correcting factor of the heat travel distance, which was calculated with heat-flow simulations and placed into the Parker’s formula. The heat-flow simulated data were compared with the real LFA measurement results, which enabled estimation of the joint properties, e.g. its porosity.
Wang, Lulu; Wang, Liya; Han, Lei; Yin, Weijing
2015-01-01
To identify the causative fungi of fungal keratitis, test their susceptibility to antifungal agents with the disk diffusion method and study the relationship between the organisms, the inhibition zones and the clinical outcomes. 535 patients with fungal keratitis in one eye were included in this study. Pathogenic fungi were isolated by corneal scraping, identified by fungal cultivation and subjected to drug sensitivity tests conducted with the disk diffusion method. The patients were treated initially with voriconazole, terbinafine and natamycin eye drops for one week. Further treatment continued using the most effective drug according to the drug sensitivity results. The patients were followed up every week until three months after cured. The inhibition zones of fungi cultured with voriconazole, terbinafine and natamycin were compared. The relationship between inhibition zones and organism, organism and treatment results measure, and each treatment results measure and inhibition zones were evaluated. Of 535 patients, 53.84%, 19.25% and 26.91% were infected with Aspergillus, Fusarium and other fungi, respectively. Keratitis patients infected with Aspergillus keratitis had the worst outcome. The size of the inhibition zones of Aspergillus spp., Fusarium spp. and other fungal genera differed significantly in response to voriconazole, terbinafine and natamycin. The inhibition zone associated with natamycin correlated significantly with the clinical outcome of fungal keratitis (OR = 0.925), but no other such correlations were found for the other drugs tested. Aspergillus and Fusarium were the predominant pathogenic genera causing fungal keratitis in our patients. Among the causative fungi, infections due to Aspergillus spp. were associated with the worst outcomes. The inhibition zones of fungal isolates in response to natamycin significantly correlated with the treatment outcomes of keratitis. Specifically, the smaller the natamycin inhibition zone, the lower the
Anandh, K R; Sujatha, C M; Ramakrishnan, S
2015-01-01
Alzheimers Disease (AD) is a common form of dementia that affects gray and white matter structures of brain. Manifestation of AD leads to cognitive deficits such as memory impairment problems, ability to think and difficulties in performing day to day activities. Although the etiology of this disease is unclear, imaging biomarkers are highly useful in the early diagnosis of AD. Magnetic resonance imaging is an indispensible non-invasive imaging modality that reflects both the geometry and pathology of the brain. Corpus Callosum (CC) is the largest white matter structure as well as the main inter-hemispheric fiber connection that undergoes regional alterations due to AD. Therefore, segmentation and feature extraction are predominantly essential to characterize the CC atrophy. In this work, an attempt has been made to segment CC using edge based level set method. Prior to segmentation, the images are pre-processed using Total Variation (TV) based diffusion filtering to enhance the edge information. Shape based geometric features are extracted from the segmented CC images to analyze the CC atrophy. Results show that the edge based level set method is able to segment CC in both the normal and AD images. TV based diffusion filtering has performed uniform region specific smoothing thereby preserving the texture and small scale details of the image. Consequently, the edge map of CC in both the normal and AD are apparently sharp and distinct with continuous boundaries. This facilitates the final contour to correctly segment CC from the nearby structures. The extracted geometric features such as area, perimeter and minor axis are found to have the percentage difference of 5.97%, 22.22% and 9.52% respectively in the demarcation of AD subjects. As callosal atrophy is significant in the diagnosis of AD, this study seems to be clinically useful.
He, Ping; Ghoniem, Ahmed F.
2017-03-01
Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder-Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.
Lozovoi, A.; Mattea, C.; Herrmann, A.; Rössler, E. A.; Stapf, S.; Fatkullin, N.
2016-06-01
A simple and fast method for the investigation of segmental diffusion in high molar mass polymer melts is presented. The method is based on a special function, called proton dipolar-correlation build-up function, which is constructed from Hahn Echo signals measured at times t and t/2. The initial rise of this function contains additive contributions from both inter- and intramolecular magnetic dipole-dipole interactions. The intermolecular contribution depends on the relative mean squared displacements (MSDs) of polymer segments from different macromolecules, while the intramolecular part reflects segmental reorientations. Separation of both contributions via isotope dilution provides access to segmental displacements in polymer melts at millisecond range, which is hardly accessible by other methods. The feasibility of the method is illustrated by investigating protonated and deuterated polybutadiene melts with molecular mass 196 000 g/mol at different temperatures. The observed exponent of the power law of the segmental MSD is close to 0.32 ± 0.03 at times when the root MSD is in between 45 Å and 75 Å, and the intermolecular proton dipole-dipole contribution to the total proton Hahn Echo NMR signal is larger than 50% and increases with time.
A two-zone method with an enhanced accuracy for a numerical solution of the diffusion equation
Cheon, Jin-Sik; Koo, Yang-Hyun; Lee, Byung-Ho; Oh, Je-Yong; Sohn, Dong-Seong
2006-12-01
A variational principle is applied to the diffusion equation to numerically obtain the fission gas release from a spherical grain. The two-zone method, originally proposed by Matthews and Wood, is modified to overcome its insufficient accuracy for a low release. The results of the variational approaches are examined by observing the gas concentration along the grain radius. At the early stage, the concentration near the grain boundary is higher than that at the inner points of the grain in the cases of the two-zone method as well as the finite element analysis with the number of the elements at as many as 10. The accuracy of the two-zone method is considerably enhanced by relocating the nodal points of the two zones. The trial functions are derived as a function of the released fraction. During the calculations, the number of degrees of freedom needs to be reduced to guarantee physically admissible concentration profiles. Numerical verifications are performed extensively. By taking a computational time comparable to the algorithm by Forsberg and Massih, the present method provides a solution with reasonable accuracy in the whole range of the released fraction.
Chunye Gong
2014-01-01
Full Text Available It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE with iterative implicit finite difference method is O(MxMyN2. In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.
2014-05-01
We present a computational method for solving the coupled problem of chemical transport in a fluid (blood) with binding/unbinding of the chemical to/from cellular (platelet) surfaces in contact with the fluid, and with transport of the chemical on the cellular surfaces. The overall framework is the Augmented Forcing Point Method (AFM) (\\emph{L. Yao and A.L. Fogelson, Simulations of chemical transport and reaction in a suspension of cells I: An augmented forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for solving fluid-phase transport in a region outside of a collection of cells suspended in the fluid. We introduce a novel Radial Basis Function-Finite Difference (RBF-FD) method to solve reaction-diffusion equations on the surface of each of a collection of 2D stationary platelets suspended in blood. Parametric RBFs are used to represent the geometry of the platelets and give accurate geometric information needed for the RBF-FD method. Symmetric Hermite-RBF interpolants are used for enforcing the boundary conditions on the fluid-phase chemical concentration, and their use removes a significant limitation of the original AFM. The efficacy of the new methods are shown through a series of numerical experiments; in particular, second order convergence for the coupled problem is demonstrated.
Hansen, Carl L.; Skordalakes, Emmanuel; Berger, James M.; Quake, Stephen R.
2002-12-01
Producing robust and scalable fluid metering in a microfluidic device is a challenging problem. We developed a scheme for metering fluids on the picoliter scale that is scalable to highly integrated parallel architectures and is independent of the properties of the working fluid. We demonstrated the power of this method by fabricating and testing a microfluidic chip for rapid screening of protein crystallization conditions, a major hurdle in structural biology efforts. The chip has 480 active valves and performs 144 parallel reactions, each of which uses only 10 nl of protein sample. The properties of microfluidic mixing allow an efficient kinetic trajectory for crystallization, and the microfluidic device outperforms conventional techniques by detecting more crystallization conditions while using 2 orders of magnitude less protein sample. We demonstrate that diffraction-quality crystals may be grown and harvested from such nanoliter-volume reactions.
Dinesh Kumar Jain
2010-03-01
Full Text Available Microballoons floatable on JPXIII No.1 solution were developed as a dosage formcapable of floating in the stomach. Microballoons were prepared by the emulsion solventdiffusion method using enteric acrylic and other polymers with drug in a mixture ofdichloromethane and ethanol. It was found that preparation temperature determined theformation of cavity inside the microsphere and the surface smoothness, determining thefloatability and the drug release rate of the microballoons. The correlation between thebuoyancy of microballoons and their physical properties, e.g. apparent density androundness of microballoons were elucidated. The drug loading efficiency ofmicroballoons was also determined. The optimum loading amount of metformin in themicroballoons was found to impart ideal floatable properties to the microballoons. Byfitting the data into zero order, first order and Highuchi model it was concluded that therelease followed zero order release.
Hansen, Carl L.; Skordalakes, Emmanuel; Berger, James M.; Quake, Stephen R.
2002-01-01
Producing robust and scalable fluid metering in a microfluidic device is a challenging problem. We developed a scheme for metering fluids on the picoliter scale that is scalable to highly integrated parallel architectures and is independent of the properties of the working fluid. We demonstrated the power of this method by fabricating and testing a microfluidic chip for rapid screening of protein crystallization conditions, a major hurdle in structural biology efforts. The chip has 480 active valves and performs 144 parallel reactions, each of which uses only 10 nl of protein sample. The properties of microfluidic mixing allow an efficient kinetic trajectory for crystallization, and the microfluidic device outperforms conventional techniques by detecting more crystallization conditions while using 2 orders of magnitude less protein sample. We demonstrate that diffraction-quality crystals may be grown and harvested from such nanoliter-volume reactions. PMID:12486223
Krajnc, Andraž; Bueken, Bart; De Vos, Dirk; Mali, Gregor
2017-06-01
Nuclear magnetic resonance spectroscopy combined with modeling represents a powerful tool for the structural analysis of heterogeneous materials. In this contribution we describe an upgraded method, particularly suited for the structural analysis of mixed-linker metal-organic framework materials, which is based on the measurement and modeling of proton spin diffusion among constituents. We tested the method on a UiO-66-type metal-organic material, in which the organic building units were 1,4-benzenedicarboxylate and trans-1,4-cyclohexanedicarboxylate anions distributed within the framework in an unknown manner. We showed that resolution of the signals of different building units could be significantly enhanced by the carbon-detected version of the proton spin-diffusion measurement. Because this kind of measurement is much more time consuming than the proton-detected measurement and because one has to carry out several two-dimensional measurements to extract spin-diffusion curves, we inspected the possibility of reducing the number of such measurements. This could be done by limiting the analysis to short mixing times, for which, as shown in this contribution, linear approximation is valid. When working in the linear regime, only a few experimental points are needed to determine the slope of spin-diffusion curves. Usage of short spin-diffusion mixing times significantly shortened the total measurement time and also markedly simplified the modeling of spin-diffusion curves.
Haydari, M.; Moksin, Mohd Maarof; Yunus, W. Mahmood M.; Grozescu, Ionel Valeriu; Hamadneh, I.; Halim, S. A.
2004-10-01
We report the effect of sintering time on thermal diffusivity of BSCCO (Bi-Pb-Sr-Ca-Cu-O) superconductors doped with Sm with different concentration. The superconductor samples were sintered for 24, 48 and 100 hours respectively at 850 Celsius. Thermal diffusivity measurement was carried out at 80 - 300 K by using photoflash technique. The sintering time was found indirectly affect the thermal diffusivity in the way it influenced the grain size and grain alignment.
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Spectral decomposition in advection-diffusion analysis by finite element methods
Nickell, R.E.; Gartling, D.K.; Strang, G.
1978-08-11
In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies.
Dreij, Kristian; Chaudhry, Qasim Ali; Jernström, Bengt; Morgenstern, Ralf; Hanke, Michael
2011-01-01
A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.
Kristian Dreij
Full Text Available A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.
Hombach, Michael; Maurer, Florian P; Pfiffner, Tamara; Böttger, Erik C; Furrer, Reinhard
2015-12-01
Parameters like zone reading, inoculum density, and plate streaking influence the precision and accuracy of disk diffusion antibiotic susceptibility testing (AST). While improved reading precision has been demonstrated using automated imaging systems, standardization of the inoculum and of plate streaking have not been systematically investigated yet. This study analyzed whether photometrically controlled inoculum preparation and/or automated inoculation could further improve the standardization of disk diffusion. Suspensions of Escherichia coli ATCC 25922 and Staphylococcus aureus ATCC 29213 of 0.5 McFarland standard were prepared by 10 operators using both visual comparison to turbidity standards and a Densichek photometer (bioMérieux), and the resulting CFU counts were determined. Furthermore, eight experienced operators each inoculated 10 Mueller-Hinton agar plates using a single 0.5 McFarland standard bacterial suspension of E. coli ATCC 25922 using regular cotton swabs, dry flocked swabs (Copan, Brescia, Italy), or an automated streaking device (BD-Kiestra, Drachten, Netherlands). The mean CFU counts obtained from 0.5 McFarland standard E. coli ATCC 25922 suspensions were significantly different for suspensions prepared by eye and by Densichek (P counts that were closer to the CLSI/EUCAST target of 10(8) CFU/ml than those resulting from Densichek preparation. No significant differences in the standard deviations of the CFU counts were observed. The interoperator differences in standard deviations when dry flocked swabs were used decreased significantly compared to the differences when regular cotton swabs were used, whereas the mean of the standard deviations of all operators together was not significantly altered. In contrast, automated streaking significantly reduced both interoperator differences, i.e., the individual standard deviations, compared to the standard deviations for the manual method, and the mean of the standard deviations of all operators
Ji, Zhi [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad 2001, Col. Chamilpa, 62210 Cuernavaca, Morelos (Mexico); Contreras-Torres, Flavio F., E-mail: flavioc@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, DF (Mexico); Jalbout, Abraham F.; Ramírez-Treviño, Alberto [Instituto Tecnológico de Estudios Superiores de Cajeme, Ciudad Obregon, Sonora (Mexico)
2013-11-15
The adsorption of Li atom on graphene is examined using density functional theory methods. Three different adsorption sites are considered, including the on top of a carbon atom (OT), on top of a C-C bond (Bri), and on top of a hexagon (Hol), as well as Li adsorbed at different coverage. The Hol site is found to be the most stable, followed by the Bri and OT sites. The order of stabilization is independent of coverage. The localization of Li–graphene interaction at all sites has reverse order with stabilization. The localization will cause different repulsive interaction between Li atoms which is believed to take responsibility for the difference between the charge transfer order and adsorption energy order of Li adsorption at all possible sites. Repulsive interaction also causes the decreasing of adsorption energies of Li at Hol site with increasing coverage, but the corresponding influence is bigger at low coverage range (0.020–0.056 monolayers) than that at high coverage range (0.056–0.250 monolayers). The trend of charge transfer and dipole moment with increasing coverage is also in agreement with that of adsorption energy. It is also found that the distance of Li above graphene will increase with increasing coverage, but a so-called “zigzag” curve appears, which exhibits an oscillatory behavior as a function of increasing coverage. The diffusion of Li atom on graphene is also studied. Li atom migrates from a Hol site to a neighboring Hol site through the Bri site between them is found to be the minimum energy path. Within the studied coverage range, the diffusion barrier decreases with increasing coverage which can be ascribed to the phenomenon of different repulsion interactions when Li atom adsorbs at different sites. The increasing coverage amplified the phenomenon.
Ji, Zhi; Contreras-Torres, Flavio F.; Jalbout, Abraham F.; Ramírez-Treviño, Alberto
2013-11-01
The adsorption of Li atom on graphene is examined using density functional theory methods. Three different adsorption sites are considered, including the on top of a carbon atom (OT), on top of a CC bond (Bri), and on top of a hexagon (Hol), as well as Li adsorbed at different coverage. The Hol site is found to be the most stable, followed by the Bri and OT sites. The order of stabilization is independent of coverage. The localization of Li-graphene interaction at all sites has reverse order with stabilization. The localization will cause different repulsive interaction between Li atoms which is believed to take responsibility for the difference between the charge transfer order and adsorption energy order of Li adsorption at all possible sites. Repulsive interaction also causes the decreasing of adsorption energies of Li at Hol site with increasing coverage, but the corresponding influence is bigger at low coverage range (0.020-0.056 monolayers) than that at high coverage range (0.056-0.250 monolayers). The trend of charge transfer and dipole moment with increasing coverage is also in agreement with that of adsorption energy. It is also found that the distance of Li above graphene will increase with increasing coverage, but a so-called "zigzag" curve appears, which exhibits an oscillatory behavior as a function of increasing coverage. The diffusion of Li atom on graphene is also studied. Li atom migrates from a Hol site to a neighboring Hol site through the Bri site between them is found to be the minimum energy path. Within the studied coverage range, the diffusion barrier decreases with increasing coverage which can be ascribed to the phenomenon of different repulsion interactions when Li atom adsorbs at different sites. The increasing coverage amplified the phenomenon.
Diffuse sources of human fecal pollution allow for the direct discharge of waste into receiving waters with minimal or no treatment. Traditional culture-based methods are commonly used to characterize fecal pollution in ambient waters, however these methods do not discern between...
Peed, Lindsay A; Nietch, Christopher T; Kelty, Catherine A; Meckes, Mark; Mooney, Thomas; Sivaganesan, Mano; Shanks, Orin C
2011-07-01
Diffuse sources of human fecal pollution allow for the direct discharge of waste into receiving waters with minimal or no treatment. Traditional culture-based methods are commonly used to characterize fecal pollution in ambient waters, however these methods do not discern between human and other animal sources of fecal pollution making it difficult to identify diffuse pollution sources. Human-associated quantitative real-time PCR (qPCR) methods in combination with low-order headwatershed sampling, precipitation information, and high-resolution geographic information system land use data can be useful for identifying diffuse source of human fecal pollution in receiving waters. To test this assertion, this study monitored nine headwatersheds over a two-year period potentially impacted by faulty septic systems and leaky sanitary sewer lines. Human fecal pollution was measured using three different human-associated qPCR methods and a positive significant correlation was seen between abundance of human-associated genetic markers and septic systems following wet weather events. In contrast, a negative correlation was observed with sanitary sewer line densities suggesting septic systems are the predominant diffuse source of human fecal pollution in the study area. These results demonstrate the advantages of combining water sampling, climate information, land-use computer-based modeling, and molecular biology disciplines to better characterize diffuse sources of human fecal pollution in environmental waters.
Hui, Zi; Tang, Xiaoyue; Li, Wei; Greneche, Jean-Marc; Wang, Qiuping A.
2015-04-01
In this work, we study the problem of diffusing a product (idea, opinion, disease etc.) among agents on spatial network. The network is constructed by random addition of nodes on the planar. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power of α. The diffusion rate between two connected nodes is inversely proportional to their spatial distance to the power of β as well. Inspired from the Fick's first law, we introduce the diffusion coefficient to measure the diffusion ability of the spatial network. Using both theoretical analysis and Monte Carlo simulation, we get the fact that the diffusion coefficient always decreases with the increasing of parameter α and β, and the diffusion sub-coefficient follows the power-law of the spatial distance with exponent equals to -α-β+2. Since both short-range diffusion and long-range diffusion exist, we use anomalous diffusion method in diffusion process. We get the fact that the slope index δ in anomalous diffusion is always smaller that 1. The diffusion process in our model is sub-diffusion.
Parmar, Vijaykumar K; Parikh, Rajesh H; Patel, Ravish J
2016-08-01
Topiramate, 2,3:4,5-bis-O-(1-methylethylidene)-β-d-fructopyranose, is an anticonvulsant drug indicated in the treatment and control of partial seizures and severe tonic-clonic (grand mal) seizures in adults and children. An economic and rapid high-performance thin-layer chromatographic (HPTLC) method was developed and was validated for the quantitative determination of topiramate in plasma, brain homogenate and pharmaceutical formulation. The simple extraction method was used for the isolation of topiramate from formulation, plasma and brain homogenate samples. HPTLC separation was achieved on an aluminum-backed layer of silica gel 60F254 plates using toluene : acetone (5.0 : 2.0, v/v) as mobile phase. Spots of developed plates were visualized by spraying of reagent [3.0% phenol in the mixture of ethanol : sulfuric acid (95 : 5, v/v)]. Quantitation was achieved by densitometric analysis at 340 nm over the concentration range of 1,000-5,000 ng/spot. The method was found to give compact spot for the drug (Rf: 0.61 ± 0.018). The regression analysis data for the calibration plots showed good relationship with a correlation coefficient of 0.9983. The minimum detectable amount was found to be 165 ng/spot, whereas the limit of quantitation was found to be 500 ng/spot. Statistical analysis of the data showed that the method is precise, accurate, reproducible and selective for the analysis of topiramate. The developed method was successfully employed for the estimation of topiramate in samples of equilibrium solubility study, diffusion study, microemulsion formulation and suspension formulation (developed in-house), rat plasma and rat brain homogenate samples.
Lu, Yao; Chan, Heang-Ping; Wei, Jun; Hadjiiski, Lubomir M.; Samala, Ravi K.
2017-10-01
In digital breast tomosynthesis (DBT), the high-attenuation metallic clips marking a previous biopsy site in the breast cause errors in the estimation of attenuation along the ray paths intersecting the markers during reconstruction, which result in interplane and inplane artifacts obscuring the visibility of subtle lesions. We proposed a new metal artifact reduction (MAR) method to improve image quality. Our method uses automatic detection and segmentation to generate a marker location map for each projection (PV). A voting technique based on the geometric correlation among different PVs is designed to reduce false positives (FPs) and to label the pixels on the PVs and the voxels in the imaged volume that represent the location and shape of the markers. An iterative diffusion method replaces the labeled pixels on the PVs with estimated tissue intensity from the neighboring regions while preserving the original pixel values in the neighboring regions. The inpainted PVs are then used for DBT reconstruction. The markers are repainted on the reconstructed DBT slices for radiologists’ information. The MAR method is independent of reconstruction techniques or acquisition geometry. For the training set, the method achieved 100% success rate with one FP in 19 views. For the test set, the success rate by view was 97.2% for core biopsy microclips and 66.7% for clusters of large post-lumpectomy markers with a total of 10 FPs in 58 views. All FPs were large dense benign calcifications that also generated artifacts if they were not corrected by MAR. For the views with successful detection, the metal artifacts were reduced to a level that was not visually apparent in the reconstructed slices. The visibility of breast lesions obscured by the reconstruction artifacts from the metallic markers was restored.
Pop, Mihaela; Ghugre, Nilesh R.; Ramanan, Venkat; Morikawa, Lily; Stanisz, Greg; Dick, Alexander J.; Wright, Graham A.
2013-08-01
Many have speculated that MRI signal characteristics can be used to identify regions of heterogeneous infarct associated with an arrhythmogenic substrate; however, direct evidence of this relationship is limited. The aim of this study was to demonstrate the remodelling characteristics of fibrosis by means of histology and high-resolution MR imaging. For this purpose, we performed whole-mount histology in heart samples (n = 9) collected from five swine at six weeks post-infarction and compared the extent of fibrosis in the infarcted areas delineated in these histological images with that obtained ex vivo by MRI using late gadolinium-enhancement (LGE) and diffusion-weighted imaging (DWI) methods. All MR images were obtained at a submillimetre resolution (i.e., voxel size of 0.6×0.6×1.2 mm3). Specifically, in the histology images, we differentiated moderate fibrosis (consisting of a mixture of viable and non-viable myocytes, known as border zone, BZ) from severe fibrosis (i.e., the dense scar). Correspondingly, tissue heterogeneities in the MR images were categorized by a Gaussian mixture model into healthy, BZ and scar. Our results showed that (a) both MRI methods were capable of qualitatively distinguishing sharp edges between dense scar and healthy tissue from regions of heterogeneous BZ; (b) the BZ and dense scar areas had intermediate-to-high increased values of signal intensity in the LGE images and of apparent diffusion coefficient in the DWI, respectively. In addition, as demonstrated by the Picrosirius Red and immunohistochemistry stains, the viable bundles in the BZ were clearly separated by thin collagen strands and had reduced expression of Cx43, whereas the core scar was composed of dense fibrosis. A quantitative analysis demonstrated that the comparison between BZ/scar extent in LGE and DWI to the corresponding areas identified in histology yielded very good correlations (i.e., for the scar identified by LGE, R2 was 0.96 compared to R2 = 0.93 for the
Schneider, D
2001-07-01
The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)
Lee, Jeongjin; Seo, Joon Beom; Kim, Namkug; Park, Sang Ok; Lee, Ho; Shin, Yeong Gil; Kim, Soo-Hong
2009-02-01
In this paper, we propose an algorithm for reliable segmentation of the lung at HRCT of DILD. Our method consists of four main steps. First, the airway and colon are segmented and excluded by thresholding(-974 HU) and connected component analysis. Second, initial lung is identified by thresholding(-474 HU). Third, shape propagation outward the lung is performed on the initial lung. Actual lung boundaries exist inside the propagated boundaries. Finally, subsequent shape modeling level-set inward the lung from the propagated boundary can identify the lung boundary when the curvature term was highly weighted. To assess the accuracy of the proposed algorithm, the segmentation results of 54 patients are compared with those of manual segmentation done by an expert radiologist. The value of 1 minus volumetric overlap is less than 5% error. Accurate result of our method would be useful in determining the lung parenchyma at HRCT, which is the essential step for the automatic classification and quantification of diffuse interstitial lung disease.
da Silva, Aline Santana; Fernandes, Flávio Cesar Bedatty; Tognolli, João Olímpio; Pezza, Leonardo; Pezza, Helena Redigolo
2011-09-01
This article describes a simple, inexpensive, and environmentally friendly method for the monitoring of glyphosate using diffuse reflectance spectroscopy. The proposed method is based on reflectance measurements of the colored compound produced from the spot test reaction between glyphosate and p-dimethylaminocinnamaldehyde ( p-DAC) in acid medium, using a filter paper as solid support. Experimental designs were used to optimize the analytical conditions. All reflectance measurements were carried out at 495 nm. Under optimal conditions, the glyphosate calibration graphs obtained by plotting the optical density of the reflectance signal (A R) against the concentration were linear in the range 50-500 μg mL -1, with a correlation coefficient of 0.9987. The limit of detection (LOD) for glyphosate was 7.28 μg mL -1. The technique was successfully applied to the direct determination of glyphosate in commercial formulations, as well as in water samples (river water, pure water and mineral drinking water) after a previous clean-up or pre-concentration step. Recoveries were in the ranges 93.2-102.6% and 91.3-102.9% for the commercial formulations and water samples, respectively.
Höller, S.; Benigni, H.; Jaberg, H.
2016-11-01
The complete pump characteristics including its 4-quadrant behaviour are of essential interest for off-design operations such as a pump trip. At this exceptional load case the pump enters the dissipation mode and moves further into the turbine mode while the direction of rotation and the flow direction will change. The time-consuming and expensive experimental investigation of the 4-quadrant behaviour requires a specific test rig, allowing the flow direction as well as the rotational direction of the investigated pump to be reverted. By measuring the pump performance (head and efficiency) at variable positive and negative discharge and rotation the complete pump characteristics are evaluated. Nowadays CFD- analysis allows for the reliable prediction of the hydraulic performance of a pump near the design point. However, abnormal operating conditions lead to complex and unsteady flow phenomena inside the pump. Besides steady-state calculations in the normal operating conditions quite comprehensive transient CFD-investigations are required to simulate the whole pump characteristics accurately. The present study focuses on the comparison of the results obtained on the test rig and by numerical methods and shows a remarkably good agreement between them. It can be shown that it is possible to reliably simulate the 4-quadrant behaviour of a mixed flow diffuser pump based on CFD-methods. Furthermore an exemplary waterhammer calculation shows the successful application of the numerically calculated 4- quadrant behaviour.
LUO Bin; LI Jun; HE Sai-ling
2005-01-01
Monte Carlo simulation of the diffusing temporal light correlation in a multi-layered turbid medium is considered.A straightforward formula is introduced to calculate accurately and efficiently the autocorrelation function at any detector position.The simulation results are in an excellent agreement with an analytical solution of the correlation diffusion equation.
Lushnikov, D. S.; Zherdev, A. Y.; Odinokov, S. B.; Markin, V. V.; Smirnov, A. V.
2016-10-01
The paper presents the practical results of recording holographic stereograms. Advantages and disadvantages of methods for producing holographic stereograms using diffusers with different indicatrices scattering of the radiation in the object branch and without the use of a diffuser are presented. A new security element - multi-color microtext, is presented. Shows how to use multi-color microtext as a hidden security element. The method of multi-color microtext visualization is shown. The work was partially funded under the Agreement with the RF Ministry of Education and Science no. 14.577.21.0197, grant RFMEFI57715X0197.
Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
Farida Lanawati Darsono
2003-06-01
Full Text Available A study has been performed on the antimicrobial activities of "jambu biji" (Psidium guajava Linn leaves from several cultivars(red, white and yellow cultivar against Staphylococcus aureus ATCC 25923 representing the Gram positive bacteria. The reason for conducting this research is that the leaves of "jambu biji" are frequently used in traditional medicine as a remedy against diarrhea.The hole-plate diffusion method was used for conducting the antimicrobial activity test with antibiotics (Ampicilline trihidrat as reference standards. The extracts of "jambu biji" for each cultivar were obtained by reflux with ethanol 96%. The concentrations of the extracts applied to the holes were 10%, 20%, and 30% w/v, the extracts were reconstituted with tween 80 and ethanol 96%. Based on the result of the study, it can be concluded that the extract of "jambu biji" from each cultivar with the concentration of 10%, 20%, and 30%w/v showed antibacterial activities against Staphylococcus aureus ATCC 25923. The result obtained statictically evaluated using Anova Factorial 3Ã—3 and furthery tested for significancy (Î± = 0.05. Based on the results of study, it can be concluded that the extract of jambu biji leaves from red cultivar, white cultivar and yellow cultivar showed antibacterial activities against Staphylococcus aureus ATCC 25923.
Amores, Sonia; Domenech, José; Colom, Helena; Calpena, Ana C; Clares, Beatriz; Gimeno, Álvaro; Lauroba, Jacinto
2014-08-18
The use of isolated animal models to assess percutaneous absorption of molecules is frequently reported. The porcine buccal mucosa has been proposed as a substitute for the buccal mucosa barrier on ex vivo permeability studies avoiding unnecessary sacrifice of animals. But it is not always easy to obtain fresh buccal mucosa. Consequently, human and porcine buccal mucosa is sometimes frozen and stored in liquid nitrogen, but this procedure is not always feasible. One cheaper and simpler alternative is to freeze the buccal mucosa of freshly slaughtered pigs in a mechanical freezer, using DMSO and albumin as cryoprotective agents. This study compared the ex vivo permeability parameters of propranolol hydrochloride through porcine buccal mucosa using a Franz diffusion cell system and HPLC as detection method. The freezing effects on drug permeability parameters were evaluated. Equally histological studies were performed. Furthermore, the use of the parameter transmucosal water loss (TMWL) as an indicator of the buccal mucosa integrity was evaluated just as transepidermal water loss (TEWL) is utilized for skin integrity. The results showed no difference between fresh and frozen mucosal flux, permeability coefficient or lag time of propranolol. However, statistical significant difference in TMWL between fresh and frozen mucosa was observed.
Norhayati Luddin
2013-01-01
Full Text Available Complete debridement and disinfection of the root canal system are fundamental requirements for successful endodontic treatment. Despite the morphological challenges of the internal root anatomy, root canal irrigants play an important role in the optimization of the root canal preparation, which is essentially a chemo-mechanical procedure. Enterococcus faecalis is one of the most resistant microorganisms that dominants the microbial ecosystem of persistent periradicular lesions in retreatment cases. For that reason, many in vitro and in vivo studies evaluated and compared the antibacterial activity of sodium hypochlorite and chlorhexidine at varying concentrations using different experimental models against this microorganism. However, many controversies with regard to the ideal irrigant and concentration do in fact exist. Hence, this review aims to discuss the antibacterial activity of these two main root canal irrigants against Enterococcus faecalis using the agar diffusion and direct contact methods and the possible modulating factors responsible for inconsistent findings among different studies. In addition, the disinfection potential of both chemical agents on gutta percha and Resilon cones are also discussed. The source of this review was conducted through an electronic literature search using PubMed database from December 1997 until December 2011, which analyze the related laboratory investigations of both irrigants, published in major endodontic journals.
Tan, Xiaoyu
2016-05-18
In the last decade, many attempts were made to put metal organic frameworks (MOFs) in industrial applications, but most of these efforts weren’t successfully. As one of the few MOFs produced on industrial scale, ZIF-8 has interesting pore size, huge internal surface area and great thermal and chemical stability. Therefore, ZIF-8 might become the first MOF, which will be applied in industrial separation processes. In this thesis, a synthesis study is presented, which leads to a cheap and convenient way to fabricate defect-free and thin ZIF-8 membranes on porous polymeric supports showing high selectivity and high gas permeance. The ZIF-8 layers were produced via a contra-diffusion method. Several polymeric membranes were employed as support in this study, such as PAN, PEI, PSU, PA and PTSC. We studied the influence of the polymeric support properties for the ZIF-8 membrane preparation and optimized the ZIF-8 preparation conditions. The ZIF-8 membranes were characterized via scanning electron microscopy (SEM) and X-ray diffraction (XRD). For gas permeation test, we chose a Wicke-Kallenbach apparatus to measure membrane’s gas permeance and selectivity. One of the best ZIF-8 membranes exhibited a hydrogen permeance of 3.45 × 10-8 mol m-2 s-1 Pa-1 and an ideal selectivity of hydrogen over propane of about 500.
Abookasis, David; Volkov, Boris; Kofman, Itamar
2017-02-01
During the last four decades, various optical techniques have been proposed and intensively used for biomedical diagnosis and therapy both in animal model and in human. These techniques have several advantages over the traditional existing methods: simplicity in structure, low-cost, easy to handle, portable, can be used repeatedly over time near the patient bedside for continues monitoring, and offer high spatiotemporal resolution. In this work, we demonstrate the use of two optical imaging modalities namely, spatially modulated illumination and dual-wavelength laser speckle to image the changes in brain tissue chromophores, morphology, and metabolic before, during, and after the onset of focal traumatic brain injury in intact mouse head (n=15). Injury was applied in anesthetized mice by weight-drop apparatus using 50gram metal rod striking the mouse's head. Following data analysis, we show a series of hemodynamic and structural changes over time including higher deoxyhemoglobin, reduction in oxygen saturation and blood flow, cell swelling, etc., in comparison with baseline measurements. In addition, to validate the monitoring of cerebral blood flow by the imaging system, measurements with laser Doppler flowmetry were also performed (n=5), which confirmed reduction in blood flow following injury. Overall, our result demonstrates the capability of diffuse optical modalities to monitor and map brain tissue optical and physiological properties following brain trauma.
Landay, Marshall E.; Wheat, Robert W.; Conant, Norman F.; Lowe, Edwin P.
1967-01-01
Hyperimmune sera against spherules and against arthrospores of Coccidioides immitis were prepared by inoculation of rabbits. The antibody content of these sera was studied by the agar gel diffusion method. It was observed that antispherule pooled sera formed multiple precipitin bands with extracts of spherules and of arthrospores. The antiarthrospore pooled serum, however, failed to precipitate with the spherule extract, and formed a single band in the presence of an arthrospore solution. When the spherule and the arthrospore extracts were tested with a variety of different antisera, it was observed that the spherule preparation formed bands only in combination with anti-purified spherule pooled serum, whereas the arthrospore extract precipitated with anti-purified spherule, antiarthrospore, and anti-Histoplasma capsulatum pooled sera. It was also observed that a spherule culture supernatant solution formed five precipitin bands in combination with anti-spherule pooled sera, formed one band with pooled antiserum from rabbits with coccidioidomycosis, and did not precipitate in the presence of antiarthrospore pooled serum. Coccidioidin, however, formed two bands in the presence of any of these antisera. It was therefore concluded that extracts from the spherule phase of C. immitis differed from solutions obtained from the arthrospore and mycelial phases. Images PMID:4960151
Lyon, B.F.
1996-02-01
During the summer of 1995, ultrasonic wall thickness data were collected for 100 steel cylinders containing depleted uranium (DU) hexafluoride located at Paducah Gaseous Diffusion Plant (PGDP) in Paducah, Kentucky. The cylinders were selected for measurement to assess the condition of the more vulnerable portion of the cylinder inventory at PGDP. The purpose of this report is to apply the method used in Lyon to estimate the effects of corrosion for larger unsampled populations as a function of time. The scope of this report is limited and is not intended to represent the final analyses of available data. Future efforts will include continuing analyses of available data to investigate defensible deviations from the conservative assumptions made to date. For each cylinder population considered, two basic types of analyses were conducted: (1) estimates were made of the number of cylinders as a function of time that will have a minimum wall thickness of either 0 mils (1 mil = 0.00 1 in.) or 250 mils and (2) the current minimum wall thickness distributions across cylinders were estimated for each cylinder population considered. Additional analyses were also performed investigating comparisons of the results for F and G yards with the results presented in Lyon (1995).