Free surface modelling with two-fluid model and reduced numerical diffusion of the interface
International Nuclear Information System (INIS)
Strubelj, Luka; Tiselj, Izrok
2008-01-01
Full text of publication follows: The free surface flows are successfully modelled with one of existing free surface models, such as: level set method, volume of fluid method (with/without surface reconstruction), front tracking, two-fluid model (two momentum equations) with modified interphase force and others. The main disadvantage of two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced using the method presented in this paper. Several techniques for reduction of numerical diffusion of the interface have been implemented in the volume of fluid model and are based on modified numerical schemes for advection of volume fraction near the interface. The same approach could be used also for two-fluid method, but according to our experience more successful reduction of numerical diffusion of the interface can be achieved with conservative level set method. Within the conservative level set method, continuity equation for volume fraction is solved and after that the numerical diffusion of the interface is reduced in such a way that the thickness of the interface is kept constant during the simulation. Reduction of the interface diffusion can be also called interface sharpening. In present paper the two-fluid model with interface sharpening is validated on Rayleigh-Taylor instability. Under assumptions of isothermal and incompressible flow of two immiscible fluids, we simulated a system with the fluid of higher density located above the fluid of smaller density in two dimensions. Due to gravity in the system, fluid with higher density moves below the fluid with smaller density. Initial condition is not a flat interface between the fluids, but a sine wave with small amplitude, which develops into a mushroom-like structure. Mushroom-like structure in simulation of Rayleigh-Taylor instability later develops to small droplets as result of numerical dispersion of interface (interface sharpening
International Nuclear Information System (INIS)
Lee, Goung Jin; Kim, Soong Pyung
1990-01-01
In solving the convection-diffusion phenomena, it is common to use central difference scheme or upwind scheme. The central difference scheme has second order accuracy, while the upwind scheme is only first order accurate. However, since the variation rising in the convection-diffusion problem is exponential, central difference scheme ceased to be a good method for anything but extremely small values of Δx. At large values of Δx, which is all one can afford in most practical problems, it is the upwind scheme that gives more reasonable results than the central scheme. But in the conventional upwind scheme, since the accuracy is only first order, false diffusion is somewhat large, and when the real diffusion is smaller than the numerical diffusion, solutions may be very errorneous. So in this paper, a method to reduce the numerical diffusion of upwind scheme is studied. Developed scheme uses same number of nodes as conventional upwind scheme, but it considers the direction of flow more sophistically. As a conclusion, the developed scheme shows very good results. It can reduce false diffusion greatly with the cost of small complexity. Also, algorithm of the developed scheme is presented at appendix. (Author)
Numerical vs. turbulent diffusion in geophysical flow modelling
International Nuclear Information System (INIS)
D'Isidoro, M.; Maurizi, A.; Tampieri, F.
2008-01-01
Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using the WAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases.
Numerical Diffusion Effect in Dynamic Simulation of Thermohydraulic Systems
International Nuclear Information System (INIS)
Zanocco, Pablo; Gimenez, Marcelo; Delmastro, Dario
2003-01-01
In this work, the behavior of the explicit - up-wind method is studied in two phase natural convection circuit, near the instabilities boundaries.The effect of the numerical diffusion of the scheme upon the system stability is evaluated by means of linearization by small perturbations.The results are compared with a non-diffusive method, in the frequency domain, that solves analytically the linearized equations around a steady state condition.Moreover, a conservation equation transport model using the method of characteristics is implemented and studied.This method is compared with the explicit - up-wind scheme and it is found that it significantly reduces numerical diffusion in the equations solution. Several advantages are visualized for particular cases
Felici, Helene M.; Drela, Mark
1993-01-01
A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.
Numerical modelling of random walk one-dimensional diffusion
International Nuclear Information System (INIS)
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations
Padrino, Juan C.; Zhang, Duan Z.
2016-11-01
The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.
Accurate numerical simulation of reaction-diffusion processes for heavy oil recovery
Energy Technology Data Exchange (ETDEWEB)
Govind, P.A.; Srinivasan, S. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)
2008-10-15
This study evaluated a reaction-diffusion simulation tool designed to analyze the displacement of carbon dioxide (CO{sub 2}) in a simultaneous injection of carbon dioxide and elemental sodium in a heavy oil reservoir. Sodium was used due to the exothermic reaction of sodium with in situ that occurs when heat is used to reduce oil viscosity. The process also results in the formation of sodium hydroxide that reduces interfacial tension at the bitumen interface. A commercial simulation tool was used to model the sodium transport mechanism to the reaction interface through diffusion as well as the reaction zone's subsequent displacement. The aim of the study was to verify if the in situ reaction was able to generate sufficient heat to reduce oil viscosity and improve the displacement of the heavy oil. The study also assessed the accuracy of the reaction front simulation tool, in which an alternate method was used to model the propagation front as a moving heat source. The sensitivity of the simulation results were then evaluated in relation to the diffusion coefficient in order to understand the scaling characteristics of the reaction-diffusion zone. A pore-scale simulation was then up-scaled to grid blocks. Results of the study showed that when sodium suspended in liquid CO{sub 2} is injected into reservoirs, it diffuses through the carrier phase and interacts with water. A random walk diffusion algorithm with reactive dissipation was implemented to more accurately characterize reaction and diffusion processes. It was concluded that the algorithm modelled physical dispersion while neglecting the effect of numerical dispersion. 10 refs., 3 tabs., 24 figs.
International Nuclear Information System (INIS)
Zhou, Xiafeng; Guo, Jiong; Li, Fu
2015-01-01
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
Energy Technology Data Exchange (ETDEWEB)
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
Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline
Directory of Open Access Journals (Sweden)
Ravi Kanth A.S.V.
2016-01-01
Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.
A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations
Boudin , Laurent; Grec , Bérénice; Salvarani , Francesco
2012-01-01
International audience; We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. We provide a qualitative and quantitative mathematical analysis of the model. The main properties of the standard explicit numerical scheme are also analyzed. We eventually include some numerical simulations pointing out the uphill diffusion phenome...
Numerical solutions of diffusive logistic equation
International Nuclear Information System (INIS)
Afrouzi, G.A.; Khademloo, S.
2007-01-01
In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years
Numerical approach to the inverse convection-diffusion problem
International Nuclear Information System (INIS)
Yang, X-H; She, D-X; Li, J-Q
2008-01-01
In this paper, the inverse problem on source term identification in convection-diffusion equation is transformed into an optimization problem. To reduce the computational cost and improve computational accuracy for the optimization problem, a new algorithm, chaos real-coded hybrid-accelerating evolution algorithm (CRHAEA), is proposed, in which an initial population is generated by chaos mapping, and new chaos mutation and simplex evolution operation are used. With the shrinking of searching range, CRHAEA gradually directs to an optimal result with the excellent individuals obtained by real-coded evolution algorithm. Its convergence is analyzed. Its efficiency is demonstrated by 15 test functions. Numerical simulation shows that CRHAEA has some advantages over the real-coded accelerated evolution algorithm, the chaos algorithm and the pure random search algorithm
International Nuclear Information System (INIS)
Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi
2002-01-01
Because effluent gas is sometimes released from low positions, viz., near the ground surface and around buildings, the effects caused by buildings within the site area are not negligible for gas diffusion predictions. For these reasons, the effects caused by buildings for gas diffusion are considered under the terrain following calculation coordinate system in this report. Numerical calculation meshes on the ground surface are treated as the building with the adaptation of wall function techniques of turbulent quantities in the flow calculations using a turbulence closure model. The reflection conditions of released particles on building surfaces are taken into consideration in the diffusion calculation using the Lagrangian particle model. Obtained flow and diffusion calculation results are compared with those of wind tunnel experiments around the building. It was apparent that features observed in a wind tunnel, viz., the formation of cavity regions behind the building and the gas diffusion to the ground surface behind the building, are also obtained by numerical calculation. (author)
DEFF Research Database (Denmark)
Liu, Yuanrong; Chen, Weimin; Zhong, Jing
2017-01-01
The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....
The numerical simulation of convection delayed dominated diffusion equation
Directory of Open Access Journals (Sweden)
Mohan Kumar P. Murali
2016-01-01
Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.
Application of a numerical transport correction in diffusion calculations
International Nuclear Information System (INIS)
Tomatis, Daniele; Dall'Osso, Aldo
2011-01-01
Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)
Radiation Diffusion: An Overview of Physical and Numerical Concepts
International Nuclear Information System (INIS)
Graziani, F R
2005-01-01
An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed
A asymptotic numerical method for the steady-state convection diffusion equation
International Nuclear Information System (INIS)
Wu Qiguang
1988-01-01
In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...
Fast solution of neutron diffusion problem by reduced basis finite element method
International Nuclear Information System (INIS)
Chunyu, Zhang; Gong, Chen
2018-01-01
Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.
Numerical analysis of anisotropic diffusion effect on ICF hydrodynamic instabilities
Directory of Open Access Journals (Sweden)
Olazabal-Loumé M.
2013-11-01
Full Text Available The effect of anisotropic diffusion on hydrodynamic instabilities in the context of Inertial Confinement Fusion (ICF flows is numerically assessed. This anisotropy occurs in indirect-drive when laminated ablators are used to modify the lateral transport [1,2]. In direct-drive, non-local transport mechanisms and magnetic fields may modify the lateral conduction [3]. In this work, numerical simulations obtained with the code PERLE [4], dedicated to linear stability analysis, are compared with previous theoretical results [5]. In these approaches, the diffusion anisotropy can be controlled by a characteristic coefficient which enables a comprehensive study. This work provides new results on the ablative Rayleigh-Taylor (RT, ablative Richtmyer-Meshkov (RM and Darrieus-Landau (DL instabilities.
Numerical study of turbulent diffusion
International Nuclear Information System (INIS)
McCoy, M.G.
1975-01-01
The problem of the numerical simulation of turbulent diffusion is studied. The two-dimensional velocity fields are assumed to be incompressible, homogeneous and stationary, and they are represented as stochastic processes. A technique is offered which creates velocity fields accurately representing the input statistics once a two point correlation function or an energy spectrum is given. Various complicated energy spectra may be represented utilizing this model. The program is then used to extract information concerning Gaussian diffusion processes. Various theories of other workers are tested including Taylor's classical representation of dispersion for times long compared with the Lagrangian correlation time. Also, a study is made of the relation between the Lagrangian and the Eulerian correlation function and a hypothesis is advanced and successfully tested. Questions concerning the relation between small eddies and the energy spectrum are considered. A criterion is advanced and successfully tested to decide whether small scale flow can be detected within the large eddies for any given spectrum. A method is developed to determine whether this small scale motion is in any sense periodic. Finally, the relation between two particle dispersion and the energy spectrum is studied anew and various theories are tested
Bremmer, Rolf H; van Gemert, Martin J C; Faber, Dirk J; van Leeuwen, Ton G; Aalders, Maurice C G
2013-08-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 mm-1 at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys.19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime
BCJ numerators from reduced Pfaffian
Energy Technology Data Exchange (ETDEWEB)
Du, Yi-Jian [Center for Theoretical Physics, School of Physics and Technology, Wuhan University,No. 299 Bayi Road, Wuhan 430072 (China); Teng, Fei [Department of Physics and Astronomy, University of Utah,115 South 1400 East, Salt Lake City, UT 84112 (United States)
2017-04-07
By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the (n−2)! DDM form BCJ numerators contains exactly (n−1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most (n−2)!−(n−3)!, less than those of several previous constructions.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
International Nuclear Information System (INIS)
Ferreri, J. C.; Carmen, A. del
1998-01-01
A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs
On the numerical solution of the neutron fractional diffusion equation
International Nuclear Information System (INIS)
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto
2014-01-01
Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative
Numerical simulation of compressible two-phase flow using a diffuse interface method
International Nuclear Information System (INIS)
Ansari, M.R.; Daramizadeh, A.
2013-01-01
Highlights: ► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is investigated. ► The numerical results exhibit very good agreement with experimental results. -- Abstract: In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems
Numerical solution of a reaction-diffusion equation
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2000-01-01
The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)
International Nuclear Information System (INIS)
Gao Zhi; Shen Yi-Qing
2012-01-01
The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme
Parametrical analysis on the diffuse ceiling ventilation by experimental and numerical studies
DEFF Research Database (Denmark)
Zhang, Chen; Kristensen, Martin Heine; Jensen, Jakob Sølund
2016-01-01
This paper aims to investigate the performance of diffuse ceiling ventilation in a classroom. An experimental study is carried out in a test chamber to examine the impact of diffuse ceiling opening area on the system cooling capacity and thermal comfort. The results indicate that diffuse ceiling ....... The numerical results reveal that even distribution of heat sources gives a lower draught risk environment than centralized distribution. In addition, there is a significant increase on the draught risk with increase of room height....
Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.
Elperin, T; Kleeorin, N; Liberman, M; Lipatnikov, A N; Rogachevskii, I; Yu, R
2017-11-01
The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.
DEFF Research Database (Denmark)
Shojaee Nasirabadi, Parizad; Jabbaribehnam, Mirmasoud; Hattel, Jesper Henri
2016-01-01
) is widely used in the electronics industry. Thus, in this work the water diffusion coefficient into PC is investigated. Furthermore, numerical methods used for estimation of the diffusion coefficient and their assumptions are discussed. 1D and 3D numerical solutions are compared and based on this, itis......Nowadays, many electronic systems are exposed to harsh conditions of relative humidity and temperature. Masstransport properties of electronic packaging materials are needed in order to investigate the influence of moisture andtemperature on reliability of electronic devices. Polycarbonate (PC...... shown how the estimated value can be different depending on the choice of dimensionality in the model....
Elimination of numerical diffusion in 1 - phase and 2 - phase flows
Energy Technology Data Exchange (ETDEWEB)
Rajamaeki, M. [VTT Energy (Finland)
1997-07-01
The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.
Elimination of numerical diffusion in 1 - phase and 2 - phase flows
International Nuclear Information System (INIS)
Rajamaeki, M.
1997-01-01
The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods
Energy Technology Data Exchange (ETDEWEB)
Nasirabadi, P. Shojaee; Jabbari, M.; Hattel, J. H. [Process Modelling Group, Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, 2800 Kgs. Lyngby (Denmark)
2016-06-08
Nowadays, many electronic systems are exposed to harsh conditions of relative humidity and temperature. Mass transport properties of electronic packaging materials are needed in order to investigate the influence of moisture and temperature on reliability of electronic devices. Polycarbonate (PC) is widely used in the electronics industry. Thus, in this work the water diffusion coefficient into PC is investigated. Furthermore, numerical methods used for estimation of the diffusion coefficient and their assumptions are discussed. 1D and 3D numerical solutions are compared and based on this, it is shown how the estimated value can be different depending on the choice of dimensionality in the model.
Can slow-diffusing solute atoms reduce vacancy diffusion in advanced high-temperature alloys?
International Nuclear Information System (INIS)
Goswami, Kamal Nayan; Mottura, Alessandro
2014-01-01
The high-temperature mechanical properties of precipitate-strengthened advanced alloys can be heavily influenced by adjusting chemical composition. The widely-accepted argument within the community is that, under certain temperature and loading conditions, plasticity occurs only in the matrix, and dislocations have to rely on thermally-activated climb mechanisms to overcome the barriers to glide posed by the hard precipitates. This is the case for γ′-strengthened Ni-based superalloys. The presence of dilute amounts of slow-diffusing solute atoms, such as Re and W, in the softer matrix phase is thought to reduce plasticity by retarding the climb of dislocations at the interface with the hard precipitate phase. One hypothesis is that the presence of these solutes must hinder the flow of vacancies, which are essential to the climb process. In this work, density functional theory calculations are used to inform two analytical models to describe the effect of solute atoms on the diffusion of vacancies. Results suggest that slow-diffusing solute atoms are not effective at reducing the diffusion of vacancies in these systems
International Nuclear Information System (INIS)
Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong
2017-01-01
Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and
ESTIMATION OF TURBULENT DIFFUSIVITY WITH DIRECT NUMERICAL SIMULATION OF STELLAR CONVECTION
Energy Technology Data Exchange (ETDEWEB)
Hotta, H.; Iida, Y.; Yokoyama, T., E-mail: hotta.h@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2012-05-20
We investigate the value of horizontal turbulent diffusivity {eta} by numerical calculation of thermal convection. In this study, we introduce a new method whereby the turbulent diffusivity is estimated by monitoring the time development of the passive scalar, which is initially distributed in a given Gaussian function with a spatial scale d{sub 0}. Our conclusions are as follows: (1) assuming the relation {eta} = L{sub c} v{sub rms}/3, where v{sub rms} is the root-mean-square (rms) velocity, the characteristic length L{sub c} is restricted by the shortest one among the pressure (density) scale height and the region depth. (2) The value of turbulent diffusivity becomes greater with the larger initial distribution scale d{sub 0}. (3) The approximation of turbulent diffusion holds better when the ratio of the initial distribution scale d{sub 0} to the characteristic length L{sub c} is larger.
Directory of Open Access Journals (Sweden)
Daniel Pérez-Grande
2016-11-01
Full Text Available This manuscript explores numerical errors in highly anisotropic diffusion problems. First, the paper addresses the use of regular structured meshes in numerical solutions versus meshes aligned with the preferential directions of the problem. Numerical diffusion in structured meshes is quantified by solving the classical anisotropic diffusion problem; the analysis is exemplified with the application to a numerical model of conducting fluids under magnetic confinement, where rates of transport in directions parallel and perpendicular to a magnetic field are quite different. Numerical diffusion errors in this problem promote the use of magnetic field aligned meshes (MFAM. The generation of this type of meshes presents some challenges; several meshing strategies are implemented and analyzed in order to provide insight into achieving acceptable mesh regularity. Second, Gradient Reconstruction methods for magnetically aligned meshes are addressed and numerical errors are compared for the structured and magnetically aligned meshes. It is concluded that using the latter provides a more correct and straightforward approach to solving problems where anisotropicity is present, especially, if the anisotropicity level is high or difficult to quantify. The conclusions of the study may be extrapolated to the study of anisotropic flows different from conducting fluids.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
International Nuclear Information System (INIS)
Vamos, Calin; Suciu, Nicolae; Vereecken, Harry
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested
A numerical solution for a class of time fractional diffusion equations with delay
Directory of Open Access Journals (Sweden)
Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Assessment of the numerical diffusion effect in the advection of a passive tracer in BOLCHEM
International Nuclear Information System (INIS)
D'Isidoro, M.; Tiesi, A.
2005-01-01
The effects of the numerical scheme implemented in the advection equation of BOLCHEM have been quantified with reference to the diffusion of a passive tracer. An equivalent horizontal diffusion coefficient has been measured and is found to be dependent on wind field and resolution
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon
International Nuclear Information System (INIS)
Ma, Fa-Jun; Duttagupta, Shubham; Shetty, Kishan Devappa; Meng, Lei; Hoex, Bram; Peters, Ian Marius; Samudra, Ganesh S.
2014-01-01
Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boron diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed
Yao, Lingxing; Mori, Yoichiro
2017-12-01
Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.
A numerical model for diffusion of helium in a hydrogen plasma
International Nuclear Information System (INIS)
Potters, J.H.H.M.
1983-07-01
A quasi-cylindrical steady-state numerical model for the diffusion of helium in a hydrogen plasma is presented, adopting collisional plus either ALCATOR-INTOR- or ASDEX-like anomalous transport for the charged species. The coupled momentum and conservation equations for H + , He + and He ++ are solved to obtain radial profiles of their densities, consistent with those of the neutral species. For the neutrals, a diffusion equation is used for the transport of H, whereas He is assumed to enter the plasma with an energy equal to the temperature of the plasma immediately in front of the wall. A stable numerical scheme for the solution of the coupled ion and electron energy balances is discussed. Results are presented for the JET-tokamak, using prescribed temperature profiles. Collisional effects are shown to produce an enhancement of the alpha particle density about 10 centimetres in front of the wall, especially in combination with ALCATOR-INTOR-like scaling. The neutral helium density that accumulates in the outer plasma is too low to allow for pumping helium from a cool plasma/gas blanket
Directory of Open Access Journals (Sweden)
Ali Izadi
2015-10-01
Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.
Numerical method for solving the three-dimensional time-dependent neutron diffusion equation
International Nuclear Information System (INIS)
Khaled, S.M.; Szatmary, Z.
2005-01-01
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)
Jain, Sonal
2018-01-01
In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.
Directory of Open Access Journals (Sweden)
Dmitry V. Lukyanenko
2017-01-01
Full Text Available This work develops a theory of the asymptotic-numerical investigation of the moving fronts in reaction-diffusion-advection models. By considering the numerical solution of the singularly perturbed Burgers’s equation we discuss a method of dynamically adapted mesh construction that is able to significantly improve the numerical solution of this type of equations. For the construction we use a priori information that is based on the asymptotic analysis of the problem. In particular, we take into account the information about the speed of the transition layer, its width and structure. Our algorithms are able to reduce significantly complexity and enhance stability of the numerical calculations in comparison with classical approaches for solving this class of problems. The numerical experiment is presented to demonstrate the effectiveness of the proposed method.The article is published in the authors’ wording.
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
Maierova, P.; Steinle-Neumann, G.; Cadek, O.
2010-12-01
A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
International Nuclear Information System (INIS)
Larsen, E.W.; Morel, J.E.; Miller, W.F. Jr.
1987-01-01
We present an asymptotic analysis of spatial differencing schemes for the discrete-ordinates equations, for diffusive media with spatial cells that are not optically thin. Our theoretical tool is an asymptotic expansion that has previously been used to describe the transform from analytic transport to analytic diffusion theory for such media. To introduce this expansion and its physical rationale, we first describe it for the analytic discrete-ordinates equations. Then, we apply the expansion to the spatially discretized discrete-ordinates equations, with the spatial mesh scaled in either of two physically relevant ways such that the optical thickness of the spatial cells is not small. If the result of either expansion is a legitimate diffusion description for either the cell-averaged or cell-edge fluxes, then we say that the approximate flux has the appropriate diffusion limit; otherwise, we say it does not. We consider several transport differencing schemes that are applicable in neutron transport and thermal radiation applications. We also include numerical results which demonstrate the validity of our theory and show that differencing schemes that do have a particular diffusion limit are substantially more accurate, in the regime described by the limit, than those that do not. copyright 1987 Academic Press, Inc
Derivation and Numerical Approximation of the Quantum Drift Diffusion Model for Semiconductors
International Nuclear Information System (INIS)
Ohnmar Nwe
2004-06-01
This paper is concerned with the study of the quantum drift diffusion equation for semiconductors. Derivation of the mathematical model, which describes the electeon flow through a semiconductor device due to the application of a voltage, is considered and studied in numerical point of view by using some methods
A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method
Bondesan , Andrea; Boudin , Laurent; Grec , Bérénice
2018-01-01
In this article, we consider a multi-species kinetic model which leads to the Maxwell-Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe the as...
Numerical Solution of Diffusion Models in Biomedical Imaging on Multicore Processors
Directory of Open Access Journals (Sweden)
Luisa D'Amore
2011-01-01
Full Text Available In this paper, we consider nonlinear partial differential equations (PDEs of diffusion/advection type underlying most problems in image analysis. As case study, we address the segmentation of medical structures. We perform a comparative study of numerical algorithms arising from using the semi-implicit and the fully implicit discretization schemes. Comparison criteria take into account both the accuracy and the efficiency of the algorithms. As measure of accuracy, we consider the Hausdorff distance and the residuals of numerical solvers, while as measure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.
International Nuclear Information System (INIS)
Zee, S.K.
1987-01-01
A numeric algorithm and an associated computer code were developed for the rapid solution of the finite-difference method representation of the few-group neutron-diffusion equations on parallel computers. Applications of the numeric algorithm on both SIMD (vector pipeline) and MIMD/SIMD (multi-CUP/vector pipeline) architectures were explored. The algorithm was successfully implemented in the two-group, 3-D neutron diffusion computer code named DIFPAR3D (DIFfusion PARallel 3-Dimension). Numerical-solution techniques used in the code include the Chebyshev polynomial acceleration technique in conjunction with the power method of outer iteration. For inner iterations, a parallel form of red-black (cyclic) line SOR with automated determination of group dependent relaxation factors and iteration numbers required to achieve specified inner iteration error tolerance is incorporated. The code employs a macroscopic depletion model with trace capability for selected fission products' transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the DIFPAR3D code, for realistic simulation of power reactor cores. The physics models used were proven acceptable in separate benchmarking studies
International Nuclear Information System (INIS)
Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi; Komiyama, Sumito
2009-01-01
A numerical simulation method has been developed to predict atmospheric flow and stack gas diffusion, considering the buildings and complex terrain located near and relatively far from a stack, respectively. The turbulence closure technique was used for flow calculation, some calculation grids on the ground near a stack were treated as buildings, and stack gas diffusion was predicted using the Lagrangian particle model. The calculated flow and stack gas diffusion results were compared with those obtained by wind tunnel experiments under actual terrain containing buildings. Effective stack height was estimated by comparing the surface concentration along the plume axis with those under a flat-plate condition, and it was apparent that the effective stack heights estimated by calculations were almost the same as those obtained by the wind tunnel experiment. Then, the effective dose and relative concentration of stack gas were calculated using the effective stack heights obtained by a numerical model. Almost the same effective dose and relative concentration were obtained when compared with those using the effective stack height obtained by wind tunnel experiment. (author)
DEFF Research Database (Denmark)
Hviid, Christian Anker; Petersen, Steffen
2014-01-01
is a numerical study of the performance of a six person office equipped with diffuse ventilation ceiling. In total six extreme, yet realistic, operation scenarios were simulated to study the performance including different occupancy, ventilation rates and supply air temperatures. The performance was studied...
HIGH-ENERGY COSMIC-RAY DIFFUSION IN MOLECULAR CLOUDS: A NUMERICAL APPROACH
International Nuclear Information System (INIS)
Fatuzzo, M.; Melia, F.; Todd, E.; Adams, F. C.
2010-01-01
The propagation of high-energy cosmic rays (CRs) through giant molecular clouds constitutes a fundamental process in astronomy and astrophysics. The diffusion of CRs through these magnetically turbulent environments is often studied through the use of energy-dependent diffusion coefficients, although these are not always well motivated theoretically. Now, however, it is feasible to perform detailed numerical simulations of the diffusion process computationally. While the general problem depends upon both the field structure and particle energy, the analysis may be greatly simplified by dimensionless analysis. That is, for a specified purely turbulent field, the analysis depends almost exclusively on a single parameter-the ratio of the maximum wavelength of the turbulent field cells to the particle gyration radius. For turbulent magnetic fluctuations superimposed over an underlying uniform magnetic field, particle diffusion depends on a second dimensionless parameter that characterizes the ratio of the turbulent to uniform magnetic field energy densities. We consider both of these possibilities and parametrize our results to provide simple quantitative expressions that suitably characterize the diffusion process within molecular cloud environments. Doing so, we find that the simple scaling laws often invoked by the high-energy astrophysics community to model CR diffusion through such regions appear to be fairly robust for the case of a uniform magnetic field with a strong turbulent component, but are only valid up to ∼50 TeV particle energies for a purely turbulent field. These results have important consequences for the analysis of CR processes based on TeV emission spectra associated with dense molecular clouds.
A numerical study of the eigenvalues in the neutron diffusion theory
International Nuclear Information System (INIS)
Lima Bezerra, J. de.
1982-12-01
A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt
Directory of Open Access Journals (Sweden)
Claudia M. Colciago
2018-06-01
Full Text Available This paper deals with fast simulations of the hemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical discretisation. The resulting method is both accurate and computationally cheap. This goal is achieved by means of two levels of reduction: first, we describe the model equations with a reduced mathematical formulation which allows to write the fluid-structure interaction problem as a Navier-Stokes system with non-standard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The non standard boundary condition is of a generalized Robin type, with a boundary mass and boundary stiffness terms accounting for the arterial wall compliance. The numerical reduction is obtained coupling two well-known techniques: the proper orthogonal decomposition and the reduced basis method, in particular the greedy algorithm. We start by reducing the numerical dimension of the problem at hand with a proper orthogonal decomposition and we measure the system energy with specific norms; this allows to take into account the different orders of magnitude of the state variables, the velocity and the pressure. Then, we introduce a strategy based on a greedy procedure which aims at enriching the reduced discretization space with low offline computational costs. As application, we consider a realistic hemodynamics problem with a perturbation in the boundary conditions and we show the good performances of the reduction techniques presented in the paper. The results obtained with the numerical reduction algorithm are compared with the one obtained by a standard finite element method. The gains obtained in term of CPU time are of three orders of magnitude.
GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD
2016-01-01
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...
Directory of Open Access Journals (Sweden)
Rajneesh Kumar
Full Text Available This paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar isotropic microstretch thermoelastic diffusion medium in the context of generalized theories of thermoelasticity. The dispersion equation of Stoneley waves is derived in the form of a determinant by using the boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficients with wave number are computed numerically. Numerically computed results are shown graphically to depict the diffusion effect alongwith the relaxation times in microstretch thermoelastic diffusion solid half spaces for thermally insulated and impermeable boundaries, respectively. The components of displacement, stress, couple stress, microstress, and temperature change are presented graphically for two dissimilar microstretch thermoelastic diffusion half-spaces. Several cases of interest under different conditions are also deduced and discussed.
Edge Probability and Pixel Relativity-Based Speckle Reducing Anisotropic Diffusion.
Mishra, Deepak; Chaudhury, Santanu; Sarkar, Mukul; Soin, Arvinder Singh; Sharma, Vivek
2018-02-01
Anisotropic diffusion filters are one of the best choices for speckle reduction in the ultrasound images. These filters control the diffusion flux flow using local image statistics and provide the desired speckle suppression. However, inefficient use of edge characteristics results in either oversmooth image or an image containing misinterpreted spurious edges. As a result, the diagnostic quality of the images becomes a concern. To alleviate such problems, a novel anisotropic diffusion-based speckle reducing filter is proposed in this paper. A probability density function of the edges along with pixel relativity information is used to control the diffusion flux flow. The probability density function helps in removing the spurious edges and the pixel relativity reduces the oversmoothing effects. Furthermore, the filtering is performed in superpixel domain to reduce the execution time, wherein a minimum of 15% of the total number of image pixels can be used. For performance evaluation, 31 frames of three synthetic images and 40 real ultrasound images are used. In most of the experiments, the proposed filter shows a better performance as compared to the state-of-the-art filters in terms of the speckle region's signal-to-noise ratio and mean square error. It also shows a comparative performance for figure of merit and structural similarity measure index. Furthermore, in the subjective evaluation, performed by the expert radiologists, the proposed filter's outputs are preferred for the improved contrast and sharpness of the object boundaries. Hence, the proposed filtering framework is suitable to reduce the unwanted speckle and improve the quality of the ultrasound images.
Anta, Juan A; Mora-Seró, Iván; Dittrich, Thomas; Bisquert, Juan
2008-08-14
We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.
Energy Technology Data Exchange (ETDEWEB)
Bennacer, R. [Neuville sur Oise, LEEVAM 5 mail Gay Lussac, Cergy-Pontoise Cedex (France); Mohamad, A.A. [CEERE University of Calgary, Department of Mechanical and Manufacturing Engineering, Calgary, Alberta (Canada); Ganaoui, M.El [Faculte des Sciences et Techniques de Limoges, Limoges (France)
2005-02-01
Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media. (orig.)
International Nuclear Information System (INIS)
Zamengo, Massimiliano; Funada, Tomohiro; Morikawa, Junko
2017-01-01
Highlights: • Thermal diffusivity of Erythritol was measured by temperature wave method. • Thermal diffusivity was measured in function of temperature and during phase change. • Database of temperature-dependent thermal properties is used for numerical analysis. • Heat transfer and heat storage were analyzed in a fin-type heat exchanger. • Use of temperature-dependent properties in calculations lead to longer melting time. - Abstract: Temperature dependency of thermal diffusivity of erythritol was measured by temperature wave analysis (TWA) method. This modulating technique allowed measuring thermal diffusivity continuously, even during the phase transition solid-liquid. Together with specific heat capacity and specific enthalpy measured by differential scanning calorimetry, the values of measured properties were utilized in a bi-dimensional numerical model for analysis of heat transfer and heat storage performance. The geometry of the model is representative of a cross section of a fin-type heat exchanger, in which erythritol is filling the interspaces between fins. Time-dependent temperature change and heat storage performance were analyzed by considering the variation of thermophysical properties as a function of temperature. The numerical method can be utilized for a fast parametric analysis of heat transfer and heat storage performance into heat storage systems of phase-change materials and composites.
Sensitivity analysis of numerical results of one- and two-dimensional advection-diffusion problems
International Nuclear Information System (INIS)
Motoyama, Yasunori; Tanaka, Nobuatsu
2005-01-01
Numerical simulation has been playing an increasingly important role in the fields of science and engineering. However, every numerical result contains errors such as modeling, truncation, and computing errors, and the magnitude of the errors that are quantitatively contained in the results is unknown. This situation causes a large design margin in designing by analyses and prevents further cost reduction by optimizing design. To overcome this situation, we developed a new method to numerically analyze the quantitative error of a numerical solution by using the sensitivity analysis method and modified equation approach. If a reference case of typical parameters is calculated once by this method, then no additional calculation is required to estimate the results of other numerical parameters such as those of parameters with higher resolutions. Furthermore, we can predict the exact solution from the sensitivity analysis results and can quantitatively evaluate the error of numerical solutions. Since the method incorporates the features of the conventional sensitivity analysis method, it can evaluate the effect of the modeling error as well as the truncation error. In this study, we confirm the effectiveness of the method through some numerical benchmark problems of one- and two-dimensional advection-diffusion problems. (author)
Directory of Open Access Journals (Sweden)
Wu Jie
Full Text Available This paper presents an experimental and numerical model describing the effects of the aggregate shapes and exposure duration of chloride diffusion into cement-based materials. A simple chloride diffusion test was performed on a concrete specimen composed of a mixture of cement mortar with crushed granites and round gravels. A simulation was done and the numerical model developed was applied to the matrix at the meso-scale level and the chloride diffusivity was investigated at 30, 60, and 90 days. The experimental and simulation results showed that the aggregate shape and the exposure duration of chloride diffusing into concrete are of high significance. It was indicated that the model with crushed granite presents a good resistance against chloride ingress, while the model with rounded gravels shows some sensitivity to the chloride penetration. It was also found out that when the time dependence of the diffusion coefficient is not taken into account, the diffusion rate will be overestimated. The meso-scale model developed in this study also provides a new method applied in the analysis of the chloride and water transport that causes damage to concrete considering the particle inclusion and the diffusion duration. Keywords: Meso-scale modeling, Chloride diffusivity, Concrete, Effects of aggregates shape and exposure duration, FEM
Directory of Open Access Journals (Sweden)
Ahti Jaatinen-Värri
2014-01-01
Full Text Available The effect of the width of the vaneless diffuser on the stage performance and flow fields of a centrifugal compressor is studied numerically and experimentally. The diffuser width is varied by reducing the diffuser flow area from the shroud side (i.e., pinching the diffuser. Seven different diffuser widths are studied with numerical simulation. In the modeling, the diffuser width b/b2 is varied within the range 1.00 to 0.50. The numerical results are compared with results obtained in previous studies. In addition, two of the diffusers are further investigated with experimental measurement. The main finding of the work is that the pinch reduces losses in the impeller associated with the tip-clearance flow. Furthermore, it is shown that a too large width reduction causes the flow to accelerate excessively, resulting in a highly nonuniform flow field and flow separation near the shroud.
Kojic, M; Milosevic, M; Kojic, N; Kim, K; Ferrari, M; Ziemys, A
2014-02-01
Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts.
International Nuclear Information System (INIS)
Owolabi, Kolade M.
2016-01-01
The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.
International Nuclear Information System (INIS)
Kitazumi, Yuki; Shirai, Osamu; Yamamoto, Masahiro; Kano, Kenji
2013-01-01
Graphical abstract: - Highlights: • Diffuse double layers overlap with each other in the micropore. • The overlapping of the diffuse double layer affects the double layer capacitance. • The electric field becomes weak in the micropore. • The electroneutrality is unsatisfactory in the micropore. - Abstract: The structure of the diffuse double layer around a nm-sized micropore on porous electrodes has been studied by numerical simulation using the Poisson–Boltzmann equation. The double layer capacitance of the microporous electrode strongly depends on the electrode potential, the electrolyte concentration, and the size of the micropore. The potential and the electrolyte concentration dependence of the capacitance is different from that of the planner electrode based on the Gouy's theory. The overlapping of the diffuse double layer becomes conspicuous in the micropore. The overlapped diffuse double layer provides the mild electric field. The intensified electric field exists at the rim of the orifice of the micropore because of the expansion of the diffuse double layers. The characteristic features of microporous electrodes are caused by the heterogeneity of the electric field around the micropores
Kojic, M.; Milosevic, M.; Kojic, N.; Kim, K.; Ferrari, M.; Ziemys, A.
2014-01-01
Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts. PMID:24578582
Numerical Investigations of Unsteady Flow in a Centrifugal Pump with a Vaned Diffuser
Directory of Open Access Journals (Sweden)
Olivier Petit
2013-01-01
Full Text Available Computational fluid dynamics (CFD analyses were made to study the unsteady three-dimensional turbulence in the ERCOFTAC centrifugal pump test case. The simulations were carried out using the OpenFOAM Open Source CFD software. The test case consists of an unshrouded centrifugal impeller with seven blades and a radial vaned diffuser with 12 vanes. A large number of measurements are available in the radial gap between the impeller and the diffuse, making this case ideal for validating numerical methods. Results of steady and unsteady calculations of the flow in the pump are compared with the experimental ones, and four different turbulent models are analyzed. The steady simulation uses the frozen rotor concept, while the unsteady simulation uses a fully resolved sliding grid approach. The comparisons show that the unsteady numerical results accurately predict the unsteadiness of the flow, demonstrating the validity and applicability of that methodology for unsteady incompressible turbomachinery flow computations. The steady approach is less accurate, with an unphysical advection of the impeller wakes, but accurate enough for a crude approximation. The different turbulence models predict the flow at the same level of accuracy, with slightly different results.
Rybalkin, Andrey
Numerical assessments of radon diffusion together with analytical estimates for short-time and long-time exposure were the first objective of this thesis with the goal to demonstrate how radon propagates in various media. Theoretical predictions were compared to numerical simulations, and obtained values of total radon activities inside each material match quite well with the analytical estimates. These estimates, for activated and nonactivated charcoal, were then used to evaluate the possibility of designing a charcoal system to be used as a radon detector. Another objective was to use nonactivated charcoal samples and measure the level of radon accumulation, and use these data to estimate radon diffusion and adsorption coefficients. The analytical approach was developed to estimate these values. Radon adsorption coefficient in nonactivated charcoal was found to be from 0.2 to 0.4 m3/kg. Radon diffusion coefficient for nonactivated charcoal is in the range of 1.2×10-11 to 5.1×10-10 m2/s in comparison to activated charcoal with adsorption coefficient of 4 m3/kg and diffusion coefficient of 1.43×10-9 m2/s. The third objective was to use GEANT4 numerical code to simulate decay of 238U series and 222Rn in an arbitrary soil sample. Based on that model, the goal was to provide a guideline for merging GEANT4 radioactive decay modeling with the diffusion of radon in a soil sample. It is known that radon can be used as an earthquake predictor by measuring its concentration in groundwater, or if possible, along the faults. Numerical simulations of radon migration by diffusion only were made to estimate how fast and how far radon can move along the fault strands. Among the known cases of successful correlations between radon concentration anomalies and earthquake are the 1966 Tashkent and 1976 Songpan-Pingwu earthquakes. Thus, an idea of radon monitoring along the Wasatch Fault, using system of activated/nonactivated charcoals together with solid state radon detectors is
Analytical-numerical method for treatment of turbulent diffusion of particles in the air
International Nuclear Information System (INIS)
Arsov, L.J.
1976-01-01
This work deals with the problem of air pollution around a stationary punctual source. For description of air pollution from a punctual source a mathematical model is suggested, and for calculation of effluents concentration an analytical-numerical algorithm is given. In addition to the analitical treatment the mathematical model is far more flexible and complete. Eddy diffusivity is represented by an arbitrary function, and an arbitrary wind velocity profile ahs been proposed. The apsorption of the ground is introduced through a variable apsorption coefficient, and the sedimentation through the mean velocity of deposition. To determine the movement of particles a parabolic equation of diffusion is used. The method has been tested through calculation of effluents concentration for different values of physical parameters
International Nuclear Information System (INIS)
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
D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice
2018-05-01
In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
Danel, J.-F.; Kazandjian, L.; Zérah, G.
2012-06-01
Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.
Energy Technology Data Exchange (ETDEWEB)
Ahmadian, M T; Mehrabian, Amin [Center of Excellence in Design, Robotics and Automation, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2006-04-01
Valveless piezoelectric micropumps are in wide practical use due to their ability to conduct particles with absence of interior moving mechanical parts. In this paper, an extended numerical study on fluid flow through micropump chamber and diffuser valves is conducted to find out the optimum working conditions of micropump. In order to obtain maximum generality of the reported results, an analytical study along with a dimensional analysis is presented primarily, to investigate the main dimensionless groups of parameters affecting the micropump net flux. Consequently, the parameters appeared in the main dimensionless groups have been changed in order to understand how the pump rectification efficiency and optimum diffuser angle depend on these parameters. A set of characteristic curves are constructed which show these dependencies. The application of these curves would have far reaching implications for valveless micropumps design and selection purposes.
International Nuclear Information System (INIS)
Ahmadian, M T; Mehrabian, Amin
2006-01-01
Valveless piezoelectric micropumps are in wide practical use due to their ability to conduct particles with absence of interior moving mechanical parts. In this paper, an extended numerical study on fluid flow through micropump chamber and diffuser valves is conducted to find out the optimum working conditions of micropump. In order to obtain maximum generality of the reported results, an analytical study along with a dimensional analysis is presented primarily, to investigate the main dimensionless groups of parameters affecting the micropump net flux. Consequently, the parameters appeared in the main dimensionless groups have been changed in order to understand how the pump rectification efficiency and optimum diffuser angle depend on these parameters. A set of characteristic curves are constructed which show these dependencies. The application of these curves would have far reaching implications for valveless micropumps design and selection purposes
International Nuclear Information System (INIS)
Esmail, S.F.H.
2011-01-01
The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
Analysis of current diffusive ballooning mode in tokamaks
International Nuclear Information System (INIS)
Uchida, M.; Fukuyama, A.; Itoh, S.-I.; Yagi, M.
1999-12-01
The effect of finite gyroradius on the current diffusive ballooning mode is examined. Starting from the reduced MHD equations including turbulent transports, coupling with drift motion and finite gyroradius effect of ions, we derive a ballooning mode equation with complex transport coefficients. The eigenfrequency, saturation level and thermal diffusivity are evaluated numerically from the marginal stability condition. Preliminary results of their parameter dependence is presented. (author)
The brush model - a new approach to numerical modeling of matrix diffusion in fractured clay stone
International Nuclear Information System (INIS)
Lege, T.; Shao, H.
1998-01-01
A special approach for numerical modeling of contaminant transport in fractured clay stone is presented. The rock matrix and the fractures are simulated with individual formulations for FE grids and transport, coupled into a single model. The capacity of the rock matrix to take up contaminants is taken into consideration with a discrete simulation of matrix diffusion. Thus, the natural process of retardation due to matrix diffusion can be better simulated than by a standard introduction of an empirical parameter into the transport equation. Transport in groundwater in fractured clay stone can be simulated using a model called a 'brush model'. The 'brush handle' is discretized by 2-D finite elements. Advective-dispersive transport in groundwater in the fractures is assumed. The contaminant diffuses into 1D finite elements perpendicular to the fractures, i.e., the 'bristles of the brush'. The conclusion is drawn that matrix diffusion is an important property of fractured clay stone for contaminant retardation. (author)
Numerical simulation of a PSA system using a pore diffusion model
Energy Technology Data Exchange (ETDEWEB)
Raghavan, N S; Hassan, M M; Ruthven, D M
1986-01-01
A mathematical model has been developed for a pressure swing adsorption (PSA) system (heatless drier) in which the controlling resistance to mass transfer is diffusion within the pores of the adsorbent particles. The model equations are solved numerically by the method of orthogonal collocation. By comparing the solutions from this model with the solutions derived from the simpler linear driving force model it is shown that the simpler model provides an acceptable approximation provided that the coefficient (omega in eq. (1)) is chosen correctly. The appropriate value of omega depends on the cycle time and to a lesser extent on the degree of isotherm non-linearity and the nature of the diffusion mechanism, varying from about 40 at low cycle times to 15 or even lower at large cycle times. However, over a fairly wide range of conditions typical of PSA operation the linear driving force model with omega = 40 provides an acceptable approximation, except in the initial region of the transient. The value of omega recommended by Glueckauf for modelling of a fixed bed (omega = 15) is approached only at rather large cycle times and is clearly inappropriate for a PSA system under most practical conditions.
Diffusion of Zonal Variables Using Node-Centered Diffusion Solver
Energy Technology Data Exchange (ETDEWEB)
Yang, T B
2007-08-06
Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirable to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.
The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1995-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs
International Nuclear Information System (INIS)
Colombant, Denis; Manheimer, Wallace
2010-01-01
Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.
Ginsburger, Kévin; Poupon, Fabrice; Beaujoin, Justine; Estournet, Delphine; Matuschke, Felix; Mangin, Jean-François; Axer, Markus; Poupon, Cyril
2018-02-01
White matter is composed of irregularly packed axons leading to a structural disorder in the extra-axonal space. Diffusion MRI experiments using oscillating gradient spin echo sequences have shown that the diffusivity transverse to axons in this extra-axonal space is dependent on the frequency of the employed sequence. In this study, we observe the same frequency-dependence using 3D simulations of the diffusion process in disordered media. We design a novel white matter numerical phantom generation algorithm which constructs biomimicking geometric configurations with few design parameters, and enables to control the level of disorder of the generated phantoms. The influence of various geometrical parameters present in white matter, such as global angular dispersion, tortuosity, presence of Ranvier nodes, beading, on the extra-cellular perpendicular diffusivity frequency dependence was investigated by simulating the diffusion process in numerical phantoms of increasing complexity and fitting the resulting simulated diffusion MR signal attenuation with an adequate analytical model designed for trapezoidal OGSE sequences. This work suggests that angular dispersion and especially beading have non-negligible effects on this extracellular diffusion metrics that may be measured using standard OGSE DW-MRI clinical protocols.
Energy Technology Data Exchange (ETDEWEB)
Teamah, M.A. [Faculty of Engineering, Alexandria University, Mech. Eng. Dept, Alexandria (Egypt); El-Maghlany, W.M. [Faculty of Engineering, Suez Canal University, Ismailia (Egypt)
2010-09-15
The present study is concerned with the mixed convection in a rectangular lid-driven cavity under the combined buoyancy effects of thermal and mass diffusion. Double-diffusive convective flow in a rectangular enclosure with moving upper surface is studied numerically. Both upper and lower surfaces are being insulated and impermeable. Constant different temperatures and concentration are imposed along the vertical walls of the enclosure, steady state laminar regime is considered. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of Richardson number, Lewis number, and buoyancy ratio on the iso-contours of stream line, temperature, and concentration. In addition, the predicted results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for 0.1 <= Le <= 50 and Prandtl number Pr = 0.7. Through out the study the Grashof number and aspect ratio are kept constant at 10{sup 4} and 2 respectively and -10 <= N <= 10, while Richardson number has been varied from 0.01 to 10 to simulate forced convection dominated flow, mixed convection and natural convection dominated flow. (authors)
International Nuclear Information System (INIS)
Wang, Wenyan; Han, Bo; Yamamoto, Masahiro
2013-01-01
We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)
Numerical estimation of the effective electrical conductivity in carbon paper diffusion media
International Nuclear Information System (INIS)
Zamel, Nada; Li, Xianguo; Shen, Jun
2012-01-01
Highlights: ► Anisotropic effective electrical conductivity of the GDL is estimated numerically. ► The electrical conductivity is a key component in understanding the structure of the GDL. ► Expressions for evaluating the electrical conductivity were proposed. ► The tortuosity factor was evaluated as 1.7 and 3.4 in the in- and through-plane directions, respectively. - Abstract: The transport of electrons through the gas diffusion layer (GDL) of polymer electrolyte membrane (PEM) fuel cells has a significant impact on the optimal design and operation of PEM fuel cells and is directly affected by the anisotropic nature of the carbon paper material. In this study, a three-dimensional reconstruction of the GDL is used to numerically estimate the directional dependent effective electrical conductivity of the layer for various porosity values. The distribution of the fibers in the through-plane direction results in high electrical resistivity; hence, decreasing the overall effective electrical conductivity in this direction. This finding is in agreement with measured experimental data. Further, using the numerical results of this study, two mathematical expressions were proposed for the calculation of the effective electrical conductivity of the carbon paper GDL. Finally, the tortuosity factor was evaluated as 1.7 and 3.4 in the in- and through-plane directions, respectively.
Directory of Open Access Journals (Sweden)
Zhi-Jun Shuai
2015-08-01
Full Text Available The complex three-dimensional turbulent flow field in a centrifugal water pump with three asymmetrical diffusers was numerically simulated. The characteristics of pressure and force fluctuations inside the model pump were investigated. Fast Fourier transformation was performed to obtain the spectra of pressure and force fluctuations. It indicates that the dominant frequency of pressure fluctuations is the blade passing frequency in all the sub-domains inside the pump and the first blade passing frequency energy (first order of blade passing frequency is the most significant. The dominant frequency of pressure fluctuations at the location of diffuser outlet is featured by low frequency (less than 1 Hz, which may be due to the locally generated eddy structures. Besides, the dominant frequency force fluctuations on the impeller blades are also the blade passing frequency. The existence of the three asymmetrical diffusers has damping effect on the pressure fluctuation amplitude and energy amplitude of pressure fluctuations in the diffuser domain dramatically, which indicates that the diffusers can effectively control the hydraulically excited vibration in the pump. Besides, the prediction of the dominant frequency of pressure fluctuations inside the pump can help to utilize the pump effectively and to extend the pump life. The main findings of this work can provide prediction of the pump performance and information for further optimal design of centrifugal pumps as well.
International Nuclear Information System (INIS)
Schneider, D.
2001-01-01
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 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)
International Nuclear Information System (INIS)
Chih-Lung Chen; Institute of Nuclear Energy Research, Taoyuan, Taiwan; Tsing-Hai Wang; Shi-Ping Teng; Ching-Hor Lee
2014-01-01
Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet reservoir (OR)] can be fixed or vary. The combinations involve four distinct models (i.e., the CC-CC model, CC-VC model, VC-CC model, and the VC-VC model). Studies discussing the VC-CC model are scant. An analytical method considering the decay effect is required to accurately interpret the radioactive nuclide diffusion experiment results. Therefore, we developed a CC-CC model and a CC-VC model with a decay effect and the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC-CC method and CC-VC method). We also proposed two simplified methods using the VC-VC model to determine the diffusion coefficient straightforwardly based upon the concentration variation in IR and OR. More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment. In addition, applying our CC-VC method to those data reported from Radiochemica Acta 96:111-117, 2008; and J Contam Hydrol 35:55-65, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude. Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method. Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time. (author)
Polyhedral meshing in numerical analysis of conjugate heat transfer
Sosnowski, Marcin; Krzywanski, Jaroslaw; Grabowska, Karolina; Gnatowska, Renata
2018-06-01
Computational methods have been widely applied in conjugate heat transfer analysis. The very first and crucial step in such research is the meshing process which consists in dividing the analysed geometry into numerous small control volumes (cells). In Computational Fluid Dynamics (CFD) applications it is desirable to use the hexahedral cells as the resulting mesh is characterized by low numerical diffusion. Unfortunately generating such mesh can be a very time-consuming task and in case of complicated geometry - it may not be possible to generate cells of good quality. Therefore tetrahedral cells have been implemented into commercial pre-processors. Their advantage is the ease of its generation even in case of very complex geometry. On the other hand tetrahedrons cannot be stretched excessively without decreasing the mesh quality factor, so significantly larger number of cells has to be used in comparison to hexahedral mesh in order to achieve a reasonable accuracy. Moreover the numerical diffusion of tetrahedral elements is significantly higher. Therefore the polyhedral cells are proposed within the paper in order to combine the advantages of hexahedrons (low numerical diffusion resulting in accurate solution) and tetrahedrons (rapid semi-automatic generation) as well as to overcome the disadvantages of both the above mentioned mesh types. The major benefit of polyhedral mesh is that each individual cell has many neighbours, so gradients can be well approximated. Polyhedrons are also less sensitive to stretching than tetrahedrons which results in better mesh quality leading to improved numerical stability of the model. In addition, numerical diffusion is reduced due to mass exchange over numerous faces. This leads to a more accurate solution achieved with a lower cell count. Therefore detailed comparison of numerical modelling results concerning conjugate heat transfer using tetrahedral and polyhedral meshes is presented in the paper.
SNAP - a three dimensional neutron diffusion code
International Nuclear Information System (INIS)
McCallien, C.W.J.
1993-02-01
This report describes a one- two- three-dimensional multi-group diffusion code, SNAP, which is primarily intended for neutron diffusion calculations but can also carry out gamma calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP can solve the multi-group neutron diffusion equations using finite difference methods. The one-dimensional slab, cylindrical and spherical geometries and the two-dimensional case are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. (Author)
International Nuclear Information System (INIS)
Mittal, R.C.; Rohila, Rajni
2016-01-01
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
A New Numerical Scheme for Cosmic-Ray Transport
Jiang, Yan-Fei; Oh, S. Peng
2018-02-01
Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1994-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
rpe v5: an emulator for reduced floating-point precision in large numerical simulations
Dawson, Andrew; Düben, Peter D.
2017-06-01
This paper describes the rpe (reduced-precision emulator) library which has the capability to emulate the use of arbitrary reduced floating-point precision within large numerical models written in Fortran. The rpe software allows model developers to test how reduced floating-point precision affects the result of their simulations without having to make extensive code changes or port the model onto specialized hardware. The software can be used to identify parts of a program that are problematic for numerical precision and to guide changes to the program to allow a stronger reduction in precision.The development of rpe was motivated by the strong demand for more computing power. If numerical precision can be reduced for an application under consideration while still achieving results of acceptable quality, computational cost can be reduced, since a reduction in numerical precision may allow an increase in performance or a reduction in power consumption. For simulations with weather and climate models, savings due to a reduction in precision could be reinvested to allow model simulations at higher spatial resolution or complexity, or to increase the number of ensemble members to improve predictions. rpe was developed with a particular focus on the community of weather and climate modelling, but the software could be used with numerical simulations from other domains.
Diffusion Influenced Adsorption Kinetics.
Miura, Toshiaki; Seki, Kazuhiko
2015-08-27
When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.
Diffusion by extrinsic noise in the kicked Harper map
International Nuclear Information System (INIS)
Park, Gunyoung; Chang, C. S.
2001-01-01
A significantly improved analytic understanding of the extrinsically driven diffusion process is presented in a nonlinear dynamical system in which the phase space is divided into periodic two-dimensional tiles of regular motion, separated by a connected separatrix network (web) [previously studied by A. J. Lichtenberg and Blake P. Wood, Phys. Rev. Lett. >62, 2213 (1989)]. The system is represented by the usual 'kicked Harper map' with added extrinsic noise terms. Three different diffusion regimes are found depending upon the strength of the extrinsic perturbation l relative to the web and regular motions. When the extrinsic noise is dominant over the intrinsic stochasticity and the regular rotation motions in the tile, diffusion obeys the random phase scaling l 2 . When the extrinsic noise is dominant over the intrinsic stochasticity, but weaker than the regular rotation motion, the diffusion scales as lK 1/2 , where K is the strength of the intrinsic kick. These findings agree well with numerical simulation results. When the extrinsic noise process is weaker than the stochastic web process, we analytically reproduce the well-known numerical result: The web diffusion is reduced by the ratio of phase-space areas of intrinsic to extrinsic stochasticity
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Energy Technology Data Exchange (ETDEWEB)
Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Maday, Yvon, E-mail: maday@ann.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions and Institut Universitaire de France, F-75005, Paris (France); Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); Brown Univ, Division of Applied Maths, Providence, RI (United States); Riahi, Mohamed Kamel, E-mail: riahi@cmap.polytechnique.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CMAP, Inria-Saclay and X-Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); Salomon, Julien, E-mail: salomon@ceremade.dauphine.fr [CEREMADE, Univ Paris-Dauphine, Pl. du Mal. de Lattre de Tassigny, F-75016, Paris (France)
2014-12-15
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
Numerical methods for calculating thermal residual stresses and hydrogen diffusion
International Nuclear Information System (INIS)
Leblond, J.B.; Devaux, J.; Dubois, D.
1983-01-01
Thermal residual stresses and hydrogen concentrations are two major factors intervening in cracking phenomena. These parameters were numerically calculated by a computer programme (TITUS) using the FEM, during the deposition of a stainless clad on a low-alloy plate. The calculation was performed with a 2-dimensional option in four successive steps: thermal transient calculation, metallurgical transient calculation (determination of the metallurgical phase proportions), elastic-plastic transient (plain strain conditions), hydrogen diffusion transient. Temperature and phase dependence of hydrogen diffusion coefficient and solubility constant. The following results were obtained: thermal calculations are very consistent with experiments at higher temperatures (due to the introduction of fusion and solidification latent heats); the consistency is not as good (by 70 degrees) for lower temperatures (below 650 degrees C); this was attributed to the non-introduction of gamma-alpha transformation latent heat. The metallurgical phase calculation indicates that the heat affected zone is almost entirely transformed into bainite after cooling down (the martensite proportion does not exceed 5%). The elastic-plastic calculations indicate that the stresses in the heat affected zone are compressive or slightly tensile; on the other hand, higher tensile stresses develop on the boundary of the heat affected zone. The transformation plasticity has a definite influence on the final stress level. The return of hydrogen to the clad during the bainitic transformation is but an incomplete phenomenon and the hydrogen concentration in the heat affected zone after cooling down to room temperature is therefore sufficient to cause cold cracking (if no heat treatment is applied). Heat treatments are efficient in lowering the hydrogen concentration. These results enable us to draw preliminary conclusions on practical means to avoid cracking. (orig.)
Nested element method in multidimensional neutron diffusion calculations
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1983-01-01
A new numerical method is developed that is particularly efficient in solving the multidimensional neutron diffusion equation in geometrically complex systems. The needs for a generally applicable and fast running computer code have stimulated the inroad of a nonclassical (R-function) numerical method into the nuclear field. By using the R-functions, the geometrical components of the diffusion problem are a priori analytically implemented into the approximate solution. The class of functions, to which the approximate solution belongs, is chosen as close to the exact solution class as practically acceptable from the time consumption point of view. That implies a drastic reduction of the number of degrees of freedom, compared to the other methods. Furthermore, the reduced number of degrees of freedom enables calculation of large multidimensional problems on small computers
International Nuclear Information System (INIS)
Barros, R.C. de.
1992-05-01
Presented here is a new numerical nodal method for the simulation of the axial power distribution within nuclear reactors using the one-dimensional one speed kinetics diffusion model with one group of delayed neutron precursors. Our method is based on a spectral analysis of the nodal kinetics equations. These equations are obtained by integrating the original kinetics equations separately over a time step and over a spatial node, and then considering flat approximations for the forward difference terms. These flat approximations are the only approximations that are considered in the method. As a result, the spectral nodal method for space - time reactor kinetics generates numerical solutions for space independent problems or for time independent problems that are completely free from truncation errors. We show numerical results to illustrate the method's accuracy for coarse mesh calculations. (author)
Water transport in gas diffusion media for PEM fuel cells. Experimental and numerical investigation
Energy Technology Data Exchange (ETDEWEB)
Roth, Joerg
2010-08-20
The water flux in partially saturated hydrophobic carbon fibre paper for polymer electrolyte membrane fuel cell applications is investigated and compared with the frequently used constitutive two-phase flow model based on Darcy's law. Further, the first steps towards a math-based material design for gas diffusion media are explored in this thesis. Two self-developed ex-situ experiments to investigate the liquid water transport are introduced. The first is a newly developed buoyancy-based measurement of the pressuresaturation relationship on thin porous material with an accuracy of 0.5 kPa for the pressure and {+-} 5% for the saturation. The second experiment measures the pressure drop in dependence of flow rates down to magnitudes of {mu}L/s across the partially saturated thin porous material. This flow rate is relevant for the fuel cell application. The liquid water transport through Toray 060 carbon fibre paper, impregnated with 7% and 10% PTFE is investigated at wet and dry boundary conditions. The experiments are also accompanied by analytical and numerical free surface modelling with the consideration of the material morphology and liquid-solid interaction. The imbibing and draining cases of an arrangement of six fibres at varying solid-liquid interaction and boundary conditions are studied with 'Surface Evolver'. In order to evaluate the findings of ex-situ and modelling work for applicability to water transport in fuel cell operation, the technique of nuclear magnetic resonance (NMR) imaging is assessed. The focus is on the visualisation of 2D and 3D water distribution in the operating fuel cell. The compatibility of the NMR experiment with fuel cell operation in relation to material selection, operating temperature, and current density is addressed. NMR imaging is employed for different current densities, stoichiometries, and fuel cell arrangements. The fuel cell arrangements differ by the cathode diffusion medium. Plain, hydrophobic, and
Numerical simulation of alteration of sodium bentonite by diffusion of ionic groundwater components
International Nuclear Information System (INIS)
Jacobsen, J.S.; Carnahan, C.L.
1987-12-01
Experiments measuring the movement of trace amounts of radionuclides through compacted bentonite have typically used unaltered bentonite. Models based on experiments such as these may not lead to accurate predictions of the migration through altered or partially altered bentonite of radionuclides that undergo ion exchange. To address this problem, we have modified an existing transport code to include ion exchange and aqueous complexation reactions. The code is thus able to simulate the diffusion of major ionic groundwater components through bentonite and reactions between the bentonite and groundwater. Numerical simulations have been made to investigate the conversion of sodium bentonite to calcium bentonite for a reference groundwater characteristic of deep granitic formations. 20 refs., 2 figs., 2 tabs
Research on numerical simulation technology about regional important pollutant diffusion of haze
Du, Boying; Ma, Yunfeng; Li, Qiangqiang; Wang, Qi; Hu, Qiongqiong; Bian, Yushan
2018-02-01
In order to analyze the formation of haze in Shenyang and the factors that affect the diffusion of pollutants, the simulation experiment adopted in this paper is based on the numerical model of WRF/CALPUFF coupling. Simulation experiment was conducted to select PM10 of Shenyang City in the period from March 1 to 8, and the PM10 in the regional important haze was simulated. The survey was conducted with more than 120 enterprises section the point of the emission source of this experiment. The contrastive data were analyzed with 11 air quality monitoring points, and the simulation results were compared. Analyze the contribution rate of each typical enterprise to the air quality, verify the correctness of the simulation results, and then use the model to establish the prediction model.
3-D anisotropic neutron diffusion in optically thick media with optically thin channels
International Nuclear Information System (INIS)
Trahan, Travis J.; Larsen, Edward W.
2011-01-01
Standard neutron diffusion theory accurately approximates the neutron transport process for optically thick, scattering-dominated systems in which the angular neutron flux is a weak (nearly linear) function of angle. Therefore, standard diffusion theory is not directly applicable for Very High Temperature Reactor (VHTR) cores, which contain numerous narrow, axially-oriented, nearly-voided coolant channels. However, we have derived a new, accurate diffusion equation for such problems, which contains nonstandard anisotropic diffusion coefficients near and within the channels, but which reduces to the standard diffusion approximation away from the channels. The new diffusion approximation significantly improves the accuracy of VHTR diffusion simulations, while having lower computational cost than higher-order transport methods. (author)
Directory of Open Access Journals (Sweden)
Chen-Xing Jiang
2014-08-01
Full Text Available Natural supercavitations in water and turbulent drag-reducing solution were numerically simulated using unsteady Reynolds averaged Navier-Stokes (RANS scheme with mixture-multiphase model. The Cross viscosity equation was adopted to represent the fluid property of aqueous solution of drag-reducing additives. The characteristics of natural supercavity configuration and overall resistance of the navigating body were presented, respectively. The numerical simulation results indicated that, at the same cavitation number, the length and diameter of supercavity in drag-reducing solution are larger than those in water, and the drag coefficient of navigating body in solution is smaller than that in water; the surface tension plays an important role in incepting and maintaining the cavity. Turbulent drag-reducing additives have the potential in enhancement of supercavitation, drag reduction, and decrease of turbulent vortex structures. Numerical simulation results are consistent with the available experimental data.
Numerical models for differential problems
Quarteroni, Alfio
2017-01-01
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...
Multicomponent diffusion in two-temperature magnetohydrodynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.; Chang, C.H.
1996-01-01
A recent hydrodynamic theory of multicomponent diffusion in multitemperature gas mixtures [J. D. Ramshaw, J. Non-Equilib. Thermodyn. 18, 121 (1993)] is generalized to include the velocity-dependent Lorentz force on charged species in a magnetic field B. This generalization is used to extend a previous treatment of ambipolar diffusion in two-temperature multicomponent plasmas [J. D. Ramshaw and C. H. Chang, Plasma Chem. Plasma Process. 13, 489 (1993)] to situations in which B and the electrical current density are nonzero. General expressions are thereby derived for the species diffusion fluxes, including thermal diffusion, in both single- and two-temperature multicomponent magnetohydrodynamics (MHD). It is shown that the usual zero-field form of the Stefan-Maxwell equations can be preserved in the presence of B by introducing generalized binary diffusion tensors dependent on B. A self-consistent effective binary diffusion approximation is presented that provides explicit approximate expressions for the diffusion fluxes. Simplifications due to the small electron mass are exploited to obtain an ideal MHD description in which the electron diffusion coefficients drop out, resistive effects vanish, and the electric field reduces to a particularly simple form. This description should be well suited for numerical calculations. copyright 1996 The American Physical Society
Directory of Open Access Journals (Sweden)
E. D. Gopalakrishnan
2011-06-01
Full Text Available Numerical investigation of laminar diffusion flames established on a flat plate in a parallel air stream is presented. A numerical model with a multi-step chemical kinetics mechanism, variable thermo-physical properties, multi-component species diffusion and a radiation sub-model is employed for this purpose. Both upward and downward injection of fuel has been considered in a normal gravity environment. The thermal and aerodynamic structure of the flame has been explained with the help of temperature and species contours, net reaction rate of fuel and streamlines. Flame characteristics and stability aspects for several air and fuel velocity combinations have been studied. An important characteristic of a laminar boundary layer diffusion flame with upward injection of fuel is the velocity overshoot that occurs near the flame zone. This is not observed when the fuel is injected in the downward direction. The flame standoff distance is slightly higher for the downward injection of fuel due to increase in displacement thickness of boundary layer. Influence of an obstacle, namely the backward facing step, on the flame characteristics and stability aspects is also investigated. Effects of air and fuel velocities, size and location of the step are studied in detail. Based on the air and fuel velocities, different types of flames are predicted. The use of a backward-facing step as a flame holding mechanism for upward injection of fuel, results in increased stability limits due to the formation of a recirculation zone behind the step. The predicted stability limits match with experimentally observed limits. The step location is seen to play a more important role as compared to the step height in influencing the stability aspects of flames.
Numerical solution of multigroup diffuse equations of one-dimensional geometry
International Nuclear Information System (INIS)
Pavelesku, M.; Adam, S.
1975-01-01
The one-dimensional diffuse theory is used for reactor physics calculations of fast reactors. Computer program based on the one-dimensional diffuse theory is speedy and not memory consuming. The algorithm is described for the three-zone fast reactor criticality computation in one-dimensional diffusion approximation. This algorithm is realised on IBM 370/135 computer. (I.T.)
Directory of Open Access Journals (Sweden)
Elmira Ashpazzadeh
2018-04-01
Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Kozitskiy, Sergey
2018-05-01
Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.
Choi, Byungchul
2011-03-26
Experimental and numerical analyses of laminar diffusion flames were performed to identify the effect of fuel mixing on soot formation in a counterflow burner. In this experiment, the volume fraction, number density, and particle size of soot were investigated using light extinction/scattering systems. The experimental results showed that the synergistic effect of an ethylene-propane flame is appreciable. Numerical simulations showed that the benzene (C6H6) concentration in mixture flames was higher than in ethylene-base flames because of the increase in the concentration of propargyl radicals. Methyl radicals were found to play an important role in the formation of propargyl, and the recombination of propargyl with benzene was found to lead to an increase in the number density for cases exhibiting synergistic effects. These results imply that methyl radicals play an important role in soot formation, particularly with regard to the number density. © 2011 The Korean Society of Automotive Engineers and Springer-Verlag Berlin Heidelberg.
Zhao, Hong-Bao
2014-01-01
Taking the standard size coal block samples defined by ISRM as research objects, both properties of methane diffusion of coal block under triaxial compressive stress and characteristic influences caused by methane pressure were systematically studied with thermo-fluid-solid coupling with triaxial servocontrolled seepage equipment of methane-containing coal. The result shows the methane diffusion property of coal block under triaxial compressive stress was shown in four-stage as follow, first is sharply reduce stage, second is hyperbolic reduce stage, third is close to a fixed value stage, fourth stage is 0. There is a special point making the reduced rate of characteristic curve of methane diffusion speed become sharply small; the influences of shape of methane diffusion speed characteristic curve caused by methane pressure are not obvious, which only is shown in numerical size of methane diffusion speed. Test time was extended required by appear of the special point makes the reduce rate of methane diffusion speed become sharply small. The fitting four-phase relation of methane diffusion of coal block under triaxial compressive stress was obtained, and the idea is proposed that influences of the fitting four-phase relation caused by methane pressure were only shown in value of fitting parameters. PMID:25531000
International Nuclear Information System (INIS)
Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi; Komiyama, Sumito; Numata, Kunio
2009-01-01
A numerical simulation method for predicting atmospheric flow and stack gas diffusion using a calculation domain of several km around a stack under complex terrain conditions containing buildings has been developed. The turbulence closure technique using a modified k-ε-type model without a hydrostatic approximation was used for flow calculation, and some of the calculation grids near the ground were treated as buildings using a terrain-following coordinate system. Stack gas diffusion was predicted using the Lagrangian particle model, that is, the stack gas was represented by trajectories of released particles. The developed numerical model was applied to a virtual terrain and building conditions in this study prior to the applications of a numerical model for real terrain and building conditions. The height of the additional building (H a ), located about 200 m leeward from the stack, was varied (i.e., H a =0, 20, 30 and 50 m), and its effects on airflow and the concentration of stack gas at a released height of 75 m were calculated. Furthermore, effective stack height, which was used in the safety analysis of atmospheric diffusion for nuclear facilities in Japan, was evaluated from the calculated ground-level concentration of stack gas. The cavity region behind the additional building was calculated, and turbulence near the cavity was observed to decrease when the additional building was present. According to these flow variations with the additional building, tracer gas tended to diffuse to the ground surface rapidly with the additional building at the leeward position of the cavity, and the ground-level stack gas concentration along the plume axis also increased with the height of the additional building. However, the variations in effective stack height with the height of the additional building were relatively small and ranged within several m in this study. (author)
Directory of Open Access Journals (Sweden)
Chen-Xing Jiang
2014-04-01
Full Text Available The configurational and dynamic characteristics of water entry supercavities influenced by turbulent drag-reducing additives were studied through supercavitating projectile approach, experimentally and numerically. The projectile was projected vertically into water and aqueous solution of CTAC with weight concentrations of 100, 500, and 1000 ppm, respectively, using a pneumatic nail gun. The trajectories of the projectile and the supercavity configuration were recorded by a high-speed CCD camera. Besides, water entry supercavities in water and CTAC solution were numerically simulated based on unsteady RANS scheme, together with application of VOF multiphase model. The Cross viscosity model was adopted to represent the fluid property of CTAC solution. It was obtained that the numerical simulation results are in consistence with experimental data. Numerical and experimental results all show that the length and diameter of supercavity in drag-reducing solution are larger than those in water, and the drag coefficient is smaller than that in water; the maintaining time of supercavity is longer in solution as well. The surface tension plays an important role in maintaining the cavity. Turbulent drag-reducing additives have the potential in enhancement of supercavitation and drag reduction.
Trapped ion depletion by anomalous diffusion due to the dissipative trapped ion instability
International Nuclear Information System (INIS)
Wimmel, H.K.
1975-07-01
At high temperatures the KADOMTSEV-POGUTSE diffusion in tokamaks can become so large as to cause depletion of trapped ions if these are replaced with free ions by means of collisions rather than being directly recycled or injected. Modified KADOMTSEV-POGUTSE diffusion formulas are employed in order to estimate this effect in the cases of classical and anomalous collisions. The maximum trapped-ion depletion is estimated from the PENROSE stability condition. For anomalous collisions a BOHM-type diffusion is derived. Numerical examples are given for JET-like parameters (JET = Joint European Torus). Depletion is found to reduce diffusion by factors of up to 10 and more. (orig.) [de
Sushko, Gennady B; Verkhovtsev, Alexey V; Yakubovich, Alexander V; Schramm, Stefan; Solov'yov, Andrey V
2014-08-21
The process of self-diffusion of titanium atoms in a bulk material, on grain junctions and on surface is explored numerically in a broad temperature range by means of classical molecular dynamics simulation. The analysis is carried out for a nanoscale cylindrical sample consisting of three adjacent sectors and various junctions between nanocrystals. The calculated diffusion coefficient varies by several orders of magnitude for different regions of the sample. The calculated values of the bulk diffusion coefficient correspond reasonably well to the experimental data obtained for solid and molten states of titanium. Investigation of diffusion in the nanocrystalline titanium is of a significant importance because of its numerous technological applications. This paper aims to reduce the lack of data on diffusion in titanium and describe the processes occurring in bulk, at different interfaces and on surface of the crystalline titanium.
International Nuclear Information System (INIS)
Jiang, C X; Cheng, J P; Li, F C
2015-01-01
This paper attempts to introduce a numerical simulation procedure to simulate water-entry problems influenced by turbulent drag-reducing additives in a viscous incompressible medium. Firstly we performed a numerical investigation on water-entry supercavities in water and turbulent drag-reducing solution at the impact velocity of 28.4 m/s to confirm the accuracy of the numerical method. Based on the verification, projectile entering water and turbulent drag-reducing solution at relatively high velocity of 142.7 m/s (phase transition is considered) is simulated. The cross viscosity equation was adopted to represent the shear-thinning characteristic of aqueous solution of drag-reducing additives. The configuration and dynamic characteristics of water entry supercavity, flow resistance were discussed respectively. It was obtained that the numerical simulation results are in consistence with experimental data. Numerical results show that the supercavity length in drag-reducing solution is larger than one in water and the velocity attenuates faster at high velocity than at low velocity; the influence of drag-reducing solution is more obvious at high impact velocity. Turbulent drag-reducing additives have the great potential for enhancement of supercavity
Numerical simulation model of hyperacute/acute stage white matter infarction.
Sakai, Koji; Yamada, Kei; Oouchi, Hiroyuki; Nishimura, Tsunehiko
2008-01-01
Although previous studies have revealed the mechanisms of changes in diffusivity (apparent diffusion coefficient [ADC]) in acute brain infarction, changes in diffusion anisotropy (fractional anisotropy [FA]) in white matter have not been examined. We hypothesized that membrane permeability as well as axonal swelling play important roles, and we therefore constructed a simulation model using random walk simulation to replicate the diffusion of water molecules. We implemented a numerical diffusion simulation model of normal and infarcted human brains using C++ language. We constructed this 2-pool model using simple tubes aligned in a single direction. Random walk simulation diffused water. Axon diameters and membrane permeability were then altered in step-wise fashion. To estimate the effects of axonal swelling, axon diameters were changed from 6 to 10 microm. Membrane permeability was altered from 0% to 40%. Finally, both elements were combined to explain increasing FA in the hyperacute stage of white matter infarction. The simulation demonstrated that simple water shift into the intracellular space reduces ADC and increases FA, but not to the extent expected from actual human cases (ADC approximately 50%; FA approximately +20%). Similarly, membrane permeability alone was insufficient to explain this phenomenon. However, a combination of both factors successfully replicated changes in diffusivity indices. Both axonal swelling and reduced membrane permeability appear important in explaining changes in ADC and FA based on eigenvalues in hyperacute-stage white matter infarction.
Event-triggered synchronization for reaction-diffusion complex networks via random sampling
Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng
2018-04-01
In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.
Diffusion of radionuclide chains through an adsorbing medium
International Nuclear Information System (INIS)
Burkholder, H.C.; DeFigh-Price, C.
1977-01-01
The diffusion of radionuclide chains from an underground nuclear waste disposal site through the surrounding geologic medium to the surface is investigated for impulse and band releases. Numerical calculation of the analytical solutions shows that differences in adsorption characteristics among chain members and radioactive decay during transit reduce radionuclide discharges to the biosphere. Results suggest that molecular diffusion is unlikely to be an important transfer mechanism from geologic isolation, and that disposal of radionuclides in deep geologic formations and in the seabed under conditions of very low or nonexistent water flow is likely to be very effective in preventing radioactivity releases to the biosphere
International Nuclear Information System (INIS)
Xuelin, Tang Xue; Liyuan, Bian; Fujun, Wang; Xiaoqin, Lin; Man, Hao
2013-01-01
A cavitation model with thermodynamic effects for cavitating flows in a diffuser-type centrifugal pump is developed based on the bubble two-phase flow model. The proposed cavitation model includes mass, momentum, and energy transportations according to the thermodynamic mechanism of cavitation. Numerical simulations are conducted inside the entire passage of the centrifugal pump by using the proposed cavitation model and the renormalization group-based k - ε turbulent model coupled with the energy transportation equation. By using the commercial computational fluid dynamics software FLUENT 6.3, we have shown that the predicted performance characteristics of the pump, as well as the pressure, vapor, and density distributions in the impeller, agree well with that calculated by the full cavitation model. Simulation results show that cavitation initially occurs slightly behind the inlet of the blade suction surface, i.e., the area with maximum vapor concentration and minimum pressure. The predicted temperature field shows that the reduction in temperature restrains the growth of cavitating bubbles. Therefore, the thermodynamic effect should be treated as a necessary factor in cavitation models. Comparison results validate the efficiency and accuracy of the numerical technique in simulating cavitation flows in centrifugal pumps.
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Implementation and assessment of high-resolution numerical methods in TRACE
Energy Technology Data Exchange (ETDEWEB)
Wang, Dean, E-mail: wangda@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley RD 6167, Oak Ridge, TN 37831 (United States); Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G. [U.S. Nuclear Regulatory Commission, Washington, DC 20555 (United States)
2013-10-15
Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency.
Implementation and assessment of high-resolution numerical methods in TRACE
International Nuclear Information System (INIS)
Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G.
2013-01-01
Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency
Directory of Open Access Journals (Sweden)
Nobumichi Fujisawa
2017-01-01
Full Text Available The transition process from a diffuser rotating stall to a stage stall in a centrifugal compressor with a vaned diffuser was investigated by experimental and numerical analyses. From the velocity measurements, it was found that the rotating stall existed on the shroud side of the diffuser passage in the off-design flow condition. The numerical results revealed the typical vortical structure of the diffuser stall. The diffuser stall cell was caused by the systematic vortical structure which consisted of the tornado-type vortex, the longitudinal vortex at the shroud/suction surface corner (i.e., leading edge vortex (LEV, and the vortex in the throat area of the diffuser passages. Furthermore, the stage stall, which rotated within both the impeller and diffuser passages, occurred instead of the diffuser stall as the mass flow rate was decreased. According to the velocity measurements at the diffuser inlet, the diffuser stall which rotated on the shroud side was shifted to the hub side. Then, the diffuser stall moved into the impeller passages and formed the stage stall. Therefore, the stage stall was caused by the development of the diffuser stall, which transferred from the shroud side to the hub side in the vaneless space and expanded to the impeller passages.
Nodal spectrum method for solving neutron diffusion equation
International Nuclear Information System (INIS)
Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.
1999-01-01
Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations
Lynn, K. J.; Warren, J. M.
2017-12-01
Nominally anhydrous minerals (NAMs) are important for characterizing deep-Earth water reservoirs, but the water contents of olivine (ol), orthopyroxene (opx), and clinopyroxene (cpx) in peridotites generally do not reflect mantle equilibrium conditions. Ol is typically "dry" and decoupled from H in cpx and opx, which is inconsistent with models of partial melting and/or diffusive loss of H during upwelling beneath mid-ocean ridges. The rehydration of mantle pyroxenes via late-stage re-fertilization has been invoked to explain their relatively high water contents. Here, we use sophisticated 3D diffusion models (after Shea et al., 2015, Am Min) of H in ol, opx, and cpx to investigate the timescales of rehydration across a range of conditions relevant for melt-rock interaction and serpentinization of peridotites. Numerical crystals with 1 mm c-axis lengths and realistic crystal morphologies are modeled using recent H diffusivities that account for compositional variation and diffusion anisotropy. Models were run over timescales of minutes to millions of years and temperatures from 300 to 1200°C. Our 3D models show that, at the high-T end of the range, H concentrations in the cores of NAMs are partially re-equilibrated in as little as a few minutes, and completely re-equilibrated within hours to weeks. At low-T (300°C), serpentinization can induce considerable diffusion in cpx and opx. H contents are 30% re-equilibrated after continuous exposure to hydrothermal fluids for 102 and 105 years, respectively, which is inconsistent with previous interpretations that there is no effect on H in opx under similar conditions. Ol is unaffected after 1 Myr due to the slower diffusivity of the proton-vacancy mechanism at 300°C (2-4 log units lower than for opx). In the middle of the T range (700-1000°C), rehydration of opx and cpx occurs over hours to days, while ol is somewhat slower to respond (days to weeks), potentially allowing the decoupling observed in natural samples to
China's numerical management system for reducing national energy intensity
International Nuclear Information System (INIS)
Li, Huimin; Zhao, Xiaofan; Yu, Yuqing; Wu, Tong; Qi, Ye
2016-01-01
In China, the national target for energy intensity reduction, when integrated with target disaggregation and information feedback systems, constitutes a numerical management system, which is a hallmark of modern governance. This paper points out the technical weaknesses of China's current numerical management system. In the process of target disaggregation, the national target cannot be fully disaggregated to local governments, sectors and enterprises without omissions. At the same time, governments at lower levels face pressure for reducing energy intensity that exceeds their respective jurisdictions. In the process of information feedback, information failure is inevitable due to statistical inaccuracy. Furthermore, the monitoring system is unable to correct all errors, and data verification plays a limited role in the examination system. To address these problems, we recommend that the government: use total energy consumption as the primary indicator of energy management; reform the accounting and reporting of energy statistics toward greater consistency, timeliness and transparency; clearly define the responsibility of the higher levels of government. - Highlights: •We assess drawbacks of China's numerical management system for energy intensity. •The national energy intensity target cannot be fully disaggregated without omissions. •Data distortion is due to failures in statistics, monitoring and examination system. •Lower-level governments’ ability to meet energy target is weaker than their pressure. •We provide three policy recommendations for China's policy-makers.
Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations
International Nuclear Information System (INIS)
Arkhincheev, V.E.
2001-04-01
To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)
Mustapha, K.
2017-06-03
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le
2017-01-01
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Solute redistribution in dendritic solidification with diffusion in the solid
Ganesan, S.; Poirier, D. R.
1989-01-01
An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion is characterized by the instantaneous and average diffusion parameters. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. Numerical results are presented as an approximate model, which is used to predict the average diffusion parameter and calculate the composition of the interdendritic liquid during solidification.
Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.
2013-01-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to
Axial dispersion via shear-enhanced diffusion in colloidal suspensions
Griffiths, I. M.
2012-03-01
The familiar example of Taylor dispersion of molecular solutes is extended to describe colloidal suspensions, where the fluctuations that contribute to dispersion arise from hydrodynamic interactions. The generic scheme is illustrated for a suspension of particles in a pressure-driven pipe flow, with a concentration-dependent diffusivity that captures both the shear-induced and Brownian contributions. The effect of the cross-stream migration via shear-induced diffusion is shown to dramatically reduce the axial dispersion predicted by classical Taylor dispersion for a molecular solute. Analytic and numerical solutions are presented that illustrate the effect of the concentration dependence of this nonlinear hydrodynamic mechanism. Copyright © EPLA, 2012.
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
Zhou, Zhen; Hernandez Perez, Francisco; Shoshin, Yuriy; van Oijen, Jeroen A.; de Goey, Laurentius P.H.
2017-01-01
The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H2 while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H2 is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H2 on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H2 caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.
Zhou, Zhen
2017-04-12
The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H2 while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H2 is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H2 on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H2 caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.
Atmospheric diffusion of large clouds
Energy Technology Data Exchange (ETDEWEB)
Crawford, T. V. [Univ. of California, Lawrence Radiation Lab., Livermore, California (United States)
1967-07-01
Clouds of pollutants travel within a coordinate system that is fixed to the earth's surface, and they diffuse and grow within a coordinate system fixed to the cloud's center. This paper discusses an approach to predicting the cloud's properties, within the latter coordinate system, on space scales of a few hundred meters to a few hundred kilometers and for time periods of a few days. A numerical cloud diffusion model is presented which starts with a cloud placed arbitrarily within the troposphere. Similarity theories of atmospheric turbulence are used to predict the horizontal diffusivity as a function of initial cloud size, turbulent atmospheric dissipation, and time. Vertical diffusivity is input as a function of time and height. Therefore, diurnal variations of turbulent diffusion in the boundary layer and effects of temperature inversions, etc. can be modeled. Nondiffusive cloud depletion mechanisms, such as dry deposition, washout, and radioactive decay, are also a part of this numerical model. An effluent cloud, produced by a reactor run at the Nuclear Rocket Development Station, Nevada, is discussed in this paper. Measurements on this cloud, for a period of two days, are compared to calculations with the above numerical cloud diffusion model. In general, there is agreement. within a factor of two, for airborne concentrations, cloud horizontal area, surface air concentrations, and dry deposition as airborne concentration decreased by seven orders of magnitude during the two-day period. (author)
Takeda, M; Hiratsuka, T; Ito, K; Finsterle, S
2011-04-25
Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an
Energy Technology Data Exchange (ETDEWEB)
Takeda, M.; Hiratsuka, T.; Ito, K.; Finsterle, S.
2011-02-01
Diffusion anisotropy is a critical property in predicting migration of substances in sedimentary formations with very low permeability. The diffusion anisotropy of sedimentary rocks has been evaluated mainly from laboratory diffusion experiments, in which the directional diffusivities are separately estimated by through-diffusion experiments using different rock samples, or concurrently by in-diffusion experiments in which only the tracer profile in a rock block is measured. To estimate the diffusion anisotropy from a single rock sample, this study proposes an axisymmetric diffusion test, in which tracer diffuses between a cylindrical rock sample and a surrounding solution reservoir. The tracer diffusion between the sample and reservoir can be monitored from the reservoir tracer concentrations, and the tracer profile could also be obtained after dismantling the sample. Semi-analytical solutions are derived for tracer concentrations in both the reservoir and sample, accounting for an anisotropic diffusion tensor of rank two as well as the dilution effects from sampling and replacement of reservoir solution. The transient and steady-state analyses were examined experimentally and numerically for different experimental configurations, but without the need for tracer profiling. These experimental configurations are tested for in- and out-diffusion experiments using Koetoi and Wakkanai mudstones and Shirahama sandstone, and are scrutinized by a numerical approach to identify favorable conditions for parameter estimation. The analysis reveals the difficulty in estimating diffusion anisotropy; test configurations are proposed for enhanced identifiability of diffusion anisotropy. Moreover, it is demonstrated that the axisymmetric diffusion test is efficient in obtaining the sorption parameter from both steady-state and transient data, and in determining the effective diffusion coefficient if isotropic diffusion is assumed. Moreover, measuring reservoir concentrations in an
A case of mumps-related acute encephalopathy with biphasic seizures and late reduced diffusion.
Hazama, Kyoko; Shiihara, Takashi; Tsukagoshi, Hiroyuki; Hasegawa, Shunji; Dowa, Yuri; Watanabe, Mio
2017-10-01
Mumps is a common childhood viral disease characterized by fever and swelling of the parotid gland. The prognosis is generally good, although some complications, such as encephalitis (0.1%), exist. Acute encephalopathy with biphasic seizures and late reduced diffusion is the most common type of acute encephalopathy. However, this type of encephalopathy has not been reported in association with mumps infection. A previously healthy 3-year-old Japanese boy had a brief convulsion after fever for 3days, and then had conscious disturbance and parotitis. After several days, he had a second brief convulsion and was admitted. Increased serum amylase levels and presence of anti-mumps immunoglobulin M antibody confirmed mumps parotitis. The patient had another brief seizure later the day of admission. He did not have status or cluster seizures, although the biphasic nature of his seizures, conscious disturbance between the seizures, no pleocytosis in cerebrospinal fluid, and brain magnetic resonance images were consistent with acute encephalopathy with biphasic seizures and late reduced diffusion. In Japan, the mumps vaccine is not administered as a part of routine immunizations. It thus has low coverage (30-40%), and as a result, mumps infections are still common. However, this is the first case of mumps-related acute encephalopathy with biphasic seizures and late reduced diffusion. This case may be representative of only a minority of patients with mumps-associated central nervous system involvement. Nevertheless, this diagnostic possibility may be considered. In order to prevent mumps-related complications, routine mumps vaccination might be warranted. Copyright © 2017 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.
Effect of Ambipolar Diffusion on Ion Abundances in Contracting Protostellar Cores
Ciolek, Glenn E.; Mouschovias, Telemachos Ch.
1998-09-01
Numerical simulations and analytical solutions have established that ambipolar diffusion can reduce the dust-to-gas ratio in magnetically and thermally supercritical cores during the epoch of core formation. We study the effect that this has on the ion chemistry in contracting protostellar cores and present a simplified analytical method that allows one to calculate the ion power-law exponent k (≡d ln ni/d ln nn, where ni and nn are the ion and neutral densities, respectively) as a function of core density. We find that, as in earlier numerical simulations, no single value of k can adequately describe the ion abundance for nn 1/2 during the core formation epoch (densities principle, to determine whether ambipolar diffusion is responsible for core formation in interstellar molecular clouds. For densities >>105 cm-3, k is generally <<1/2.
Directory of Open Access Journals (Sweden)
A. R. Appadu
2013-01-01
for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to the L1 norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values of k and h. Two optimisation techniques are then implemented to find the optimal values of k when h=0.02 for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.
Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M
2010-06-01
Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.
Calculating effective diffusivities in the limit of vanishing molecular diffusion
International Nuclear Information System (INIS)
Pavliotis, G.A.; Stuart, A.M.; Zygalakis, K.C.
2009-01-01
In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the limit of vanishing molecular diffusion. In this limit traditional numerical methods typically fail, since they do not represent accurately the geometry of the underlying deterministic dynamics. We propose a stochastic splitting method that takes into account the volume-preserving property of the equations of motion in the absence of noise, and when inertial effects can be neglected. An extension of the method is then proposed for the cases where the noise has a non-trivial time-correlation structure and when inertial effects cannot be neglected. The method of modified equations is used to explain failings of Euler-based methods. The new stochastic geometric integrators are shown to outperform standard Euler-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators
Ortiz, J. P.; Ortega, A. D.; Harp, D. R.; Boukhalfa, H.; Stauffer, P. H.
2017-12-01
Gas transport in unsaturated fractured media plays an important role in a variety of applications, including detection of underground nuclear explosions, transport from volatile contaminant plumes, shallow CO2 leakage from carbon sequestration sites, and methane leaks from hydraulic fracturing operations. Gas breakthrough times are highly sensitive to uncertainties associated with a variety of hydrogeologic parameters, including: rock type, fracture aperture, matrix permeability, porosity, and saturation. Furthermore, a couple simplifying assumptions are typically employed when representing fracture flow and transport. Aqueous phase transport is typically considered insignificant compared to gas phase transport in unsaturated fracture flow regimes, and an assumption of instantaneous dissolution/volatilization of radionuclide gas is commonly used to reduce computational expense. We conduct this research using a twofold approach that combines laboratory gas experimentation and numerical modeling to verify and refine these simplifying assumptions in our current models of gas transport. Using a gas diffusion cell, we are able to measure air pressure transmission through fractured tuff core samples while also measuring Xe gas breakthrough measured using a mass spectrometer. We can thus create synthetic barometric fluctuations akin to those observed in field tests and measure the associated gas flow through the fracture and matrix pore space for varying degrees of fluid saturation. We then attempt to reproduce the experimental results using numerical models in PLFOTRAN and FEHM codes to better understand the importance of different parameters and assumptions on gas transport. Our numerical approaches represent both single-phase gas flow with immobile water, as well as full multi-phase transport in order to test the validity of assuming immobile pore water. Our approaches also include the ability to simulate the reaction equilibrium kinetics of dissolution
Diffusion bonding of reduced activation ferritic steel F82H for demo blanket application
International Nuclear Information System (INIS)
Kurasawa, T.; Tamura, M.
1996-01-01
A reduced activation ferritic steel, a grade F82H developed by JAERI, is a promising candidate structural material for the blanket and the first wall of DEMO reactors. In the present study, diffusion bonding of F82H has been investigated to develop the fabrication procedures of the blanket box and the first wall panel with cooling channels embedded by F82H. The parameters examined are the bonding temperature (810-1050 C), bonding pressure (2-10 MPa) and roughness of the bonding surface (0.5-12.8 μR max ), and metallurgical examination and mechanical tests of the diffusion bonded joints have been conducted. From the tests, sufficient bonding was obtained under the temperatures of 840-1 050 C (compressive stress of 3-12 MPa), and it was found that heat treatment following diffusion bonding is essential to obtain the mechanical properties similar to that of the base metal. (orig.)
Sooting Characteristics and Modeling in Counterflow Diffusion Flames
Wang, Yu
2013-11-01
Soot formation is one of the most complex phenomena in combustion science and an understanding of the underlying physico-chemical mechanisms is important. This work adopted both experimental and numerical approaches to study soot formation in laminar counterfl ow diffusion flames. As polycyclic aromatic hydrocarbons (PAHs) are the precursors of soot particles, a detailed gas-phase chemical mechanism describing PAH growth upto coronene for fuels with 1 to 4 carbon atoms was validated against laminar premixed and counter- flow diffusion fl ames. Built upon this gas-phase mechanism, a soot model was then developed to describe soot inception and surface growth. This soot model was sub- sequently used to study fuel mixing effect on soot formation in counterfl ow diffusion flames. Simulation results showed that compared to the baseline case of the ethylene flame, the doping of 5% (by volume) propane or ethane in ethylene tends to increase the soot volume fraction and number density while keeping the average soot size almost unchanged. These results are in agreement with experimental observations. Laser light extinction/scattering as well as laser induced fluorescence techniques were used to study the effect of strain rate on soot and PAH formation in counterfl ow diffusion ames. The results showed that as strain rate increased both soot volume fraction and PAH concentrations decreased. The concentrations of larger PAH were more sensitive to strain rate compared to smaller ones. The effect of CO2 addition on soot formation was also studied using similar experimental techniques. Soot loading was reduced with CO2 dilution. Subsequent numerical modeling studies were able to reproduce the experimental trend. In addition, the chemical effect of CO2 addition was analyzed using numerical data. Critical conditions for the onset of soot were systematically studied in counterfl ow diffusion ames for various gaseous hydrocarbon fuels and at different strain rates. A sooting
Heat Transfer and Mass Diffusion in Nanofluids over a Moving Permeable Convective Surface
Directory of Open Access Journals (Sweden)
Muhammad Qasim
2013-01-01
Full Text Available Heat transfer and mass diffusion in nanofluid over a permeable moving surface are investigated. The surface exhibits convective boundary conditions and constant mass diffusion. Effects of Brownian motion and thermophoresis are considered. The resulting partial differential equations are reduced into coupled nonlinear ordinary differential equations using suitable transformations. Shooting technique is implemented for the numerical solution. Velocity, temperature, and concentration profiles are analyzed for different key parameters entering into the problem. Performed comparative study shows an excellent agreement with the previous analysis.
Energy Technology Data Exchange (ETDEWEB)
Lee, Su Ryong [Seoul National University of Technology, Seoul (Korea, Republic of)
2014-06-15
Nonlinear characteristics of cellular counterflow diffusion flame near the radiative extinction limit at large Damköhler number are numerically investigated. Lewis number is assumed to be 0.5 and flame evolution is calculated by imposing an infinitesimal disturbance to a one-dimensional(1-D) steady state flame. The early stage of nonlinear development is very similar to that predicted in a linear stability analysis. The disturbance with the wavenumber of the fastest growing mode emerges and grows gradually. Eventual, an alternating pattern of reacting and quenching stripes is developed. The cellular flame temperature is higher than that of 1-D flame because of the gain of the total enthalpy. As the Damköhler number is further increased, the shape of the cell becomes circular to increase the surface area per unit reacting volume. The cellular flames do not extinguish but survive even above the 1-D steady state extinction condition.
Directory of Open Access Journals (Sweden)
Jinzhou Zhao
2016-06-01
Full Text Available Hydraulic fracturing is an essential technology in developing shale gas reservoirs, not to mention, accurate prediction of productivity in fractured shale gas wells is the foundation of an efficient development in shale gas reservoirs. This paper establishes a gas–water two-phase flow percolation mathematical model by a determined numerical simulation and calculation method under desorption and diffusion conditions. By means of simulating for a post-frac performance of the shale gas reservoir, this paper devotes to a quantitative analysis the impact of fracture parameters, physical parameters, and desorption–diffusion parameters. The outcome of this research indicates that hydraulic fracturing can improve single well production and it's an effective measure in the development of shale gas. The conductivity of hydraulic fractures and the permeability of natural fractures are the main influences on shale gas production. The higher these factors are, the higher the gas and water productions are. In comparison, the matrix permeability and diffusion coefficients have minimal influences on production.
Sandu, Mihnea; Nastase, Ilinca; Bode, Florin; Croitoru, CristianaVerona; Tacutu, Laurentiu
2018-02-01
The paper focus on the air quality inside the Crew Quarters on board of the International Space Station. Several issues to improve were recorded by NASA and ESA and most important of them are the following: noise level reduction, CO2 accumulation reduction and dust accumulation reduction. The study in this paper is centred on a reduced scaled model used to provide simulations related to the air diffusion inside the CQ. It is obvious that a new ventilation system is required to achieve the three issues mentioned above, and the solutions obtained by means of numerical simulation need to be validated by experimental approach. First of all we have built a reduced scaled physical model to simulate the flow pattern inside the CQ and the equipment inside the CQ has been reproduced using a geometrical scale ratio. The flow pattern was considered isothermal and incompressible. The similarity criteria used was the Reynolds number to characterize the flow pattern and the length scale was set at value 1/4. Water has been used inside the model to simulate air. Velocity magnitude vectors have been obtained using PIV measurement techniques.
Directory of Open Access Journals (Sweden)
Sandu Mihnea
2018-01-01
Full Text Available The paper focus on the air quality inside the Crew Quarters on board of the International Space Station. Several issues to improve were recorded by NASA and ESA and most important of them are the following: noise level reduction, CO2 accumulation reduction and dust accumulation reduction. The study in this paper is centred on a reduced scaled model used to provide simulations related to the air diffusion inside the CQ. It is obvious that a new ventilation system is required to achieve the three issues mentioned above, and the solutions obtained by means of numerical simulation need to be validated by experimental approach. First of all we have built a reduced scaled physical model to simulate the flow pattern inside the CQ and the equipment inside the CQ has been reproduced using a geometrical scale ratio. The flow pattern was considered isothermal and incompressible. The similarity criteria used was the Reynolds number to characterize the flow pattern and the length scale was set at value 1/4. Water has been used inside the model to simulate air. Velocity magnitude vectors have been obtained using PIV measurement techniques.
Numerical simulation of anisotropic preheating ablative Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Wang Lifeng; Ye Wenhua; Li Yingjun
2010-01-01
The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T)=κ SH [1+f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse. (authors)
Nonlinear Diffusion and Transient Osmosis
International Nuclear Information System (INIS)
Igarashi, Akira; Rondoni, Lamberto; Botrugno, Antonio; Pizzi, Marco
2011-01-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call ''transient osmosis . We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
A numerical study of shock-acceleration of a diffuse helium cylinder
International Nuclear Information System (INIS)
Greenough, J.A.; Bell, J.; Colella, P.
1995-08-01
The development of a shock-accelerated diffuse Helium cylindrical inhomogeneity is investigated using a new numerical method. The new algorithm is a higher-order Godunov implementation of the so-called multi-fluid equations. This system correctly models multiple component mixtures by accounting for differential compressibility effects. This base integrator is embedded in an implementation of adaptive mesh refinement (AMR) that allows efficient increase in resolution where the computational effort is concentrated where high accuracy, or increased resolution, are required. Qualitative and quantitative comparison with previous experimental data is excellent. The simulations show that counter-sign vortex blobs are deposited in the jet core by baroclinic generation of the curved shock wave as it traverses the jet. This vorticity deposition occurs over timescales that scale with the shock passage time (∼ 10μsec). Three phases of development are identified and characterized. The first is the weak deformation (WD) phase, where there is weak distortion of the Helium jet due to weak vorticity induced velocity effects. The second phase is the strong deformation (SD) phase where there is large distortion for the jet and the vortex blobs due to large induced velocity effects. The last is a relaxation/reorganization (RR) phase where the vorticity field reorganizes into point-like vortex pair
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.
Oceanic diffusion in the coastal area
International Nuclear Information System (INIS)
Rukuda, Masaaki
1980-03-01
Described in this paper is the eddy diffusion in the area off Tokai Village investigated by means of dye diffusion experiment and of oceanic observation. In order to assess the oceanic diffusion in coastal areas, improved methods effective in complex field were developed. The oceanic diffusion was separated in two groups, horizontal and vertical diffusion respectively. Both these diffusions are combined and their analysis together is difficult. The oceanic diffusion is thus considered separately. Instantaneous point release is the basis of horizontal diffusion analysis. Continuous release is then the overlap of numerous instantaneous releases. It was shown that the diffusion parameters derived from the results of diffusion experiment or oceanic observation vary widely with time and place and with sea conditions. A simple diffusion equation was developed from the equation of continuity. The results were in good agreement with seasonal mean horizontal distribution of river water in the sea area. The vertical observation in diffusion experiment is difficult and the vertical structure of oceanic condition is complex, so that the research on vertical diffusion generally is not advanced yet. With river water as the tracer, a method of estimating vertical diffusion parameters with a Gaussian model or one-dimensional model was developed. The vertical diffusion near sea bottom was numerically analized with suspended particles in seawater as the tracer. Diffusion was computed for each particle size, and by summing up the vertical distribution of beam attenuation coefficient was estimated. By comparing the results of estimation and those of observation the vertical diffusivity and the particle size distribution at sea bottom could be estimated. (author)
Energy Technology Data Exchange (ETDEWEB)
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)
de Farias Aires, Juarez Everton; da Silva, Wilton Pereira; de Almeida Farias Aires, Kalina Lígia Cavalcante; da Silva Júnior, Aluízio Freire; da Silva e Silva, Cleide Maria Diniz Pereira
2018-04-01
The main objective of this study is the presentation of a numerical model of liquid diffusion for the description of the convective drying of apple slices submitted to pretreatment of osmotic dehydration able of predicting the spatial distribution of effective mass diffusivity values in apple slabs. Two models that use numerical solutions of the two-dimensional diffusion equation in Cartesian coordinates with the boundary condition of third kind were proposed to describe drying. The first one does not consider the shrinkage of the product and assumes that the process parameters remain constant along the convective drying. The second one considers the shrinkage of the product and assumes that the effective mass diffusivity of water varies according to the local value of the water content in the apple samples. Process parameters were estimated from experimental data through an optimizer coupled to the numerical solutions. The osmotic pretreatment did not reduce the drying time in relation to the fresh fruits when the drying temperature was equal to 40 °C. The use of the temperature of 60 °C led to a reduction in the drying time. The model that considers the variations in the dimensions of the product and the variation in the effective mass diffusivity proved to be more adequate to describe the process.
Numerical simulation of drag-reducing channel flow by using bead-spring chain model
International Nuclear Information System (INIS)
Fujimura, M.; Atsumi, T.; Mamori, H.; Iwamoto, K.; Murata, A.; Masuda, M.; Ando, H.
2017-01-01
Highlights: • Numerical simulations of drag-reduced turbulent flow by polymer additives were performed by using a discrete element model. • A decreasing pressure-strain correlation mainly contributes to drag reduction by polymer addition. • Energy transport by the polymer attenuates the turbulence. • The viscoelastic effects on the drag-reducing flow are intensified with increasing relaxation time of polymer. • The polymer energy transport is related to the orientation of the polymer. - Abstract: Numerical simulations of the drag-reducing turbulent channel flow caused by polymer addition are performed. A bead-spring chain model is employed as a model of polymer aggregation. The model consists of beads and springs to represent the polymer dynamics. Three drag-reduction cases are studied with different spring constants that correspond to the relaxation time of the polymer. The energy budget is mainly focused upon to discuss the drag-reduction mechanism. Our results show that a decreasing pressure-strain correlation mainly contributes to strengthening the anisotropy of the turbulence. Furthermore, energy transport by the polymer models attenuates the turbulence. These viscoelastic effects on the drag-reducing flow are intensified with decreasing spring constant. By visualizing the flow field, it is found that this polymer energy transport is related to the orientation of the polymer.
Diffusing diffusivity: Rotational diffusion in two and three dimensions
Jain, Rohit; Sebastian, K. L.
2017-06-01
We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.
Internal modifications to reduce pollutant emissions from marine engines. A numerical approach
Lamas, M. I.; Rodríguez, C. G.; Rodríguez, J. D.; Telmo, J.
2013-12-01
Taking into account the increasingly stringent legislation on emissions from marine engines, this work aims to analyze several internal engine modifications to reduce NOx (nitrogen oxides) and other pollutants. To this end, a numerical model was employed to simulate the operation cycle and characterize the exhaust gas composition. After a preliminary validation process was carried out using experimental data from a four-stroke, medium-speed marine engine, the numerical model was employed to study the influence of several internal modifications, such as water addition from 0 to 100% water to fuel ratios, exhaust gas recirculation from 0 to 100% EGR rates, modification of the overlap timing from 60 to 120°, modification of the intake valve closing from 510 to 570°, and modification of the cooling water temperature from 70 to 90 oC. NOx was reduced by nearly 100%. As expected, it was found that, by lowering the combustion temperature, there is a notable reduction in NOx, but an increase in CO (carbon monoxide), HC (hydrocarbons) and consumption.
Internal modifications to reduce pollutant emissions from marine engines. A numerical approach
Directory of Open Access Journals (Sweden)
M.I. Lamas
2013-12-01
Full Text Available Taking into account the increasingly stringent legislation on emissions from marine engines, this work aims to analyze several internal engine modifications to reduce NOx (nitrogen oxides and other pollutants. To this end, a numerical model was employed to simulate the operation cycle and characterize the exhaust gas composition. After a preliminary validation process was carried out using experimental data from a four-stroke, medium-speed marine engine, the numerical model was employed to study the influence of several internal modifications, such as water addition from 0 to 100% water to fuel ratios, exhaust gas recirculation from 0 to 100% EGR rates, modification of the overlap timing from 60 to 120°, modification of the intake valve closing from 510 to 570°, and modification of the cooling water temperature from 70 to 90 °C. NOx was reduced by nearly 100%. As expected, it was found that, by lowering the combustion temperature, there is a notable reduction in NOx, but an increase in CO (carbon monoxide, HC (hydrocarbons and consumption.
Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane
Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.
2002-03-01
The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.
Causal electric charge diffusion and balance functions in relativistic heavy-ion collisions
Kapusta, Joseph I.; Plumberg, Christopher
2018-01-01
We study the propagation and diffusion of electric charge fluctuations in high-energy heavy-ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1-dimensional Bjorken hydrodynamical model. Limiting the speed of propagation of charge fluctuations increases the height and reduces the width of these balance functions when plotted versus rapidity. We also estimate the numerical value of the associated diffusion time constant from anti-de Sitter-space/conformal-field theory.
An innovative method for determining the diffusion coefficient of product nuclide
Energy Technology Data Exchange (ETDEWEB)
Chen, Chih Lung [Dept. of Nuclear Back-end Management, Taiwan Power Company, Taipei (China); Wang, Tsing Hai [Dept. Biomedical Engineering and Environment Sciences, National Tsing Hua University, Hsinchu (China)
2017-08-15
Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN{sub 1} → RN{sub 2} → RN{sub 3}) and a parallel reaction (RN{sub 1} → RN{sub 2}A + RN{sub 2}B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.
International Nuclear Information System (INIS)
Wilhelmsson, H.; Le Roux, M.N.
1991-01-01
Results are presented accounting for a selection of extensive numerical calculations of the evolution in space and time for a dynamic system, governed by a nonlinear diffusion equation with source and loss terms (which could also be nonlinear). The system is assumed to be circularly symmetric and limited by an external boundary where the value of the depending variable (e.g. temperature) is supposed to be zero. (au)
Numerical Simulation of Anisotropic Preheating Ablative Rayleigh–Taylor Instability
International Nuclear Information System (INIS)
Li-Feng, Wang; Wen-Hua, Ye; Ying-Jun, Li
2010-01-01
The linear growth rate of the anisotropic preheating ablative Rayleigh–Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T) = κ SH [1 + f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 (2007) 245001]. (physics of gases, plasmas, and electric discharges)
Numerical schemes for one-point closure turbulence models
International Nuclear Information System (INIS)
Larcher, Aurelien
2010-01-01
First-order Reynolds Averaged Navier-Stokes (RANS) turbulence models are studied in this thesis. These latter consist of the Navier-Stokes equations, supplemented with a system of balance equations describing the evolution of characteristic scalar quantities called 'turbulent scales'. In so doing, the contribution of the turbulent agitation to the momentum can be determined by adding a diffusive coefficient (called 'turbulent viscosity') in the Navier-Stokes equations, such that it is defined as a function of the turbulent scales. The numerical analysis problems, which are studied in this dissertation, are treated in the frame of a fractional step algorithm, consisting of an approximation on regular meshes of the Navier-Stokes equations by the nonconforming Crouzeix-Raviart finite elements, and a set of scalar convection-diffusion balance equations discretized by the standard finite volume method. A monotone numerical scheme based on the standard finite volume method is proposed so as to ensure that the turbulent scales, like the turbulent kinetic energy (k) and its dissipation rate (ε), remain positive in the case of the standard k - ε model, as well as the k - ε RNG and the extended k - ε - ν 2 models. The convergence of the proposed numerical scheme is then studied on a system composed of the incompressible Stokes equations and a steady convection-diffusion equation, which are both coupled by the viscosities and the turbulent production term. This reduced model allows to deal with the main difficulty encountered in the analysis of such problems: the definition of the turbulent production term leads to consider a class of convection-diffusion problems with an irregular right-hand side belonging to L 1 . Finally, to step towards the unsteady problem, the convergence of the finite volume scheme for a model convection-diffusion equation with L 1 data is proved. The a priori estimates on the solution and on its time derivative are obtained in discrete norms, for
Characterization of supersonic radiation diffusion waves
International Nuclear Information System (INIS)
Moore, Alastair S.; Guymer, Thomas M.; Morton, John; Williams, Benjamin; Kline, John L.; Bazin, Nicholas; Bentley, Christopher; Allan, Shelly; Brent, Katie; Comley, Andrew J.; Flippo, Kirk; Cowan, Joseph; Taccetti, J. Martin; Mussack-Tamashiro, Katie; Schmidt, Derek W.; Hamilton, Christopher E.; Obrey, Kimberly; Lanier, Nicholas E.; Workman, Jonathan B.; Stevenson, R. Mark
2015-01-01
Supersonic and diffusive radiation flow is an important test problem for the radiative transfer models used in radiation-hydrodynamics computer codes owing to solutions being accessible via analytic and numeric methods. We present experimental results with which we compare these solutions by studying supersonic and diffusive flow in the laboratory. We present results of higher-accuracy experiments than previously possible studying radiation flow through up to 7 high-temperature mean free paths of low-density, chlorine-doped polystyrene foam and silicon dioxide aerogel contained by an Au tube. Measurements of the heat front position and absolute measurements of the x-ray emission arrival at the end of the tube are used to test numerical and analytical models. We find excellent absolute agreement with simulations provided that the opacity and the equation of state are adjusted within expected uncertainties; analytical models provide a good phenomenological match to measurements but are not in quantitative agreement due to their limited scope. - Highlights: • The supersonic, diffusion of x-rays through sub-solid density materials is studied. • The data are more diffusive and of higher velocity than any prior work. • Scaled 1D analytic diffusion models reproduce the heat front evolution. • Refined radiation transport approximations are tested in numerical simulations. • Simulations match the data if material properties are adjusted within uncertainties
Problems with Discontinuous Diffusion/Dispersion Coefficients
Directory of Open Access Journals (Sweden)
Stefano Ferraris
2012-01-01
accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.
Energy Technology Data Exchange (ETDEWEB)
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)
A LES-CMC formulation for premixed flames including differential diffusion
Farrace, Daniele; Chung, Kyoungseoun; Bolla, Michele; Wright, Yuri M.; Boulouchos, Konstantinos; Mastorakos, Epaminondas
2018-05-01
A finite volume large eddy simulation-conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane-air flame with Leeff = 0.99 and a lean hydrogen-air flame with Leeff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane-air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.
Fuller, Nathaniel J.; Licata, Nicholas A.
2018-05-01
Obtaining a detailed understanding of the physical interactions between a cell and its environment often requires information about the flow of fluid surrounding the cell. Cells must be able to effectively absorb and discard material in order to survive. Strategies for nutrient acquisition and toxin disposal, which have been evolutionarily selected for their efficacy, should reflect knowledge of the physics underlying this mass transport problem. Motivated by these considerations, in this paper we discuss the results from an undergraduate research project on the advection-diffusion equation at small Reynolds number and large Péclet number. In particular, we consider the problem of mass transport for a Stokesian spherical swimmer. We approach the problem numerically and analytically through a rescaling of the concentration boundary layer. A biophysically motivated first-passage problem for the absorption of material by the swimming cell demonstrates quantitative agreement between the numerical and analytical approaches. We conclude by discussing the connections between our results and the design of smart toxin disposal systems.
Preconditioned iterative methods for space-time fractional advection-diffusion equations
Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.
2016-08-01
In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.
Two-dimensional boundary-value problem for ion-ion diffusion
International Nuclear Information System (INIS)
Tuszewski, M.; Lichtenberg, A.J.
1977-01-01
Like-particle diffusion is usually negligible compared with unlike-particle diffusion because it is two orders higher in spatial derivatives. When the ratio of the ion gyroradius to the plasma transverse dimension is of the order of the fourth root of the mass ratio, previous one-dimensional analysis indicated that like-particle diffusion is significant. A two-dimensional boundary-value problem for ion-ion diffusion is investigated. Numerical solutions are found with models for which the nonlinear partial differential equation reduces to an ordinary fourth-order differential equation. These solutions indicate that the ion-ion losses are higher by a factor of six for a slab geometry, and by a factor of four for circular geometry, than estimated from dimensional analysis. The solutions are applied to a multiple mirror experiment stabilized with a quadrupole magnetic field which generates highly elliptical flux surfaces. It is found that the ion-ion losses dominate the electron-ion losses and that these classical radial losses contribute to a significant decrease of plasma lifetime, in qualitiative agreement with the experimental results
Dmitriev, S. S.; Vasil'ev, K. E.; Mokhamed, S. M. S. O.; Gusev, A. A.; Barbashin, A. V.
2017-11-01
In modern combined cycle gas turbines (CCGT), when designing the reducers from the output diffuser of a gas turbine to a boiler-utilizer, wide-angle diffusers are used, in which practically from the input a flow separation and transition to jet stream regime occurs. In such channels, the energy loss in the field of velocities sharply rise and the field of velocities in the output from them is characterized by considerable unevenness that worsens the heat transfer process in the first by motion tube bundles of the boiler-utilizer. The results of experimental research of the method for reducing the energy loss and alignment of the field of velocities at the output from a flat asymmetrical diffuser channel with one deflecting wall with the opening angle of 40° by means of placing inside the channel the flat plate parallel to the deflecting wall are presented in the paper. It is revealed that, at this placement of the plate in the channel, it has a chance to reduce the energy loss by 20%, considerably align the output field of velocities, and decrease the dynamic loads on the walls in the output cross-section. The studied method of resistance reduction and alignment of the fields of velocities in the flat diffuser channels was used for optimization of the reducer from the output diffuser of the gas turbine to the boiler-utilizer of CCGT of PGU-450T type of Kaliningrad Thermal Power Plant-2. The obtained results are evidence that the configuration of the reducer installed in the PGU-450T of Kaliningrad Thermal Power Plant-2 is not optimal. It follows also from the obtained data that working-off the reducer should be necessarily conducted by the test results of the channel consisting of the model of reducer with the model of boiler-utilizer installed behind it. Application of the method of alignment of output field of velocities and reducing the resistance in the wide-angle diffusers investigated in the work made it possible—when using the known model of diffusion
Muhiddin, F. A.; Sulaiman, J.
2017-09-01
The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.
Quasi-equilibria in reduced Liouville spaces.
Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon
2012-06-14
The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.
Lagrangian numerical methods for ocean biogeochemical simulations
Paparella, Francesco; Popolizio, Marina
2018-05-01
We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.
Gold Cluster Diffusion Kinetics on Stoichiometric and Reduced Surfaces of Rutile TiO _{2} (110)
Energy Technology Data Exchange (ETDEWEB)
Goldman, Nir; Browning, Nigel D.
2011-06-16
Gold clusters on rutile TiO_{2} are known to serve as efficient oxidation catalysts for pollutants and environmental contaminants. However, the mechanism by which highly mobile small clusters migrate and aggregate into larger species relevant to gold’s catalytic activity remains unresolved. We report herein on ab initio simulations of the diffusion of atomic gold clusters up to the trimer on rutile TiO_{2}(110) surfaces. We show that, on the stoichiometric surface, both the dimer and the trimer can exhibit relatively low surface mobility due to high energetic barriers for diffusion out of their energetic minima coupled with low barriers for the reverse motion. On the reduced surface, these clusters can diffuse relatively quickly between energetic minima within the oxygen vacancy site due to the large degree of vibrational entropy in their transition states. Our computed diffusion times provide a point of comparison for future experiments and will aid in development of models of gold cluster island sintering.
DEFF Research Database (Denmark)
Zhang, Chen
Diffuse ceiling ventilation is an innovative ventilation concept where the suspended ceiling serves as air diffuser to supply fresh air into the room. Compared with conventional ventilation systems, diffuse ceiling ventilation can significantly reduce or even eliminate draught risk due to the low...
Turing Patterns in a Reaction-Diffusion System
International Nuclear Information System (INIS)
Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang
2006-01-01
We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.
New imaging algorithm in diffusion tomography
Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.
1997-08-01
A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.
Zhang, Yuxin; Holmes, James; Rabanillo, Iñaki; Guidon, Arnaud; Wells, Shane; Hernando, Diego
2018-04-17
To evaluate the reproducibility of quantitative diffusion measurements obtained with reduced Field of View (rFOV) and Multi-shot EPI (msEPI) acquisitions, using single-shot EPI (ssEPI) as a reference. Diffusion phantom experiments, and prostate diffusion-weighted imaging in healthy volunteers and patients with known or suspected prostate cancer were performed across the three different sequences. Quantitative diffusion measurements of apparent diffusion coefficient, and diffusion kurtosis parameters (healthy volunteers), were obtained and compared across diffusion sequences (rFOV, msEPI, and ssEPI). Other possible confounding factors like b-value combinations and acquisition parameters were also investigated. Both msEPI and rFOV have shown reproducible quantitative diffusion measurements relative to ssEPI; no significant difference in ADC was observed across pulse sequences in the standard diffusion phantom (p = 0.156), healthy volunteers (p ≥ 0.12) or patients (p ≥ 0.26). The ADC values within the non-cancerous central gland and peripheral zone of patients were 1.29 ± 0.17 × 10 -3 mm 2 /s and 1.74 ± 0.23 × 10 -3 mm 2 /s respectively. However, differences in quantitative diffusion parameters were observed across different number of averages for rFOV, and across b-value groups and diffusion models for all the three sequences. Both rFOV and msEPI have the potential to provide high image quality with reproducible quantitative diffusion measurements in prostate diffusion MRI. Copyright © 2018 Elsevier Inc. All rights reserved.
Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients
Directory of Open Access Journals (Sweden)
Nauman Raza
2013-01-01
Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.
Diffusive Interaction Between Ni-Cr-Al Alloys
Tkacz-Śmiech, Katarzyna; Danielewski, Marek; Bożek, Bogusław; Berent, Katarzyna; Zientara, Dariusz; Zajusz, Marek
2017-05-01
In high-temperature coatings, welded parts, and a range of other applications, components in the contact zone interdiffuse at elevated temperatures and may react to change the phase composition. The diffusion zone can be complex and can consist of sequential layers of intermediate phases, solid solutions, and in the case of multicomponent systems also of multiphase layers. In this work, the interdiffusion in Ni-Cr-Al alloys is studied experimentally and modeled numerically. The diffusion multiples were prepared by hot isostatic pressing and post-annealing at 1473 K (1200 °C). The concentration profiles were measured with wide-line EDS technique which allowed obtaining high-accuracy diffusion paths. The experimental profiles and diffusion paths were compared with numerical results simulated with application of very recent model of interdiffusion in muticomponent-multiphase systems. The calculated and experimental data show good agreement.
Energy Technology Data Exchange (ETDEWEB)
Fisher, A. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bailey, D. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kaiser, T. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eder, D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gunney, B. T. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Masters, N. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Koniges, A. E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Anderson, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Matsuura, Koji
2014-06-01
Recent studies suggest that the microenvironment and embryo density used during embryo culture considerably affect development to the blastocyst stage. High embryo density allows for autocrine secretions to diffuse to neighbouring embryos during group culture, with a positive effect on further development. A variation of group culture is the well-of-the-well (WOW) culture system, allowing for individual identification of embryos cultured in small holes in a microdroplet. Bovine blastocyst development is higher in the WOW culture system than in conventional group culture. To compare the concentration of chemical factors between conventional and WOW culture, a model was constructed to calculate the concentration of secreted factors based on Fick's second law of diffusion using spreadsheet software. Furthermore, model was used to determine the concentration of growth factors and waste materials adjacent to the embryo periphery. The results of these calculations suggest that the highest difference in the concentration of secreted small molecules and macromolecules was at the most two- to threefold, with the concentrations reduced more and diffusion kinetics facilitated to a greater extent in the WOW culture system. The average ratio of the concentration of secreted macromolecules (10nm diameter) around the embryos was also compared between systems with well widths of 0.1 and 0.3mm. The concentration of secreted materials surrounding embryos increased in a narrow tapered well. The findings suggest that the WOW culture system is better than conventional group culture because of the increased final concentration of autocrine factors and higher diffusion kinetics of waste materials.
An inverse diffusivity problem for the helium production–diffusion equation
International Nuclear Information System (INIS)
Bao, Gang; Xu, Xiang
2012-01-01
Thermochronology is a technique for the extraction of information about the thermal history of rocks. Such information is crucial for determining the depth below the surface at which rocks were located at a given time (Bao G et al 2011 Commun. Comput. Phys. 9 129). Mathematically, extracting the time–temperature path can be formulated as an inverse diffusivity problem for the helium production–diffusion equation which is the underlying process of thermochronology. In this paper, to reconstruct the diffusivity which depends on space only and accounts for the structural information of rocks, a local Hölder conditional stability is obtained by a Carleman estimate. A uniqueness result is also proven for extracting the thermal history, i.e. identifying the time-dependant part of the diffusion coefficient, provided that it is analytical with respect to time. Numerical examples are presented to illustrate the validity and effectiveness of the proposed regularization scheme. (paper)
A moving mesh finite difference method for equilibrium radiation diffusion equations
Energy Technology Data Exchange (ETDEWEB)
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 moving mesh finite difference method for equilibrium radiation diffusion equations
International Nuclear Information System (INIS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-01-01
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
Accelerated numerical processing of electronically recorded holograms with reduced speckle noise.
Trujillo, Carlos; Garcia-Sucerquia, Jorge
2013-09-01
The numerical reconstruction of digitally recorded holograms suffers from speckle noise. An accelerated method that uses general-purpose computing in graphics processing units to reduce that noise is shown. The proposed methodology utilizes parallelized algorithms to record, reconstruct, and superimpose multiple uncorrelated holograms of a static scene. For the best tradeoff between reduction of the speckle noise and processing time, the method records, reconstructs, and superimposes six holograms of 1024 × 1024 pixels in 68 ms; for this case, the methodology reduces the speckle noise by 58% compared with that exhibited by a single hologram. The fully parallelized method running on a commodity graphics processing unit is one order of magnitude faster than the same technique implemented on a regular CPU using its multithreading capabilities. Experimental results are shown to validate the proposal.
Coupling effects of chemical stresses and external mechanical stresses on diffusion
International Nuclear Information System (INIS)
Xuan Fuzhen; Shao Shanshan; Wang Zhengdong; Tu Shantung
2009-01-01
Interaction between diffusion and stress fields has been investigated extensively in the past. However, most of the previous investigations were focused on the effect of chemical stress on diffusion due to the unbalanced mass transport. In this work, the coupling effects of external mechanical stress and chemical stress on diffusion are studied. A self-consistent diffusion equation including the chemical stress and external mechanical stress gradient is developed under the framework of the thermodynamic theory and Fick's law. For a thin plate subjected to unidirectional tensile stress fields, the external stress coupled diffusion equation is solved numerically with the help of the finite difference method for one-side and both-side charging processes. Results show that, for such two types of charging processes, the external stress gradient will accelerate the diffusion process and thus increase the value of concentration while reducing the magnitude of chemical stress when the direction of diffusion is identical to that of the stress gradient. In contrast, when the direction of diffusion is opposite to that of the stress gradient, the external stress gradient will obstruct the process of solute penetration by decreasing the value of concentration and increasing the magnitude of chemical stress. For both-side charging process, compared with that without the coupling effect of external stress, an asymmetric distribution of concentration is produced due to the asymmetric mechanical stress field feedback to diffusion.
Energy Technology Data Exchange (ETDEWEB)
Mousavi Shirazi, Seyed Alireza [Islamic Azad Univ. (I.A.U.), Dept. of Physics, Tehran (Iran, Islamic Republic of)
2015-07-15
In this symbolic investigation, a cylindrical cell in a LWR, which consists of one fuel pin and moderator (water), is considered. The width of this cylindrical cell is divided into 100 equal units. Since the neutron flux in a cylindrical fuel pin is resulting from the diffusion equation: -(1)/(r)(d)/(dr)Dr(d)/(dr)φ(r) + Σ{sub a}φ(r) = S(r), the amount of fast neutron fluxes are obtained on the basis of the numeric solution of this equation, and the applied boundary conditions are considered: φ'(0) = φ'(1) = 0. This differential equation is solved by the tridiagonal method for variant enrichments of uranium. Neutron fluxes are obtained in variant radii of fuel pin and moderator and are finally compared with each other. There are some interesting outcomes resulting from this investigation. It can be inferred that because of the fuel enrichment increment, the fast neutron flux increases significantly at the centre of core, while many of the fast neutrons produced are absorbed after entering the water region, moderation of lots of them causes the reduced neutron flux to get improved in this region.
Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence
Energy Technology Data Exchange (ETDEWEB)
Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)
2017-04-20
In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.
Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence
International Nuclear Information System (INIS)
Heusen, M.; Shalchi, A.
2017-01-01
In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.
International Nuclear Information System (INIS)
Hsu, Ching-Chun; Yeh, Ho-Ming
2014-01-01
Highlights: • Recovery of deuterium by thermal diffusion from water–isotope mixture has been investigated. • The undesirable remixing effect can be reduced by employing the device of branch columns. • Deuterium recoveries were compared with that in a single column of the same total column length. • Considerable recovery improvement is obtainable in the device of branch columns, instead of in a single-column device. - Abstract: Deuterium recovery from water–isotopes mixture using thermal diffusion can be improved by employing the branch column device, instead of single column devices, with the same total column length. The remixing effect due to convection currents in a thermal diffusion column for heavy water enrichment is thus reduced and separation improvement increases when the flow rate or the total column length increases. The improvement in separation can reach about 50% for the numerical example given
Emissivity of discretized diffusion problems
International Nuclear Information System (INIS)
Densmore, Jeffery D.; Davidson, Gregory; Carrington, David B.
2006-01-01
The numerical modeling of radiative transfer by the diffusion approximation can produce artificially damped radiation propagation if spatial cells are too optically thick. In this paper, we investigate this nonphysical behavior at external problem boundaries by examining the emissivity of the discretized diffusion approximation. We demonstrate that the standard cell-centered discretization produces an emissivity that is too low for optically thick cells, a situation that leads to the lack of radiation propagation. We then present a modified boundary condition that yields an accurate emissivity regardless of cell size. This modified boundary condition can be used with a deterministic calculation or as part of a hybrid transport-diffusion method for increasing the efficiency of Monte Carlo simulations. We also discuss the range of applicability, as a function of cell size and material properties, when this modified boundary condition is employed in a hybrid technique. With a set of numerical calculations, we demonstrate the accuracy and usefulness of this modified boundary condition
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
Diffusion transport of nanoparticles at nanochannel boundaries
International Nuclear Information System (INIS)
Mahadevan, T. S.; Milosevic, M.; Kojic, M.; Hussain, F.; Kojic, N.; Serda, R.; Ferrari, M.; Ziemys, A.
2013-01-01
The manipulation of matter at the nanoscale has unleashed a great potential for engineering biomedical drug carriers, but the transport of nanoparticles (NPs) under nanoscale confinement is still poorly understood. Using colloidal physics to describe NP interactions, we have computationally studied the passive transport of NPs using experimentally relevant conditions from bulk into a nanochannel of 60–90 nm height. NP size, channel height, and the Debye length are comparable so that changes in nanoscale dimensions may induce substantial changes in NP transport kinetics. We show that subtle changes in nanochannel dimensions may alter the energy barrier by about six orders of magnitude resulting in different NP penetration depths and diffusion mechanisms: ballistic, first-order and quasi zero-order transport regimes. The analysis of NP diffusion by continuum methods reveals that apparent diffusivity is reduced by decreasing channel size. The continuum finite element (FE) numerical method reproduced the colloidal model results only when surface interactions were accounted for. These results give a new insight into NP passive transport at the boundaries of nanoconfined domains, and have implications on the design of nanoscale fluidics and NP systems for biomedical and engineering applications.
Structured inverse modeling in parabolic diffusion processess
Schulz, Volker; Siebenborn, Martin; Welker, Kathrin
2014-01-01
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A novel shape gradient is derived in parabolic processes. Furthermore quasi-Newton techniques are used in order to accelerate shape gradient based iterations in shape space. Numerical investigations support the theoretical results.
Lu, Benzhuo; Zhou, Y.C.
2011-01-01
The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. PMID:21575582
Synchronized stability in a reaction–diffusion neural network model
Energy Technology Data Exchange (ETDEWEB)
Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com
2014-11-14
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.
Synchronized stability in a reaction–diffusion neural network model
International Nuclear Information System (INIS)
Wang, Ling; Zhao, Hongyong
2014-01-01
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability
Directory of Open Access Journals (Sweden)
Michał Lipian
2016-01-01
Full Text Available Different numerical computation methods used to develop a methodology for fast, efficient, reliable design and comparison of Diffuser-Augmented Wind Turbine (DAWT geometries are presented. The demand for such methods is evident, following the multitude of geometrical parameters that influence the flow character through ducted turbines. The results of the Actuator Disk Model (ADM simulations will be confronted with a simulation method of higher order of accuracy, i.e. the 3D Fully-resolved Rotor Model (FRM in the rotor design point. Both will be checked for consistency with the experimental results measured in the wind tunnel at the Institute of Turbo-machinery (IMP, Lodz University of Technology (TUL. An attempt to find an efficient method (with a compromise between accuracy and design time for the flow analysis pertinent to the DAWT is a novel approach presented in this paper.
Coulomb Green's function and image potential near a cylindrical diffuse interface
Xue, Changfeng; Huang, Qiongwei; Deng, Shaozhong
2015-12-01
In a preceding paper [Comput. Phys. Commun. 184 (1): 51-59, 2013], we revisited the problem of calculating Coulomb Green's function and image potential near a planar diffuse interface within which the dielectric permittivity of the inhomogeneous medium changes continuously along one Cartesian direction in a transition layer between two dissimilar dielectric materials. In the present paper, we consider a cylindrical diffuse interface within which the dielectric permittivity changes continuously along the radial direction instead. First we propose a specific cylindrical diffuse interface model, termed the quasi-harmonic diffuse interface model, that can admit analytical solution for the Green's function in terms of the modified Bessel functions. Then and more importantly we develop a robust numerical method for building Green's functions for any cylindrical diffuse interface models. The main idea of the numerical method is, after dividing a diffuse interface into multiple sublayers, to approximate the dielectric permittivity profile in each one of the sublayers by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. Next we describe how to efficiently compute well-behaved ratios, products, and logarithmic derivatives of the modified Bessel functions so as to avoid direct evaluations of individual modified Bessel functions in our formulations. Finally we conduct numerical experiments to show the effectiveness of the quasi-harmonic diffuse interface model in overcoming the divergence of the image potential, to validate the numerical method in terms of its accuracy and convergence, and to demonstrate its capability for computing Green's functions for any cylindrical diffuse interface models.
Pure Left Neglect for Arabic Numerals
Priftis, Konstantinos; Albanese, Silvia; Meneghello, Francesca; Pitteri, Marco
2013-01-01
Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arranged along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial…
Zhou, Yuan; Tang, Eric; Luo, Jianwen; Yao, Junjie
2018-01-01
Temperature mapping during thermotherapy can help precisely control the heating process, both temporally and spatially, to efficiently kill the tumor cells and prevent the healthy tissues from heating damage. Photoacoustic tomography (PAT) has been used for noninvasive temperature mapping with high sensitivity, based on the linear correlation between the tissue's Grüneisen parameter and temperature. However, limited by the tissue's unknown optical properties and thus the optical fluence at depths beyond the optical diffusion limit, the reported PAT thermometry usually takes a ratiometric measurement at different temperatures and thus cannot provide absolute measurements. Moreover, ratiometric measurement over time at different temperatures has to assume that the tissue's optical properties do not change with temperatures, which is usually not valid due to the temperature-induced hemodynamic changes. We propose an optical-diffusion-model-enhanced PAT temperature mapping that can obtain the absolute temperature distribution in deep tissue, without the need of multiple measurements at different temperatures. Based on the initial acoustic pressure reconstructed from multi-illumination photoacoustic signals, both the local optical fluence and the optical parameters including absorption and scattering coefficients are first estimated by the optical-diffusion model, then the temperature distribution is obtained from the reconstructed Grüneisen parameters. We have developed a mathematic model for the multi-illumination PAT of absolute temperatures, and our two-dimensional numerical simulations have shown the feasibility of this new method. The proposed absolute temperature mapping method may set the technical foundation for better temperature control in deep tissue in thermotherapy.
Performance improvement of a centrifugal compressor stage by using different vaned diffusers
International Nuclear Information System (INIS)
Zhang, Y C; Kong, X Z; Li, F; Sun, W; Chen, Q G
2013-01-01
The vaneless diffuser (VLD) is usually adopted in the traditional design of the multi-stage centrifugal compressor because of the stage's match problem. The drawback of the stage with vaneless diffusers is low efficiency. In order to increase the efficiency and at the same time, induce no significant decline in the operating range of the stage, three different types of vaned diffusers are designed and numerically investigated: the traditional vaned diffuser (TVD), the low-solidity cascade diffuser (LSD) and the partial-height vane diffuser (PVD). These three types of vaned diffusers have different influences on the performance of the centrifugal compressor. In the present investigation, the first part investigates the performance of a centrifugal compressor stage with three different vaned diffusers. The second part studies the influences of the height and the position of partial height vanes on the stage performance, and discusses the matching problem between the PVD and the downstream return channel. The stage investigated in this paper includes the impeller, the diffuser, the bend and the return channel. In the process of numerical investigation, the flow is assumed to be steady, and this process includes calculation and simulation. The calculation of 3-D turbulent flow in the stage uses the commercial CFD code NUMECA together with the Spalart-Allmaras turbulence model. The simulation of the computational region includes the impeller passages, the diffuser passages and return channel passages. The structure and surrounding region are assumed to have a perfect cyclic symmetry, so the single channel model and periodic boundary condition are applied at the middle of the passage, that is to reduce the calculation region to only one region. The investigation showed that the low-solidity cascade diffuser would be a better choice as a middle course for the first stage of the multistage centrifugal compressor. Besides, the influences of the height and the position
Chu, Khim Hoong
2017-11-09
Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6 cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.
Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems
International Nuclear Information System (INIS)
Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da
2001-01-01
Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)
Numerical solution of singularity-perturbed two-point boundary-value problems
International Nuclear Information System (INIS)
Masenge, R.W.P.
1993-07-01
Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab
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.
Numerical simulation methods for phase-transitional flow
Pecenko, A.
2010-01-01
The object of the present dissertation is a numerical study of multiphase flow of one fluid component. In particular, the research described in this thesis focuses on the development of numerical methods that are based on a diffuse-interface model (DIM). With this approach, the modeling problem
Multidimensional epidemic thresholds in diffusion processes over interdependent networks
International Nuclear Information System (INIS)
Salehi, Mostafa; Siyari, Payam; Magnani, Matteo; Montesi, Danilo
2015-01-01
Highlights: •We propose a new concept of multidimensional epidemic threshold for interdependent networks. •We analytically derive and numerically illustrate the conditions for multilayer epidemics. •We study the evolution of infection density and diffusion dynamics. -- Abstract: Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring over such coupled networks. In this paper we propose a new concept of multidimensional epidemic threshold characterizing diffusion processes over interdependent networks, allowing different diffusion rates on the different networks and arbitrary degree distributions. We analytically derive and numerically illustrate the conditions for multilayer epidemics, i.e., the appearance of a giant connected component spanning all the networks. Furthermore, we study the evolution of infection density and diffusion dynamics with extensive simulation experiments on synthetic and real networks
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Energy Technology Data Exchange (ETDEWEB)
Dosch, J
1991-12-31
The aim of this work is the development of a numerical process independent of the geometry of the flow space. The temperature, concentration and speed fields set up with double diffusive convection should be determined by this and their effect on heat transfer should be determined. The numerical process should be used for non-steady state double diffusive convection in various geometries. The results should be verified experimentally with the aid of holographic interferometry. (orig./IHL) [Deutsch] Ziel der vorliegenden Arbeit ist die Entwicklung eines von der Geometrie des Stroemungsraumes unabhaengigen numerischen Verfahrens. Mit ihm sollen die sich bei doppelt diffusiver Konvektion einstellenden Temperatur-, Konzentrations- und Geschwindigkeitsfelder bestimmt und deren Einfluss auf die Waermeuebertragung ermittelt werden. Das numerische Verfahren soll auf die instationaere doppelt diffusive Konvektion in verschiedenen Geometrien angewendet werden. Die Ergebnisse sollen experimentell mit Hilfe der holographischen Interferometrie verifiziert werden. (orig./IHL)
Evaluation of policy measures and methods to reduce diffuse water pollution
Energy Technology Data Exchange (ETDEWEB)
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
Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems
International Nuclear Information System (INIS)
Ma, Z.; Whitley, R.D.; Wang, N.H.L.
1996-01-01
A generalized parallel pore and surface diffusion model for multicomponent adsorption and liquid chromatography is formulated and solved numerically. Analytical solution for first- and second-order central moments for a pulse on a plateau input is used as benchmarks for the numerical solutions. Theoretical predictions are compared with experimental data for two systems: ion-exchange of strontium, sodium, and calcium in a zeolite and competitive adsorption of two organics on activated carbon. In a linear isotherm region of single-component systems, both surface and pore diffusion cause symmetric spreading in breakthrough curves. In a highly nonlinear isotherm region, however, surface diffusion causes pronounced tailing in breakthrough curves; the larger the step change in concentration, the more pronounced tailing, in contrast to relatively symmetric breakthroughs due to pore diffusion. If only a single diffusion mechanism is assumed in analyzing the data of parallel diffusion systems, a concentration-dependent apparent surface diffusivity or pore diffusivity results; for a convex isotherm, the apparent surface diffusivity increases, whereas the apparent pore diffusivity decreases with increasing concentration. For a multicomponent nonlinear system, elution order can change if pore diffusion dominates for a low-affinity solute, whereas surface diffusion dominates for a high-affinity solute
Directory of Open Access Journals (Sweden)
Zhang, M. Z.
2010-12-01
Full Text Available Concrete diffusivity is a function of its microstructure on many scales, ranging from nanometres to millimetres. Multi-scale techniques are therefore needed to model this parameter. Representative elementary volume (REV, in conjunction with the homogenization principle, is one of the most common multi-scale approaches. This study aimed to establish a procedure for establishing the REV required to determine cement paste diffusivity based on a three-step, numerical-statistical approach. First, several series of 3D cement paste microstructures were generated with HYMOSTRUC3D, a cement hydration and microstructure model, for different volumes of cement paste and w/c ratios ranging from 0.30 to 0.60. Second, the finite element method was used to simulate the diffusion of tritiated water through these microstructures. Effective cement paste diffusivity values for different REVs were obtained by applying Fick’s law. Finally, statistical analysis was used to find the fluctuation in effective diffusivity with cement paste volume, from which the REV was then determined. The conclusion drawn was that the REV for measuring diffusivity in cement paste is 100x100x100 μm^{3}.
La difusividad del hormigón depende de su microestructura a numerosas escalas, desde nanómetros hasta milímetros, por lo que se precisa de técnicas multiescala para representar este parámetro. Junto con el principio de homogeneización, uno de los métodos multiescala más habituales es el volumen elemental representativo (VER. El objeto de este estudio era establecer un procedimiento que permitiera determinar el VER necesario para calcular la difusividad de la pasta de cemento, basándose en un método numéricoestadístico que consta de tres etapas. Primero, se crearon varias series de microestructuras de pasta de cemento en 3D con HYMOSTRUC3D, un programa que permite crear un modelo de la hidratación y microestructura del cemento. Luego se empleó el método de
A spatial structural derivative model for ultraslow diffusion
Directory of Open Access Journals (Sweden)
Xu Wei
2017-01-01
Full Text Available This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.
International Nuclear Information System (INIS)
Valdes Parra, J.J.
1986-01-01
One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)
Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L
2014-03-01
Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
Silva Diniz, D.; Almeida Silva, A. [Federal University of Campina Grande, Campina Grande-PB (Brazil); Andrade Barbosa, J.M. [Federal University of Pernambuco, Recife-PE (Brazil); Palma Carrasco, J.
2012-05-15
This paper presents a numerical simulation of the effect of hydrogen atomic diffusion on fatigue crack propagation on structural steels. The simulation was performed with a specimen type CT of API 5CT P110 steel, loaded in the tensile opening mode, in plane strain state and under the effects of a cyclic mechanical load and the hydrogen concentration at the crack tip. As hydrogen source, a cathodic protection system was considered, commonly used in subsea pipelines. The equations of evolution of variables at the crack tip form a non-linear system of ordinary differential equations that was solved by means of the 4th order Runge-Kutta method. The solid-solid diffusion through the lattice ahead of the crack tip was simulated using the finite difference method. The simulations results show that under these conditions, the fatigue crack evolution process is enhanced by the hydrogen presence in the material, and that the start time of the crack propagation decreases as its concentration increases. These results show good correlation and consistency with macroscopic observations, providing a better understanding of hydrogen embrittlement in fatigue crack propagation processes in structural steels. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Tracer concentration contours in grain lattice and grain boundary diffusion
International Nuclear Information System (INIS)
Kim, Y. S.; Olander, D. R.
1997-01-01
Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low burn-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination). (author)
Diffusion processes and memory effects
International Nuclear Information System (INIS)
Mokshin, Anatolii V; Yulmetyev, Renat M; Haenggi, Peter
2005-01-01
We report the results of the numerical estimation of statistical memory effects in diffusion for two various systems: Lennard-Jones fluids and the model of the Brownian particle in a one-dimensional harmonic lattice. We have found the relation between the diffusion coefficient and the non-Markovity parameter, which is linear for the Lennard-Jones systems in liquid state. The relation between the memory measure and the excess entropy is also discussed here
On Diffusive Climatological Models.
Griffel, D. H.; Drazin, P. G.
1981-11-01
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Atmospheric diffusion study and its application to nuclear energy
International Nuclear Information System (INIS)
Chino, Masamichi
1990-01-01
The report reviews studies on atmospheric diffusion of radioactive substances released from a smokestack. Smoke containing radioactive substances, or radioactive plume, diffuses into air while being affected by atmospheric turbulent flows in various ways depending on the scale of the plume. The diffusion of a radioactive plume released from a smokestack is discussed first, focusing on the diffusion process in the vicinity of the smokestack, in the atmospheric boundary layer and in the troposphere. Many theoretical studies have been conducted by using the Gaussian plume model, though it is too simple to take into account the topographic effects and unstationary atmospheric conditions. Various numerical calculation models (designed for numerical calculation by a computer) have recently been developed, particularly for the implementation of environmental impact evaluation. Diagnostic and forecast type models are available for atmospheric air flow calculation. Other models available for diffusion analysis include the puff model, segment model, PIC (particle in cell)model, and random walk model. (N.K.)
Directory of Open Access Journals (Sweden)
Ming Ma
2015-08-01
Full Text Available It has long been recognized that the diffusion of adsorbed molecules and clusters is the key controlling factor in most dynamical processes occurring on surfaces and in nanoscale-confined spaces. The ability to manipulate diffusion is essential for achieving efficient transport in nano- and microstructures and for many other applications. Through simulations and experiments, we found that under the influence of mechanical oscillations, the diffusion coefficient in nanoscale-confined regions can be greatly enhanced. This effect occurs due to bifurcations of particle trajectories caused by the reconstruction of the energy landscape during oscillations. We derive a parameter-free analytical model for the enhanced diffusion that is in excellent agreement with results of our numerical simulations. The oscillation-induced enhancement of diffusion may have interesting and promising applications in such areas as directed molecular transport, sorting of particles, and tribology. Here, our findings have been applied to studies of mechanical cleaning of surfaces from contamination. Through both experiments and simulations, we have shown that using an oscillating slider, one can significantly reduce the concentration of contaminants in a confined region, which is crucial for achieving superlow friction.
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Tao Min
2014-01-01
Full Text Available This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.
Simulation of diffusion in concentrated lattice gases
International Nuclear Information System (INIS)
Kehr, K.W.
1986-01-01
Recently the diffusion of particles in lattice gases was studied extensively by theoretical methods and numerical simulations. This paper reviews work on collective and, in particular, on tracer diffusion. The diffusion of tagged particles is characterized by a correlation factor whose behavior as a function of concentration is now well understood. Also the detailed kinetics of the tracer transitions was investigated. A special case is the one-dimensional lattice gas where the tracer diffusion coefficient vanishes. An interesting extension is the case of tagged atoms with a different transition rate. This model allows to study various physical situations, including impurity diffusion, percolation, and diffusion in partially blocked lattices. Finally some recent work on diffusion in lattice gases under the influence of a drift field will be reported. (author)
Design Method for Channel Diffusers of Centrifugal Compressors
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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.
Siemon, R. E.; Atchison, W. L.; Awe, T.; Bauer, B. S.; Buyko, A. M.; Chernyshev, V. K.; Cowan, T. E.; Degnan, J. H.; Faehl, R. J.; Fuelling, S.; Garanin, S. F.; Goodrich, T.; Ivanovsky, A. V.; Lindemuth, I. R.; Makhin, V.; Mokhov, V. N.; Reinovsky, R. E.; Ryutov, D. D.; Scudder, D. W.; Taylor, T.; Yakubov, V. B.
2005-09-01
In the 'metal liner' approach to magnetized target fusion (MTF), a preheated magnetized plasma target is compressed to thermonuclear temperature and high density by externally driving the implosion of a flux conserving metal enclosure, or liner, which contains the plasma target. As in inertial confinement fusion, the principal fusion fuel heating mechanism is pdV work by the imploding enclosure, called a pusher in ICF. One possible MTF target, the hard-core diffuse z pinch, has been studied in MAGO experiments at VNIIEF and is one possible target being considered for experiments on the Atlas pulsed power facility. Numerical MHD simulations show two intriguing and helpful features of the diffuse z pinch with respect to compressional heating. First, in two-dimensional simulations the m = 0 interchange modes, arising from an unstable pressure profile, result in turbulent motions and self-organization into a stable pressure profile. The turbulence also gives rise to convective thermal transport, but the level of turbulence saturates at a finite level, and simulations show substantial heating during liner compression despite the turbulence. The second helpful feature is that pressure profile evolution during compression tends towards improved stability rather than instability when analysed according to the Kadomtsev criteria. A liner experiment is planned for Atlas to study compression of magnetic flux without plasma, as a first step. The Atlas geometry is compatible with a diffuse z pinch, and simulations of possible future experiments show that kiloelectronvolt temperatures and useful neutron production for diagnostic purposes should be possible if a suitable plasma injector is added to the Atlas facility.
International Nuclear Information System (INIS)
Sohn, Chae Hoon
2007-01-01
Extinction characteristics of hydrogen-air diffusion flames are investigated numerically by adopting counterflow flame configuration. At various pressures, effect of radiative heat loss on flame extinction is examined. Only gas-phase radiation is considered here. Radiative heat loss depends on flame thickness, temperature, H 2 O concentration, and pressure. From flame structures at various pressures, flame thickness decreases with pressure, but its gradient decreases at high pressure. Flame temperature and mole fraction of H 2 O increase slightly with pressure. Accordingly, as pressure increases, radiative heat loss becomes dominant. When radiative heat loss is considered, radiation-induced extinction is observed at low strain rate in addition to transport-induced extinction. As pressure increases, flammable region shifts to the high-temperature region and then, shrunk to the point on the coordinate plane of flame temperature and strain rate
International Nuclear Information System (INIS)
Takeda, H.; Isha, H.
1981-01-01
The paper is concerned with the displacement-assumed-finite elements by applying the reduced numerical integration technique in structural problems. The first part is a general consideration on the technique. Its purpose is to examine a variational interpretation of the finite element displacement formulation with the reduced integration technique in structural problems. The formulation is critically studied from a standpoint of the natural stiffness approach. It is shown that these types of elements are equivalent to a certain type of displacement and stress assumed mixed elements. The rank deficiency of the stiffness matrix of these elements is interpreted as a problem in the transformation from the natural system to a Cartesian system. It will be shown that a variational basis of the equivalent mixed formulation is closely related to the Hellinger-Reissner's functional. It is presented that for simple elements, e.g. bilinear quadrilateral plane stress and plate bending there are corresponding mixed elements from the functional. For relatively complex types of these elements, it is shown that they are equivalent to localized mixed elements from the Hellinger-Reissner's functional. In the second part, typical finite elements with the reduced integration technique are studied to demonstrate this equivalence. A bilinear displacement and rotation assumed shear beam element, a bilinear displacement assumed quadrilateral plane stress element and a bilinear deflection and rotation assumed quadrilateral plate bending element are examined to present equivalent mixed elements. Not only the theoretical consideration is presented but numerical studies are shown to demonstrate the effectiveness of these elements in practical analysis. (orig.)
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems
Energy Technology Data Exchange (ETDEWEB)
D’Elia, M., E-mail: mdelia@fsu.edu, E-mail: mdelia@sandia.gov [Sandia National Laboratories (United States); Gunzburger, M. [Florida State University (United States)
2016-04-15
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable. The analysis makes use of a nonlocal vector calculus that allows one to define a variational formulation of the nonlocal problem. In a manner analogous to the local partial differential equations counterpart, we demonstrate, for certain kernel functions, the existence of at least one optimal solution in the space of admissible parameters. We introduce a Galerkin finite element discretization of the optimal control problem and derive a priori error estimates for the approximate state and control variables. Using one-dimensional numerical experiments, we illustrate the theoretical results and show that by using nonlocal models it is possible to estimate non-smooth and discontinuous diffusion parameters.
Mathematical and numerical analysis of PN models for photons transport problems
International Nuclear Information System (INIS)
Valentin, Xavier
2015-01-01
Computational costs for direct numerical simulations of photon transport problems are very high in terms of CPU time and memory. One way to tackle this issue is to develop reduced models that a cheaper to solve numerically. There exists number of these models: moments models, discrete ordinates models (S N ), diffusion-like models... In this thesis, we focus on P N models in which the transport operator is approached by mean of a truncated development on the spherical harmonics basis. These models are arbitrary accurate in the angular dimension and are rotationally invariants (in multiple space dimensions). The latter point is fundamental when one wants to simulate inertial confinement fusion (ICF) experiments where the spherical symmetry plays an important part in the accuracy of the numerical solutions. We study the mathematical structure of the PN models and construct a new numerical method in the special case of a one dimensional space dimension with spherical symmetry photon transport problems. We first focus on a linear transport problem in the vacuum. Even in this simple case, it appears in the P N equations geometrical source terms that are stiff in the neighborhood of r = 0 and thus hard to discretize. Existing numerical methods are not satisfactory for multiple reasons: (1) inaccuracy in the neighborhood of r = 0 ('flux-dip'), (2) do not capture steady states (well-balanced scheme), (3) no stability proof. Following recent works, we develop a new well-balanced scheme for which we show the L 2 stability. We then extend the scheme for photon transport problems within a no moving media, the linear Boltzmann equation, and interest ourselves on its behavior in the diffusion limit (asymptotic-preserving property). In a second part, we consider radiation hydrodynamics problems. Since modelization of these problems is still under discussion in the literature, we compare a set of existing models by mean of mathematical analysis and establish a hierarchy
Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser
Cui, H.; Wang, H.; Chen, S.
2015-04-01
In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.
Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method
International Nuclear Information System (INIS)
Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong
2014-01-01
In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)
Numerical investigations of hybrid rocket engines
Betelin, V. B.; Kushnirenko, A. G.; Smirnov, N. N.; Nikitin, V. F.; Tyurenkova, V. V.; Stamov, L. I.
2018-03-01
Paper presents the results of numerical studies of hybrid rocket engines operating cycle including unsteady-state transition stage. A mathematical model is developed accounting for the peculiarities of diffusion combustion of fuel in the flow of oxidant, which is composed of oxygen-nitrogen mixture. Three dimensional unsteady-state simulations of chemically reacting gas mixture above thermochemically destructing surface are performed. The results show that the diffusion combustion brings to strongly non-uniform fuel mass regression rate in the flow direction. Diffusive deceleration of chemical reaction brings to the decrease of fuel regression rate in the longitudinal direction.
Diffusion coefficient of three-dimensional Yukawa liquids
International Nuclear Information System (INIS)
Dzhumagulova, K. N.; Ramazanov, T. S.; Masheeva, R. U.
2013-01-01
The purpose of this work is an investigation of the diffusion coefficient of the dust component in complex plasma. The computer simulation of the Yukawa liquids was made on the basis of the Langevin equation, which takes into account the influence of buffer plasma on the dust particles dynamics. The Green–Kubo relation was used to calculate the diffusion coefficient. Calculations of the diffusion coefficient for a wide range of the system parameters were performed. Using obtained numerical data, we constructed the interpolation formula for the diffusion coefficient. We also show that the interpolation formula correctly describes experimental data obtained under microgravity conditions
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
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Chunlong Sun
2017-01-01
Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.
High performance hydraulic design techniques of mixed-flow pump impeller and diffuser
International Nuclear Information System (INIS)
Kim, Sung; Lee, Kyoung Yong; Kim, Joon Hyung; Kim, Jin Hyuk; Jung, Uk Hee; Choi, Young Seok
2015-01-01
In this paper, we describe a numerical study about the performance improvement of a mixed-flow pump by optimizing the design of the impeller and diffuser using a commercial computational fluid dynamics (CFD) code and design-of-experiments (DOE). The design variables of impeller and diffuser in the vane plane development were defined with a fixed meridional plane. The design variables were defined by the vane plane development, which indicates the blade-angle distributions and length of the impeller and diffuser. The vane plane development was controlled using the blade-angle in a fixed meridional plane. The blade shape of the impeller and diffuser were designed using a traditional method in which the inlet and exit angles are connected smoothly. First, the impeller optimum design was performed with impeller design variables. The diffuser optimum design was performed with diffuser design variables while the optimally designed impeller shape was fixed. The importance of the impeller and diffuser design variables was analyzed using 2 k factorial designs, and the design optimization of the impeller and diffuser design variables was determined using the response surface method (RSM). The objective functions were defined as the total head (Ht) and the total efficiency (ηt) at the design flow rate. The optimally designed model was verified using numerical analysis, and the numerical analysis results for both the optimum model and the reference model were compared to determine the reasons for the improved pump performance. A pump performance test was carried out for the optimum model, and its reliability was proved by a comparative analysis of the results of the numerical analysis and an experiment using the optimum model.
Formation of Soot in Counterflow Diffusion Flames with Carbon Dioxide Dilution
Wang, Yu
2016-05-04
Experimental and numerical modeling studies have been performed to investigate the effect of CO2 dilution on soot formation in ethylene counterflow diffusion flames. Thermal and chemical effects of CO2 addition on soot growth was numerically identified by using a fictitious CO2 species, which was treated as inert in terms of chemical reactions. The results showed that CO2 addition reduces soot formation both thermodynamically and chemically. In terms of chemical effect, the addition of CO2 decreases soot formation through various pathways, including: (1) reduced soot precursor (PAH) formation leading to lower inception rates and soot number density, which in turn results in lower surface area for soot mass addition; (2) reduced H, CH3, and C3H3 concentrations causing lower H abstraction rate and therefore less active site per surface area for soot growth; and (3) reduced C2H2 mole fraction and thus a slower C2H2 mass addition rate. In addition, the sooting limits were also measured for ethylene counterflow flames in both N2 and CO2 atmosphere and the results showed that sooting region was significantly reduced in the CO2 case compared to the N2 case. © 2016 Taylor & Francis.
Numerical modeling of the dynamic response of a bioluminescent bacterial biosensor.
Affi, Mahmoud; Solliec, Camille; Legentilhomme, Patrick; Comiti, Jacques; Legrand, Jack; Jouanneau, Sulivan; Thouand, Gérald
2016-12-01
Water quality and water management are worldwide issues. The analysis of pollutants and in particular, heavy metals, is generally conducted by sensitive but expensive physicochemical methods. Other alternative methods of analysis, such as microbial biosensors, have been developed for their potential simplicity and expected moderate cost. Using a biosensor for a long time generates many changes in the growth of the immobilized bacteria and consequently alters the robustness of the detection. This work simulated the operation of a biosensor for the long-term detection of cadmium and improved our understanding of the bioluminescence reaction dynamics of bioreporter bacteria inside an agarose matrix. The choice of the numerical tools is justified by the difficulty to measure experimentally in every condition the biosensor functioning during a long time (several days). The numerical simulation of a biomass profile is made by coupling the diffusion equation and the consumption/reaction of the nutrients by the bacteria. The numerical results show very good agreement with the experimental profiles. The growth model verified that the bacterial growth is conditioned by both the diffusion and the consumption of the nutrients. Thus, there is a high bacterial density in the first millimeter of the immobilization matrix. The growth model has been very useful for the development of the bioluminescence model inside the gel and shows that a concentration of oxygen greater than or equal to 22 % of saturation is required to maintain a significant level of bioluminescence. A continuous feeding of nutrients during the process of detection of cadmium leads to a biofilm which reduces the diffusion of nutrients and restricts the presence of oxygen from the first layer of the agarose (1 mm) and affects the intensity of the bioluminescent reaction. The main advantage of this work is to link experimental works with numerical models of growth and bioluminescence in order to provide a
Energy Technology Data Exchange (ETDEWEB)
Melkior, Th
2000-07-01
The subject of this work deals with the project of underground disposal of radioactive wastes in deep geological formations. It concerns the study of the migration of radionuclides through clays. In these materials, the main transport mechanism is assumed to be diffusion under natural conditions. Therefore, some diffusion experiments are conducted. With interacting solutes which present a strong affinity for the material, the duration of these tests will be too long, for the range of concentrations of interest. An alternative is to determine on one hand the geochemical retention properties using batch tests and crushed rock samples and, on the other hand, to deduce the transport parameters from diffusion tests realised with a non-interacting tracer, tritiated water. These data are then used to simulate the migration of the reactive elements with a numerical code which can deal with coupled chemistry-diffusion equations. The validity of this approach is tested by comparing the numerical simulations with the results of diffusion experiments of cations through a clay. The subject is investigated in the case of the diffusion of cesium, lithium and sodium through a compacted sodium bentonite. The diffusion tests are realised with the through-diffusion method. The comparison between the experimental results and the simulations shows that the latter tends to under estimate the propagation of the considered species. The differences could be attributed to surface diffusion and to a decrease of the accessibility to the sites of fixation of the bentonite, from the conditions of clay suspensions in batch tests to the situation of compacted samples. The influence of the experimental apparatus used during the diffusion tests on the results of the measurement has also been tested. It showed that these apparatus have to be taken into consideration when the experimental data are interpreted. A specific model has been therefore developed with the numerical code CASTEM 2000. (author)
International Nuclear Information System (INIS)
Larroche, O.
2007-01-01
A locally split-step explicit (LSSE) algorithm was developed for efficiently solving a multi-dimensional advection-diffusion type equation involving a highly inhomogeneous and highly anisotropic diffusion tensor, which makes the problem very ill-conditioned for standard implicit methods involving the iterative solution of large linear systems. The need for such an optimized algorithm arises, in particular, in the frame of thermonuclear fusion applications, for the purpose of simulating fast charged-particle slowing-down with an ion Fokker-Planck code. The LSSE algorithm is presented in this paper along with the results of a model slowing-down problem to which it has been applied
Rate of riboflavin diffusion from intrastromal channels before corneal crosslinking.
McQuaid, Rebecca; Mrochen, Michael; Vohnsen, Brian
2016-03-01
To determine the diffusion of riboflavin from intrastromal channels through the effective diffusion coefficients compared with traditional axial diffusion with epithelium on or off. Advanced Optical Imaging Laboratory, University College Dublin, and Wellington Eye Clinic, Sandyford, Dublin, Ireland. Experimental study. The rate of diffusion in whole-mounted porcine eyes was monitored for a 30 minutes using an optical setup with a charge-coupled device camera and a bandpass filter (central wavelength 550 nm and 40 nm bandpass) to image the fluorescence under ultraviolet illumination (365 nm wavelength). For comparison, an isotropic corneal stroma with an annular channel was modeled numerically for different diffusion constants and boundary conditions. Numerical and experimental results were compared, allowing determination of the effective diffusion coefficient for each case. Experimental results for 6 different riboflavin solutions were in all cases found to be higher than for the common crosslinking (CXL) riboflavin protocol, where the diffusion constant is D0 = 6.5 × 10(-5) mm(2)/sec. For the intrastromal channel, 2 isotonic solutions containing riboflavin 0.1% correlated with a diffusion constant of 5D0 = 32.5 × 10(-5) mm(2)/sec. Hypotonic solutions and transepithelium had a higher diffusion coefficient approaching 10D0 = 65.0 × 10(-5) mm(2)/sec, which is an order-of-magnitude increase compared with the typical diffusion coefficient found in standard CXL. In this study, riboflavin had a faster stromal diffusion when injected into a corneal channel than when applied as drops to the anterior corneal surface. Further numerical modeling might allow optimization of the channel structure for any specific choice of riboflavin. Copyright © 2016 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.
Kochukhov, O.; Ryabchikova, T. A.
2018-02-01
A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.
Anomalous diffusion in a symbolic model
International Nuclear Information System (INIS)
Ribeiro, H V; Lenzi, E K; Mendes, R S; Santoro, P A
2011-01-01
In this work, we investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following the power-law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach reveals a rich diffusive scenario characterized by non-Gaussian distribution and, depending on the power-law exponent or the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare the analytic results with the numerical data, thereby finding good agreement. Because of its simplicity and flexibility, this model can be a candidate for describing real systems governed by power-law probability densities.
Numerical modelling of flow and transport in rough fractures
Directory of Open Access Journals (Sweden)
Scott Briggs
2014-12-01
Full Text Available Simulation of flow and transport through rough walled rock fractures is investigated using the lattice Boltzmann method (LBM and random walk (RW, respectively. The numerical implementation is developed and validated on general purpose graphic processing units (GPGPUs. Both the LBM and RW method are well suited to parallel implementation on GPGPUs because they require only next-neighbour communication and thus can reduce expenses. The LBM model is an order of magnitude faster on GPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified for parallel plate flow, backward facing step and single fracture flow; and the RW model is verified for point-source diffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithms place limitations on the discrete displacement of fluid or particle transport per time step to minimise the numerical error that must be considered during implementation.
A numerical study of shock-acceleration of a diffuse helium cylinder. Revision 1
International Nuclear Information System (INIS)
Greenough, J.A.; Jacobs, J.W.
1995-08-01
The development of a shock-accelerated diffuse Helium cylindrical inhomogeneity is investigated using a new numerical method. The new algorithm is a higher-order Godunov implementation of the so-called multi-fluid equations. This system correctly models multiple component mixtures by accounting for differential compressibility effects. This base integrator is embedded in an implementation of adaptive mesh refinement (AMR) that allows efficient increase in resolution by concentrating the computational effort where high accuracy, or increased resolution, are required. Qualitative and quantitative comparison with previous experimental data is excellent. The simulations show that counter-sign vortex blobs are deposited in the jet core by baroclinic generation of the curved shock wave as it traverses the jet. This vorticity deposition occurs over timescales that scale with the shock passage time (∼ 10microsec). Three phases of development are identified and characterized. The first is the weak deformation (WD) phase, where there is weak distortion of the Helium jet due to weak vorticity induced velocity effects. The second phase is the strong deformation (SD) phase where there is large distortion for the jet and the vortex blobs due to large induced velocity effects. The last is a relaxation/reorganization (RR) phase where the vorticity field is reorganized into point-like vortex pair. This class of problem has applications in such disparate fields as inertial confinement fusion (ICF) and high-speed combustion
Diffusion of drag-reducing polymer solutions within a rough-walled turbulent boundary layer
Elbing, Brian R.; Dowling, David R.; Perlin, Marc; Ceccio, Steven L.
2010-04-01
The influence of surface roughness on diffusion of wall-injected, drag-reducing polymer solutions within a turbulent boundary layer was studied with a 0.94 m long flat-plate test model at speeds of up to 10.6 m s-1 and Reynolds numbers of up to 9×106. The surface was hydraulically smooth, transitionally rough, or fully rough. Mean concentration profiles were acquired with planar laser induced fluorescence, which was the primary flow diagnostic. Polymer concentration profiles with high injection concentrations (≥1000 wppm) had the peak concentration shifted away from the wall, which was partially attributed to a lifting phenomenon. The diffusion process was divided into three zones—initial, intermediate, and final. Studies of polymer injection into a polymer ocean at concentrations sufficient for maximum drag reduction indicated that the maximum initial zone length is of the order of 100 boundary layer thicknesses. The intermediate zone results indicate that friction velocity and roughness height are important scaling parameters in addition to flow and injection conditions. Lastly, the current results were combined with those in Petrie et al. ["Polymer drag reduction with surface roughness in flat-plate turbulent boundary layer flow," Exp. Fluids 35, 8 (2003)] to demonstrate that the influence of polymer degradation increases with increased surface roughness.
On the theory of helium diffusion in stellar outer layers
International Nuclear Information System (INIS)
Ponce D, S.; Verga, A.D.
1986-01-01
We discuss the approximations usually made in the different approaches to diffusion in stellar outer layers. We analyze the hypotheses of binary diffusion and diffusion over a non altered background both analytically and numerically. Numerical calculations are applied to central stars of planetary nebulae in which a depletion of helium is observed. We find that in this case helium diffusion may be considered as a binary process but cannot be decoupled from the structure computation. We present an alternative method for studying diffusion and apply it to the central stars. We thus solve a stationary hydrodynamic model for a completely ionized H-He plasma, which takes into account consistently the behavior of all the species. We find equilibrium abundance distributions very different from those obtained according to the trace element approaches while helium and electron densities increase with depth in the atmosphere, protons tend to decrease. However, preliminary studies of the stability show that these are not the actual distributions. (author)
High resolution CT in diffuse lung disease
International Nuclear Information System (INIS)
Webb, W.R.
1995-01-01
High resolution CT (computerized tomography) was discussed in detail. The conclusions were HRCT is able to define lung anatomy at the secondary lobular level and define a variety of abnormalities in patients with diffuse lung diseases. Evidence from numerous studies indicates that HRCT can play a major role in the assessment of diffuse infiltrative lung disease and is indicate clinically (95 refs.)
Diffuse scattering from crystals with point defects
International Nuclear Information System (INIS)
Andrushevsky, N.M.; Shchedrin, B.M.; Simonov, V.I.; Malakhova, L.F.
2002-01-01
The analytical expressions for calculating the intensities of X-ray diffuse scattering from a crystal of finite dimensions and monatomic substitutional, interstitial, or vacancy-type point defects have been derived. The method for the determination of the three-dimensional structure by experimental diffuse-scattering data from crystals with point defects having various concentrations is discussed and corresponding numerical algorithms are suggested
High resolution CT in diffuse lung disease
Energy Technology Data Exchange (ETDEWEB)
Webb, W R [California Univ., San Francisco, CA (United States). Dept. of Radiology
1996-12-31
High resolution CT (computerized tomography) was discussed in detail. The conclusions were HRCT is able to define lung anatomy at the secondary lobular level and define a variety of abnormalities in patients with diffuse lung diseases. Evidence from numerous studies indicates that HRCT can play a major role in the assessment of diffuse infiltrative lung disease and is indicate clinically (95 refs.).
Numerical modelling of swirling diffusive flames
Directory of Open Access Journals (Sweden)
Parra-Santos Teresa
2016-01-01
Full Text Available Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Energy Technology Data Exchange (ETDEWEB)
Cargo, P.; Samba, G
2007-07-01
We consider the P{sub n} model to approximate the transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it gives the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by L. Gosse to solve the P{sub 1} model without absorption term. Moreover, it has the well-balanced property: it preserves the steady solutions of the system. (authors)
Energy Technology Data Exchange (ETDEWEB)
Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)
2016-01-15
We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.
A tutorial on inverse problems for anomalous diffusion processes
International Nuclear Information System (INIS)
Jin, Bangti; Rundell, William
2015-01-01
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several ‘classical’ inverse problems for fractional differential equations involving a Djrbashian–Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm–Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning
Numerical modeling and optimization of the Iguassu gas centrifuge
Bogovalov, S. V.; Borman, V. D.; Borisevich, V. D.; Tronin, V. N.; Tronin, I. V.
2017-07-01
The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.
Stochastic and collisional diffusion in two-dimensional periodic flows
International Nuclear Information System (INIS)
Doxas, I.; Horton, W.; Berk, H.L.
1990-05-01
The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time dependent perturbation added, is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov-Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow, to produce the global effective diffusion coefficient D*, which we can calculate theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations. 23 refs., 4 figs
Mitigation of numerical noise for beam loss simulations
Kesting, Frederik
2017-01-01
Numerical noise emerges in self-consistent simulations of charged particles, and its mitigation is investigated since the first numerical studies in plasma physics. In accelerator physics, recent studies find an artificial diffusion of the particle beam due to numerical noise in particle-in-cell tracking, which is of particular importance for high intensity machines with a long storage time, as the SIS100 at FAIR or in context of the LIU upgrade at CERN. In beam loss simulations for these projects artificial effects must be distinguished from physical beam loss. Therefore, it is important to relate artificial diffusion to artificial beam loss, and to choose simulation parameters such that physical beam loss is well resolved. As a practical tool, we therefore suggest a scaling law to find optimal simulation parameters for a given maximum percentage of acceptable artificial beam loss.
Continuous diffusion signal, EAP and ODF estimation via Compressive Sensing in diffusion MRI.
Merlet, Sylvain L; Deriche, Rachid
2013-07-01
In this paper, we exploit the ability of Compressed Sensing (CS) to recover the whole 3D Diffusion MRI (dMRI) signal from a limited number of samples while efficiently recovering important diffusion features such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF). Some attempts to use CS in estimating diffusion signals have been done recently. However, this was mainly an experimental insight of CS capabilities in dMRI and the CS theory has not been fully exploited. In this work, we also propose to study the impact of the sparsity, the incoherence and the RIP property on the reconstruction of diffusion signals. We show that an efficient use of the CS theory enables to drastically reduce the number of measurements commonly used in dMRI acquisitions. Only 20-30 measurements, optimally spread on several b-value shells, are shown to be necessary, which is less than previous attempts to recover the diffusion signal using CS. This opens an attractive perspective to measure the diffusion signals in white matter within a reduced acquisition time and shows that CS holds great promise and opens new and exciting perspectives in diffusion MRI (dMRI). Copyright © 2013 Elsevier B.V. All rights reserved.
Non-diffusive transport in 3-D pressure driven plasma turbulence
International Nuclear Information System (INIS)
Del-Castillo-Negrete, D.; Carreras, B.A.; Lynch, V.
2005-01-01
Numerical evidence of non-diffusive transport in 3-dimensional, resistive, pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracers is strongly non-Gaussian and exhibits algebraic decaying tails. To describe these results, a transport model using fractional derivative operators in proposed. The model incorporates in a unified way non-locality (i.e., non-Fickian transport), memory effects (i.e., non-Markovian transport), and non-diffusive scaling features known to be present in fusion plasmas. There is quantitative agreement between the model and the turbulent transport numerical calculations. In particular, the model reproduces the shape and space-time scaling of the pdf, and the super-diffusive scaling of the moments. (author)
Goh, Sien Fong
An experimental and numerical study of a turbulent smoke point diffusion flame in a quiescent and cross-flow condition was performed. The fuel mass flow rate of a turbulent smoke point flame was determined at a quiescent condition and in cross-flow with velocity ranging from 2 to 4 m/s. This fuel mass flow rate is defined as the Critical Fuel Mass Flow Rate (CFMFR). At a fuel mass flow rate below the CFMFR the flame produces smoke. In the dilution study, an amount of inert gas (nitrogen) was added to the fuel stream to achieve the smoke point condition for ten different fractions of CFMFR. From this dilution study, three regions were defined, the chemically-dominated region, transition region, and momentum-dominated region. The first objective of this study was to determine the factors behind the distinction of these three regions. The second objective was to understand the effect of cross-flow velocity on the smoke point flame structure. The flame temperature, radiation, geometrical dimension of flame, velocity, and global emissions and in-flame species concentration were measured. The third objective was to study a numerical model that can simulate the turbulent smoke point flame structure. The dilution study showed that the flames in quiescent condition and in the 3.5 and 4 m/s cross-flow condition had the chemically-dominated region at 5% to 20% CFMFR, the transition region at 20% to 40% CFMFR, and the momentum-dominated region at 40% to 100% CFMFR. On the other hand, the flame in cross-flow of 2 to 3 m/s showed the chemically-dominated region at 5% to 10% CFMFR, the transition region at 10% to 30% CFMFR, and the momentum-dominated region at 30% to 100% CFMFR. The chemically-dominated flame had a sharp dual-peak structure for the flame temperature, CO2 and NO concentration profiles at 25% and 50% flame length. However, the momentum-dominated region flame exhibited a dual peak structure only at 25% flame length. The decrease of flow rate from 30% to 10% CFMFR
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria; Chapman, S. Jonathan
2013-01-01
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
International Nuclear Information System (INIS)
Melkior, Th.
2000-01-01
The subject of this work deals with the project of underground disposal of radioactive wastes in deep geological formations. It concerns the study of the migration of radionuclides through clays. In these materials, the main transport mechanism is assumed to be diffusion under natural conditions. Therefore, some diffusion experiments are conducted. With interacting solutes which present a strong affinity for the material, the duration of these tests will be too long, for the range of concentrations of interest. An alternative is to determine on one hand the geochemical retention properties using batch tests and crushed rock samples and, on the other hand, to deduce the transport parameters from diffusion tests realised with a non-interacting tracer, tritiated water. These data are then used to simulate the migration of the reactive elements with a numerical code which can deal with coupled chemistry-diffusion equations. The validity of this approach is tested by comparing the numerical simulations with the results of diffusion experiments of cations through a clay. The subject is investigated in the case of the diffusion of cesium, lithium and sodium through a compacted sodium bentonite. The diffusion tests are realised with the through-diffusion method. The comparison between the experimental results and the simulations shows that the latter tends to under estimate the propagation of the considered species. The differences could be attributed to surface diffusion and to a decrease of the accessibility to the sites of fixation of the bentonite, from the conditions of clay suspensions in batch tests to the situation of compacted samples. The influence of the experimental apparatus used during the diffusion tests on the results of the measurement has also been tested. It showed that these apparatus have to be taken into consideration when the experimental data are interpreted. A specific model has been therefore developed with the numerical code CASTEM 2000. (author)
Gyrya, V.; Lipnikov, K.
2017-11-01
We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.
Magnetic field line diffusion at the onset of stochasticity
International Nuclear Information System (INIS)
Elsaesser, K.; Deeskow, P.
1987-01-01
The Hamiltonian equations of a particle in a random set of waves just above the stochasticity threshold are considered both theoretically and numerically. First we derive the diffusion coefficient and the autocorrelation time perturbatively without using the thermodynamic limit, and we discuss the relevance of the Hamiltonian problem for particle acceleration and magnetic field line flow. Then we integrate the equations for an ensemble of magnetic field lines numerically for a model problem and show the time evolution of moments and correlations. Twice above the threshold we observe diffusive behaviour from the beginning, but the diffusion coefficient includes also the non-resonant modes. Just at threshold we find first a short phase of free acceleration, later a diffusion which is lower than predicted by the theoretical formula. The best way to analyze the problem is in terms of cumulants, but a reliable comparison with any theory requires also a time integration of the corresponding kinetic equations. (orig.)
Flux-limited diffusion models in radiation hydrodynamics
International Nuclear Information System (INIS)
Pomraning, G.C.; Szilard, R.H.
1993-01-01
The authors discuss certain flux-limited diffusion theories which approximately describe radiative transfer in the presence of steep spatial gradients. A new formulation is presented which generalizes a flux-limited description currently in widespread use for large radiation hydrodynamic calculations. This new formation allows more than one Case discrete mode to be described by a flux-limited diffusion equation. Such behavior is not extant in existing formulations. Numerical results predicted by these flux-limited diffusion models are presented for radiation penetration into an initially cold halfspace. 37 refs., 5 figs
Periodic solutions in reaction–diffusion equations with time delay
International Nuclear Information System (INIS)
Li, Li
2015-01-01
Spatial diffusion and time delay are two main factors in biological and chemical systems. However, the combined effects of them on diffusion systems are not well studied. As a result, we investigate a nonlinear diffusion system with delay and obtain the existence of the periodic solutions using coincidence degree theory. Moreover, two numerical examples confirm our theoretical results. The obtained results can also be applied in other related fields
Significantly reduced c-axis thermal diffusivity of graphene-based papers
Han, Meng; Xie, Yangsu; Liu, Jing; Zhang, Jingchao; Wang, Xinwei
2018-06-01
Owing to their very high thermal conductivity as well as large surface-to-volume ratio, graphene-based films/papers have been proposed as promising candidates of lightweight thermal interface materials and lateral heat spreaders. In this work, we study the cross-plane (c-axis) thermal conductivity (k c ) and diffusivity (α c ) of two typical graphene-based papers, which are partially reduced graphene paper (PRGP) and graphene oxide paper (GOP), and compare their thermal properties with highly-reduced graphene paper and graphite. The determined α c of PRGP varies from (1.02 ± 0.09) × 10‑7 m2 s‑1 at 295 K to (2.31 ± 0.18) × 10‑7 m2 s‑1 at 12 K. This low α c is mainly attributed to the strong phonon scattering at the grain boundaries and defect centers due to the small grain sizes and high-level defects. For GOP, α c varies from (1.52 ± 0.05) × 10‑7 m2 s‑1 at 295 K to (2.28 ± 0.08) × 10‑7 m2 s‑1 at 12.5 K. The cross-plane thermal transport of GOP is attributed to the high density of functional groups between carbon layers which provide weak thermal transport tunnels across the layers in the absence of direct energy coupling among layers. This work sheds light on the understanding and optimizing of nanostructure of graphene-based paper-like materials for desired thermal performance.
Enhanced separation of diffusing particles by chaotic advection
International Nuclear Information System (INIS)
Aref, H.; Jones, S.W.
1989-01-01
Combining the reversibility of advection by a Stokes flow with the irreversibility of diffusion leads to a separation strategy for diffusing substances. This basic idea goes back to Taylor and Heller. It is shown here that the sensitivity of the method can be greatly enhanced by making the advection chaotic. The separation is particularly efficient when the thinnest structures resulting from advection are made comparable in size to a diffusion length. Simple heuristic estimates based on an understanding of chaotic motion and diffusion lead to a certain scaling that is seen in numerical experiments on this separation method
Directory of Open Access Journals (Sweden)
Chehhat A.
2016-12-01
Full Text Available Low solidity diffuser in centrifugal compressors can achieve both high efficiency and wide operating ranges which is of great importance for turbocharger compressor. Low solidity is achieved by using a low chord to pitch ratio. In this work, a CFD simulation is carried out to examine the effect of solidity on airflow field of a turbocharger centrifugal compressor which consists of a simple-splitter impeller and a vaned diffuser. By changing the number of diffuser vanes while keeping the number of impeller blades constant, the solidity value of the diffuser is varied. The characteristics of the compressor are evaluated for 6, 8, 10 and 12 stator vanes which correspond to solidity of: 0.78, 1.04, 1.29 and 1.55, respectively. The spatial distribution of the pressure, velocity and turbulent kinetic energy show that the diffuser solidity has significant effect on flow field and compressor performance map. The compressor with a 6 vanes diffuser has higher efficiency and operates at a wider range of flow rate relative to that obtained with larger vans number. However a non-uniform flow at the compressor exit was observed with relatively high turbulent kinetic energy.
Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana
2016-02-01
The methodology of Dual Reciprocity Boundary Element Method (DRBEM) is applied to the convection-diffusion problems and investigating its performance is our first objective of the work. Seven types of Radial Basis Functions (RBF); Linear, Thin-plate Spline, Cubic, Compactly Supported, Inverse Multiquadric, Quadratic, and that proposed by [12], were closely investigated in order to numerically compare their effectiveness drawbacks etc. and this is taken as our second objective. A sufficient number of simulations were performed covering as many aspects as possible. Varidated against both exacts and other numerical works, the final results imply strongly that the Thin-Plate Spline and Linear type of RBF are superior to others in terms of both solutions' quality and CPU-time spent while the Inverse Multiquadric seems to poorly yield the results. It is also found that DRBEM can perform relatively well at moderate level of convective force and as anticipated becomes unstable when the problem becomes more convective-dominated, as normally found in all classical mesh-dependence methods.
Numerical analyses on the effect of capillary condensation on gas diffusivities in porous media
Yoshimoto, Yuta; Hori, Takuma; Kinefuchi, Ikuya; Takagi, Shu
2017-11-01
We investigate the effect of capillary condensation on gas diffusivities in porous media composed of randomly packed spheres with moderate wettability. Lattice density functional theory simulations successfully reproduce realistic adsorption/desorption isotherms and provide fluid density distributions inside the porous media. We find that capillary condensations lead to the occlusion of narrow pores because they preferentially occur at confined spaces surrounded by the solid walls. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Most importantly, we find that the porosity-to-tortuosity ratio, which is a crucial parameter that determines the effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.
Vrentas, James S
2013-01-01
The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedime...
Computational Diffusion MRI : MICCAI Workshop
Grussu, Francesco; Ning, Lipeng; Tax, Chantal; Veraart, Jelle
2018-01-01
This volume presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as frontline applications in neuroscience research and clinical practice. These proceedings contain the papers presented at the 2017 MICCAI Workshop on Computational Diffusion MRI (CDMRI’17) held in Québec, Canada on September 10, 2017, sharing new perspectives on the most recent research challenges for those currently working in the field, but also offering a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. This book includes rigorous mathematical derivations, a large number of rich, full-colour visualisations and clinically relevant results. As such, it wil...
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria
2013-05-10
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle\\'s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
Matrix-dependent multigrid-homogenization for diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Knapek, S. [Institut fuer Informatik tu Muenchen (Germany)
1996-12-31
We present a method to approximately determine the effective diffusion coefficient on the coarse scale level of problems with strongly varying or discontinuous diffusion coefficients. It is based on techniques used also in multigrid, like Dendy`s matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximation. In numerical experiments, we compare our multigrid-homogenization method with homogenization, renormalization and averaging approaches.
Diffusion barriers of Al2O3 to reduce the bondcoat-oxidation of MCrAlY alloys
International Nuclear Information System (INIS)
Schmitt-Thomas, K.G.; Dietl, U.
1992-01-01
Under operating conditions in gas turbines plasma sprayed MCrAlY bondcoats (M = Co and/or Ni) for thermal barrier coatings are exposed to a strong oxidation attack. One possibility to reduce bondcoat oxidation is the application of diffusion barriers. Onto the bondcoat, diffusion barriers of Al 2 O 3 are deposited by CVD, PVD and plasma pulse process. The oxidation behaviour of these coating systems were examined at a temperature of 1273 K for times up to 250 hours. The CVD and PVD Al 2 O 3 - coated specimens show compared to the uncoated specimens smaller oxidation rates. The porous Al 2 O 3 coatings, produced by plasma pulse process are not fit for oxidation protection of the bondcoat. There is hope for further improvement of the oxidation resistance by optimizing the CVD- and PVD-process parameters. (orig.) [de
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
International Nuclear Information System (INIS)
Silva, T.L. da.
1987-01-01
Is this thesis, a numerical method for the solution of the linear diffusion equation for a plasma containing two types of ions, with the possibility of charge exchange, has been developed. It has been shown that the decay time of the electron and ion densities is much smaller than that in a plasma containing only a single type of ion. A non-linear diffusion equation, which includes the effects of an external electric field varying linearly in time, to describe a slightly ionized plasma has also been developed. It has been verified that the decay of the electron density in the presence of such an electric field is very slow. (author)
Reduced thermal conductivity of isotopically modulated silicon multilayer structures
DEFF Research Database (Denmark)
Bracht, H.; Wehmeier, N.; Eon, S.
2012-01-01
We report measurements of the thermal conductivity of isotopically modulated silicon that consists of alternating layers of highly enriched silicon-28 and silicon-29. A reduced thermal conductivity of the isotopically modulated silicon compared to natural silicon was measured by means of time......-resolved x-ray scattering. Comparison of the experimental results to numerical solutions of the corresponding heat diffusion equations reveals a factor of three lower thermal conductivity of the isotope structure compared to natural Si. Our results demonstrate that the thermal conductivity of silicon can...
Concentration contours in lattics and grain boundary diffusion in a polycrystalline solid
International Nuclear Information System (INIS)
Kim, Yong Soo; Jae, Won Mok; El Saied, Usama; Olander, Donald R.
1995-01-01
Grain boundary diffusion plays significant role in the fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated inside fuel pellet have to diffuse in the lattice and in the grain boundary before they reach open space in the fuel rod. In the mean time, the grains in the fuel pellet grow and shrink according to grain growth kinetics, especially at elevated temperature at which nuclear reactors are operating. Thus the boundary movement ascribed to the grain growth greatly influences the fission gas release rate by lengthening or shortening the lattice diffusion distance, which is the rate limiting step. Sweeping fission gases by the moving boundary contributes to the increment of the fission gas release as well. Lattice and grain boundary diffusion processes in the fission gas release can be studied by 'tracer diffusion' technique, by which grain boundary diffusivity can be estimated and used directly for low burn up fission gas release analysis. However, even for tracer diffusion analysis, taking both the intragranular grain growth and the diffusion processes simultaneously into consideration is not easy. Only a few models accounting for the both processes are available and mostly handle them numerically. Numerical solutions are limited in the practical use. Here in this paper, an approximate analytical solution of the lattice and stationary grain boundary diffusion in a polycrystalline solid is developed for the tracer diffusion techniques. This short closed form solution is compared to available exact and numerical solutions and turns out to be acceptably accurate. It can be applied to the theoretical modeling and the experimental analysis, especially PIE (post irradiation examination), of low burn up fission gas release
Preliminary study of diffusion effects in Fricke gel dosimeters
International Nuclear Information System (INIS)
Quiroga, A.; Vedelago, J.; Valente, M.
2014-08-01
Diffusion of ferric ions in ferrous sulfate (Fricke) gels represents one of the main drawbacks of some radiation detectors, like Fricke gel dosimeters. In practice, this disadvantage can be overcome by prompt dosimeter analysis, constraining strongly the time between irradiation and analysis. Due to required integral accuracy levels, special dedicated protocols are implemented with the aim of minimizing signal blurring due to diffusion effects. This work presents dedicated analytic modelling and numerical calculations of diffusion coefficients in Fricke gel radiation sensitive material. Samples are optically analysed by means of visible light transmission measurements capturing images with a Ccd camera provided with a monochromatic 585 nm filter corresponding to the X O-infused Fricke solution absorbance peak. Dose distributions in Fricke gels are suitably delivered in order to assess specific initial conditions further studied by periodical sample image acquisitions. In a first analytic approach, experimental data are fit with linear models in order to achieve a value for the diffusion coefficient. The second approach to the problem consists on a group of computational algorithms based on inverse problem formulation, along with suitable 2D diffusion model capable of estimating diffusion coefficients by fitting the obtained algorithm numerical solutions with the corresponding experimental data. Comparisons are performed by introducing an appropriate functional in order to analyse both experimental and numerical values. Solutions to second order diffusion equation are calculated in the framework of a dedicated method that incorporates Finite Element Method. Moreover, optimised solutions can be attained by gradient type minimisation algorithms. Knowledge about diffusion coefficient for Fricke gel radiation detector might be helpful in accounting for effects regarding elapsed time between dosimeter irradiation and further analysis. Hence, corrections might be included
International Nuclear Information System (INIS)
Vokal, A.; Vopalka, D.; Vecernik, P.; Institute of Chemical Technology in Prague, Prague
2010-01-01
Repositories for radioactive wastes are sited in the environment with very low permeability. One of the most important processes leading to the release of radionuclides to the environment is therefore diffusion of radionuclides in both natural and engineered barriers. Data for its description are crucial for the results of safety assessment of these repositories. They are obtained usually by comparison of the results of laboratory diffusion experiments with analytical and/or numerical solution of the diffusion equation with specified initial and boundary conditions. Results of the through-diffusion experiments are obviously evaluated by the 'time-lag' method that needs for most of sorbing species unfortunately very long time of the experiment duration. In this paper a modified approach is proposed for the evaluation of diffusion data for safety assessment, which decreases the influence of propagation uncertainties using incorrect data and reduces time for acquiring data for safety assessment. This approach consist in the following steps: (i) experimental measurement of material diffusion parameters under various conditions using non-sorbing tritiated water or chlorine for which it is easy to reach conditions under which the 'time-lag' method of evaluation of the result of the through-diffusion experiment is applicable - this step provides well established diffusion characteristics of materials for neutral species and anions, then (ii) to evaluate sorption isotherms for sorbing radionuclides from batch experiments under conditions corresponding to composition of material pore water, (iii) to assess the values of effective and apparent diffusion coefficients for sorbing radionuclides from well-defined diffusion coefficients of species in free water and (iv) to verify the obtained results using relatively short-term diffusion experiments with sorbing radionuclides, which will be evaluated using the time dependent decrease of the concentration in the input reservoir of
International Nuclear Information System (INIS)
Monnier, Joel
1971-01-01
To make a connection between technological parameters and electrical models it is necessary to know with a good accuracy the shape of the diffusion profiles. To do that we solve Fick's equations taking into account almost all physical phenomena known for diffusion in semiconductors: presence of an oxide layer, point defect diffusion coefficient dependence, impact of internal electric field, limited input flux, segregation coefficient... We have used DIFFUSI to predict diffusion profiles for device simulation programs; greater accuracy is then obtain to compute device properties and to optimize the device itself it is easy. Never accurate methods have still been studied like ionic probe and nuclear reactions to measure with an increased accuracy on the shape of the doping profiles. (author) [fr
Airflow Pattern Genereated by Three Air Diffusers
DEFF Research Database (Denmark)
Olmedo, Inés; Nielsen, Peter V.; de Adana, Manuel Ruiz
The correct description of air diffusers plays a crucial role in the CFD predictions of the airflow pattern into a room. The numerical simulation of air distribution in an indoor space is challenging because of the complicated airflow pattern generated. An experimental study has been carried out...... in a full scale test room, 4.10 m (length), 3.20 m (width), and 2.70 m (height), in order to take velocity measurements of the airflow pattern generated by three different air diffusers: displacement, mixing and a low impulse diffuser. Smoke visualization has been developed to determine the direction...
Directory of Open Access Journals (Sweden)
Lei Kun
2015-03-01
Full Text Available The present work was a study on global reaction rate of methanol synthesis. We measured experimentally the global reaction rate in the internal recycle gradientless reactor over catalyst SC309. The diffusion-reaction model of methanol synthesis was suggested. For model we chose the hydrogenation of CO and CO2 as key reaction. CO and CO2 were key components in our model. The internal diffusion effectiveness factors of CO and CO2 in the catalyst were calculated by the numerical integration. A comparison with the experiment showed that all the absolute values of the relative error were less than 10%. The simulation results showed that decreasing reaction temperature and catalyst diameter were conducive to reduce the influence of the internal diffusion on the methanol synthesis.
Diffusion simulation of ferric ions in dosemeter Fricke-gel with variable diffusion coefficient
International Nuclear Information System (INIS)
Milani, Caio Jacob; Bevilacqua, Joyce da Silva; Rodrigues Junior, Orlando
2014-01-01
Dosimetry using dosimeters Fricke-xylenol-Gel (FXG) allows confirmation and better understanding of radiotherapy treatments. The technique involves the evaluation of volumes irradiated by magnetic resonance imaging (MRI) or CT-optical. In both cases, the time spent between the irradiation and measurement is an important factor that directly influences the results. The quality of the images can be compromised by the mobility of ferric ions (Fe 3+), formed during the interaction of radiation with matter, increasing the uncertainty in determining the isodose. In this work, we simulated the dynamic involving ferric ions formed in one irradiated region irradiated in a two-dimensional domain with a variable diffusion coefficient. This phenomenon is modeled by a differential equation and solved numerically by an efficient algorithm that generalizes the Crank-Nicolson method. The stability and consistency of the method guarantee the convergence of the numerical solution for a predefined tolerance based in the choice of discretization steps of time and space. Different continuous functions were chosen to represent the diffusion coefficient and graphical views of the phenomenon are presented for a better understanding of the process
Wang, Zi Shuai; Sha, Wei E. I.; Choy, Wallace C. H.
2016-12-01
Modeling the charge-generation process is highly important to understand device physics and optimize power conversion efficiency of bulk-heterojunction organic solar cells (OSCs). Free carriers are generated by both ultrafast exciton delocalization and slow exciton diffusion and dissociation at the heterojunction interface. In this work, we developed a systematic numerical simulation to describe the charge-generation process by a modified drift-diffusion model. The transport, recombination, and collection of free carriers are incorporated to fully capture the device response. The theoretical results match well with the state-of-the-art high-performance organic solar cells. It is demonstrated that the increase of exciton delocalization ratio reduces the energy loss in the exciton diffusion-dissociation process, and thus, significantly improves the device efficiency, especially for the short-circuit current. By changing the exciton delocalization ratio, OSC performances are comprehensively investigated under the conditions of short-circuit and open-circuit. Particularly, bulk recombination dependent fill factor saturation is unveiled and understood. As a fundamental electrical analysis of the delocalization mechanism, our work is important to understand and optimize the high-performance OSCs.
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Direct measurement of VOC diffusivities in tree tissues
DEFF Research Database (Denmark)
Baduru, K.K.; Trapp, Stefan; Burken, Joel G.
2008-01-01
Recent discoveries in the phytoremediation of volatile organic compounds (VOCs) show that vapor-phase transport into roots leads to VOC removal from the vadose zone and diffusion and volatilization out of plants is an important fate following uptake. Volatilization to the atmosphere constitutes one...... in numerous vegetation−VOC interactions, including the phytoremediation of soil vapors and dissolved aqueous-phase contaminants. The diffusion of VOCs through freshly excised tree tissue was directly measured for common groundwater contaminants, chlorinated compounds such as trichloroethylene, perchloroethene......, and tetrachloroethane and aromatic hydrocarbons such as benzene, toluene, and methyl tert-butyl ether. All compounds tested are currently being treated at full scale with tree-based phytoremediation. Diffusivities were determined by modeling the diffusive transport data with a one-dimensional diffusive flux model...
TANASA, C.; MUNTEAN, S.; CIOCAN, T.; SUSAN-RESIGA, R. F.
2016-11-01
The hydraulic turbines operated at partial discharge (especially hydraulic turbines with fixed blades, i.e. Francis turbine), developing a swirling flow in the conical diffuser of draft tube. As a result, the helical vortex breakdown, also known in the literature as “precessing vortex rope” is developed. A passive method to mitigate the pressure pulsations associated to the vortex rope in the draft tube cone of hydraulic turbines is presented in this paper. The method involves the development of a progressive and controlled throttling (shutter), of the flow cross section at the bottom of the conical diffuser. The adjustable cross section is made on the basis of the shutter-opening of circular diaphragms, while maintaining in all positions the circular cross-sectional shape, centred on the axis of the turbine. The stagnant region and the pressure pulsations associated to the vortex rope are mitigated when it is controlled with the turbine operating regime. Consequently, the severe flow deceleration and corresponding central stagnant are diminished with an efficient mitigation of the precessing helical vortex. Four cases (one without diaphragm and three with diaphragm), are numerically and experimentally investigated, respectively. The present paper focuses on a 3D turbulent swirling flow simulation in order to evaluate the control method. Numerical results are compared against measured pressure recovery coefficient and Fourier spectra. The results prove the vortex rope mitigation and its associated pressure pulsations when employing the diaphragm.
Diffusion from cylindrical waste forms
International Nuclear Information System (INIS)
Thomas, G.F.
1985-05-01
The diffusion of a single component material from a finite cylindrical waste form, initially containing a uniform concentration of the material, is investigated. Under the condition that the cylinder is maintained in a well-stirred bath, expressions for the fractional inventory leached and the leach rate are derived with allowance for the possible permanent immobilization of the diffusant through its decay to a stable product and/or its irreversible reaction with the waste form matrix. The usefulness of the reported results in nuclear waste disposal applications is emphasized. The results reported herein are related to those previously derived at Oak Ridge National Laboratory by Bell and Nestor. A numerical scheme involving the partial decoupling of nested infinite summations and the use of rapidly converging rational approximants is recommended for the efficient implementation of the expressions derived to obtain reliable estimates of the bulk diffusion constant and the rate constant describing the diffusant-waste form interaction from laboratory data
Diffusion in multicomponent systems: a free energy approach
International Nuclear Information System (INIS)
Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian
2004-01-01
This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (M aa , M ab , M ba , and M bb ), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ ac and χ bc ) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested
Multiscale stabilization for convection-dominated diffusion in heterogeneous media
Calo, Victor M.
2016-02-23
We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not be sufficient to stabilize multiscale systems. We seek a local reduced-order model for this kind of multiscale transport problems and thus, develop a systematic approach for finding reduced-order approximations of the solution. We start from a Petrov-Galerkin framework using optimal weighting functions. We introduce an auxiliary variable to a mixed formulation of the problem. The auxiliary variable stands for the optimal weighting function. The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full solution on the dimensionally reduced space that approximates the solution. To find the test space, we reformulate some recent mixed Generalized Multiscale Finite Element Methods. We introduce snapshots and local spectral problems that appropriately define local weight and trial spaces. In particular, we use energy minimizing snapshots and local spectral decompositions in the natural norm associated with the auxiliary variable. The resulting spectral decomposition adaptively identifies and builds the optimal multiscale space to stabilize the system. We discuss the stability and its relation to the approximation property of the test space. We design online basis functions, which accelerate convergence in the test space, and consequently, improve stability. We present several numerical examples and show that one needs a few test functions to achieve an error similar to the projection error in the primal variable irrespective of the Peclet number.
International Nuclear Information System (INIS)
Kay, D.; Aitken, M.; Crowther, J.; Dickson, I.; Edwards, A.C.; Francis, C.; Hopkins, M.; Jeffrey, W.; Kay, C.; McDonald, A.T.; McDonald, D.; Stapleton, C.M.; Watkins, J.; Wilkinson, J.; Wyer, M.D.
2007-01-01
The European Water Framework Directive requires the integrated management of point and diffuse pollution to achieve 'good' water quality in 'protected areas'. These include bathing waters, which are regulated using faecal indicator organisms as compliance parameters. Thus, for the first time, European regulators are faced with the control of faecal indicator fluxes from agricultural sources where these impact on bathing water compliance locations. Concurrently, reforms to the European Union (EU) Common Agricultural Policy offer scope for supporting on-farm measures producing environmental benefits through the new 'single farm payments' and the concept of 'cross-compliance'. This paper reports the first UK study involving remedial measures, principally stream bank fencing, designed to reduce faecal indicator fluxes at the catchment scale. Considerable reduction in faecal indicator flux was observed, but this was insufficient to ensure bathing water compliance with either Directive 76/160/EEC standards or new health-evidence-based criteria proposed by WHO and the European Commission. - Diffuse microbiological pollution from farming activities can be reduced by protected riparian zones
The passive diffusion of Leptospira interrogans
Koens, Lyndon; Lauga, Eric
2014-12-01
Motivated by recent experimental measurements, the passive diffusion of the bacterium Leptospira interrogans is investigated theoretically. By approximating the cell shape as a straight helix and using the slender-body-theory approximation of Stokesian hydrodynamics, the resistance matrix of Leptospira is first determined numerically. The passive diffusion of the helical cell is then obtained computationally using a Langevin formulation which is sampled in time in a manner consistent with the experimental procedure. Our results are in excellent quantitative agreement with the experimental results with no adjustable parameters.
Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics
Directory of Open Access Journals (Sweden)
N. J. Biderman
2016-05-01
Full Text Available Two sets of diffusion-reaction numerical simulations using a finite difference method (FDM were conducted to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,GaSe2 (CIGS and Cu2ZnSn(S, Se4 (CZTSSe or CZTS via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases the equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. According to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.
International Nuclear Information System (INIS)
Heitfeld, Kevin A.; Schaefer, Dale W.
2009-01-01
Encapsulation is used to decrease the premature release of volatile flavour ingredients while offering protection against environmental damage such as oxidation, light-induced reactions, etc. Hydroxypropyl cellulose (HPC) is investigated here as a 'smart,' temperature responsive membrane for flavour encapsulation and delivery. Gel films were synthesized and characterized by diffusion and small-angle neutron and X-ray scattering techniques. Increasing temperature typically increases the diffusion rate across a membrane; HPC, however, can be tailored to give substantially improved elevated temperature properties. Scattering results indicate processing conditions have a significant impact on membrane morphology (micro phase separation). Under certain synthetic conditions, micro phase separation is mitigated and the membranes show temperature-independent diffusivity between 25 C and 60 C.
Parametric spatiotemporal oscillation in reaction-diffusion systems.
Ghosh, Shyamolina; Ray, Deb Shankar
2016-03-01
We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
Directory of Open Access Journals (Sweden)
Xuan Wu
2013-01-01
Full Text Available Direct numerical simulation has been performed to study a polymer drag-reducing channel flow by using a discrete-element model. And then, wavelet analyses are employed to investigate the multiresolution characteristics of velocity components based on DNS data. Wavelet decomposition is applied to decompose velocity fluctuation time series into ten different frequency components including approximate component and detailed components, which show more regular intermittency and burst events in drag-reducing flow. The energy contribution, intermittent factor, and intermittent energy are calculated to investigate characteristics of different frequency components. The results indicate that energy contributions of different frequency components are redistributed by polymer additives. The energy contribution of streamwise approximate component in drag-reducing flow is up to 82%, much more than 25% in the Newtonian flow. Feature of turbulent multiscale structures is shown intuitively by continuous wavelet transform, verifying that turbulent structures become much more regular in drag-reducing flow.
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients
Energy Technology Data Exchange (ETDEWEB)
Evoli, Carmelo [Gran Sasso Science Institute, viale Francesco Crispi 7, 67100 L' Aquila (AQ) (Italy); Gaggero, Daniele [GRAPPA Institute, University of Amsterdam, Science Park 904, 1090 GL Amsterdam (Netherlands); Vittino, Andrea [Physik-Department T30d, Technische Universität München, James-Franck-Straße 1, D-85748 Garching (Germany); Bernardo, Giuseppe Di [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85740 Garching bei München (Germany); Mauro, Mattia Di [W.W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305 (United States); Ligorini, Arianna [Instytut Fizyki J\\cadrowej—PAN, ul. Radzikowskiego 152, 31-342 Kraków (Poland); Ullio, Piero [Scuola Internazionale di Studi Superiori Avanzati, via Bonomea 265, 34136 Trieste (Italy); Grasso, Dario, E-mail: carmelo.evoli@gssi.infn.it, E-mail: d.gaggero@uva.nl, E-mail: andrea.vittino@tum.de, E-mail: bernardo@mpa-garching.mpg.de, E-mail: mdimauro@slac.stanford.edu, E-mail: arianna.ligorini@ifj.edu.pl, E-mail: piero.ullio@sissa.it, E-mail: dario.grasso@pi.infn.it [INFN and Dipartimento di Fisica ' ' E. Fermi' ' , Pisa University, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2017-02-01
We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion, either in space and momentum, advective transport and energy losses), under realistic conditions. The new version includes an updated numerical solver and several models for the astrophysical ingredients involved in the transport equation. Improvements in the accuracy of the numerical solution are proved against analytical solutions and in reference diffusion scenarios. The novel features implemented in the code allow to simulate the diverse scenarios proposed to reproduce the most recent measurements of local and diffuse CR fluxes, going beyond the limitations of the homogeneous galactic transport paradigm. To this end, several applications using DRAGON2 are presented as well. This new version facilitates the users to include their own physical models by means of a modular C++ structure.
Infrared radiation parameterizations in numerical climate models
Chou, Ming-Dah; Kratz, David P.; Ridgway, William
1991-01-01
This study presents various approaches to parameterizing the broadband transmission functions for utilization in numerical climate models. One-parameter scaling is applied to approximate a nonhomogeneous path with an equivalent homogeneous path, and the diffuse transmittances are either interpolated from precomputed tables or fit by analytical functions. Two-parameter scaling is applied to parameterizing the carbon dioxide and ozone transmission functions in both the lower and middle atmosphere. Parameterizations are given for the nitrous oxide and methane diffuse transmission functions.
Role of Rayleigh numbers on characteristics of double diffusive salt fingers
Rehman, F.; Singh, O. P.
2018-05-01
Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.
Field theory of propagating reaction-diffusion fronts
International Nuclear Information System (INIS)
Escudero, C.
2004-01-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations
Advectional enhancement of eddy diffusivity under parametric disorder
International Nuclear Information System (INIS)
Goldobin, Denis S
2010-01-01
Frozen parametric disorder can lead to the appearance of sets of localized convective currents in an otherwise stable (quiescent) fluid layer heated from below. These currents significantly influence the transport of an admixture (or any other passive scalar) along the layer. When the molecular diffusivity of the admixture is small in comparison to the thermal one, which is quite typical in nature, disorder can enhance the effective (eddy) diffusivity by several orders of magnitude in comparison to the molecular diffusivity. In this paper, we study the effect of an imposed longitudinal advection on the delocalization of convective currents, both numerically and analytically, and report a subsequent drastic boost of the effective diffusivity for weak advection.
Numerical simulation of internal flow in mixed-flow waterjet propulsion
International Nuclear Information System (INIS)
Wu, T T; Pan, Z Y; Zhang, D Q; Jia, Y Y
2012-01-01
In order to reveal the internal flow characteristic of a mixed-flow waterjet propulsion, a mixed-flow waterjet propulsion under different conditions was simulated based on multi-reference frame(MRF), the standard k − ε turbulent model and SIMPLEC algorithm. The relationship between pump performance instability and internal flow was obtained. The numerical results showed that characteristic instability occurred at 0.65-0.67Q BEP , the reason is that the backflow on the vaned diffuser hub-side blocks the downstream flow from the impeller. Therefore, the flow separates on the pressure surface of the impeller outlet and a strong vortex is generated, then the characteristic instability appeared due to the instability of internal flow. Backflow was found in diffuser passage at 0.65 Q BEP and 0.85 Q BEP , as flow rate decreases, the backflow region and velocity increases. Pressure fluctuation at diffuser inlet and diffuser passages was severe at at 0.65 Q BEP . According to the numerical simulation, the mixed-flow waterjet propulsion has characteristic instability at partial flow rate condition.
Düben, Peter D.; Subramanian, Aneesh; Dawson, Andrew; Palmer, T. N.
2017-03-01
The use of reduced numerical precision to reduce computing costs for the cloud resolving model of superparameterized simulations of the atmosphere is investigated. An approach to identify the optimal level of precision for many different model components is presented, and a detailed analysis of precision is performed. This is nontrivial for a complex model that shows chaotic behavior such as the cloud resolving model in this paper. It is shown not only that numerical precision can be reduced significantly but also that the results of the reduced precision analysis provide valuable information for the quantification of model uncertainty for individual model components. The precision analysis is also used to identify model parts that are of less importance thus enabling a reduction of model complexity. It is shown that the precision analysis can be used to improve model efficiency for both simulations in double precision and in reduced precision. Model simulations are performed with a superparameterized single-column model version of the OpenIFS model that is forced by observational data sets. A software emulator was used to mimic the use of reduced precision floating point arithmetic in simulations.
Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations
International Nuclear Information System (INIS)
Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.
2005-01-01
In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects
Heat transfer enhancement in nanofluids. A numerical approach
International Nuclear Information System (INIS)
Fariñas Alvariño, P; Sáiz Jabardo, J M; Arce, A; Llamas Galdo, M I
2012-01-01
The aim of the reported investigation is to asses the effect of brownian and thermophoretic diffusion in nanofluids convective heat transfer. In order to capture these effects, a new equation for particles distribution had to be consider. Momentum and energy equations have been reformulated in order to include brownian and thermophretic diffusion. These modes of diffusion have been suggested extensively in the literature but their effect on momentum and energy transport has not yet been numerically analyzed. In order to obtain a solution for the modified set of governing equations, a new CFD solver had to be devised. The new solver has been applied to a case study involving hydrodynamic and thermally developing laminar flow regime in a pipe. Pure base fluid solutions have been used to asses the accuracy of the model. Numerical nanofluid solutions compare reasonably well with both experimental results obtained elsewhere and the Churchill and Ozoe correlation. The observed heat transfer enhancement by the nanofluid has been attributed to its transport properties rather than to another transport mechanism.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
The passive diffusion of Leptospira interrogans
International Nuclear Information System (INIS)
Koens, Lyndon; Lauga, Eric
2014-01-01
Motivated by recent experimental measurements, the passive diffusion of the bacterium Leptospira interrogans is investigated theoretically. By approximating the cell shape as a straight helix and using the slender-body-theory approximation of Stokesian hydrodynamics, the resistance matrix of Leptospira is first determined numerically. The passive diffusion of the helical cell is then obtained computationally using a Langevin formulation which is sampled in time in a manner consistent with the experimental procedure. Our results are in excellent quantitative agreement with the experimental results with no adjustable parameters. (paper)
Oxygen diffusion in bilayer polymer films
DEFF Research Database (Denmark)
Poulsen, Lars; Zebger, Ingo; Tofte, Jannik Pentti
2004-01-01
Experiments to quantify oxygen diffusion have been performed on polymer samples in which a film of poly(ethylene-co-norbornene) was cast onto a film of polystyrene which, in turn, was cast onto an oxygen-impermeable substrate. In the technique employed, the time evolution of oxygen transport...... through the film of poly(ethylene-co-norbornene) and into the polystyrene film was monitored using the phosphorescence of singlet oxygen as a spectroscopic probe. To analyze the data, it was necessary to solve Fick's second law of diffusion for both polymer films. Tractable analytical and numerical...
Directory of Open Access Journals (Sweden)
Rasoul Nikbakhti
2016-03-01
Full Text Available This paper deals with a numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The length of the thermally active part equals half of the height. The non-dimensional forms of governing transport equations that describe double-diffusive natural convection for two-dimensional incompressible flow are functions of temperature or energy, concentration, vorticity, and stream-function. The coupled differential equations are discretized via FDM (Finite Difference Method. The Successive-Over-Relaxation (SOR method is used in the solution of the stream function equation. The analysis has been done for an enclosure with different aspect ratios ranging from 0.5 to 11 for three different combinations of partially active sections. The results are presented graphically in terms of streamlines, isotherms and isoconcentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers for various parameters including thermal Grashof number, Lewis number, buoyancy ratio and aspect ratio. It is revealed that the placement order of partially thermally active walls and the buoyancy ratio influence significantly the flow pattern and the corresponding heat and mass transfer performance in the cavity.
Preliminary study of diffusion effects in Fricke gel dosimeters
Energy Technology Data Exchange (ETDEWEB)
Quiroga, A. [Centro de Investigacion y Estudios de Matematica de Cordoba, Oficina 318 FaMAF - UNC, Ciudad Universitaria, 5000 Cordoba (Argentina); Vedelago, J. [Laboratorio de Investigaciones e Instrumentacion en Fisica Aplicada a la Medicina e Imagenes por Rayos X, Laboratorio 448 FaMAF - UNC, Ciudad Universitaria, 5000 Cordoba (Argentina); Valente, M., E-mail: aiquiroga@famaf.unc.edu [Instituto de Fisica Enrique Gaviola, Oficina 102 FaMAF - UNC, Av. Luis Medina Allende, Ciudad Universitaria, 5000 Cordoba (Argentina)
2014-08-15
Diffusion of ferric ions in ferrous sulfate (Fricke) gels represents one of the main drawbacks of some radiation detectors, like Fricke gel dosimeters. In practice, this disadvantage can be overcome by prompt dosimeter analysis, constraining strongly the time between irradiation and analysis. Due to required integral accuracy levels, special dedicated protocols are implemented with the aim of minimizing signal blurring due to diffusion effects. This work presents dedicated analytic modelling and numerical calculations of diffusion coefficients in Fricke gel radiation sensitive material. Samples are optically analysed by means of visible light transmission measurements capturing images with a Ccd camera provided with a monochromatic 585 nm filter corresponding to the X O-infused Fricke solution absorbance peak. Dose distributions in Fricke gels are suitably delivered in order to assess specific initial conditions further studied by periodical sample image acquisitions. In a first analytic approach, experimental data are fit with linear models in order to achieve a value for the diffusion coefficient. The second approach to the problem consists on a group of computational algorithms based on inverse problem formulation, along with suitable 2D diffusion model capable of estimating diffusion coefficients by fitting the obtained algorithm numerical solutions with the corresponding experimental data. Comparisons are performed by introducing an appropriate functional in order to analyse both experimental and numerical values. Solutions to second order diffusion equation are calculated in the framework of a dedicated method that incorporates Finite Element Method. Moreover, optimised solutions can be attained by gradient type minimisation algorithms. Knowledge about diffusion coefficient for Fricke gel radiation detector might be helpful in accounting for effects regarding elapsed time between dosimeter irradiation and further analysis. Hence, corrections might be included
Diffusion tensor in electron swarm transport
International Nuclear Information System (INIS)
Makabe, T.; Mori, T.
1983-01-01
Expression for the diffusion tensor of the electron (or light ion) swarm is presented from the higher-order expansion of the velocity distribution in the Boltzmann equation in hydrodynamic stage. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field with the usual-two-term expressions. Numerical analysis is given for the electron swarm in model gases having the momentum transfer cross section Qsub(m)(epsilon)=Q 0 epsilon sup(beta) (β=0, 1/2, 1) using the present theory. As the result, appreciable degree of discrepancy appears between the transverse diffusion coefficient defined here and the conventional expression with increasing of β in Qsub(m). (Author)
Ortleb, Sigrun; Seidel, Christian
2017-07-01
In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi
2014-04-11
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming
Numerical calculation of the tensor of diffusion in the nuclear reactor cells by Monte-Carlo method
International Nuclear Information System (INIS)
Gorodkov, S.S.; Kalugin, M.A.
2009-01-01
New algorithm based on the sequential application of the RMS path method has been proposed for the diffusion constants calculation. The offered algorithm conforms to the diffusion constants calculation in arbitrary segments of nuclear reactors without detail description of geometry, dependence of cross-sections from energy or neutron scattering anisotropy by kernel medium. The proposed algorithm is used for the diffusion constants calculation in uranium-graphite reactor sells
Numerical study of water diffusion in biological tissues using an improved finite difference method
International Nuclear Information System (INIS)
Xu Junzhong; Does, Mark D; Gore, John C
2007-01-01
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. (note)
Diffusion rates for elevated releases
International Nuclear Information System (INIS)
Ramsdell, J.V.
1983-11-01
A search of the literature related to diffusion from elevated sources has determined that an adequate data base exists for use in developing parameterizations for estimating diffusion rates for material released from free standing stacks at nuclear power plants. A review of published data analyses indicates that a new parameterization of horizontal diffusion rates specifically for elevated releases is not likely to significantly change the magnitudes of horizontal diffusion coefficients on the average. However, the uncertainties associated with horizontal diffusion coefficient estimates under any given set of atmospheric conditions could be reduced by a new parameterization. Similarly, a new parameterization of vertical diffusion rates would be unlikely to significantly alter the magnitudes of diffusion coefficients for unstable atmospheric conditons. However, for neutral and stable atmospheric conditions, a new parameterization of vertical diffusion rates might increase vertical diffusion coefficients significantly. The increase would move ground-level time-integrated concentration maxima closer to the plant and would increase the maxima. 55 references, 2 figures, 4 tables
A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit
Directory of Open Access Journals (Sweden)
Jin-Han Xie
2017-01-01
Full Text Available A simple model of nonlinear salt-ﬁnger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modiﬁed Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute ﬁeld and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identiﬁed for the second model: the weakly driven regime is characterized by a large-scale ﬂow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically conﬁrm the dependence of the kinetic energy and salinity ﬂuxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed.
Energy Technology Data Exchange (ETDEWEB)
Babu, Sundaram Ganesh; Ramalingam Vinoth [SRM Research Institute, SRM University, Kattankulathur 603203, Chennai, Tamilnadu (India); Neppolian, Bernaurdshaw, E-mail: neppolian.b@res.srmuniv.ac.in [SRM Research Institute, SRM University, Kattankulathur 603203, Chennai, Tamilnadu (India); Dionysiou, Dionysios D. [Environmental Engineering and Science Program, Department of Biomedical, Chemical and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45221-0012 (United States); Ashokkumar, Muthupandian [The School of Chemistry, University of Melbourne, Parkville, Melbourne, Victoria 3010 (Australia)
2015-06-30
Highlights: • Diffused sunlight is firstly used as an effective source for the degradation of organics. • More than 10 fold synergistic effect is achieved by sono-photocatalysis. • rGO enhances the degradation efficiency up to 54% as compared with CuO–TiO{sub 2} alone. • Plausible mechanism and intermediates formed are supported with experimental studies. - Abstract: Diffused sunlight is found to be an effective light source for the efficient degradation and mineralization of organic pollutant (methyl orange as a probe) by sono-photocatalytic degradation using reduced graphene oxide (rGO) supported CuO–TiO{sub 2} photocatalyst. The prepared catalysts are characterized by XRD, XPS, UV–vis DRS, PL, photoelectrochemical, SEM-EDS and TEM. A 10 fold synergy is achieved for the first time by combining sonochemical and photocatalytic degradation under diffused sunlight. rGO loading augments the activity of bare CuO–TiO{sub 2} more than two fold. The ability of rGO in storing, transferring, and shuttling electrons at the heterojunction between TiO{sub 2} and CuO facilitates the separation of photogenerated electron–hole pairs, as evidenced by the photoluminescence results. The complete mineralization of MO and the by-products within a short span of time is confirmed by TOC analysis. Further, hydroxyl radical mediated degradation under diffused sunlight is confirmed by LC–MS. This system shows similar activity for the degradation of methylene blue and 4-chlorophenol indicating the versatility of the catalyst for the degradation of various pollutants. This investigation is likely to open new possibilities for the development of highly efficient diffused sunlight driven TiO{sub 2} based photocatalysts for the complete mineralization of organic contaminants.
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng
2017-01-01
The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data...
Interface methods for hybrid Monte Carlo-diffusion radiation-transport simulations
International Nuclear Information System (INIS)
Densmore, Jeffery D.
2006-01-01
Discrete diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo simulations in diffusive media. An important aspect of DDMC is the treatment of interfaces between diffusive regions, where DDMC is used, and transport regions, where standard Monte Carlo is employed. Three previously developed methods exist for treating transport-diffusion interfaces: the Marshak interface method, based on the Marshak boundary condition, the asymptotic interface method, based on the asymptotic diffusion-limit boundary condition, and the Nth-collided source technique, a scheme that allows Monte Carlo particles to undergo several collisions in a diffusive region before DDMC is used. Numerical calculations have shown that each of these interface methods gives reasonable results as part of larger radiation-transport simulations. In this paper, we use both analytic and numerical examples to compare the ability of these three interface techniques to treat simpler, transport-diffusion interface problems outside of a more complex radiation-transport calculation. We find that the asymptotic interface method is accurate regardless of the angular distribution of Monte Carlo particles incident on the interface surface. In contrast, the Marshak boundary condition only produces correct solutions if the incident particles are isotropic. We also show that the Nth-collided source technique has the capacity to yield accurate results if spatial cells are optically small and Monte Carlo particles are allowed to undergo many collisions within a diffusive region before DDMC is employed. These requirements make the Nth-collided source technique impractical for realistic radiation-transport calculations
Improved diffusion coefficients generated from Monte Carlo codes
International Nuclear Information System (INIS)
Herman, B. R.; Forget, B.; Smith, K.; Aviles, B. N.
2013-01-01
Monte Carlo codes are becoming more widely used for reactor analysis. Some of these applications involve the generation of diffusion theory parameters including macroscopic cross sections and diffusion coefficients. Two approximations used to generate diffusion coefficients are assessed using the Monte Carlo code MC21. The first is the method of homogenization; whether to weight either fine-group transport cross sections or fine-group diffusion coefficients when collapsing to few-group diffusion coefficients. The second is a fundamental approximation made to the energy-dependent P1 equations to derive the energy-dependent diffusion equations. Standard Monte Carlo codes usually generate a flux-weighted transport cross section with no correction to the diffusion approximation. Results indicate that this causes noticeable tilting in reconstructed pin powers in simple test lattices with L2 norm error of 3.6%. This error is reduced significantly to 0.27% when weighting fine-group diffusion coefficients by the flux and applying a correction to the diffusion approximation. Noticeable tilting in reconstructed fluxes and pin powers was reduced when applying these corrections. (authors)
Unbiased diffusion of Brownian particles on disordered correlated potentials
International Nuclear Information System (INIS)
Salgado-Garcia, Raúl; Maldonado, Cesar
2015-01-01
In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us to prove that the unbiased diffusion of overdamped particles on a random polymer does not depend on the correlations of the disordered potentials. This universal behavior of the unbiased diffusivity is a direct consequence of the validity of the Einstein relation and the decay of correlations of the random polymer. We test the independence on correlations of the diffusion coefficient for correlated polymers produced by two different stochastic processes, a one-step Markov chain and the expansion-modification system. Within the accuracy of our simulations, we found that the numerically obtained diffusion coefficient for these systems agree with the analytically calculated ones, confirming our predictions. (paper)
DEFF Research Database (Denmark)
Hughes, A L; Buitenhuis, A J
2010-01-01
among populations with respect to mean expression scores, but numerous transcripts showed reduced variance in expression scores in the high FP population in comparison to control and low FP populations. The reduction in variance in the high FP population generally involved transcripts whose expression...
Malkyarenko, Dariya I; Chenevert, Thomas L
2014-12-01
To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.
Fujisawa, Nobumichi; Hara, Shotaro; Ohta, Yutaka
2016-02-01
The characteristics of a rotating stall of an impeller and diffuser and the evolution of a vortex generated at the diffuser leading-edge (i.e., the leading-edge vortex (LEV)) in a centrifugal compressor were investigated by experiments and numerical analysis. The results of the experiments revealed that both the impeller and diffuser rotating stalls occurred at 55 and 25 Hz during off-design flow operation. For both, stall cells existed only on the shroud side of the flow passages, which is very close to the source location of the LEV. According to the CFD results, the LEV is made up of multiple vortices. The LEV is a combination of a separated vortex near the leading- edge and a longitudinal vortex generated by the extended tip-leakage flow from the impeller. Therefore, the LEV is generated by the accumulation of vorticity caused by the velocity gradient of the impeller discharge flow. In partial-flow operation, the spanwise extent and the position of the LEV origin are temporarily transmuted. The LEV develops with a drop in the velocity in the diffuser passage and forms a significant blockage within the diffuser passage. Therefore, the LEV may be regarded as being one of the causes of a diffuser stall in a centrifugal compressor.
Effects of radial diffuser hydraulic design on a double-suction centrifugal pump
Hou, H. C.; Zhang, Y. X.; Xu, C.; Zhang, J. Y.; Li, Z. L.
2016-05-01
In order to study effects of radial diffuser on hydraulic performance of crude oil pump, the steady CFD numerical method is applied and one large double-suction oil pump running in long-distance pipeline is considered. The research focuses on analysing the influence of its diffuser vane profile on hydraulic performance of oil pump. The four different types of cylindrical vane have been designed by in-house codes mainly including double arcs (DA), triple arcs (TA), equiangular spiral line (ES) and linear variable angle spiral line (LVS). During design process diffuser vane angles at inlet and outlet are tentatively given within a certain range and then the wrapping angle of the four types of diffuser vanes can be calculated automatically. Under the given inlet and outlet angles, the linear variable angle spiral line profile has the biggest wrapping angle and profile length which is good to delay channel diffusion but bring more friction hydraulic loss. Finally the vane camber line is thickened at the certain uniform thickness distribution and the 3D diffuser models are generated. The whole flow passage of oil pump with different types of diffusers under various flow rate conditions are numerically simulated based on RNG k-ɛ turbulent model and SIMPLEC algorithm. The numerical results show that different types of diffusers can bring about great difference on the hydraulic performance of oil pump, of which the ES profile diffuser with its proper setting angle shows the best hydraulic performance and its inner flow field is improved obviously. Compared with the head data from model sample, all designed diffusers can make a certain improvement on head characteristic. At the large flow rate conditions the hydraulic efficiency increases obviously and the best efficiency point shift to the large flow rate range. The ES profile diffuser embodies the better advantages on pump performance which can be explained theoretically that the diffuser actually acts as a diffusion
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
International Nuclear Information System (INIS)
Effenberger, F.; Fichtner, H.; Scherer, K.; Barra, S.; Kleimann, J.; Strauss, R. D.
2012-01-01
The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e., one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulae to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the 'traditional' diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we describe the motivation for the choice of the Frenet-Serret trihedron, which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and Parker fields. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard three-dimensional model for the modulation of galactic protons. For this, we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the 'traditional' one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.
Inertial effects in diffusion-limited reactions
International Nuclear Information System (INIS)
Dorsaz, N; Foffi, G; De Michele, C; Piazza, F
2010-01-01
Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.
Numerical models for high beta magnetohydrodynamic flow
International Nuclear Information System (INIS)
Brackbill, J.U.
1987-01-01
The fundamentals of numerical magnetohydrodynamics for highly conducting, high-beta plasmas are outlined. The discussions emphasize the physical properties of the flow, and how elementary concepts in numerical analysis can be applied to the construction of finite difference approximations that capture these features. The linear and nonlinear stability of explicit and implicit differencing in time is examined, the origin and effect of numerical diffusion in the calculation of convective transport is described, and a technique for maintaining solenoidality in the magnetic field is developed. Many of the points are illustrated by numerical examples. The techniques described are applicable to the time-dependent, high-beta flows normally encountered in magnetically confined plasmas, plasma switches, and space and astrophysical plasmas. 40 refs
Model for Anomalous Moisture Diffusion through a Polymer-Clay Nanocomposite
DEFF Research Database (Denmark)
Drozdov, Aleksey D.; Christiansen, Jesper de Claville; Gupta, R.K.
2003-01-01
Experimental data are reported on moisture diffusion and the elastoplastic response of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests showed that water transport in the neat resin is Fickian, whereas...... platelets. Constitutive equations are developed for moisture diffusion through and the elastoplastic behavior of a nanocomposite. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical...
Contribution to the evaluation of diffusion coefficients in plasmas containing argon and fluorine
International Nuclear Information System (INIS)
Novakovic, N V
2006-01-01
The theoretical values of the numerical evaluation of the electron and ion diffusion coefficients in plasmas from mixtures of argon and fluorine are presented. The temperature dependence of the diffusion coefficients for low-pressure (from 0.1 to 1.0 kPa) and low-temperature (from 500 to 5000 K) argon plasmas with 20% and 30% of added fluorine are investigated. These values are results of the applications of the specific numerical model to the evaluation plasma composition and transport coefficients in argon plasma with fluorine as additive. It is assumed that the system is kept under constant pressure and that a corresponding state of local thermodynamical equilibrium (LTE) is attained. Since the LTE can be assumed, a Maxwellian electron distribution function will be adopted. The hypothesis of LTE, which is commonly used in most of the numerical evaluations, is analysed with the modified Debye radius r D *. The binary electron and ion diffusion coefficients are calculated with the equilibrium plasma composition and with the collision frequencies. Strictly speaking, Maxwellian distribution function (in the state LTE) is not valid for low pressure, but in this case with the aid of the modified Debye radius, a Maxwellian f e M is assumed correctly. It is shown that the electron diffusion coefficients are about four orders of magnitude larger than the corresponding overall diffusion coefficients of ions. Both diffusion coefficients are lower in argon plasma with 30% than with 20% of fluorine additives, in the whole temperature range examined
Pattern formation induced by cross-diffusion in a predator–prey system
International Nuclear Information System (INIS)
Sun Guiquan; Jin Zhen; Liu Quanxing; Li Li
2008-01-01
This paper considers the Holling–Tanner model for predator–prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator–prey system. (general)
Numerical methods in nuclear engineering. Part 1
International Nuclear Information System (INIS)
Phillips, G.J.
1983-08-01
These proceedings, published in two parts contain the full text of 56 papers and summaries of six papers presented at the conference. They cover the use of numerical methods in thermal hydraulics, reactor physics, neutron diffusion, subchannel analysis, risk assessment, transport theory, and fuel behaviour
International Nuclear Information System (INIS)
Guenza, M.; Schweizer, K.S.
1998-01-01
The predictions of polymer-mode-coupling theory for self-diffusion in entangled structurally and interaction symmetric diblock copolymer fluids are illustrated by explicit numerical calculations. We find that retardation of translational motion emerges near and somewhat below the order endash disorder transition (ODT) in an approximately exponential and/or thermally activated manner. At fixed reduced temperature, suppression of diffusion is enhanced with increasing diblock molecular weight, compositional symmetry, and/or copolymer concentration. At very low temperatures, a new entropic-like regime of mobility suppression is predicted based on an isotropic supercooled liquid description of the copolymer structure. Preliminary generalization of the theory to treat diblock tracer diffusion is also presented. Quantitative applications to recent self and tracer diffusion measurements on compositionally symmetric polyolefin diblock materials have been carried out, and very good agreement between theory and experiment is found. Asymmetry in block local friction constants is predicted to significantly influence mobility suppression, with the largest effects occurring when the minority block is also the high friction species. New experiments to further test the predictions of the theory are suggested. copyright 1998 American Institute of Physics
A model for anomalous moisture diffusion through a polymer-clay nanocomposite
DEFF Research Database (Denmark)
Drozdov, Aleksey D.; Christiansen, Jesper de Claville; Gupta, R.K.
2002-01-01
Experimental data are reported on moisture diffusion and the elastoplastic response in uniaxial tensile tests of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests show that the moisture transport...... diffusion through a nanocomposite and for its elastoplastic behavior. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation....
Numerical computation of the linear stability of the diffusion model for crystal growth simulation
Energy Technology Data Exchange (ETDEWEB)
Yang, C.; Sorensen, D.C. [Rice Univ., Houston, TX (United States); Meiron, D.I.; Wedeman, B. [California Institute of Technology, Pasadena, CA (United States)
1996-12-31
We consider a computational scheme for determining the linear stability of a diffusion model arising from the simulation of crystal growth. The process of a needle crystal solidifying into some undercooled liquid can be described by the dual diffusion equations with appropriate initial and boundary conditions. Here U{sub t} and U{sub a} denote the temperature of the liquid and solid respectively, and {alpha} represents the thermal diffusivity. At the solid-liquid interface, the motion of the interface denoted by r and the temperature field are related by the conservation relation where n is the unit outward pointing normal to the interface. A basic stationary solution to this free boundary problem can be obtained by writing the equations of motion in a moving frame and transforming the problem to parabolic coordinates. This is known as the Ivantsov parabola solution. Linear stability theory applied to this stationary solution gives rise to an eigenvalue problem of the form.
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
International Nuclear Information System (INIS)
Rosa, S.; Pinho, F.T.
2006-01-01
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
Energy Technology Data Exchange (ETDEWEB)
Rosa, S. [Escola Superior de Tecnologia e Gestao, Instituto Politecnico, Campus de Santa Apolonia, 5301-857 Braganca (Portugal)]. E-mail: srosa@ipb.pt; Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEM, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)]. E-mail: fpinho@fe.up.pt
2006-04-15
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section.
Analysis of current diffusive ballooning mode
International Nuclear Information System (INIS)
Yagi, M.; Azumi, M.; Itoh, K.; Itoh, S.; Fukuyama, A.
1993-04-01
The current diffusive ballooning mode is analysed in the tokamak plasma. This mode is destabilized by the current diffusivity (i.e., the electron viscosity) and stabilized by the thermal conductivity and ion viscosity. By use of the ballooning transformation, the eigenmode equation is solved. Analytic solution is obtained by the strong ballooning limit. Numerical calculation is also performed to confirm the analytic theory. The growth rate of the mode and the mode structure are analysed. The stability boundary is derived in terms of the current diffusivity, thermal conductivity, ion viscosity and the pressure gradient for the given shear parameter. This result is applied to express the thermal conductivity in terms of the pressure gradient, magnetic configurational parameters (such as the safety factor, shear and aspect ratio) and the Prandtl numbers. (author)
Numerical analysis of the influence of ultrasonic vibration on crystallization processes
Energy Technology Data Exchange (ETDEWEB)
Ubbenjans, B.; Nacke, B. [Institute of Electrotechnology, Hannover (Germany); Frank-Rotsch, C.; Rudolph, P. [Institute for Crystal Growth, Berlin (Germany); Virbulis, J. [University of Latvia, Laboratory for Mathematical Modelling of Environmental and Technological Processes, Riga (Latvia)
2012-03-15
The challenge in the future fabrication of semiconductor bulk crystals is the improvement of the crystal quality with a simultaneous increase of the yield. For that, a proper control of mass transfer within the fluid phase is required. Besides the damping of violent convective fluctuations, the thickness of the diffusion boundary layer, causing morphological instability, has to be decreased. The influence of ultrasound in molten Germanium was analyzed by numerical simulations. The simulations were provided by applying commercial software packages ANSYS {sup registered} and FLUENT {sup registered}. ANSYS {sup registered} was used to model the ultrasonic wave propagation in the whole growth system consisting of melt and crystal, crucible and surrounding media. As a result the sound pressure distribution in every point of the melt and the displacement in every point of the solid have been obtained. The melt flow and the temperature distribution were simulated with the help of FLUENT {sup registered}. The main focus was the analysis of Schlichting streams that occur at the crystallization front which affect the diffusion boundary layer. It was shown that ultrasonic treatment can help to reduce the harmful diffusion boundary layer very effectively. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Luchko, Yuri
2013-05-30
In this paper, we consider a reaction-diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction-diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented. © 2013 IOP Publishing Ltd.
International Nuclear Information System (INIS)
Seddeek, M.A.; Abdelmeguid, M.S.
2006-01-01
The effect of radiation and thermal diffusivity on heat transfer over a stretching surface with variable heat flux has been studied. The thermal diffusivity is assumed to vary as a linear function of temperature. The governing partial differential equations have been transformed to ordinary differential equations. The exact analytical solution for the velocity and the numerical solution for the temperature field are given. Numerical solutions are obtained for different values of variable thermal diffusivity, radiation, temperature parameter and Prandtl number
Numerical simulations of a reduced model for blood coagulation
Pavlova, Jevgenija; Fasano, Antonio; Sequeira, Adélia
2016-04-01
In this work, the three-dimensional numerical resolution of a complex mathematical model for the blood coagulation process is presented. The model was illustrated in Fasano et al. (Clin Hemorheol Microcirc 51:1-14, 2012), Pavlova et al. (Theor Biol 380:367-379, 2015). It incorporates the action of the biochemical and cellular components of blood as well as the effects of the flow. The model is characterized by a reduction in the biochemical network and considers the impact of the blood slip at the vessel wall. Numerical results showing the capacity of the model to predict different perturbations in the hemostatic system are discussed.
Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime
Directory of Open Access Journals (Sweden)
Rakesh Kumar
Full Text Available A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM. The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables. Keywords: Unsteadiness, Bio-convection, Slip regime, Stagnation point flow, Numerical modeling
International Nuclear Information System (INIS)
Chudhry, Q.N.; Ahmed, P.; Ullah, K.; Satti, T.M.; Raza, S.; Mehmood, S.K.; Akram, M.; Ahmed, S.
2010-01-01
A 42 years old male with relapsed diffuse large B-cell lymphoma was given second-line chemotherapy followed by reduced intensity allogeneic stem cell transplantation from HLA matched brother. Twelve weeks post transplant, his disease relapsed evidenced by the appearance of lymphoma cells in the peripheral blood and declining donor chimerism. Donor lymphocyte infusion was given that induced complete lymphoma remission. The patient is well 3 years post transplant with his disease in complete remission. (author)
Numerical modeling of turbulent jet diffusion flames in the atmospheric surface layer
Hernández, J.; Crespo, A.; Duijm, N.J.
1995-01-01
The evolution of turbulent jet diffusion flames of natural gas in air is predicted using a finite-volume procedure for solving the flow equations. The model is three dimensional, elliptic and based on the conserved-scalar approach and the laminar flamelet concept. A laminar flamelet prescription for
Nanoparticles in dilute solution : A numerical study of rotational diffusion
Energy Technology Data Exchange (ETDEWEB)
Evensen, Tom Richard
2008-06-15
This thesis is dedicated to Brownian dynamics simulations of rotational diffusion. A rotation dynamics engine has been implemented and tested. This engine will in the future be integrated as a part of a complete Brownian dynamics simulation tool. The special case, when translational motion can be ignored, has thoroughly been studied. Two choices of generalized coordinates describing angular orientation of the particles are used. The Euler angles, which constitute the classical choice, and the Cartesian components of the rotation vector, which was recently introduced as an alternative, are being compared with regards to computational efficiency. Results from both equilibrium and non-equilibrium simulations are presented. The consistency of two new algorithms is demonstrated on systems of free rigid particles with arbitrary surface topographies. The algorithms make use of only the principal values of the rotational mobility tensor, assuming the corresponding principal axes coincide with the body-fixed coordinate system. These three scalars contain all information about the particle surface topography relevant for rotational diffusion. The calculation of the mobility tensor can be performed in a pre-calculation step, which makes the algorithm itself highly efficient. Both choices of generalized coordinates correctly reproduce theoretical predictions, but we have found that the algorithm using the Cartesian components of the rotation vector as generalized coordinates outperform its counterpart using the Euler angles by up to a factor 1000 in extreme cases. The reason for this improvement is that the algorithm using the Cartesian components of the rotation vector is free of singularities. (Author). refs. figs
Diffusion piecewise homogenization via flux discontinuity ratios
International Nuclear Information System (INIS)
Sanchez, Richard; Dante, Giorgio; Zmijarevic, Igor
2013-01-01
We analyze piecewise homogenization with flux-weighted cross sections and preservation of averaged currents at the boundary of the homogenized domain. Introduction of a set of flux discontinuity ratios (FDR) that preserve reference interface currents leads to preservation of averaged region reaction rates and fluxes. We consider the class of numerical discretizations with one degree of freedom per volume and per surface and prove that when the homogenization and computing meshes are equal there is a unique solution for the FDRs which exactly preserve interface currents. For diffusion sub-meshing we introduce a Jacobian-Free Newton-Krylov method and for all cases considered obtain an 'exact' numerical solution (eight digits for the interface currents). The homogenization is completed by extending the familiar full assembly homogenization via flux discontinuity factors to the sides of regions laying on the boundary of the piecewise homogenized domain. Finally, for the familiar nodal discretization we numerically find that the FDRs obtained with no sub-mesh (nearly at no cost) can be effectively used for whole-core diffusion calculations with sub-mesh. This is not the case, however, for cell-centered finite differences. (authors)
International Nuclear Information System (INIS)
Figueroa, Aldo; Meunier, Patrice; Villermaux, Emmanuel; Cuevas, Sergio; Ramos, Eduardo
2014-01-01
We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, “The diffusive strip method for scalar mixing in two-dimensions,” J. Fluid Mech. 662, 134–172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement with quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors
Numerical modeling of two-phase binary fluid mixing using mixed finite elements
Sun, Shuyu
2012-07-27
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
Allen, Rebecca
2011-05-01
An increase in the earth’s surface temperature has been directly linked to the rise of carbon dioxide (CO2) levels In the atmosphere and an enhanced greenhouse effect. CO2 sequestration is one of the proposed mitigation Strategies in the effort to reduce atmospheric CO2 concentrations. Globally speaking, saline aquifers provide an adequate storage capacity for the world’s carbon emissions, and CO2 sequestration projects are currently underway in countries such as Norway, Germany, Japan, USA, and others. Numerical simulators serve as predictive tools for CO2 storage, yet must model fluid transport behavior while coupling different transport processes together accurately. With regards to CO2 sequestration, an extensive amount of research has been done on the diffusive-convective transport that occurs under a cap of CO2-saturated fluid, which results after CO2 is injected into an aquifer and spreads laterally under an area of low permeability. The diffusive-convective modeling reveals an enhanced storage capacity in saline aquifers, due to the density increase between pure fluid and CO2‐saturated fluid. This work presents the transport modeling equations that are used for diffusive- convective modeling. A cell-centered finite difference method is used, and simulations are run using MATLAB. Two cases are explored in order to compare the results from this work’s self-generated code with the results published in literature. Simulation results match relatively well, and the discrepancy for a delayed onset time of convective transport observed in this work is attributed to numerical artifacts. In fact, onset time in this work is directly attributed to the instability of the physical system: this instability arises from non-linear coupling of fluid flow, transport, and convection, but is triggered by numerical errors in these simulations. Results from this work enable the computation of a value for the numerical constant that appears in the onset time equation that
Trapped-ion anomalous diffusion coefficient on the basis of single mode saturation
International Nuclear Information System (INIS)
Koshi, Yuji; Hatayama, Akiyoshi; Ogasawara, Masatada.
1982-03-01
Expressions of the anomalous diffusion coefficient due to the dissipative trapped ion instability (DTII) are derived for the case with and without the effect of magnetic shear. Derivation is made by taking into account of the single mode saturation of the DTII previously obtained numerically. In the absence of the shear effect, the diffusion coefficient is proportional to #betta#sub(i)a 2 (#betta#sub(i) is the effective collision frequency of the trapped ions and a is the minor radius of a torus) and is much larger than the neoclassical ion heat conductivity. In the presence of the shear effect, the diffusion coefficient is much smaller than the Kadomtsev and Pogutse's value and is the same order of magnitude as the neoclassical ion heat conductivity. Dependences of the diffusion coefficient on the temperature and on the total particle number density are rather complicated due to the additional spectral cut-off, which is introduced to regularize the short wavelength modes in the numerical analysis. (author)
Speckle noise reduction for computer generated holograms of objects with diffuse surfaces
Symeonidou, Athanasia; Blinder, David; Ahar, Ayyoub; Schretter, Colas; Munteanu, Adrian; Schelkens, Peter
2016-04-01
Digital holography is mainly used today for metrology and microscopic imaging and is emerging as an important potential technology for future holographic television. To generate the holographic content, computer-generated holography (CGH) techniques convert geometric descriptions of a 3D scene content. To model different surface types, an accurate model of light propagation has to be considered, including for example, specular and diffuse reflection. In previous work, we proposed a fast CGH method for point cloud data using multiple wavefront recording planes, look-up tables (LUTs) and occlusion processing. This work extends our method to account for diffuse reflections, enabling rendering of deep 3D scenes in high resolution with wide viewing angle support. This is achieved by modifying the spectral response of the light propagation kernels contained by the look-up tables. However, holograms encoding diffuse reflective surfaces depict significant amounts of speckle noise, a problem inherent to holography. Hence, techniques to improve the reduce speckle noise are evaluated in this paper. Moreover, we propose as well a technique to suppress the aperture diffraction during numerical, viewdependent rendering by apodizing the hologram. Results are compared visually and in terms of their respective computational efficiency. The experiments show that by modelling diffuse reflection in the LUTs, a more realistic yet computationally efficient framework for generating high-resolution CGH is achieved.
Field theory of absorbing phase transitions with a non-diffusive conserved field
International Nuclear Information System (INIS)
Pastor-Satorras, R.; Vespignani, A.
2000-04-01
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class. (author)
A point-centered diffusion differencing for unstructured meshes in 3-D
International Nuclear Information System (INIS)
Palmer, T.S.
1994-01-01
We describe a point-centered diffusion discretization for 3-D unstructured meshes of polyhedra. The method has several attractive qualities, including second-order accuracy and preservation of linear solutions. A potential drawback to the scheme is that the diffusion matrix is asymmetric, in general. Results of numerical test problems illustrate the behavior of the scheme
International Nuclear Information System (INIS)
Shimizu, M.; Tekashita, K.
2002-01-01
A new tritium extraction system composed of a trickle-bed hydrogen/water isotopic exchange column using a hydrophobic Pt catalyst combined with an SPE-water electrolyser (EXEL-process) and a thermal diffusion column cascade was proposed for the removal of the tritium from heavy water irradiated in HMR ((Heavy Water Moderated Power Reactor), volume of heavy water = 140 m 3 and mean neutron flux = 5x10 13 n/cm 2 s). Numerical study on the extraction of tritium from the heavy water was carried out and the dimensions of proposed system were determined under the conditions that the concentration of tritium in the heavy water was kept less than 2.5 Ci/l HW . The calculation results indicated that the proposed system was designed practically. (author)
International Nuclear Information System (INIS)
Corominas-Murtra, Bernat; Hanel, Rudolf; Thurner, Stefan
2016-01-01
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such sample space reducing processes offer an alternative new mechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related to noise levels in the process. Here we show that the emergence of scaling is not limited to the simplest SSRPs, but holds for a huge domain of stochastic processes that are characterised by non-uniform prior distributions. We demonstrate mathematically that in the absence of noise the scaling exponents converge to −1 (Zipf’s law) for almost all prior distributions. As a consequence it becomes possible to fully understand targeted diffusion on weighted directed networks and its associated scaling laws in node visit distributions. The presence of cycles can be properly interpreted as playing the same role as noise in SSRPs and, accordingly, determine the scaling exponents. The result that Zipf’s law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for a series of applications in traffic-, transport- and supply chain management. (paper)
Lee, Sooyoung; Sanefuji, Masafumi; Torio, Michiko; Kaku, Noriyuki; Ichimiya, Yuko; Mizuguchi, Soichi; Baba, Haruhisa; Sakai, Yasunari; Ishizaki, Yoshito; Torisu, Hiroyuki; Kira, Ryutaro; Hara, Toshiro; Ohga, Shouichi
2016-11-15
Acute encephalopathy with biphasic seizures and late reduced diffusion (AESD) occurs in children associated with infection. It is characterized by a prolonged febrile seizure in the first phase, and a cluster of seizures, deterioration of consciousness and the white matter lesions with reduced diffusion in the second phase. The patients often have severe neurological sequelae, but the prognostic indicators remain unknown. The present study aimed to clarify the characteristics of AESD patients who subsequently exhibited severe neurological sequelae. We retrospectively analyzed the clinical and laboratory findings along with the brain imaging in patients who had severe (n=8) and non-severe neurodevelopmental outcomes (n=12). Severe group more frequently showed coma (p=0.014) or involuntary movements including dystonia and oral dyskinesia (p=0.018) before the second phase than non-severe group. Severe group exhibited higher levels of serum alanine aminotransferase than non-severe group (p=0.001). Quantitatively assessed MRI in the second phase revealed that severe group had more extensive lesions than non-severe group, in the anterior (p=0.015) and posterior parts (p=0.011) of the cerebrum and basal ganglia (p=0.020). Early appearing involuntary movements or coma might account for the extension of acute brain lesions and the poor neurological outcomes in AESD patients. Copyright © 2016 Elsevier B.V. All rights reserved.
Determination of the diffusion coefficient of hydrogen ion in hydrogels.
Schuszter, Gábor; Gehér-Herczegh, Tünde; Szűcs, Árpád; Tóth, Ágota; Horváth, Dezső
2017-05-17
The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H + -autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.
Study on neutron diffusion and time dependence heat ina fluidized bed nuclear reactor
International Nuclear Information System (INIS)
Vilhena, M.T. de.
1988-01-01
The purpose of this work is to model the neutron diffusion and heat transfer for a Fluidized Bed Nuclear Reactor and its solution by Laplace Transform Technique with numerical inversion using Fourier Series. Also Gaussian quadrature and residues techniques were applied for numerical inversion. The neutron transport, diffusion, and point Kinetic equation for this nuclear reactor concept are developed. A matricial and Taylor Series methods are proposed for the solution of the point Kinetic equation which is a time scale problem of Stiff type
Measurements of charged fusion product diffusion in TFTR
Energy Technology Data Exchange (ETDEWEB)
Boivin, Rejean Louis [Princeton Univ., NJ (United States)
1991-12-01
The single particle confinement of charged fusion products, namely the 1 MeV triton and the 3 MeV proton, has been studied using a detector located near the outer midplane of TFTR. The detector, which measure the flux of escaping particles, is composed of a scintillator [ZnS(Ag)] and a system of collimating apertures, which permit pitch angle, energy and time resolution. It is mounted on a movable probe which can be inserted 25 cm into the vacuum vessel. Measurements indicate a level of losses higher than expected from a first-orbit loss mechanism alone. The primary candidate for explaining the observed anomalous losses is the toroidal field (TF) stochastic ripple diffusion, theoretically discovered by Goldston, White and Boozer. This loss mechanism is expected to be localized near the outer midplane where, at least at high current (≳ 1.0 MA) it would locally dominate over first-orbit losses. Calculations made with a mapping particle orbit code (MAPLOS) show a semi-quantitative agreement with the measurements. The predominant uncertainties in the numerical simulations were found to originate from the modeling of the first wall geometry and also from the assumed plasma current and source profiles. Direct measurements of the diffusion rate were performed by shadowing the detector with a second movable probe used as an obstacle. The diffusion rate was also measured by moving the detector behind the radius of the RF limiters, located on the outer wall. Comparisons of these experimental results with numerical simulations, which include diffusive mechanisms, indicate a quantitative agreement with the TF stochastic ripple diffusion model.
Numerical dissipation and dispersion of the homogenenous and complete flux schemes
Thije Boonkkamp, ten J.H.M.; Anthonissen, M.J.H.
2014-01-01
We analyse numerical dissipation and dispersion of the homogeneous ¿ux (HF) and complete ¿ux (CF) schemes, ¿nite volume methods introduced in [1]. To that purpose we derive the modi¿ed equation of both schemes. We show that the HF scheme suffers from numerical diffusion for dominant advection, which
Numerical time integration for air pollution models
J.G. Verwer (Jan); W. Hundsdorfer (Willem); J.G. Blom (Joke)
1998-01-01
textabstractDue to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [ fracpar{c{t + nabla cdot left( vu{u c right) = nabla cdot left(
Interactions of diffuse and focused allogenic recharge in an eogenetic karst aquifer (Florida, USA)
Langston, Abigail L.; Screaton, Elizabeth J.; Martin, Jonathan B.; Bailly-Comte, Vincent
2012-06-01
The karstic upper Floridan aquifer in north-central Florida (USA) is recharged by both diffuse and allogenic recharge. To understand how recharged water moves within the aquifer, water levels and specific conductivities were monitored and slug tests were conducted in wells installed in the aquifer surrounding the Santa Fe River Sink and Rise. Results indicate that diffuse recharge does not mix rapidly within the aquifer but instead flows horizontally. Stratification may be aided by the high matrix porosity of the eogenetic karst aquifer. Purging wells for sample collection perturbed conductivity for several days, reflecting mixing of the stratified water and rendering collection of representative samples difficult. Interpretive numerical simulations suggest that diffuse recharge impacts the intrusion of allogenic water from the conduit by increasing hydraulic head in the surrounding aquifer and thereby reducing influx to the aquifer from the conduit. In turn, the increase of head within the conduits affects flow paths of diffuse recharge by moving newly recharged water vertically as the water table rises and falls. This movement may result in a broad vertical zone of dissolution at the water table above the conduit system, with thinner and more focused water-table dissolution at greater distance from the conduit.
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
Directory of Open Access Journals (Sweden)
Shuping Li
2014-01-01
Full Text Available We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.
Extended numerical modeling of impurity neoclassical transport in tokamak edge plasmas
International Nuclear Information System (INIS)
Inoue, H.; Yamoto, S.; Hatayama, A.; Homma, Y.
2016-01-01
Understanding of impurity transport in tokamaks is an important issue in order to reduce the impurity contamination in fusion core plasmas. Recently, a new kinetic numerical scheme of impurity classical/neoclassical transport has been developed. This numerical scheme makes it possible to include classical self-diffusion (CL SD), classical inward pinch (CL IWP), and classical temperature screening effect (CL TSE) of impurity ions. However, impurity neoclassical transport has been modeled only in the case where background plasmas are in the Pfirsch-Schluter (PS) regime. The purpose of this study is to extend our previous model to wider range of collisionality regimes, i.e., not only the PS regime, but also the plateau regime. As in the previous study, a kinetic model with Binary Collision Monte-Carlo Model (BMC) has been adopted. We focus on the modeling of the neoclassical self-diffusion (NC SD) and the neoclassical inward pinch (NC IWP). In order to simulate the neoclassical transport with the BCM, velocity distribution of background plasma ions has been modeled as a deformed Maxwell distribution which includes plasma density gradient. Some test simulations have been done. As for NC SD of impurity ions, our scheme reproduces the dependence on the collisionality parameter in wide range of collisionality regime. As for NC IWP, in cases where test impurity ions and background ions are in the PS and plateau regimes, parameter dependences have been reproduced. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Extended numerical modeling of impurity neoclassical transport in tokamak edge plasmas
Energy Technology Data Exchange (ETDEWEB)
Inoue, H.; Yamoto, S.; Hatayama, A. [Graduate School of Science and Technology, Keio University, Hiyoshi, Yokohama (Japan); Homma, Y. [Graduate School of Science and Technology, Keio University, Hiyoshi, Yokohama (Japan); Research Fellow of Japan Society for the Promotion of Science, Tokyo (Japan)
2016-08-15
Understanding of impurity transport in tokamaks is an important issue in order to reduce the impurity contamination in fusion core plasmas. Recently, a new kinetic numerical scheme of impurity classical/neoclassical transport has been developed. This numerical scheme makes it possible to include classical self-diffusion (CL SD), classical inward pinch (CL IWP), and classical temperature screening effect (CL TSE) of impurity ions. However, impurity neoclassical transport has been modeled only in the case where background plasmas are in the Pfirsch-Schluter (PS) regime. The purpose of this study is to extend our previous model to wider range of collisionality regimes, i.e., not only the PS regime, but also the plateau regime. As in the previous study, a kinetic model with Binary Collision Monte-Carlo Model (BMC) has been adopted. We focus on the modeling of the neoclassical self-diffusion (NC SD) and the neoclassical inward pinch (NC IWP). In order to simulate the neoclassical transport with the BCM, velocity distribution of background plasma ions has been modeled as a deformed Maxwell distribution which includes plasma density gradient. Some test simulations have been done. As for NC SD of impurity ions, our scheme reproduces the dependence on the collisionality parameter in wide range of collisionality regime. As for NC IWP, in cases where test impurity ions and background ions are in the PS and plateau regimes, parameter dependences have been reproduced. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Recent advances in computational-analytical integral transforms for convection-diffusion problems
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.
2017-10-01
An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.
Water Vapor Diffusion and Adsorption of Sandstones: Influence of Rock Texture and Composition
Directory of Open Access Journals (Sweden)
Martin Keppert
2016-01-01
Full Text Available The term sandstone is used for wide range of rocks containing quartz clasts which can be cemented by secondary precipitated quartz or calcite; moreover the space between clasts can be filled by matrix. These facts result in existence of numerous rocks having highly various properties. Sandstones have been used as construction materials due to their good accessibility and workability. Since most of sandstones are porous, water vapor can penetrate through sandstone constructions. The rate of water vapor diffusion, as well as the vapor sorption isotherm, was determined for range of sandstone types. The diffusion resistance factor was found to be dependent on the total porosity of sandstone but the sorption behavior was strongly influenced by nature of the particular sandstone; the specific surface area of stone and presence of clay matrix are determining its sorption isotherm. The published data enable estimating (i diffusion resistance factor of a sandstone via knowledge of its total porosity and (ii the sorption isotherm via knowledge of the stone’s nature and specific surface area. This approach can significantly reduce the time necessary to acquire vapor-related properties of a sandstone.
Edge-promoting reconstruction of absorption and diffusivity in optical tomography
DEFF Research Database (Denmark)
Hannukainen, A.; Harhanen, Lauri Oskari; Hyvönen, N.
2015-01-01
In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged...... measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments...
International Nuclear Information System (INIS)
Rao, K.A.; Pushpa, K.K.; Iyer, R.M.
1980-01-01
γ-irradiation of polymers results in further crosslinking in the polymer or breakdown of the polymer or a combination of both these phenomena depending on the type of polymer, the dose as well as the environment in which irradiation is carried out. The gas diffusion through polymer films is expected to vary depending on these changes. With a view to A evaluate the feasibility of effecting selective diffusion of specific gases and also to correlate the change in diffusion rates with the polymer characteristics these studies have been initiated. Hydrogen diffusion through mylar film γ-irradiated under varying conditions upto a dose of approximately 50 Mrads is reported in this paper. The results indicate negligible change in hydrogen diffusion rates on γ-irradiation. However, γ-irradiation induced crosslinking of acrylic acid on Mylar reduced the hydrogen diffusion rate. The hydrogen diffusion studies may also be useful in finding the glass transition temperature of polymer films as is apparent from the gas diffusion curves. (author)
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
Parallel solutions of the two-group neutron diffusion equations
International Nuclear Information System (INIS)
Zee, K.S.; Turinsky, P.J.
1987-01-01
Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
Multimodel analysis of anisotropic diffusive tracer-gas transport in a deep arid unsaturated zone
Green, Christopher T.; Walvoord, Michelle Ann; Andraski, Brian J.; Striegl, Robert G.; Stonestrom, David A.
2015-01-01
Gas transport in the unsaturated zone affects contaminant flux and remediation, interpretation of groundwater travel times from atmospheric tracers, and mass budgets of environmentally important gases. Although unsaturated zone transport of gases is commonly treated as dominated by diffusion, the characteristics of transport in deep layered sediments remain uncertain. In this study, we use a multimodel approach to analyze results of a gas-tracer (SF6) test to clarify characteristics of gas transport in deep unsaturated alluvium. Thirty-five separate models with distinct diffusivity structures were calibrated to the tracer-test data and were compared on the basis of Akaike Information Criteria estimates of posterior model probability. Models included analytical and numerical solutions. Analytical models provided estimates of bulk-scale apparent diffusivities at the scale of tens of meters. Numerical models provided information on local-scale diffusivities and feasible lithological features producing the observed tracer breakthrough curves. The combined approaches indicate significant anisotropy of bulk-scale diffusivity, likely associated with high-diffusivity layers. Both approaches indicated that diffusivities in some intervals were greater than expected from standard models relating porosity to diffusivity. High apparent diffusivities and anisotropic diffusivity structures were consistent with previous observations at the study site of rapid lateral transport and limited vertical spreading of gas-phase contaminants. Additional processes such as advective oscillations may be involved. These results indicate that gases in deep, layered unsaturated zone sediments can spread laterally more quickly, and produce higher peak concentrations, than predicted by homogeneous, isotropic diffusion models.
Analytic and numerical studies of Scyllac equilibrium
International Nuclear Information System (INIS)
Barnes, D.C.; Brackbill, J.U.; Dagazian, R.Y.; Freidberg, J.P.; Schneider, W.; Betancourt, O.; Garabedian, P.
1976-01-01
The results of both numerical and analytic studies of the Scyllac equilibria are presented. Analytic expansions are used to derive equilibrium equations appropriate to noncircular cross sections, and compute the stellarator fields which produce toroidal force balance. Numerical algorithms are used to solve both the equilibrium equations and the full system of dynamical equations in three dimensions. Numerical equilibria are found for both l = 1,0 and l= 1,2 systems. It is found that the stellarator fields which produce equilibria in the l = 1.0 system are larger for diffuse than for sharp boundary plasma profiles, and that the stability of the equilibria depends strongly on the harmonic content of the stellarator fields
Airflow Pattern Generated by Three Air Diffusers
DEFF Research Database (Denmark)
Olmedo, Inés; Nielsen, Peter V.; Ruiz de Adana, Manuel
2011-01-01
The correct description of air diffusers plays a crucial role in the CFD predictions of the airflow pattern into a room. The numerical simulation of air distribution in an indoor space is challenging because of the complicated airflow pattern generated. Many authors have developed simplified geom...
On Solution of a Fractional Diffusion Equation by Homotopy Transform Method
International Nuclear Information System (INIS)
Salah, A.; Hassan, S.S.A.
2012-01-01
The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.
Energy Technology Data Exchange (ETDEWEB)
Berlowitz, D.R.
1996-11-01
In the last few decades the negative impact by humans on the thin atmospheric layer enveloping the earth, the basis for life on this planet, has increased steadily. In order to halt, or at least slow down this development, the knowledge and study of these anthropogenic influence has to be increased and possible remedies have to be suggested. An important tool for these studies are computer models. With their help the atmospheric system can be approximated and the various processes, which have led to the current situation can be quantified. They also serve as an instrument to assess short or medium term strategies to reduce this human impact. However, to assure efficiency as well as accuracy, a careful analysis of the numerous processes involved in the dispersion of pollutants in the atmosphere is called for. This should help to concentrate on the essentials and also prevent excessive usage of sometimes scarce computing resources. The basis of the presented work is the EUMAC Zooming Model (ETM), and particularly the component calculating the dispersion of pollutants in the atmosphere, the model MARS. The model has two main parts: an explicit solver, where the advection and the horizontal diffusion of pollutants are calculated, and an implicit solution mechanism, allowing the joint computation of the change of concentration due to chemical reactions, coupled with the respective influence of the vertical diffusion of the species. The aim of this thesis is to determine particularly the influence of the horizontal components of the turbulent diffusion on the existing implicit solver of the model. Suggestions for a more comprehensive inclusion of the full three dimensional diffusion operator in the implicit solver are made. This is achieved by an appropriate operator splitting. A selection of numerical approaches to tighten the coupling of the diffusion processes with the calculation of the applied chemical reaction mechanisms are examined. (author) figs., tabs., refs.
Analytical solutions to matrix diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)
2014-10-06
We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.
Competing opinion diffusion on social networks.
Hu, Haibo
2017-11-01
Opinion competition is a common phenomenon in real life, such as with opinions on controversial issues or political candidates; however, modelling this competition remains largely unexplored. To bridge this gap, we propose a model of competing opinion diffusion on social networks taking into account degree-dependent fitness or persuasiveness. We study the combined influence of social networks, individual fitnesses and attributes, as well as mass media on people's opinions, and find that both social networks and mass media act as amplifiers in opinion diffusion, the amplifying effect of which can be quantitatively characterized. We analytically obtain the probability that each opinion will ultimately pervade the whole society when there are no committed people in networks, and the final proportion of each opinion at the steady state when there are committed people in networks. The results of numerical simulations show good agreement with those obtained through an analytical approach. This study provides insight into the collective influence of individual attributes, local social networks and global media on opinion diffusion, and contributes to a comprehensive understanding of competing diffusion behaviours in the real world.
Numerical Tokamak Project code comparison
International Nuclear Information System (INIS)
Waltz, R.E.; Cohen, B.I.; Beer, M.A.
1994-01-01
The Numerical Tokamak Project undertook a code comparison using a set of TFTR tokamak parameters. Local radial annulus codes of both gyrokinetic and gyrofluid types were compared for both slab and toroidal case limits assuming ion temperature gradient mode turbulence in a pure plasma with adiabatic electrons. The heat diffusivities were found to be in good internal agreement within ± 50% of the group average over five codes
Discrete formulation for two-dimensional multigroup neutron diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid
2003-02-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
International Nuclear Information System (INIS)
Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid
2003-01-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion
International Nuclear Information System (INIS)
Guo, Ran; Du, Jiulin
2015-01-01
We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution
The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com
2015-08-15
We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.
Anisotropic diffusion in a toroidal geometry
International Nuclear Information System (INIS)
Fischer, Paul F
2005-01-01
As part of the Department of Energy's applications oriented SciDAC project, three model problems have been proposed by the Center for Extended Magnetohydrodynamics Modeling to test the potential of numerical algorithms for challenging magnetohydrodynamics (MHD) problems that are required for future fusion development. The first of these, anisotropic diffusion in a toroidal geometry, is considered in this note
Diffusion of intrinsic localized modes by attractor hopping
International Nuclear Information System (INIS)
Meister, Matthias; Vazquez, Luis
2003-01-01
Propagating intrinsic localized modes exist in the damped-driven discrete sine-Gordon chain as attractors of the dynamics. The equations of motion of the system are augmented with Gaussian white noise in order to model the effects of temperature on the system. The noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode, which leads to a diffusive motion of the excitation. The Heun method is used to numerically generate the stochastic time-evolution of the configuration. We also present a theoretical model for the diffusion which contains two parameters, a transition probability θ and a delay time τ A . The mean value and the variance of the position of the intrinsic localized mode, obtained from simulations, can be fitted well with the predictions of our model, θ and τ A being used as parameters in the fit. After a transition period following the switching on of the noise, the variance shows a linear behaviour as a function of time and the mean value remains constant. An increase in the strength of the noise lowers the variance, leads to an increase in θ, a decrease in τ A and reduces the average distance a mode travels during the transition period
Diffusion of intrinsic localized modes by attractor hopping
Energy Technology Data Exchange (ETDEWEB)
Meister, Matthias [Dpto FIsica de la Materia Condensada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y FIsica de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza (Spain); Vazquez, Luis [Dpto Matematica Aplicada, Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de AstrobiologIa (CSIC-INTA), 28850 Torrejon de Ardoz (Spain)
2003-11-28
Propagating intrinsic localized modes exist in the damped-driven discrete sine-Gordon chain as attractors of the dynamics. The equations of motion of the system are augmented with Gaussian white noise in order to model the effects of temperature on the system. The noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode, which leads to a diffusive motion of the excitation. The Heun method is used to numerically generate the stochastic time-evolution of the configuration. We also present a theoretical model for the diffusion which contains two parameters, a transition probability {theta} and a delay time {tau}{sub A}. The mean value and the variance of the position of the intrinsic localized mode, obtained from simulations, can be fitted well with the predictions of our model, {theta} and {tau}{sub A} being used as parameters in the fit. After a transition period following the switching on of the noise, the variance shows a linear behaviour as a function of time and the mean value remains constant. An increase in the strength of the noise lowers the variance, leads to an increase in {theta}, a decrease in {tau}{sub A} and reduces the average distance a mode travels during the transition period.
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
International Nuclear Information System (INIS)
Larsen, E.W.; Morel, J.E.
1989-01-01
In a recent article (Larsen, Morel, and Miller, J. Comput. Phys. 69, 283 (1987)), a theoretical method is described for assessing the accuracy of transport differencing schemes in highly scattering media with optically thick spatial meshes. In the present article, this method is extended to enable one to determine the accuracy of such schemes in the presence of numerically unresolved boundary layers. Numerical results are presented that demonstrate the validity and accuracy of our analysis. copyright 1989 Academic Press, Inc
Nuclear interaction potential in a folded-Yukawa model with diffuse densities
International Nuclear Information System (INIS)
Randrup, J.
1975-09-01
The folded-Yukawa model for the nuclear interaction potential is generalized to diffuse density distributions which are generated by folding a Yukawa function into sharp generating distributions. The effect of a finite density diffuseness or of a finite interaction range is studied. The Proximity Formula corresponding to the generalized model is derived and numerical comparison is made with the exact results. (8 figures)
Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations
Energy Technology Data Exchange (ETDEWEB)
Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)
2016-01-20
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.
Assessment of perceptual diffuseness in the time domain
DEFF Research Database (Denmark)
Garcia, Julian Martinez-Villalba; Jeong, Cheol-Ho; Brunskog, Jonas
2017-01-01
This study proposes a numerical and experimental framework for evaluating the perceptual aspect of the diffuse field condition with intended final use in music auditoria. Multiple Impulse Responses are simulated based on the time domain Poisson process with increasing reflection density. Different...
Measurements of charged fusion product diffusion in TFTR
Energy Technology Data Exchange (ETDEWEB)
Boivin, R.L.
1991-12-01
The single particle confinement of charged fusion products, namely the 1 MeV triton and the 3 MeV proton, has been studied using a detector located near the outer midplane of TFTR. The detector, which measure the flux of escaping particles, is composed of a scintillator (ZnS(Ag)) and a system of collimating apertures, which permit pitch angle, energy and time resolution. It is mounted on a movable probe which can be inserted 25 cm into the vacuum vessel. Measurements indicate a level of losses higher than expected from a first-orbit loss mechanism alone. The primary candidate for explaining the observed anomalous losses is the toroidal field (TF) stochastic ripple diffusion, theoretically discovered by Goldston, White and Boozer. This loss mechanism is expected to be localized near the outer midplane where, at least at high current ({approx gt} 1.0 MA) it would locally dominate over first-orbit losses. Calculations made with a mapping particle orbit code (MAPLOS) show a semi-quantitative agreement with the measurements. The predominant uncertainties in the numerical simulations were found to originate from the modeling of the first wall geometry and also from the assumed plasma current and source profiles. Direct measurements of the diffusion rate were performed by shadowing the detector with a second movable probe used as an obstacle. The diffusion rate was also measured by moving the detector behind the radius of the RF limiters, located on the outer wall. Comparisons of these experimental results with numerical simulations, which include diffusive mechanisms, indicate a quantitative agreement with the TF stochastic ripple diffusion model.
Measurements of charged fusion product diffusion in TFTR
International Nuclear Information System (INIS)
Boivin, R.L.
1991-12-01
The single particle confinement of charged fusion products, namely the 1 MeV triton and the 3 MeV proton, has been studied using a detector located near the outer midplane of TFTR. The detector, which measure the flux of escaping particles, is composed of a scintillator [ZnS(Ag)] and a system of collimating apertures, which permit pitch angle, energy and time resolution. It is mounted on a movable probe which can be inserted 25 cm into the vacuum vessel. Measurements indicate a level of losses higher than expected from a first-orbit loss mechanism alone. The primary candidate for explaining the observed anomalous losses is the toroidal field (TF) stochastic ripple diffusion, theoretically discovered by Goldston, White and Boozer. This loss mechanism is expected to be localized near the outer midplane where, at least at high current (approx-gt 1.0 MA) it would locally dominate over first-orbit losses. Calculations made with a mapping particle orbit code (MAPLOS) show a semi-quantitative agreement with the measurements. The predominant uncertainties in the numerical simulations were found to originate from the modeling of the first wall geometry and also from the assumed plasma current and source profiles. Direct measurements of the diffusion rate were performed by shadowing the detector with a second movable probe used as an obstacle. The diffusion rate was also measured by moving the detector behind the radius of the RF limiters, located on the outer wall. Comparisons of these experimental results with numerical simulations, which include diffusive mechanisms, indicate a quantitative agreement with the TF stochastic ripple diffusion model
DEFF Research Database (Denmark)
Johannesson, Björn; Hosokawa, Yoshifumi; Yamada, Kazuo
2009-01-01
A method to analyse and calculate concentration profiles of different types of ions in the pore solution of porous materials such as concrete subjected to external wetting and drying is described. The equations in use have a solid theoretical meaning and are derived from a porous media technique......, which is a special branch of the more general mixture theory. The effect of chemical action is ignored making the presented model suitable to be implemented into codes dealing solely with chemical equilibrium. The coupled set of equations for diffusion of ionic species, the internal electrical potential...... of the model should be judged from the assumptions made when developing the balance laws and the constitutive equations and the assumptions made in obtaining a working numerical calculation scheme....
Simple computation of reaction–diffusion processes on point clouds
Macdonald, Colin B.
2013-05-20
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
Simple computation of reaction–diffusion processes on point clouds
Macdonald, Colin B.; Merriman, Barry; Ruuth, Steven J.
2013-01-01
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
Investigation of radiation-enhanced oxygen diffusion in Li-Ti ferrites
International Nuclear Information System (INIS)
Surzhikov, A.P.; Pritulov, A.M.; Gyngazov, S.A.; Lysenko, E.N.
1999-01-01
The radiation-enhanced oxygen diffusion in polycrystalline Li-Ti ferrites was investigated. The electron accelerator ELV-6 (Institute of Nuclear Physics, Russian Academy of Sciences) was used to generate the radiothermal annealing. The radiation effects were established by comparison of diffusion profiles of the samples, which were radiothermally treated, and data obtained during the thermal annealing in the resistance furnace. It was discovered that there was an increase of numerical values of Ed (activation diffusion energy) and Do (preexponential factor) during the radiothermal annealing, if compared with the thermal one. The investigations were financed by the Russian Fundamental Research Fund
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Nodal methods in numerical reactor calculations
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del
2004-01-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Nodal methods in numerical reactor calculations
Energy Technology Data Exchange (ETDEWEB)
Hennart, J P [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico); Valle, E del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)
2004-07-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Assessment of cooling performance of a diffuse plate in HYPER target
International Nuclear Information System (INIS)
Tak, N. I.; Song, T. Y.; Park, W. S.
2001-01-01
Major difficulties are caused by cooling problems of the beam window of the spallation target in designing of 1000 MWth HYPER (HYbrid Power Extraction Reactor). Numerical studies to improve the cooling capability of the window are on the way. In the present work, numerical analysis has been performed to assess the cooling performance of a diffuse plate in HYPER target conditions. The fluid dynamics code CFX 4 was used for the analysis. Heat depositions in the window and the target were calculated by the LAHEAT code systems and used as input data of the CFX 4 code. The diffuse plate was modeled as a porous media having three porosities. The analysis was performed for various design parameters (the porosity, the thickness of a diffuse plate, the distance between the plate and the window). The results of CFX 4 show that ∼10 .deg. C of the reduction of the maximum window temperature, which is not enough for the HYPER design, can be obtained with a diffuse plate. Therefore, another methods such as an introduction of a bypass injection have to be considered to improve the window cooling
Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow
Gonzalez, M.
2018-04-01
The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Diffusion-synthetic acceleration methods for discrete-ordinates problems
International Nuclear Information System (INIS)
Larsen, E.W.
1984-01-01
The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems an the status of current efforts aimed at solving these problems
DEFF Research Database (Denmark)
Zhang, Chen; Yu, Tao; Heiselberg, Per Kvols
with conventional ventilation systems (mixing or displacement ventilation), diffuse ceiling ventilation can significantly reduce or even eliminate draught risk in the occupied zone. Moreover, this ventilation system presents a promising opportunity for energy saving, because of the low pressure loss, extended free...
Diffusion formation and psychiatric diseases
International Nuclear Information System (INIS)
Reith, W.; Kulikovski, J.
2015-01-01
The basic principle behind diffusion is Brownian motion. The diffusion parameters obtained in a clinical association provide information on the spatial distribution of water molecule mobility and, therefore, evidence of the morphological integrity of the white and grey matters of the brain. In recent years functional magnetic resonance imaging (fMRI) could contribute to obtaining a detailed understanding of the cortical and subcortical cerebral networks. Diffusion tensor imaging (DTI) investigations can demonstrate the extent of anisotropy and the fiber pathways in so-called parametric images. For example, in Alzheimer's disease DTI reveals a reduced structural connectivity between the posterior cingulum and the hippocampus. This article shows examples of the application of diffusion-weighted imaging (DWI) in psychiatric disorders. (orig.) [de
The Social Origins of Networks and Diffusion.
Centola, Damon
2015-03-01
Recent research on social contagion has demonstrated significant effects of network topology on the dynamics of diffusion. However, network topologies are not given a priori. Rather, they are patterns of relations that emerge from individual and structural features of society, such as population composition, group heterogeneity, homophily, and social consolidation. Following Blau and Schwartz, the author develops a model of social network formation that explores how social and structural constraints on tie formation generate emergent social topologies and then explores the effectiveness of these social networks for the dynamics of social diffusion. Results show that, at one extreme, high levels of consolidation can create highly balkanized communities with poor integration of shared norms and practices. As suggested by Blau and Schwartz, reducing consolidation creates more crosscutting circles and significantly improves the dynamics of social diffusion across the population. However, the author finds that further reducing consolidation creates highly intersecting social networks that fail to support the widespread diffusion of norms and practices, indicating that successful social diffusion can depend on moderate to high levels of structural consolidation.
Glutathionylation-Dependence of Na+-K+-Pump Currents Can Mimic Reduced Subsarcolemmal Na+ Diffusion
Garcia, Alvaro; Liu, Chia-Chi; Cornelius, Flemming; Clarke, Ronald?J.; Rasmussen, Helge?H.
2016-01-01
The existence of a subsarcolemmal space with restricted diffusion for Na+ in cardiac myocytes has been inferred from a transient peak electrogenic Na+-K+ pump current beyond steady state on reexposure of myocytes to K+ after a period of exposure to K+-free extracellular solution. The transient peak current is attributed to enhanced electrogenic pumping of Na+ that accumulated in the diffusion-restricted space during pump inhibition in K+-free extracellular solution. However, there are no know...
Pressure recovery in a diffuser for gas centrifuge
International Nuclear Information System (INIS)
Hanzawa, Masatoshi; Takashima, Yoichi; Mikami, Hisashi
1977-01-01
The pressure recovery of supersonic flow at very low density was studied in a vane-island type diffuser for gas centrifuge. A tester of diffuser with a rapidly rotating cylinder was used in experiments. Wall static pressures were measured at many points in the diffuser to observe the static pressure distribution. The change of pressure distribution with back pressure and the effect of flow rate were investigated. Pressure distribution showed that the pressure recovery occurred in the converging section. The pressure ratio increased linearly with the back pressure in this experimental range and the effect of flow rate was not observed. A numerical analysis of the pressure recovery in the channel section of the diffuser was made by applying the finite difference method to the slender-channel equations. The pressure distribution obtained in experiments could be explained as a result of supersonic compression with reverse flow. (auth.)
On the numerical simulation of tracer flows in porous media
International Nuclear Information System (INIS)
Aquino, J.; Pereira, F.; Amaral Souto, H.P.; Francisco, A.S.
2007-01-01
We discuss in detail a new Lagrangian, locally conservative procedure which has been proposed for the numerical solution of linear transport problems in porous media. The new scheme is computationally efficient, virtually free of numerical diffusion, and can be applied to investigate numerically the time evolution of radionuclide contaminant plumes. Results of two-dimensional simulations of tracer flows will be presented to show the influence on the computed solutions of distinct interpolation functions for evaluating the velocity field at any position of the physical domain, as required by the Lagrangian scheme. (author)
Numerical method for a 2D drift diffusion model arising in strained n ...
Indian Academy of Sciences (India)
Abstract. 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 ...
Transport-diffusion comparisons for small core LMFBR disruptive accidents
International Nuclear Information System (INIS)
Tomlinson, E.T.
1977-11-01
A number of numerical experiments were performed to assess the validity of diffusion theory for calculating the reactivity state of various small core LMFBR disrupted geometries. The disrupted configurations correspond, in general, to various configurations predicted by SAS3A for transient undercooling (TUC) and transient overpower (TOP) accidents for homogeneous cores and to the ZPPR-7 configurations for heterogeneous core. In all TUC cases diffusion theory was shown to be inadequate for the calculation of reactivity changes during core disassembly
International Nuclear Information System (INIS)
Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro
2013-01-01
This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper)
A minimally-resolved immersed boundary model for reaction-diffusion problems
Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A
2013-01-01
We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...
Diffusive separation of particles by diffusion in swirled turbulent flows
International Nuclear Information System (INIS)
Arbuzov, V.N.; Shiliaev, M.I.
1984-01-01
An analysis of the dynamics of turbulent flow and diffusive separation of solid particles in a centrifugal air separator (consisting of two flat disks rotating at the same angular velocity) is presented. A closed set of balances for all the components of the tensor of turbulent stresses, extended to the entire flow region, is employed in the numerical analysis of transition and turbulent air flows between the rotating disks. The analytical relationships obtained for the case of the mixed flow for the various components of the average velocity, energy of fluctuations, and turbulence level in the circumferential direction agreed well with the theoretical and experimental distributions of Bakke, et al. (1973). It is shown that at high Reynolds numbers the flow is isotropic, the dependence of the circumferential component of the average velocity obeys a power law, and the generation of the radial component is controlled by the local centrifugal field. The sharpness of particle separation was calculated by the eddy diffusion equation and was found to depend on the geometry and the operating conditions. 8 references
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
A Bloch-Torrey Equation for Diffusion in a Deforming Media
Energy Technology Data Exchange (ETDEWEB)
Rohmer, Damien; Gullberg, Grant T.
2006-12-29
Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore,informs on the structure of the biological tissue. This technique isapplied with success to the static organs such as brain. However, thediffusion measurement on the dynamically deformable organs such as thein-vivo heart is a complex problem that has however a great potential inthe measurement of cardiac health. In order to understand the behavior ofthe Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torreyequation that leads the MR behavior is expressed in general curvilinearcoordinates. These coordinates enable to follow the heart geometry anddeformations through time. The equation is finally discretized andpresented in a numerical formulation using implicit methods, in order toget a stable scheme that can be applied to any smooth deformations.Diffusion process enables the link between the macroscopic behavior ofmolecules and themicroscopic structure in which they evolve. Themeasurement of diffusion in biological tissues is therefore of majorimportance in understanding the complex underlying structure that cannotbe studied directly. The Diffusion Tensor Magnetic ResonanceImaging(DTMRI) technique enables the measurement of diffusion parametersand therefore provides information on the structure of the biologicaltissue. This technique has been applied with success to static organssuch as the brain. However, diffusion measurement of dynamicallydeformable organs such as the in-vivo heart remains a complex problem,which holds great potential in determining cardiac health. In order tounderstand the behavior of the magnetic resonance (MR) signal in adeforming media, the Bloch-Torrey equation that defines the MR behavioris expressed in general curvilinear coordinates. These coordinates enableus to follow the heart geometry and deformations through time. Theequation is finally discretized and presented in a numerical formulationusing
Numerical method for a 2D drift diffusion model arising in strained n ...
Indian Academy of Sciences (India)
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 ...
Numerical study of agglomerate abrasion in a tumbling mixer
Thanh Nguyen, [No Value; Willemsz, Tofan; Frijlink, Henderik; Maarschalk, Kees van der Voort
2014-01-01
A numerical simulation using the Discrete Element Method (DEM) was performed to investigate the phenomena concerning the abrasion and breakage of agglomerates in a diffusion powder mixer. Agglomerates were created by defining a single structure of particles with bonds of different strengths using
Influence of the pore network on hydrogen diffusion through blended cement pastes
International Nuclear Information System (INIS)
Boher, Cedric; Frizon, Fabien; Bart, Florence; Lorente, Sylvie
2013-01-01
This article presents a study on the influence of the pore size distribution on gas diffusion through CEM V cement pastes, for different water saturation degrees. The numerical results are compared to the experimental hydrogen diffusion coefficients obtained with water saturation levels ranging from 20% to 95%. The model developed in our research group accounts for the various types of transfer through the pore network: Knudsen diffusion or molecular diffusion depending on the pore size, together with hydrogen diffusion through water. The virtual pore network is created from mercury porosimetry data as a result of the combination of different sizes pore families. By testing different combinations, we could propose pore arrangements leading to diffusion coefficients corresponding to the experimental ones, and show how the combinations of the biggest pore family contribute to control the gas diffusion process. (authors)
Heat Diffusion in Gases, Including Effects of Chemical Reaction
Hansen, C. Frederick
1960-01-01
The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.
Basic Studies of Non-Diffusive Transport in Plasmas
Energy Technology Data Exchange (ETDEWEB)
Morales, George J. [University of California, Los Angeles, CA (United States); Maggs, James E. [University of California, Los Angeles, CA (United States)
2014-10-25
The project expanded and developed mathematical descriptions, and corresponding numerical modeling, of non-diffusive transport to incorporate new perspectives derived from basic transport experiments performed in the LAPD device at UCLA, and at fusion devices throughout the world. By non-diffusive it is meant that the transport of fundamental macroscopic parameters of a system, such as temperature and density, does not follow the standard diffusive behavior predicted by a classical Fokker-Planck equation. The appearance of non-diffusive behavior is often related to underlying microscopic processes that cause the value of a system parameter, at one spatial position, to be linked to distant events, i.e., non-locality. In the LAPD experiments the underlying process was traced to large amplitude, coherent drift-waves that give rise to chaotic trajectories. Significant advances were made in this project. The results have lead to a new perspective about the fundamentals of edge transport in magnetically confined plasmas; the insight has important consequences for worldwide studies in fusion devices. Progress was also made in advancing the mathematical techniques used to describe fractional diffusion.
Directory of Open Access Journals (Sweden)
Ghazikhanlou-sani K.
2016-06-01
Full Text Available Introduction: There is many ways to assessing the electrical conductivity anisotropy of a tumor. Applying the values of tissue electrical conductivity anisotropy is crucial in numerical modeling of the electric and thermal field distribution in electroporation treatments. This study aims to calculate the tissues electrical conductivity anisotropy in patients with sarcoma tumors using diffusion tensor imaging technique. Materials and Method: A total of 3 subjects were involved in this study. All of patients had clinically apparent sarcoma tumors at the extremities. The T1, T2 and DTI images were performed using a 3-Tesla multi-coil, multi-channel MRI system. The fractional anisotropy (FA maps were performed using the FSL (FMRI software library software regarding the DTI images. The 3D matrix of the FA maps of each area (tumor, normal soft tissue and bone/s was reconstructed and the anisotropy matrix was calculated regarding to the FA values. Result: The mean FA values in direction of main axis in sarcoma tumors were ranged between 0.475–0.690. With assumption of isotropy of the electrical conductivity, the FA value of electrical conductivity at each X, Y and Z coordinate axes would be equal to 0.577. The gathered results showed that there is a mean error band of 20% in electrical conductivity, if the electrical conductivity anisotropy not concluded at the calculations. The comparison of FA values showed that there is a significant statistical difference between the mean FA value of tumor and normal soft tissues (P<0.05. Conclusion: DTI is a feasible technique for the assessment of electrical conductivity anisotropy of tissues. It is crucial to quantify the electrical conductivity anisotropy data of tissues for numerical modeling of electroporation treatments.
Numerical simulation of transient, incongruent vaporization induced by high power laser
International Nuclear Information System (INIS)
Tsai, C.H.
1981-01-01
A mathematical model and numerical calculations were developed to solve the heat and mass transfer problems specifically for uranum oxide subject to laser irradiation. It can easily be modified for other heat sources or/and other materials. In the uranium-oxygen system, oxygen is the preferentially vaporizing component, and as a result of the finite mobility of oxygen in the solid, an oxygen deficiency is set up near the surface. Because of the bivariant behavior of uranium oxide, the heat transfer problem and the oxygen diffusion problem are coupled and a numerical method of simultaneously solving the two boundary value problems is studied. The temperature dependence of the thermal properties and oxygen diffusivity, as well as the highly ablative effect on the surface, leads to considerable non-linearities in both the governing differential equations and the boundary conditions. Based on the earlier work done in this laboratory by Olstad and Olander on Iron and on Zirconium hydride, the generality of the problem is expanded and the efficiency of the numerical scheme is improved. The finite difference method, along with some advanced numerical techniques, is found to be an efficient way to solve this problem
On an adaptive time stepping strategy for solving nonlinear diffusion equations
International Nuclear Information System (INIS)
Chen, K.; Baines, M.J.; Sweby, P.K.
1993-01-01
A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs
Adsorption and diffusion of plutonium in soil
International Nuclear Information System (INIS)
Relyea, J.F.; Brown, D.A.
1978-01-01
The behavior of plutonium in soil--water systems was studied by measuring its apparent diffusion coefficient in the aqueous and solid phases and by finding the adsorption--desorption relationships between soil and solution. Apparent diffusion coefficients of plutonium in soil were measured using a quick-freeze method. Aqueous diffusion was studied in a capillary-tube diffusion cell. Adsorption studies were done by equilibrating a tagged soil--water mixture on a rotary shaker before centrifuging and sampling. As expected from high adsorption coefficients (Kd) (300--10,000), the apparent diffusion coefficients were low compared with normal soil cations (1.4 x 10 -8 cm 2 /sec in a sandy soil to less than 2.4 x 10 -11 cm 2 /sec in a silt loam). The Kd of plutonium in aqueous solution containing the chelate ethylenediaminetetraacetic acid (EDTA) was reduced compared with the Kd in dilute HNO 3 . As the EDTA concentration was increased, the Kd was decreased. The chelate diethylenetriaminepentaacetic acid (DTPA) reduced the Kd more than EDTA at comparable concentrations. The aqueous diffusion coefficients varied from 3.1 x 10 -7 cm 2 /sec in a solution extracted from the silt loam up to 2.7 x 10 -5 cm 2 /sec in a solution extracted from the sandy soil
International Nuclear Information System (INIS)
Kong, Im Mo; Jung, Aeri; Kim, Min Soo
2016-01-01
Highlights: • The performance of self-humidified PEMFCs can be improved with double GDBL. • The effect of double GDBL on water retention capability and membrane hydration was investigated. • In addition to HFR and EIS measurements, numerical analysis was conducted. • Optimized design of double GDBL for self-humidified PEMFC was investigated. • This study provides an inspiration on how to design the double GDBL. - Abstract: In order to simplify the system configuration and downsize the volume, a proton exchange membrane fuel cell (PEMFC) needs to be operated in a self-humidified mode without any external humidifiers. However, in self-humidified PEMFCs, relatively low cell performance is a problem to be solved. In our previous study, a gas diffusion layer (GDL) containing double gas diffusion backing layer (GDBL) coated by single micro porous layer (MPL) was introduced and its effect on the cell performance was evaluated. In the present study, the effect of the double GDBL was investigated by measuring high frequency resistance (HFR) and electrochemical impedance spectroscopy (EIS). In the experiments, the HFR value was remarkably reduced, while the diameter of semicircle of EIS was increased. It means that the membrane hydration was improved due to enhanced water retention capability of the GDL despite of interrupted gas diffusion. The result of numerical analysis also showed that the water retention capability of GDL can be improved with proper structure design of double GDBL. Based on the result, optimized design of double GDBL for water retention was obtained numerically. The result of this study provides useful information on the structural design of GDBL for self-humidified PEMFCs.
New complex variable meshless method for advection—diffusion problems
International Nuclear Information System (INIS)
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 inestigate 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
Directory of Open Access Journals (Sweden)
R.T. DeHoff
2002-09-01
Full Text Available The phenomenological formalism, which yields Fick's Laws for diffusion in single phase multicomponent systems, is widely accepted as the basis for the mathematical description of diffusion. This paper focuses on problems associated with this formalism. This mode of description of the process is cumbersome, defining as it does matrices of interdiffusion coefficients (the central material properties that require a large experimental investment for their evaluation in three component systems, and, indeed cannot be evaluated for systems with more than three components. It is also argued that the physical meaning of the numerical values of these properties with respect to the atom motions in the system remains unknown. The attempt to understand the physical content of the diffusion coefficients in the phenomenological formalism has been the central fundamental problem in the theory of diffusion in crystalline alloys. The observation by Kirkendall that the crystal lattice moves during diffusion led Darken to develop the concept of intrinsic diffusion, i.e., atom motion relative to the crystal lattice. Darken and his successors sought to relate the diffusion coefficients computed for intrinsic fluxes to those obtained from the motion of radioactive tracers in chemically homogeneous samples which directly report the jump frequencies of the atoms as a function of composition and temperature. This theoretical connection between tracer, intrinsic and interdiffusion behavior would provide the basis for understanding the physical content of interdiffusion coefficients. Definitive tests of the resulting theoretical connection have been carried out for a number of binary systems for which all three kinds of observations are available. In a number of systems predictions of intrinsic coefficients from tracer data do not agree with measured values although predictions of interdiffusion coefficients appear to give reasonable agreement. Thus, the complete
Reduced-Order Direct Numerical Simulation of Solute Transport in Porous Media
Mehmani, Yashar; Tchelepi, Hamdi
2017-11-01
Pore-scale models are an important tool for analyzing fluid dynamics in porous materials (e.g., rocks, soils, fuel cells). Current direct numerical simulation (DNS) techniques, while very accurate, are computationally prohibitive for sample sizes that are statistically representative of the porous structure. Reduced-order approaches such as pore-network models (PNM) aim to approximate the pore-space geometry and physics to remedy this problem. Predictions from current techniques, however, have not always been successful. This work focuses on single-phase transport of a passive solute under advection-dominated regimes and delineates the minimum set of approximations that consistently produce accurate PNM predictions. Novel network extraction (discretization) and particle simulation techniques are developed and compared to high-fidelity DNS simulations for a wide range of micromodel heterogeneities and a single sphere pack. Moreover, common modeling assumptions in the literature are analyzed and shown that they can lead to first-order errors under advection-dominated regimes. This work has implications for optimizing material design and operations in manufactured (electrodes) and natural (rocks) porous media pertaining to energy systems. This work was supported by the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).
Diffusion in crushed rock and in bentonite clay
International Nuclear Information System (INIS)
Olin, M.
1994-04-01
Diffusion theories for porous media with sorption are reviewed to serve as a basis for considering diffusion in simple systems like sand of crushed rock. A Fickian diffusion and linear sorption model is solved both by analytical Laplance transform and Green's function methods and by numerical methods, and then applied to small-scale experiments for Finnish low- and medium-level operating waste repositories. The main properties of bentonite are reviewed. The hydraulic conductivity of compacted bentonite is so low that the major transport mechanism is diffusion. A Fickian diffusion and linear sorption model is applied to bentonite. The main component of bentonite, montmorillonite, has a high ion-exchange capacity and thus, transport in bentonite consists of interactive chemical and diffusion phenomena. A chemical equilibrium model, CHEQ, is developed for ion-exchange reactions in bentonite water systems. CHEQ is applied to some bentonite experiments with success, especially for monovalent ions. The fitted log-binding constants for sodium exchange with potassium, magnesium, and calcium were 0.27, 1.50, and 2.10, respectively. A coupled chemical and diffusion model, CHEQDIFF, is developed to take account of diffusion in pore water, surface diffusion and ion-exchange reactions. The model is applied to the same experiments as CHEQ, and validation is partly successful. In the diffusion case, the above-mentioned values for binding constants are used. The apparent diffusion (both anions and cations) and surface diffusion (only for cations) constants used are 3.0*10 -11 m 2 /s and 6.0*10 -12 m 2 /s, respectively, but these values are questionable, as experimental results good enough for fitting are not available. (orig.). (74 refs., 27 figs., 12 tabs.)
An epidemic model of rumor diffusion in online social networks
Cheng, Jun-Jun; Liu, Yun; Shen, Bo; Yuan, Wei-Guo
2013-01-01
So far, in some standard rumor spreading models, the transition probability from ignorants to spreaders is always treated as a constant. However, from a practical perspective, the case that individual whether or not be infected by the neighbor spreader greatly depends on the trustiness of ties between them. In order to solve this problem, we introduce a stochastic epidemic model of the rumor diffusion, in which the infectious probability is defined as a function of the strength of ties. Moreover, we investigate numerically the behavior of the model on a real scale-free social site with the exponent γ = 2.2. We verify that the strength of ties plays a critical role in the rumor diffusion process. Specially, selecting weak ties preferentially cannot make rumor spread faster and wider, but the efficiency of diffusion will be greatly affected after removing them. Another significant finding is that the maximum number of spreaders max( S) is very sensitive to the immune probability μ and the decay probability v. We show that a smaller μ or v leads to a larger spreading of the rumor, and their relationships can be described as the function ln(max( S)) = Av + B, in which the intercept B and the slope A can be fitted perfectly as power-law functions of μ. Our findings may offer some useful insights, helping guide the application in practice and reduce the damage brought by the rumor.
Numerical Simulation on Smoke Spread and Temperature Distribution in a Corn Starch Explosion
Lin, CherngShing; Hsu, JuiPei
2018-01-01
It is discovered from dust explosion accidents in recent years that deep causes of the accidents lies in insufficient cognition of dust explosion danger, and no understanding on danger and information of the dust explosion. In the study, Fire Dynamics Simulator (FDS) evaluation tool is used aiming at Taiwan Formosa Fun Coast explosion accidents. The calculator is used for rebuilding the explosion situation. The factors affecting casualties under explosion are studied. The injured personnel participating in the party are evaluated according to smoke diffusion and temperature distribution for numerical simulation results. Some problems noted in the fire disaster after actual explosion are proposed, rational site analysis is given, thereby reducing dust explosion risk grade.
Numerical methods and analysis of multiscale problems
Madureira, Alexandre L
2017-01-01
This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.
Gaseous diffusion -- the enrichment workhorse
International Nuclear Information System (INIS)
Shoemaker, J.E. Jr.
1984-01-01
Construction of the first large-scale gaseous diffusion facility was started as part of the Manhattan Project in Oak Ridge, Tennessee, in 1943. This facility, code named ''K-25,'' began operation in January 1945 and was fully on stream by September 1945. Four additional process buildings were later added in Oak Ridge as the demand for enriched uranium escalated. New gaseous diffusion plants were constructed at Paducah, Kentucky, and Portsmouth, Ohio, during this period. The three gaseous diffusion plants were the ''workhorses'' which provided the entire enriched uranium demand for the United States during the 1950s and 1960s. As the demand for enriched uranium for military purposes decreased during the early 1960s, power to the diffusion plants was curtailed to reduce production. During the 1960s, as plans for the nuclear power industry were formulated, the role of the diffusion plants gradually changed from providing highly-enriched uranium for the military to providing low-enriched uranium for power reactors
Asinari, Pietro
2009-11-01
A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.
The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
Giordano, C. M.; Cincotta, P. M.
2018-05-01
In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
Diffusion of solid fuelon a vibrating grate
DEFF Research Database (Denmark)
Sabelström, Hanna Katarina
of vibrations can be incorporated into a numerical model. The chosen model approach has been to separate the gas and solid phases into two independent models related to each other through the bed porosity. By treating the bed as a porous media and using Ergun's equation for the gas flow, the numerical work...... is simplified and the computational time shortened. The vibrations are affecting the transport and mixing of the fuel and incorporated into the model through the diffusion coefficient in the conservation equation of the solid phase. Experimental work has been carried out with the aim to study the behaviour...
International Nuclear Information System (INIS)
Zalan, T.A.
1988-01-01
Multi-energy-group neutron diffusion theory is used to numerically evaluate the utility of two different dual-detector neutron porosity logging devices, a 14 MeV (accelerator) neutron source - epithermal neutron detector device and a 4 MeV neutron source - capture gamma-ray detector device, relative to the traditional 4 MeV neutron source - thermal neutron detector device. Fast and epithermal neutron diffusion parameters are calculated using Monte Carlo - derived neutron flux distributions. Thermal parameters are calculated from tabulated cross sections. An existing analytical method to describe the transport of gamma-rays through common earth materials is modified in order to accommodate the modeling of the 4 MeV neutron - capture gamma-ray device. The 14 MeV neutron - epithermal neutron device is found to be less sensitive to porosity than the 4 MeV neutron - capture gamma-ray device, which in turn is found to be less sensitive to porosity than the traditional 4 MeV neutron - thermal neutron device. Salinity effects are found to be comparable for the 4 MeV neutron - capture gamma-ray and 4 MeV neutron - thermal neutron devices. The 4 MeV neutron capture gamma-ray measurement is found to be deepest investigating
Classical diffusion: theory and simulation codes
International Nuclear Information System (INIS)
Grad, H.; Hu, P.N.
1978-03-01
A survey is given of the development of classical diffusion theory which arose from the observation of Grad and Hogan that the Pfirsch-Schluter and Neoclassical theories are very special and frequently inapplicable because they require that plasma mass flow be treated as transport rather than as a state variable of the plasma. The subsequent theory, efficient numerical algorithms, and results of various operating codes are described
A Bloch-Torrey Equation for Diffusion in a Deforming Media
International Nuclear Information System (INIS)
Rohmer, Damien; Gullberg, Grant T.
2006-01-01
Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore, informs on the structure of the biological tissue. This technique is applied with success to the static organs such as brain. However, the diffusion measurement on the dynamically deformable organs such as the in-vivo heart is a complex problem that has however a great potential in the measurement of cardiac health. In order to understand the behavior of the Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torrey equation that leads the MR behavior is expressed in general curvilinear coordinates. These coordinates enable to follow the heart geometry and deformations through time. The equation is finally discredited and presented in a numerical formulation using implicit methods, in order to get a stable scheme that can be applied to any smooth deformations. Diffusion process enables the link between the macroscopic behavior of molecules and the microscopic structure in which they evolve. The measurement of diffusion in biological tissues is therefore of major importance in understanding the complex underlying structure that cannot be studied directly. The Diffusion Tensor Magnetic Resonance Imaging(DTMRI) technique enables the measurement of diffusion parameters and therefore provides information on the structure of the biological tissue. This technique has been applied with success to static organs such as the brain. However, diffusion measurement of dynamically deformable organs such as the in-vivo heart remains a complex problem, which holds great potential in determining cardiac health. In order to understand the behavior of the magnetic resonance (MR) signal in a deforming media, the Bloch-Torrey equation that defines the MR behavior is expressed in general curvilinear coordinates. These coordinates enable us to follow the heart geometry and deformations through time. The equation is finally discredited and presented in a
Diffusion tensor MR microscopy of tissues with low diffusional anisotropy.
Bajd, Franci; Mattea, Carlos; Stapf, Siegfried; Sersa, Igor
2016-06-01
Diffusion tensor imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion tensor elements. In the study, several experimental factors affecting accuracy of diffusion tensor determination were analyzed. Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion tensor magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. In both, the simulations and the experiments, the multivariate linear regression of the diffusion-tensor analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low.
Unconditionally stable diffusion-acceleration of the transport equation
International Nuclear Information System (INIS)
Larsen, E.W.
1982-01-01
The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically large regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results
Unconditionally stable diffusion-acceleration of the transport equation
International Nuclear Information System (INIS)
Larson, E.W.
1982-01-01
The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results
Effective hydrogen diffusion coefficient for solidifying aluminium alloys
International Nuclear Information System (INIS)
Felberbaum, M.; Landry-Desy, E.; Weber, L.; Rappaz, M.
2011-01-01
An effective hydrogen diffusion coefficient has been calculated for two solidifying Al - 4.5 wt.% Cu and Al - 10 wt.% Cu alloys as a function of the volume fraction of solid. For this purpose, in situ X-ray tomography was performed on these alloys. For each volume fraction of solid between 0.6 and 0.9, a representative volume element of the microstructure was extracted. Solid and liquid voxels were assimilated to solid and liquid nodes in order to solve the hydrogen diffusion equation based on the chemical potential and using a finite volume formulation. An effective hydrogen diffusion coefficient based on the volume fraction of solid only could be deduced from the results of the numerical model at steady state. The results are compared with various effective medium theories.
Schwartz, L M; Bergman, D J; Dunn, K J; Mitra, P P
1996-01-01
Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.
Glutathionylation-Dependence of Na+-K+-Pump Currents Can Mimic Reduced Subsarcolemmal Na+ Diffusion
Garcia, Alvaro; Liu, Chia-Chi; Cornelius, Flemming; Clarke, Ronald J.; Rasmussen, Helge H.
2016-01-01
The existence of a subsarcolemmal space with restricted diffusion for Na+ in cardiac myocytes has been inferred from a transient peak electrogenic Na+-K+ pump current beyond steady state on reexposure of myocytes to K+ after a period of exposure to K+-free extracellular solution. The transient peak current is attributed to enhanced electrogenic pumping of Na+ that accumulated in the diffusion-restricted space during pump inhibition in K+-free extracellular solution. However, there are no known physical barriers that account for such restricted Na+ diffusion, and we examined if changes of activity of the Na+-K+ pump itself cause the transient peak current. Reexposure to K+ reproduced a transient current beyond steady state in voltage-clamped ventricular myocytes as reported by others. Persistence of it when the Na+ concentration in patch pipette solutions perfusing the intracellular compartment was high and elimination of it with K+-free pipette solution could not be reconciled with restricted subsarcolemmal Na+ diffusion. The pattern of the transient current early after pump activation was dependent on transmembrane Na+- and K+ concentration gradients suggesting the currents were related to the conformational poise imposed on the pump. We examined if the currents might be accounted for by changes in glutathionylation of the β1 Na+-K+ pump subunit, a reversible oxidative modification that inhibits the pump. Susceptibility of the β1 subunit to glutathionylation depends on the conformational poise of the Na+-K+ pump, and glutathionylation with the pump stabilized in conformations equivalent to those expected to be imposed on voltage-clamped myocytes supported this hypothesis. So did elimination of the transient K+-induced peak Na+-K+ pump current when we included glutaredoxin 1 in patch pipette solutions to reverse glutathionylation. We conclude that transient K+-induced peak Na+-K+ pump current reflects the effect of conformation-dependent β1 pump subunit
Garcia, Alvaro; Liu, Chia-Chi; Cornelius, Flemming; Clarke, Ronald J; Rasmussen, Helge H
2016-03-08
The existence of a subsarcolemmal space with restricted diffusion for Na(+) in cardiac myocytes has been inferred from a transient peak electrogenic Na(+)-K(+) pump current beyond steady state on reexposure of myocytes to K(+) after a period of exposure to K(+)-free extracellular solution. The transient peak current is attributed to enhanced electrogenic pumping of Na(+) that accumulated in the diffusion-restricted space during pump inhibition in K(+)-free extracellular solution. However, there are no known physical barriers that account for such restricted Na(+) diffusion, and we examined if changes of activity of the Na(+)-K(+) pump itself cause the transient peak current. Reexposure to K(+) reproduced a transient current beyond steady state in voltage-clamped ventricular myocytes as reported by others. Persistence of it when the Na(+) concentration in patch pipette solutions perfusing the intracellular compartment was high and elimination of it with K(+)-free pipette solution could not be reconciled with restricted subsarcolemmal Na(+) diffusion. The pattern of the transient current early after pump activation was dependent on transmembrane Na(+)- and K(+) concentration gradients suggesting the currents were related to the conformational poise imposed on the pump. We examined if the currents might be accounted for by changes in glutathionylation of the β1 Na(+)-K(+) pump subunit, a reversible oxidative modification that inhibits the pump. Susceptibility of the β1 subunit to glutathionylation depends on the conformational poise of the Na(+)-K(+) pump, and glutathionylation with the pump stabilized in conformations equivalent to those expected to be imposed on voltage-clamped myocytes supported this hypothesis. So did elimination of the transient K(+)-induced peak Na(+)-K(+) pump current when we included glutaredoxin 1 in patch pipette solutions to reverse glutathionylation. We conclude that transient K(+)-induced peak Na(+)-K(+) pump current reflects the effect
Matas, Richard; Syka, Tomáš; Luňáček, Ondřej
The article deals with a description of results from research and development of a radial compressor stage. The experimental compressor and used numerical models are briefly described. In the first part, the comparisons of characteristics obtained experimentally and by numerical simulations for stage with vaneless diffuser are described. In the second part, the results for stage with vanned diffuser are presented. The results are relevant for next studies in research and development process.
Diffusion-limited mixing by incompressible flows
Miles, Christopher J.; Doering, Charles R.
2018-05-01
Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenize a passive tracer. However we provide numerical evidence that, in cases where advection and diffusion are both actively present, diffusion may produce negative effects by limiting the mixing effectiveness of incompressible optimal flows. This limitation appears to be due to the presence of a limiting length scale given by a generalised Batchelor length (Batchelor 1959 J. Fluid Mech. 5 113–33). This length scale limitation may in turn affect long-term mixing rates. More specifically, we consider local-in-time flow optimisation under energy and enstrophy flow constraints with the objective of maximising the mixing rate. We observe that, for enstrophy-bounded optimal flows, the strength of diffusion may not impact the long-term mixing rate. For energy-constrained optimal flows, however, an increase in the strength of diffusion can decrease the mixing rate. We provide analytical lower bounds on mixing rates and length scales achievable under related constraints (point-wise bounded speed and rate-of-strain) by extending the work of Lin et al (2011 J. Fluid Mech. 675 465–76) and Poon (1996 Commun. PDE 21 521–39).
Diffusive limits for linear transport equations
International Nuclear Information System (INIS)
Pomraning, G.C.
1992-01-01
The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion
A new model of anomalous phosphorus diffusion in silicon
International Nuclear Information System (INIS)
Budil, M.; Poetzl, H.; Stingeder, G.; Grasserbauer, M.
1989-01-01
A model is presented to describe the 'kink and tail' diffusion of phosphorus. The diffusion behaviour of phosphorus is expplained by the motion of phosphorus-interstitial and phosphorus-vacancy pairs in different charge states. The model yields the enhancement of diffusion in the tail region depending on surface concentration. Furthermore it yields the same selfdiffusion coefficient for interstitials as the gold diffusion experiments. A transformation of the diffusion equation was found to reduce the number of simulation equations. (author) 7 refs., 5 figs
Discontinuous Galerkin methods and a posteriori error analysis for heterogenous diffusion problems
International Nuclear Information System (INIS)
Stephansen, A.F.
2007-12-01
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)
Asymmetric diffusion model for oblique-incidence reflectometry
Institute of Scientific and Technical Information of China (English)
Yaqin Chen; Liji Cao; Liqun Sun
2011-01-01
A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectom-etry. By fitting to this asymmetric diffusion model, the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10% from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp') away from the incident point; particularly, μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10% accuracy. The method is verified by Monte Carlo simulations and experimentally tested on a phantom.%A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectometry.By fitting to this asymmetric diffusion model,the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10％ from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp')away from the incident point;particularly,μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10％ accuracy.The method is verified by Monte Carlo simulations and experimentally tested on a phantom.Knowledge about the optical properties,including the absorption coefficient (μa) and the reduced scattering coefficient (μ's =μs(1-g)),where μs is the scattering coefficient and g is the anisotropy factor of scattering,of biological tissues plays an important role for optical therapeutic and diagnostic techniques in medicine.
International Nuclear Information System (INIS)
Joubert, H.D.; Terblans, J.J.; Swart, H.C.
2009-01-01
Classical inter-diffusion studies assume a constant time of annealing when samples are annealed in a furnace. It is assumed that the sample temperature reaches the annealing temperature immediately after insertion, while the sample temperature immediately drops to room temperature after removal, the annealing time being taken as the time between insertion and removal. Using the above assumption, the diffusion coefficient can be calculated in a number of ways. In reality, the sample temperature does not immediately reach the annealing temperature; instead it rises at a rate governed by several heat transfer mechanisms, depending on the annealing procedure. For short annealing times, the sample temperature may not attain the annealing temperature, while for extended annealing times the sample temperature may reach the annealing temperature only for a fraction of the annealing time. To eliminate the effect of heat transfer mechanisms, a linear temperature ramping regime is proposed. Used in conjunction with a suitable profile reconstructing technique and a numerical solution of Fick's second law, the inter-diffusion parameters obtained from a linear ramping of Ni/Cu thin film samples can be compared to those obtained from calculations performed with the so-called Mixing-Roughness-Information model or any other suitable method used to determine classical diffusion coefficients.
Energy Technology Data Exchange (ETDEWEB)
Lee, Won Woong; Lee, Jeong Ik [KAIST, Daejeon (Korea, Republic of)
2016-05-15
The existing nuclear system analysis codes such as RELAP5, TRAC, MARS and SPACE use the first-order numerical scheme in both space and time discretization. However, the first-order scheme is highly diffusive and less accurate due to the first order of truncation error. So, the numerical diffusion problem which makes the gradients to be smooth in the regions where the gradients should be steep can occur during the analysis, which often predicts less conservatively than the reality. Therefore, the first-order scheme is not always useful in many applications such as boron solute transport. RELAP7 which is an advanced nuclear reactor system safety analysis code using the second-order numerical scheme in temporal and spatial discretization is being developed by INL (Idaho National Laboratory) since 2011. Therefore, for better predictive performance of the safety of nuclear reactor systems, more accurate nuclear reactor system analysis code is needed for Korea too to follow the global trend of nuclear safety analysis. Thus, this study will evaluate the feasibility of applying the higher-order numerical scheme to the next generation nuclear system analysis code to provide the basis for the better nuclear system analysis code development. The accuracy is enhanced in the spatial second-order scheme and the numerical diffusion problem is alleviated while indicates significantly lower maximum Courant limit and the numerical dispersion issue which produces spurious oscillation and non-physical results in the higher-order scheme. If the spatial scheme is the first order scheme then the temporal second-order scheme provides almost the same result with the temporal firstorder scheme. However, when the temporal second order scheme and the spatial second-order scheme are applied together, the numerical dispersion can occur more severely. For the more in-depth study, the verification and validation of the NTS code built in MATLAB will be conducted further and expanded to handle two
Edge-promoting reconstruction of absorption and diffusivity in optical tomography
International Nuclear Information System (INIS)
Hannukainen, A; Hyvönen, N; Majander, H; Harhanen, L
2016-01-01
In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments with simulated data. (paper)
Numerical simulation of pulverized coal combustion to reduce pollutants
International Nuclear Information System (INIS)
Mohammad Bagher Ayani; Behnam Rahmanian
2010-01-01
Full text: In this research, the numerical simulation of pollutant reduction and in a pulverized coal combustion at 2D combustion chamber have been studied. Finite volume method using structured grid arrangement was utilized for modeling the pulverized coal combustion. The pressure base algorithm and implicit solver has been employed to simulate non-premix combustion model. The air was diluted by some participative gaseous such as whose percentages varied from 0 % to 20 %. Participative gases and air were preheated by a high-temperature gas generator, and the preheated oxidizer temperature could achieve. The combustion simulation with the generalized finite rate chemistry model, referred to as the Magnussen model and the reacting flow with the mixture fraction PDF/ equilibrium chemistry model, referred to as the PDF model are studied. Quick scheme was adopted for the discretization of all convective terms of the advective transport equations. So, as a result of addition participative gases into oxidizer the rate of formation of pollutants as well as NO x suppressed. The addition only a few percent of halogen components can make some systems nonflammable. The effects of addition halogen components and non-reaction gaseous such as Helium and Argon are fuel dilution and its acts as catalysts in reducing the H atom concentration necessary for the chain branching reaction sequence. Moreover, they act like surface and they make the increment of surface ratio versus volume. Because of this, the number of radical conflicts and hence destruction them will be increase. Furthermore, the rate of formation of pollutants will be decreased if the halogen components and non-reaction gaseous injection will be increased. However, as a result of this research, in the case of injection in pulverized coal combustion the flame temperature is lower than Steam, Argon and Helium. So, the emission levels of carbon dioxide is significantly lower than other participative gases, but in this
Turbine exhaust diffuser with region of reduced flow area and outer boundary gas flow
Orosa, John
2014-03-11
An exhaust diffuser system and method for a turbine engine. The outer boundary may include a region in which the outer boundary extends radially inwardly toward the hub structure and may direct at least a portion of an exhaust flow in the diffuser toward the hub structure. At least one gas jet is provided including a jet exit located on the outer boundary. The jet exit may discharge a flow of gas downstream substantially parallel to an inner surface of the outer boundary to direct a portion of the exhaust flow in the diffuser toward the outer boundary to effect a radially outward flow of at least a portion of the exhaust gas flow toward the outer boundary to balance an aerodynamic load between the outer and inner boundaries.
Energy Technology Data Exchange (ETDEWEB)
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)
Impurity diffusion in transition-metal oxides
International Nuclear Information System (INIS)
Peterson, N.L.
1982-06-01
Intrinsic tracer impurity diffusion measurements in ceramic oxides have been primarily confined to CoO, NiO, and Fe 3 O 4 . Tracer impurity diffusion in these materials and TiO 2 , together with measurements of the effect of impurities on tracer diffusion (Co in NiO and Cr in CoO), are reviewed and discussed in terms of impurity-defect interactions and mechanisms of diffusion. Divalent impurities in divalent solvents seem to have a weak interaction with vacancies whereas trivalent impurities in divalent solvents strongly influence the vacancy concentrations and significantly reduce solvent jump frequencies near a trivalent impurity. Impurities with small ionic radii diffuse more slowly with a larger activation energy than impurities with larger ionic radii for all systems considered in this review. Cobalt ions (a moderate size impurity) diffuse rapidly along the open channels parallel to the c-axis in TiO 2 whereas chromium ions (a smaller-sized impurity) do not. 60 references, 11 figures
Numerical simulations of thermal conductivity in dissipative two-dimensional Yukawa systems.
Khrustalyov, Yu V; Vaulina, O S
2012-04-01
Numerical data on the heat transfer constants in two-dimensional Yukawa systems were obtained. Numerical study of the thermal conductivity and diffusivity was carried out for the equilibrium systems with parameters close to conditions of laboratory experiments with dusty plasma. For calculations of heat transfer constants the Green-Kubo formulas were used. The influence of dissipation (friction) on the heat transfer processes in nonideal systems was investigated. The approximation of the coefficient of thermal conductivity is proposed. Comparison of the obtained results to the existing experimental and numerical data is discussed.
Banish, R. Michael; Brantschen, Segolene; Pourpoint, Timothee L.; Wessling, Francis; Sekerka, Robert F.
2003-01-01
This paper presents methodologies for measuring the thermal diffusivity using the difference between temperatures measured at two, essentially independent, locations. A heat pulse is applied for an arbitrary time to one region of the sample; either the inner core or the outer wall. Temperature changes are then monitored versus time. The thermal diffusivity is calculated from the temperature difference versus time. No initial conditions are used directly in the final results.