A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

Science.gov (United States)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Solution of the two-dimensional spectral factorization problem

Science.gov (United States)

Lawton, W. M.

1985-01-01

An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

One dimensional benchmark calculations using diffusion theory

International Nuclear Information System (INIS)

Ustun, G.; Turgut, M.H.

1986-01-01

This is a comparative study by using different one dimensional diffusion codes which are available at our Nuclear Engineering Department. Some modifications have been made in the used codes to fit the problems. One of the codes, DIFFUSE, solves the neutron diffusion equation in slab, cylindrical and spherical geometries by using 'Forward elimination- Backward substitution' technique. DIFFUSE code calculates criticality, critical dimensions and critical material concentrations and adjoint fluxes as well. It is used for the space and energy dependent neutron flux distribution. The whole scattering matrix can be used if desired. Normalisation of the relative flux distributions to the reactor power, plotting of the flux distributions and leakage terms for the other two dimensions have been added. Some modifications also have been made for the code output. Two Benchmark problems have been calculated with the modified version and the results are compared with BBD code which is available at our department and uses same techniques of calculation. Agreements are quite good in results such as k-eff and the flux distributions for the two cases studies. (author)

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

Science.gov (United States)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Development of a coarse mesh code for the solution of two group static diffusion problems

International Nuclear Information System (INIS)

Barros, R.C. de.

1985-01-01

This new coarse mesh code designed for the solution of 2 and 3 dimensional static diffusion problems, is based on an alternating direction method which consists in the solution of one dimensional problem along each coordinate direction with leakage terms for the remaining directions estimated from previous interactions. Four versions of this code have been developed: AD21 - 2D - 1/4, AD21 - 2D - 4/4, AD21 - 3D - 1/4 and AD21 - 3D - 4/4; these versions have been designed for 2 and 3 dimensional problems with or without 1/4 symmetry. (Author) [pt

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

Science.gov (United States)

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.

Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

International Nuclear Information System (INIS)

Takeshi, Y.; Keisuke, K.

1983-01-01

The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

International Nuclear Information System (INIS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-01-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Generalized Runge-Kutta method for two- and three-dimensional space-time diffusion equations with a variable time step

International Nuclear Information System (INIS)

Aboanber, A.E.; Hamada, Y.M.

2008-01-01

An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for 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 time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods

Iterative Two- and One-Dimensional Methods for Three-Dimensional Neutron Diffusion Calculations

International Nuclear Information System (INIS)

Lee, Hyun Chul; Lee, Deokjung; Downar, Thomas J.

2005-01-01

Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications

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)

Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions

International Nuclear Information System (INIS)

Carpenter, D.C.

1997-01-01

Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions

A multilevel in space and energy solver for multigroup diffusion eigenvalue problems

Directory of Open Access Journals (Sweden)

Ben C. Yee

2017-09-01

Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

Science.gov (United States)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Effective diffusion constant in a two-dimensional medium of charged point scatterers

International Nuclear Information System (INIS)

Dean, D S; Drummond, I T; Horgan, R R

2004-01-01

We obtain exact results for the effective diffusion constant of a two-dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer

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.

Shear viscosity and spin-diffusion coefficient of a two-dimensional Fermi gas

DEFF Research Database (Denmark)

Bruun, Georg

2012-01-01

Using kinetic theory, we calculate the shear viscosity and the spin-diffusion coefficient as well as the associated relaxation times for a two-component Fermi gas in two dimensions, as a function of temperature, coupling strength, polarization, and mass ratio of the two components. It is demonstr......Using kinetic theory, we calculate the shear viscosity and the spin-diffusion coefficient as well as the associated relaxation times for a two-component Fermi gas in two dimensions, as a function of temperature, coupling strength, polarization, and mass ratio of the two components....... It is demonstrated that the minimum value of the viscosity decreases with the mass ratio, since Fermi blocking becomes less efficient. We furthermore analyze recent experimental results for the quadrupole mode of a two-dimensional gas in terms of viscous damping, obtaining a qualitative agreement using no fitting...

Quantum diffusion in two-dimensional random systems with particle–hole symmetry

International Nuclear Information System (INIS)

Ziegler, K

2012-01-01

We study the scattering dynamics of an n-component spinor wavefunction in a random environment on a two-dimensional lattice. If the particle–hole symmetry of the Hamiltonian is spontaneously broken the dynamics of the quantum particles becomes diffusive on large scales. The latter is described by a non-interacting Grassmann field, indicating a special kind of asymptotic freedom on large scales in d = 2. (paper)

A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry

International Nuclear Information System (INIS)

Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan

1988-01-01

The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory

Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.

Science.gov (United States)

Xiao, Perry; Imhof, Robert E

2012-10-01

Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.

HEXAGA-II-120, -60, -30 two-dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering

International Nuclear Information System (INIS)

Woznicki, Z.

1979-06-01

This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de

Diffusion with Varying Drag; the Runaway Problem.

Science.gov (United States)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

Diffusion with varying drag; the runaway problem

International Nuclear Information System (INIS)

Rollins, D.K.

1986-01-01

The motion of electrons in an ionized plasma of electrons and ions in an external electric field is studied. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron-runaway phenomenon. The electric field is treated as a small perturbation. Various diffusion coefficients are considered for the one dimensional problem, and the runaway current is determined as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coeffient decays with velocity are then considered. To determine the runaway current, the equivalent Schroedinger eigenvalue problem is analyzed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching, a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem

Inverse radiative transfer problems in two-dimensional heterogeneous media

International Nuclear Information System (INIS)

Tito, Mariella Janette Berrocal

2001-01-01

The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)

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.

An analytical approach for a nodal scheme of two-dimensional neutron transport problems

International Nuclear Information System (INIS)

Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.

2011-01-01

Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.

DIF3D: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems

International Nuclear Information System (INIS)

Derstine, K.L.

1984-04-01

The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. Guidelines are included for implementing the DIF3D export package on several large scale computers. Optimized iteration methods for the solution of large-scale fast-reactor finite-difference diffusion theory calculations are presented, along with their theoretical basis. The computational and data management considerations that went into their formulation are discussed. The methods utilized include a variant of the Chebyshev acceleration technique applied to the outer fission source iterations and an optimized block successive overrelaxation method for the within-group iterations. A nodal solution option intended for analysis of LMFBR designs in two- and three-dimensional hexagonal geometries is incorporated in the DIF3D package and is documented in a companion report, ANL-83-1

Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method

International Nuclear Information System (INIS)

Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.

2010-01-01

The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.

A balancing domain decomposition method by constraints for advection-diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Tu, Xuemin; Li, Jing

2008-12-10

The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.

Problemas difusivos bidimensionais em regime permanente com fonte arbitrária: soluções exatas Steady two-dimensional diffusion problems with arbitrary sources: exact solutions

Directory of Open Access Journals (Sweden)

Jorge Rodolfo Silva Zabadal

2006-06-01

Full Text Available Neste trabalho são apresentados métodos híbridos para solução de problemas difusivos relativos à dispersão de poluentes em meio aquático. Estes métodos aplicam variáveis complexas a fim de executar mapeamentos sobre a equação diferencial a ser resolvida bem como sobre o domínio considerado. O mapeamento sobre a equação diferencial converte o operador laplaciano bidimensional em uma derivada cruzada de segunda ordem na variável espacial. O mapeamento do domínio transforma regiões de formato complexo em regiões retangulares. Ambos mapeamentos são usados a fim de reduzir o tempo total requerido de processamento para solução de problemas difusivos não-homogêneos. Resultados numéricos são apresentados.In this work hybrid methods for solving diffusion problems related to pollutants dispersion in water bodies are presented. These methods employ complex variables in order to perform mappings over the differential equation to be solved as well as over the considered domain. The mapping over the differential equation converts the two dimensional laplacian operator into a second order mixed derivative in the complex variables. The mapping of the domain transforms complex-shaped regions into rectangular ones. Both mappings are used in order to reduce the total time proccessing required for solving non-homogeneous diffusion problems. Numerical results are reported.

A tutorial on inverse problems for anomalous diffusion processes

International Nuclear Information System (INIS)

Jin, Bangti; Rundell, William

2015-01-01

of related inverse problems, depending crucially on the specific type of given data and quantity of interest. Further, the study exhibits distinct new features of ‘fractional’ inverse problems, and a partial list of surprising observations is given below. (a) Classical backward diffusion is exponentially ill-posed, whereas time fractional backward diffusion is only mildly ill-posed in the sense of norms on the domain and range spaces. However, this does not imply that the latter always allows a more effective reconstruction. (b) Theoretically, the time fractional sideways problem is severely ill-posed like its classical counterpart, but numerically can be nearly well-posed. (c) The classical Sturm–Liouville problem requires two pieces of spectral data to uniquely determine a general potential, but in the fractional case, one single Dirichlet spectrum may suffice. (d) The space fractional sideways problem can be far more or far less ill-posed than the classical counterpart, depending on the location of the lateral Cauchy data. In many cases, the precise mechanism of these surprising observations is unclear, and awaits further analytical and numerical exploration, which requires new mathematical tools and ingenuities. Further, our findings indicate fractional diffusion inverse problems also provide an excellent case study in the differences between theoretical ill-conditioning involving domain and range norms and the numerical analysis of a finite-dimensional reconstruction procedure. Throughout we will also describe known analytical and numerical results in the literature. (paper)

The simulation of a two-dimensional (2D) transport problem in a rectangular region with Lattice Boltzmann method with two-relaxation-time

Science.gov (United States)

Sugiyanto, S.; Hardyanto, W.; Marwoto, P.

2018-03-01

Transport phenomena are found in many problems in many engineering and industrial sectors. We analyzed a Lattice Boltzmann method with Two-Relaxation Time (LTRT) collision operators for simulation of pollutant moving through the medium as a two-dimensional (2D) transport problem in a rectangular region model. This model consists of a 2D rectangular region with 54 length (x), 27 width (y), and it has isotropic homogeneous medium. Initially, the concentration is zero and is distributed evenly throughout the region of interest. A concentration of 1 is maintained at 9 < y < 18, whereas the concentration of zero is maintained at 0 < y < 9 and 18 < y < 27. A specific discharge (Darcy velocity) of 1.006 is assumed. A diffusion coefficient of 0.8333 is distributed uniformly with a uniform porosity of 0.35. A computer program is written in MATLAB to compute the concentration of pollutant at any specified place and time. The program shows that LTRT solution with quadratic equilibrium distribution functions (EDFs) and relaxation time τa=1.0 are in good agreement result with other numerical solutions methods such as 3DLEWASTE (Hybrid Three-dimensional Lagrangian-Eulerian Finite Element Model of Waste Transport Through Saturated-Unsaturated Media) obtained by Yeh and 3DFEMWATER-LHS (Three-dimensional Finite Element Model of Water Flow Through Saturated-Unsaturated Media with Latin Hypercube Sampling) obtained by Hardyanto.

Monitoring the functionalization of single-walled carbon nanotubes with chitosan and folic acid by two-dimensional diffusion-ordered nmr spectroscopy

DEFF Research Database (Denmark)

Castillo, John J.; Torres, Mary H.; Molina, Daniel R.

2012-01-01

A conjugate between single-walled carbon nanotubes, chitosan and folic acid has been prepared. It was characterized by diffusion ordered two-dimensional hydrogen-1 nuclear magnetic resonance and hydrogen-1 nuclear magnetic resonance spectroscopy which revealed the presence of a conjugate that was......A conjugate between single-walled carbon nanotubes, chitosan and folic acid has been prepared. It was characterized by diffusion ordered two-dimensional hydrogen-1 nuclear magnetic resonance and hydrogen-1 nuclear magnetic resonance spectroscopy which revealed the presence of a conjugate...... that was generated by the linkage between the carboxyl moiety of the folic acid and the amino group of the chitosan, which in turn was non-covalently bound to the single-walled carbon nanotubes. The obtained diffusion coefficient values demonstrated that free folic acid diffused more rapidly than the folic acid...... conjugated to single-walled carbon nanotubes-chitosan. The values of the proton signal of hydrogen-1 nuclear magnetic resonance spectroscopy and two-dimensional hydrogen-1 nuclear magnetic resonance spectroscopy further confirmed that the folic acid was conjugated to the chitosan, wrapping the single...

Elaboration of a computer code for the solution of a two-dimensional two-energy group diffusion problem using the matrix response method

International Nuclear Information System (INIS)

Alvarenga, M.A.B.

1980-12-01

An analytical procedure to solve the neutron diffusion equation in two dimensions and two energy groups was developed. The response matrix method was used coupled with an expansion of the neutron flux in finite Fourier series. A computer code 'MRF2D' was elaborated to implement the above mentioned procedure for PWR reactor core calculations. Different core symmetry options are allowed by the code, which is also flexible enough to allow for improvements by means of algorithm optimization. The code performance was compared with a corner mesh finite difference code named TVEDIM by using a International Atomic Energy Agency (IAEA) standard problem. Computer processing time 12,7% smaller is required by the MRF2D code to reach the same precision on criticality eigenvalue. (Author) [pt

TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.

Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

International Nuclear Information System (INIS)

Polivanskij, V.P.

1989-01-01

The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs

Two-dimensional unsteady lift problems in supersonic flight

Science.gov (United States)

Heaslet, Max A; Lomax, Harvard

1949-01-01

The variation of pressure distribution is calculated for a two-dimensional supersonic airfoil either experiencing a sudden angle-of-attack change or entering a sharp-edge gust. From these pressure distributions the indicial lift functions applicable to unsteady lift problems are determined for two cases. Results are presented which permit the determination of maximum increment in lift coefficient attained by an unrestrained airfoil during its flight through a gust. As an application of these results, the minimum altitude for safe flight through a specific gust is calculated for a particular supersonic wing of given strength and wing loading.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

Science.gov (United States)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

X-ray studies on a two-dimensional diffusion limited system for cell growth

International Nuclear Information System (INIS)

Hlatky, L.R.; Alpen, E.L.

1985-01-01

X-ray studies were performed on cells grown in a new type of in vitro multicellular system, the ''sandwich'' system. This system is a two-dimensional array of cells, sandwiched between transparent slides which are impermeable to oxygen. The cell system is subject to self-created diffusion gradients of nutrients, metabolic products and, most importantly, oxygen. Sandwiches are analogous to living cross sections of multicellular spheroids or of poorly vascularized tumors. They contain a necrotic center, which the authors show to be due to diffusion limitations, an intermediate region which has a large fraction of quiescent cells and a cycling outer rim. One advantage sandwiches have over three-dimensional tumor models (sheproids) is that can control the amount of cell to cell contact and thereby separate effects due to oxygen or other gradients from effects due to contact. The authors present x-ray survival curves for sandwiches of various cell densities and compare them to x-ray survival curves done for spheroids and monolayers of the same cell line

Border-crossing model for the diffusive coarsening of two-dimensional and quasi-two-dimensional wet foams

Science.gov (United States)

Schimming, C. D.; Durian, D. J.

2017-09-01

For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called "border-blocking" models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet or unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-two-dimensional foams. And we show how the d A /d t =K0(n -6 ) von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble area, which is not constant.

SNAP-3D: a three-dimensional neutron diffusion code

International Nuclear Information System (INIS)

McCallien, C.W.J.

1975-10-01

A preliminary report is presented describing the data requirements of a one- two- or three-dimensional multi-group diffusion code, SNAP-3D. This code is primarily intended for neutron diffusion calculations but it can also carry out gamma calculations if the diffuse approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. It is assumed the reader is familiar with the older, two-dimensional code SNAP and can refer to the report [TRG-Report-1990], describing it. The present report concentrates on the enhancements to SNAP that have been made to produce the three-dimensional version, SNAP-3D, and is intended to act a a guide on data preparation until a single, comprehensive report can be published. (author)

Two numerical methods for the solution of two-dimensional eddy current problems

International Nuclear Information System (INIS)

Biddlecombe, C.S.

1978-07-01

A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)

Two dimensional dopant diffusion study by scanning capacitance microscopy and TSUPREM IV process simulation

International Nuclear Information System (INIS)

Kim, J.; McMurray, J. S.; Williams, C. C.; Slinkman, J.

1998-01-01

We report the results of a 2-step two-dimensional (2D) diffusion study by Scanning Capacitance Microscopy (SCM) and 2D TSUPREM IV process simulation. A quantitative 2D dopant profile of gate-like structures consisting heavily implanted n+ regions separated by a lighter doped n-type region underneath 0.56 μm gates is measured with the SCM. The SCM is operated in the constant-change-in-capacitance mode. The 2-D SCM data is converted to dopant density through a physical model of the SCM/silicon interaction. This profile has been directly compared with 2D TSUPREM IV process simulation and used to calibrate the simulation parameters. The sample is then further subjected to an additional diffusion in a furnace for 80 minutes at 1000C. The SCM measurement is repeated on the diffused sample. This final 2D dopant profile is compared with a TSUPREM IV process simulation tuned to fit the earlier profile with no change in the parameters except the temperature and time for the additional diffusion. Our results indicate that there is still a significant disagreement between the two profiles in the lateral direction. TSUPREM IV simulation considerably underestimates the diffusion under the gate region

The two-dimensional cutting stock problem within the roller blind production process

NARCIS (Netherlands)

E.R. de Gelder; A.P.M. Wagelmans (Albert)

2007-01-01

textabstractIn this paper we consider a two-dimensional cutting stock problem encountered at a large manufacturer of window covering products. The problem occurs in the production process of made-to-measure roller blinds. We develop a solution method that takes into account the characteristics of

Covariance problem in two-dimensional quantum chromodynamics

International Nuclear Information System (INIS)

Hagen, C.R.

1979-01-01

The problem of covariance in the field theory of a two-dimensional non-Abelian gauge field is considered. Since earlier work has shown that covariance fails (in charged sectors) for the Schwinger model, particular attention is given to an evaluation of the role played by the non-Abelian nature of the fields. In contrast to all earlier attempts at this problem, it is found that the potential covariance-breaking terms are identical to those found in the Abelian theory provided that one expresses them in terms of the total (i.e., conserved) current operator. The question of covariance is thus seen to reduce in all cases to a determination as to whether there exists a conserved global charge in the theory. Since the charge operator in the Schwinger model is conserved only in neutral sectors, one is thereby led to infer a probable failure of covariance in the non-Abelian theory, but one which is identical to that found for the U(1) case

Dimensional reduction of a general advection–diffusion equation in 2D channels

Science.gov (United States)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Anisotropic diffusion of point defects in a two-dimensional crystal of streptavidin observed by high-speed atomic force microscopy

International Nuclear Information System (INIS)

Yamamoto, Daisuke; Uchihashi, Takayuki; Kodera, Noriyuki; Ando, Toshio

2008-01-01

The diffusion of individual point defects in a two-dimensional streptavidin crystal formed on biotin-containing supported lipid bilayers was observed by high-speed atomic force microscopy. The two-dimensional diffusion of monovacancy defects exhibited anisotropy correlated with the two crystallographic axes in the orthorhombic C 222 crystal; in the 2D plane, one axis (the a-axis) is comprised of contiguous biotin-bound subunit pairs whereas the other axis (the b-axis) is comprised of contiguous biotin-unbound subunit pairs. The diffusivity along the b-axis is approximately 2.4 times larger than that along the a-axis. This anisotropy is ascribed to the difference in the association free energy between the biotin-bound subunit-subunit interaction and the biotin-unbound subunit-subunit interaction. The preferred intermolecular contact occurs between the biotin-unbound subunits. The difference in the intermolecular binding energy between the two types of subunit pair is estimated to be approximately 0.52 kcal mol -1 . Another observed dynamic behavior of point defects was fusion of two point defects into a larger defect, which occurred much more frequently than the fission of a point defect into smaller defects. The diffusivity of point defects increased with increasing defect size. The fusion and the higher diffusivity of larger defects are suggested to be involved in the mechanism for the formation of defect-free crystals

Total variation regularization for a backward time-fractional diffusion problem

International Nuclear Information System (INIS)

Wang, Liyan; Liu, Jijun

2013-01-01

Consider a two-dimensional backward problem for a time-fractional diffusion process, which can be considered as image de-blurring where the blurring process is assumed to be slow diffusion. In order to avoid the over-smoothing effect for object image with edges and to construct a fast reconstruction scheme, the total variation regularizing term and the data residual error in the frequency domain are coupled to construct the cost functional. The well posedness of this optimization problem is studied. The minimizer is sought approximately using the iteration process for a series of optimization problems with Bregman distance as a penalty term. This iteration reconstruction scheme is essentially a new regularizing scheme with coupling parameter in the cost functional and the iteration stopping times as two regularizing parameters. We give the choice strategy for the regularizing parameters in terms of the noise level of measurement data, which yields the optimal error estimate on the iterative solution. The series optimization problems are solved by alternative iteration with explicit exact solution and therefore the amount of computation is much weakened. Numerical implementations are given to support our theoretical analysis on the convergence rate and to show the significant reconstruction improvements. (paper)

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

Science.gov (United States)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

HEXAGA-II. A two-dimensional multi-group neutron diffusion programme for a uniform triangular mesh with arbitrary group scattering for the IBM/370-168 computer

International Nuclear Information System (INIS)

Woznicki, Z.

1976-05-01

This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de

Decay rate in a multi-dimensional fission problem

Energy Technology Data Exchange (ETDEWEB)

Brink, D M; Canto, L F

1986-06-01

The multi-dimensional diffusion approach of Zhang Jing Shang and Weidenmueller (1983 Phys. Rev. C28, 2190) is used to study a simplified model for induced fission. In this model it is shown that the coupling of the fission coordinate to the intrinsic degrees of freedom is equivalent to an extra friction and a mass correction in the corresponding one-dimensional problem.

Diffusing diffusivity: Rotational diffusion in two and three dimensions

Science.gov (United States)

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.

Dispersion in two dimensional channels—the Fick-Jacobs approximation revisited

Science.gov (United States)

Mangeat, M.; Guérin, T.; Dean, D. S.

2017-12-01

We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs’ approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we derive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition, a perturbation theory can be developed in \\varepsilon = h_0/L where h 0 is the characteristic channel height and L the period. This perturbation theory confirms the results of Kalinay and Percus (2006 Phys. Rev. E 74 041203), based on the reduction, to one dimensional diffusion are exact at least to {{ O}}(\\varepsilon^6) . Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results in the limit \\varepsilon \\to ∞ , we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover, we show that the correction to the effective diffusion constant is of order 1/\\varepsilon and remarkably has some universal characteristics. Numerically we compare the analytic results obtained with exact numerical calculations for a number of interesting channel geometries.

The ADO-nodal method for solving two-dimensional discrete ordinates transport problems

International Nuclear Information System (INIS)

Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da

2017-01-01

Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.

The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111)

International Nuclear Information System (INIS)

Karim, Altaf; Kara, Abdelkader; Rahman, Talat S; Trushin, Oleg

2011-01-01

The diffusion of two-dimensional adatom-islands (up to 100 atoms) on Cu(111) has been studied, using the self-learning kinetic Monte Carlo method (Trushin et al 2005 Phys. Rev. B 72 115401). A variety of multiple- and single-atom processes are revealed in the simulations, and the size dependences of the diffusion coefficients and effective diffusion barriers are calculated for each. From the tabulated frequencies of events found in the simulation, we show a crossover from diffusion due to the collective motion of the island to a regime in which the island diffuses through periphery-dominated mass transport. This crossover occurs for island sizes between 13 and 19 atoms. For islands containing 19-100 atoms the scaling exponent is 1.5, which is in good agreement with previous work. The diffusion of islands containing 2-13 atoms can be explained primarily on the basis of a linear increase of the barrier for the collective motion with the size of the island. (fast track communication)

Linear finite element method for one-dimensional diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

2011-07-01

We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

Noise-induced drift in two-dimensional anisotropic systems

Science.gov (United States)

Farago, Oded

2017-10-01

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Cassandre : a two-dimensional multigroup diffusion code for reactor transient analysis

International Nuclear Information System (INIS)

Arien, B.; Daniels, J.

1986-12-01

CASSANDRE is a two-dimensional (x-y or r-z) finite element neutronics code with thermohydraulics feedback for reactor dynamics prior to the disassembly phase. It uses the multigroup neutron diffusion theory. Its main characteristics are the use of a generalized quasistatic model, the use of a flexible multigroup point-kinetics algorithm allowing for spectral matching and the use of a finite element description. The code was conceived in order to be coupled with any thermohydraulics module, although thermohydraulics feedback is only considered in r-z geometry. In steady state criticality search is possible either by control rod insertion or by homogeneous poisoning of the coolant. This report describes the main characterstics of the code structure and provides all the information needed to use the code. (Author)

A comparison of two efficient nonlinear heat conduction methodologies using a two-dimensional time-dependent benchmark problem

International Nuclear Information System (INIS)

Wilson, G.L.; Rydin, R.A.; Orivuori, S.

1988-01-01

Two highly efficient nonlinear time-dependent heat conduction methodologies, the nonlinear time-dependent nodal integral technique (NTDNT) and IVOHEAT are compared using one- and two-dimensional time-dependent benchmark problems. The NTDNT is completely based on newly developed time-dependent nodal integral methods, whereas IVOHEAT is based on finite elements in space and Crank-Nicholson finite differences in time. IVOHEAT contains the geometric flexibility of the finite element approach, whereas the nodal integral method is constrained at present to Cartesian geometry. For test problems where both methods are equally applicable, the nodal integral method is approximately six times more efficient per dimension than IVOHEAT when a comparable overall accuracy is chosen. This translates to a factor of 200 for a three-dimensional problem having relatively homogeneous regions, and to a smaller advantage as the degree of heterogeneity increases

Theory and application of the RAZOR two-dimensional continuous energy lattice physics code

International Nuclear Information System (INIS)

Zerkle, M.L.; Abu-Shumays, I.K.; Ott, M.W.; Winwood, J.P.

1997-01-01

The theory and application of the RAZOR two-dimensional, continuous energy lattice physics code are discussed. RAZOR solves the continuous energy neutron transport equation in one- and two-dimensional geometries, and calculates equivalent few-group diffusion theory constants that rigorously account for spatial and spectral self-shielding effects. A dual energy resolution slowing down algorithm is used to reduce computer memory and disk storage requirements for the slowing down calculation. Results are presented for a 2D BWR pin cell depletion benchmark problem

LABAN-PEL: a two-dimensional, multigroup diffusion, high-order response matrix code

International Nuclear Information System (INIS)

Mueller, E.Z.

1991-06-01

The capabilities of LABAN-PEL is described. LABAN-PEL is a modified version of the two-dimensional, high-order response matrix code, LABAN, written by Lindahl. The new version extends the capabilities of the original code with regard to the treatment of neutron migration by including an option to utilize full group-to-group diffusion coefficient matrices. In addition, the code has been converted from single to double precision and the necessary routines added to activate its multigroup capability. The coding has also been converted to standard FORTRAN-77 to enhance the portability of the code. Details regarding the input data requirements and calculational options of LABAN-PEL are provided. 13 refs

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schroedinger problem and the KPI equation

International Nuclear Information System (INIS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Polivanov, M.C.

1993-01-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. The authors demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schroedinger equation as an example, it is shown that all types of solutions of the linear problem, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated. 7 refs

Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem; Methodes de decomposition de domaine pour la formulation mixte duale du probleme critique de la diffusion des neutrons

Energy Technology Data Exchange (ETDEWEB)

Guerin, P

2007-12-15

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

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.

Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

CERN Document Server

Serdyukova, S I

2000-01-01

For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-kproblem to the end in the process of concrete calculations. Deriving and solving the huge polynomial systems had been perfor...

Uniqueness for cross-diffusion systems issuing from seawater intrusion problems

Directory of Open Access Journals (Sweden)

Catherine Choquet

2017-10-01

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

Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem

International Nuclear Information System (INIS)

Guerin, P.

2007-12-01

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

International Nuclear Information System (INIS)

Ishiguro, Misako; Higuchi, Kenji

1983-01-01

The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

International Nuclear Information System (INIS)

Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; Chen, Xiao

2017-01-01

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.

A two-dimensional embedded-boundary method for convection problems with moving boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2010-01-01

htmlabstractIn this work, a two-dimensional embedded-boundary algorithm for convection problems is presented. A moving body of arbitrary boundary shape is immersed in a Cartesian finite-volume grid, which is fixed in space. The boundary surface is reconstructed in such a way that only certain fluxes

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

Science.gov (United States)

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Inverse anisotropic diffusion from power density measurements in two dimensions

International Nuclear Information System (INIS)

Monard, François; Bal, Guillaume

2012-01-01

This paper concerns the reconstruction of an anisotropic diffusion tensor γ = (γ ij ) 1⩽i,j⩽2 from knowledge of internal functionals of the form γ∇u i · ∇u j with u i for 1 ⩽ i ⩽ I solutions of the elliptic equation ∇ · γ∇u i = 0 on a two-dimensional bounded domain with appropriate boundary conditions. We show that for I = 4 and appropriately chosen boundary conditions, γ may uniquely and stably be reconstructed from such internal functionals, which appear in coupled-physics inverse problems involving the ultrasound modulation of electrical or optical coefficients. Explicit reconstruction procedures for the diffusion tensor are presented and implemented numerically. (paper)

On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation

Directory of Open Access Journals (Sweden)

Yuri Luchko

2017-12-01

Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Two-dimensional core calculation research for fuel management optimization based on CPACT code

International Nuclear Information System (INIS)

Chen Xiaosong; Peng Lianghui; Gang Zhi

2013-01-01

Fuel management optimization process requires rapid assessment for the core layout program, and the commonly used methods include two-dimensional diffusion nodal method, perturbation method, neural network method and etc. A two-dimensional loading patterns evaluation code was developed based on the three-dimensional LWR diffusion calculation program CPACT. Axial buckling introduced to simulate the axial leakage was searched in sub-burnup sections to correct the two-dimensional core diffusion calculation results. Meanwhile, in order to get better accuracy, the weight equivalent volume method of the control rod assembly cross-section was improved. (authors)

Finite element method for neutron diffusion problems in hexagonal geometry

International Nuclear Information System (INIS)

Wei, T.Y.C.; Hansen, K.F.

1975-06-01

The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes

Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model

International Nuclear Information System (INIS)

Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang

2016-01-01

A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.

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

Two-dimensional full-core transport theory Benchmarks for the WWER reactors

International Nuclear Information System (INIS)

Petkov, P.T.

2002-01-01

Several two-dimensional full-core real geometry many-group steady-state problems for the WWER-440 and WWER-1000 reactors have been solved by the MARIKO code, based on the method of characteristics. The reference transport theory solutions include assembly-wise and pin-wise power distributions. Homogenized two-group diffusion parameters and discontinuity factors have been calculated by MARIKO for each assembly type both for the whole assembly and for each cell in the smallest sector of symmetry, using the B1 method for calculation of the critical spectrum. Accurate albedo-type boundary conditions have been calculated by MARIKO for the core-reflector and core-absorber boundaries, both for each outer assembly face and for each outer cell face. Comparison with the reference solutions of the two-group nodal diffusion code SPPS-1.6 and the few-group fine-mesh diffusion codes HEX2DA and HEX2DB are presented (Authors)

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

Science.gov (United States)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.

1992-11-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

Energy Technology Data Exchange (ETDEWEB)

Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.

Development of the hierarchical domain decomposition boundary element method for solving the three-dimensional multiregion neutron diffusion equations

International Nuclear Information System (INIS)

Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro

2001-01-01

A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the 'lower level' calculations. At the 'higher level' calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time. (author)

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.)

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

Moving-boundary problems for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Sabrina D. Roscani

2017-02-01

Full Text Available We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation. The time-fractional derivative of order $\\alpha\\in (0,1$ is taken in the sense of Caputo. We study the asymptotic behaivor, as t tends to infinity, of a general solution by using a fractional weak maximum principle. Also, we give some particular exact solutions in terms of Wright functions.

Collisional plasma transport: two-dimensional scalar formulation of the initial boundary value problem and quasi one-dimensional models

International Nuclear Information System (INIS)

Mugge, J.W.

1979-10-01

The collisional plasma transport problem is formulated as an initial boundary value problem for general characteristic boundary conditions. Starting from the full set of hydrodynamic and electrodynamic equations an expansion in the electron-ion mass ratio together with a multiple timescale method yields simplified equations on each timescale. On timescales where many collisions have taken place for the simplified equations the initial boundary value problem is formulated. Through the introduction of potentials a two-dimensional scalar formulation in terms of quasi-linear integro-differential equations of second order for a domain consisting of plasma and vacuum sub-domains is obtained. (Auth.)

Timing comparison of two-dimensional discrete-ordinates codes for criticality calculations

International Nuclear Information System (INIS)

Miller, W.F. Jr.; Alcouffe, R.E.; Bosler, G.E.; Brinkley, F.W. Jr.; O'dell, R.D.

1979-01-01

The authors compare two-dimensional discrete-ordinates neutron transport computer codes to solve reactor criticality problems. The fundamental interest is in determining which code requires the minimum Central Processing Unit (CPU) time for a given numerical model of a reasonably realistic fast reactor core and peripherals. The computer codes considered are the most advanced available and, in three cases, are not officially released. The conclusion, based on the study of four fast reactor core models, is that for this class of problems the diffusion synthetic accelerated version of TWOTRAN, labeled TWOTRAN-DA, is superior to the other codes in terms of CPU requirements

Computational modelling for diffusion of neutrons problems inside nuclear multiplying medium on bidimensional cartesian rectangular geometry; Modelagem computacional de problemas de difusao de neutrons em meios multiplicativos em geometria retangular cartesiana bi-dimensional

Energy Technology Data Exchange (ETDEWEB)

Couto, Nozimar do

2003-07-01

Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

Science.gov (United States)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

A symmetrized quasi-diffusion method for solving multidimensional transport problems

International Nuclear Information System (INIS)

Miften, M.M.; Larsen, E.W.

1992-01-01

In this paper, the authors propose a 'symmetrized' QD (SQD) method in which the non-self-adjoint QD diffusion problem is replaced by two self-adjoint diffusion problems. These problems are more easily discretized and more efficiently solved than in the standard QD method. They also give SQD calculational results for transport problems in x-y geometry

Effect of Rotation for Two-Temperature Generalized Thermoelasticity of Two-Dimensional under Thermal Shock Problem

Directory of Open Access Journals (Sweden)

Kh. Lotfy

2013-01-01

Full Text Available The theory of two-temperature generalized thermoelasticity based on the theory of Youssef is used to solve boundary value problems of two-dimensional half-space. The governing equations are solved using normal mode method under the purview of the Lord-Şhulman (LS and the classical dynamical coupled theory (CD. The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating, the thermal shock type. We study the influence of rotation on the total deformation of thermoelastic half-space and the interaction with each other under the influence of two temperature theory. The material is homogeneous isotropic elastic half-space. The methodology applied here is use of the normal mode analysis techniques that are used to solve the resulting nondimensional coupled field equations for the two theories. Numerical results for the displacement components, force stresses, and temperature distribution are presented graphically and discussed. The conductive temperature, the dynamical temperature, the stress, and the strain distributions are shown graphically with some comparisons.

Modeling of three-dimensional diffusible resistors with the one-dimensional tube multiplexing method

International Nuclear Information System (INIS)

Gillet, Jean-Numa; Degorce, Jean-Yves; Meunier, Michel

2009-01-01

Electronic-behavior modeling of three-dimensional (3D) p + -π-p + and n + -ν-n + semiconducting diffusible devices with highly accurate resistances for the design of analog resistors, which are compatible with the CMOS (complementary-metal-oxide-semiconductor) technologies, is performed in three dimensions with the fast tube multiplexing method (TMM). The current–voltage (I–V) curve of a silicon device is usually computed with traditional device simulators of technology computer-aided design (TCAD) based on the finite-element method (FEM). However, for the design of 3D p + -π-p + and n + -ν-n + diffusible resistors, they show a high computational cost and convergence that may fail with fully non-separable 3D dopant concentration profiles as observed in many diffusible resistors resulting from laser trimming. These problems are avoided with the proposed TMM, which divides the 3D resistor into one-dimensional (1D) thin tubes with longitudinal axes following the main orientation of the average electrical field in the tubes. The I–V curve is rapidly obtained for a device with a realistic 3D dopant profile, since a system of three first-order ordinary differential equations has to be solved for each 1D multiplexed tube with the TMM instead of three second-order partial differential equations in the traditional TCADs. Simulations with the TMM are successfully compared to experimental results from silicon-based 3D resistors fabricated by laser-induced dopant diffusion in the gaps of MOSFETs (metal-oxide-semiconductor field-effect transistors) without initial gate. Using thin tubes with other shapes than parallelepipeds as ring segments with toroidal lateral surfaces, the TMM can be generalized to electronic devices with other types of 3D diffusible microstructures

Friction and diffusion of a nano-colloidal disk in a two-dimensional solvent with a liquid-liquid transition.

Science.gov (United States)

Torres-Carbajal, Alexis; Castañeda-Priego, Ramón

2018-03-07

We report on the friction and diffusion of a single mobile nano-colloidal disk, whose size and mass are one and two orders of magnitude, respectively, greater than the molecules of the host solvent; all particles are restricted to move in a two-dimensional space. Using molecular dynamics simulations, the variation of the transport coefficients as a function of the thermodynamic state of the supporting fluid, in particular, around those states in the neighbourhood of the liquid-liquid phase coexistence, is investigated. The diffusion coefficient is determined through the fit of the mean-square displacement at long times and with the Green-Kubo relationship for the velocity autocorrelation function, whereas the friction coefficient is computed from the correlation of the fluctuating force. From the determination of the transport properties, the applicability of the Stokes-Einstein relation in two dimensions around the second critical point is discussed.

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

Computational modelling for diffusion of neutrons problems inside nuclear multiplying medium on bidimensional cartesian rectangular geometry

International Nuclear Information System (INIS)

Couto, Nozimar do

2003-01-01

Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k eff ) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)

Reliability Analysis Based on a Jump Diffusion Model with Two Wiener Processes for Cloud Computing with Big Data

Directory of Open Access Journals (Sweden)

Yoshinobu Tamura

2015-06-01

Full Text Available At present, many cloud services are managed by using open source software, such as OpenStack and Eucalyptus, because of the unification management of data, cost reduction, quick delivery and work savings. The operation phase of cloud computing has a unique feature, such as the provisioning processes, the network-based operation and the diversity of data, because the operation phase of cloud computing changes depending on many external factors. We propose a jump diffusion model with two-dimensional Wiener processes in order to consider the interesting aspects of the network traffic and big data on cloud computing. In particular, we assess the stability of cloud software by using the sample paths obtained from the jump diffusion model with two-dimensional Wiener processes. Moreover, we discuss the optimal maintenance problem based on the proposed jump diffusion model. Furthermore, we analyze actual data to show numerical examples of dependability optimization based on the software maintenance cost considering big data on cloud computing.

Computational modelling for diffusion of neutrons problems inside nuclear multiplying medium on bidimensional cartesian rectangular geometry; Modelagem computacional de problemas de difusao de neutrons em meios multiplicativos em geometria retangular cartesiana bi-dimensional

Energy Technology Data Exchange (ETDEWEB)

Couto, Nozimar do

2003-07-01

Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)

A simplified, coarse-mesh, three-dimensional diffusion scheme for calculating the gross power distribution in a boiling water reactor

International Nuclear Information System (INIS)

Borresen, S.

1995-01-01

A simplified, finite-difference diffusion scheme for a three-dimensional calculation of the gross power distribution in the core of a boiling water reactor (BWR) is presented. Results obtained in a series of one- and two-dimensional test cases indicate that this method may be of sufficient accuracy and simplicity for implementation in BWR-simulator computer programs. Computer requirements are very modest; thus, only 3N memory locations are required for in-core treatment of the inner iteration in the solution of a problem with N mesh points. The mesh width may be chosen equal to the fuel assembly pitch. Input data are in the form of conventional 2-group diffusion parameters. It is concluded that the method presented has definite advantages in comparison with the nodal coupling method. (author)

Diffusive transport in a one dimensional disordered potential involving correlations

International Nuclear Information System (INIS)

Monthus, C.; Paris-6 Univ., 75

1995-03-01

Transport properties of one dimensional Brownian diffusion under the influence of a quenched random force, distributed as a two-level Poisson process is discussed. Large time scaling laws of the position of the Brownian particle, and the probability distribution of the stationary flux going through a sample between two prescribed concentrations are studied. (author) 14 refs.; 3 figs

Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2012-01-01

We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the Schrödinger equation. The transformed Fokker-Planck equation and its solutions are obtained in explicit form.

Optimized two-dimensional Sn transport (BISTRO)

International Nuclear Information System (INIS)

Palmiotti, G.; Salvatores, M.; Gho, C.

1990-01-01

This paper reports on an S n two-dimensional transport module developed for the French fast reactor code system CCRR to optimize algorithms in order to obtain the best performance in terms of computational time. A form of diffusion synthetic acceleration was adopted, and a special effort was made to solve the associated diffusion equation efficiently. The improvements in the algorithms, along with the use of an efficient programming language, led to a significant gain in computational time with respect to the DOT code

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

International Nuclear Information System (INIS)

Okabe, Y.

1985-01-01

The [α,β,γ]-Langevin equation describes the time evolution of a real stationary process with T-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [α,β,γ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics. (orig.)

Application of space-angle synthesis to two-dimensional neutral-particle transport problems of weapon physics

International Nuclear Information System (INIS)

Roberds, R.M.

1975-01-01

A space-angle synthesis (SAS) method has been developed for treating the steady-state, two-dimensional transport of neutrons and gamma rays from a point source of simulated nuclear weapon radiation in air. The method was validated by applying it to the problem of neutron transport from a point source in air over a ground interface, and then comparing the results to those obtained by DOT, a state-of-the-art, discrete-ordinates code. In the SAS method, the energy dependence of the Boltzmann transport equation was treated in the standard multigroup manner. The angular dependence was treated by expanding the flux in specially tailored trial functions and applying the method of weighted residuals which analytically integrated the transport equation over all angles. The weighted-residual approach was analogous to the conventional spherical-harmonics (P/sub N/) method with the exception that the tailored expansion allowed for more rapid convergence than a spherical-harmonics P 1 expansion and resulted in a greater degree of accuracy. The trial functions used in the expansion were odd and even combinations of selected trial solutions, the trial solutions being shaped ellipsoids which approximated the angular distribution of the neutron flux in one-dimensional space. The parameters which described the shape of the ellipsoid varied with energy group and the spatial medium, only, and were obtained from a one-dimensional discrete-ordinates calculation. Thus, approximate transport solutions were made available for all two-dimensional problems of a certain class by using tabulated parameters obtained from a single, one-dimensional calculation

Void Formation during Diffusion - Two-Dimensional Approach

Science.gov (United States)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

Complex of two-dimensional multigroup programs for neutron-physical computations of nuclear reactor

International Nuclear Information System (INIS)

Karpov, V.A.; Protsenko, A.N.

1975-01-01

Briefly stated mathematical aspects of the two-dimensional multigroup method of neutron-physical computation of nuclear reactor. Problems of algorithmization and BESM-6 computer realisation of multigroup diffuse approximations in hexagonal and rectangular calculated lattices are analysed. The results of computation of fast critical assembly having complicated composition of the core are given. The estimation of computation accuracy of criticality, neutron fields distribution and efficiency of absorbing rods by means of computer programs developed is done. (author)

THE DECAY OF A WEAK LARGE-SCALE MAGNETIC FIELD IN TWO-DIMENSIONAL TURBULENCE

Energy Technology Data Exchange (ETDEWEB)

Kondić, Todor; Hughes, David W.; Tobias, Steven M., E-mail: t.kondic@leeds.ac.uk [Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)

2016-06-01

We investigate the decay of a large-scale magnetic field in the context of incompressible, two-dimensional magnetohydrodynamic turbulence. It is well established that a very weak mean field, of strength significantly below equipartition value, induces a small-scale field strong enough to inhibit the process of turbulent magnetic diffusion. In light of ever-increasing computer power, we revisit this problem to investigate fluids and magnetic Reynolds numbers that were previously inaccessible. Furthermore, by exploiting the relation between the turbulent diffusion of the magnetic potential and that of the magnetic field, we are able to calculate the turbulent magnetic diffusivity extremely accurately through the imposition of a uniform mean magnetic field. We confirm the strong dependence of the turbulent diffusivity on the product of the magnetic Reynolds number and the energy of the large-scale magnetic field. We compare our findings with various theoretical descriptions of this process.

Diffusion and sorption in particles and two-dimensional dispersion in a porous media

International Nuclear Information System (INIS)

Rasmuson, A.

1980-01-01

A solution of the two-dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double-integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady-state condition is obtained after long time. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady-state value. A method for integrating the infinite double integral is given. Some typical examples are shown. (Auth.)

Two-dimensional transport of tokamak plasmas

International Nuclear Information System (INIS)

Hirshman, S.P.; Jardin, S.C.

1979-01-01

A reduced set of two-fluid transport equations is obtained from the conservation equations describing the time evolution of the differential particle number, entropy, and magnetic fluxes in an axisymmetric toroidal plasma with nested magnetic surfaces. Expanding in the small ratio of perpendicular to parallel mobilities and thermal conductivities yields as solubility constraints one-dimensional equations for the surface-averaged thermodynamic variables and magnetic fluxes. Since Ohm's law E +u x B =R', where R' accounts for any nonideal effects, only determines the particle flow relative to the diffusing magnetic surfaces, it is necessary to solve a single two-dimensional generalized differential equation, (partial/partialt) delpsi. (delp - J x B) =0, to find the absolute velocity of a magnetic surface enclosing a fixed toroidal flux. This equation is linear but nonstandard in that it involves flux surface averages of the unknown velocity. Specification of R' and the cross-field ion and electron heat fluxes provides a closed system of equations. A time-dependent coordinate transformation is used to describe the diffusion of plasma quantities through magnetic surfaces of changing shape

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

Science.gov (United States)

Lai, King C.; Liu, Da-Jiang; Evans, James W.

2017-12-01

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal (100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN˜ N-β with β =3 /2 . However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N mediated diffusion with small β 2 for N =Np+1 and Np+2 also for moderate sizes 9 ≤N ≤O (102) ; (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲β analysis must account for a strong enhancement of diffusivity for short time increments due to back correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground-state and low-lying excited state cluster configurations, and also of kink populations.

Basic problems and solution methods for two-dimensional continuous 3 × 3 order hidden Markov model

International Nuclear Information System (INIS)

Wang, Guo-gang; Tang, Gui-jin; Gan, Zong-liang; Cui, Zi-guan; Zhu, Xiu-chang

2016-01-01

A novel model referred to as two-dimensional continuous 3 × 3 order hidden Markov model is put forward to avoid the disadvantages of the classical hypothesis of two-dimensional continuous hidden Markov model. This paper presents three equivalent definitions of the model, in which the state transition probability relies on not only immediate horizontal and vertical states but also immediate diagonal state, and in which the probability density of the observation relies on not only current state but also immediate horizontal and vertical states. The paper focuses on the three basic problems of the model, namely probability density calculation, parameters estimation and path backtracking. Some algorithms solving the questions are theoretically derived, by exploiting the idea that the sequences of states on rows or columns of the model can be viewed as states of a one-dimensional continuous 1 × 2 order hidden Markov model. Simulation results further demonstrate the performance of the algorithms. Because there are more statistical characteristics in the structure of the proposed new model, it can more accurately describe some practical problems, as compared to two-dimensional continuous hidden Markov model.

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.

Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method

Directory of Open Access Journals (Sweden)

Marek Danielewski

2015-01-01

Full Text Available The problem of Kirkendall’s trajectories in finite, three- and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: (i multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, (ii multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and (iii a Kirkendall plane that coincides with the interphase interface. The details of the deformation (material trajectories in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.

A study to reduce the numerical diffusion of upwind scheme in two dimensional convection phenomena analysis

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)

An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

Science.gov (United States)

Shiangjen, Kanokwatt; Chaijaruwanich, Jeerayut; Srisujjalertwaja, Wijak; Unachak, Prakarn; Somhom, Samerkae

2018-02-01

This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. The iterative local search along with a shift strategy is developed and applied to the heuristic to balance the exploitation and exploration tasks in the solution space without the tuning of any parameters. The experimental results on many scales of packing problems show that this approach can produce high-quality solutions for most of the benchmark datasets, especially for large-scale problems, within a reasonable duration of computational time.

Diffusion Under Geometrical Constraint

OpenAIRE

Ogawa, Naohisa

2014-01-01

Here we discus the diffusion of particles in a curved tube. This kind of transport phenomenon is observed in biological cells and porous media. To solve such a problem, we discuss the three dimensional diffusion equation with a confining wall forming a thinner tube. We find that the curvature appears in a effective diffusion coefficient for such a quasi-one-dimensional system. As an application to higher dimensional case, we discuss the diffusion in a curved surface with ...

Neutronics code VALE for two-dimensional triagonal (hexagonal) and three-dimensional geometries

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.

1981-08-01

This report documents the computer code VALE designed to solve multigroup neutronics problems with the diffusion theory approximation to neutron transport for a triagonal arrangement of mesh points on planes in two- and three-dimensional geometry. This code parallels the VENTURE neutronics code in the local computation system, making exposure and fuel management capabilities available. It uses and generates interface data files adopted in the cooperative effort sponsored by Reactor Physics RRT Division of the US DOE. The programming in FORTRAN is straightforward, although data is transferred in blocks between auxiliary storage devices and main core, and direct access schemes are used. The size of problems which can be handled is essentially limited only by cost of calculation since the arrays are variably dimensioned. The memory requirement is held down while data transfer during iteration is increased only as necessary with problem size. There is provision for the more common boundary conditions including the repeating boundary, 180 0 rotational symmetry, and the rotational symmetry conditions for the 30 0 , 60 0 , and 120 0 triangular grids on planes. A variety of types of problems may be solved: the usual neutron flux eignevalue problem, or a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations. The adjoint problem and fixed source problem may be solved, as well as the dominating higher harmonic, or the importance problem for an arbitrary fixed source

Quasilinear diffusion in inhomogeneous plasmas

International Nuclear Information System (INIS)

Hooley, D.L.

1975-05-01

The problem of inhomogeneous diffusion in a plasma is considered with emphasis on its possible application to relativistic electron beams. A one-dimensional model with a background electrostatic field is used to illustrate the basic approach, which is then extended to a two-dimensional plasma with a background magnetic field. Only preliminary results are available. (U.S.)

Two-dimensional time dependent Riemann solvers for neutron transport

International Nuclear Information System (INIS)

Brunner, Thomas A.; Holloway, James Paul

2005-01-01

A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

Fractional calculus phenomenology in two-dimensional plasma models

Science.gov (United States)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Modifications in the Teach-C computer code for convection analysis-two-dimensional transient diffusion

International Nuclear Information System (INIS)

Sampaio, P.A.B. de.

1987-08-01

Some modifications in Teach-C computer program to analyse the heat conduction with convective heat transport are presented. The utilization of the program to solve a convective - diffusion problem is studied and the results are compared with an analysis of the same problem, in steady - state conditions, by finite element method [pt

Moving boundary - Oxygen diffusion. Two algorithms using Landau transformation

International Nuclear Information System (INIS)

Moyano, E.A.

1991-01-01

A description is made of two algorithms which solve a mathematical model destinated for the study of one-dimensional problems with moving boundaries and implicit boundary conditions. The Landau transformation is used in both methods for each temporal level so as to work all through with the same amount of nodes. Thus, it is necessary to deal with a partial differential equation whose diffusive and convective terms are accompanied by variable coefficients. The partial differential equation is made discrete implicitly, using the Laasonen scheme -which is always stable- instead of the Crank-Nicholson scheme, as performed by Ferris and Hill (5), in the fixed time passing method. The second method employs the tridiagonal algorithm. The first algorithm uses fixed time passing and iterates with variable interface positions, that is to say, it varies δs until it satisfies the boundary condition. The mathematical model describes oxygen diffusion in live tissues. Its numerical solution is obtained by finite differences. An important application of this method could be the estimation of the radiation dose in cancerous tumor treatment. (Author) [es

Probability representations of a class of two-way diffusions

Energy Technology Data Exchange (ETDEWEB)

Clifford, P.; Green, N.J.P. [Department of Statistics, University of Oxford, Oxford (United Kingdom); Feng, J.F. [COGS, Sussex University, Brighton (United Kingdom); Wei, G. [Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong (China)

2002-07-19

There has been little progress in the analysis of two-way diffusion in the last few decades due to the difficulties brought by the interface section similar to a free boundary condition. In this paper, however, the equivalent probability model is considered and the interface section is precisely described by an integral equation. The solution of two-way diffusion is then expressed in an integral form with the integrand being the solution of a classical first passage time model and the solution of a one-dimensional integral equation which is relatively easier to solve. The exact expression of the two-way diffusion enables us to find the explicit solution of the model with infinite horizontal boundaries and without drifting. (author)

On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

Directory of Open Access Journals (Sweden)

Luisa Consiglieri

2011-01-01

Full Text Available We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration. The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple. Our first novelty comes from this general dynamical boundary condition. The second one is the three-dimensional behaviour of the extracellular stimulus. An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.

Two-dimensional position sensitive Si(Li) detector

International Nuclear Information System (INIS)

Walton, J.T.; Hubbard, G.S.; Haller, E.E.; Sommer, H.A.

1978-11-01

Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n + resisitive layer for one contact and a boron implanted p + resistive layer for the second contact. A position resolution of the order of 100 μm is indicated

On two-spectra inverse problems

OpenAIRE

Guliyev, Namig J.

2018-01-01

We consider a two-spectra inverse problem for the one-dimensional Schr\\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this problem.

Two-dimensional geometrical corner singularities in neutron diffusion. Part 2: Application to the SNR-300 benchmark

International Nuclear Information System (INIS)

Cacuci, D.G.; Univ. of Karlsruhe; Kiefhaber, E.; Stehle, B.

1998-01-01

The explicit solution developed by Cacuci for the multigroup neutron diffusion equation at interior corners in two-dimensional two-region domains has been applied to the SNR-300 fast reactor prototype design to obtain the exact behavior of the multigroup fluxes at and around typical corners arising between absorber/fuel and follower/fuel assemblies. The calculations have been performed in hexagonal geometry using four energy groups, and the results clearly show that the multigroup fluxes are finite but not analytical at interior corners. In particular, already the first-order spatial derivatives of the multigroup fluxes become unbounded at the corners between follower and fuel assemblies. These results highlight the need to treat properly the influence of corners, both for the direct calculation and for the reconstruction of pointwise neutron flux and power distributions in heterogeneous reactor cores

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

BASHAN: A few-group three-dimensional diffusion code with burnup and fuel management features

International Nuclear Information System (INIS)

Pearce, D.F.

1970-12-01

The diffusion equation for a two or three-dimensional, two-group or multi-group downscatter problem is solved by conventional finite difference techniques. An x-y-z geometry is assumed with an 'in-channel' mesh point representation. Options are available which allow representation of a soluble poison dispersed throughout the reactor, and also absorber rods in specified channels. The power distribution and multiplication factor k eff are calculated and a point rating map is used to advance the irradiation at each mesh point by a specified time-step so that burnup is followed. Fuel changes may be made so that radial shuffling and axial shuffling fuel management schemes can be studies. The code has been written in FORTRAN S2 for an IBM 7030 (STRETCH) computer which, with a fast store of 80,000 locations, allows problems of up to 15,000 mesh points to be dealt with. Conversion to FORTRAN IV for IBM 360 has now been completed. (author)

CINESP - computational program of spatial kinetics for nuclear reactors in the one-two dimension multigroup diffusion theory

International Nuclear Information System (INIS)

Santos, R.S. dos

1993-01-01

This paper presents a computational program to solve numerically the reactor kinetics equations in the multigroup diffusion theory. One or two-dimensional problems in cylindrical or Cartesian geometries, with any number of energy and delayed-neutron precursors groups are dealt with. The main input and output of the program are briefly discussed. Various results demonstrate the accuracy and versatility of the program, when compared with other kinetics programs. (author)

All-optical evaluation of spin-orbit interaction based on diffusive spin motion in a two-dimensional electron gas

Energy Technology Data Exchange (ETDEWEB)

Kohda, M. [IBM Research–Zürich, Säumerstrasse 4, CH-8803 Rüschlikon (Switzerland); Department of Materials Science, Tohoku University, 980-8579 Sendai (Japan); Altmann, P.; Salis, G. [IBM Research–Zürich, Säumerstrasse 4, CH-8803 Rüschlikon (Switzerland); Schuh, D.; Ganichev, S. D. [Institute of Experimental and Applied Physics, University of Regensburg, D-93040 Regensburg (Germany); Wegscheider, W. [Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich (Switzerland)

2015-10-26

A method is presented that enables the measurement of spin-orbit coefficients in a diffusive two-dimensional electron gas without the need for processing the sample structure, applying electrical currents or resolving the spatial pattern of the spin mode. It is based on the dependence of the average electron velocity on the spatial distance between local excitation and detection of spin polarization, resulting in a variation of spin precession frequency that in an external magnetic field is linear in the spatial separation. By scanning the relative positions of the exciting and probing spots in a time-resolved Kerr rotation microscope, frequency gradients along the [100] and [010] crystal axes of GaAs/AlGaAs QWs are measured to obtain the Rashba and Dresselhaus spin-orbit coefficients, α and β. This simple method can be applied in a variety of materials with electron diffusion for evaluating spin-orbit coefficients.

Generation of a library of two-group diffusion parameters for SPPS-1,6 by HELIOS

International Nuclear Information System (INIS)

Petkov, P.T.; Haralampieva, C.V.; Simeonov, T.; Stojanova, I.; Kamenov, K.

2000-01-01

The two-group three-dimensional nodal diffusion code SPPS-1.6 has been used for many years for steady-state neutronics calculations of the WWER-440 reactors at Kozloduy NPP. The old library of two-group diffusion parameters for SPPS-1.6 has been generated by WIMSD4 with a nuclear data library compiled from three different libraries. The current paper presents our experience in generating a new library for SPPS-1.6 by the HELIOS lattice code. The accuracy of the current-coupling collision probability (CCCP) method in calculating a single WWER-440 assembly has been studied first. Among all possible angular discretization of the interface partial currents, called coupling orders, only coupling order 3 is suitable for hexagonal cells. Dividing each cell side into 3 segments an accuracy of 100 pcm has been achieved. The accuracy in calculating the absorber problem was estimated at 1%, which means about 10% error in the control assemblies efficiency. The accuracy for small core-reflector problems is 1% as well. The general conclusion is that HELIOS is accurate enough for assembly calculations, but inadequate for absorber and core-reflector problems. (Authors)

Perturbation on diffusion problems in domain with interfaces

International Nuclear Information System (INIS)

Watson, F.V.

1985-01-01

A perturbative type algorithm for the solution of linear diffusion equation at two dimensions, in domain with interfaces is presented. The perturbative scheme should be assembled in the weak formulation of diffusion equation, even if the strong solution exists, and when it is taken in terms superiors to first order, it should be calculated analytically, in one of the dimensions to avoid problems of slow convergence. (M.C.K.) [pt

Developing cross entropy genetic algorithm for solving Two-Dimensional Loading Heterogeneous Fleet Vehicle Routing Problem (2L-HFVRP)

Science.gov (United States)

Paramestha, D. L.; Santosa, B.

2018-04-01

Two-dimensional Loading Heterogeneous Fleet Vehicle Routing Problem (2L-HFVRP) is a combination of Heterogeneous Fleet VRP and a packing problem well-known as Two-Dimensional Bin Packing Problem (BPP). 2L-HFVRP is a Heterogeneous Fleet VRP in which these costumer demands are formed by a set of two-dimensional rectangular weighted item. These demands must be served by a heterogeneous fleet of vehicles with a fix and variable cost from the depot. The objective function 2L-HFVRP is to minimize the total transportation cost. All formed routes must be consistent with the capacity and loading process of the vehicle. Sequential and unrestricted scenarios are considered in this paper. We propose a metaheuristic which is a combination of the Genetic Algorithm (GA) and the Cross Entropy (CE) named Cross Entropy Genetic Algorithm (CEGA) to solve the 2L-HFVRP. The mutation concept on GA is used to speed up the algorithm CE to find the optimal solution. The mutation mechanism was based on local improvement (2-opt, 1-1 Exchange, and 1-0 Exchange). The probability transition matrix mechanism on CE is used to avoid getting stuck in the local optimum. The effectiveness of CEGA was tested on benchmark instance based 2L-HFVRP. The result of experiments shows a competitive result compared with the other algorithm.

Vibrations of thin piezoelectric shallow shells: Two-dimensional ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

In this paper we consider the eigenvalue problem for piezoelectric shallow shells and we show that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a two- dimensional eigenvalue problem. Keywords. Vibrations; piezoelectricity ...

Explicit formulation of a nodal transport method for discrete ordinates calculations in two-dimensional fixed-source problems

Energy Technology Data Exchange (ETDEWEB)

Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Prolo Filho, Joao Francisco [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica, Estatistica e Fisica; Dias da Cunha, Rudnei; Basso Barichello, Liliane [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica

2014-04-15

In this work a study of two-dimensional fixed-source neutron transport problems, in Cartesian geometry, is reported. The approach reduces the complexity of the multidimensional problem using a combination of nodal schemes and the Analytical Discrete Ordinates Method (ADO). The unknown leakage terms on the boundaries that appear from the use of the derivation of the nodal scheme are incorporated to the problem source term, such as to couple the one-dimensional integrated solutions, made explicit in terms of the x and y spatial variables. The formulation leads to a considerable reduction of the order of the associated eigenvalue problems when combined with the usual symmetric quadratures, thereby providing solutions that have a higher degree of computational efficiency. Reflective-type boundary conditions are introduced to represent the domain on a simpler form than that previously considered in connection with the ADO method. Numerical results obtained with the technique are provided and compared to those present in the literature. (orig.)

Application of the finite element method to neutronics problems with inhomogeneous boundray conditions

International Nuclear Information System (INIS)

Yoo, K.J.

1982-01-01

The albedo boundary conditions are incorporated into the finite element method using bicubic Hermite element functions in order to reduce the computer memory and computation time in two-group diffusion calculations by excluding the reflector regions in computation space. The basis functions at the core-reflector interfaces are newly established to satisfy the albedo boundary conditions, and then the ''weak'' form of two-group diffusion equations is discretized using the principle of the weighted residual method in combination with the Galerkin approximation. The discretized two-group diffusion equation is then solved by the Gaussian elimination method with the scaled column pivoting algorithm in one-dimensional problem and Gauss-Seidel method in two-dimensional problem. Prior to the application of the method to two-group diffusion problems, the same method is applied to the one-speed neutron transport equation in a bare slab reactor with the vacuum boundary condition to confirm its usefulness in the diffusion calculations. To investigate the applicability of our diffusion method, several numerical calculations are performed: two-dimensional IAEA benchmark problem and two-dimensional ZION problem. The results are compared with the available results from the conventional finite difference and other finite element methods. If the albedo values are appropriately adjusted, our results of the two-dimensional IAEA benchmark problem are agreed within 0.002% of ksub(eff) with the fine mesh PDQ results. Comparing with CITATION results, one-eighth of core memory and one-fifteenth of computing time are required to obtain the same accuracy even though no acceleration technique is used in the present case. Also, it is found that the results are comparable with the other finite element results. However, no significant saving is obtained in computation time comparing with the other finite element results, where the reflector regions are explicity included. This mainly comes from

Two-dimensional theory of ionization waves in the contracted discharge of noble gases

International Nuclear Information System (INIS)

Golubovskij, Ju.B.; Kolobov, V.I.; Tsendin, L.D.

1985-01-01

The mechanism of instability generating ionization waves in contracted neon and argon discharges is connected to its two-dimensional structure. The two-dimensional perturbations of sausage-type may have the most increment. The numerical solution of the ambipolar diffusion equation and qualitative asymptotic solutions showed that the situation differs greatly from diffuse discharges at low pressure, where the waves of large wave number are instable. In the case discussed, there is a wave number interval of unstable waves. (D.Gy.)

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Science.gov (United States)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Control Operator for the Two-Dimensional Energized Wave Equation

Directory of Open Access Journals (Sweden)

Sunday Augustus REJU

2006-07-01

Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

Self-diffusion in monodisperse three-dimensional magnetic fluids by molecular dynamics simulations

Energy Technology Data Exchange (ETDEWEB)

Dobroserdova, A.B. [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); Kantorovich, S.S., E-mail: alla.dobroserdova@urfu.ru [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); University of Vienna, Sensengasse 8, Vienna (Austria)

2017-06-01

In the present work we study the self-diffusion behaviour in the three-dimensional monodisperse magnetic fluids using the Molecular Dynamics Simulation and Density Functional Theory. The peculiarity of computer simulation is to study two different systems: dipolar and soft sphere ones. In the theoretical method, it is important to choose the approximation for the main structures, which are chains. We compare the theoretical results and the computer simulation data for the self-diffusion coefficient as a function of the particle volume fraction and magnetic dipole-dipole interaction parameter and find the qualitative and quantitative agreement to be good. - Highlights: • The paper deals with the study of the self-diffusion in monodisperse three-dimensional magnetic fluids. • The theoretical approach contains the free energy density functional minimization. • Computer simulations are performed by the molecular dynamics method. • We have a good qualitative and quantitative agreement between the theoretical results and computer simulation data.

DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry

International Nuclear Information System (INIS)

Lawrence, R.D.

1983-03-01

A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code

Few helium atoms in quasi two-dimensional space

International Nuclear Information System (INIS)

Kilic, Srecko; Vranjes, Leandra

2003-01-01

Two, three and four 3 He and 4 He atoms in quasi two-dimensional space above graphite and cesium surfaces and in 'harmonic' potential perpendicular to the surface have been studied. Using some previously examined variational wave functions and the Diffusion Monte Carlo procedure, it has been shown that all molecules: dimers, trimers and tetramers, are bound more strongly than in pure two- and three-dimensional space. The enhancement of binding with respect to unrestricted space is more pronounced on cesium than on graphite. Furthermore, for 3 He 3 ( 3 He 4 ) on all studied surfaces, there is an indication that the configuration of a dimer and a 'free' particle (two dimers) may be equivalently established

Relativistic collective diffusion in one-dimensional systems

Science.gov (United States)

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

2018-05-01

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

A two-dimensional transport-problem in magnetized plasmas

International Nuclear Information System (INIS)

Sigmar, D.J.; Adam, G.; Hittmair, O.

1975-01-01

It is shown that by a generalization of the classical theory for a cylindrical plasma the expression for the so-called banana-diffusion in a toroidal plasma may be deduced. The ratio of the coefficient of the banana-diffusion to the one of classical diffusion is discussed. (Auth.)

Two-dimensional calculus

CERN Document Server

Osserman, Robert

2011-01-01

The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

Influence of the transversal diffusion/dispersion on the radionuclide migration in porous media - investigation of analytically solvable problems for geological layer structures. Der Einfluss der transversalen Diffusion/Dispersion auf die Migration von Radionukliden in poroesen Medien - Untersuchung analytisch loesbarer Probleme fuer geolog. Schichtstrukturen

Energy Technology Data Exchange (ETDEWEB)

Schmocker, U

1980-07-01

Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository. In risk analyses for waste repositories the migration of radionuclides through the geosphere is usually described mathematically by a one-dimensional transport model. On the other hand the hydrological calculational models used for determining the critical migration paths are invariably two- or three-dimensional. A one-dimensional transport calculation always gives conservative results for a specific migration path because the influence of the transverse dispersion/diffusion effect is neglected. This effect results in an additional decrease of the nuclide concentration along the migration path. On the other hand radionuclides can spread to adjacent geological formations which are not taken into account in a one-dimensional model. If the water velocities in these formations are higher than along the original (one-dimensional) migration path or if the distance to the biosphere (e.g. lake, river or well) is shorter, then the process of the transverse diffusion/dispersion can represent an additional risk. The present work deals with the influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere. We restrict ourselves to migration in porous media which is the standard approach of most existing transport models. For modelling the transport of radionuclides in fissured systems there exist only a few preliminary calculational approaches to date. We are mainly interested in analytically soluble problems which take into account the transverse diffusion/dispersion effect. This procedure permits investigation of the most important effects in a simple and direct manner. 17 refs., 36 figs., 2 tabs.

A two-dimensional, semi-analytic expansion method for nodal calculations

International Nuclear Information System (INIS)

Palmtag, S.P.

1995-08-01

Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure

Two-dimensional diffusion limited system for cell growth

International Nuclear Information System (INIS)

Hlatky, L.

1985-11-01

A new cell system, the ''sandwich'' system, was developed to supplement multicellular spheroids as tumor analogues. Sandwiches allow new experimental approaches to questions of diffusion, cell cycle effects and radiation resistance in tumors. In this thesis the method for setting up sandwiches is described both theoretically and experimentally followed by its use in x-ray irradiation studies. In the sandwich system, cells are grown in a narrow gap between two glass slides. Where nutrients and waste products can move into or out of the local environment of the cells only by diffusing through the narrow gap between the slides. Due to the competition between cells, self-created gradients of nutrients and metabolic products are set up resulting in a layer of cells which resembles a living spheroid cross section. Unlike the cells of the spheroid, however, cells in all regions of the sandwich are visible. Therefore, the relative sizes of the regions and their time-dependent growth can be monitored visually without fixation or sectioning. The oxygen and nutrient gradients can be ''turned off'' at any time without disrupting the spatial arrangement of the cells by removing the top slide of the assembly and subsequently turned back on if desired. Removal of the top slide also provides access to all the cells, including those near the necrotic center, of the sandwich. The cells can then be removed for analysis outside the sandwich system. 61 refs., 17 figs

Influence of blocking effect and energetic disorder on diffusion in one-dimensional lattice

International Nuclear Information System (INIS)

Mai Thi Lan; Nguyen Van Hong; Nguyen Thu Nhan; Hoang Van Hue

2014-01-01

The diffusion in one-dimensional disordered lattice with Gaussian distribution of site and transition energies has been studied by mean of kinetic Monte-Carlo simulation. We focus on investigating the influence of energetic disorders and diffusive particle density on diffusivity. In single-particle case, we used both analytical method and kinetic Monte-Carlo simulation to calculate the quantities that relate to diffusive behavior in disordered systems such as the mean time between two consecutive jumps, correlation factor and diffusion coefficient. The calculation shows a good agreement between analytical and simulation results for all disordered lattice types. In many - particle case, the blocking effect results in decreasing correlation factor F and average time τ jump between two consecutive jumps. With increasing the number of particles, the diffusion coefficient D M decreases for site-energy and transition-energy disordered lattices due to the F-effect affect affects stronger than τ-effect. Furthermore, the blocking effect almost is temperature independent for both lattices. (author)

Sufficient Controllability Condition for Affine Systems with Two-Dimensional Control and Two-Dimensional Zero Dynamics

Directory of Open Access Journals (Sweden)

D. A. Fetisov

2015-01-01

Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved

Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems.

Science.gov (United States)

Yalavarthy, Phaneendra K; Lynch, Daniel R; Pogue, Brian W; Dehghani, Hamid; Paulsen, Keith D

2008-05-01

Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

An Adaptive Approach to Variational Nodal Diffusion Problems

International Nuclear Information System (INIS)

Zhang Hui; Lewis, E.E.

2001-01-01

An adaptive grid method is presented for the solution of neutron diffusion problems in two dimensions. The primal hybrid finite elements employed in the variational nodal method are used to reduce the diffusion equation to a coupled set of elemental response matrices. An a posteriori error estimator is developed to indicate the magnitude of local errors stemming from the low-order elemental interface approximations. An iterative procedure is implemented in which p refinement is applied locally by increasing the polynomial order of the interface approximations. The automated algorithm utilizes the a posteriori estimator to achieve local error reductions until an acceptable level of accuracy is reached throughout the problem domain. Application to a series of X-Y benchmark problems indicates the reduction of computational effort achievable by replacing uniform with adaptive refinement of the spatial approximations

Lorentz covariant tempered distributions in two-dimensional space-time

International Nuclear Information System (INIS)

Zinov'ev, Yu.M.

1989-01-01

The problem of describing Lorentz covariant distributions without any spectral condition has hitherto remained unsolved even for two-dimensional space-time. Attempts to solve this problem have already been made. Zharinov obtained an integral representation for the Laplace transform of Lorentz invariant distributions with support in the product of two-dimensional future light cones. However, this integral representation does not make it possible to obtain a complete description of the corresponding Lorentz invariant distributions. In this paper the author gives a complete description of Lorentz covariant distributions for two-dimensional space-time. No spectral conditions is assumed

Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities

International Nuclear Information System (INIS)

Warsa, James S.; Wareing, Todd A.; Morel, Jim E.

2004-01-01

A loss in the effectiveness of diffusion synthetic acceleration (DSA) schemes has been observed with certain S N discretizations on two-dimensional Cartesian grids in the presence of material discontinuities. We will present more evidence supporting the conjecture that DSA effectiveness will degrade for multidimensional problems with discontinuous total cross sections, regardless of the particular physical configuration or spatial discretization. Fourier analysis and numerical experiments help us identify a set of representative problems for which established DSA schemes are ineffective, focusing on diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look at a fully consistent and a 'partially consistent' DSA method for this discretization. The effectiveness of both methods is shown to degrade significantly. A Fourier analysis of the fully consistent DSA scheme in the limit of decreasing cell optical thickness supports the view that the DSA itself is failing when material discontinuities are present in a problem. We show that a Krylov iterative method, preconditioned with DSA, is an effective remedy that can be used to efficiently compute solutions for this class of problems. We show that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate. In fact, it is preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily. The Krylov method can be implemented in terms of the original S N source iteration coding with only slight modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration

A TWO-DIMENSIONAL POSITION SENSITIVE SI(LI) DETECTOR

Energy Technology Data Exchange (ETDEWEB)

Walton, Jack T.; Hubbard, G. Scott; Haller, Eugene E.; Sommer, Heinrich A.

1978-11-01

Circular, large-area two-dimensional Si(Li) position sensitive detectors have been fabricated. The detectors employ a thin lithium-diffused n{sup +} resistive layer for one contact and a boron implanted p{sup +} resistive layer for the second contact. A position resolution of the order of 100 {micro}m is indicated.

K-FIX: a computer program for transient, two-dimensional, two-fluid flow. THREED: an extension of the K-FIX code for three-dimensional calculations

International Nuclear Information System (INIS)

Rivard, W.C.; Torrey, M.D.

1978-10-01

The transient, two-dimensional, two-fluid code K-FIX has been extended to perform three-dimensional calculations. This capability is achieved by adding five modification sets of FORTRAN statements to the basic two-dimensional code. The modifications are listed and described, and a complete listing of the three-dimensional code is provided. Results of an example problem are provided for verification

Surface harmonics method for two-dimensional time-dependent neutron transport problems of square-lattice nuclear reactors

Energy Technology Data Exchange (ETDEWEB)

Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A. [National Research Centre Kurchatov Institute, Kurchatov Sq. 1, Moscow (Russian Federation)

2013-07-01

Time-dependent equations of the Surface Harmonics Method (SHM) have been derived from the time-dependent neutron transport equation with explicit representation of delayed neutrons for solving the two-dimensional time-dependent problems. These equations have been realized in the SUHAM-TD code. The TWIGL benchmark problem has been used for verification of the SUHAM-TD code. The results of the study showed that computational costs required to achieve necessary accuracy of the solution can be an order of magnitude less than with the use of the conventional finite difference method (FDM). (authors)

One-dimensional Gromov minimal filling problem

International Nuclear Information System (INIS)

Ivanov, Alexandr O; Tuzhilin, Alexey A

2012-01-01

The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures. Bibliography: 38 titles.

Tracer dispersion in two-dimensional rough fractures.

Science.gov (United States)

Drazer, G; Koplik, J

2001-05-01

Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness are studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a boundary condition for tracer particles that improves the accuracy of the method. The reduction in the diffusive transport, due to the fractal geometry of the fracture surfaces, is analyzed for different fracture apertures. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for the irregular geometry of the fractures. Dispersion is studied when the two fracture surfaces are simply displaced normally to the mean fracture plane and when there is a lateral shift as well. Numerical results are analyzed using the Lambda parameter, related to convective transport within the fracture, and simple arguments based on lubrication approximation. At very low Péclet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces dispersion.

Inverse radiative transfer problems in two-dimensional heterogeneous media; Problemas inversos em transferencia radiativa em meios heterogeneos bidimensionais

Energy Technology Data Exchange (ETDEWEB)

Tito, Mariella Janette Berrocal

2001-01-01

The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)

Two-dimensional capillary origami

Energy Technology Data Exchange (ETDEWEB)

Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu

2016-01-08

We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

Two-dimensional capillary origami

International Nuclear Information System (INIS)

Brubaker, N.D.; Lega, J.

2016-01-01

We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

Abrikosov flux-lines in two-band superconductors with mixed dimensionality

International Nuclear Information System (INIS)

Tanaka, K; Eschrig, M

2009-01-01

We study vortex structure in a two-band superconductor, in which one band is ballistic and quasi-two-dimensional (2D), and the other is diffusive and three-dimensional (3D). A circular cell approximation of the vortex lattice within the quasiclassical theory of superconductivity is applied to a recently developed model appropriate for such a two-band system (Tanaka et al 2006 Phys. Rev. B 73 220501(R); Tanaka et al 2007 Phys. Rev. B 75 214512). We assume that superconductivity in the 3D diffusive band is 'weak', i.e. mostly induced, as is the case in MgB 2 . Hybridization with the 'weak' 3D diffusive band has significant and intriguing influence on the electronic structure of the 'strong' 2D ballistic band. In particular, the Coulomb repulsion and the diffusivity in the 'weak' band enhance suppression of the order parameter and enlargement of the vortex core by magnetic field in the 'strong' band, resulting in reduced critical temperature and field. Moreover, increased diffusivity in the 'weak' band can result in an upward curvature of the upper critical field near the transition temperature. A particularly interesting feature found in our model is the appearance of additional bound states at the gap edge in the 'strong' ballistic band, which are absent in the single-band case. Furthermore, coupling with the 'weak' diffusive band leads to reduced bandgaps and van Hove singularities of energy bands of the vortex lattice in the 'strong' ballistic band. We find these intriguing features for parameter values appropriate for MgB 2 .

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

Science.gov (United States)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

HEXAGA-III-120, -30. Three dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering

International Nuclear Information System (INIS)

Woznicki, Z.I.

1983-07-01

This report presents the HEXAGA-III-programme solving multi-group time-independent real and/or adjoint neutron diffusion equations for three-dimensional-triangular-z-geometry. The method of solution is based on the AGA two-sweep iterative method belonging to the family of factorization techniques. An arbitrary neutron scattering model is permitted. The report written for users provides the description of the programme input and output and the use of HEXAGA-III is illustrated by a sample reactor problem. (orig.) [de

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

Science.gov (United States)

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Large Deviations for Two-Time-Scale Diffusions, with Delays

International Nuclear Information System (INIS)

Kushner, Harold J.

2010-01-01

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.

Solution of two energy-group neutron diffusion equation by triangular elements

International Nuclear Information System (INIS)

Correia Filho, A.

1981-01-01

The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt

Method for coupling two-dimensional to three-dimensional discrete ordinates calculations

International Nuclear Information System (INIS)

Thompson, J.L.; Emmett, M.B.; Rhoades, W.A.; Dodds, H.L. Jr.

1985-01-01

A three-dimensional (3-D) discrete ordinates transport code, TORT, has been developed at the Oak Ridge National Laboratory for radiation penetration studies. It is not feasible to solve some 3-D penetration problems with TORT, such as a building located a large distance from a point source, because (a) the discretized 3-D problem is simply too big to fit on the computer or (b) the computing time (and corresponding cost) is prohibitive. Fortunately, such problems can be solved with a hybrid approach by coupling a two-dimensional (2-D) description of the point source, which is assumed to be azimuthally symmetric, to a 3-D description of the building, the region of interest. The purpose of this paper is to describe this hybrid methodology along with its implementation and evaluation in the DOTTOR (Discrete Ordinates to Three-dimensional Oak Ridge Transport) code

Two-dimensional thermofield bosonization

International Nuclear Information System (INIS)

Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

2005-01-01

The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized

An analytical approach for a nodal formulation of a two-dimensional fixed-source neutron transport problem in heterogeneous medium

Energy Technology Data Exchange (ETDEWEB)

Basso Barichello, Liliane; Dias da Cunha, Rudnei [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst. de Matematica; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada

2015-05-15

A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.

User's manual for ONEDANT: a code package for one-dimensional, diffusion-accelerated, neutral-particle transport

International Nuclear Information System (INIS)

O'Dell, R.D.; Brinkley, F.W. Jr.; Marr, D.R.

1982-02-01

ONEDANT is designed for the CDC-7600, but the program has been implemented and run on the IBM-370/190 and CRAY-I computers. ONEDANT solves the one-dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue search) problems subject to vacuum, reflective, periodic, white, albedo, or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. ONEDANT numerically solves the one-dimensional, multigroup form of the neutral-particle, steady-state form of the Boltzmann transport equation. The discrete-ordinates approximation is used for treating the angular variation of the particle distribution and the diamond-difference scheme is used for phase space discretization. Negative fluxes are eliminated by a local set-to-zero-and-correct algorithm. A standard inner (within-group) iteration, outer (energy-group-dependent source) iteration technique is used. Both inner and outer iterations are accelerated using the diffusion synthetic acceleration method

VAMPIR - A two-group two-dimensional diffusion computer code for burnup calculation

International Nuclear Information System (INIS)

Zmijarevic, I.; Petrovic, I.

1985-01-01

VAMPIR is a computer code which simulates the burnup within a reactor coe. It computes the neutron flux, power distribution and burnup taking into account spatial variations of temperature and xenon poisoning. Its overall reactor calculation uses diffusion theory with finite differences approximation in X-Y or R-Z geometry. Two-group macroscopic cross section data are prepared by the lattice cell code WIMS-D4 and stored in the library form of multi entry tabulation against the various parameters that significantly affect the physical conditions in the reactor core. herein, the main features of the program are presented. (author)

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

Science.gov (United States)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Lawrence, R.D.

1983-03-01

A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.

Two-dimensional simulation of reactive diffusion in binary systems

Czech Academy of Sciences Publication Activity Database

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

2014-01-01

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

Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains

Directory of Open Access Journals (Sweden)

Arnaldo Simal do Nascimento

1997-12-01

Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.

NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

International Nuclear Information System (INIS)

Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.

1994-06-01

NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation

Quantum oscillations in quasi-two-dimensional conductors

CERN Document Server

Galbova, O

2002-01-01

The electronic absorption of sound waves in quasi-two-dimensional conductors in strong magnetic fields, is investigated theoretically. A longitudinal acoustic wave, propagating along the normal n-> to the layer of quasi-two-dimensional conductor (k-> = left brace 0,0,k right brace; u-> = left brace 0,0,u right brace) in magnetic field (B-> = left brace 0, 0, B right brace), is considered. The quasiclassical approach for this geometry is of no interest, due to the absence of interaction between electromagnetic and acoustic waves. The problem is of interest in strong magnetic field when quantization of the charge carriers energy levels takes place. The quantum oscillations in the sound absorption coefficient, as a function of the magnetic field, are theoretically observed. The experimental study of the quantum oscillations in quasi-two-dimensional conductors makes it possible to solve the inverse problem of determining from experimental data the extrema closed sections of the Fermi surface by a plane p sub z = ...

Micromachined two dimensional resistor arrays for determination of gas parameters

NARCIS (Netherlands)

van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt

A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of

Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion

Directory of Open Access Journals (Sweden)

H. Kucharek

2000-01-01

Full Text Available In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid. The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2 with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.

Two-dimensional lift-up problem for a rigid porous bed

Energy Technology Data Exchange (ETDEWEB)

Chang, Y.; Huang, L. H.; Yang, F. P. Y. [Department of Civil Engineering, National Taiwan University, Taipei, Taiwan (China)

2015-05-15

The present study analytically reinvestigates the two-dimensional lift-up problem for a rigid porous bed that was studied by Mei, Yeung, and Liu [“Lifting of a large object from a porous seabed,” J. Fluid Mech. 152, 203 (1985)]. Mei, Yeung, and Liu proposed a model that treats the bed as a rigid porous medium and performed relevant experiments. In their model, they assumed the gap flow comes from the periphery of the gap, and there is a shear layer in the porous medium; the flow in the gap is described by adhesion approximation [D. J. Acheson, Elementary Fluid Dynamics (Clarendon, Oxford, 1990), pp. 243-245.] and the pore flow by Darcy’s law, and the slip-flow condition proposed by Beavers and Joseph [“Boundary conditions at a naturally permeable wall,” J. Fluid Mech. 30, 197 (1967)] is applied to the bed interface. In this problem, however, the gap flow initially mainly comes from the porous bed, and the shear layer may not exist. Although later the shear effect becomes important, the empirical slip-flow condition might not physically respond to the shear effect, and the existence of the vertical velocity affects the situation so greatly that the slip-flow condition might not be appropriate. In contrast, the present study proposes a more general model for the problem, applying Stokes flow to the gap, the Brinkman equation to the porous medium, and Song and Huang’s [“Laminar poroelastic media flow,” J. Eng. Mech. 126, 358 (2000)] complete interfacial conditions to the bed interface. The exact solution to the problem is found and fits Mei’s experiments well. The breakout phenomenon is examined for different soil beds, mechanics that cannot be illustrated by Mei’s model are revealed, and the theoretical breakout times obtained using Mei’s model and our model are compared. The results show that the proposed model is more compatible with physics and provides results that are more precise.

Exact Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet

Science.gov (United States)

Belik, V. D.

2018-05-01

The two-dimensional problem on the collision of a potential ideal-liquid jet, outflowing from a reservoir through a nozzle, with an infinite plane obstacle was considered for the case where the distance between the nozzle exit section and the obstacle is finite. An exact solution of this problem has been found using methods of the complex-variable function theory. Simple analytical expressions for the complex velocity of the liquid, its flow rate, and the force of action of the jet on the obstacle have been obtained. The velocity distributions of the liquid at the nozzle exit section, in the region of spreading of the jet, and at the obstacle have been constructed for different distances between the nozzle exit section and the obstacle. Analytical expressions for the thickness of the boundary layer and the Nusselt number at the point of stagnation of the jet have been obtained. A number of distributions of the local friction coefficient and the Nusselt number of the indicated jet are presented.

Determination of neutron buildup factor using analytical solution of one-dimensional neutron diffusion equation in cylindrical geometry

Energy Technology Data Exchange (ETDEWEB)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2011-07-01

The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)

Determination of neutron buildup factor using analytical solution of one-dimensional neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest

2011-01-01

The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)

The Multigroup Neutron Diffusion Equations/1 Space Dimension

Energy Technology Data Exchange (ETDEWEB)

Linde, Sven

1960-06-15

A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix.

The Multigroup Neutron Diffusion Equations/1 Space Dimension

International Nuclear Information System (INIS)

Linde, Sven

1960-06-01

A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix

Experimental determination of the diffusion coefficient in two-dimensions in ferrous sulphate gels using the finite element method

International Nuclear Information System (INIS)

Baldock, C.; Harris, P.J.; Piercy, A.R.; Healy, B.

2001-01-01

A novel two-dimensional finite element method for modelling the diffusion which occurs in Fricke or ferrous sulphate type radiation dosimetry gels is presented. In most of the previous work, the diffusion coefficient has been estimated using simple one-dimensional models. This work presents a two-dimensional model which enables the diffusion coefficient to be determined in a much wider range of experimental situations. The model includes the provision for the determination of a drift parameter. To demonstrate the technique comparative diffusion measurements between ferrous sulphate radiation dosimetry gels, with and without xylenol orange chelating agent and carbohydrate additives have been undertaken. Diffusion coefficients of 9.7±0.4, 13.3±0.6 and 9.5±0.8 10-3 cm 2 per h -1 were determined for ferrous sulphate radiation dosimetry gels with and without xylenol orange and with xylenol orange and sucrose additives respectively. Copyright (2001) Australasian College of Physical Scientists and Engineers in Medicine

Nodal methods with non linear feedback for the three dimensional resolution of the diffusion's multigroup equations

International Nuclear Information System (INIS)

Ferri, A.A.

1986-01-01

Nodal methods applied in order to calculate the power distribution in a nuclear reactor core are presented. These methods have received special attention, because they yield accurate results in short computing times. Present nodal schemes contain several unknowns per node and per group. In the methods presented here, non linear feedback of the coupling coefficients has been applied to reduce this number to only one unknown per node and per group. The resulting algorithm is a 7- points formula, and the iterative process has proved stable in the response matrix scheme. The intranodal flux shape is determined by partial integration of the diffusion equations over two of the coordinates, leading to a set of three coupled one-dimensional equations. These can be solved by using a polynomial approximation or by integration (analytic solution). The tranverse net leakage is responsible for the coupling between the spatial directions, and two alternative methods are presented to evaluate its shape: direct parabolic approximation and local model expansion. Numerical results, which include the IAEA two-dimensional benchmark problem illustrate the efficiency of the developed methods. (M.E.L.) [es

The Dirichlet problem of a conformable advection-diffusion equation

Directory of Open Access Journals (Sweden)

Avci Derya

2017-01-01

Full Text Available The fractional advection-diffusion equations are obtained from a fractional power law for the matter flux. Diffusion processes in special types of porous media which has fractal geometry can be modelled accurately by using these equations. However, the existing nonlocal fractional derivatives seem complicated and also lose some basic properties satisfied by usual derivatives. For these reasons, local fractional calculus has recently been emerged to simplify the complexities of fractional models defined by nonlocal fractional operators. In this work, the conformable, a local, well-behaved and limit-based definition, is used to obtain a local generalized form of advection-diffusion equation. In addition, this study is devoted to give a local generalized description to the combination of diffusive flux governed by Fick’s law and the advection flux associated with the velocity field. As a result, the constitutive conformable advection-diffusion equation can be easily achieved. A Dirichlet problem for conformable advection-diffusion equation is derived by applying fractional Laplace transform with respect to time t and finite sin-Fourier transform with respect to spatial coordinate x. Two illustrative examples are presented to show the behaviours of this new local generalized model. The dependence of the solution on the fractional order of conformable derivative and the changing values of problem parameters are validated using graphics held by MATLcodes.

An analytical discrete ordinates solution for a nodal model of a two-dimensional neutron transport problem

International Nuclear Information System (INIS)

Filho, J. F. P.; Barichello, L. B.

2013-01-01

In this work, an analytical discrete ordinates method is used to solve a nodal formulation of a neutron transport problem in x, y-geometry. The proposed approach leads to an important reduction in the order of the associated eigenvalue systems, when combined with the classical level symmetric quadrature scheme. Auxiliary equations are proposed, as usually required for nodal methods, to express the unknown fluxes at the boundary introduced as additional unknowns in the integrated equations. Numerical results, for the problem defined by a two-dimensional region with a spatially constant and isotropically emitting source, are presented and compared with those available in the literature. (authors)

Waterlike anomalies in a two-dimensional core-softened potential

Science.gov (United States)

Bordin, José Rafael; Barbosa, Marcia C.

2018-02-01

We investigate the structural, thermodynamic, and dynamic behavior of a two-dimensional (2D) core-corona system using Langevin dynamics simulations. The particles are modeled by employing a core-softened potential which exhibits waterlike anomalies in three dimensions. In previous studies in a quasi-2D system a new region in the pressure versus temperature phase diagram of structural anomalies was observed. Here we show that for the two-dimensional case two regions in the pressure versus temperature phase diagram with structural, density, and diffusion anomalies are observed. Our findings indicate that, while the anomalous region at lower densities is due the competition between the two length scales in the potential at higher densities, the anomalous region is related to the reentrance of the melting line.

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

Science.gov (United States)

Lebovka, Nikolai I.; Tarasevich, Yuri Yu.; Vygornitskii, Nikolai V.

2018-02-01

The vertical drying of a two-dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction, and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), pi, and solvent evaporation rates, u . For completely dried films, the spatial distributions of the sticks, the order parameters, and the electrical conductivities of the films in both the horizontal, x , and vertical, y , directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of u . The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of pi and u .

The finite element solution of two-dimensional transverse magnetic scattering problems on the connection machine

International Nuclear Information System (INIS)

Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.

1990-01-01

A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems

Separating variables in two-way diffusion equations

International Nuclear Information System (INIS)

Fisch, N.J.; Kruskal, M.D.

1979-10-01

It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain

Two- and three-dimensional CT analysis of ankle fractures

International Nuclear Information System (INIS)

Magid, D.; Fishman, E.K.; Ney, D.R.; Kuhlman, J.E.

1988-01-01

CT with coronal and sagittal reformatting (two-dimensional CT) and animated volumetric image rendering (three-dimensional CT) was used to assess ankle fractures. Partial volume limits transaxial CT in assessments of horizontally oriented structures. Two-dimensional CT, being orthogonal to the plafond, superior mortise, talar dome, and tibial epiphysis, often provides the most clinically useful images. Two-dimensional CT is most useful in characterizing potentially confusing fractures, such as Tillaux (anterior tubercle), triplane, osteochondral talar dome, or nondisplaced talar neck fractures, and it is the best study to confirm intraarticular fragments. Two-and three-dimensional CT best indicate the percentage of articular surface involvement and best demonstrate postoperative results or complications (hardware migration, residual step-off, delayed union, DJD, AVN, etc). Animated three-dimensional images are the preferred means of integrating the two-dimensional findings for surgical planning, as these images more closely simulate the clinical problem

The dimension split element-free Galerkin method for three-dimensional potential problems

Science.gov (United States)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-02-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

Science.gov (United States)

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(0divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables. While the solution for normal diffusion problems is, at most, divergent as t-->0 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

Science.gov (United States)

Sid, S.; Terrapon, V. E.; Dubief, Y.

2018-02-01

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed

The measurement problem on classical diffusion process: inverse method on stochastic processes

International Nuclear Information System (INIS)

Bigerelle, M.; Iost, A.

2004-01-01

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time-distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement

Kubo conductivity of a strongly magnetized two-dimensional plasma.

Science.gov (United States)

Montgomery, D.; Tappert, F.

1971-01-01

The Kubo formula is used to evaluate the bulk electrical conductivity of a two-dimensional guiding-center plasma in a strong dc magnetic field. The particles interact only electrostatically. An ?anomalous' electrical conductivity is derived for this system, which parallels a recent result of Taylor and McNamara for the coefficient of spatial diffusion.

Impact of local diffusion on macroscopic dispersion in three-dimensional porous media

Science.gov (United States)

Dartois, Arthur; Beaudoin, Anthony; Huberson, Serge

2018-02-01

While macroscopic longitudinal and transverse dispersion in three-dimensional porous media has been simulated previously mostly under purely advective conditions, the impact of diffusion on macroscopic dispersion in 3D remains an open question. Furthermore, both in 2D and 3D, recurring difficulties have been encountered due to computer limitation or analytical approximation. In this work, we use the Lagrangian velocity covariance function and the temporal derivative of second-order moments to study the influence of diffusion on dispersion in highly heterogeneous 2D and 3D porous media. The first approach characterizes the correlation between the values of Eulerian velocity components sampled by particles undergoing diffusion at two times. The second approach allows the estimation of dispersion coefficients and the analysis of their behaviours as functions of diffusion. These two approaches allowed us to reach new results. The influence of diffusion on dispersion seems to be globally similar between highly heterogeneous 2D and 3D porous media. Diffusion induces a decrease in the dispersion in the direction parallel to the flow direction and an increase in the dispersion in the direction perpendicular to the flow direction. However, the amplification of these two effects with the permeability variance is clearly different between 2D and 3D. For the direction parallel to the flow direction, the amplification is more important in 3D than in 2D. It is reversed in the direction perpendicular to the flow direction.

Diffusion in higher dimensional SYK model with complex fermions

Science.gov (United States)

Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

2018-01-01

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Finding two-dimensional peaks

International Nuclear Information System (INIS)

Silagadze, Z.K.

2007-01-01

Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this 'quantum' ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems

A two-dimensional finite element method for analysis of solid body contact problems in fuel rod mechanics

International Nuclear Information System (INIS)

Nissen, K.L.

1988-06-01

Two computer codes for the analysis of fuel rod behavior have been developed. Fuel rod mechanics is treated by a two-dimensional, axisymmetric finite element method. The program KONTAKT is used for detailed examinations on fuel rod sections, whereas the second program METHOD2D allows instationary calculations of whole fuel rods. The mechanical contact of fuel and cladding during heating of the fuel rod is very important for it's integrity. Both computer codes use a Newton-Raphson iteration for the solution of the nonlinear solid body contact problem. A constitutive equation is applied for the dependency of contact pressure on normal approach of the surfaces which are assumed to be rough. If friction is present on the contacting surfaces, Coulomb's friction law is used. Code validation is done by comparison with known analytical solutions for special problems. Results of the contact algorithm for an elastic ball pressing against a rigid surface are confronted with Hertzian theory. Influences of fuel-pellet geometry as well as influences of discretisation of displacements and stresses of a single fuel pellet are studied. Contact of fuel and cladding is calculated for a fuel rod section with two fuel pellets. The influence of friction forces between fuel and cladding on their axial expansion is demonstrated. By calculation of deformations and temperatures during an instationary fuel rod experiment of the CABRI-series the feasibility of two-dimensional finite element analysis of whole fuel rods is shown. (orig.) [de

Calculation of accurate albedo boundary conditions for three-dimensional nodal diffusion codes by the method of characteristics

International Nuclear Information System (INIS)

Petkov, Petko T.

2000-01-01

Most of the few-group three-dimensional nodal diffusion codes used for neutronics calculations of the WWER reactors use albedo type boundary conditions on the core-reflector boundary. The conventional albedo are group-to-group reflection probabilities, defined on each outer node face. The method of characteristics is used to calculate accurate albedo by the following procedure. A many-group two-dimensional heterogeneous core-reflector problem, including a sufficient part of the core and detailed description of the adjacent reflector, is solved first. From this solution the angular flux on the core-reflector boundary is calculated in all groups for all traced neutron directions. Accurate boundary conditions can be calculated for the radial, top and bottom reflectors as well as for the absorber part of the WWER-440 reactor control assemblies. The algorithm can be used to estimate also albedo, coupling outer node faces on the radial reflector in the axial direction. Numerical results for the WWER-440 reactor are presented. (Authors)

Vectorization of three-dimensional neutron diffusion code CITATION

International Nuclear Information System (INIS)

Harada, Hiroo; Ishiguro, Misako

1985-01-01

Three-dimensional multi-group neutron diffusion code CITATION has been widely used for reactor criticality calculations. The code is expected to be run at a high speed by using recent vector supercomputers, when it is appropriately vectorized. In this paper, vectorization methods and their effects are described for the CITATION code. Especially, calculation algorithms suited for vectorization of the inner-outer iterative calculations which spend most of the computing time are discussed. The SLOR method, which is used in the original CITATION code, and the SOR method, which is adopted in the revised code, are vectorized by odd-even mesh ordering. The vectorized CITATION code is executed on the FACOM VP-100 and VP-200 computers, and is found to run over six times faster than the original code for a practical-scale problem. The initial value of the relaxation factor and the number of inner-iterations given as input data are also investigated since the computing time depends on these values. (author)

Diffusion between evolving interfaces

International Nuclear Information System (INIS)

Juntunen, Janne; Merikoski, Juha

2010-01-01

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

Two-dimensional ferroelectrics

Energy Technology Data Exchange (ETDEWEB)

Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)

2000-03-31

The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)

Quantum transport of atomic matter waves in anisotropic two-dimensional and three-dimensional disorder

International Nuclear Information System (INIS)

Piraud, M; Pezzé, L; Sanchez-Palencia, L

2013-01-01

The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich in counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D. (paper)

Two-dimensional analytical solution for nodal calculation of nuclear reactors

International Nuclear Information System (INIS)

Silva, Adilson C.; Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.

2017-01-01

Highlights: • A proposal for a coarse mesh nodal method is presented. • The proposal uses the analytical solution of the two-dimensional neutrons diffusion equation. • The solution is performed homogeneous nodes with dimensions of the fuel assembly. • The solution uses four average fluxes on the node surfaces as boundary conditions. • The results show good accuracy and efficiency. - Abstract: In this paper, the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G). The spatial domain of reactor core is divided into a set of nodes with uniform nuclear parameters. To determine iteratively the multiplication factor and the neutron flux in the reactor we combine the analytical solution of the neutron diffusion equation with an iterative method known as power method. The analytical solution for different types of regions that compose the reactor is obtained, such as fuel and reflector regions. Four average fluxes in the node surfaces are used as boundary conditions for analytical solution. Discontinuity factors on the node surfaces derived from the homogenization process are applied to maintain averages reaction rates and the net current in the fuel assembly (FA). To validate the results obtained by the analytical solution a relative power density distribution in the FAs is determined from the neutron flux distribution and compared with the reference values. The results show good accuracy and efficiency.

Estimation of surface temperature by using inverse problem. Part 1. Steady state analyses of two-dimensional cylindrical system

International Nuclear Information System (INIS)

Takahashi, Toshio; Terada, Atsuhiko

2006-03-01

In the corrosive process environment of thermochemical hydrogen production Iodine-Sulfur process plant, there is a difficulty in the direct measurement of surface temperature of the structural materials. An inverse problem method can effectively be applied for this problem, which enables estimation of the surface temperature using the temperature data at the inside of structural materials. This paper shows analytical results of steady state temperature distributions in a two-dimensional cylindrical system cooled by impinging jet flow, and clarifies necessary order of multiple-valued function from the viewpoint of engineeringly satisfactory precision. (author)

Determination of oxygen effective diffusivity in porous gas diffusion layer using a three-dimensional pore network model

International Nuclear Information System (INIS)

Wu Rui; Zhu Xun; Liao Qiang; Wang Hong; Ding Yudong; Li Jun; Ye Dingding

2010-01-01

In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.

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

The discrete cones methods for two-dimensional neutral particle transport problems with voids

International Nuclear Information System (INIS)

Watanabe, Y.; Maynard, C.W.

1983-01-01

One of the most widely applied deterministic methods for time-independent, two-dimensional neutron transport calculations is the discrete ordinates method (DSN). The DSN solution, however, fails to be accurate in a void due to the ray effect. In order to circumvent this drawback, the authors have been developing a novel approximation: the discrete cones method (DCN), where a group of particles in a cone are simultaneously traced instead of particles in discrete directions for the DSN method. Programs, which apply to the DSN method in a non-vacuum region and the DCN method in a void, have been written for transport calculations in X-Y coordinates. The solutions for test problems demonstrate mitigation of the ray effect in voids without loosing the computational efficiency of the DSN method

RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry

International Nuclear Information System (INIS)

Valle, Edmundo del; Mund, Ernest H.

2004-01-01

This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature

Domain decomposition methods for the neutron diffusion problem

International Nuclear Information System (INIS)

Guerin, P.; Baudron, A. M.; Lautard, J. J.

2010-01-01

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (SPN) or diffusion approximations are often used. The MINOS solver developed at CEA Saclay uses a mixed dual finite element method for the resolution of these problems. and has shown his efficiency. In order to take into account the heterogeneities of the geometry, a very fine mesh is generally required, and leads to expensive calculations for industrial applications. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose here two domain decomposition methods based on the MINOS solver. The first approach is a component mode synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is an iterative method based on a non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the adjacent sub-domains estimated at the previous iteration. Numerical results on parallel computers are presented for the diffusion model on realistic 2D and 3D cores. (authors)

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion.

Science.gov (United States)

Maldonado, Sergio; Borthwick, Alistair G L

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119 , 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion

Science.gov (United States)

Maldonado, Sergio; Borthwick, Alistair G. L.

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119, 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Assessing one-dimensional diffusion in nanoporous materials from transient concentration profiles

International Nuclear Information System (INIS)

Heinke, Lars; Kaerger, Joerg

2008-01-01

The use of interference microscopy has enabled the direct observation of transient concentration profiles generated by intracrystalline transport diffusion in nanoporous materials. The thus accessible intracrystalline concentration profiles contain a wealth of information which cannot be deduced by any macroscopic method. In this paper, we illustrate five different ways for determining the concentration-dependent diffusivity in one-dimensional systems and two for the surface permeability. These methods are discussed by application to concentration profiles evolving during the uptake of methanol by the zeolite ferrierite and of methanol by the metal organic framework (MOF) manganese(II) formate. We show that the diffusivity can be calculated most precisely by means of Fick's 1st law. As the circumstances permit, Boltzmann's integration method also yields very precise results. Furthermore, we present a simple procedure that enables the estimation of the influence of the surface barrier on the overall uptake process by plotting the boundary concentration versus the overall uptake

Note: Interpolation for evaluation of a two-dimensional spatial profile of plasma densities at low gas pressures

International Nuclear Information System (INIS)

Oh, Se-Jin; Kim, Young-Chul; Chung, Chin-Wook

2011-01-01

An interpolation algorithm for the evaluation of the spatial profile of plasma densities in a cylindrical reactor was developed for low gas pressures. The algorithm is based on a collisionless two-dimensional fluid model. Contrary to the collisional case, i.e., diffusion fluid model, the fitting algorithm depends on the aspect ratio of the cylindrical reactor. The spatial density profile of the collisionless fitting algorithm is presented in two-dimensional images and compared with the results of the diffusion fluid model.

Two solvable problems of planar geometrical optics.

Science.gov (United States)

Borghero, Francesco; Bozis, George

2006-12-01

In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.

Diffusion of two-dimensional epitaxial clusters on metal (100) surfaces: Facile versus nucleation-mediated behavior and their merging for larger sizes

International Nuclear Information System (INIS)

Lai, King C.; Liu, Da-Jiang; Evans, James W.

2017-01-01

For diffusion of two-dimensional homoepitaxial clusters of N atoms on metal(100) surfaces mediated by edge atom hopping, macroscale continuum theory suggests that the diffusion coefficient scales like DN ~ N -β with β = 3/2. However, we find quite different and diverse behavior in multiple size regimes. These include: (i) facile diffusion for small sizes N < 9; (ii) slow nucleation-mediated diffusion with small β < 1 for “perfect” sizes N = N p = L 2 or L(L+1), for L = 3, 4,… having unique ground state shapes, for moderate sizes 9 ≤ N ≤ O(10 2 ); the same also applies for N = N p +3, N p + 4,… (iii) facile diffusion but with large β > 2 for N = Np + 1 and N p + 2 also for moderate sizes 9 ≤ N ≤ O(10 2 ); (iv) merging of the above distinct branches and subsequent anomalous scaling with 1 ≲ β < 3/2, reflecting the quasi-facetted structure of clusters, for larger N = O(10 2 ) to N = O(10 3 ); and (v) classic scaling with β = 3/2 for very large N = O(103) and above. The specified size ranges apply for typical model parameters. We focus on the moderate size regime where show that diffusivity cycles quasi-periodically from the slowest branch for N p + 3 (not Np) to the fastest branch for Np + 1. Behavior is quantified by Kinetic Monte Carlo simulation of an appropriate stochastic lattice-gas model. However, precise analysis must account for a strong enhancement of diffusivity for short time increments due to back-correlation in the cluster motion. Further understanding of this enhancement, of anomalous size scaling behavior, and of the merging of various branches, is facilitated by combinatorial analysis of the number of the ground state and low-lying excited state cluster configurations, and also of kink populations.

An investigation on a two-dimensional problem of Mode-I crack in a thermoelastic medium

Science.gov (United States)

Kant, Shashi; Gupta, Manushi; Shivay, Om Namha; Mukhopadhyay, Santwana

2018-04-01

In this work, we consider a two-dimensional dynamical problem of an infinite space with finite linear Mode-I crack and employ a recently proposed heat conduction model: an exact heat conduction with a single delay term. The thermoelastic medium is taken to be homogeneous and isotropic. However, the boundary of the crack is subjected to a prescribed temperature and stress distributions. The Fourier and Laplace transform techniques are used to solve the problem. Mathematical modeling of the present problem reduces the solution of the problem into the solution of a system of four dual integral equations. The solution of these equations is equivalent to the solution of the Fredholm's integral equation of the first kind which has been solved by using the regularization method. Inverse Laplace transform is carried out by using the Bellman method, and we obtain the numerical solution for all the physical field variables in the physical domain. Results are shown graphically, and we highlight the effects of the presence of crack in the behavior of thermoelastic interactions inside the medium in the present context, and its results are compared with the results of the thermoelasticity of type-III.

Classical solutions of two dimensional Stokes problems on non smooth domains. 1: The Radon integral operators

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-05-01

The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two-dimensional Stokes operator on a non smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness on C(Γ) of the velocity double layer potential W as well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius of W is greater than 2. Under these conditions, the Radon boundary integral equations defined by the above mentioned jump relations are solvable by the Fredholm theory; the double (for Dirichlet) and the single (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems. (author). 48 refs

Three dimensional simulated modelling of diffusion capacitance of ...

African Journals Online (AJOL)

A three dimensional (3-D) simulated modelling was developed to analyse the excess minority carrier density in the base of a polycrystalline bifacial silicon solar cell. The concept of junction recombination velocity was ado-pted to quantify carrier flow through the junction, and to examine the solar cell diffusion capacitance for ...

Analytical approach for collective diffusion: one-dimensional heterogeneous lattice

Czech Academy of Sciences Publication Activity Database

Tarasenko, Alexander

2016-01-01

Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016

Pattern formation in three-dimensional reaction-diffusion systems

Science.gov (United States)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

Three-dimensional tokamak equilibria and stellarators with two-dimensional magnetic symmetry

International Nuclear Information System (INIS)

Garabedian, P.R.

1997-01-01

Three-dimensional computer codes have been developed to simulate equilibrium, stability and transport in tokamaks and stellarators. Bifurcated solutions of the tokamak problem suggest that three-dimensional effects may be more important than has generally been thought. Extensive calculations have led to the discovery of a stellarator configuration with just two field periods and with aspect ratio 3.2 that has a magnetic field spectrum B mn with toroidal symmetry. Numerical studies of equilibrium, stability and transport for this new device, called the Modular Helias-like Heliac 2 (MHH2), will be presented. (author)

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Science.gov (United States)

Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

2016-05-01

Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (˜5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

Pericles and Attila results for the C5G7 MOX benchmark problems

International Nuclear Information System (INIS)

Wareing, T.A.; McGhee, J.M.

2002-01-01

Recently the Nuclear Energy Agency has published a new benchmark entitled, 'C5G7 MOX Benchmark.' This benchmark is to test the ability of current transport codes to treat reactor core problems without spatial homogenization. The benchmark includes both a two- and three-dimensional problem. We have calculated results for these benchmark problems with our Pericles and Attila codes. Pericles is a one-,two-, and three-dimensional unstructured grid discrete-ordinates code and was used for the twodimensional benchmark problem. Attila is a three-dimensional unstructured tetrahedral mesh discrete-ordinate code and was used for the three-dimensional problem. Both codes use discontinuous finite element spatial differencing. Both codes use diffusion synthetic acceleration (DSA) for accelerating the inner iterations.

Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

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)

Stabilizing local boundary conditions for two-dimensional shallow water equations

KAUST Repository

Dia, Ben Mansour; Oppelstrup, Jesper

2018-01-01

In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary

Velocity and Dispersion for a Two-Dimensional Random Walk

International Nuclear Information System (INIS)

Li Jinghui

2009-01-01

In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem. (general)

Finite element solution of two dimensional time dependent heat equation

International Nuclear Information System (INIS)

Maaz

1999-01-01

A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)

Two-dimensional errors

International Nuclear Information System (INIS)

Anon.

1991-01-01

This chapter addresses the extension of previous work in one-dimensional (linear) error theory to two-dimensional error analysis. The topics of the chapter include the definition of two-dimensional error, the probability ellipse, the probability circle, elliptical (circular) error evaluation, the application to position accuracy, and the use of control systems (points) in measurements

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)

Solution of the two dimensional diffusion and transport equations in a rectangular lattice with an elliptical fuel element using Fourier transform methods: One and two group cases

International Nuclear Information System (INIS)

Williams, M.M.R.; Hall, S.K.; Eaton, M.D.

2014-01-01

Highlights: • A rectangular reactor cell with an elliptical fuel element. • Solution of transport and diffusion equations by Fourier expansion. • Numerical examples showing convergence. • Two group cell problems. - Abstract: A method for solving the diffusion and transport equations in a rectangular lattice cell with an elliptical fuel element has been developed using a Fourier expansion of the neutron flux. The method is applied to a one group model with a source in the moderator. The cell flux is obtained and also the associated disadvantage factor. In addition to the one speed case, we also consider the two group equations in the cell which now become an eigenvalue problem for the lattice multiplication factor. The method of solution relies upon an efficient procedure to solve a large set of simultaneous linear equations and for this we use the IMSL library routines. Our method is compared with the results from a finite element code. The main drawback of the problem arises from the very large number of terms required in the Fourier series which taxes the storage and speed of the computer. Nevertheless, useful solutions are obtained in geometries that would normally require the use of finite element or analogous methods, for this reason the Fourier method is useful for comparison with that type of numerical approach. Extension of the method to more intricate fuel shapes, such as stars and cruciforms as well as superpositions of these, is possible

Evolution of the vorticity-area density during the formation of coherent structures in two-dimensional flows

NARCIS (Netherlands)

Capel, H.W.; Pasmanter, R.A.

2000-01-01

It is shown: (1) that in two-dimensional, incompressible, viscous flows the vorticity-area distribution evolves according to an advection-diffusion equation with a negative, time dependent diffusion coefficient and (2) how to use the vorticity-stream function relations, i.e., the so-called

DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

International Nuclear Information System (INIS)

Leaf, G.K.; Minkoff, M.

1982-01-01

1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

Self-organized defect strings in two-dimensional crystals.

Science.gov (United States)

Lechner, Wolfgang; Polster, David; Maret, Georg; Keim, Peter; Dellago, Christoph

2013-12-01

Using experiments with single-particle resolution and computer simulations we study the collective behavior of multiple vacancies injected into two-dimensional crystals. We find that the defects assemble into linear strings, terminated by dislocations with antiparallel Burgers vectors. We show that these defect strings propagate through the crystal in a succession of rapid one-dimensional gliding and rare rotations. While the rotation rate decreases exponentially with the number of defects in the string, the diffusion constant is constant for large strings. By monitoring the separation of the dislocations at the end points, we measure their effective interactions with high precision beyond their spontaneous formation and annihilation, and we explain the double-well form of the dislocation interaction in terms of continuum elasticity theory.

Analysis of Two-Dimensional Electrophoresis Gel Images

DEFF Research Database (Denmark)

Pedersen, Lars

2002-01-01

This thesis describes and proposes solutions to some of the currently most important problems in pattern recognition and image analysis of two-dimensional gel electrophoresis (2DGE) images. 2DGE is the leading technique to separate individual proteins in biological samples with many biological...

Intertwined Hamiltonians in two-dimensional curved spaces

International Nuclear Information System (INIS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-01-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

Energy Technology Data Exchange (ETDEWEB)

Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

International Nuclear Information System (INIS)

Agaltsov, A. D.; Novikov, R. G.

2014-01-01

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given

SCOTCH: a program for solution of the one-dimensional, two-group, space-time neutron diffusion equations with temperature feedback of multi-channel fluid dynamics for HTGR cores

International Nuclear Information System (INIS)

Ezaki, Masahiro; Mitake, Susumu; Ozawa, Tamotsu

1979-06-01

The SCOTCH program solves the one-dimensional (R or Z), two-group reactor kinetics equations with multi-channel temperature transients and fluid dynamics. Sub-program SCOTCH-RX simulates the space-time neutron diffusion in radial direction, and sub-program SCOTCH-AX simulates the same in axial direction. The program has about 8,000 steps of FORTRAN statement and requires about 102 kilo-words of computer memory. (author)

Theory of collective diffusion in two-dimensional colloidal suspensions

Czech Academy of Sciences Publication Activity Database

Chvoj, Zdeněk; Lahtinen, J. M.; Ala-Nissila, T.

-, - (2004), s. 1-8 ISSN 1742-5468 R&D Projects: GA AV ČR IAA1010207 Institutional research plan: CEZ:AV0Z1010914 Keywords : surface diffusion * Brownian motion * fluctuations Subject RIV: BE - Theoretical Physics

Global Search of a Three-dimensional Low Solidity Circular Cascade Diffuser for Centrifugal Blowers by Meta-model Assisted Optimization

Science.gov (United States)

Sakaguchi, Daisaku; Sakue, Daiki; Tun, Min Thaw

2018-04-01

A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

Computation of diffusion coefficients for waters of Gauthami Godavari estuary using one-dimensional advection-diffusion model

Digital Repository Service at National Institute of Oceanography (India)

Jyothi, D.; Murty, T.V.R.; Sarma, V.V.; Rao, D.P.

conditions. As the pollutant load on the estuary increases, the. water quality may deteriorate rapidly and therefore the scientific interests are centered on the analysis of water quality. The pollutants will be subjected to a number of physical, chemical... study we have applied one-dimensional advection-diffusion model for the waters of Gauthami Godavari estuary to determine the axial diffusion coefficients and thereby to predict the impact assessment. The study area (Fig. 1) is the lower most 32 km...

Tracer particles in two-dimensional elastic networks diffuse logarithmically slow

International Nuclear Information System (INIS)

Lizana, Ludvig; Ambjörnsson, Tobias; Lomholt, Michael A

2017-01-01

Several experiments on tagged molecules or particles in living systems suggest that they move anomalously slow—their mean squared displacement (MSD) increase slower than linearly with time. Leading models aimed at understanding these experiments predict that the MSD grows as a power law with a growth exponent that is smaller than unity. However, in some experiments the growth is so slow (fitted exponent  ∼0.1–0.2) that they hint towards other mechanisms at play. In this paper, we theoretically demonstrate how in-plane collective modes excited by thermal fluctuations in a two dimensional membrane lead to logarithmic time dependence for the the tracer particle’s MSD. (paper)

Two-dimensional wave propagation in layered periodic media

KAUST Repository

Quezada de Luna, Manuel

2014-09-16

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.

Incorrectness of conventional one-dimensional parallel thermal resistance circuit model for two-dimensional circular composite pipes

International Nuclear Information System (INIS)

Wong, K.-L.; Hsien, T.-L.; Chen, W.-L.; Yu, S.-J.

2008-01-01

This study is to prove that two-dimensional steady state heat transfer problems of composite circular pipes cannot be appropriately solved by the conventional one-dimensional parallel thermal resistance circuits (PTRC) model because its interface temperatures are not unique. Thus, the PTRC model is definitely different from its conventional recognized analogy, parallel electrical resistance circuits (PERC) model, which has unique node electric voltages. Two typical composite circular pipe examples are solved by CFD software, and the numerical results are compared with those obtained by the PTRC model. This shows that the PTRC model generates large error. Thus, this conventional model, introduced in most heat transfer text books, cannot be applied to two-dimensional composite circular pipes. On the contrary, an alternative one-dimensional separately series thermal resistance circuit (SSTRC) model is proposed and applied to a two-dimensional composite circular pipe with isothermal boundaries, and acceptable results are returned

Transport equivalent diffusion constants for reflector region in PWRs

International Nuclear Information System (INIS)

Tahara, Yoshihisa; Sekimoto, Hiroshi

2002-01-01

The diffusion-theory-based nodal method is widely used in PWR core designs for reason of its high computing speed in three-dimensional calculations. The baffle/reflector (B/R) constants used in nodal calculations are usually calculated based on a one-dimensional transport calculation. However, to achieve high accuracy of assembly power prediction, two-dimensional model is needed. For this reason, the method for calculating transport equivalent diffusion constants of reflector material was developed so that the neutron currents on the material boundaries could be calculated exactly in diffusion calculations. Two-dimensional B/R constants were calculated using the transport equivalent diffusion constants in the two-dimensional diffusion calculation whose geometry reflected the actual material configuration in the reflector region. The two-dimensional B/R constants enabled us to predict assembly power within an error of 1.5% at hot full power conditions. (author)

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Directory of Open Access Journals (Sweden)

Djordjevich Alexandar

2017-12-01

Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

Procedures for two-dimensional electrophoresis of proteins

Energy Technology Data Exchange (ETDEWEB)

Tollaksen, S.L.; Giometti, C.S.

1996-10-01

High-resolution two-dimensional gel electrophoresis (2DE) of proteins, using isoelectric focusing in the first dimension and sodium dodecyl sulfate/polyacrylamide gel electrophoresis (SDS-PAGE) in the second, was first described in 1975. In the 20 years since those publications, numerous modifications of the original method have evolved. The ISO-DALT system of 2DE is a high-throughput approach that has stood the test of time. The problem of casting many isoelectric focusing gels and SDS-PAGE slab gels (up to 20) in a reproducible manner has been solved by the use of the techniques and equipment described in this manual. The ISO-DALT system of two-dimensional gel electrophoresis originated in the late 1970s and has been modified many times to improve its high-resolution, high-throughput capabilities. This report provides the detailed procedures used with the current ISO-DALT system to prepare, run, stain, and photograph two-dimensional gels for protein analysis.

ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES

Directory of Open Access Journals (Sweden)

Nikola Stefanović

2007-06-01

Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.

A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system

Science.gov (United States)

Chen, Kewei; Zhan, Hongbin

2018-06-01

The reactive solute transport in a single fracture bounded by upper and lower matrixes is a classical problem that captures the dominant factors affecting transport behavior beyond pore scale. A parallel fracture-matrix system which considers the interaction among multiple paralleled fractures is an extension to a single fracture-matrix system. The existing analytical or semi-analytical solution for solute transport in a parallel fracture-matrix simplifies the problem to various degrees, such as neglecting the transverse dispersion in the fracture and/or the longitudinal diffusion in the matrix. The difficulty of solving the full two-dimensional (2-D) problem lies in the calculation of the mass exchange between the fracture and matrix. In this study, we propose an innovative Green's function approach to address the 2-D reactive solute transport in a parallel fracture-matrix system. The flux at the interface is calculated numerically. It is found that the transverse dispersion in the fracture can be safely neglected due to the small scale of fracture aperture. However, neglecting the longitudinal matrix diffusion would overestimate the concentration profile near the solute entrance face and underestimate the concentration profile at the far side. The error caused by neglecting the longitudinal matrix diffusion decreases with increasing Peclet number. The longitudinal matrix diffusion does not have obvious influence on the concentration profile in long-term. The developed model is applied to a non-aqueous-phase-liquid (DNAPL) contamination field case in New Haven Arkose of Connecticut in USA to estimate the Trichloroethylene (TCE) behavior over 40 years. The ratio of TCE mass stored in the matrix and the injected TCE mass increases above 90% in less than 10 years.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level

Asymptotics for Two-dimensional Atoms

DEFF Research Database (Denmark)

Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip

2012-01-01

We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....

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

Entropic Barriers for Two-Dimensional Quantum Memories

Science.gov (United States)

Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.

2014-03-01

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.

The inaccuracy of conventional one-dimensional parallel thermal resistance circuit model for two-dimensional composite walls

International Nuclear Information System (INIS)

Wong, K.-L.; Hsien, T.-L.; Hsiao, M.-C.; Chen, W.-L.; Lin, K.-C.

2008-01-01

This investigation is to show that two-dimensional steady state heat transfer problems of composite walls should not be solved by the conventionally one-dimensional parallel thermal resistance circuits (PTRC) model because the interface temperatures are not unique. Thus PTRC model cannot be used like its conventional recognized analogy, parallel electrical resistance circuits (PERC) model which has the unique node electric voltage. Two typical composite wall examples, solved by CFD software, are used to demonstrate the incorrectness. The numerical results are compared with those obtained by PTRC model, and very large differences are observed between their results. This proves that the application of conventional heat transfer PTRC model to two-dimensional composite walls, introduced in most heat transfer text book, is totally incorrect. An alternative one-dimensional separately series thermal resistance circuit (SSTRC) model is proposed and applied to the two-dimensional composite walls with isothermal boundaries. Results with acceptable accuracy can be obtained by the new model

CHOLESK, Diffusion Calculation with 2-D Source in X-Y or R-Z Geometry

International Nuclear Information System (INIS)

1988-01-01

1 - Description of problem or function: Solution of the diffusion equation with source in two-dimensional geometries x-y or r-z. 2 - Method of solution: The finite-element method of Ritz-Galerkin is applied

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

International Nuclear Information System (INIS)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-01

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

Energy Technology Data Exchange (ETDEWEB)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-15

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities.

Energy of N two-dimensional bosons with zero-range interactions

Science.gov (United States)

Bazak, B.; Petrov, D. S.

2018-02-01

We derive an integral equation describing N two-dimensional bosons with zero-range interactions and solve it for the ground state energy B N by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling B N ∝ 8.567 N predicted by Hammer and Son (2004 Phys. Rev. Lett. 93 250408) in the large-N limit.

On the application of finite element method in the solution of steady state diffusion equation

International Nuclear Information System (INIS)

Ono, S.

1982-01-01

The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Institute of Scientific and Technical Information of China (English)

Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN

2017-01-01

Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Geotechnical applications of a two-dimensional elastodynamic displacement discontinuity method

CSIR Research Space (South Africa)

Siebrits, E

1993-12-01

Full Text Available A general two-dimensional elastodynamic displacement discontinuity method is used to model a variety of application problems. The plane strain problems are: the elastodynamic motions induced on a cavity by shear slip on a nearby crack; the dynamic...

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem.

Science.gov (United States)

Benson, Christopher R; Maffeo, Christopher; Fatila, Elisabeth M; Liu, Yun; Sheetz, Edward G; Aksimentiev, Aleksei; Singharoy, Abhishek; Flood, Amar H

2018-05-07

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

Two-dimensional NMR spectrometry

International Nuclear Information System (INIS)

Farrar, T.C.

1987-01-01

This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2

MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers

Energy Technology Data Exchange (ETDEWEB)

Okumura, Keisuke [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1998-10-01

MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm `boundary separated checkerboard sweep method` appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it`s similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)

MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers

International Nuclear Information System (INIS)

Okumura, Keisuke

1998-10-01

MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm 'boundary separated checkerboard sweep method' appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it's similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)

Solution of the two-dimensional space-time reactor kinetics equation by a locally one-dimensional method

International Nuclear Information System (INIS)

Chen, G.S.; Christenson, J.M.

1985-01-01

In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program

Two dimensional, two fluid model for sodium boiling in LMFBR fuel assemblies

International Nuclear Information System (INIS)

Granziera, M.R.; Kazimi, M.S.

1980-05-01

A two dimensional numerical model for the simulation of sodium boiling transient was developed using the two fluid set of conservation equations. A semiimplicit numerical differencing scheme capable of handling the problems associated with the ill-posedness implied by the complex characteristic roots of the two fluid problems was used, which took advantage of the dumping effect of the exchange terms. Of particular interest in the development of the model was the identification of the numerical problems caused by the strong disparity between the axial and radial dimensions of fuel assemblies. A solution to this problem was found which uses the particular geometry of fuel assemblies to accelerate the convergence of the iterative technique used in the model. Three sodium boiling experiments were simulated with the model, with good agreement between the experimental results and the model predictions

Design of a rotational three-dimensional nonimaging device by a compensated two-dimensional design process.

Science.gov (United States)

Yang, Yi; Qian, Ke-Yuan; Luo, Yi

2006-07-20

A compensation process has been developed to design rotational three-dimensional (3D) nonimaging devices. By compensating the desired light distribution during a two-dimensional (2D) design process for an extended Lambertian source using a compensation coefficient, the meridian plane of a 3D device with good performance can be obtained. This method is suitable in many cases with fast calculation speed. Solutions to two kinds of optical design problems have been proposed, and the limitation of this compensated 2D design method is discussed.

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.

Classical many-body problems amenable to exact treatments (solvable and/or integrable and/or linearizable...) in one-, two- and three-dimensional space

CERN Document Server

Calogero, Francesco

2001-01-01

This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.

New method of three-dimensional reconstruction from two-dimensional MR data sets

International Nuclear Information System (INIS)

Wrazidlo, W.; Schneider, S.; Brambs, H.J.; Richter, G.M.; Kauffmann, G.W.; Geiger, B.; Fischer, C.

1989-01-01

In medical diagnosis and therapy, cross-sectional images are obtained by means of US, CT, or MR imaging. The authors propose a new solution to the problem of constructing a shape over a set of cross-sectional contours from two-dimensional (2D) MR data sets. The authors' method reduces the problem of constructing a shape over the cross sections to one of constructing a sequence of partial shapes, each of them connecting two cross sections lying on adjacent planes. The solution makes use of the Delaunay triangulation, which is isomorphic in that specific situation. The authors compute this Delaunay triangulation. Shape reconstruction is then achieved section by pruning Delaunay triangulations

Complexity of hierarchically and 1-dimensional periodically specified problems

Energy Technology Data Exchange (ETDEWEB)

Marathe, M.V.; Hunt, H.B. III; Stearns, R.E.; Radhakrishnan, V.

1995-08-23

We study the complexity of various combinatorial and satisfiability problems when instances are specified using one of the following specifications: (1) the 1-dimensional finite periodic narrow specifications of Wanke and Ford et al. (2) the 1-dimensional finite periodic narrow specifications with explicit boundary conditions of Gale (3) the 2-way infinite1-dimensional narrow periodic specifications of Orlin et al. and (4) the hierarchical specifications of Lengauer et al. we obtain three general types of results. First, we prove that there is a polynomial time algorithm that given a 1-FPN- or 1-FPN(BC)specification of a graph (or a C N F formula) constructs a level-restricted L-specification of an isomorphic graph (or formula). This theorem along with the hardness results proved here provides alternative and unified proofs of many hardness results proved in the past either by Lengauer and Wagner or by Orlin. Second, we study the complexity of generalized CNF satisfiability problems of Schaefer. Assuming P {ne} PSPACE, we characterize completely the polynomial time solvability of these problems, when instances are specified as in (1), (2),(3) or (4). As applications of our first two types of results, we obtain a number of new PSPACE-hardness and polynomial time algorithms for problems specified as in (1), (2), (3) or(4). Many of our results also hold for O(log N) bandwidth bounded planar instances.

Network patterns in exponentially growing two-dimensional biofilms

Science.gov (United States)

Zachreson, Cameron; Yap, Xinhui; Gloag, Erin S.; Shimoni, Raz; Whitchurch, Cynthia B.; Toth, Milos

2017-10-01

Anisotropic collective patterns occur frequently in the morphogenesis of two-dimensional biofilms. These patterns are often attributed to growth regulation mechanisms and differentiation based on gradients of diffusing nutrients and signaling molecules. Here, we employ a model of bacterial growth dynamics to show that even in the absence of growth regulation or differentiation, confinement by an enclosing medium such as agar can itself lead to stable pattern formation over time scales that are employed in experiments. The underlying mechanism relies on path formation through physical deformation of the enclosing environment.

The 'thousand words' problem: Summarizing multi-dimensional data

International Nuclear Information System (INIS)

Scott, David M.

2011-01-01

Research highlights: → Sophisticated process sensors produce large multi-dimensional data sets. → Plant control systems cannot handle images or large amounts of data. → Various techniques reduce the dimensionality, extracting information from raw data. → Simple 1D and 2D methods can often be extended to 3D and 4D applications. - Abstract: An inherent difficulty in the application of multi-dimensional sensing to process monitoring and control is the extraction and interpretation of useful information. Ultimately the measured data must be collapsed into a relatively small number of values that capture the salient characteristics of the process. Although multiple dimensions are frequently necessary to isolate a particular physical attribute (such as the distribution of a particular chemical species in a reactor), plant control systems are not equipped to use such data directly. The production of a multi-dimensional data set (often displayed as an image) is not the final step of the measurement process, because information must still be extracted from the raw data. In the metaphor of one picture being equal to a thousand words, the problem becomes one of paraphrasing a lengthy description of the image with one or two well-chosen words. Various approaches to solving this problem are discussed using examples from the fields of particle characterization, image processing, and process tomography.

Two-dimensional electron gas in monolayer InN quantum wells

International Nuclear Information System (INIS)

Pan, W.; Wang, G. T.; Dimakis, E.; Moustakas, T. D.; Tsui, D. C.

2014-01-01

We report in this letter experimental results that confirm the two-dimensional nature of the electron systems in a superlattice structure of 40 InN quantum wells consisting of one monolayer of InN embedded between 10 nm GaN barriers. The electron density and mobility of the two-dimensional electron system (2DES) in these InN quantum wells are 5 × 10 15  cm −2 (or 1.25 × 10 14  cm −2 per InN quantum well, assuming all the quantum wells are connected by diffused indium contacts) and 420 cm 2 /Vs, respectively. Moreover, the diagonal resistance of the 2DES shows virtually no temperature dependence in a wide temperature range, indicating the topological nature of the 2DES

RKC time-stepping for advection-diffusion-reaction problems

International Nuclear Information System (INIS)

Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.

2004-01-01

The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

A two-dimensional mathematical model of percutaneous drug absorption

Directory of Open Access Journals (Sweden)

Kubota K

2004-06-01

Full Text Available Abstract Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1 the flow rate of the drug, (2 the flux and the cumulative amount of drug eliminated into the receptor cell, (3 the steady-state value of the flux, (4 the time to reach the steady

Quasi-three dimensional dynamic modeling of a proton exchange membrane fuel cell with consideration of two-phase water transport through a gas diffusion layer

International Nuclear Information System (INIS)

Kang, Sanggyu

2015-01-01

Water management is one of the challenging issues for low-temperature PEMFCs (proton exchange membrane fuel cells). When liquid water is formed at the GDL (gas diffusion layer), the pathway of reactant gas can be blocked, which inhibits the electrochemical reaction of PEMFC. Thus, liquid water transport through GDL is a critical factor determining the performance of a PEMFC. In present study, quasi-three dimensional dynamic modeling of PEMFC with consideration of two-phase water transport through GDL is developed. To investigate the distributions of PEMFC characteristics, including current density, species mole fraction, and membrane hydration, the PEMFC was discretized into twenty control volumes along the anode channel. To resolve the mass and energy conservation, the PEMFC is discretized into eleven and fifteen control volumes in the perpendicular direction, respectively. The dynamic variation of PEMFC characteristics of cell voltage, overvoltage of activation and ohmic, liquid water saturation through a GDL, and oxygen concentration were captured during transient behavior. - Highlights: • A quasi-three dimensional two-phase dynamic model of PEMFC is developed. • Presented model is validated by comparison with experimental data. • Two-phase model is compared with one-phase model at steady-states and transients.

1DB, a one-dimensional diffusion code for nuclear reactor analysis

International Nuclear Information System (INIS)

Little, W.W. Jr.

1991-09-01

1DB is a multipurpose, one-dimensional (plane, cylinder, sphere) diffusion theory code for use in reactor analysis. The code is designed to do the following: To compute k eff and perform criticality searches on time absorption, reactor composition, reactor dimensions, and buckling by means of either a flux or an adjoint model; to compute collapsed microscopic and macroscopic cross sections averaged over the spectrum in any specified zone; to compute resonance-shielded cross sections using data in the shielding factor formnd to compute isotopic burnup using decay chains specified by the user. All programming is in FORTRAN. Because variable dimensioning is employed, no simple restrictions on problem complexity can be stated. The number of spatial mesh points, energy groups, upscattering terms, etc. is limited only by the available memory. The source file contains about 3000 cards. 4 refs

Local Correlation during Ostwald ripening of two-dimensional islands on Ag(111)

NARCIS (Netherlands)

Morgenstern, Karina; Rosenfeld, G.; Comsa, George

1999-01-01

Using two-dimensional Ag adatom islands on Ag(111) as a model system, we study the importance of local correlations in diffusion-limited Ostwald ripening. For the coverages studied (0.08, 0.21, and 0.3 ML), we find that the ripening can be surprisingly well described in a nearest neighbour model

Stabilizing local boundary conditions for two-dimensional shallow water equations

KAUST Repository

Dia, Ben Mansour

2018-03-27

In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-04-15

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

Dimensional reduction of a generalized flux problem

International Nuclear Information System (INIS)

Moroz, A.

1992-01-01

In this paper, a generalized flux problem with Abelian and non-Abelian fluxes is considered. In the Abelian case we shall show that the generalized flux problem for tight-binding models of noninteracting electrons on either 2n- or (2n + 1)-dimensional lattice can always be reduced to an n-dimensional hopping problem. A residual freedom in this reduction enables one to identify equivalence classes of hopping Hamiltonians which have the same spectrum. In the non-Abelian case, the reduction is not possible in general unless the flux tensor factorizes into an Abelian one times are element of the corresponding algebra

Numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities

International Nuclear Information System (INIS)

Milioli, F.E.

1985-01-01

In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt

Study of ODE limit problems for reaction-diffusion equations

Directory of Open Access Journals (Sweden)

Jacson Simsen

2018-01-01

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

The self-similar field and its application to a diffusion problem

International Nuclear Information System (INIS)

Michelitsch, Thomas M

2011-01-01

We introduce a continuum approach which accounts for self-similarity as a symmetry property of an infinite medium. A self-similar Laplacian operator is introduced which is the source of self-similar continuous fields. In this way ‘self-similar symmetry’ appears in an analogous manner as transverse isotropy or cubic symmetry of a medium. As a consequence of the self-similarity the Laplacian is a non-local fractional operator obtained as the continuum limit of the discrete self-similar Laplacian introduced recently by Michelitsch et al (2009 Phys. Rev. E 80 011135). The dispersion relation of the Laplacian and its Green’s function is deduced in closed forms. As a physical application of the approach we analyze a self-similar diffusion problem. The statistical distributions, which constitute the solutions of this problem, turn out to be Lévi-stable distributions with infinite variances characterizing the statistics of one-dimensional Lévi flights. The self-similar continuum approach introduced in this paper has the potential to be applied on a variety of scale invariant and fractal problems in physics such as in continuum mechanics, electrodynamics and in other fields. (paper)

Exterior calculus and two-dimensional supersymmetric models

International Nuclear Information System (INIS)

Sciuto, S.

1980-01-01

An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)

Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods

DEFF Research Database (Denmark)

Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.

2010-01-01

In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...

Coupled diffusion of two species in a slab with an eroding boundary

International Nuclear Information System (INIS)

Leite, S.B.; Ozisik, M.N.; Verghese, K.

1981-01-01

The diffusion of two interchangeable species in a medium with an eroding boundary is analyzed by modeling the problem as the solution of two diffusion equations coupled at the source term for a slab with a moving boundary. Formal solutions are developed for the concentration of the two species as a function of time and position in the slab for arbitrary initial distributions of the diffusing species, arbitrary sources within the medium and boundary conditions of the third kind at the bounding surfaces. It is shown with an illustrative example, that the resulting coupled integral equations for the species can be solved very efficiently by an approach employing both a lower- and upper-bound starting function for the concentrations. (author)

Two-dimensional discrete dislocation models of deformation in polycrystalline thin metal films on substrates

International Nuclear Information System (INIS)

Hartmaier, Alexander; Buehler, Markus J.; Gao, Huajian

2005-01-01

The time-dependent irreversible deformation of polycrystalline thin metal films on substrates is investigated using two-dimensional discrete dislocation dynamics models incorporating essential parameters determined from atomistic studies. The work is focused on the mechanical properties of uncapped films, where diffusive processes play an important role. The simulations incorporate dislocation climb along the grain boundary as well as conservative glide. Despite of severe limitations of the two-dimensional dislocation models, the simulation results are found to largely corroborate experimental findings on different dominant deformation mechanisms at different film thicknesses

Fourier convergence analysis applied to neutron diffusion Eigenvalue problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2004-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge

Mixed finite element simulations in two-dimensional groundwater flow problems

International Nuclear Information System (INIS)

Kimura, Hideo

1989-01-01

A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)

Galerkin method for solving diffusion equations

International Nuclear Information System (INIS)

Tsapelkin, E.S.

1975-01-01

A programme for the solution of the three-dimensional two-group multizone neutron diffusion problem in (x, y, z)-geometry is described. The programme XYZ-5 gives the currents of both groups, the effective neutron multiplication coefficient and several integral properties of the reactor. The solution was found with the Galerkin method using speciallly constructed and chosen coordinate functions. The programme is written in ALGOL-60 and consists of 5 parts. Its text is given

Solving the two-dimensional Schrödinger equation using basis ...

Indian Academy of Sciences (India)

Ihab H Naeim

2017-10-19

Oct 19, 2017 ... We shall study the case of a two-dimensional quantum system .... Solving (6) for ck,l is tantamount to pro- ... case, the final computational problem becomes quite ..... matrix approach fails in the case of two particles con-.

Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2005-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

Solution of two-dimensional electromagnetic scattering problem by FDTD with optimal step size, based on a semi-norm analysis

International Nuclear Information System (INIS)

Monsefi, Farid; Carlsson, Linus; Silvestrov, Sergei; Rančić, Milica; Otterskog, Magnus

2014-01-01

To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm

Solution of two-dimensional electromagnetic scattering problem by FDTD with optimal step size, based on a semi-norm analysis

Energy Technology Data Exchange (ETDEWEB)

Monsefi, Farid [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås, Sweden and School of Innovation, Design and Engineering, IDT, Mälardalen University, MDH Väs (Sweden); Carlsson, Linus; Silvestrov, Sergei [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås (Sweden); Rančić, Milica [Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen University, MDH, Västerås, Sweden and Department of Theoretical Electrical Engineering, Faculty of Electronic Engineering, University (Serbia); Otterskog, Magnus [School of Innovation, Design and Engineering, IDT, Mälardalen University, MDH Västerås (Sweden)

2014-12-10

To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm.

Equilibrium: two-dimensional configurations

International Nuclear Information System (INIS)

Anon.

1987-01-01

In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7

Orbits of the n-dimensional Kepler-Coulomb problem and universality of the Kepler laws

International Nuclear Information System (INIS)

Oender, M; Vercin, A

2006-01-01

In the standard classical mechanics textbooks used at undergraduate and graduate levels, no attention is paid to the dimensional aspects of the Kepler-Coulomb problem. We have shown that the orbits of the n-dimensional classical Kepler-Coulomb problem are the usual conic sections in a fixed two-dimensional subspace and the Kepler laws with their well-known forms are valid independent of dimension. The basic characteristics of motion in a central force field are also established in an arbitrary dimension. The approach followed is easily accessible to late undergraduate and recent graduate students

Turing instability in reaction-diffusion systems with nonlinear diffusion

Energy Technology Data Exchange (ETDEWEB)

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

2013-10-15

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

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.

Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

Energy Technology Data Exchange (ETDEWEB)

Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico

2014-12-15

In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.

Two-Dimensional Depth-Averaged Beach Evolution Modeling: Case Study of the Kizilirmak River Mouth, Turkey

DEFF Research Database (Denmark)

Baykal, Cüneyt; Ergin, Ayşen; Güler, Işikhan

2014-01-01

investigated by satellite images, physical model tests, and one-dimensional numerical models. The current study uses a two-dimensional depth-averaged numerical beach evolution model, developed based on existing methodologies. This model is mainly composed of four main submodels: a phase-averaged spectral wave......This study presents an application of a two-dimensional beach evolution model to a shoreline change problem at the Kizilirmak River mouth, which has been facing severe coastal erosion problems for more than 20 years. The shoreline changes at the Kizilirmak River mouth have been thus far...... transformation model, a two-dimensional depth-averaged numerical waveinduced circulation model, a sediment transport model, and a bottom evolution model. To validate and verify the numerical model, it is applied to several cases of laboratory experiments. Later, the model is applied to a shoreline change problem...

Two-dimensional effects in the problem of tearing modes control by electron cyclotron current drive

International Nuclear Information System (INIS)

Comisso, L.; Lazzaro, E.

2010-01-01

The design of means to counteract robustly the classical and neoclassical tearing modes in a tokamak by localized injection of an external control current requires an ever growing understanding of the physical process, beyond the Rutherford-type zero-dimensional models. Here a set of extended magnetohydrodynamic nonlinear equations for four continuum fields is used to investigate the two-dimensional effects in the response of the reconnecting modes to specific inputs of the localized external current. New information is gained on the space- and time-dependent effects of the external action on the two-dimensional structure of magnetic islands, which is very important to formulate applicable control strategies.

Analytical solution of the multigroup neutron diffusion kinetic equation in one-dimensional cartesian geometry by the integral transform technique

International Nuclear Information System (INIS)

Ceolin, Celina

2010-01-01

The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

Science.gov (United States)

Wen, Baole; Chini, Gregory P.; Kerswell, Rich R.; Doering, Charles R.

2015-10-01

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu˜PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L =2 √{2 },Nu≤0.106 Pr0Ra5/12 , which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

International Nuclear Information System (INIS)

Olson, Gordon L.

2011-01-01

Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

A diffusion model of protected population on bilocal habitat with generalized resource

Science.gov (United States)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Turing instability for a two-dimensional Logistic coupled map lattice

International Nuclear Information System (INIS)

Xu, L.; Zhang, G.; Han, B.; Zhang, L.; Li, M.F.; Han, Y.T.

2010-01-01

In this Letter, stability analysis is applied to a two-dimensional Logistic coupled map lattice with the periodic boundary conditions. The conditions of Turing instability are obtained, and various patterns can be exhibited by numerical simulations in the Turing instability region. For example, space-time periodic structures, periodic or quasiperiodic traveling wave solutions, stationary wave solutions, spiral waves, and spatiotemporal chaos, etc. have been observed. In particular, the different pattern structures have also been observed for same parameters and different initial values. That is, pattern structures also depend on the initial values. The similar patterns have also been seen in relevant references. However, the present Letter owes to pattern formation via diffusion-driven instabilities because the system is stable in the absence of diffusion.

Two-dimensional models in statistical mechanics and field theory

International Nuclear Information System (INIS)

Koberle, R.

1980-01-01

Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

A Hennart nodal method for the diffusion equation

International Nuclear Information System (INIS)

Lesaint, P.; Noceir, S.; Verwaerde, D.

1995-01-01

A modification of the Hennart nodal method for neutron diffusion problems is presented. The final system of equations obtained by this method is not positive definite. However, a flux elimination technique leads to a simple positive definite system, which can be solved by the traditional iterative methods. Calculations of a two-dimensional International Atomic Energy Agency benchmark problem are performed and compared with results of the original Hennart nodal method and some finite element methods. The high computational efficiency of this modified nodal method is clearly demonstrated

NUMERICAL ANALYSIS OF AN INVERSE PROBLEM ORIGINATED IN PHENOMENON OF POLLUTION AIR URBAN

Directory of Open Access Journals (Sweden)

Aníbal Coronel

2016-12-01

Full Text Available This paper presents the calibration study of a two - dimensional mathematical model for the problem of urban air pollution. It is mainly assumed that air pollution is afected by wind convection, diffusion and chemical reactions of pollutants. Consequently, a convection-diffusion-reaction equation is obtained as a direct problem. In the inverse problem, the determination of the diffusion is analyzed, assuming that one has an observation of the pollutants in a nite time. To solve it numerically the nite volume method is used, the least squares function is considered as cost function and the gradient is calculated with the sensitivity method.

Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment

Science.gov (United States)

Huveneers, François

2018-04-01

We investigate the long-time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant D . We consider two cases: (a) The particle is pulled forward by a small external constant force and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large D limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the crossover to the true asymptotic behavior.

A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations

KAUST Repository

Wang, Zhiheng

2014-12-10

A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

Quantum trajectories in complex space: One-dimensional stationary scattering problems

International Nuclear Information System (INIS)

Chou, C.-C.; Wyatt, Robert E.

2008-01-01

One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems

Optical Transient-Grating Measurements of Spin Diffusion and Relaxation in a Two-Dimensional Electron Gas

International Nuclear Information System (INIS)

Weber, Christopher P.

2005-01-01

Spin diffusion in n-GaAs quantum wells, as measured by our optical transient-grating technique, is strongly suppressed relative to that of charge. Over a broad range of temperatures and dopings, the suppression of Ds relative to Dc agrees quantitatively with the prediction of ''spin Coulomb dra'' theory, which takes into account the exchange of spin in electron-electron collisions. Moreover, the spin-diffusion length, Ls, is a nearly constant 1 micrometer over the same range of T and n, despite Ds's varying by nearly two orders of magnitude. This constancy supports the D'yakonov-Perel'-Kachorovskii model of spin relaxation through interrupted precessional dephasing in the spin-orbit field

Numerical simulation for two-phase jet problem

International Nuclear Information System (INIS)

Lee, W.H.; Shah, V.L.

1981-01-01

A computer program TWOP was developed for obtaining the numerical solutions of three-dimensional, transient, two-phase flow system with nonequilibrium and nonhomogeneous conditions. TWOP employs two-fluid model and a set of the conservation equations formulated by Harlow and Amsden along with their Implicit Multi-Field (IMF) numerical technique that allows all degrees of couplings between the two fields. We have further extended the procedure of Harlow and Amsden by incorporating the implicit couplings of phase transition and interfacial heat transfer terms in the energy equations. Numerical results of two tested problems are presented to demonstrate the capabilities of the TWOP code. The first problem is the separation of vapor and liquid, showing that the code can handle the computational difficulties such as liquid packing and sharp interface phenomena. The second problem is the high pressure two-phase jet impinged on vertical plate, demonstrating the important role of the interfacial mass and momentum exchange

Three-dimensional versus two-dimensional vision in laparoscopy

DEFF Research Database (Denmark)

Sørensen, Stine D; Savran, Mona Meral; Konge, Lars

2016-01-01

were cohort size and characteristics, skill trained or operation performed, instrument used, outcome measures, and conclusions. Two independent authors performed the search and data extraction. RESULTS: Three hundred and forty articles were screened for eligibility, and 31 RCTs were included...... through a two-dimensional (2D) projection on a monitor, which results in loss of depth perception. To counter this problem, 3D imaging for laparoscopy was developed. A systematic review of the literature was performed to assess the effect of 3D laparoscopy. METHODS: A systematic search of the literature...... in the review. Three trials were carried out in a clinical setting, and 28 trials used a simulated setting. Time was used as an outcome measure in all of the trials, and number of errors was used in 19 out of 31 trials. Twenty-two out of 31 trials (71 %) showed a reduction in performance time, and 12 out of 19...

On the exact spectra of two electrons confined by two-dimensional quantum dots

International Nuclear Information System (INIS)

Soldatov, A.V.; Bogolubov Jr, N.N.

2005-12-01

Applicability of the method of intermediate problems to investigation of the energy spectrum and eigenstates of a two- electron two-dimensional quantum dot (QD) formed by a parabolic confining potential is discussed. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus providing an efficient tool of verification of the results obtained so far by various analytical and numerical methods being of current usage for studies of quantum dot models. (author)

Problems associated with dimensional analysis of electroencephalogram data

Energy Technology Data Exchange (ETDEWEB)

Layne, S.; Mayer-Kress, G.; Holzfuss, J.

1985-01-01

The goal was to evaluate anesthetic depth for a series of 5 to 10 patients by dimensional analysis. It has been very difficult to obtain clean EEG records from the operating room. Noise is prominent due to electrocautery and to movement of the patient's head by operating room personnel. In addition, specialized EEG equipment must be used to reduce noise and to accommodate limited space in the room. This report discusses problems associated with dimensional analysis of the EEG. We choose one EEG record from a single patient, in order to study the method but not to draw general conclusions. For simplicity, we consider only two states: awake but quiet, and medium anesthesia. 14 refs., 8 figs., 1 tab.

The exploration of stability of two-dimensional nanocrystalline metallic composites depending on temperature

International Nuclear Information System (INIS)

Poletayev, G.M.; Starostenkov, M.D.; Popova, G.V.; Skakov, M.K.

2004-01-01

Full text: In nanocrystalline compositional materials the borders of phase separation play special role. The detection of stability of the borders of phase separation depending on external conditions, such pressure, temperature of alloying is the important task in the case of nanocrystalline materials. In the current paper the stability of two-dimensional nanocrystal, composite on the basis of Ni-Al system, depending on the structure of compositional material and vacancy availability is studied. Atomic packing in two-dimensional crystal corresponds to the plane (111) of fee crystal structure, or the plane (111) of superstructure L1 2 of intermetallide system Ni-Al. The interaction between atoms is set by pair potential functions of Morse, that consider interatomic bonding in the first six coordinate spheres. The calculated block was expressed in atomic packing in the cell 40x40. Beyond the bounds of the calculated block crystal is repeated with the help of periodical border conditions. Computer modeling is performed according to the method of molecular dynamics, when speeds of atom dislocations depending on temperature are set in accidental way, according to Boltzmann allocation. Two-dimensional material was represented by different packs of phases, clean Ni, Al and intermetallic superstructure NiAl in accordance with concentrations, structures and forms. It was understood that when the concentration in composite of phase of clean Al increases, or when the number of Al atoms in intermetallide rises, the initial temperature of thermo activated diffusing destruction of interphase borders turns out to be very low. On the other hand, when the part of clean nickel increases or when the concentration of clean Ni atoms in the structure (L1 2 ) rises, diffusion stability of interphase borders is observes right up to high temperatures. According to the results, basic diffusion processes take place right on interphase borders

Mentalizing and interpersonal problems in borderline personality disorder: The mediating role of identity diffusion.

Science.gov (United States)

De Meulemeester, Celine; Lowyck, Benedicte; Vermote, Rudi; Verhaest, Yannic; Luyten, Patrick

2017-12-01

Individuals with borderline personality disorder (BPD) are characterized by problems in interpersonal functioning and their long-term social integration often remains problematic. Extant theories have linked identity diffusion to many of the interpersonal problems characteristic of BPD patients. Recent theoretical accounts have suggested that identity diffusion results from problems with mentalizing or reflective functioning, that is, the capacity to understand oneself and others in terms of intentional mental states. In this study we tested these assumptions, i.e., whether identity diffusion plays a mediating role in the relationship between mentalizing difficulties and interpersonal problems, in a sample of 167 BPD patients. Highly significant correlations were found between mentalizing impairments, identity diffusion and interpersonal problems. Mediation analyses showed that identity diffusion fully mediated the relationship between mentalizing difficulties and interpersonal problems. This study provides preliminary evidence that impairments in mentalizing are related to identity diffusion, which in turn is related to interpersonal problems in BPD. Further longitudinal research is needed to further substantiate these conclusions. Copyright © 2017 Elsevier B.V. All rights reserved.

A highly efficient parallel algorithm for solving the neutron diffusion nodal equations on shared-memory computers

International Nuclear Information System (INIS)

Azmy, Y.Y.; Kirk, B.L.

1990-01-01

Modern parallel computer architectures offer an enormous potential for reducing CPU and wall-clock execution times of large-scale computations commonly performed in various applications in science and engineering. Recently, several authors have reported their efforts in developing and implementing parallel algorithms for solving the neutron diffusion equation on a variety of shared- and distributed-memory parallel computers. Testing of these algorithms for a variety of two- and three-dimensional meshes showed significant speedup of the computation. Even for very large problems (i.e., three-dimensional fine meshes) executed concurrently on a few nodes in serial (nonvector) mode, however, the measured computational efficiency is very low (40 to 86%). In this paper, the authors present a highly efficient (∼85 to 99.9%) algorithm for solving the two-dimensional nodal diffusion equations on the Sequent Balance 8000 parallel computer. Also presented is a model for the performance, represented by the efficiency, as a function of problem size and the number of participating processors. The model is validated through several tests and then extrapolated to larger problems and more processors to predict the performance of the algorithm in more computationally demanding situations

Transport properties of diazonium functionalized graphene: chiral two-dimensional hole gases

International Nuclear Information System (INIS)

Huang Ping; Jing Long; Zhu Huarui; Gao Xueyun

2012-01-01

The electric transport properties of diazonium functionalized graphene (DFG) were investigated. The temperature dependence of the resistivity (ρ-T) and the Shubnikov-de Haas oscillation of the DFG revealed two-dimensional hole gas (2DHG) behaviors. The DFGs exhibited unusual weak localization behaviors in which both inelastic and chirality-breaking elastic scattering processes should be taken into account, meaning that graphene chirality was maintained. Because of the giant decrease in the diffusion coefficient, the scattering rates remained relatively low in the presence of suppression of the scattering lengths. The decreases of both the mean free path and the Fermi velocity were responsible for the suppression of the diffusion coefficient and hence the charge mobility. (paper)

Anomalous diffusion and Levy random walk of magnetic field lines in three dimensional turbulence

International Nuclear Information System (INIS)

Zimbardo, G.; Veltri, P.; Basile, G.; Principato, S.

1995-01-01

The transport of magnetic field lines is studied numerically where three dimensional (3-D) magnetic fluctuations, with a power law spectrum, and periodic over the simulation box are superimposed on an average uniform magnetic field. The weak and the strong turbulence regime, δB∼B 0 , are investigated. In the weak turbulence case, magnetic flux tubes are separated from each other by percolating layers in which field lines undergo a chaotic motion. In this regime the field lines may exhibit Levy, rather than Gaussian, random walk, changing from Levy flights to trapped motion. The anomalous diffusion laws left-angle Δx 2 i right-angle ∝s α with α>1 and α<1, are obtained for a number of cases, and the non-Gaussian character of the field line random walk is pointed out by computing the kurtosis. Increasing the fluctuation level, and, therefore stochasticity, normal diffusion (α congruent 1) is recovered and the kurtoses reach their Gaussian value. However, the numerical results show that neither the quasi-linear theory nor the two dimensional percolation theory can be safely extrapolated to the considered 3-D strong turbulence regime. copyright 1995 American Institute of Physics

One-velocity neutron diffusion calculations based on a two-group reactor model

Energy Technology Data Exchange (ETDEWEB)

Bingulac, S; Radanovic, L; Lazarevic, B; Matausek, M; Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

Many processes in reactor physics are described by the energy dependent neutron diffusion equations which for many practical purposes can often be reduced to one-dimensional two-group equations. Though such two-group models are satisfactory from the standpoint of accuracy, they require rather extensive computations which are usually iterative and involve the use of digital computers. In many applications, however, and particularly in dynamic analyses, where the studies are performed on analogue computers, it is preferable to avoid iterative calculations. The usual practice in such situations is to resort to one group models, which allow the solution to be expressed analytically. However, the loss in accuracy is rather great particularly when several media of different properties are involved. This paper describes a procedure by which the solution of the two-group neutron diffusion. equations can be expressed analytically in the form which, from the computational standpoint, is as simple as the one-group model, but retains the accuracy of the two-group treatment. In describing the procedure, the case of a multi-region nuclear reactor of cylindrical geometry is treated, but the method applied and the results obtained are of more general application. Another approach in approximate solution of diffusion equations, suggested by Galanin is applicable only in special ideal cases.

Fluctuations and symmetries in two-dimensional active gels.

Science.gov (United States)

Sarkar, N; Basu, A

2011-04-01

Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.

Effect of capillary forces on immiscible two-phase flow in heterogeneous porous media

Energy Technology Data Exchange (ETDEWEB)

van Duijn, C.J.; Molenaar, J.; de Neef, M.J.

1994-12-31

We consider the one-dimensional two-phase flow including capillary effects through a heterogeneous porous medium. The heterogeneity is due to the spatial variation of the absolute permeability and the porosity. Both these quantities are assumed to be piecewise constant. At interfaces where the rock properties are discontinuous, we derive, by a regularization technique, conditions to match the values of the saturation on both sides. There are two conditions: a flux condition and an extended pressure condition. Applying these conditions we show that trapping of the wetting phase may occur near hetergeneities. To illustrate the behavior of the saturation we consider a time-dependent diffusion problem without convection, a stationary convection-diffusion problem, and the full time-dependent convection-diffusion problem (numerically). In particular the last two problems explicitly show the trapping behavior.

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

Science.gov (United States)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Advanced numerical methods for three dimensional two-phase flow calculations

Energy Technology Data Exchange (ETDEWEB)

Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)

1997-07-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.

Advanced numerical methods for three dimensional two-phase flow calculations

International Nuclear Information System (INIS)

Toumi, I.; Caruge, D.

1997-01-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations

Multi-dimensional Bin Packing Problems with Guillotine Constraints

DEFF Research Database (Denmark)

Amossen, Rasmus Resen; Pisinger, David

2010-01-01

The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face...... parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a box and no box has been intersected by a cut. The unrestricted problem is known to be NP-hard. In this paper we present a generalization of a constructive algorithm for the multi-dimensional bin packing...... problem, with and without the guillotine constraint, based on constraint programming....

Performance characteristics of specified power reactors in multidimensional neutron diffusion problems

International Nuclear Information System (INIS)

Kim, M.G.

1980-01-01

The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the grown fluxes and net currents with Taylor expansions of internal fluxes at the interface positions. A few sample problems are selected to test the validity of the method. It is found that the proposed method of solution is similar to the finite Fourier sine transform. Numerical results for the solutions obtained by the method of straight lines are compared with the results of the exact analytical solutions for simple geometries. These comparisons indicate that the proposed method is compatible with the analytical method, and in some problems considered the straight-line solutions are much more efficient than the exact solutions. The method is also extended to the reactor kinetics problem by expressing the kinetics parameters in terms of the basis functions which are used to obtain the solutions of the steady-state neutron diffusion equations

Optical Transient-Grating Measurements of Spin Diffusion andRelaxation in a Two-Dimensional Electron Gas

Energy Technology Data Exchange (ETDEWEB)

Weber, Christopher Phillip [Univ. of California, Berkeley, CA (United States)

2005-01-01

Spin diffusion in n-GaAs quantum wells, as measured by our optical transient-grating technique, is strongly suppressed relative to that of charge. Over a broad range of temperatures and dopings, the suppression of Ds relative to Dc agrees quantitatively with the prediction of ''spin Coulomb dra'' theory, which takes into account the exchange of spin in electron-electron collisions. Moreover, the spin-diffusion length, Ls, is a nearly constant 1 micrometer over the same range of T and n, despite Ds's varying by nearly two orders of magnitude. This constancy supports the D'yakonov-Perel'-Kachorovskii model of spin relaxation through interrupted precessional dephasing in the spin-orbit field.

A parameter identification problem arising from a two-dimensional airfoil section model

International Nuclear Information System (INIS)

Cerezo, G.M.

1994-01-01

The development of state space models for aeroelastic systems, including unsteady aerodynamics, is particularly important for the design of highly maneuverable aircraft. In this work we present a state space formulation for a special class of singular neutral functional differential equations (SNFDE) with initial data in C(-1, 0). This work is motivated by the two-dimensional airfoil model presented by Burns, Cliff and Herdman in. In the same authors discuss the validity of the assumptions under which the model was formulated. They pay special attention to the derivation of the evolution equation for the circulation on the airfoil. This equation was coupled to the rigid-body dynamics of the airfoil in order to obtain a complete set of functional differential equations that describes the composite system. The resulting mathematical model for the aeroelastic system has a weakly singular component. In this work we consider a finite delay approximation to the model presented in. We work with a scalar model in which we consider the weak singularity appearing in the original problem. The main goal of this work is to develop numerical techniques for the identification of the parameters appearing in the kernel of the associated scalar integral equation. Clearly this is the first step in the study of parameter identification for the original model and the corresponding validation of this model for the aeroelastic system

Three-dimensional formulation of the relativistic two-body problem in terms of rapidities

International Nuclear Information System (INIS)

Amirkhanov, I.V.; Grusha, G.V.; Mir-Kasimov, R.M.

1976-01-01

The scheme, based on the three-dimensional relativistic equation of the quasi-potential type is developed. As a basic variable rapidity, canonically conjugated to the relativistic relative distance is adopted. The free Green function has a simple pole in the complex rapidity plane, ensuring the fulfillment of the elastic unitarity for real potentials. In the local potential case the corresponding partial wave equation in configurational r-representation is a differential second-order equation. The problem of boundary conditions, which is a non-trivial one in the relativistic r-space, is studied. The exact solutions of the equation in simple cases have been found

Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models

Science.gov (United States)

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.

Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods

International Nuclear Information System (INIS)

Men, H.; Nguyen, N.C.; Freund, R.M.; Parrilo, P.A.; Peraire, J.

2010-01-01

In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design.

On wakefields with two-dimensional planar geometry

International Nuclear Information System (INIS)

Chao, A.W.; Bane, K.L.F.

1996-10-01

In order to reach higher acceleration gradients in linear accelerators, it is advantageous to use a higher accelerating RF frequency, which in turn requires smaller accelerating structures. As the structure size becomes smaller, rectangular structures become increasingly interesting because they are easier to construct than cylindrically symmetric ones. One drawback of small structures, however, is that the wakefields generated by the beam in such structures tend to be strong. Recently, it has been suggested that one way of ameliorating this problem is to use rectangular structures that are very flat and to use flat beams. In the limiting case of a very flat planar geometry, the problem resembles a purely two-dimensional (2-D) problem, the wakefields of which have been studied

Flux-limited diffusion coefficients in reactor physics applications

International Nuclear Information System (INIS)

Pounders, J.; Rahnema, F.; Szilard, R.

2007-01-01

Flux-limited diffusion theory has been successfully applied to problems in radiative transfer and radiation hydrodynamics, but its relevance to reactor physics has not yet been explored. The current investigation compares the performance of a flux-limited diffusion coefficient against the traditionally defined transport cross section. A one-dimensional BWR benchmark problem is examined at both the assembly and full-core level with varying degrees of heterogeneity. (authors)

A contribution on the problem of ground water pollution

International Nuclear Information System (INIS)

Zilliox, L.; Muntzer, P.; Kresser, W.

1982-01-01

The authors present the underlying physics of processes relevant to the problem of ground water pollution. A series of models are discussed which include two-dimensional diffusion from a point source of pollution in a uniform homogeneous medium and the modifying effect of inhomogeneities, together with displacement processes for miscible liquids in saturated porous media. In conclusion an account of laboratory and theoretical investigations of these diffusion processes in layered media of different permeabilities is given. (J.R.B.)

A two-stage preventive maintenance optimization model incorporating two-dimensional extended warranty

International Nuclear Information System (INIS)

Su, Chun; Wang, Xiaolin

2016-01-01

In practice, customers can decide whether to buy an extended warranty or not, at the time of item sale or at the end of the basic warranty. In this paper, by taking into account the moments of customers purchasing two-dimensional extended warranty, the optimization of imperfect preventive maintenance for repairable items is investigated from the manufacturer's perspective. A two-dimensional preventive maintenance strategy is proposed, under which the item is preventively maintained according to a specified age interval or usage interval, whichever occurs first. It is highlighted that when the extended warranty is purchased upon the expiration of the basic warranty, the manufacturer faces a two-stage preventive maintenance optimization problem. Moreover, in the second stage, the possibility of reducing the servicing cost over the extended warranty period is explored by classifying customers on the basis of their usage rates and then providing them with customized preventive maintenance programs. Numerical examples show that offering customized preventive maintenance programs can reduce the manufacturer's warranty cost, while a larger saving in warranty cost comes from encouraging customers to buy the extended warranty at the time of item sale. - Highlights: • A two-dimensional PM strategy is investigated. • Imperfect PM strategy is optimized by considering both two-dimensional BW and EW. • Customers are categorized based on their usage rates throughout the BW period. • Servicing cost of the EW is reduced by offering customized PM programs. • Customers buying the EW at the time of sale is preferred for the manufacturer.

Zakharov-Shabat-Mikhailov scheme of construction of two-dimensional completely integrable field theories

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Columbia Univ., New York; Chudnovsky, G.V.; Columbia Univ., New York

1980-01-01

General algebraic and analytic formalism for derivation and solution of general two dimensional field theory equations of Zakharov-Shabat-Mikhailov type is presented. The examples presented show that this class of equations covers most of the known two-dimensional completely integrable equations. Possible generalizations for four dimensional systems require detailed analysis of Baecklund transformation of these equations. Baecklund transformation is presented in the form of Riemann problem and one special case of dual symmetry is worked out. (orig.)

Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

Directory of Open Access Journals (Sweden)

Shoubin Wang

2017-01-01

Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

Two-dimensional and relativistic effects in lower-hybrid current drive

International Nuclear Information System (INIS)

Hewett, D.; Hizanidis, K.; Krapchev, V.; Bers, A.

1983-06-01

We present new numerical and analytic solutions of the two-dimensional Fokker-Planck equation supplemented by a parallel quasilinear diffusion term. The results show a large enhancement of the perpendicular temperature of both the electrons resonant with the applied RF fields and the more energetic electrons in the tail. Both the RF-generated current and power dissipated are substantially increased by the perpendicular energy broadening in the resonant region. In the presence of a small DC electric field the RF current generated is very much enhanced, much more than in a simple additive fashion. In addition, we present a relativistic formulation of the two-dimensional Fokker-Planck quasilinear equation. From conservation equations, based upon this formulation, we derive the characteristics of RF current drive with energetic electrons. These show how the RF-driven current and its figure of merit (I/P/sub d/) increase with the energy of the current-carrying electrons, and that their perpendicular, random momentum must also increase

The Particle inside a Ring: A Two-Dimensional Quantum Problem Visualized by Scanning Tunneling Microscopy

Science.gov (United States)

Ellison, Mark D.

2008-01-01

The one-dimensional particle-in-a-box model used to introduce quantum mechanics to students suffers from a tenuous connection to a real physical system. This article presents a two-dimensional model, the particle confined within a ring, that directly corresponds to observations of surface electrons in a metal trapped inside a circular barrier.…

Two dimensional Hall MHD modeling of a plasma opening switch with density inhomogeneities

Energy Technology Data Exchange (ETDEWEB)

Zabaidullin, O [Kurchatov Institute, Moscow (Russian Federation); Chuvatin, A; Etlicher, B [Ecole Polytechnique, Palaiseau (France). Laboratoire de Physique des Milieux Ionises

1997-12-31

The results of two-dimensional numerical modeling of the Plasma Opening Switch in the MHD framework with Hall effect are presented. An enhanced Hall diffusion coefficient was used in the simulations. Recent experiments justify the application of this approach. The result of the modeling also correlates better with the experiment than in the case of the classical diffusion coefficient. Numerically generated pictures propose a switching scenario in which the translation between the conduction and opening phases can be explained by an abrupt `switching on` and further domination of the Hall effect at the end of the conduction phase. (author). 3 figs., 6 refs.

Magnetoresistance in two-dimensional array of Ge/Si quantum dots

Science.gov (United States)

Stepina, N. P.; Koptev, E. S.; Pogosov, A. G.; Dvurechenskii, A. V.; Nikiforov, A. I.; Zhdanov, E. Yu

2012-07-01

Magnetoresistance in two-dimensional array of Ge/Si was studied for a wide range of the conductance, where the transport regime changes from hopping to diffusive one. The behavior of magnetoresistance is similar for all samples; it is negative in weak fields and becomes positive with increasing of magnetic field. Negative magnetoresistance can be described in the frame of weak localization approach with suggestion that quantum interference contribution to the conductance is restricted not only by the phase breaking length but also by the localization length.

Magnetoresistance in two-dimensional array of Ge/Si quantum dots

International Nuclear Information System (INIS)

Stepina, N P; Koptev, E S; Pogosov, A G; Dvurechenskii, A V; Nikiforov, A I; Zhdanov, E Yu

2012-01-01

Magnetoresistance in two-dimensional array of Ge/Si was studied for a wide range of the conductance, where the transport regime changes from hopping to diffusive one. The behavior of magnetoresistance is similar for all samples; it is negative in weak fields and becomes positive with increasing of magnetic field. Negative magnetoresistance can be described in the frame of weak localization approach with suggestion that quantum interference contribution to the conductance is restricted not only by the phase breaking length but also by the localization length.

(Weakly) three-dimensional caseology

International Nuclear Information System (INIS)

Pomraning, G.C.

1996-01-01

The singular eigenfunction technique of Case for solving one-dimensional planar symmetry linear transport problems is extended to a restricted class of three-dimensional problems. This class involves planar geometry, but with forcing terms (either boundary conditions or internal sources) which are weakly dependent upon the transverse spatial variables. Our analysis involves a singular perturbation about the classic planar analysis, and leads to the usual Case discrete and continuum modes, but modulated by weakly dependent three-dimensional spatial functions. These functions satisfy parabolic differential equations, with a different diffusion coefficient for each mode. Representative one-speed time-independent transport problems are solved in terms of these generalised Case eigenfunctions. Our treatment is very heuristic, but may provide an impetus for more rigorous analysis. (author)

An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst

2011-01-01

Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

Solution of the Multigroup-Diffusion equation by the response matrix method

International Nuclear Information System (INIS)

Oliveira, C.R.E.

1980-10-01

A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt

Classification problem for exactly integrable embeddings of two-dimensional manifolds and coefficients of the third fundametal forms

International Nuclear Information System (INIS)

Saveliev, M.V.

1983-01-01

A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L

A new approach to the problem of bulk-mediated surface diffusion.

Science.gov (United States)

Berezhkovskii, Alexander M; Dagdug, Leonardo; Bezrukov, Sergey M

2015-08-28

This paper is devoted to bulk-mediated surface diffusion of a particle which can diffuse both on a flat surface and in the bulk layer above the surface. It is assumed that the particle is on the surface initially (at t = 0) and at time t, while in between it may escape from the surface and come back any number of times. We propose a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time t. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle observed for time t. This solution is used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. We also establish a relation between the double Laplace transform of the conditional probability density and the Fourier-Laplace transform of the particle propagator over the surface. The proposed approach treats the cases of both finite and infinite bulk layer thicknesses (where bulk-mediated surface diffusion is normal and anomalous at asymptotically long times, respectively) on equal footing.

Characterizing microbial communities and processes in a modern stromatolite (Shark Bay) using lipid biomarkers and two-dimensional distributions of porewater solutes

DEFF Research Database (Denmark)

Pagès, Anais; Grice, Kliti; Vacher, Michael

2014-01-01

Summary: Modern microbial mats are highly complex and dynamic ecosystems. Diffusive equilibration in thin films (DET) and diffusive gradients in thin films (DGT) samplers were deployed in a modern smooth microbial mat from Shark Bay in order to observe, for the first time, two-dimensional distrib......Summary: Modern microbial mats are highly complex and dynamic ecosystems. Diffusive equilibration in thin films (DET) and diffusive gradients in thin films (DGT) samplers were deployed in a modern smooth microbial mat from Shark Bay in order to observe, for the first time, two...

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

Two dimensional nonlinear spectral estimation techniques for breast cancer localization

International Nuclear Information System (INIS)

Stathaki, P.T.; Constantinides, A.G.

1994-01-01

In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging

Two dimensional numerical simulations of carrier dynamics during time-resolved photoluminescence decays in two-photon microscopy measurements in semiconductors

International Nuclear Information System (INIS)

Kanevce, Ana; Kuciauskas, Darius; Levi, Dean H.; Johnston, Steven W.; Allende Motz, Alyssa M.

2015-01-01

We use two-dimensional numerical simulations to analyze high spatial resolution time-resolved spectroscopy data. This analysis is applied to two-photon excitation time-resolved photoluminescence (2PE-TRPL) but is broadly applicable to all microscopic time-resolved techniques. By solving time-dependent drift-diffusion equations, we gain insight into carrier dynamics and transport characteristics. Accurate understanding of measurement results establishes the limits and potential of the measurement and enhances its value as a characterization method. Diffusion of carriers outside of the collection volume can have a significant impact on the measured decay but can also provide an estimate of carrier mobility as well as lifetime. In addition to material parameters, the experimental conditions, such as spot size and injection level, can impact the measurement results. Although small spot size provides better resolution, it also increases the impact of diffusion on the decay; if the spot size is much smaller than the diffusion length, it impacts the entire decay. By reproducing experimental 2PE-TRPL decays, the simulations determine the bulk carrier lifetime from the data. The analysis is applied to single-crystal and heteroepitaxial CdTe, material important for solar cells, but it is also applicable to other semiconductors where carrier diffusion from the excitation volume could affect experimental measurements

Machine Learning Based Dimensionality Reduction Facilitates Ligand Diffusion Paths Assessment: A Case of Cytochrome P450cam.

Science.gov (United States)

Rydzewski, J; Nowak, W

2016-04-12

In this work we propose an application of a nonlinear dimensionality reduction method to represent the high-dimensional configuration space of the ligand-protein dissociation process in a manner facilitating interpretation. Rugged ligand expulsion paths are mapped into 2-dimensional space. The mapping retains the main structural changes occurring during the dissociation. The topological similarity of the reduced paths may be easily studied using the Fréchet distances, and we show that this measure facilitates machine learning classification of the diffusion pathways. Further, low-dimensional configuration space allows for identification of residues active in transport during the ligand diffusion from a protein. The utility of this approach is illustrated by examination of the configuration space of cytochrome P450cam involved in expulsing camphor by means of enhanced all-atom molecular dynamics simulations. The expulsion trajectories are sampled and constructed on-the-fly during molecular dynamics simulations using the recently developed memetic algorithms [ Rydzewski, J.; Nowak, W. J. Chem. Phys. 2015 , 143 ( 12 ), 124101 ]. We show that the memetic algorithms are effective for enforcing the ligand diffusion and cavity exploration in the P450cam-camphor complex. Furthermore, we demonstrate that machine learning techniques are helpful in inspecting ligand diffusion landscapes and provide useful tools to examine structural changes accompanying rare events.

Equivalence of two-dimensional gravities

International Nuclear Information System (INIS)

Mohammedi, N.

1990-01-01

The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given

DISPL: a software package for one and two spatially dimensioned kinetics-diffusion problems. [FORTRAN for IBM computers

Energy Technology Data Exchange (ETDEWEB)

Leaf, G K; Minkoff, M; Byrne, G D; Sorensen, D; Bleakney, T; Saltzman, J

1978-11-01

DISPL is a software package for solving some second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types such as parabolic--elliptic equations. Fairly general nonlinear boundary conditions are allowed as well as interface conditions for problems in an inhomogeneous media. The spatial domain is one- or two-dimensional with Cartesian, cylindrical, or spherical (in one dimension only) geometry. The numerical method is based on the use of Galerkin's procedure combined with the use of B-splines in order to reduce the system of PDE's to a system of ODE's. The latter system is then solved with a sophisticated ODE software package. Software features include extensive dump/restart facilities, free format input, moderate printed output capability, dynamic storage allocation, and three graphics packages. 17 figures, 9 tables.

A two-dimensional analytical model of laminar flame in lycopodium dust particles

Energy Technology Data Exchange (ETDEWEB)

Rahbari, Alireza [Shahid Rajaee Teacher Training University, Tehran (Iran, Islamic Republic of); Shakibi, Ashkan [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Bidabadi, Mehdi [Combustion Research Laboratory, Narmak, Tehran (Iran, Islamic Republic of)

2015-09-15

A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.

A two-dimensional analytical model of laminar flame in lycopodium dust particles

International Nuclear Information System (INIS)

Rahbari, Alireza; Shakibi, Ashkan; Bidabadi, Mehdi

2015-01-01

A two-dimensional analytical model is presented to determine the flame speed and temperature distribution of micro-sized lycopodium dust particles. This model is based on the assumptions that the particle burning rate in the flame front is controlled by the process of oxygen diffusion and the flame structure consists of preheat, reaction and post flame zones. In the first step, the energy conservation equations for fuel-lean condition are expressed in two dimensions, and then these differential equations are solved using the required boundary condition and matching the temperature and heat flux at the interfacial boundaries. Consequently, the obtained flame temperature and flame speed distributions in terms of different particle diameters and equivalence ratio for lean mixture are compared with the corresponding experimental data for lycopodium dust particles. Consequently, it is shown that this two-dimensional model demonstrates better agreement with the experimental results compared to the previous models.

Two-dimensional metamaterial optics

International Nuclear Information System (INIS)

Smolyaninov, I I

2010-01-01

While three-dimensional photonic metamaterials are difficult to fabricate, many new concepts and ideas in the metamaterial optics can be realized in two spatial dimensions using planar optics of surface plasmon polaritons. In this paper we review recent progress in this direction. Two-dimensional photonic crystals, hyperbolic metamaterials, and plasmonic focusing devices are demonstrated and used in novel microscopy and waveguiding schemes

The simulation of two-dimensional migration patterns - a novel approach

International Nuclear Information System (INIS)

Villar, Heldio Pereira

1997-01-01

A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author)

Speed ot travelling waves in reaction-diffusion equations

International Nuclear Information System (INIS)

Benguria, R.D.; Depassier, M.C.; Mendez, V.

2002-01-01

Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)

FURNACE-J, 2-D Diffusion Burnup for Fast Reactors from JAERI Fast-Set

International Nuclear Information System (INIS)

Ikawa, Koji

1984-01-01

1 - Nature of physical problem solved: FURNACEJ is a two-dimensional diffusion-burnup code for use in the detailed burnup analysis of fast reactors. The code is an extension code of the FURNACE. There exists no essential difference between FURNACE and FURNACEJ. However, the latter can deal with JAERI-Fast-Set as its cross section library, while the former is designed to use ABBN set. Additionally, in FURNACEJ, group-dependent and -independent transverse buckling of each region can be computed and punched on cards, if desired. This is prepared for users so as to use them as input data for detailed two-dimensional x-y calculations. 2 - Restrictions on the complexity of the problem: Only r-z geometry is available

Approximate solutions of the two-dimensional integral transport equation by collision probability methods

International Nuclear Information System (INIS)

Sanchez, Richard

1977-01-01

A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr

Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

International Nuclear Information System (INIS)

Mori, N.; Kobayashi, K.

1996-01-01

A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

Green's function method and its application to verification of diffusion models of GASFLOW code

International Nuclear Information System (INIS)

Xu, Z.; Travis, J.R.; Breitung, W.

2007-07-01

To validate the diffusion model and the aerosol particle model of the GASFLOW computer code, theoretical solutions of advection diffusion problems are developed by using the Green's function method. The work consists of a theory part and an application part. In the first part, the Green's functions of one-dimensional advection diffusion problems are solved in infinite, semi-infinite and finite domains with the Dirichlet, the Neumann and/or the Robin boundary conditions. Novel and effective image systems especially for the advection diffusion problems are made to find the Green's functions in a semi-infinite domain. Eigenfunction method is utilized to find the Green's functions in a bounded domain. In the case, key steps of a coordinate transform based on a concept of reversed time scale, a Laplace transform and an exponential transform are proposed to solve the Green's functions. Then the product rule of the multi-dimensional Green's functions is discussed in a Cartesian coordinate system. Based on the building blocks of one-dimensional Green's functions, the multi-dimensional Green's function solution can be constructed by applying the product rule. Green's function tables are summarized to facilitate the application of the Green's function. In the second part, the obtained Green's function solutions benchmark a series of validations to the diffusion model of gas species in continuous phase and the diffusion model of discrete aerosol particles in the GASFLOW code. Perfect agreements are obtained between the GASFLOW simulations and the Green's function solutions in case of the gas diffusion. Very good consistencies are found between the theoretical solutions of the advection diffusion equations and the numerical particle distributions in advective flows, when the drag force between the micron-sized particles and the conveying gas flow meets the Stokes' law about resistance. This situation is corresponding to a very small Reynolds number based on the particle

Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

International Nuclear Information System (INIS)

Han, Renji; Dai, Binxiang

2017-01-01

Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

Quantum vacuum energy in two dimensional space-times

International Nuclear Information System (INIS)

Davies, P.C.W.; Fulling, S.A.

1977-01-01

The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)

Quantum vacuum energy in two dimensional space-times

Energy Technology Data Exchange (ETDEWEB)

Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics

1977-04-21

The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.

Determination of mouse skeletal muscle architecture using three dimensional diffusion tensor imaging

NARCIS (Netherlands)

Heemskerk, A.M.; Strijkers, G.J.; Vilanova, A.; Drost, M.R.; Nicolaij, K.

2005-01-01

Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six

Determination of mouse skeletal muscle architecture using three-dimensional diffusion tensor imaging

NARCIS (Netherlands)

Heemskerk, Anneriet M.; Strijkers, Gustav J.; Vilanova, Anna; Drost, Maarten R.; Nicolay, Klaas

2005-01-01

Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six

Specifications for a two-dimensional multi-group scattering code: ALCI; Specification d'un code de diffusion multigroupe a deux dimensions: ALCI

Energy Technology Data Exchange (ETDEWEB)

Bayard, J P; Guillou, A; Lago, B; Bureau du Colombier, M J; Guillou, G; Vasseur, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1965-02-01

This report describes the specifications of the ALCI programme. This programme resolves the system of difference equations similar to the homogeneous problem of multigroup neutron scattering, with two dimensions in space, in the three geometries XY, RZ, R{theta}. It is possible with this method to calculate geometric and composition criticalities and also to calculate the accessory problem on demand. The maximum number of points dealt with is 6000. The maximum permissible number of groups is 12. The internal iterations are treated by the method of alternating directions. The external iterations are accelerated using the extrapolation method due to Tchebychev. (authors) [French] Ce rapport decrit les specifications du programme ALCI. Ce programme resout le systeme d'equations aux differences approchant le probleme homogene de la diffusion neutronique multigroupe, a deux dimensions d'espace, dans les trois geometries XY, RZ, R{theta}. Il permet des calculs de criticalite geometrique et de composition et calcule sur demande le probleme adjoint. Le nombre maximum de points traites est de 6000. Le nombre maximum de groupes permis est de 12. Les iterations interieure sont traitees par la methode des directions alternees. Les iterations exterieures sont accelerees par la methode d'extrapolation de Tchebychev. (auteurs)

Diffusion-controlled growth of molecular heterostructures: fabrication of two-, one-, and zero-dimensional C(60) nanostructures on pentacene substrates.

Science.gov (United States)

Breuer, Tobias; Witte, Gregor

2013-10-09

A variety of low dimensional C60 structures has been grown on supporting pentacene multilayers. By choice of substrate temperature during growth the effective diffusion length of evaporated fullerenes and their nucleation at terraces or step edges can be precisely controlled. AFM and SEM measurements show that this enables the fabrication of either 2D adlayers or solely 1D chains decorating substrate steps, while at elevated growth temperature continuous wetting of step edges is prohibited and instead the formation of separated C60 clusters pinned at the pentacene step edges occurs. Remarkably, all structures remain thermally stable at room temperature once they are formed. In addition the various fullerene structures have been overgrown by an additional pentacene capping layer. Utilizing the different probe depth of XRD and NEXAFS, we found that no contiguous pentacene film is formed on the 2D C60 structure, whereas an encapsulation of the 1D and 0D structures with uniformly upright oriented pentacene is achieved, hence allowing the fabrication of low dimensional buried organic heterostructures.

TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA MODELS WITH MULTI-DIMENSIONAL TRANSPORT

International Nuclear Information System (INIS)

Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun

2015-01-01

We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant O(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate O(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ''ray-by-ray'' approach employed by all other groups may be compromising their results. We show that ''ray-by-ray'' calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion

Two dimensional nonlinear spectral estimation techniques for breast cancer localization

Energy Technology Data Exchange (ETDEWEB)

Stathaki, P T; Constantinides, A G [Signal Processing Section, Department of Electrical and Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, UK (United Kingdom)

1994-12-31

In this paper the problem of image texture analysis in the presence of noise is examined from a higher-order statistical perspective. The approach taken involves the use of two dimensional second order Volterra filters where the filter weights are derived from third order cumulants of the two dimensional signal. The specific application contained in this contribution is in mammography, an area in which it is difficult to discern the appropriate features. The paper describes the fundamental issues of the various components of the approach. The results of the entire texture modelling, classification and segmentation scheme contained in this paper are very encouraging. 7 refs, 2 figs.

Recent advances in computational-analytical integral transforms for convection-diffusion problems

Science.gov (United States)

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.

Dynamical properties of magnetized two-dimensional one-component plasma

Science.gov (United States)

Dubey, Girija S.; Gumbs, Godfrey; Fessatidis, Vassilios

2018-05-01

Molecular dynamics simulation are used to examine the effect of a uniform perpendicular magnetic field on a two-dimensional interacting electron system. In this simulation we include the effect of the magnetic field classically through the Lorentz force. Both the Coulomb and the magnetic forces are included directly in the electron dynamics to study their combined effect on the dynamical properties of the 2D system. Results are presented for the velocity autocorrelation function and the diffusion constants in the presence and absence of an external magnetic field. Our simulation results clearly show that the external magnetic field has an effect on the dynamical properties of the system.

Use of endochronic plasticity for multi-dimensional small and large strain problems

International Nuclear Information System (INIS)

Hsieh, B.J.

1980-04-01

The endochronic plasticity theory was proposed in its general form by K.C. Valanis. An intrinsic time measure, which is a property of the material, is used in the theory. the explicit forms of the constitutive equation resemble closely those of the classical theory of linear viscoelasticity. Excellent agreement between the predicted and experimental results is obtained for some metallic and non-metallic materials for one dimensional cases. No reference on the use of endochronic plasticity consistent with the general theory proposed by Valanis is available in the open literature. In this report, the explicit constitutive equations are derived that are consistent with the general theory for one-dimensional (simple tension or compression), two-dimensional plane strain or stress and three-dimensional axisymmetric problems

Two-dimensional manifolds with metrics of revolution

International Nuclear Information System (INIS)

Sabitov, I Kh

2000-01-01

This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)

Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

OpenAIRE

Li, Zhiyuan; Yamamoto, Masahiro

2014-01-01

This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.

Two-dimensional model of coupled heat and moisture transport in frost-heaving soils

International Nuclear Information System (INIS)

Guymon, G.L.; Berg, R.L.; Hromadka, T.V.

1984-01-01

A two-dimensional model of coupled heat and moisture flow in frost-heaving soils is developed based upon well known equations of heat and moisture flow in soils. Numerical solution is by the nodal domain integration method which includes the integrated finite difference and the Galerkin finite element methods. Solution of the phase change process is approximated by an isothermal approach and phenomenological equations are assumed for processes occurring in freezing or thawing zones. The model has been verified against experimental one-dimensional freezing soil column data and experimental two-dimensional soil thawing tank data as well as two-dimensional soil seepage data. The model has been applied to several simple but useful field problems such as roadway embankment freezing and frost heaving

A new analytical solution to the diffusion problem: Fourier series ...

African Journals Online (AJOL)

This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.

Finite-Dimensional Representations for Controlled Diffusions with Delay

Energy Technology Data Exchange (ETDEWEB)

Federico, Salvatore, E-mail: salvatore.federico@unimi.it [Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy); Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr [Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

The one-particle scenario for the metal-insulator transition in two-dimensional systems at T = 0

CERN Document Server

Tarasov, Y V

2003-01-01

The conductance of bounded disordered electron systems is calculated by reducing the original dynamic problem of arbitrary dimensionality to a set of strictly one-dimensional problems for one-particle mode propagators. The metallic ground state of a two-dimensional conductor, which is considered as a limiting case of three-dimensional quantum waveguide, is shown to result from its multi-modeness. As the waveguide thickness is reduced, e.g., by applying a 'pressing' potential, the electron system undergoes a set of continuous phase transitions related to discrete variations of the number of extended modes. The closing of the last current carrying mode is regarded as a phase transition of the electron system from metallic to dielectric state. The obtained results agree qualitatively with the observed 'anomalies' of resistivity of different two-dimensional electron and hole systems.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently

The simulation of two-dimensional migration patterns - a novel approach

Energy Technology Data Exchange (ETDEWEB)

Villar, Heldio Pereira [Universidade de Pernambuco, Recife, PE (Brazil). Escola Politecnica]|[Centro Regional de Ciencias Nucleares, Recife, PE (Brazil)

1997-12-31

A novel approach to the problem of simulation of two-dimensional migration of solutes in saturated soils is presented. In this approach, the two-dimensional advection-dispersion equation is solved by finite-differences in a stepwise fashion, by employing the one-dimensional solution first in the direction of flow and then perpendicularly, using the same time increment in both cases. As the results of this numerical model were to be verified against experimental results obtained by radioactive tracer experiments, an attenuation factor, to account for the contribution of the gamma rays emitted by the whole plume of tracer to the readings of the adopted radiation detectors, was introduced into the model. The comparison between experimental and simulated concentration contours showed good agreement, thus establishing the feasibility of the approach proposed herein. (author) 6 refs., 6 figs.

Two-dimensional simulation of the MHD stability, (1)

International Nuclear Information System (INIS)

Kurita, Gen-ichi; Amano, Tsuneo.

1976-03-01

The two-dimensional computer code has been prepared to study MHD stability of an axisymmetric toroidal plasma with and without the surrounding vacuum region. It also includes the effect of magnetic surfaces with non-circular cross sections. The linearized equations of motion are solved as an initial value problem. The results by computer simulation are compared with those by the theory for the cylindrical plasma; they are in good agreement. (auth.)

Relativistic bound-state problem of a one-dimensional system

International Nuclear Information System (INIS)

Sato, T.; Niwa, T.; Ohtsubo, H.; Tamura, K.

1991-01-01

A Poincare-covariant description of the two-body bound-state problem in one-dimensional space is studied by using the relativistic Schrodinger equation. We derive the many-body Hamiltonian, electromagnetic current and generators of the Poincare group in the framework of one-boson exchange. Our theory satisfies Poincare algebra within the one-boson-exchange approximation. We numerically study the relativistic effects on the bound-state wavefunction and the elastic electromagnetic form factor. The Lorentz boost of the bound-state wavefunction and the two-body exchange current are shown to play an important role in guaranteeing the Lorentz invariance of the form factor. (author)

Two-dimensional heterostructures for energy storage

Energy Technology Data Exchange (ETDEWEB)

Gogotsi, Yury G. [Drexel Univ., Philadelphia, PA (United States); Pomerantseva, Ekaterina [Drexel Univ., Philadelphia, PA (United States)

2017-06-12

Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. As a result, we also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.

Two-dimensional nuclear magnetic resonance of quadrupolar systems

Energy Technology Data Exchange (ETDEWEB)

Wang, Shuanhu [Univ. of California, Berkeley, CA (United States)

1997-09-01

This dissertation describes two-dimensional nuclear magnetic resonance theory and experiments which have been developed to study quadruples in the solid state. The technique of multiple-quantum magic-angle spinning (MQMAS) is extensively reviewed and expanded upon in this thesis. Specifically, MQMAS is first compared with another technique, dynamic-angle spinning (DAS). The similarity between the two techniques allows us to extend much of the DAS work to the MQMAS case. Application of MQMAS to a series of aluminum containing materials is then presented. The superior resolution enhancement through MQMAS is exploited to detect the five- and six-coordinated aluminum in many aluminosilicate glasses. Combining the MQMAS method with other experiments, such as HETCOR, greatly expands the possibility of the use of MQMAS to study a large range of problems and is demonstrated in Chapter 5. Finally, the technique switching-angle spinning (SAS) is applied to quadrupolar nuclei to fully characterize a quadrupolar spin system in which all of the 8 NMR parameters are accurately determined. This dissertation is meant to demonstrate that with the combination of two-dimensional NMR concepts and new advanced spinning technologies, a series of multiple-dimensional NMR techniques can be designed to allow a detailed study of quadrupolar nuclei in the solid state.

Two-dimensional analysis of axial segregation in batchwise and continuous Czochralski process

Science.gov (United States)

Hoe Wang, Jong; Hyun Kim, Do; Yoo, Hak-Do

1999-03-01

Transient two-dimensional convection-diffusion model has been developed to simulate the segregation phenomena in batchwise and continuous Czochralski process. Numerical simulations have been performed using the finite element method and implicit Euler time integration. The mesh deformation due to the change of the melt depth in batchwise Czochralski process was considered. Experimental values of the growth and system parameters for Czochralski growth of boron-doped, 4-in silicon single crystal were used in the numerical calculations. The experimental axial segregation in batchwise Czochralski process can be described successfully using convection-diffusion model. It has been demonstrated with this model that silicon single crystal with uniform axial dopant concentration can be grown and radial segregation can be suppressed in the continuous Czochralski process.

Quantitative application of Fermi-Dirac functions of two- and three-dimensional systems

International Nuclear Information System (INIS)

Grimmer, D.P.; Luszczynski, K.; Salibi, N.

1981-01-01

Expressions for the various physical parameters of the ideal Fermi-Dirac gas in two dimensions are derived and compared to the corresponding three-dimensional expressions. These derivations show that the Fermi-Dirac functions most applicable to the two-dimensional problem are F/sub o/(eta), F 1 (eta), and F' 0 (eta). Analogous to the work of McDougall and Stoner in three dimensions, these functions and parameters derived from them are tabulated over the range of the argument, -4 3 He monolayer and bulk liquid 3 He nuclear magnetic susceptibilities, respectively, are considered. Calculational procedures of fitting data to theoretical parameters and criteria for judging the quality of fit of data to both two- and three-dimensional Fermi-Dirac values are discussed

Analytic structure and power series expansion of the Jost function for the two-dimensional problem

International Nuclear Information System (INIS)

Rakityansky, S A; Elander, N

2012-01-01

For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)

Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories

Science.gov (United States)

Zemba, Guillermo Raul

A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

Energy Technology Data Exchange (ETDEWEB)

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu; Chen, Hongya [College of Science, Air Force Engineering University, Xi' an, Shaanxi 710051 (China); Zhang, Jieqiu [College of Science, Air Force Engineering University, Xi' an, Shaanxi 710051 (China); Electronic Materials Research Laboratory, Key Laboratory of Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Xu, Zhuo [Electronic Materials Research Laboratory, Key Laboratory of Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Zhang, Anxue [School of Electronics and Information Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2014-06-02

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

International Nuclear Information System (INIS)

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu; Chen, Hongya; Zhang, Jieqiu; Xu, Zhuo; Zhang, Anxue

2014-01-01

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

A finite-dimensional reduction method for slightly supercritical elliptic problems

Directory of Open Access Journals (Sweden)

Riccardo Molle

2004-01-01

Full Text Available We describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.